Finite Group Databasebeta

← C71×#36887 #31857759

Subgroups — C71×#36887 #31857759

Order 18176.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#2849C211yesmaximal, characteristic, complemented
2C71×#2847C211yesmaximal, characteristic, complemented
3C71×#2778C211yesmaximal, characteristic, complemented
4C71×#2768C211yesmaximal, characteristic, complemented
5C71×#2753C211yesmaximal, characteristic, complemented
6C71×#2746C211yesmaximal, characteristic, complemented
7C71×#2739C211yesmaximal, characteristic, complemented
8C71×#2714C211yesmaximal, characteristic, complemented
9C71×#2709C211yesmaximal, characteristic, complemented
10C71×#2705C211yesmaximal, characteristic, complemented
11C71×#2699C211yesmaximal, characteristic, complemented
12C71×#2691C211yesmaximal, characteristic, complemented
13C71×#2685C211yesmaximal, characteristic, complemented
14C71×#2678C211yesmaximal, characteristic, complemented
15C71×#2678C211yesmaximal, characteristic, complemented
16C71×#2671C211yesmaximal, characteristic, complemented
17C71×#2671C211yesmaximal, characteristic, complemented
18C71×#2669C211yesmaximal, characteristic, complemented
19C71×#2636C211yesmaximal, characteristic, complemented
20C71×#2635C211yesmaximal, characteristic, complemented
21C71×#2576C211yesmaximal, characteristic, complemented
22C71×#2559C211yesmaximal, characteristic, complemented
23C71×#2554C211yesmaximal, characteristic, complemented
24C71×#2553C211yesmaximal, characteristic, complemented
25C71×#2468C211yesmaximal, characteristic, complemented
26C71×#2464C211yesmaximal, characteristic, complemented
27C71×#2428C211yesmaximal, characteristic, complemented
28C71×#2420C211yesmaximal, characteristic, complemented
29C71×#2335C211yesmaximal, characteristic, complemented
30C71×#2333C211yesmaximal, characteristic, complemented
31C4×#120×C71C211yesmaximal, characteristic, complemented
32C24×C4×C71C2211yescharacteristic
33C2×#127×C71C2211yescharacteristic
34C2×#126×C71C2211yescharacteristic
35C2×#126×C71C2211yescharacteristic, complemented
36C2×#126×C71C2211yescharacteristic, complemented
37C2×#123×C71C2211yescharacteristic
38C2×#123×C71C2211yescharacteristic
39C2×#123×C71C2211yescharacteristic
40C2×#123×C71C2211yescharacteristic
41C2×#121×C71C2211yescharacteristic
42C2×#121×C71C2211yescharacteristic
43C2×#121×C71C2211yescharacteristic
44C2×#121×C71C2211yescharacteristic
45C2×#121×C71C2211yescharacteristic
46C2×#121×C71C2211yescharacteristic
47C2×#121×C71C2211yescharacteristic
48C2×#121×C71C2211yescharacteristic, complemented
49C2×#121×C71C2211yescharacteristic, complemented
50C2×#120×C71C2211yescharacteristic
51C2×#120×C71C2211yescharacteristic
52C2×#120×C71C2211yescharacteristic
53C2×#120×C71C2211yescharacteristic
54C2×C4×D4×C71C2211yescharacteristic
55C2×C4×D4×C71C2211yescharacteristic
56C2×C4×D4×C71C2211yescharacteristic
57#401×C71C2211yescharacteristic, complemented
58#400×C71C2211yescharacteristic, complemented
59#400×C71C2211yescharacteristic, complemented
60#400×C71C2211yescharacteristic, complemented
61#399×C71C2211yescharacteristic
62#399×C71C2211yescharacteristic, complemented
63#399×C71C2211yescharacteristic, complemented
64#398×C71C2211yescharacteristic, complemented
65#398×C71C2211yescharacteristic, complemented
66#398×C71C2211yescharacteristic, complemented
67#398×C71C2211yescharacteristic, complemented
68#398×C71C2211yescharacteristic, complemented
69#397×C71C2211yescharacteristic
70#397×C71C2211yescharacteristic
71#397×C71C2211yescharacteristic, complemented
72#397×C71C2211yescharacteristic, complemented
73#396×C71C2211yescharacteristic
74#396×C71C2211yescharacteristic
75#396×C71C2211yescharacteristic
76#396×C71C2211yescharacteristic, complemented
77#394×C71C2211yescharacteristic
78#394×C71C2211yescharacteristic
79#394×C71C2211yescharacteristic
80#394×C71C2211yescharacteristic
81#394×C71C2211yescharacteristic
82#394×C71C2211yescharacteristic
83#394×C71C2211yescharacteristic
84#394×C71C2211yescharacteristic
85#394×C71C2211yescharacteristic
86#394×C71C2211yescharacteristic
87#394×C71C2211yescharacteristic, complemented
88#394×C71C2211yescharacteristic, complemented
89#394×C71C2211yescharacteristic, complemented
90#394×C71C2211yescharacteristic, complemented
91#394×C71C2211yescharacteristic, complemented
92#394×C71C2211yescharacteristic, complemented
93#394×C71C2211yescharacteristic, complemented
94#394×C71C2211yescharacteristic, complemented
95#394×C71C2211yescharacteristic, complemented
96#392×C71C2211yescharacteristic
97#392×C71C2211yescharacteristic
98#392×C71C2211yescharacteristic
99#392×C71C2211yescharacteristic
100#392×C71C2211yescharacteristic
101#392×C71C2211yescharacteristic
102#392×C71C2211yescharacteristic
103#392×C71C2211yescharacteristic
104#392×C71C2211yescharacteristic, complemented
105#390×C71C2211yescharacteristic
106#390×C71C2211yescharacteristic
107#390×C71C2211yescharacteristic
108#390×C71C2211yescharacteristic
109#390×C71C2211yescharacteristic
110#390×C71C2211yescharacteristic
111#390×C71C2211yescharacteristic, complemented
112#390×C71C2211yescharacteristic, complemented
113#389×C71C2211yescharacteristic, complemented
114#389×C71C2211yescharacteristic, complemented
115#389×C71C2211yescharacteristic, complemented
116#388×C71C2211yescharacteristic
117#388×C71C2211yescharacteristic
118#388×C71C2211yescharacteristic
119#388×C71C2211yescharacteristic
120#388×C71C2211yescharacteristic
121#388×C71C2211yescharacteristic
122#388×C71C2211yescharacteristic
123#388×C71C2211yescharacteristic, complemented
124#388×C71C2211yescharacteristic, complemented
125#388×C71C2211yescharacteristic, complemented
126#388×C71C2211yescharacteristic, complemented
127#388×C71C2211yescharacteristic, complemented
128#388×C71C2211yescharacteristic, complemented
129#388×C71C2211yescharacteristic, complemented
130#388×C71C2211yescharacteristic, complemented
131#387×C71C2211yescharacteristic, complemented
132#387×C71C2211yescharacteristic, complemented
133#387×C71C2211yescharacteristic, complemented
134#387×C71C2211yescharacteristic, complemented
135#387×C71C2211yescharacteristic, complemented
136#387×C71C2211yescharacteristic, complemented
137#386×C71C2211yescharacteristic
138#386×C71C2211yescharacteristic
139#386×C71C2211yescharacteristic
140#386×C71C2211yescharacteristic
141#386×C71C2211yescharacteristic
142#386×C71C2211yescharacteristic
143#386×C71C2211yescharacteristic
144#386×C71C2211yescharacteristic
145#386×C71C2211yescharacteristic
146#386×C71C2211yescharacteristic
147#386×C71C2211yescharacteristic
148#386×C71C2211yescharacteristic
149#386×C71C2211yescharacteristic
150#386×C71C2211yescharacteristic
151#386×C71C2211yescharacteristic
152#386×C71C2211yescharacteristic
153#386×C71C2211yescharacteristic, complemented
154#386×C71C2211yescharacteristic, complemented
155#386×C71C2211yescharacteristic, complemented
156#386×C71C2211yescharacteristic, complemented
157#385×C71C2211yescharacteristic
158#385×C71C2211yescharacteristic
159#385×C71C2211yescharacteristic
160#385×C71C2211yescharacteristic
161#385×C71C2211yescharacteristic
162#385×C71C2211yescharacteristic
163#385×C71C2211yescharacteristic
164#385×C71C2211yescharacteristic, complemented
165#385×C71C2211yescharacteristic, complemented
166#385×C71C2211yescharacteristic, complemented
167#382×C71C2211yescharacteristic, complemented
168#382×C71C2211yescharacteristic, complemented
169#381×C71C2211yescharacteristic
170#381×C71C2211yescharacteristic
171#381×C71C2211yescharacteristic, complemented
172#381×C71C2211yescharacteristic, complemented
173#380×C71C2211yescharacteristic
174#380×C71C2211yescharacteristic
175#380×C71C2211yescharacteristic
176#380×C71C2211yescharacteristic, complemented
177#380×C71C2211yescharacteristic, complemented
178#379×C71C2211yescharacteristic
179#379×C71C2211yescharacteristic
180C4×C4⋊C4×C71C2211yescharacteristic, complemented
181C4×C22⋊C4×C71C2211yescharacteristic
182C4×C22⋊C4×C71C2211yescharacteristic
183C4×C22⋊C4×C71C2211yescharacteristic
184C4×C22⋊C4×C71C2211yescharacteristic, complemented
185C4×C22⋊C4×C71C2211yescharacteristic, complemented
186C4×C22⋊C4×C71C2211yescharacteristic, complemented
187C25×C71C2311yescharacteristic
188C22×D4×C71C2311yescharacteristic
189C22×D4×C71C2311yescharacteristic
190C22×D4×C71C2311yescharacteristic
191C22×D4×C71C2311yescharacteristic
192C22×D4×C71C2311yescharacteristic
193C22×D4×C71C2311yescharacteristic
194C22×D4×C71C2311yescharacteristic
195C22×D4×C71C2311yescharacteristic
196C22×D4×C71C2311yescharacteristic
197C22×D4×C71C2311yescharacteristic
198C22×D4×C71C2311yescharacteristic
199C22×D4×C71C2311yescharacteristic
200C22×D4×C71C2311yescharacteristic
201C22×D4×C71C2311yescharacteristic
202C22×D4×C71C2311yescharacteristic
203C22×D4×C71C2311yescharacteristic
204C22×D4×C71C2311yescharacteristic
205C22×D4×C71C2311yescharacteristic
206C23×C4×C71—42no—
207C23×C4×C71—42no—
208C23×C4×C71—42no—
209C23×C4×C71C2311yescharacteristic
210C23×C4×C71C2311yescharacteristic
211C23×C4×C71C2311yescharacteristic
212C23×C4×C71C2311yescharacteristic
213C23×C4×C71C2311yescharacteristic
214C23×C4×C71C2311yescharacteristic
215C23×C4×C71C2311yescharacteristic
216C23×C4×C71C2311yescharacteristic
217C23×C4×C71C2311yescharacteristic
218C23×C4×C71C2311yescharacteristic
219#127×C71—42no—
220#126×C71—42no—
221#126×C71—42no—
222#126×C71—42no—
223#123×C71—24no—
224#123×C71—42no—
225#123×C71—42no—
226#123×C71—42no—
227#121×C71—24no—
228#121×C71—42no—
229#121×C71—42no—
230#121×C71—42no—
231#121×C71—42no—
232#121×C71—42no—
233#121×C71—42no—
234#121×C71—42no—
235#121×C71—42no—
236#120×C71—24no—
237#120×C71—42no—
238#120×C71—42no—
239#120×C71—42no—
240C4×D4×C71—42no—
241C4×D4×C71—42no—
242C4×D4×C71—42no—
243C2×C4⋊C4×C71C2311yescharacteristic
244C2×C4⋊C4×C71C2311yescharacteristic
245C2×C4⋊C4×C71C2311yescharacteristic
246C2×C4⋊C4×C71C2311yescharacteristic
247C2×C4⋊C4×C71C2311yescharacteristic
248C2×C4⋊C4×C71C2311yescharacteristic
249C2×C4⋊C4×C71C2311yescharacteristic
250C2×C4⋊C4×C71C2311yescharacteristic
251C2×C4⋊C4×C71C2311yescharacteristic
252C2×C4⋊C4×C71C2311yescharacteristic
253C2×C4⋊C4×C71C2311yescharacteristic
254C2×C4⋊C4×C71C2311yescharacteristic
255C2×C4⋊C4×C71C2311yescharacteristic
256C2×C4⋊C4×C71C2311yescharacteristic
257C2×C4⋊C4×C71C2311yescharacteristic
258C2×C4⋊C4×C71C2311yescharacteristic
259C2×C4⋊C4×C71C2311yescharacteristic
260C2×C4⋊C4×C71C2311yescharacteristic
261C2×C4⋊C4×C71C2311yescharacteristic
262C2×C4⋊C4×C71C2311yescharacteristic
263C2×C4⋊C4×C71C2311yescharacteristic
264C2×C4⋊C4×C71C2311yescharacteristic
265C2×C4⋊C4×C71C2311yescharacteristic
266C2×C4⋊C4×C71C2311yescharacteristic
267C2×C4⋊C4×C71C2311yescharacteristic
268C2×C4⋊C4×C71C2311yescharacteristic
269C2×C22⋊C4×C71C2311yescharacteristic
270C2×C22⋊C4×C71C2311yescharacteristic
271C2×C22⋊C4×C71C2311yescharacteristic
272C2×C22⋊C4×C71C2311yescharacteristic
273C2×C22⋊C4×C71C2311yescharacteristic
274C2×C22⋊C4×C71C2311yescharacteristic
275C2×C22⋊C4×C71C2311yescharacteristic
276C2×C22⋊C4×C71C2311yescharacteristic
277C2×C22⋊C4×C71C2311yescharacteristic
278C2×C22⋊C4×C71C2311yescharacteristic
279C2×C22⋊C4×C71C2311yescharacteristic
280C2×C22⋊C4×C71C2311yescharacteristic
281C2×C22⋊C4×C71C2311yescharacteristic
282C2×C22⋊C4×C71C2311yescharacteristic
283C2×C22⋊C4×C71C2311yescharacteristic
284C2×C22⋊C4×C71C2311yescharacteristic
285C2×C22⋊C4×C71C2311yescharacteristic
286C2×C22⋊C4×C71C2311yescharacteristic
287C2×C22⋊C4×C71C2311yescharacteristic
288C2×C22⋊C4×C71C2311yescharacteristic
289C2×C22⋊C4×C71C2311yescharacteristic
290C2×C22⋊C4×C71C2311yescharacteristic
291C2×C22⋊C4×C71C2311yescharacteristic
292C2×C22⋊C4×C71C2311yescharacteristic
293C2×C22⋊C4×C71C2311yescharacteristic
294C2×C22⋊C4×C71C2311yescharacteristic
295C2×C22⋊C4×C71C2311yescharacteristic
296C2×C22⋊C4×C71C2311yescharacteristic
297C2×C22⋊C4×C71C2311yescharacteristic
298C2×C22⋊C4×C71C2311yescharacteristic
299C2×C22⋊C4×C71C2311yescharacteristic
300C2×C22⋊C4×C71C2311yescharacteristic
301C2×C22⋊C4×C71C2311yescharacteristic
302C2×C22⋊C4×C71C2311yescharacteristic
303C2×C22⋊C4×C71C2311yescharacteristic
304C2×C22⋊C4×C71C2311yescharacteristic
305C2×C22⋊C4×C71C2311yescharacteristic
306C2×C22⋊C4×C71C2311yescharacteristic
307C2×C22⋊C4×C71C2311yescharacteristic
308C2×C22⋊C4×C71C2311yescharacteristic
309C2×C22⋊C4×C71C2311yescharacteristic
310C2×C22⋊C4×C71C2311yescharacteristic
311C2×C22⋊C4×C71C2311yescharacteristic
312C2×C22⋊C4×C71C2311yescharacteristic
313C2×C22⋊C4×C71C2311yescharacteristic
314C2×C22⋊C4×C71C2311yescharacteristic
315C2×C22⋊C4×C71C2311yescharacteristic
316C2×C22⋊C4×C71C2311yescharacteristic
317C2×C22⋊C4×C71C2311yescharacteristic
318C2×C22⋊C4×C71C2311yescharacteristic
319C2×C22⋊C4×C71C2311yescharacteristic
320C2×C22⋊C4×C71C2311yescharacteristic
321C2×C22⋊C4×C71C2311yescharacteristic
322C2×C22⋊C4×C71C2311yescharacteristic
323C2×C22⋊C4×C71C2311yescharacteristic
324C2×C22⋊C4×C71C2311yescharacteristic
325C2×C42×C71C2311yescharacteristic
326C2×C42×C71C2311yescharacteristic
327C2×C42×C71C2311yescharacteristic
328C2×C42×C71C2311yescharacteristic
329C2×C42×C71C2311yescharacteristic
330C2×C42×C71C2311yescharacteristic
331C2×C42×C71C2311yescharacteristic
332C2×C42×C71C2311yescharacteristic
333#95×C71C2311yescharacteristic
334#95×C71C2311yescharacteristic
335#95×C71C2311yescharacteristic
336#95×C71C2311yescharacteristic
337#95×C71C2311yescharacteristic
338#95×C71C2311yescharacteristic
339#95×C71C2311yescharacteristic
340#95×C71C2311yescharacteristic
341#95×C71C2311yescharacteristic
342#95×C71C2311yescharacteristic
343#95×C71C2311yescharacteristic
344#95×C71C2311yescharacteristic
345#95×C71C2311yescharacteristic
346#95×C71C2311yescharacteristic
347#95×C71C2311yescharacteristic
348#95×C71C2311yescharacteristic
349#95×C71C2311yescharacteristic
350#95×C71C2311yescharacteristic
351#95×C71C2311yescharacteristic
352#95×C71C2311yescharacteristic
353#95×C71C2311yescharacteristic
354#95×C71C2311yescharacteristic
355#95×C71C2311yescharacteristic
356#95×C71C2311yescharacteristic
357#95×C71C2311yescharacteristic
358#95×C71C2311yescharacteristic
359#95×C71C2311yescharacteristic
360#95×C71C2311yescharacteristic
361#95×C71C2311yescharacteristic
362#95×C71C2311yescharacteristic
363#95×C71C2311yescharacteristic
364#95×C71C2311yescharacteristic
365#95×C71C2311yescharacteristic
366#95×C71C2311yescharacteristic
367#95×C71C2311yescharacteristic
368#95×C71C2311yescharacteristic
369C24×C71—22no—
370C24×C71—22no—
371C24×C71—22no—
372C24×C71—41no—
373C24×C71—41no—
374C24×C71—41no—
375C24×C71—41no—
376C24×C71C2411yescharacteristic
377C24×C71C2411yescharacteristic
378C24×C71C2411yescharacteristic
379C24×C71C2411yescharacteristic
380C24×C71C2411yescharacteristic
381C24×C71C2411yescharacteristic
382C24×C71C2411yescharacteristic
383C2×D4×C71—22no—
384C2×D4×C71—22no—
385C2×D4×C71—22no—
386C2×D4×C71—22no—
387C2×D4×C71—22no—
388C2×D4×C71—22no—
389C2×D4×C71—22no—
390C2×D4×C71—22no—
391C2×D4×C71—22no—
392C2×D4×C71—22no—
393C2×D4×C71—22no—
394C2×D4×C71—22no—
395C2×D4×C71—22no—
396C2×D4×C71—22no—
397C2×D4×C71—22no—
398C2×D4×C71—22no—
399C2×D4×C71—41no—
400C2×D4×C71—41no—
401C2×D4×C71—41no—
402C2×D4×C71—41no—
403C2×D4×C71—41no—
404C2×D4×C71—41no—
405C2×D4×C71—41no—
406C2×D4×C71—41no—
407C2×D4×C71—41no—
408C2×D4×C71—41no—
409C2×D4×C71—41no—
410C2×D4×C71—41no—
411C2×D4×C71—41no—
412C2×D4×C71—41no—
413C2×D4×C71—41no—
414C2×D4×C71—41no—
415C2×D4×C71—41no—
416C2×D4×C71—41no—
417C2×D4×C71—41no—
418C2×D4×C71—41no—
419C2×D4×C71—41no—
420C2×D4×C71—41no—
421C2×D4×C71—41no—
422C2×D4×C71—41no—
423C2×D4×C71—41no—
424C2×D4×C71—41no—
425C2×D4×C71—41no—
426C2×D4×C71—41no—
427C2×D4×C71—41no—
428C2×D4×C71—41no—
429C2×D4×C71—41no—
430C2×D4×C71—41no—
431C2×D4×C71—41no—
432C2×D4×C71—41no—
433C2×D4×C71—41no—
434C2×D4×C71—41no—
435C2×D4×C71—41no—
436C2×D4×C71—41no—
437C22×C4×C71—22no—
438C22×C4×C71—22no—
439C22×C4×C71—22no—
440C22×C4×C71—22no—
441C22×C4×C71—22no—
442C22×C4×C71—22no—
443C22×C4×C71—22no—
444C22×C4×C71—22no—
445C22×C4×C71—22no—
446C22×C4×C71—22no—
447C22×C4×C71—22no—
448C22×C4×C71—41no—
449C22×C4×C71—41no—
450C22×C4×C71—41no—
451C22×C4×C71—41no—
452C22×C4×C71—41no—
453C22×C4×C71—41no—
454C22×C4×C71—41no—
455C22×C4×C71—41no—
456C22×C4×C71—41no—
457C22×C4×C71—41no—
458C22×C4×C71—41no—
459C22×C4×C71—41no—
460C22×C4×C71—41no—
461C22×C4×C71—41no—
462C22×C4×C71—41no—
463C22×C4×C71—41no—
464C22×C4×C71—41no—
465C22×C4×C71—41no—
466C22×C4×C71—41no—
467C22×C4×C71—416no—
468C22×C4×C71C2411yescharacteristic
469C22×C4×C71C2411yescharacteristic
470C22×C4×C71C2411yescharacteristic
471C22×C4×C71C2411yescharacteristic
472C22×C4×C71C2411yescharacteristic
473C22×C4×C71C2411yescharacteristic
474C22×C4×C71C2411yescharacteristic
475C22×C4×C71C2411yescharacteristic
476C22×C4×C71C2411yescharacteristic
477C22×C4×C71C2411yescharacteristic
478C22×C4×C71C2411yescharacteristic
479C22×C4×C71C2411yescharacteristic
480C22×C4×C71C2411yescharacteristic
481C22×C4×C71C2411yescharacteristic
482C22×C4×C71C2411yescharacteristic
483C22×C4×C71C2411yescharacteristic
484C22×C4×C71C2411yescharacteristic
485C22×C4×C71C2411yescharacteristic
486C22×C4×C71C2411yescharacteristic
487C22×C4×C71C2411yescharacteristic
488C22×C4×C71C2411yescharacteristic
489C22×C4×C71C2411yescharacteristic
490C22×C4×C71C2411yescharacteristic
491C22×C4×C71C2411yescharacteristic
492C4⋊C4×C71—22no—
493C4⋊C4×C71—22no—
494C4⋊C4×C71—22no—
495C4⋊C4×C71—22no—
496C4⋊C4×C71—22no—
497C4⋊C4×C71—22no—
498C4⋊C4×C71—22no—
499C4⋊C4×C71—41no—
500C4⋊C4×C71—41no—
501C4⋊C4×C71—41no—
502C4⋊C4×C71—41no—
503C4⋊C4×C71—41no—
504C4⋊C4×C71—41no—
505C4⋊C4×C71—41no—
506C4⋊C4×C71—41no—
507C4⋊C4×C71—41no—
508C4⋊C4×C71—41no—
509C4⋊C4×C71—41no—
510C4⋊C4×C71—41no—
511C4⋊C4×C71—41no—
512C4⋊C4×C71—41no—
513C4⋊C4×C71—41no—
514C4⋊C4×C71—41no—
515C4⋊C4×C71—41no—
516C4⋊C4×C71—41no—
517C4⋊C4×C71—41no—
518C22⋊C4×C71—22no—
519C22⋊C4×C71—22no—
520C22⋊C4×C71—22no—
521C22⋊C4×C71—22no—
522C22⋊C4×C71—22no—
523C22⋊C4×C71—22no—
524C22⋊C4×C71—22no—
525C22⋊C4×C71—22no—
526C22⋊C4×C71—22no—
527C22⋊C4×C71—22no—
528C22⋊C4×C71—22no—
529C22⋊C4×C71—22no—
530C22⋊C4×C71—22no—
531C22⋊C4×C71—22no—
532C22⋊C4×C71—22no—
533C22⋊C4×C71—22no—
534C22⋊C4×C71—41no—
535C22⋊C4×C71—41no—
536C22⋊C4×C71—41no—
537C22⋊C4×C71—41no—
538C22⋊C4×C71—41no—
539C22⋊C4×C71—41no—
540C22⋊C4×C71—41no—
541C22⋊C4×C71—41no—
542C22⋊C4×C71—41no—
543C22⋊C4×C71—41no—
544C22⋊C4×C71—41no—
545C22⋊C4×C71—41no—
546C22⋊C4×C71—41no—
547C22⋊C4×C71—41no—
548C22⋊C4×C71—41no—
549C22⋊C4×C71—41no—
550C22⋊C4×C71—41no—
551C22⋊C4×C71—41no—
552C22⋊C4×C71—41no—
553C22⋊C4×C71—41no—
554C22⋊C4×C71—41no—
555C22⋊C4×C71—41no—
556C22⋊C4×C71—41no—
557C22⋊C4×C71—41no—
558C22⋊C4×C71—41no—
559C22⋊C4×C71—41no—
560C22⋊C4×C71—41no—
561C22⋊C4×C71—41no—
562C22⋊C4×C71—41no—
563C22⋊C4×C71—41no—
564C22⋊C4×C71—41no—
565C22⋊C4×C71—41no—
566C22⋊C4×C71—41no—
567C22⋊C4×C71—41no—
568C22⋊C4×C71—41no—
569C22⋊C4×C71—41no—
570C22⋊C4×C71—41no—
571C22⋊C4×C71—41no—
572C22⋊C4×C71—41no—
573C22⋊C4×C71#4114yes—
574C42×C71—22no—
575C42×C71—41no—
576C42×C71—41no—
577C42×C71—41no—
578C42×C71—41no—
579C42×C71—41no—
580C42×C71—41no—
581C42×C71—41no—
582C23×C71—21no—
583C23×C71—21no—
584C23×C71—21no—
585C23×C71—21no—
586C23×C71—21no—
587C23×C71—21no—
588C23×C71—21no—
589C23×C71—21no—
590C23×C71—21no—
591C23×C71—21no—
592C23×C71—21no—
593C23×C71—21no—
594C23×C71—21no—
595C23×C71—21no—
596C23×C71—21no—
597C23×C71—21no—
598C23×C71—21no—
599C23×C71—21no—
600C23×C71—21no—
601C23×C71—21no—
602C23×C71—21no—
603C23×C71—21no—
604C23×C71—21no—
605C23×C71—21no—
606C23×C71—21no—
607C23×C71—21no—
608C23×C71—21no—
609C23×C71—21no—
610C23×C71—21no—
611C23×C71—21no—
612C23×C71—21no—
613C23×C71—21no—
614C23×C71—21no—
615C23×C71—21no—
616C23×C71—21no—
617C23×C71—21no—
618C23×C71—21no—
619C23×C71—21no—
620C23×C71—21no—
621C23×C71—21no—
622C23×C71—21no—
623C23×C71—21no—
624C23×C71—21no—
625C23×C71—21no—
626C23×C71—21no—
627C23×C71—21no—
628C23×C71—44no—
629C23×C71—44no—
630C23×C71—44no—
631C23×C71—44no—
632C23×C71—44no—
633C23×C71—44no—
634C23×C71—44no—
635C23×C71C2×#4112yes—
636C23×C71H(5,𝔽2)12yes—
637C23×C71H(5,𝔽2)12yes—
638C23×C71C2511yescharacteristic
639D4×C71—44no—
640D4×C71—44no—
641D4×C71—44no—
642D4×C71—82no—
643D4×C71—82no—
644D4×C71—82no—
645D4×C71—82no—
646D4×C71—82no—
647D4×C71—82no—
648D4×C71—82no—
649D4×C71—82no—
650D4×C71—82no—
651D4×C71—82no—
652D4×C71—82no—
653D4×C71—82no—
654D4×C71—82no—
655D4×C71—82no—
656D4×C71—82no—
657C2×C4×C71—21no—
658C2×C4×C71—21no—
659C2×C4×C71—21no—
660C2×C4×C71—21no—
661C2×C4×C71—21no—
662C2×C4×C71—21no—
663C2×C4×C71—21no—
664C2×C4×C71—21no—
665C2×C4×C71—21no—
666C2×C4×C71—21no—
667C2×C4×C71—21no—
668C2×C4×C71—21no—
669C2×C4×C71—21no—
670C2×C4×C71—21no—
671C2×C4×C71—21no—
672C2×C4×C71—21no—
673C2×C4×C71—21no—
674C2×C4×C71—21no—
675C2×C4×C71—21no—
676C2×C4×C71—21no—
677C2×C4×C71—21no—
678C2×C4×C71—21no—
679C2×C4×C71—21no—
680C2×C4×C71—21no—
681C2×C4×C71—21no—
682C2×C4×C71—21no—
683C2×C4×C71—21no—
684C2×C4×C71—21no—
685C2×C4×C71—21no—
686C2×C4×C71—21no—
687C2×C4×C71—21no—
688C2×C4×C71—21no—
689C2×C4×C71—21no—
690C2×C4×C71—21no—
691C2×C4×C71—21no—
692C2×C4×C71—21no—
693C2×C4×C71—21no—
694C2×C4×C71—21no—
695C2×C4×C71—21no—
696C2×C4×C71—21no—
697C2×C4×C71—21no—
698C2×C4×C71—21no—
699C2×C4×C71—21no—
700C2×C4×C71—21no—
701C2×C4×C71—21no—
702C2×C4×C71—21no—
703C2×C4×C71—21no—
704C2×C4×C71—21no—
705C2×C4×C71—21no—
706C2×C4×C71—21no—
707C2×C4×C71—21no—
708C2×C4×C71—21no—
709C2×C4×C71—21no—
710C2×C4×C71—21no—
711C2×C4×C71—21no—
712C2×C4×C71—21no—
713C2×C4×C71—21no—
714C2×C4×C71—21no—
715C2×C4×C71—21no—
716C2×C4×C71—21no—
717C2×C4×C71—21no—
718C2×C4×C71—21no—
719C2×C4×C71—21no—
720C2×C4×C71—21no—
721C2×C4×C71—21no—
722C2×C4×C71—21no—
723C2×C4×C71—21no—
724C2×C4×C71—21no—
725C2×C4×C71—44no—
726C2×C4×C71—44no—
727C2×C4×C71—44no—
728C2×C4×C71—44no—
729C2×C4×C71—44no—
730C2×C4×C71—44no—
731C2×C4×C71—82no—
732C2×C4×C71—82no—
733C2×C4×C71—82no—
734C2×C4×C71—82no—
735C2×C4×C71C2×#4112yes—
736C2×C4×C71C2×#4112yes—
737C2×C4×C71H(5,𝔽2)12yes—
738C2×C4×C71H(5,𝔽2)12yes—
739C22×C71—22no—
740C22×C71—22no—
741C22×C71—22no—
742C22×C71—22no—
743C22×C71—22no—
744C22×C71—22no—
745C22×C71—22no—
746C22×C71—22no—
747C22×C71—22no—
748C22×C71—416no—
749C22×C71—41no—
750C22×C71—41no—
751C22×C71—41no—
752C22×C71—41no—
753C22×C71—41no—
754C22×C71—41no—
755C22×C71—41no—
756C22×C71—41no—
757C22×C71—41no—
758C22×C71—41no—
759C22×C71—41no—
760C22×C71—41no—
761C22×C71—41no—
762C22×C71—41no—
763C22×C71—41no—
764C22×C71—41no—
765C22×C71—41no—
766C22×C71—41no—
767C22×C71—41no—
768C22×C71—41no—
769C22×C71—41no—
770C22×C71—41no—
771C22×C71—41no—
772C22×C71—41no—
773C22×C71—41no—
774C22×C71—41no—
775C22×C71—41no—
776C22×C71—41no—
777C22×C71—41no—
778C22×C71—41no—
779C22×C71—41no—
780C22×C71—41no—
781C22×C71—41no—
782C22×C71—41no—
783C22×C71—41no—
784C22×C71—41no—
785C22×C71—41no—
786C22×C71—41no—
787C22×C71—41no—
788C22×C71—41no—
789C22×C71C22×#4111yescharacteristic
790C22×C71C2×H(5,𝔽2)11yescharacteristic
791C22×C71C2×H(5,𝔽2)11yescharacteristic
792C22×C71C2×H(5,𝔽2)11yescharacteristic
793C22×C71C2×H(5,𝔽2)11yescharacteristic
794C22×C71#58511yescharacteristic
795C22×C71#58511yescharacteristic
796C4×C71—22no—
797C4×C71—22no—
798C4×C71—22no—
799C4×C71—22no—
800C4×C71—41no—
801C4×C71—41no—
802C4×C71—41no—
803C4×C71—41no—
804C4×C71—41no—
805C4×C71—41no—
806C4×C71—41no—
807C4×C71—41no—
808C4×C71—41no—
809C4×C71—41no—
810C4×C71—41no—
811C4×C71—41no—
812C4×C71—41no—
813C4×C71—41no—
814C4×C71—41no—
815C4×C71—41no—
816C4×C71—41no—
817C4×C71—41no—
818C4×C71—41no—
819C4×C71—41no—
820#36887C7111yesmaximal, characteristic, direct product factor, Sylow
821C2×C71—42no—
822C2×C71—42no—
823C2×C71—42no—
824C2×C71—81no—
825C2×C71—81no—
826C2×C71—81no—
827C2×C71—81no—
828C2×C71#346011yescharacteristic
829C2×C71#351311yescharacteristic
830C2×C71#351911yescharacteristic
831C2×C71#353211yescharacteristic
832C2×C71#353411yescharacteristic
833C2×C71#353911yescharacteristic
834C2×C71#354211yescharacteristic
835#2849C2×C7111yescharacteristic, complemented
836#2847C2×C7111yescharacteristic, complemented
837#2778C2×C7111yescharacteristic, complemented
838#2768C2×C7111yescharacteristic, complemented
839#2753C2×C7111yescharacteristic, complemented
840#2746C2×C7111yescharacteristic, complemented
841#2739C2×C7111yescharacteristic, complemented
842#2714C2×C7111yescharacteristic, complemented
843#2709C2×C7111yescharacteristic, complemented
844#2705C2×C7111yescharacteristic, complemented
845#2699C2×C7111yescharacteristic, complemented
846#2691C2×C7111yescharacteristic, complemented
847#2685C2×C7111yescharacteristic, complemented
848#2678C2×C7111yescharacteristic, complemented
849#2678C2×C7111yescharacteristic, complemented
850#2671C2×C7111yescharacteristic, complemented
851#2671C2×C7111yescharacteristic, complemented
852#2669C2×C7111yescharacteristic, complemented
853#2636C2×C7111yescharacteristic, complemented
854#2635C2×C7111yescharacteristic, complemented
855#2576C2×C7111yescharacteristic, complemented
856#2559C2×C7111yescharacteristic, complemented
857#2554C2×C7111yescharacteristic, complemented
858#2553C2×C7111yescharacteristic, complemented
859#2468C2×C7111yescharacteristic, complemented
860#2464C2×C7111yescharacteristic, complemented
861#2428C2×C7111yescharacteristic, complemented
862#2420C2×C7111yescharacteristic, complemented
863#2335C2×C7111yescharacteristic, complemented
864#2333C2×C7111yescharacteristic, complemented
865C4×#120C2×C7111yescharacteristic, complemented
866C71#3688711yescharacteristic, direct product factor, Sylow
867C24×C4C22×C7111yescharacteristic
868C2×#127C22×C7111yescharacteristic
869C2×#126C22×C7111yescharacteristic
870C2×#126C22×C7111yescharacteristic, complemented
871C2×#126C22×C7111yescharacteristic, complemented
872C2×#123C22×C7111yescharacteristic
873C2×#123C22×C7111yescharacteristic
874C2×#123C22×C7111yescharacteristic
875C2×#123C22×C7111yescharacteristic
876C2×#121C22×C7111yescharacteristic
877C2×#121C22×C7111yescharacteristic
878C2×#121C22×C7111yescharacteristic
879C2×#121C22×C7111yescharacteristic
880C2×#121C22×C7111yescharacteristic
881C2×#121C22×C7111yescharacteristic
882C2×#121C22×C7111yescharacteristic
883C2×#121C22×C7111yescharacteristic, complemented
884C2×#121C22×C7111yescharacteristic, complemented
885C2×#120C22×C7111yescharacteristic
886C2×#120C22×C7111yescharacteristic
887C2×#120C22×C7111yescharacteristic
888C2×#120C22×C7111yescharacteristic
889C2×C4×D4C22×C7111yescharacteristic
890C2×C4×D4C22×C7111yescharacteristic
891C2×C4×D4C22×C7111yescharacteristic
892#401C22×C7111yescharacteristic, complemented
893#400C22×C7111yescharacteristic, complemented
894#400C22×C7111yescharacteristic, complemented
895#400C22×C7111yescharacteristic, complemented
896#399C22×C7111yescharacteristic
897#399C22×C7111yescharacteristic, complemented
898#399C22×C7111yescharacteristic, complemented
899#398C22×C7111yescharacteristic, complemented
900#398C22×C7111yescharacteristic, complemented
901#398C22×C7111yescharacteristic, complemented
902#398C22×C7111yescharacteristic, complemented
903#398C22×C7111yescharacteristic, complemented
904#397C22×C7111yescharacteristic
905#397C22×C7111yescharacteristic
906#397C22×C7111yescharacteristic, complemented
907#397C22×C7111yescharacteristic, complemented
908#396C22×C7111yescharacteristic
909#396C22×C7111yescharacteristic
910#396C22×C7111yescharacteristic
911#396C22×C7111yescharacteristic, complemented
912#394C22×C7111yescharacteristic
913#394C22×C7111yescharacteristic
914#394C22×C7111yescharacteristic
915#394C22×C7111yescharacteristic
916#394C22×C7111yescharacteristic
917#394C22×C7111yescharacteristic
918#394C22×C7111yescharacteristic
919#394C22×C7111yescharacteristic
920#394C22×C7111yescharacteristic
921#394C22×C7111yescharacteristic
922#394C22×C7111yescharacteristic, complemented
923#394C22×C7111yescharacteristic, complemented
924#394C22×C7111yescharacteristic, complemented
925#394C22×C7111yescharacteristic, complemented
926#394C22×C7111yescharacteristic, complemented
927#394C22×C7111yescharacteristic, complemented
928#394C22×C7111yescharacteristic, complemented
929#394C22×C7111yescharacteristic, complemented
930#394C22×C7111yescharacteristic, complemented
931#392C22×C7111yescharacteristic
932#392C22×C7111yescharacteristic
933#392C22×C7111yescharacteristic
934#392C22×C7111yescharacteristic
935#392C22×C7111yescharacteristic
936#392C22×C7111yescharacteristic
937#392C22×C7111yescharacteristic
938#392C22×C7111yescharacteristic
939#392C22×C7111yescharacteristic, complemented
940#390C22×C7111yescharacteristic
941#390C22×C7111yescharacteristic
942#390C22×C7111yescharacteristic
943#390C22×C7111yescharacteristic
944#390C22×C7111yescharacteristic
945#390C22×C7111yescharacteristic
946#390C22×C7111yescharacteristic, complemented
947#390C22×C7111yescharacteristic, complemented
948#389C22×C7111yescharacteristic, complemented
949#389C22×C7111yescharacteristic, complemented
950#389C22×C7111yescharacteristic, complemented
951#388C22×C7111yescharacteristic
952#388C22×C7111yescharacteristic
953#388C22×C7111yescharacteristic
954#388C22×C7111yescharacteristic
955#388C22×C7111yescharacteristic
956#388C22×C7111yescharacteristic
957#388C22×C7111yescharacteristic
958#388C22×C7111yescharacteristic, complemented
959#388C22×C7111yescharacteristic, complemented
960#388C22×C7111yescharacteristic, complemented
961#388C22×C7111yescharacteristic, complemented
962#388C22×C7111yescharacteristic, complemented
963#388C22×C7111yescharacteristic, complemented
964#388C22×C7111yescharacteristic, complemented
965#388C22×C7111yescharacteristic, complemented
966#387C22×C7111yescharacteristic, complemented
967#387C22×C7111yescharacteristic, complemented
968#387C22×C7111yescharacteristic, complemented
969#387C22×C7111yescharacteristic, complemented
970#387C22×C7111yescharacteristic, complemented
971#387C22×C7111yescharacteristic, complemented
972#386C22×C7111yescharacteristic
973#386C22×C7111yescharacteristic
974#386C22×C7111yescharacteristic
975#386C22×C7111yescharacteristic
976#386C22×C7111yescharacteristic
977#386C22×C7111yescharacteristic
978#386C22×C7111yescharacteristic
979#386C22×C7111yescharacteristic
980#386C22×C7111yescharacteristic
981#386C22×C7111yescharacteristic
982#386C22×C7111yescharacteristic
983#386C22×C7111yescharacteristic
984#386C22×C7111yescharacteristic
985#386C22×C7111yescharacteristic
986#386C22×C7111yescharacteristic
987#386C22×C7111yescharacteristic
988#386C22×C7111yescharacteristic, complemented
989#386C22×C7111yescharacteristic, complemented
990#386C22×C7111yescharacteristic, complemented
991#386C22×C7111yescharacteristic, complemented
992#385C22×C7111yescharacteristic
993#385C22×C7111yescharacteristic
994#385C22×C7111yescharacteristic
995#385C22×C7111yescharacteristic
996#385C22×C7111yescharacteristic
997#385C22×C7111yescharacteristic
998#385C22×C7111yescharacteristic
999#385C22×C7111yescharacteristic, complemented
1000#385C22×C7111yescharacteristic, complemented
1001#385C22×C7111yescharacteristic, complemented
1002#382C22×C7111yescharacteristic, complemented
1003#382C22×C7111yescharacteristic, complemented
1004#381C22×C7111yescharacteristic
1005#381C22×C7111yescharacteristic
1006#381C22×C7111yescharacteristic, complemented
1007#381C22×C7111yescharacteristic, complemented
1008#380C22×C7111yescharacteristic
1009#380C22×C7111yescharacteristic
1010#380C22×C7111yescharacteristic
1011#380C22×C7111yescharacteristic, complemented
1012#380C22×C7111yescharacteristic, complemented
1013#379C22×C7111yescharacteristic
1014#379C22×C7111yescharacteristic
1015C4×C4⋊C4C22×C7111yescharacteristic, complemented
1016C4×C22⋊C4C22×C7111yescharacteristic
1017C4×C22⋊C4C22×C7111yescharacteristic
1018C4×C22⋊C4C22×C7111yescharacteristic
1019C4×C22⋊C4C22×C7111yescharacteristic, complemented
1020C4×C22⋊C4C22×C7111yescharacteristic, complemented
1021C4×C22⋊C4C22×C7111yescharacteristic, complemented
1022C25C23×C7111yescharacteristic
1023C22×D4C23×C7111yescharacteristic
1024C22×D4C23×C7111yescharacteristic
1025C22×D4C23×C7111yescharacteristic
1026C22×D4C23×C7111yescharacteristic
1027C22×D4C23×C7111yescharacteristic
1028C22×D4C23×C7111yescharacteristic
1029C22×D4C23×C7111yescharacteristic
1030C22×D4C23×C7111yescharacteristic
1031C22×D4C23×C7111yescharacteristic
1032C22×D4C23×C7111yescharacteristic
1033C22×D4C23×C7111yescharacteristic
1034C22×D4C23×C7111yescharacteristic
1035C22×D4C23×C7111yescharacteristic
1036C22×D4C23×C7111yescharacteristic
1037C22×D4C23×C7111yescharacteristic
1038C22×D4C23×C7111yescharacteristic
1039C22×D4C23×C7111yescharacteristic
1040C22×D4C23×C7111yescharacteristic
1041C23×C4—42no—
1042C23×C4—42no—
1043C23×C4—42no—
1044C23×C4C23×C7111yescharacteristic
1045C23×C4C23×C7111yescharacteristic
1046C23×C4C23×C7111yescharacteristic
1047C23×C4C23×C7111yescharacteristic
1048C23×C4C23×C7111yescharacteristic
1049C23×C4C23×C7111yescharacteristic
1050C23×C4C23×C7111yescharacteristic
1051C23×C4C23×C7111yescharacteristic
1052C23×C4C23×C7111yescharacteristic
1053C23×C4C23×C7111yescharacteristic
1054#127—42no—
1055#126—42no—
1056#126—42no—
1057#126—42no—
1058#123—24no—
1059#123—42no—
1060#123—42no—
1061#123—42no—
1062#121—24no—
1063#121—42no—
1064#121—42no—
1065#121—42no—
1066#121—42no—
1067#121—42no—
1068#121—42no—
1069#121—42no—
1070#121—42no—
1071#120—24no—
1072#120—42no—
1073#120—42no—
1074#120—42no—
1075C4×D4—42no—
1076C4×D4—42no—
1077C4×D4—42no—
1078C2×C4⋊C4C23×C7111yescharacteristic
1079C2×C4⋊C4C23×C7111yescharacteristic
1080C2×C4⋊C4C23×C7111yescharacteristic
1081C2×C4⋊C4C23×C7111yescharacteristic
1082C2×C4⋊C4C23×C7111yescharacteristic
1083C2×C4⋊C4C23×C7111yescharacteristic
1084C2×C4⋊C4C23×C7111yescharacteristic
1085C2×C4⋊C4C23×C7111yescharacteristic
1086C2×C4⋊C4C23×C7111yescharacteristic
1087C2×C4⋊C4C23×C7111yescharacteristic
1088C2×C4⋊C4C23×C7111yescharacteristic
1089C2×C4⋊C4C23×C7111yescharacteristic
1090C2×C4⋊C4C23×C7111yescharacteristic
1091C2×C4⋊C4C23×C7111yescharacteristic
1092C2×C4⋊C4C23×C7111yescharacteristic
1093C2×C4⋊C4C23×C7111yescharacteristic
1094C2×C4⋊C4C23×C7111yescharacteristic
1095C2×C4⋊C4C23×C7111yescharacteristic
1096C2×C4⋊C4C23×C7111yescharacteristic
1097C2×C4⋊C4C23×C7111yescharacteristic
1098C2×C4⋊C4C23×C7111yescharacteristic
1099C2×C4⋊C4C23×C7111yescharacteristic
1100C2×C4⋊C4C23×C7111yescharacteristic
1101C2×C4⋊C4C23×C7111yescharacteristic
1102C2×C4⋊C4C23×C7111yescharacteristic
1103C2×C4⋊C4C23×C7111yescharacteristic
1104C2×C22⋊C4C23×C7111yescharacteristic
1105C2×C22⋊C4C23×C7111yescharacteristic
1106C2×C22⋊C4C23×C7111yescharacteristic
1107C2×C22⋊C4C23×C7111yescharacteristic
1108C2×C22⋊C4C23×C7111yescharacteristic
1109C2×C22⋊C4C23×C7111yescharacteristic
1110C2×C22⋊C4C23×C7111yescharacteristic
1111C2×C22⋊C4C23×C7111yescharacteristic
1112C2×C22⋊C4C23×C7111yescharacteristic
1113C2×C22⋊C4C23×C7111yescharacteristic
1114C2×C22⋊C4C23×C7111yescharacteristic
1115C2×C22⋊C4C23×C7111yescharacteristic
1116C2×C22⋊C4C23×C7111yescharacteristic
1117C2×C22⋊C4C23×C7111yescharacteristic
1118C2×C22⋊C4C23×C7111yescharacteristic
1119C2×C22⋊C4C23×C7111yescharacteristic
1120C2×C22⋊C4C23×C7111yescharacteristic
1121C2×C22⋊C4C23×C7111yescharacteristic
1122C2×C22⋊C4C23×C7111yescharacteristic
1123C2×C22⋊C4C23×C7111yescharacteristic
1124C2×C22⋊C4C23×C7111yescharacteristic
1125C2×C22⋊C4C23×C7111yescharacteristic
1126C2×C22⋊C4C23×C7111yescharacteristic
1127C2×C22⋊C4C23×C7111yescharacteristic
1128C2×C22⋊C4C23×C7111yescharacteristic
1129C2×C22⋊C4C23×C7111yescharacteristic
1130C2×C22⋊C4C23×C7111yescharacteristic
1131C2×C22⋊C4C23×C7111yescharacteristic
1132C2×C22⋊C4C23×C7111yescharacteristic
1133C2×C22⋊C4C23×C7111yescharacteristic
1134C2×C22⋊C4C23×C7111yescharacteristic
1135C2×C22⋊C4C23×C7111yescharacteristic
1136C2×C22⋊C4C23×C7111yescharacteristic
1137C2×C22⋊C4C23×C7111yescharacteristic
1138C2×C22⋊C4C23×C7111yescharacteristic
1139C2×C22⋊C4C23×C7111yescharacteristic
1140C2×C22⋊C4C23×C7111yescharacteristic
1141C2×C22⋊C4C23×C7111yescharacteristic
1142C2×C22⋊C4C23×C7111yescharacteristic
1143C2×C22⋊C4C23×C7111yescharacteristic
1144C2×C22⋊C4C23×C7111yescharacteristic
1145C2×C22⋊C4C23×C7111yescharacteristic
1146C2×C22⋊C4C23×C7111yescharacteristic
1147C2×C22⋊C4C23×C7111yescharacteristic
1148C2×C22⋊C4C23×C7111yescharacteristic
1149C2×C22⋊C4C23×C7111yescharacteristic
1150C2×C22⋊C4C23×C7111yescharacteristic
1151C2×C22⋊C4C23×C7111yescharacteristic
1152C2×C22⋊C4C23×C7111yescharacteristic
1153C2×C22⋊C4C23×C7111yescharacteristic
1154C2×C22⋊C4C23×C7111yescharacteristic
1155C2×C22⋊C4C23×C7111yescharacteristic
1156C2×C22⋊C4C23×C7111yescharacteristic
1157C2×C22⋊C4C23×C7111yescharacteristic
1158C2×C22⋊C4C23×C7111yescharacteristic
1159C2×C22⋊C4C23×C7111yescharacteristic
1160C2×C42C23×C7111yescharacteristic
1161C2×C42C23×C7111yescharacteristic
1162C2×C42C23×C7111yescharacteristic
1163C2×C42C23×C7111yescharacteristic
1164C2×C42C23×C7111yescharacteristic
1165C2×C42C23×C7111yescharacteristic
1166C2×C42C23×C7111yescharacteristic
1167C2×C42C23×C7111yescharacteristic
1168#95C23×C7111yescharacteristic
1169#95C23×C7111yescharacteristic
1170#95C23×C7111yescharacteristic
1171#95C23×C7111yescharacteristic
1172#95C23×C7111yescharacteristic
1173#95C23×C7111yescharacteristic
1174#95C23×C7111yescharacteristic
1175#95C23×C7111yescharacteristic
1176#95C23×C7111yescharacteristic
1177#95C23×C7111yescharacteristic
1178#95C23×C7111yescharacteristic
1179#95C23×C7111yescharacteristic
1180#95C23×C7111yescharacteristic
1181#95C23×C7111yescharacteristic
1182#95C23×C7111yescharacteristic
1183#95C23×C7111yescharacteristic
1184#95C23×C7111yescharacteristic
1185#95C23×C7111yescharacteristic
1186#95C23×C7111yescharacteristic
1187#95C23×C7111yescharacteristic
1188#95C23×C7111yescharacteristic
1189#95C23×C7111yescharacteristic
1190#95C23×C7111yescharacteristic
1191#95C23×C7111yescharacteristic
1192#95C23×C7111yescharacteristic
1193#95C23×C7111yescharacteristic
1194#95C23×C7111yescharacteristic
1195#95C23×C7111yescharacteristic
1196#95C23×C7111yescharacteristic
1197#95C23×C7111yescharacteristic
1198#95C23×C7111yescharacteristic
1199#95C23×C7111yescharacteristic
1200#95C23×C7111yescharacteristic
1201#95C23×C7111yescharacteristic
1202#95C23×C7111yescharacteristic
1203#95C23×C7111yescharacteristic
1204C24—22no—
1205C24—22no—
1206C24—22no—
1207C24—41no—
1208C24—41no—
1209C24—41no—
1210C24—41no—
1211C24C24×C7111yescharacteristic
1212C24C24×C7111yescharacteristic
1213C24C24×C7111yescharacteristic
1214C24C24×C7111yescharacteristic
1215C24C24×C7111yescharacteristic
1216C24C24×C7111yescharacteristic
1217C24C24×C7111yescharacteristic
1218C2×D4—22no—
1219C2×D4—22no—
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—22no—
1233C2×D4—22no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—41no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—41no—
1248C2×D4—41no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—41no—
1254C2×D4—41no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—41no—
1258C2×D4—41no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—41no—
1262C2×D4—41no—
1263C2×D4—41no—
1264C2×D4—41no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—41no—
1270C2×D4—41no—
1271C2×D4—41no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—41no—
1302C22×C4—416no—
1303C22×C4C24×C7111yescharacteristic
1304C22×C4C24×C7111yescharacteristic
1305C22×C4C24×C7111yescharacteristic
1306C22×C4C24×C7111yescharacteristic
1307C22×C4C24×C7111yescharacteristic
1308C22×C4C24×C7111yescharacteristic
1309C22×C4C24×C7111yescharacteristic
1310C22×C4C24×C7111yescharacteristic
1311C22×C4C24×C7111yescharacteristic
1312C22×C4C24×C7111yescharacteristic
1313C22×C4C24×C7111yescharacteristic
1314C22×C4C24×C7111yescharacteristic
1315C22×C4C24×C7111yescharacteristic
1316C22×C4C24×C7111yescharacteristic
1317C22×C4C24×C7111yescharacteristic
1318C22×C4C24×C7111yescharacteristic
1319C22×C4C24×C7111yescharacteristic
1320C22×C4C24×C7111yescharacteristic
1321C22×C4C24×C7111yescharacteristic
1322C22×C4C24×C7111yescharacteristic
1323C22×C4C24×C7111yescharacteristic
1324C22×C4C24×C7111yescharacteristic
1325C22×C4C24×C7111yescharacteristic
1326C22×C4C24×C7111yescharacteristic
1327C4⋊C4—22no—
1328C4⋊C4—22no—
1329C4⋊C4—22no—
1330C4⋊C4—22no—
1331C4⋊C4—22no—
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—41no—
1335C4⋊C4—41no—
1336C4⋊C4—41no—
1337C4⋊C4—41no—
1338C4⋊C4—41no—
1339C4⋊C4—41no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—41no—
1347C4⋊C4—41no—
1348C4⋊C4—41no—
1349C4⋊C4—41no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C22⋊C4—22no—
1354C22⋊C4—22no—
1355C22⋊C4—22no—
1356C22⋊C4—22no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—22no—
1361C22⋊C4—22no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—22no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—41no—
1389C22⋊C4—41no—
1390C22⋊C4—41no—
1391C22⋊C4—41no—
1392C22⋊C4—41no—
1393C22⋊C4—41no—
1394C22⋊C4—41no—
1395C22⋊C4—41no—
1396C22⋊C4—41no—
1397C22⋊C4—41no—
1398C22⋊C4—41no—
1399C22⋊C4—41no—
1400C22⋊C4—41no—
1401C22⋊C4—41no—
1402C22⋊C4—41no—
1403C22⋊C4—41no—
1404C22⋊C4—41no—
1405C22⋊C4—41no—
1406C22⋊C4—41no—
1407C22⋊C4—41no—
1408C22⋊C4#41×C7114yes—
1409C42—22no—
1410C42—41no—
1411C42—41no—
1412C42—41no—
1413C42—41no—
1414C42—41no—
1415C42—41no—
1416C42—41no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—44no—
1464C23—44no—
1465C23—44no—
1466C23—44no—
1467C23—44no—
1468C23—44no—
1469C23—44no—
1470C23C2×#41×C7112yes—
1471C23H(5,𝔽2)×C7112yes—
1472C23H(5,𝔽2)×C7112yes—
1473C23C25×C7111yescharacteristic
1474D4—44no—
1475D4—44no—
1476D4—44no—
1477D4—82no—
1478D4—82no—
1479D4—82no—
1480D4—82no—
1481D4—82no—
1482D4—82no—
1483D4—82no—
1484D4—82no—
1485D4—82no—
1486D4—82no—
1487D4—82no—
1488D4—82no—
1489D4—82no—
1490D4—82no—
1491D4—82no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—44no—
1561C2×C4—44no—
1562C2×C4—44no—
1563C2×C4—44no—
1564C2×C4—44no—
1565C2×C4—44no—
1566C2×C4—82no—
1567C2×C4—82no—
1568C2×C4—82no—
1569C2×C4—82no—
1570C2×C4C2×#41×C7112yes—
1571C2×C4C2×#41×C7112yes—
1572C2×C4H(5,𝔽2)×C7112yes—
1573C2×C4H(5,𝔽2)×C7112yes—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—416no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22C22×#41×C7111yescharacteristic
1625C22C2×H(5,𝔽2)×C7111yescharacteristic
1626C22C2×H(5,𝔽2)×C7111yescharacteristic
1627C22C2×H(5,𝔽2)×C7111yescharacteristic
1628C22C2×H(5,𝔽2)×C7111yescharacteristic
1629C22#585×C7111yescharacteristic
1630C22#585×C7111yescharacteristic
1631C4—22no—
1632C4—22no—
1633C4—22no—
1634C4—22no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C2—42no—
1656C2—42no—
1657C2—42no—
1658C2—81no—
1659C2—81no—
1660C2—81no—
1661C2—81no—
1662C2C71×#346011yescharacteristic
1663C2C71×#351311yescharacteristic
1664C2C71×#351911yescharacteristic
1665C2C71×#353211yescharacteristic
1666C2C71×#353411yescharacteristic
1667C2C71×#353911yescharacteristic
1668C2C71×#354211yescharacteristic
subgroupG/H
center, socleC23×C71C25
commutator, Frattini, cosocleC23C25×C71
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C71 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C71×#2849C2semidirect
2. C71×#2847C2semidirect
3. C71×#2778C2semidirect
4. C71×#2768C2semidirect
5. C71×#2753C2semidirect
6. C71×#2746C2semidirect
7. C71×#2739C2semidirect
8. C71×#2714C2semidirect
9. C71×#2709C2semidirect
10. C71×#2705C2semidirect
11. C71×#2699C2semidirect
12. C71×#2691C2semidirect
13. C71×#2685C2semidirect
14. C71×#2678C2semidirect
15. C71×#2678C2semidirect
16. C71×#2671C2semidirect
17. C71×#2671C2semidirect
18. C71×#2669C2semidirect
19. C71×#2636C2semidirect
20. C71×#2635C2semidirect
21. C71×#2576C2semidirect
22. C71×#2559C2semidirect
23. C71×#2554C2semidirect
24. C71×#2553C2semidirect
25. C71×#2468C2semidirect
26. C71×#2464C2semidirect
27. C71×#2428C2semidirect
28. C71×#2420C2semidirect
29. C71×#2335C2semidirect
30. C71×#2333C2semidirect
31. C4×#120×C71C2semidirect
35. C2×#126×C71C22semidirect
36. C2×#126×C71C22semidirect
48. C2×#121×C71C22semidirect
49. C2×#121×C71C22semidirect
57. #401×C71C22semidirect
58. #400×C71C22semidirect
59. #400×C71C22semidirect
60. #400×C71C22semidirect
62. #399×C71C22semidirect
63. #399×C71C22semidirect
64. #398×C71C22semidirect
65. #398×C71C22semidirect
66. #398×C71C22semidirect
67. #398×C71C22semidirect
68. #398×C71C22semidirect
71. #397×C71C22semidirect
72. #397×C71C22semidirect
76. #396×C71C22semidirect
87. #394×C71C22semidirect
88. #394×C71C22semidirect
89. #394×C71C22semidirect
90. #394×C71C22semidirect
91. #394×C71C22semidirect
92. #394×C71C22semidirect
93. #394×C71C22semidirect
94. #394×C71C22semidirect
95. #394×C71C22semidirect
104. #392×C71C22semidirect
111. #390×C71C22semidirect
112. #390×C71C22semidirect
113. #389×C71C22semidirect
114. #389×C71C22semidirect
115. #389×C71C22semidirect
123. #388×C71C22semidirect
124. #388×C71C22semidirect
125. #388×C71C22semidirect
126. #388×C71C22semidirect
127. #388×C71C22semidirect
128. #388×C71C22semidirect
129. #388×C71C22semidirect
130. #388×C71C22semidirect
131. #387×C71C22semidirect
132. #387×C71C22semidirect
133. #387×C71C22semidirect
134. #387×C71C22semidirect
135. #387×C71C22semidirect
136. #387×C71C22semidirect
153. #386×C71C22semidirect
154. #386×C71C22semidirect
155. #386×C71C22semidirect
156. #386×C71C22semidirect
164. #385×C71C22semidirect
165. #385×C71C22semidirect
166. #385×C71C22semidirect
167. #382×C71C22semidirect
168. #382×C71C22semidirect
171. #381×C71C22semidirect
172. #381×C71C22semidirect
176. #380×C71C22semidirect
177. #380×C71C22semidirect
180. C4×C4⋊C4×C71C22semidirect
184. C4×C22⋊C4×C71C22semidirect
185. C4×C22⋊C4×C71C22semidirect
186. C4×C22⋊C4×C71C22semidirect
820. #36887C71direct (N × H)
835. #2849C2×C71semidirect
836. #2847C2×C71semidirect
837. #2778C2×C71semidirect
838. #2768C2×C71semidirect
839. #2753C2×C71semidirect
840. #2746C2×C71semidirect
841. #2739C2×C71semidirect
842. #2714C2×C71semidirect
843. #2709C2×C71semidirect
844. #2705C2×C71semidirect
845. #2699C2×C71semidirect
846. #2691C2×C71semidirect
847. #2685C2×C71semidirect
848. #2678C2×C71semidirect
849. #2678C2×C71semidirect
850. #2671C2×C71semidirect
851. #2671C2×C71semidirect
852. #2669C2×C71semidirect
853. #2636C2×C71semidirect
854. #2635C2×C71semidirect
855. #2576C2×C71semidirect
856. #2559C2×C71semidirect
857. #2554C2×C71semidirect
858. #2553C2×C71semidirect
859. #2468C2×C71semidirect
860. #2464C2×C71semidirect
861. #2428C2×C71semidirect
862. #2420C2×C71semidirect
863. #2335C2×C71semidirect
864. #2333C2×C71semidirect
865. C4×#120C2×C71semidirect
866. C71#36887direct (N × H)
870. C2×#126C22×C71semidirect
871. C2×#126C22×C71semidirect
883. C2×#121C22×C71semidirect
884. C2×#121C22×C71semidirect
892. #401C22×C71semidirect
893. #400C22×C71semidirect
894. #400C22×C71semidirect
895. #400C22×C71semidirect
897. #399C22×C71semidirect
898. #399C22×C71semidirect
899. #398C22×C71semidirect
900. #398C22×C71semidirect
901. #398C22×C71semidirect
902. #398C22×C71semidirect
903. #398C22×C71semidirect
906. #397C22×C71semidirect
907. #397C22×C71semidirect
911. #396C22×C71semidirect
922. #394C22×C71semidirect
923. #394C22×C71semidirect
924. #394C22×C71semidirect
925. #394C22×C71semidirect
926. #394C22×C71semidirect
927. #394C22×C71semidirect
928. #394C22×C71semidirect
929. #394C22×C71semidirect
930. #394C22×C71semidirect
939. #392C22×C71semidirect
946. #390C22×C71semidirect
947. #390C22×C71semidirect
948. #389C22×C71semidirect
949. #389C22×C71semidirect
950. #389C22×C71semidirect
958. #388C22×C71semidirect
959. #388C22×C71semidirect
960. #388C22×C71semidirect
961. #388C22×C71semidirect
962. #388C22×C71semidirect
963. #388C22×C71semidirect
964. #388C22×C71semidirect
965. #388C22×C71semidirect
966. #387C22×C71semidirect
967. #387C22×C71semidirect
968. #387C22×C71semidirect
969. #387C22×C71semidirect
970. #387C22×C71semidirect
971. #387C22×C71semidirect
988. #386C22×C71semidirect
989. #386C22×C71semidirect
990. #386C22×C71semidirect
991. #386C22×C71semidirect
999. #385C22×C71semidirect
1000. #385C22×C71semidirect
1001. #385C22×C71semidirect
1002. #382C22×C71semidirect
1003. #382C22×C71semidirect
1006. #381C22×C71semidirect
1007. #381C22×C71semidirect
1011. #380C22×C71semidirect
1012. #380C22×C71semidirect
1015. C4×C4⋊C4C22×C71semidirect
1019. C4×C22⋊C4C22×C71semidirect
1020. C4×C22⋊C4C22×C71semidirect
1021. C4×C22⋊C4C22×C71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C71×#28492
C71×#28472
C71×#27782
C71×#27682
C71×#27532
C71×#27462
C71×#27392
C71×#27142
C71×#27092
C71×#27052
C71×#26992
C71×#26912
C71×#26852
C71×#26782
C71×#26712
C71×#26692
C71×#26362
C71×#26352
C71×#25762
C71×#25592
C71×#25542
C71×#25532
C71×#24682
C71×#24642
C71×#24282
C71×#24202
C71×#23352
C71×#23332
C4×#120×C712
#3688771