Finite Group Databasebeta

← #32205319

Subgroups — #32205319

Order 18176.

2210 conjugacy classes of subgroups.

The subgroup lattice has 1686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596626C211yesmaximal, characteristic, complemented
2#22596619C211yesmaximal, characteristic, complemented
3#22596194C211yesmaximal, characteristic, complemented
4#22596002C211yesmaximal, characteristic, complemented
5#22595971C211yesmaximal, characteristic, complemented
6#22595963C211yesmaximal, characteristic, complemented
7#22595961C211yesmaximal, characteristic, complemented
8#22595667C211yesmaximal, characteristic, complemented
9#22595616C211yesmaximal, characteristic, complemented
10#22595567C211yesmaximal, characteristic, complemented
11#22595453C211yesmaximal, characteristic, complemented
12#22595343C211yesmaximal, characteristic, complemented
13#22595143C211yesmaximal, characteristic, complemented
14#22594990C211yesmaximal, characteristic, complemented
15#22594974C211yesmaximal, characteristic, complemented
16#22594885C211yesmaximal, characteristic, complemented
17#22594772C211yesmaximal, characteristic, complemented
18#22594635C211yesmaximal, characteristic, complemented
19#22594054C211yesmaximal, characteristic, complemented
20#22594054C211yesmaximal, characteristic, complemented
21#22592723C211yesmaximal, characteristic, complemented
22#22592668C211yesmaximal, characteristic, complemented
23#22592580C211yesmaximal, characteristic, complemented
24#22592465C211yesmaximal, characteristic, complemented
25#22591897C211yesmaximal, characteristic, complemented
26#22591811C211yesmaximal, characteristic, complemented
27#22591798C211yesmaximal, characteristic, complemented
28#22591003C211yesmaximal, characteristic, complemented
29#22590994C211yesmaximal, characteristic, complemented
30C2×#17985875C211yesmaximal, characteristic, complemented
31C71×#2424C211yesmaximal, characteristic, complemented
32C23×C22⋊D71C2211yescharacteristic
33C23×C4×D71C2211yescharacteristic
34C2×#14556121C2211yescharacteristic, complemented
35C2×#14556115C2211yescharacteristic, complemented
36C2×#14556109C2211yescharacteristic
37C2×#14556109C2211yescharacteristic
38C2×#14556109C2211yescharacteristic, complemented
39C2×#14556106C2211yescharacteristic, complemented
40C2×#14556106C2211yescharacteristic, complemented
41C2×#14556105C2211yescharacteristic
42C2×#14556099C2211yescharacteristic, complemented
43C2×#14556099C2211yescharacteristic, complemented
44C2×#14556096C2211yescharacteristic
45C2×#14556096C2211yescharacteristic
46C2×D4×Dic71C2211yescharacteristic
47C22×C22⋊Dic71C2211yescharacteristic
48C22×(C2×D71)⋊C4C2211yescharacteristic
49C71⋊#401C2211yescharacteristic, complemented
50#17985941C2211yescharacteristic, complemented
51#17985941C2211yescharacteristic, complemented
52#17985940C2211yescharacteristic, complemented
53#17985938C2211yescharacteristic, complemented
54#17985937C2211yescharacteristic, complemented
55#17985937C2211yescharacteristic, complemented
56#17985935C2211yescharacteristic, complemented
57#17985932C2211yescharacteristic, complemented
58#17985930C2211yescharacteristic, complemented
59#17985927C2211yescharacteristic, complemented
60#17985927C2211yescharacteristic, complemented
61#17985927C2211yescharacteristic, complemented
62#17985927C2211yescharacteristic, complemented
63#17985927C2211yescharacteristic, complemented
64#17985927C2211yescharacteristic, complemented
65#17985924C2211yescharacteristic, complemented
66#17985924C2211yescharacteristic, complemented
67#17985924C2211yescharacteristic, complemented
68#17985922C2211yescharacteristic, complemented
69#17985922C2211yescharacteristic, complemented
70#17985914C2211yescharacteristic
71#17985914C2211yescharacteristic
72#17985914C2211yescharacteristic
73#17985914C2211yescharacteristic
74#17985914C2211yescharacteristic
75#17985914C2211yescharacteristic
76#17985914C2211yescharacteristic
77#17985914C2211yescharacteristic
78#17985913C2211yescharacteristic, complemented
79#17985913C2211yescharacteristic, complemented
80#17985913C2211yescharacteristic, complemented
81#17985913C2211yescharacteristic, complemented
82#17985913C2211yescharacteristic, complemented
83#17985911C2211yescharacteristic, complemented
84#17985911C2211yescharacteristic, complemented
85#17985907C2211yescharacteristic
86#17985907C2211yescharacteristic
87#17985907C2211yescharacteristic
88#17985907C2211yescharacteristic
89#17985907C2211yescharacteristic
90#17985907C2211yescharacteristic
91#17985907C2211yescharacteristic
92#17985907C2211yescharacteristic
93#17985903C2211yescharacteristic, complemented
94#17985902C2211yescharacteristic, complemented
95#17985899C2211yescharacteristic, complemented
96#17985899C2211yescharacteristic, complemented
97#17985899C2211yescharacteristic, complemented
98#17985899C2211yescharacteristic, complemented
99#17985894C2211yescharacteristic, complemented
100#17985893C2211yescharacteristic, complemented
101#17985893C2211yescharacteristic, complemented
102#17985893C2211yescharacteristic, complemented
103#17985893C2211yescharacteristic, complemented
104#17985892C2211yescharacteristic, complemented
105#17985892C2211yescharacteristic, complemented
106#17985891C2211yescharacteristic, complemented
107#17985891C2211yescharacteristic, complemented
108#17985890C2211yescharacteristic, complemented
109#17985890C2211yescharacteristic, complemented
110#17985889C2211yescharacteristic, complemented
111#17985889C2211yescharacteristic, complemented
112#17985888C2211yescharacteristic, complemented
113#17985888C2211yescharacteristic, complemented
114#17985887C2211yescharacteristic, complemented
115#17985887C2211yescharacteristic, complemented
116#17985887C2211yescharacteristic, complemented
117#17985887C2211yescharacteristic, complemented
118#17985885C2211yescharacteristic, complemented
119#17985883C2211yescharacteristic, complemented
120#17985883C2211yescharacteristic, complemented
121#17985882C2211yescharacteristic, complemented
122#17985880C2211yescharacteristic, complemented
123#17985879C2211yescharacteristic
124#17985879C2211yescharacteristic
125#17985879C2211yescharacteristic
126#17985879C2211yescharacteristic, complemented
127#17985879C2211yescharacteristic, complemented
128#17985878C2211yescharacteristic, complemented
129#17985878C2211yescharacteristic, complemented
130#17985876C2211yescharacteristic, complemented
131#17985876C2211yescharacteristic, complemented
132#17985875C2211yescharacteristic
133#17985875C2211yescharacteristic
134#17985875C2211yescharacteristic
135#17985875C2211yescharacteristic
136#17985875C2211yescharacteristic
137#17985875C2211yescharacteristic
138#17985875C2211yescharacteristic
139#17985875C2211yescharacteristic
140#17985875C2211yescharacteristic, complemented
141#17985875C2211yescharacteristic, complemented
142#17985875C2211yescharacteristic, complemented
143#17985875C2211yescharacteristic, complemented
144#17985873C2211yescharacteristic, complemented
145#17985873C2211yescharacteristic, complemented
146#17985872C2211yescharacteristic
147#17985872C2211yescharacteristic
148#17985872C2211yescharacteristic, complemented
149#17985871C2211yescharacteristic
150#17985870C2211yescharacteristic, complemented
151#17985870C2211yescharacteristic, complemented
152#17985866C2211yescharacteristic, complemented
153#17985863C2211yescharacteristic, complemented
154#17985862C2211yescharacteristic, complemented
155#17985860C2211yescharacteristic
156#17985860C2211yescharacteristic
157#17985859C2211yescharacteristic
158#17985858C2211yescharacteristic, complemented
159#17985858C2211yescharacteristic, complemented
160#17985857C2211yescharacteristic
161#17985857C2211yescharacteristic, complemented
162#17985856C2211yescharacteristic, complemented
163#17985856C2211yescharacteristic, complemented
164#17985855C2211yescharacteristic
165#17985855C2211yescharacteristic
166#17985854C2211yescharacteristic
167#17985854C2211yescharacteristic
168C22⋊C4×Dic71C2211yescharacteristic
169C4×C22⋊Dic71C2211yescharacteristic
170C2×C71⋊#95C2211yescharacteristic
171C2×C71⋊#95C2211yescharacteristic
172C2×#121×C71C2211yescharacteristic
173C2×#121×C71C2211yescharacteristic, complemented
174C2×#120×C71C2211yescharacteristic
175C2×#120×C71C2211yescharacteristic
176C2×C4×D4×C71C2211yescharacteristic
177C22×C22⋊C4×C71C2211yescharacteristic
178#396×C71C2211yescharacteristic, complemented
179#394×C71C2211yescharacteristic, complemented
180#394×C71C2211yescharacteristic, complemented
181#392×C71C2211yescharacteristic, complemented
182#390×C71C2211yescharacteristic, complemented
183#388×C71C2211yescharacteristic, complemented
184#386×C71C2211yescharacteristic
185#386×C71C2211yescharacteristic, complemented
186#385×C71C2211yescharacteristic
187C24×D71C2311yescharacteristic
188C22×Dic142C2311yescharacteristic
189C22×C22⋊D71—24no—
190C22×C22⋊D71—42no—
191C22×C22⋊D71—42no—
192C22×C22⋊D71C2311yescharacteristic
193C22×C22⋊D71C2311yescharacteristic
194C22×C22⋊D71C2311yescharacteristic
195C22×C22⋊D71C2311yescharacteristic
196C22×C22⋊D71C2311yescharacteristic
197C22×C22⋊D71C2311yescharacteristic
198C22×C22⋊D71C2311yescharacteristic
199C22×C22⋊D71C2311yescharacteristic
200C23×Dic71C2311yescharacteristic
201C23×Dic71C2311yescharacteristic
202C23×Dic71C2311yescharacteristic
203C23×Dic71C2311yescharacteristic
204C22×C4×D71—42no—
205C22×C4×D71—42no—
206C22×C4×D71—42no—
207C22×C4×D71C2311yescharacteristic
208C22×C4×D71C2311yescharacteristic
209C22×C4×D71C2311yescharacteristic
210C22×C4×D71C2311yescharacteristic
211#14556121—42no—
212#14556115—42no—
213#14556109—42no—
214#14556109—42no—
215#14556109—42no—
216#14556106—42no—
217#14556106—42no—
218#14556105—42no—
219#14556099—42no—
220#14556099—42no—
221#14556096—24no—
222#14556096—24no—
223D4×Dic71—42no—
224C2×C4⋊Dic71C2311yescharacteristic
225C2×C4⋊Dic71C2311yescharacteristic
226C2×C4⋊Dic71C2311yescharacteristic
227C2×C4⋊Dic71C2311yescharacteristic
228C2×Dic71⋊C4C2311yescharacteristic
229C2×Dic71⋊C4C2311yescharacteristic
230C2×Dic71⋊C4C2311yescharacteristic
231C2×Dic71⋊C4C2311yescharacteristic
232C2×Dic71⋊C4C2311yescharacteristic
233C2×Dic71⋊C4C2311yescharacteristic
234C2×Dic71⋊C4C2311yescharacteristic
235C2×Dic71⋊C4C2311yescharacteristic
236C2×Dic71⋊C4C2311yescharacteristic
237C2×Dic71⋊C4C2311yescharacteristic
238C2×Dic71⋊C4C2311yescharacteristic
239C2×Dic71⋊C4C2311yescharacteristic
240C2×Dic71⋊C4C2311yescharacteristic
241C2×Dic71⋊C4C2311yescharacteristic
242C2×C22⋊Dic71—42no—
243C2×C22⋊Dic71C2311yescharacteristic
244C2×C22⋊Dic71C2311yescharacteristic
245C2×C22⋊Dic71C2311yescharacteristic
246C2×C22⋊Dic71C2311yescharacteristic
247C2×C22⋊Dic71C2311yescharacteristic
248C2×C22⋊Dic71C2311yescharacteristic
249C2×C22⋊Dic71C2311yescharacteristic
250C2×C22⋊Dic71C2311yescharacteristic
251C2×C22⋊Dic71C2311yescharacteristic
252C2×C22⋊Dic71C2311yescharacteristic
253C2×C22⋊Dic71C2311yescharacteristic
254C2×C22⋊Dic71C2311yescharacteristic
255C2×C22⋊Dic71C2311yescharacteristic
256C2×C22⋊Dic71C2311yescharacteristic
257C2×C22⋊Dic71C2311yescharacteristic
258C2×C22⋊Dic71C2311yescharacteristic
259C2×C22⋊Dic71C2311yescharacteristic
260C2×C22⋊Dic71C2311yescharacteristic
261C2×C22⋊Dic71C2311yescharacteristic
262C2×C22⋊Dic71C2311yescharacteristic
263C2×C22⋊Dic71C2311yescharacteristic
264C2×C22⋊Dic71C2311yescharacteristic
265C2×C22⋊Dic71C2311yescharacteristic
266C2×C22⋊Dic71C2311yescharacteristic
267C2×C22⋊Dic71C2311yescharacteristic
268C2×C22⋊Dic71C2311yescharacteristic
269C2×C22⋊Dic71C2311yescharacteristic
270C2×(C2×D71)⋊C4—42no—
271C2×(C2×D71)⋊C4C2311yescharacteristic
272C2×(C2×D71)⋊C4C2311yescharacteristic
273C2×(C2×D71)⋊C4C2311yescharacteristic
274C2×(C2×D71)⋊C4C2311yescharacteristic
275C2×(C2×D71)⋊C4C2311yescharacteristic
276C2×(C2×D71)⋊C4C2311yescharacteristic
277C2×(C2×D71)⋊C4C2311yescharacteristic
278C2×(C2×D71)⋊C4C2311yescharacteristic
279C2×(C2×D71)⋊C4C2311yescharacteristic
280C2×(C2×D71)⋊C4C2311yescharacteristic
281C2×(C2×D71)⋊C4C2311yescharacteristic
282C2×(C2×D71)⋊C4C2311yescharacteristic
283C2×(C2×D71)⋊C4C2311yescharacteristic
284C2×(C2×D71)⋊C4C2311yescharacteristic
285C2×(C2×D71)⋊C4C2311yescharacteristic
286C2×(C2×D71)⋊C4C2311yescharacteristic
287C2×C4×Dic71C2311yescharacteristic
288C2×C4×Dic71C2311yescharacteristic
289C2×C4×Dic71C2311yescharacteristic
290C2×C4×Dic71C2311yescharacteristic
291C2×C4×Dic71C2311yescharacteristic
292C71⋊#95C2311yescharacteristic
293C71⋊#95C2311yescharacteristic
294C71⋊#95C2311yescharacteristic
295C71⋊#95C2311yescharacteristic
296C71⋊#95C2311yescharacteristic
297C71⋊#95C2311yescharacteristic
298C71⋊#95C2311yescharacteristic
299C71⋊#95C2311yescharacteristic
300C71⋊#95C2311yescharacteristic
301C71⋊#95C2311yescharacteristic
302C71⋊#95C2311yescharacteristic
303C71⋊#95C2311yescharacteristic
304C71⋊#95C2311yescharacteristic
305C71⋊#95C2311yescharacteristic
306C71⋊#95C2311yescharacteristic
307C71⋊#95C2311yescharacteristic
308C71⋊#95C2311yescharacteristic
309C71⋊#95C2311yescharacteristic
310C71⋊#95C2311yescharacteristic
311C71⋊#95C2311yescharacteristic
312C71⋊#95C2311yescharacteristic
313C71⋊#95C2311yescharacteristic
314C71⋊#95C2311yescharacteristic
315C71⋊#95C2311yescharacteristic
316C71⋊#95C2311yescharacteristic
317C71⋊#95C2311yescharacteristic
318C71⋊#95C2311yescharacteristic
319C71⋊#95C2311yescharacteristic
320C71⋊#95C2311yescharacteristic
321C71⋊#95C2311yescharacteristic
322C71⋊#95C2311yescharacteristic
323C71⋊#95C2311yescharacteristic
324C71⋊#95C2311yescharacteristic
325C71⋊#95C2311yescharacteristic
326C71⋊#95C2311yescharacteristic
327C71⋊#95C2311yescharacteristic
328C25×C71C2311yescharacteristic
329C22×D4×C71C2311yescharacteristic
330C22×D4×C71C2311yescharacteristic
331C22×D4×C71C2311yescharacteristic
332C22×D4×C71C2311yescharacteristic
333C22×D4×C71C2311yescharacteristic
334C22×D4×C71C2311yescharacteristic
335C22×D4×C71C2311yescharacteristic
336C23×C4×C71C2311yescharacteristic
337C23×C4×C71C2311yescharacteristic
338C23×C4×C71C2311yescharacteristic
339#121×C71—42no—
340#121×C71—42no—
341#120×C71—42no—
342#120×C71—42no—
343C4×D4×C71—42no—
344C2×C4⋊C4×C71C2311yescharacteristic
345C2×C4⋊C4×C71C2311yescharacteristic
346C2×C4⋊C4×C71C2311yescharacteristic
347C2×C4⋊C4×C71C2311yescharacteristic
348C2×C22⋊C4×C71—42no—
349C2×C22⋊C4×C71C2311yescharacteristic
350C2×C22⋊C4×C71C2311yescharacteristic
351C2×C22⋊C4×C71C2311yescharacteristic
352C2×C22⋊C4×C71C2311yescharacteristic
353C2×C22⋊C4×C71C2311yescharacteristic
354C2×C22⋊C4×C71C2311yescharacteristic
355C2×C22⋊C4×C71C2311yescharacteristic
356C2×C22⋊C4×C71C2311yescharacteristic
357C2×C22⋊C4×C71C2311yescharacteristic
358C2×C22⋊C4×C71C2311yescharacteristic
359C2×C22⋊C4×C71C2311yescharacteristic
360C2×C22⋊C4×C71C2311yescharacteristic
361C2×C22⋊C4×C71C2311yescharacteristic
362C2×C22⋊C4×C71C2311yescharacteristic
363C2×C22⋊C4×C71C2311yescharacteristic
364C2×C42×C71C2311yescharacteristic
365#95×C71C2311yescharacteristic
366#95×C71C2311yescharacteristic
367#95×C71C2311yescharacteristic
368#95×C71C2311yescharacteristic
369C23×D71—22no—
370C23×D71—22no—
371C23×D71—41no—
372C23×D71—41no—
373C23×D71—41no—
374C23×D71—41no—
375C23×D71#4114yes—
376C23×D71C2411yescharacteristic
377C23×D71C2411yescharacteristic
378C2×Dic142—22no—
379C2×Dic142—41no—
380C2×Dic142—41no—
381C2×C22⋊D71—22no—
382C2×C22⋊D71—22no—
383C2×C22⋊D71—22no—
384C2×C22⋊D71—22no—
385C2×C22⋊D71—22no—
386C2×C22⋊D71—22no—
387C2×C22⋊D71—22no—
388C2×C22⋊D71—22no—
389C2×C22⋊D71—41no—
390C2×C22⋊D71—41no—
391C2×C22⋊D71—41no—
392C2×C22⋊D71—41no—
393C2×C22⋊D71—41no—
394C2×C22⋊D71—41no—
395C2×C22⋊D71—41no—
396C2×C22⋊D71—41no—
397C2×C22⋊D71—41no—
398C2×C22⋊D71—41no—
399C2×C22⋊D71—41no—
400C2×C22⋊D71—41no—
401C2×C22⋊D71—41no—
402C2×C22⋊D71—41no—
403C2×C22⋊D71—41no—
404C2×C22⋊D71—41no—
405C2×C22⋊D71—416no—
406C22×Dic71—22no—
407C22×Dic71—22no—
408C22×Dic71—22no—
409C22×Dic71—22no—
410C22×Dic71—22no—
411C22×Dic71—22no—
412C22×Dic71—41no—
413C22×Dic71—41no—
414C22×Dic71—41no—
415C22×Dic71—41no—
416C22×Dic71—41no—
417C22×Dic71—41no—
418C22×Dic71C2411yescharacteristic
419C22×Dic71C2411yescharacteristic
420C22×Dic71C2411yescharacteristic
421C22×Dic71C2411yescharacteristic
422C22×Dic71C2411yescharacteristic
423C22×Dic71C2411yescharacteristic
424C22×Dic71C2411yescharacteristic
425C22×Dic71C2411yescharacteristic
426C22×Dic71C2411yescharacteristic
427C22×Dic71C2411yescharacteristic
428C22×Dic71C2411yescharacteristic
429C22×Dic71C2411yescharacteristic
430C22×Dic71C2411yescharacteristic
431C22×Dic71C2411yescharacteristic
432C2×C4×D71—22no—
433C2×C4×D71—22no—
434C2×C4×D71—22no—
435C2×C4×D71—22no—
436C2×C4×D71—41no—
437C2×C4×D71—41no—
438C2×C4×D71—41no—
439C2×C4×D71—41no—
440C2×C4×D71—41no—
441C2×C4×D71—41no—
442C2×C4×D71—41no—
443C2×C4×D71—41no—
444C2×C4×D71—416no—
445C4⋊Dic71—22no—
446C4⋊Dic71—41no—
447C4⋊Dic71—41no—
448C4⋊Dic71—41no—
449Dic71⋊C4—22no—
450Dic71⋊C4—22no—
451Dic71⋊C4—41no—
452Dic71⋊C4—41no—
453Dic71⋊C4—41no—
454Dic71⋊C4—41no—
455Dic71⋊C4—41no—
456Dic71⋊C4—41no—
457Dic71⋊C4—41no—
458Dic71⋊C4—41no—
459Dic71⋊C4—41no—
460Dic71⋊C4—41no—
461Dic71⋊C4—41no—
462Dic71⋊C4—41no—
463C22⋊Dic71—22no—
464C22⋊Dic71—22no—
465C22⋊Dic71—22no—
466C22⋊Dic71—22no—
467C22⋊Dic71—22no—
468C22⋊Dic71—22no—
469C22⋊Dic71—22no—
470C22⋊Dic71—22no—
471C22⋊Dic71—41no—
472C22⋊Dic71—41no—
473C22⋊Dic71—41no—
474C22⋊Dic71—41no—
475C22⋊Dic71—41no—
476C22⋊Dic71—41no—
477C22⋊Dic71—41no—
478C22⋊Dic71—41no—
479C22⋊Dic71—41no—
480C22⋊Dic71—41no—
481C22⋊Dic71—41no—
482C22⋊Dic71—41no—
483C22⋊Dic71—41no—
484C22⋊Dic71—41no—
485C22⋊Dic71—41no—
486C22⋊Dic71—41no—
487C22⋊Dic71—41no—
488C22⋊Dic71—41no—
489C22⋊Dic71—41no—
490(C2×D71)⋊C4—22no—
491(C2×D71)⋊C4—22no—
492(C2×D71)⋊C4—22no—
493(C2×D71)⋊C4—22no—
494(C2×D71)⋊C4—41no—
495(C2×D71)⋊C4—41no—
496(C2×D71)⋊C4—41no—
497(C2×D71)⋊C4—41no—
498(C2×D71)⋊C4—41no—
499(C2×D71)⋊C4—41no—
500(C2×D71)⋊C4—41no—
501(C2×D71)⋊C4—41no—
502(C2×D71)⋊C4—41no—
503(C2×D71)⋊C4—41no—
504(C2×D71)⋊C4—41no—
505(C2×D71)⋊C4—41no—
506C4×Dic71—41no—
507C4×Dic71—41no—
508C4×Dic71—41no—
509C4×Dic71—41no—
510C4×Dic71—41no—
511C24×C71—22no—
512C24×C71—22no—
513C24×C71—22no—
514C24×C71—41no—
515C24×C71—41no—
516C24×C71—41no—
517C24×C71—41no—
518C24×C71C2411yescharacteristic
519C24×C71C2411yescharacteristic
520C24×C71C2411yescharacteristic
521C24×C71C2411yescharacteristic
522C24×C71C2411yescharacteristic
523C2×D4×C71—22no—
524C2×D4×C71—22no—
525C2×D4×C71—22no—
526C2×D4×C71—22no—
527C2×D4×C71—22no—
528C2×D4×C71—22no—
529C2×D4×C71—22no—
530C2×D4×C71—41no—
531C2×D4×C71—41no—
532C2×D4×C71—41no—
533C2×D4×C71—41no—
534C2×D4×C71—41no—
535C2×D4×C71—41no—
536C2×D4×C71—41no—
537C2×D4×C71—41no—
538C2×D4×C71—41no—
539C2×D4×C71—41no—
540C2×D4×C71—41no—
541C2×D4×C71—41no—
542C2×D4×C71—41no—
543C2×D4×C71—41no—
544C22×C4×C71—22no—
545C22×C4×C71—22no—
546C22×C4×C71—22no—
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×C71C2411yescharacteristic
554C22×C4×C71C2411yescharacteristic
555C22×C4×C71C2411yescharacteristic
556C22×C4×C71C2411yescharacteristic
557C22×C4×C71C2411yescharacteristic
558C22×C4×C71C2411yescharacteristic
559C22×C4×C71C2411yescharacteristic
560C22×C4×C71C2411yescharacteristic
561C22×C4×C71C2411yescharacteristic
562C22×C4×C71C2411yescharacteristic
563C4⋊C4×C71—22no—
564C4⋊C4×C71—41no—
565C4⋊C4×C71—41no—
566C4⋊C4×C71—41no—
567C22⋊C4×C71—22no—
568C22⋊C4×C71—22no—
569C22⋊C4×C71—22no—
570C22⋊C4×C71—22no—
571C22⋊C4×C71—41no—
572C22⋊C4×C71—41no—
573C22⋊C4×C71—41no—
574C22⋊C4×C71—41no—
575C22⋊C4×C71—41no—
576C22⋊C4×C71—41no—
577C22⋊C4×C71—41no—
578C22⋊C4×C71—41no—
579C22⋊C4×C71—41no—
580C22⋊C4×C71—41no—
581C22⋊C4×C71—41no—
582C42×C71—41no—
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—44no—
616C23×C71—44no—
617C23×C71—44no—
618C23×C71—82no—
619C23×C71—82no—
620C23×C71—82no—
621C23×C71—82no—
622C23×C71C2×#4112yes—
623C23×C71H(5,𝔽2)12yes—
624C23×C71H(5,𝔽2)12yes—
625C23×C71C2511yescharacteristic
626C22×D71—28no—
627C22×D71—21no—
628C22×D71—21no—
629C22×D71—21no—
630C22×D71—21no—
631C22×D71—21no—
632C22×D71—21no—
633C22×D71—21no—
634C22×D71—21no—
635C22×D71—21no—
636C22×D71—21no—
637C22×D71—21no—
638C22×D71—21no—
639C22×D71—44no—
640C22×D71—44no—
641C22×D71—44no—
642C22×D71—44no—
643C22×D71—44no—
644C22×D71—44no—
645C22×D71C2×#4112yes—
646C22×D71C2×#4112yes—
647D4×C71—44no—
648D4×C71—44no—
649D4×C71—82no—
650D4×C71—82no—
651D4×C71—82no—
652D4×C71—82no—
653D4×C71—82no—
654C2×C4×C71—21no—
655C2×C4×C71—21no—
656C2×C4×C71—21no—
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—44no—
684C2×C4×C71—82no—
685C2×C4×C71—82no—
686C2×C4×C71H(5,𝔽2)12yes—
687C22⋊D71—44no—
688C22⋊D71—44no—
689C22⋊D71—44no—
690C22⋊D71—44no—
691C22⋊D71—82no—
692C22⋊D71—82no—
693C22⋊D71—82no—
694C22⋊D71—82no—
695C2×Dic71—21no—
696C2×Dic71—21no—
697C2×Dic71—21no—
698C2×Dic71—21no—
699C2×Dic71—21no—
700C2×Dic71—21no—
701C2×Dic71—21no—
702C2×Dic71—21no—
703C2×Dic71—21no—
704C2×Dic71—21no—
705C2×Dic71—21no—
706C2×Dic71—21no—
707C2×Dic71—21no—
708C2×Dic71—21no—
709C2×Dic71—21no—
710C2×Dic71—21no—
711C2×Dic71—21no—
712C2×Dic71—21no—
713C2×Dic71—21no—
714C2×Dic71—21no—
715C2×Dic71—21no—
716C2×Dic71—21no—
717C2×Dic71—21no—
718C2×Dic71—21no—
719C2×Dic71—21no—
720C2×Dic71—21no—
721C2×Dic71—21no—
722C2×Dic71—21no—
723C2×Dic71—21no—
724C2×Dic71—21no—
725C2×Dic71—21no—
726C2×Dic71—21no—
727C2×Dic71—21no—
728C2×Dic71—21no—
729C2×Dic71—21no—
730C2×Dic71—21no—
731C2×Dic71—21no—
732C2×Dic71—21no—
733C2×Dic71—21no—
734C2×Dic71—21no—
735C2×Dic71—21no—
736C2×Dic71—44no—
737C2×Dic71—44no—
738C2×Dic71—82no—
739C2×Dic71—82no—
740C2×Dic71H(5,𝔽2)12yes—
741C4×D71—44no—
742C4×D71—44no—
743C4×D71—44no—
744C4×D71—44no—
745Dic142—82no—
746C22×C71—22no—
747C22×C71—22no—
748C22×C71—22no—
749C22×C71—22no—
750C22×C71—22no—
751C22×C71—22no—
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—88no—
781C22×C71#53814yes—
782C22×C71C22×#4111yescharacteristic
783C22×C71C2×H(5,𝔽2)11yescharacteristic
784C22×C71C2×H(5,𝔽2)11yescharacteristic
785C22×C71C2×H(5,𝔽2)11yescharacteristic
786C22×C71C2×H(5,𝔽2)11yescharacteristic
787C22×C71#58511yescharacteristic
788C22×C71#58511yescharacteristic
789C2×D71—22no—
790C2×D71—22no—
791C2×D71—22no—
792C2×D71—22no—
793C2×D71—22no—
794C2×D71—22no—
795C2×D71—416no—
796C2×D71—41no—
797C2×D71—41no—
798C2×D71—41no—
799C2×D71—41no—
800C2×D71—41no—
801C2×D71—41no—
802C2×D71—41no—
803C2×D71—41no—
804C4×C71—22no—
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—
814Dic71—22no—
815Dic71—41no—
816Dic71—41no—
817Dic71—41no—
818Dic71—41no—
819Dic71—41no—
820Dic71—41no—
821Dic71—41no—
822Dic71—41no—
823Dic71—41no—
824Dic71—41no—
825Dic71—41no—
826Dic71—41no—
827Dic71—41no—
828#36758—711nomaximal, Sylow
829C2×C71—24no—
830C2×C71—81no—
831C2×C71—81no—
832C2×C71—81no—
833C2×C71—81no—
834C2×C71C2×#53811yescharacteristic
835C2×C71#350511yescharacteristic
836C2×C71#350511yescharacteristic
837C2×C71#353211yescharacteristic
838C2×C71#353311yescharacteristic
839C2×C71#354211yescharacteristic
840C2×C71#354211yescharacteristic
841D71—42no—
842D71—42no—
843#2848—711no—
844#2847—711no—
845#2797—711no—
846#2781—711no—
847#2779—711no—
848#2778—711no—
849#2778—711no—
850#2756—711no—
851#2753—711no—
852#2749—711no—
853#2741—711no—
854#2730—711no—
855#2714—711no—
856#2703—711no—
857#2702—711no—
858#2696—711no—
859#2688—711no—
860#2676—711no—
861#2613—711no—
862#2613—711no—
863#2493—711no—
864#2488—711no—
865#2480—711no—
866#2472—711no—
867#2425—711no—
868#2424D7111yescharacteristic, complemented
869#2419—711no—
870#2418—711no—
871#2321—711no—
872#2321—711no—
873C2×#386—711no—
874C71#3675811yescharacteristic, complemented, Sylow
875C23×D4—711no—
876C24×C4—711no—
877C2×#126—711no—
878C2×#124—711no—
879C2×#123—711no—
880C2×#123—711no—
881C2×#123—711no—
882C2×C22⋊Q8—711no—
883C2×C22⋊Q8—711no—
884C2×C22⋊Q8—711no—
885C2×#121—711no—
886C2×#121—711no—
887C2×#121C2×D7111yescharacteristic
888C2×#121C2×D7111yescharacteristic, complemented
889C2×#120—711no—
890C2×#120—711no—
891C2×#120C2×D7111yescharacteristic
892C2×#120C2×D7111yescharacteristic
893C2×C4×D4—711no—
894C2×C4×D4C2×D7111yescharacteristic
895C22×C22⋊C4—711no—
896C22×C22⋊C4—711no—
897C22×C22⋊C4C2×D7111yescharacteristic
898#401—711no—
899#400—711no—
900#400—711no—
901#400—711no—
902#400—711no—
903#400—711no—
904#400—711no—
905#399—711no—
906#398—711no—
907#398—711no—
908#397—711no—
909#397—711no—
910#397—711no—
911#397—711no—
912#397—711no—
913#397—711no—
914#397—711no—
915#397—711no—
916#397—711no—
917#396—711no—
918#396—711no—
919#396C2×D7111yescharacteristic, complemented
920#394—711no—
921#394—711no—
922#394—711no—
923#394—711no—
924#394—711no—
925#394—711no—
926#394—711no—
927#394—711no—
928#394—711no—
929#394—711no—
930#394—711no—
931#394—711no—
932#394—711no—
933#394C2×D7111yescharacteristic, complemented
934#394C2×D7111yescharacteristic, complemented
935#393—711no—
936#393—711no—
937#392—711no—
938#392—711no—
939#392—711no—
940#392—711no—
941#392—711no—
942#392—711no—
943#392—711no—
944#392—711no—
945#392C2×D7111yescharacteristic, complemented
946#391—711no—
947#390—711no—
948#390—711no—
949#390—711no—
950#390—711no—
951#390—711no—
952#390C2×D7111yescharacteristic, complemented
953#389—711no—
954#388—711no—
955#388—711no—
956#388—711no—
957#388—711no—
958#388—711no—
959#388—711no—
960#388—711no—
961#388—711no—
962#388—711no—
963#388—711no—
964#388—711no—
965#388—711no—
966#388—711no—
967#388—711no—
968#388—711no—
969#388—711no—
970#388—711no—
971#388—711no—
972#388C2×D7111yescharacteristic, complemented
973#387—711no—
974#387—711no—
975#387—711no—
976#387—711no—
977#387—711no—
978#386—711no—
979#386—711no—
980#386—711no—
981#386—711no—
982#386—711no—
983#386—711no—
984#386—711no—
985#386—711no—
986#386—711no—
987#386—711no—
988#386—711no—
989#386—711no—
990#386—711no—
991#386—711no—
992#386—711no—
993#386—711no—
994#386—711no—
995#386—711no—
996#386—711no—
997#386—711no—
998#386—711no—
999#386C2×D7111yescharacteristic
1000#386C2×D7111yescharacteristic, complemented
1001#385—711no—
1002#385—711no—
1003#385—711no—
1004#385—711no—
1005#385—711no—
1006#385—711no—
1007#385—711no—
1008#385—711no—
1009#385C2×D7111yescharacteristic
1010#383—711no—
1011#382—711no—
1012#381—711no—
1013#381—711no—
1014#381—711no—
1015#380—711no—
1016#380—711no—
1017#380—711no—
1018#380—711no—
1019#380—711no—
1020#380—711no—
1021#380—711no—
1022#379—711no—
1023#379—711no—
1024#379—711no—
1025#379—711no—
1026C4×C22⋊C4—711no—
1027C4×C22⋊C4—711no—
1028C2×#95—711no—
1029C2×#95—711no—
1030C25—711no—
1031C25C22×D7111yescharacteristic
1032C22×Q8—711no—
1033C22×D4—2842no—
1034C22×D4—2842no—
1035C22×D4—711no—
1036C22×D4—711no—
1037C22×D4—711no—
1038C22×D4—711no—
1039C22×D4—711no—
1040C22×D4—711no—
1041C22×D4—711no—
1042C22×D4—711no—
1043C22×D4—1424no—
1044C22×D4C22×D7111yescharacteristic
1045C22×D4C22×D7111yescharacteristic
1046C22×D4C22×D7111yescharacteristic
1047C22×D4C22×D7111yescharacteristic
1048C22×D4C22×D7111yescharacteristic
1049C22×D4C22×D7111yescharacteristic
1050C22×D4C22×D7111yescharacteristic
1051C23×C4—2842no—
1052C23×C4—2842no—
1053C23×C4—2842no—
1054C23×C4—711no—
1055C23×C4—711no—
1056C23×C4—711no—
1057C23×C4—711no—
1058C23×C4—711no—
1059C23×C4—711no—
1060C23×C4—711no—
1061C23×C4—711no—
1062C23×C4C22×D7111yescharacteristic
1063C23×C4C22×D7111yescharacteristic
1064C23×C4C22×D7111yescharacteristic
1065#126—2842no—
1066#124—2842no—
1067#123—2842no—
1068#123—2842no—
1069#123—2842no—
1070C22⋊Q8—2842no—
1071C22⋊Q8—2842no—
1072C22⋊Q8—2842no—
1073#121—42no—
1074#121—42no—
1075#121—2842no—
1076#121—2842no—
1077#120—42no—
1078#120—42no—
1079#120—1424no—
1080#120—1424no—
1081C4×D4—42no—
1082C4×D4—2842no—
1083C2×C4⋊C4—711no—
1084C2×C4⋊C4—711no—
1085C2×C4⋊C4—711no—
1086C2×C4⋊C4—711no—
1087C2×C4⋊C4—711no—
1088C2×C4⋊C4—711no—
1089C2×C4⋊C4—711no—
1090C2×C4⋊C4—711no—
1091C2×C4⋊C4—711no—
1092C2×C4⋊C4—711no—
1093C2×C4⋊C4—711no—
1094C2×C4⋊C4—711no—
1095C2×C4⋊C4—711no—
1096C2×C4⋊C4—711no—
1097C2×C4⋊C4—711no—
1098C2×C4⋊C4—711no—
1099C2×C4⋊C4—711no—
1100C2×C4⋊C4—711no—
1101C2×C4⋊C4C22×D7111yescharacteristic
1102C2×C4⋊C4C22×D7111yescharacteristic
1103C2×C4⋊C4C22×D7111yescharacteristic
1104C2×C4⋊C4C22×D7111yescharacteristic
1105C2×C22⋊C4—42no—
1106C2×C22⋊C4—2842no—
1107C2×C22⋊C4—2842no—
1108C2×C22⋊C4—711no—
1109C2×C22⋊C4—711no—
1110C2×C22⋊C4—711no—
1111C2×C22⋊C4—711no—
1112C2×C22⋊C4—711no—
1113C2×C22⋊C4—711no—
1114C2×C22⋊C4—711no—
1115C2×C22⋊C4—711no—
1116C2×C22⋊C4—711no—
1117C2×C22⋊C4—711no—
1118C2×C22⋊C4—711no—
1119C2×C22⋊C4—711no—
1120C2×C22⋊C4—711no—
1121C2×C22⋊C4—711no—
1122C2×C22⋊C4—711no—
1123C2×C22⋊C4—711no—
1124C2×C22⋊C4—711no—
1125C2×C22⋊C4—711no—
1126C2×C22⋊C4—711no—
1127C2×C22⋊C4—711no—
1128C2×C22⋊C4—711no—
1129C2×C22⋊C4—711no—
1130C2×C22⋊C4—711no—
1131C2×C22⋊C4—711no—
1132C2×C22⋊C4—711no—
1133C2×C22⋊C4—711no—
1134C2×C22⋊C4—711no—
1135C2×C22⋊C4—711no—
1136C2×C22⋊C4—711no—
1137C2×C22⋊C4—711no—
1138C2×C22⋊C4—711no—
1139C2×C22⋊C4—711no—
1140C2×C22⋊C4—711no—
1141C2×C22⋊C4—711no—
1142C2×C22⋊C4—711no—
1143C2×C22⋊C4—711no—
1144C2×C22⋊C4—711no—
1145C2×C22⋊C4—711no—
1146C2×C22⋊C4—711no—
1147C2×C22⋊C4—711no—
1148C2×C22⋊C4—711no—
1149C2×C22⋊C4—711no—
1150C2×C22⋊C4—711no—
1151C2×C22⋊C4C22×D7111yescharacteristic
1152C2×C22⋊C4C22×D7111yescharacteristic
1153C2×C22⋊C4C22×D7111yescharacteristic
1154C2×C22⋊C4C22×D7111yescharacteristic
1155C2×C22⋊C4C22×D7111yescharacteristic
1156C2×C22⋊C4C22×D7111yescharacteristic
1157C2×C22⋊C4C22×D7111yescharacteristic
1158C2×C22⋊C4C22×D7111yescharacteristic
1159C2×C22⋊C4C22×D7111yescharacteristic
1160C2×C22⋊C4C22×D7111yescharacteristic
1161C2×C22⋊C4C22×D7111yescharacteristic
1162C2×C22⋊C4C22×D7111yescharacteristic
1163C2×C22⋊C4C22×D7111yescharacteristic
1164C2×C22⋊C4C22×D7111yescharacteristic
1165C2×C22⋊C4C22×D7111yescharacteristic
1166C2×C42—711no—
1167C2×C42—711no—
1168C2×C42—711no—
1169C2×C42—711no—
1170C2×C42—711no—
1171C2×C42C22×D7111yescharacteristic
1172#95—711no—
1173#95—711no—
1174#95—711no—
1175#95—711no—
1176#95—711no—
1177#95—711no—
1178#95—711no—
1179#95—711no—
1180#95—711no—
1181#95—711no—
1182#95—711no—
1183#95—711no—
1184#95—711no—
1185#95—711no—
1186#95—711no—
1187#95—711no—
1188#95—711no—
1189#95—711no—
1190#95—711no—
1191#95—711no—
1192#95—711no—
1193#95—711no—
1194#95—711no—
1195#95—711no—
1196#95—711no—
1197#95—711no—
1198#95—711no—
1199#95—711no—
1200#95—711no—
1201#95—711no—
1202#95—711no—
1203#95—711no—
1204#95—711no—
1205#95—711no—
1206#95—711no—
1207#95—711no—
1208#95C22×D7111yescharacteristic
1209#95C22×D7111yescharacteristic
1210#95C22×D7111yescharacteristic
1211#95C22×D7111yescharacteristic
1212C24—22no—
1213C24—22no—
1214C24—22no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—41no—
1219C24—2841no—
1220C24—2841no—
1221C24—2841no—
1222C24—2841no—
1223C24—714no—
1224C24—711no—
1225C24—711no—
1226C24—1422no—
1227C24—1422no—
1228C24C23×D7111yescharacteristic
1229C24C23×D7111yescharacteristic
1230C24C23×D7111yescharacteristic
1231C24C23×D7111yescharacteristic
1232C24C23×D7111yescharacteristic
1233C2×Q8—2841no—
1234C2×Q8—2841no—
1235C2×Q8—1422no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—22no—
1242C2×D4—22no—
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—28416no—
1258C2×D4—2841no—
1259C2×D4—2841no—
1260C2×D4—2841no—
1261C2×D4—2841no—
1262C2×D4—2841no—
1263C2×D4—2841no—
1264C2×D4—2841no—
1265C2×D4—2841no—
1266C2×D4—2841no—
1267C2×D4—2841no—
1268C2×D4—2841no—
1269C2×D4—2841no—
1270C2×D4—2841no—
1271C2×D4—2841no—
1272C2×D4—2841no—
1273C2×D4—2841no—
1274C2×D4—1422no—
1275C2×D4—1422no—
1276C2×D4—1422no—
1277C2×D4—1422no—
1278C2×D4—1422no—
1279C2×D4—1422no—
1280C2×D4—1422no—
1281C2×D4—1422no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—2841no—
1292C22×C4—2841no—
1293C22×C4—2841no—
1294C22×C4—2841no—
1295C22×C4—2841no—
1296C22×C4—2841no—
1297C22×C4—2841no—
1298C22×C4—2841no—
1299C22×C4—28416no—
1300C22×C4—2841no—
1301C22×C4—2841no—
1302C22×C4—2841no—
1303C22×C4—2841no—
1304C22×C4—2841no—
1305C22×C4—2841no—
1306C22×C4—711no—
1307C22×C4—711no—
1308C22×C4—711no—
1309C22×C4—711no—
1310C22×C4—711no—
1311C22×C4—711no—
1312C22×C4—711no—
1313C22×C4—711no—
1314C22×C4—711no—
1315C22×C4—711no—
1316C22×C4—711no—
1317C22×C4—711no—
1318C22×C4—711no—
1319C22×C4—711no—
1320C22×C4—1422no—
1321C22×C4—1422no—
1322C22×C4—1422no—
1323C22×C4—1422no—
1324C22×C4—1422no—
1325C22×C4—1422no—
1326C22×C4—1422no—
1327C22×C4—1422no—
1328C22×C4—1422no—
1329C22×C4—1422no—
1330C22×C4C23×D7111yescharacteristic
1331C22×C4C23×D7111yescharacteristic
1332C22×C4C23×D7111yescharacteristic
1333C22×C4C23×D7111yescharacteristic
1334C22×C4C23×D7111yescharacteristic
1335C22×C4C23×D7111yescharacteristic
1336C22×C4C23×D7111yescharacteristic
1337C22×C4C23×D7111yescharacteristic
1338C22×C4C23×D7111yescharacteristic
1339C22×C4C23×D7111yescharacteristic
1340C4⋊C4—22no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—2841no—
1345C4⋊C4—2841no—
1346C4⋊C4—2841no—
1347C4⋊C4—2841no—
1348C4⋊C4—2841no—
1349C4⋊C4—2841no—
1350C4⋊C4—2841no—
1351C4⋊C4—2841no—
1352C4⋊C4—2841no—
1353C4⋊C4—2841no—
1354C4⋊C4—2841no—
1355C4⋊C4—2841no—
1356C4⋊C4—2841no—
1357C4⋊C4—2841no—
1358C4⋊C4—2841no—
1359C4⋊C4—1422no—
1360C4⋊C4—1422no—
1361C4⋊C4—1422no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—41no—
1367C22⋊C4—41no—
1368C22⋊C4—41no—
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—2841no—
1378C22⋊C4—2841no—
1379C22⋊C4—2841no—
1380C22⋊C4—2841no—
1381C22⋊C4—2841no—
1382C22⋊C4—2841no—
1383C22⋊C4—2841no—
1384C22⋊C4—2841no—
1385C22⋊C4—2841no—
1386C22⋊C4—2841no—
1387C22⋊C4—2841no—
1388C22⋊C4—2841no—
1389C22⋊C4—2841no—
1390C22⋊C4—2841no—
1391C22⋊C4—2841no—
1392C22⋊C4—2841no—
1393C22⋊C4—2841no—
1394C22⋊C4—2841no—
1395C22⋊C4—2841no—
1396C22⋊C4—2841no—
1397C22⋊C4—2841no—
1398C22⋊C4—2841no—
1399C22⋊C4—2841no—
1400C22⋊C4—2841no—
1401C22⋊C4—2841no—
1402C22⋊C4—2841no—
1403C22⋊C4—2841no—
1404C22⋊C4—2841no—
1405C22⋊C4—2841no—
1406C22⋊C4—2841no—
1407C22⋊C4—2841no—
1408C22⋊C4—1422no—
1409C22⋊C4—1422no—
1410C22⋊C4—1422no—
1411C22⋊C4—1422no—
1412C22⋊C4—1422no—
1413C22⋊C4—1422no—
1414C22⋊C4—1422no—
1415C22⋊C4—1422no—
1416C22⋊C4—1422no—
1417C22⋊C4—1422no—
1418C22⋊C4—1422no—
1419C22⋊C4—1422no—
1420C42—41no—
1421C42—2841no—
1422C42—2841no—
1423C42—2841no—
1424C42—2841no—
1425C42—2841no—
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—44no—
1459C23—44no—
1460C23—44no—
1461C23—82no—
1462C23—82no—
1463C23—82no—
1464C23—82no—
1465C23—2844no—
1466C23—2844no—
1467C23—2844no—
1468C23—2844no—
1469C23—2844no—
1470C23—2844no—
1471C23—712no—
1472C23—712no—
1473C23—1421no—
1474C23—1421no—
1475C23—1421no—
1476C23—1421no—
1477C23—1421no—
1478C23—1421no—
1479C23—1421no—
1480C23—1421no—
1481C23—1421no—
1482C23—1421no—
1483C23—1421no—
1484C23—1421no—
1485C23—1428no—
1486C23#41×D7112yes—
1487C23#1455617312yes—
1488C23#1455617312yes—
1489C23C24×D7111yescharacteristic
1490Q8—5682no—
1491D4—44no—
1492D4—44no—
1493D4—82no—
1494D4—82no—
1495D4—82no—
1496D4—82no—
1497D4—82no—
1498D4—2844no—
1499D4—2844no—
1500D4—2844no—
1501D4—2844no—
1502D4—5682no—
1503D4—5682no—
1504D4—5682no—
1505D4—5682no—
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—44no—
1536C2×C4—82no—
1537C2×C4—82no—
1538C2×C4—2844no—
1539C2×C4—2844no—
1540C2×C4—2844no—
1541C2×C4—2844no—
1542C2×C4—2844no—
1543C2×C4—2844no—
1544C2×C4—5682no—
1545C2×C4—5682no—
1546C2×C4—712no—
1547C2×C4—1421no—
1548C2×C4—1421no—
1549C2×C4—1421no—
1550C2×C4—1421no—
1551C2×C4—1421no—
1552C2×C4—1421no—
1553C2×C4—1421no—
1554C2×C4—1421no—
1555C2×C4—1421no—
1556C2×C4—1421no—
1557C2×C4—1421no—
1558C2×C4—1421no—
1559C2×C4—1421no—
1560C2×C4—1421no—
1561C2×C4—1421no—
1562C2×C4—1421no—
1563C2×C4—1421no—
1564C2×C4—1421no—
1565C2×C4—1421no—
1566C2×C4—1421no—
1567C2×C4—1421no—
1568C2×C4—1421no—
1569C2×C4—1421no—
1570C2×C4—1421no—
1571C2×C4—1421no—
1572C2×C4—1421no—
1573C2×C4—1421no—
1574C2×C4—1421no—
1575C2×C4—1421no—
1576C2×C4—1421no—
1577C2×C4—1421no—
1578C2×C4—1421no—
1579C2×C4—1421no—
1580C2×C4—1421no—
1581C2×C4—1421no—
1582C2×C4—1421no—
1583C2×C4—1421no—
1584C2×C4—1421no—
1585C2×C4—1421no—
1586C2×C4—1421no—
1587C2×C4—1421no—
1588C2×C4#1455617312yes—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—22no—
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—88no—
1624C22—28416no—
1625C22—2841no—
1626C22—2841no—
1627C22—2841no—
1628C22—2841no—
1629C22—2841no—
1630C22—2841no—
1631C22—2841no—
1632C22—2841no—
1633C22—1422no—
1634C22—1422no—
1635C22—1422no—
1636C22—1422no—
1637C22—1422no—
1638C22—1422no—
1639C22#1798658114yes—
1640C22C2×#41×D7111yescharacteristic
1641C22H(5,𝔽2)×D7111yescharacteristic
1642C22C2×#1455617311yescharacteristic
1643C22C2×#1455617311yescharacteristic
1644C22C2×#1455617311yescharacteristic
1645C22#1798683411yescharacteristic
1646C22#1798683511yescharacteristic
1647C4—22no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—2841no—
1658C4—2841no—
1659C4—2841no—
1660C4—2841no—
1661C4—2841no—
1662C4—2841no—
1663C4—2841no—
1664C4—2841no—
1665C4—2841no—
1666C4—2841no—
1667C4—2841no—
1668C4—2841no—
1669C4—2841no—
1670C4—1422no—
1671C2—24no—
1672C2—81no—
1673C2—81no—
1674C2—81no—
1675C2—81no—
1676C2—2842no—
1677C2—2842no—
1678C2C2×#1798658111yescharacteristic
1679C2#2260216811yescharacteristic
1680C2#2260217811yescharacteristic
1681C2#2260249011yescharacteristic
1682C2#2260249911yescharacteristic
1683C2#2260264111yescharacteristic
1684C2#2260266111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2424C2
hypercenter#2424D71
hypocenterC71#36758
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2424

Complements

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

NH ≅ G/Ntype
1. #22596626C2semidirect
2. #22596619C2semidirect
3. #22596194C2semidirect
4. #22596002C2semidirect
5. #22595971C2semidirect
6. #22595963C2semidirect
7. #22595961C2semidirect
8. #22595667C2semidirect
9. #22595616C2semidirect
10. #22595567C2semidirect
11. #22595453C2semidirect
12. #22595343C2semidirect
13. #22595143C2semidirect
14. #22594990C2semidirect
15. #22594974C2semidirect
16. #22594885C2semidirect
17. #22594772C2semidirect
18. #22594635C2semidirect
19. #22594054C2semidirect
20. #22594054C2semidirect
21. #22592723C2semidirect
22. #22592668C2semidirect
23. #22592580C2semidirect
24. #22592465C2semidirect
25. #22591897C2semidirect
26. #22591811C2semidirect
27. #22591798C2semidirect
28. #22591003C2semidirect
29. #22590994C2semidirect
30. C2×#17985875C2semidirect
31. C71×#2424C2semidirect
34. C2×#14556121C22semidirect
35. C2×#14556115C22semidirect
38. C2×#14556109C22semidirect
39. C2×#14556106C22semidirect
40. C2×#14556106C22semidirect
42. C2×#14556099C22semidirect
43. C2×#14556099C22semidirect
49. C71⋊#401C22semidirect
50. #17985941C22semidirect
51. #17985941C22semidirect
52. #17985940C22semidirect
53. #17985938C22semidirect
54. #17985937C22semidirect
55. #17985937C22semidirect
56. #17985935C22semidirect
57. #17985932C22semidirect
58. #17985930C22semidirect
59. #17985927C22semidirect
60. #17985927C22semidirect
61. #17985927C22semidirect
62. #17985927C22semidirect
63. #17985927C22semidirect
64. #17985927C22semidirect
65. #17985924C22semidirect
66. #17985924C22semidirect
67. #17985924C22semidirect
68. #17985922C22semidirect
69. #17985922C22semidirect
78. #17985913C22semidirect
79. #17985913C22semidirect
80. #17985913C22semidirect
81. #17985913C22semidirect
82. #17985913C22semidirect
83. #17985911C22semidirect
84. #17985911C22semidirect
93. #17985903C22semidirect
94. #17985902C22semidirect
95. #17985899C22semidirect
96. #17985899C22semidirect
97. #17985899C22semidirect
98. #17985899C22semidirect
99. #17985894C22semidirect
100. #17985893C22semidirect
101. #17985893C22semidirect
102. #17985893C22semidirect
103. #17985893C22semidirect
104. #17985892C22semidirect
105. #17985892C22semidirect
106. #17985891C22semidirect
107. #17985891C22semidirect
108. #17985890C22semidirect
109. #17985890C22semidirect
110. #17985889C22semidirect
111. #17985889C22semidirect
112. #17985888C22semidirect
113. #17985888C22semidirect
114. #17985887C22semidirect
115. #17985887C22semidirect
116. #17985887C22semidirect
117. #17985887C22semidirect
118. #17985885C22semidirect
119. #17985883C22semidirect
120. #17985883C22semidirect
121. #17985882C22semidirect
122. #17985880C22semidirect
126. #17985879C22semidirect
127. #17985879C22semidirect
128. #17985878C22semidirect
129. #17985878C22semidirect
130. #17985876C22semidirect
131. #17985876C22semidirect
140. #17985875C22semidirect
141. #17985875C22semidirect
142. #17985875C22semidirect
143. #17985875C22semidirect
144. #17985873C22semidirect
145. #17985873C22semidirect
148. #17985872C22semidirect
150. #17985870C22semidirect
151. #17985870C22semidirect
152. #17985866C22semidirect
153. #17985863C22semidirect
154. #17985862C22semidirect
158. #17985858C22semidirect
159. #17985858C22semidirect
161. #17985857C22semidirect
162. #17985856C22semidirect
163. #17985856C22semidirect
173. C2×#121×C71C22semidirect
178. #396×C71C22semidirect
179. #394×C71C22semidirect
180. #394×C71C22semidirect
181. #392×C71C22semidirect
182. #390×C71C22semidirect
183. #388×C71C22semidirect
185. #386×C71C22semidirect
868. #2424D71semidirect
874. C71#36758semidirect
888. C2×#121C2×D71semidirect
919. #396C2×D71semidirect
933. #394C2×D71semidirect
934. #394C2×D71semidirect
945. #392C2×D71semidirect
952. #390C2×D71semidirect
972. #388C2×D71semidirect
1000. #386C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225966262
#225966192
#225961942
#225960022
#225959712
#225959632
#225959612
#225956672
#225956162
#225955672
#225954532
#225953432
#225951432
#225949902
#225949742
#225948852
#225947722
#225946352
#225940542
#225927232
#225926682
#225925802
#225924652
#225918972
#225918112
#225917982
#225910032
#225909942
C2×#179858752
C71×#24242
#3675871