Finite Group Databasebeta

← #32170251

Subgroups — #32170251

Order 18176.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596670C211yesmaximal, characteristic, complemented
2#22596660C211yesmaximal, characteristic, complemented
3#22596654C211yesmaximal, characteristic, complemented
4#22596636C211yesmaximal, characteristic, complemented
5#22594400C211yesmaximal, characteristic, complemented
6#22594340C211yesmaximal, characteristic, complemented
7#22594325C211yesmaximal, characteristic, complemented
8#22594325C211yesmaximal, characteristic, complemented
9#22593002C211yesmaximal, characteristic, complemented
10#22592995C211yesmaximal, characteristic, complemented
11#22592902C211yesmaximal, characteristic, complemented
12#22592893C211yesmaximal, characteristic, complemented
13#22592835C211yesmaximal, characteristic, complemented
14#22592659C211yesmaximal, characteristic, complemented
15#22592580C211yesmaximal, characteristic, complemented
16#22592397C211yesmaximal, characteristic, complemented
17#22592273C211yesmaximal, characteristic, complemented
18#22592083C211yesmaximal, characteristic, complemented
19#22592003C211yesmaximal, characteristic, complemented
20#22591892C211yesmaximal, characteristic, complemented
21#22591735C211yesmaximal, characteristic, complemented
22#22591710C211yesmaximal, characteristic
23#22591665C211yesmaximal, characteristic, complemented
24#22591075C211yesmaximal, characteristic, complemented
25#22591001C211yesmaximal, characteristic, complemented
26#22590966C211yesmaximal, characteristic, complemented
27#22590936C211yesmaximal, characteristic, complemented
28#22590845C211yesmaximal, characteristic, complemented
29C2×#17985875C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D71C211yesmaximal, characteristic, complemented
31C71×#2472C211yesmaximal, characteristic, complemented
32C23×C22⋊D71C2211yescharacteristic
33C23×C4×D71C2211yescharacteristic
34C2×#14556121C2211yescharacteristic, complemented
35C2×#14556110C2211yescharacteristic
36C2×#14556110C2211yescharacteristic
37C2×#14556110C2211yescharacteristic, complemented
38C2×#14556104C2211yescharacteristic, complemented
39C2×#14556099C2211yescharacteristic
40C2×#14556099C2211yescharacteristic
41C2×#14556096C2211yescharacteristic
42C2×D4×Dic71C2211yescharacteristic
43C2×(C22⋊D71)⋊C4C2211yescharacteristic, complemented
44C2×(C22⋊D71)⋊C4C2211yescharacteristic, complemented
45C22×C22⋊Dic71C2211yescharacteristic
46C22×(C2×D71)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D71C2211yescharacteristic
48C2×C22⋊C4×D71C2211yescharacteristic
49C2×C42×D71C2211yescharacteristic, complemented
50C2×C42×D71C2211yescharacteristic, complemented
51C71⋊#401C2211yescharacteristic, complemented
52#17985941C2211yescharacteristic, complemented
53#17985941C2211yescharacteristic, complemented
54#17985941C2211yescharacteristic, complemented
55#17985939C2211yescharacteristic, complemented
56#17985934C2211yescharacteristic, complemented
57#17985933C2211yescharacteristic, complemented
58#17985928C2211yescharacteristic, complemented
59#17985927C2211yescharacteristic, complemented
60#17985927C2211yescharacteristic, complemented
61#17985927C2211yescharacteristic, complemented
62#17985926C2211yescharacteristic, complemented
63#17985924C2211yescharacteristic, complemented
64#17985924C2211yescharacteristic, complemented
65#17985922C2211yescharacteristic, complemented
66#17985921C2211yescharacteristic, complemented
67#17985921C2211yescharacteristic, complemented
68#17985915C2211yescharacteristic
69#17985915C2211yescharacteristic
70#17985915C2211yescharacteristic
71#17985915C2211yescharacteristic
72#17985915C2211yescharacteristic, complemented
73#17985914C2211yescharacteristic
74#17985914C2211yescharacteristic
75#17985914C2211yescharacteristic, complemented
76#17985910C2211yescharacteristic, complemented
77#17985907C2211yescharacteristic
78#17985907C2211yescharacteristic
79#17985906C2211yescharacteristic, complemented
80#17985906C2211yescharacteristic, complemented
81#17985902C2211yescharacteristic, complemented
82#17985902C2211yescharacteristic, complemented
83#17985898C2211yescharacteristic, complemented
84#17985898C2211yescharacteristic, complemented
85#17985897C2211yescharacteristic, complemented
86#17985893C2211yescharacteristic, complemented
87#17985893C2211yescharacteristic, complemented
88#17985893C2211yescharacteristic, complemented
89#17985893C2211yescharacteristic, complemented
90#17985893C2211yescharacteristic, complemented
91#17985893C2211yescharacteristic, complemented
92#17985892C2211yescharacteristic, complemented
93#17985892C2211yescharacteristic, complemented
94#17985892C2211yescharacteristic, complemented
95#17985892C2211yescharacteristic, complemented
96#17985892C2211yescharacteristic, complemented
97#17985892C2211yescharacteristic, complemented
98#17985887C2211yescharacteristic, complemented
99#17985887C2211yescharacteristic, complemented
100#17985887C2211yescharacteristic, complemented
101#17985887C2211yescharacteristic, complemented
102#17985887C2211yescharacteristic, complemented
103#17985887C2211yescharacteristic, complemented
104#17985887C2211yescharacteristic, complemented
105#17985886C2211yescharacteristic, complemented
106#17985885C2211yescharacteristic, complemented
107#17985885C2211yescharacteristic, complemented
108#17985885C2211yescharacteristic, complemented
109#17985885C2211yescharacteristic, complemented
110#17985884C2211yescharacteristic, complemented
111#17985883C2211yescharacteristic, complemented
112#17985883C2211yescharacteristic, complemented
113#17985882C2211yescharacteristic, complemented
114#17985879C2211yescharacteristic
115#17985879C2211yescharacteristic
116#17985879C2211yescharacteristic, complemented
117#17985879C2211yescharacteristic, complemented
118#17985875C2211yescharacteristic
119#17985875C2211yescharacteristic
120#17985875C2211yescharacteristic
121#17985875C2211yescharacteristic
122#17985875C2211yescharacteristic
123#17985875C2211yescharacteristic
124#17985875C2211yescharacteristic
125#17985875C2211yescharacteristic
126#17985875C2211yescharacteristic
127#17985875C2211yescharacteristic
128#17985875C2211yescharacteristic
129#17985875C2211yescharacteristic
130#17985875C2211yescharacteristic, complemented
131#17985875C2211yescharacteristic, complemented
132#17985875C2211yescharacteristic, complemented
133#17985874C2211yescharacteristic
134#17985874C2211yescharacteristic
135#17985874C2211yescharacteristic
136#17985873C2211yescharacteristic, complemented
137#17985873C2211yescharacteristic, complemented
138#17985873C2211yescharacteristic, complemented
139#17985872C2211yescharacteristic
140#17985872C2211yescharacteristic
141#17985871C2211yescharacteristic
142#17985870C2211yescharacteristic, complemented
143#17985870C2211yescharacteristic, complemented
144#17985866C2211yescharacteristic, complemented
145#17985866C2211yescharacteristic, complemented
146#17985865C2211yescharacteristic, complemented
147#17985863C2211yescharacteristic, complemented
148#17985861C2211yescharacteristic, complemented
149#17985860C2211yescharacteristic, complemented
150#17985859C2211yescharacteristic
151#17985857C2211yescharacteristic
152#17985857C2211yescharacteristic
153#17985857C2211yescharacteristic, complemented
154#17985856C2211yescharacteristic, complemented
155#17985855C2211yescharacteristic
156#17985855C2211yescharacteristic
157#17985854C2211yescharacteristic
158C22⋊C4×Dic71C2211yescharacteristic
159C22⋊C4×Dic71C2211yescharacteristic
160C22⋊C4×Dic71C2211yescharacteristic
161C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
162C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
163C4×C22⋊Dic71C2211yescharacteristic
164#17985846C2211yescharacteristic, complemented
165#17985846C2211yescharacteristic, complemented
166#17985846C2211yescharacteristic, complemented
167#17985846C2211yescharacteristic, complemented
168C2×C71⋊#95C2211yescharacteristic
169C2×C71⋊#95C2211yescharacteristic
170#95×D71C2211yescharacteristic, complemented
171#95×D71C2211yescharacteristic, complemented
172C2×#124×C71C2211yescharacteristic, complemented
173C2×C22⋊Q8×C71C2211yescharacteristic
174C2×#120×C71C2211yescharacteristic
175C22×C22⋊C4×C71C2211yescharacteristic
176#397×C71C2211yescharacteristic, complemented
177#394×C71C2211yescharacteristic, complemented
178#394×C71C2211yescharacteristic, complemented
179#393×C71C2211yescharacteristic, complemented
180#390×C71C2211yescharacteristic, complemented
181#388×C71C2211yescharacteristic, complemented
182#388×C71C2211yescharacteristic, complemented
183#386×C71C2211yescharacteristic
184#386×C71C2211yescharacteristic
185#379×C71C2211yescharacteristic
186C4×C22⋊C4×C71C2211yescharacteristic
187C24×D71C2311yescharacteristic
188C22×C22⋊D71—24no—
189C22×C22⋊D71—42no—
190C22×C22⋊D71—42no—
191C22×C22⋊D71C2311yescharacteristic
192C22×C22⋊D71C2311yescharacteristic
193C22×C22⋊D71C2311yescharacteristic
194C22×C22⋊D71C2311yescharacteristic
195C22×C22⋊D71C2311yescharacteristic
196C22×C22⋊D71C2311yescharacteristic
197C23×Dic71C2311yescharacteristic
198C23×Dic71C2311yescharacteristic
199C23×Dic71C2311yescharacteristic
200C23×Dic71C2311yescharacteristic
201C22×C4×D71—24no—
202C22×C4×D71—42no—
203C22×C4×D71—42no—
204C22×C4×D71C2311yescharacteristic
205C22×C4×D71C2311yescharacteristic
206C22×C4×D71C2311yescharacteristic
207C22×C4×D71C2311yescharacteristic
208C22×C4×D71C2311yescharacteristic
209C22×C4×D71C2311yescharacteristic
210C22×C4×D71C2311yescharacteristic
211C22×C4×D71C2311yescharacteristic
212#14556121—42no—
213#14556110—42no—
214#14556110—42no—
215#14556110—42no—
216#14556104—42no—
217#14556099—42no—
218#14556099—42no—
219#14556096—24no—
220D4×Dic71—24no—
221(C22⋊D71)⋊C4—42no—
222(C22⋊D71)⋊C4—42no—
223C2×C4⋊Dic71C2311yescharacteristic
224C2×C4⋊Dic71C2311yescharacteristic
225C2×C4⋊Dic71C2311yescharacteristic
226C2×C4⋊Dic71C2311yescharacteristic
227C2×C4⋊Dic71C2311yescharacteristic
228C2×C4⋊Dic71C2311yescharacteristic
229C2×C4⋊Dic71C2311yescharacteristic
230C2×C4⋊Dic71C2311yescharacteristic
231C2×C4⋊Dic71C2311yescharacteristic
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—24no—
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×(C2×D71)⋊C4—42no—
265C2×(C2×D71)⋊C4C2311yescharacteristic
266C2×(C2×D71)⋊C4C2311yescharacteristic
267C2×(C2×D71)⋊C4C2311yescharacteristic
268C2×(C2×D71)⋊C4C2311yescharacteristic
269C2×(C2×D71)⋊C4C2311yescharacteristic
270C2×(C2×D71)⋊C4C2311yescharacteristic
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
279C22⋊C4×D71—24no—
280C22⋊C4×D71—24no—
281C2×C4×Dic71C2311yescharacteristic
282C2×C4×Dic71C2311yescharacteristic
283C2×C4×Dic71C2311yescharacteristic
284C2×C4×Dic71C2311yescharacteristic
285C2×C4×Dic71C2311yescharacteristic
286C2×C4×Dic71C2311yescharacteristic
287C2×C4×Dic71C2311yescharacteristic
288C2×C4×Dic71C2311yescharacteristic
289C2×C4×Dic71C2311yescharacteristic
290C42×D71—42no—
291C42×D71—42no—
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
328C71⋊#95C2311yescharacteristic
329C71⋊#95C2311yescharacteristic
330C25×C71C2311yescharacteristic
331C22×Q8×C71C2311yescharacteristic
332C22×D4×C71C2311yescharacteristic
333C22×D4×C71C2311yescharacteristic
334C22×D4×C71C2311yescharacteristic
335C23×C4×C71C2311yescharacteristic
336C23×C4×C71C2311yescharacteristic
337#124×C71—42no—
338C22⋊Q8×C71—24no—
339#120×C71—24no—
340C2×C4⋊C4×C71C2311yescharacteristic
341C2×C4⋊C4×C71C2311yescharacteristic
342C2×C4⋊C4×C71C2311yescharacteristic
343C2×C22⋊C4×C71—42no—
344C2×C22⋊C4×C71C2311yescharacteristic
345C2×C22⋊C4×C71C2311yescharacteristic
346C2×C22⋊C4×C71C2311yescharacteristic
347C2×C22⋊C4×C71C2311yescharacteristic
348C2×C22⋊C4×C71C2311yescharacteristic
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×C42×C71C2311yescharacteristic
362C2×C42×C71C2311yescharacteristic
363#95×C71C2311yescharacteristic
364#95×C71C2311yescharacteristic
365#95×C71C2311yescharacteristic
366#95×C71C2311yescharacteristic
367#95×C71C2311yescharacteristic
368#95×C71C2311yescharacteristic
369C23×D71—22no—
370C23×D71—22no—
371C23×D71—22no—
372C23×D71—22no—
373C23×D71—41no—
374C23×D71—41no—
375C23×D71#4114yes—
376C23×D71C2411yescharacteristic
377C23×D71C2411yescharacteristic
378C2×C22⋊D71—22no—
379C2×C22⋊D71—22no—
380C2×C22⋊D71—22no—
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—22no—
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—416no—
397C22×Dic71—22no—
398C22×Dic71—22no—
399C22×Dic71—22no—
400C22×Dic71—41no—
401C22×Dic71—41no—
402C22×Dic71—41no—
403C22×Dic71—41no—
404C22×Dic71—41no—
405C22×Dic71—41no—
406C22×Dic71—41no—
407C22×Dic71—41no—
408C22×Dic71#4114yes—
409C22×Dic71C2411yescharacteristic
410C22×Dic71C2411yescharacteristic
411C22×Dic71C2411yescharacteristic
412C22×Dic71C2411yescharacteristic
413C22×Dic71C2411yescharacteristic
414C22×Dic71C2411yescharacteristic
415C22×Dic71C2411yescharacteristic
416C22×Dic71C2411yescharacteristic
417C22×Dic71C2411yescharacteristic
418C22×Dic71C2411yescharacteristic
419C22×Dic71C2411yescharacteristic
420C22×Dic71C2411yescharacteristic
421C22×Dic71C2411yescharacteristic
422C22×Dic71C2411yescharacteristic
423C2×C4×D71—22no—
424C2×C4×D71—22no—
425C2×C4×D71—22no—
426C2×C4×D71—22no—
427C2×C4×D71—22no—
428C2×C4×D71—22no—
429C2×C4×D71—22no—
430C2×C4×D71—22no—
431C2×C4×D71—22no—
432C2×C4×D71—22no—
433C2×C4×D71—22no—
434C2×C4×D71—22no—
435C2×C4×D71—22no—
436C2×C4×D71—22no—
437C2×C4×D71—22no—
438C2×C4×D71—22no—
439C2×C4×D71—416no—
440C2×C4×D71—41no—
441C2×C4×D71—41no—
442C2×C4×D71—41no—
443C2×C4×D71—41no—
444C2×C4×D71—41no—
445C2×C4×D71—41no—
446C2×C4×D71—41no—
447C2×C4×D71—41no—
448C4⋊Dic71—22no—
449C4⋊Dic71—41no—
450C4⋊Dic71—41no—
451C4⋊Dic71—41no—
452C4⋊Dic71—41no—
453C4⋊Dic71—41no—
454C4⋊Dic71—41no—
455C4⋊Dic71—41no—
456C4⋊Dic71—41no—
457Dic71⋊C4—22no—
458Dic71⋊C4—41no—
459Dic71⋊C4—41no—
460Dic71⋊C4—41no—
461Dic71⋊C4—41no—
462Dic71⋊C4—41no—
463Dic71⋊C4—41no—
464Dic71⋊C4—41no—
465Dic71⋊C4—41no—
466Dic71⋊C4—41no—
467C22⋊Dic71—22no—
468C22⋊Dic71—22no—
469C22⋊Dic71—22no—
470C22⋊Dic71—22no—
471C22⋊Dic71—22no—
472C22⋊Dic71—22no—
473C22⋊Dic71—22no—
474C22⋊Dic71—22no—
475C22⋊Dic71—22no—
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—
488(C2×D71)⋊C4—22no—
489(C2×D71)⋊C4—22no—
490(C2×D71)⋊C4—22no—
491(C2×D71)⋊C4—22no—
492(C2×D71)⋊C4—22no—
493(C2×D71)⋊C4—22no—
494(C2×D71)⋊C4—22no—
495(C2×D71)⋊C4—22no—
496(C2×D71)⋊C4—22no—
497(C2×D71)⋊C4—22no—
498(C2×D71)⋊C4—41no—
499(C2×D71)⋊C4—41no—
500(C2×D71)⋊C4—41no—
501(C2×D71)⋊C4—41no—
502C4×Dic71—22no—
503C4×Dic71—22no—
504C4×Dic71—41no—
505C4×Dic71—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
522C2×Q8×C71—22no—
523C2×Q8×C71—41no—
524C2×Q8×C71—41no—
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—
534C22×C4×C71—22no—
535C22×C4×C71—22no—
536C22×C4×C71—22no—
537C22×C4×C71—41no—
538C22×C4×C71—41no—
539C22×C4×C71—41no—
540C22×C4×C71C2411yescharacteristic
541C22×C4×C71C2411yescharacteristic
542C22×C4×C71C2411yescharacteristic
543C22×C4×C71C2411yescharacteristic
544C22×C4×C71C2411yescharacteristic
545C22×C4×C71C2411yescharacteristic
546C22×C4×C71C2411yescharacteristic
547C22×C4×C71C2411yescharacteristic
548C22×C4×C71C2411yescharacteristic
549C22×C4×C71C2411yescharacteristic
550C22×C4×C71C2411yescharacteristic
551C4⋊C4×C71—22no—
552C4⋊C4×C71—22no—
553C4⋊C4×C71—22no—
554C22⋊C4×C71—22no—
555C22⋊C4×C71—22no—
556C22⋊C4×C71—22no—
557C22⋊C4×C71—22no—
558C22⋊C4×C71—22no—
559C22⋊C4×C71—22no—
560C22⋊C4×C71—22no—
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#4114yes—
571C42×C71—22no—
572C42×C71—41no—
573C23×C71—21no—
574C23×C71—21no—
575C23×C71—21no—
576C23×C71—21no—
577C23×C71—21no—
578C23×C71—21no—
579C23×C71—21no—
580C23×C71—21no—
581C23×C71—21no—
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—44no—
599C23×C71—44no—
600C23×C71—44no—
601C23×C71—82no—
602C23×C71—82no—
603C23×C71—82no—
604C23×C71—82no—
605C23×C71C2×#4112yes—
606C23×C71C2×#4112yes—
607C23×C71C2×#4112yes—
608C23×C71C2511yescharacteristic
609C22×D71—21no—
610C22×D71—21no—
611C22×D71—21no—
612C22×D71—21no—
613C22×D71—28no—
614C22×D71—21no—
615C22×D71—21no—
616C22×D71—21no—
617C22×D71—21no—
618C22×D71—21no—
619C22×D71—21no—
620C22×D71—28no—
621C22×D71—44no—
622C22×D71—44no—
623C22×D71—44no—
624C22×D71—44no—
625C22×D71—44no—
626C22×D71C2×#4112yes—
627C22×D71C2×#4112yes—
628C22×D71H(5,𝔽2)12yes—
629C22×D71H(5,𝔽2)12yes—
630Q8×C71—82no—
631D4×C71—44no—
632D4×C71—82no—
633D4×C71—82no—
634C2×C4×C71—21no—
635C2×C4×C71—21no—
636C2×C4×C71—21no—
637C2×C4×C71—21no—
638C2×C4×C71—21no—
639C2×C4×C71—21no—
640C2×C4×C71—21no—
641C2×C4×C71—21no—
642C2×C4×C71—21no—
643C2×C4×C71—21no—
644C2×C4×C71—21no—
645C2×C4×C71—21no—
646C2×C4×C71—21no—
647C2×C4×C71—21no—
648C2×C4×C71—21no—
649C2×C4×C71—21no—
650C2×C4×C71—21no—
651C2×C4×C71—21no—
652C2×C4×C71—21no—
653C2×C4×C71—21no—
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—44no—
665C2×C4×C71—82no—
666C2×C4×C71C2×#4112yes—
667C2×C4×C71C2×#4112yes—
668C2×C4×C71H(5,𝔽2)12yes—
669C22⋊D71—44no—
670C22⋊D71—44no—
671C22⋊D71—44no—
672C22⋊D71—44no—
673C22⋊D71—44no—
674C22⋊D71—44no—
675C2×Dic71—21no—
676C2×Dic71—21no—
677C2×Dic71—21no—
678C2×Dic71—21no—
679C2×Dic71—21no—
680C2×Dic71—21no—
681C2×Dic71—21no—
682C2×Dic71—21no—
683C2×Dic71—21no—
684C2×Dic71—21no—
685C2×Dic71—21no—
686C2×Dic71—21no—
687C2×Dic71—21no—
688C2×Dic71—21no—
689C2×Dic71—21no—
690C2×Dic71—21no—
691C2×Dic71—21no—
692C2×Dic71—21no—
693C2×Dic71—21no—
694C2×Dic71—21no—
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—44no—
716C2×Dic71—44no—
717C2×Dic71—82no—
718C2×Dic71—82no—
719C2×Dic71C2×#4112yes—
720C2×Dic71C2×#4112yes—
721C4×D71—28no—
722C4×D71—44no—
723C4×D71—44no—
724C4×D71—44no—
725C4×D71—44no—
726C4×D71—44no—
727C4×D71—44no—
728C4×D71—44no—
729C22×C71—22no—
730C22×C71—22no—
731C22×C71—22no—
732C22×C71—22no—
733C22×C71—22no—
734C22×C71—22no—
735C22×C71—41no—
736C22×C71—41no—
737C22×C71—41no—
738C22×C71—41no—
739C22×C71—41no—
740C22×C71—41no—
741C22×C71—41no—
742C22×C71—41no—
743C22×C71—41no—
744C22×C71—41no—
745C22×C71—41no—
746C22×C71—41no—
747C22×C71—41no—
748C22×C71—41no—
749C22×C71—41no—
750C22×C71—41no—
751C22×C71—41no—
752C22×C71—41no—
753C22×C71—41no—
754C22×C71—41no—
755C22×C71—41no—
756C22×C71—88no—
757C22×C71#52914yes—
758C22×C71C22×#4111yescharacteristic
759C22×C71C22×#4111yescharacteristic
760C22×C71C22×#4111yescharacteristic
761C22×C71C2×H(5,𝔽2)11yescharacteristic
762C22×C71C2×H(5,𝔽2)11yescharacteristic
763C22×C71C2×H(5,𝔽2)11yescharacteristic
764C22×C71#58511yescharacteristic
765C2×D71—22no—
766C2×D71—22no—
767C2×D71—22no—
768C2×D71—22no—
769C2×D71—22no—
770C2×D71—22no—
771C2×D71—22no—
772C2×D71—22no—
773C2×D71—22no—
774C2×D71—416no—
775C2×D71—41no—
776C2×D71—41no—
777C2×D71—41no—
778C2×D71—41no—
779C2×D71#53814yes—
780C4×C71—22no—
781C4×C71—22no—
782C4×C71—22no—
783C4×C71—41no—
784C4×C71—41no—
785C4×C71—41no—
786C4×C71—41no—
787C4×C71—41no—
788C4×C71—41no—
789C4×C71—41no—
790C4×C71—41no—
791Dic71—22no—
792Dic71—22no—
793Dic71—41no—
794Dic71—41no—
795Dic71—41no—
796Dic71—41no—
797Dic71—41no—
798Dic71—41no—
799Dic71—41no—
800Dic71—41no—
801Dic71—41no—
802Dic71—41no—
803Dic71—41no—
804Dic71—41no—
805#34998—711nomaximal, Sylow
806C2×C71—24no—
807C2×C71—81no—
808C2×C71—81no—
809C2×C71—81no—
810C2×C71C2×#52911yescharacteristic
811C2×C71C2×#53811yescharacteristic
812C2×C71#345911yescharacteristic
813C2×C71#349011yescharacteristic
814C2×C71#349411yescharacteristic
815C2×C71#351311yescharacteristic
816C2×C71#351911yescharacteristic
817D71—24no—
818D71—42no—
819#2854—711no—
820#2853—711no—
821#2852—711no—
822#2850—711no—
823#2653—711no—
824#2649—711no—
825#2648—711no—
826#2648—711no—
827#2518—711no—
828#2518—711no—
829#2510—711no—
830#2510—711no—
831#2505—711no—
832#2488—711no—
833#2480—711no—
834#2472D7111yescharacteristic, complemented
835#2467—711no—
836#2459—711no—
837#2444—711no—
838#2437—711no—
839#2425—711no—
840#2412—711no—
841#2410—711no—
842#2405—711no—
843#2329—711no—
844#2321—711no—
845#2318—711no—
846#2312—711no—
847C4×#120—711no—
848C2×#386—711no—
849C2×C4×C22⋊C4—711no—
850C71#3499811yescharacteristic, complemented, Sylow
851C23×D4—711no—
852C24×C4—711no—
853C2×#126—711no—
854C2×#124C2×D7111yescharacteristic, complemented
855C2×#123—711no—
856C2×#123—711no—
857C2×#123—711no—
858C2×C22⋊Q8—711no—
859C2×C22⋊Q8C2×D7111yescharacteristic
860C2×#121—711no—
861C2×#121—711no—
862C2×#120—711no—
863C2×#120C2×D7111yescharacteristic
864C2×C4×D4—711no—
865C2×C4×D4—711no—
866C2×C4×D4—711no—
867C22×C22⋊C4—711no—
868C22×C22⋊C4—711no—
869C22×C22⋊C4—711no—
870C22×C22⋊C4—711no—
871C22×C22⋊C4C2×D7111yescharacteristic
872C22×C42—711no—
873C22×C42—711no—
874#401—711no—
875#400—711no—
876#400—711no—
877#400—711no—
878#400—711no—
879#399—711no—
880#398—711no—
881#397—711no—
882#397—711no—
883#397—711no—
884#397—711no—
885#397—711no—
886#397—711no—
887#397—711no—
888#397C2×D7111yescharacteristic, complemented
889#396—711no—
890#396—711no—
891#396—711no—
892#394—711no—
893#394—711no—
894#394—711no—
895#394—711no—
896#394—711no—
897#394—711no—
898#394—711no—
899#394—711no—
900#394C2×D7111yescharacteristic, complemented
901#394C2×D7111yescharacteristic, complemented
902#393—711no—
903#393C2×D7111yescharacteristic, complemented
904#392—711no—
905#392—711no—
906#391—711no—
907#391—711no—
908#390—711no—
909#390—711no—
910#390C2×D7111yescharacteristic, complemented
911#389—711no—
912#389—711no—
913#389—711no—
914#388—711no—
915#388—711no—
916#388—711no—
917#388—711no—
918#388—711no—
919#388—711no—
920#388—711no—
921#388—711no—
922#388—711no—
923#388—711no—
924#388—711no—
925#388—711no—
926#388—711no—
927#388—711no—
928#388—711no—
929#388—711no—
930#388—711no—
931#388—711no—
932#388—711no—
933#388C2×D7111yescharacteristic, complemented
934#388C2×D7111yescharacteristic, complemented
935#387—711no—
936#387—711no—
937#387—711no—
938#387—711no—
939#387—711no—
940#387—711no—
941#387—711no—
942#387—711no—
943#387—711no—
944#386—711no—
945#386—711no—
946#386—711no—
947#386—711no—
948#386—711no—
949#386—711no—
950#386—711no—
951#386—711no—
952#386—711no—
953#386—711no—
954#386—711no—
955#386—711no—
956#386—711no—
957#386—711no—
958#386—711no—
959#386—711no—
960#386—711no—
961#386—711no—
962#386—711no—
963#386C2×D7111yescharacteristic
964#386C2×D7111yescharacteristic
965#385—711no—
966#385—711no—
967#385—711no—
968#385—711no—
969#385—711no—
970#385—711no—
971#385—711no—
972#385—711no—
973#385—711no—
974#385—711no—
975#385—711no—
976#383—711no—
977#383—711no—
978#382—711no—
979#382—711no—
980#381—711no—
981#381—711no—
982#380—711no—
983#380—711no—
984#380—711no—
985#380—711no—
986#380—711no—
987#379—711no—
988#379—711no—
989#379—711no—
990#379C2×D7111yescharacteristic
991C4×C22⋊C4—711no—
992C4×C22⋊C4—711no—
993C4×C22⋊C4—711no—
994C4×C22⋊C4—711no—
995C4×C22⋊C4—711no—
996C4×C22⋊C4—711no—
997C4×C22⋊C4—711no—
998C4×C22⋊C4—711no—
999C4×C22⋊C4—711no—
1000C4×C22⋊C4—711no—
1001C4×C22⋊C4C2×D7111yescharacteristic
1002C2×#95—711no—
1003C2×#95—711no—
1004C2×#95—711no—
1005C2×#95—711no—
1006C25—711no—
1007C25C22×D7111yescharacteristic
1008C22×Q8C22×D7111yescharacteristic
1009C22×D4—2842no—
1010C22×D4—2842no—
1011C22×D4—711no—
1012C22×D4—711no—
1013C22×D4—711no—
1014C22×D4—711no—
1015C22×D4—711no—
1016C22×D4—711no—
1017C22×D4—1424no—
1018C22×D4C22×D7111yescharacteristic
1019C22×D4C22×D7111yescharacteristic
1020C22×D4C22×D7111yescharacteristic
1021C23×C4—2842no—
1022C23×C4—2842no—
1023C23×C4—711no—
1024C23×C4—711no—
1025C23×C4—711no—
1026C23×C4—711no—
1027C23×C4—711no—
1028C23×C4—711no—
1029C23×C4—711no—
1030C23×C4—711no—
1031C23×C4—711no—
1032C23×C4—711no—
1033C23×C4—711no—
1034C23×C4—711no—
1035C23×C4—1424no—
1036C23×C4C22×D7111yescharacteristic
1037C23×C4C22×D7111yescharacteristic
1038#126—2842no—
1039#124—42no—
1040#123—2842no—
1041#123—2842no—
1042#123—2842no—
1043C22⋊Q8—24no—
1044C22⋊Q8—2842no—
1045#121—2842no—
1046#121—2842no—
1047#120—24no—
1048#120—1424no—
1049C4×D4—2842no—
1050C4×D4—2842no—
1051C4×D4—1424no—
1052C2×C4⋊C4—711no—
1053C2×C4⋊C4—711no—
1054C2×C4⋊C4—711no—
1055C2×C4⋊C4—711no—
1056C2×C4⋊C4—711no—
1057C2×C4⋊C4—711no—
1058C2×C4⋊C4—711no—
1059C2×C4⋊C4—711no—
1060C2×C4⋊C4—711no—
1061C2×C4⋊C4—711no—
1062C2×C4⋊C4—711no—
1063C2×C4⋊C4—711no—
1064C2×C4⋊C4—711no—
1065C2×C4⋊C4—711no—
1066C2×C4⋊C4—711no—
1067C2×C4⋊C4—711no—
1068C2×C4⋊C4—711no—
1069C2×C4⋊C4—711no—
1070C2×C4⋊C4—711no—
1071C2×C4⋊C4C22×D7111yescharacteristic
1072C2×C4⋊C4C22×D7111yescharacteristic
1073C2×C4⋊C4C22×D7111yescharacteristic
1074C2×C22⋊C4—42no—
1075C2×C22⋊C4—2842no—
1076C2×C22⋊C4—711no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—711no—
1082C2×C22⋊C4—711no—
1083C2×C22⋊C4—711no—
1084C2×C22⋊C4—711no—
1085C2×C22⋊C4—711no—
1086C2×C22⋊C4—711no—
1087C2×C22⋊C4—711no—
1088C2×C22⋊C4—711no—
1089C2×C22⋊C4—711no—
1090C2×C22⋊C4—711no—
1091C2×C22⋊C4—711no—
1092C2×C22⋊C4—711no—
1093C2×C22⋊C4—711no—
1094C2×C22⋊C4—711no—
1095C2×C22⋊C4—711no—
1096C2×C22⋊C4—711no—
1097C2×C22⋊C4—711no—
1098C2×C22⋊C4—711no—
1099C2×C22⋊C4—711no—
1100C2×C22⋊C4—711no—
1101C2×C22⋊C4—711no—
1102C2×C22⋊C4—711no—
1103C2×C22⋊C4—711no—
1104C2×C22⋊C4—711no—
1105C2×C22⋊C4—711no—
1106C2×C22⋊C4—711no—
1107C2×C22⋊C4—711no—
1108C2×C22⋊C4—711no—
1109C2×C22⋊C4—711no—
1110C2×C22⋊C4—711no—
1111C2×C22⋊C4—1424no—
1112C2×C22⋊C4—1424no—
1113C2×C22⋊C4—1424no—
1114C2×C22⋊C4C22×D7111yescharacteristic
1115C2×C22⋊C4C22×D7111yescharacteristic
1116C2×C22⋊C4C22×D7111yescharacteristic
1117C2×C22⋊C4C22×D7111yescharacteristic
1118C2×C22⋊C4C22×D7111yescharacteristic
1119C2×C22⋊C4C22×D7111yescharacteristic
1120C2×C22⋊C4C22×D7111yescharacteristic
1121C2×C22⋊C4C22×D7111yescharacteristic
1122C2×C22⋊C4C22×D7111yescharacteristic
1123C2×C22⋊C4C22×D7111yescharacteristic
1124C2×C22⋊C4C22×D7111yescharacteristic
1125C2×C22⋊C4C22×D7111yescharacteristic
1126C2×C22⋊C4C22×D7111yescharacteristic
1127C2×C22⋊C4C22×D7111yescharacteristic
1128C2×C22⋊C4C22×D7111yescharacteristic
1129C2×C22⋊C4C22×D7111yescharacteristic
1130C2×C22⋊C4C22×D7111yescharacteristic
1131C2×C42—2842no—
1132C2×C42—2842no—
1133C2×C42—711no—
1134C2×C42—711no—
1135C2×C42—711no—
1136C2×C42—711no—
1137C2×C42—711no—
1138C2×C42—711no—
1139C2×C42—711no—
1140C2×C42—711no—
1141C2×C42—711no—
1142C2×C42C22×D7111yescharacteristic
1143C2×C42C22×D7111yescharacteristic
1144#95—711no—
1145#95—711no—
1146#95—711no—
1147#95—711no—
1148#95—711no—
1149#95—711no—
1150#95—711no—
1151#95—711no—
1152#95—711no—
1153#95—711no—
1154#95—711no—
1155#95—711no—
1156#95—711no—
1157#95—711no—
1158#95—711no—
1159#95—711no—
1160#95—711no—
1161#95—711no—
1162#95—711no—
1163#95—711no—
1164#95—711no—
1165#95—711no—
1166#95—711no—
1167#95—711no—
1168#95—711no—
1169#95—711no—
1170#95—711no—
1171#95—711no—
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#95C22×D7111yescharacteristic
1183#95C22×D7111yescharacteristic
1184#95C22×D7111yescharacteristic
1185#95C22×D7111yescharacteristic
1186#95C22×D7111yescharacteristic
1187#95C22×D7111yescharacteristic
1188C24—22no—
1189C24—22no—
1190C24—22no—
1191C24—41no—
1192C24—41no—
1193C24—41no—
1194C24—41no—
1195C24—2841no—
1196C24—2841no—
1197C24—714no—
1198C24—711no—
1199C24—711no—
1200C24—1422no—
1201C24—1422no—
1202C24—1422no—
1203C24—1422no—
1204C24C23×D7111yescharacteristic
1205C24C23×D7111yescharacteristic
1206C24C23×D7111yescharacteristic
1207C24C23×D7111yescharacteristic
1208C2×Q8—22no—
1209C2×Q8—41no—
1210C2×Q8—41no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—28416no—
1221C2×D4—2841no—
1222C2×D4—2841no—
1223C2×D4—2841no—
1224C2×D4—2841no—
1225C2×D4—2841no—
1226C2×D4—2841no—
1227C2×D4—1422no—
1228C2×D4—1422no—
1229C2×D4—1422no—
1230C2×D4—1422no—
1231C2×D4—1422no—
1232C2×D4—1422no—
1233C2×D4—1422no—
1234C2×D4—1422no—
1235C2×D4—1422no—
1236C2×D4—1422no—
1237C2×D4—1422no—
1238C2×D4—1422no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—41no—
1243C22×C4—41no—
1244C22×C4—41no—
1245C22×C4—2841no—
1246C22×C4—2841no—
1247C22×C4—2841no—
1248C22×C4—2841no—
1249C22×C4—2841no—
1250C22×C4—2841no—
1251C22×C4—2841no—
1252C22×C4—2841no—
1253C22×C4—28416no—
1254C22×C4—2841no—
1255C22×C4—2841no—
1256C22×C4—2841no—
1257C22×C4—2841no—
1258C22×C4—2841no—
1259C22×C4—2841no—
1260C22×C4—2841no—
1261C22×C4—2841no—
1262C22×C4—714no—
1263C22×C4—711no—
1264C22×C4—711no—
1265C22×C4—711no—
1266C22×C4—711no—
1267C22×C4—711no—
1268C22×C4—711no—
1269C22×C4—711no—
1270C22×C4—711no—
1271C22×C4—711no—
1272C22×C4—711no—
1273C22×C4—711no—
1274C22×C4—711no—
1275C22×C4—711no—
1276C22×C4—711no—
1277C22×C4—1422no—
1278C22×C4—1422no—
1279C22×C4—1422no—
1280C22×C4—1422no—
1281C22×C4—1422no—
1282C22×C4—1422no—
1283C22×C4—1422no—
1284C22×C4—1422no—
1285C22×C4—1422no—
1286C22×C4—1422no—
1287C22×C4—1422no—
1288C22×C4—1422no—
1289C22×C4—1422no—
1290C22×C4—1422no—
1291C22×C4—1422no—
1292C22×C4—1422no—
1293C22×C4—1422no—
1294C22×C4—1422no—
1295C22×C4—1422no—
1296C22×C4C23×D7111yescharacteristic
1297C22×C4C23×D7111yescharacteristic
1298C22×C4C23×D7111yescharacteristic
1299C22×C4C23×D7111yescharacteristic
1300C22×C4C23×D7111yescharacteristic
1301C22×C4C23×D7111yescharacteristic
1302C22×C4C23×D7111yescharacteristic
1303C22×C4C23×D7111yescharacteristic
1304C22×C4C23×D7111yescharacteristic
1305C22×C4C23×D7111yescharacteristic
1306C22×C4C23×D7111yescharacteristic
1307C4⋊C4—22no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—2841no—
1311C4⋊C4—2841no—
1312C4⋊C4—2841no—
1313C4⋊C4—2841no—
1314C4⋊C4—2841no—
1315C4⋊C4—2841no—
1316C4⋊C4—2841no—
1317C4⋊C4—2841no—
1318C4⋊C4—2841no—
1319C4⋊C4—2841no—
1320C4⋊C4—2841no—
1321C4⋊C4—2841no—
1322C4⋊C4—2841no—
1323C4⋊C4—2841no—
1324C4⋊C4—2841no—
1325C4⋊C4—2841no—
1326C4⋊C4—2841no—
1327C4⋊C4—1422no—
1328C4⋊C4—1422no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—2841no—
1346C22⋊C4—2841no—
1347C22⋊C4—2841no—
1348C22⋊C4—2841no—
1349C22⋊C4—2841no—
1350C22⋊C4—2841no—
1351C22⋊C4—2841no—
1352C22⋊C4—2841no—
1353C22⋊C4—2841no—
1354C22⋊C4—2841no—
1355C22⋊C4—2841no—
1356C22⋊C4—2841no—
1357C22⋊C4—2841no—
1358C22⋊C4—2841no—
1359C22⋊C4—2841no—
1360C22⋊C4—2841no—
1361C22⋊C4—1422no—
1362C22⋊C4—1422no—
1363C22⋊C4—1422no—
1364C22⋊C4—1422no—
1365C22⋊C4—1422no—
1366C22⋊C4—1422no—
1367C22⋊C4—1422no—
1368C22⋊C4—1422no—
1369C22⋊C4—1422no—
1370C22⋊C4—1422no—
1371C22⋊C4—1422no—
1372C22⋊C4—1422no—
1373C22⋊C4—1422no—
1374C22⋊C4—1422no—
1375C22⋊C4—1422no—
1376C22⋊C4—1422no—
1377C22⋊C4—1422no—
1378C22⋊C4—1422no—
1379C22⋊C4—1422no—
1380C22⋊C4#1176586414yes—
1381C42—22no—
1382C42—41no—
1383C42—2841no—
1384C42—2841no—
1385C42—2841no—
1386C42—2841no—
1387C42—2841no—
1388C42—2841no—
1389C42—2841no—
1390C42—1422no—
1391C42—1422no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—44no—
1418C23—44no—
1419C23—44no—
1420C23—82no—
1421C23—82no—
1422C23—82no—
1423C23—82no—
1424C23—2844no—
1425C23—2844no—
1426C23—2844no—
1427C23—2844no—
1428C23—2844no—
1429C23—712no—
1430C23—712no—
1431C23—712no—
1432C23—712no—
1433C23—1428no—
1434C23—1421no—
1435C23—1421no—
1436C23—1421no—
1437C23—1421no—
1438C23—1421no—
1439C23—1421no—
1440C23—1428no—
1441C23—1421no—
1442C23—1421no—
1443C23—1421no—
1444C23—1421no—
1445C23#41×D7112yes—
1446C23#41×D7112yes—
1447C23C2×#1176586412yes—
1448C23C24×D7111yescharacteristic
1449Q8—82no—
1450D4—44no—
1451D4—82no—
1452D4—82no—
1453D4—2844no—
1454D4—2844no—
1455D4—2844no—
1456D4—2844no—
1457D4—2844no—
1458D4—2844no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—44no—
1490C2×C4—82no—
1491C2×C4—2844no—
1492C2×C4—2844no—
1493C2×C4—2844no—
1494C2×C4—2844no—
1495C2×C4—2844no—
1496C2×C4—2844no—
1497C2×C4—2844no—
1498C2×C4—2844no—
1499C2×C4—2844no—
1500C2×C4—5682no—
1501C2×C4—5682no—
1502C2×C4—712no—
1503C2×C4—712no—
1504C2×C4—1428no—
1505C2×C4—1421no—
1506C2×C4—1421no—
1507C2×C4—1421no—
1508C2×C4—1421no—
1509C2×C4—1421no—
1510C2×C4—1421no—
1511C2×C4—1421no—
1512C2×C4—1421no—
1513C2×C4—1421no—
1514C2×C4—1421no—
1515C2×C4—1421no—
1516C2×C4—1421no—
1517C2×C4—1421no—
1518C2×C4—1421no—
1519C2×C4—1421no—
1520C2×C4—1421no—
1521C2×C4—1421no—
1522C2×C4—1421no—
1523C2×C4—1421no—
1524C2×C4—1421no—
1525C2×C4—1421no—
1526C2×C4—1421no—
1527C2×C4—1421no—
1528C2×C4—1421no—
1529C2×C4—1421no—
1530C2×C4—1421no—
1531C2×C4—1421no—
1532C2×C4—1421no—
1533C2×C4—1421no—
1534C2×C4—1421no—
1535C2×C4—1421no—
1536C2×C4—1421no—
1537C2×C4—1421no—
1538C2×C4—1421no—
1539C2×C4—1421no—
1540C2×C4—1421no—
1541C2×C4—1421no—
1542C2×C4—1421no—
1543C2×C4—1421no—
1544C2×C4—1421no—
1545C2×C4C2×#1176586412yes—
1546C2×C4C2×#1176586412yes—
1547C2×C4#1455617312yes—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—22no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—88no—
1576C22—28416no—
1577C22—2841no—
1578C22—2841no—
1579C22—2841no—
1580C22—2841no—
1581C22—714no—
1582C22—1422no—
1583C22—1422no—
1584C22—1422no—
1585C22—1422no—
1586C22—1422no—
1587C22—1422no—
1588C22—1422no—
1589C22—1422no—
1590C22—1422no—
1591C22#1798652814yes—
1592C22C2×#41×D7111yescharacteristic
1593C22C2×#41×D7111yescharacteristic
1594C22C22×#1176586411yescharacteristic
1595C22H(5,𝔽2)×D7111yescharacteristic
1596C22H(5,𝔽2)×D7111yescharacteristic
1597C22C2×#1455617311yescharacteristic
1598C22#1798683511yescharacteristic
1599C4—22no—
1600C4—22no—
1601C4—22no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—41no—
1610C4—2841no—
1611C4—2841no—
1612C4—2841no—
1613C4—2841no—
1614C4—2841no—
1615C4—2841no—
1616C4—2841no—
1617C4—2841no—
1618C4—2841no—
1619C4—2841no—
1620C4—2841no—
1621C4—2841no—
1622C4—1422no—
1623C4—1422no—
1624C2—24no—
1625C2—81no—
1626C2—81no—
1627C2—81no—
1628C2—2842no—
1629C2—1424no—
1630C2C2×#1798652811yescharacteristic
1631C2#538×D7111yescharacteristic
1632C2#2260174711yescharacteristic
1633C2#2260202211yescharacteristic
1634C2#2260206611yescharacteristic
1635C2#2260226911yescharacteristic
1636C2#2260236311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2472C2
prime radical#22591710C2
hypercenter#2472D71
hypocenterC71#34998
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2472

Complements

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

NH ≅ G/Ntype
1. #22596670C2semidirect
2. #22596660C2semidirect
3. #22596654C2semidirect
4. #22596636C2semidirect
5. #22594400C2semidirect
6. #22594340C2semidirect
7. #22594325C2semidirect
8. #22594325C2semidirect
9. #22593002C2semidirect
10. #22592995C2semidirect
11. #22592902C2semidirect
12. #22592893C2semidirect
13. #22592835C2semidirect
14. #22592659C2semidirect
15. #22592580C2semidirect
16. #22592397C2semidirect
17. #22592273C2semidirect
18. #22592083C2semidirect
19. #22592003C2semidirect
20. #22591892C2semidirect
21. #22591735C2semidirect
23. #22591665C2semidirect
24. #22591075C2semidirect
25. #22591001C2semidirect
26. #22590966C2semidirect
27. #22590936C2semidirect
28. #22590845C2semidirect
29. C2×#17985875C2semidirect
30. C4×C22⋊C4×D71C2semidirect
31. C71×#2472C2semidirect
34. C2×#14556121C22semidirect
37. C2×#14556110C22semidirect
38. C2×#14556104C22semidirect
43. C2×(C22⋊D71)⋊C4C22semidirect
44. C2×(C22⋊D71)⋊C4C22semidirect
49. C2×C42×D71C22semidirect
50. C2×C42×D71C22semidirect
51. C71⋊#401C22semidirect
52. #17985941C22semidirect
53. #17985941C22semidirect
54. #17985941C22semidirect
55. #17985939C22semidirect
56. #17985934C22semidirect
57. #17985933C22semidirect
58. #17985928C22semidirect
59. #17985927C22semidirect
60. #17985927C22semidirect
61. #17985927C22semidirect
62. #17985926C22semidirect
63. #17985924C22semidirect
64. #17985924C22semidirect
65. #17985922C22semidirect
66. #17985921C22semidirect
67. #17985921C22semidirect
72. #17985915C22semidirect
75. #17985914C22semidirect
76. #17985910C22semidirect
79. #17985906C22semidirect
80. #17985906C22semidirect
81. #17985902C22semidirect
82. #17985902C22semidirect
83. #17985898C22semidirect
84. #17985898C22semidirect
85. #17985897C22semidirect
86. #17985893C22semidirect
87. #17985893C22semidirect
88. #17985893C22semidirect
89. #17985893C22semidirect
90. #17985893C22semidirect
91. #17985893C22semidirect
92. #17985892C22semidirect
93. #17985892C22semidirect
94. #17985892C22semidirect
95. #17985892C22semidirect
96. #17985892C22semidirect
97. #17985892C22semidirect
98. #17985887C22semidirect
99. #17985887C22semidirect
100. #17985887C22semidirect
101. #17985887C22semidirect
102. #17985887C22semidirect
103. #17985887C22semidirect
104. #17985887C22semidirect
105. #17985886C22semidirect
106. #17985885C22semidirect
107. #17985885C22semidirect
108. #17985885C22semidirect
109. #17985885C22semidirect
110. #17985884C22semidirect
111. #17985883C22semidirect
112. #17985883C22semidirect
113. #17985882C22semidirect
116. #17985879C22semidirect
117. #17985879C22semidirect
130. #17985875C22semidirect
131. #17985875C22semidirect
132. #17985875C22semidirect
136. #17985873C22semidirect
137. #17985873C22semidirect
138. #17985873C22semidirect
142. #17985870C22semidirect
143. #17985870C22semidirect
144. #17985866C22semidirect
145. #17985866C22semidirect
146. #17985865C22semidirect
147. #17985863C22semidirect
148. #17985861C22semidirect
149. #17985860C22semidirect
153. #17985857C22semidirect
154. #17985856C22semidirect
161. C4×(C2×D71)⋊C4C22semidirect
162. C4×(C2×D71)⋊C4C22semidirect
164. #17985846C22semidirect
165. #17985846C22semidirect
166. #17985846C22semidirect
167. #17985846C22semidirect
170. #95×D71C22semidirect
171. #95×D71C22semidirect
172. C2×#124×C71C22semidirect
176. #397×C71C22semidirect
177. #394×C71C22semidirect
178. #394×C71C22semidirect
179. #393×C71C22semidirect
180. #390×C71C22semidirect
181. #388×C71C22semidirect
182. #388×C71C22semidirect
834. #2472D71semidirect
850. C71#34998semidirect
854. C2×#124C2×D71semidirect
888. #397C2×D71semidirect
900. #394C2×D71semidirect
901. #394C2×D71semidirect
903. #393C2×D71semidirect
910. #390C2×D71semidirect
933. #388C2×D71semidirect
934. #388C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225966702
#225966602
#225966542
#225966362
#225944002
#225943402
#225943252
#225930022
#225929952
#225929022
#225928932
#225928352
#225926592
#225925802
#225923972
#225922732
#225920832
#225920032
#225918922
#225917352
#225917102
#225916652
#225910752
#225910012
#225909662
#225909362
#225908452
C2×#179858752
C4×C22⋊C4×D712
C71×#24722
#3499871