Finite Group Databasebeta

← #31964373

Subgroups — #31964373

Order 18176.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597307C211yesmaximal, characteristic, complemented
2#22597006C211yesmaximal, characteristic, complemented
3#22586813C211yesmaximal, characteristic, complemented
4#22586805C211yesmaximal, characteristic, complemented
5#22586800C211yesmaximal, characteristic, complemented
6#22586783C211yesmaximal, characteristic, complemented
7#22586779C211yesmaximal, characteristic, complemented
8#22586774C211yesmaximal, characteristic, complemented
9#22586761C211yesmaximal, characteristic, complemented
10#22586753C211yesmaximal, characteristic, complemented
11#22586748C211yesmaximal, characteristic, complemented
12#22586731C211yesmaximal, characteristic, complemented
13#22586727C211yesmaximal, characteristic, complemented
14#22586722C211yesmaximal, characteristic, complemented
15C71×#3475C211yesmaximal, characteristic
16#17986130—21no—
17#17986077—21no—
18#17986071—21no—
19#17986071—21no—
20#17986060—21no—
21#17986060—21no—
22#17986056C2211yescharacteristic
23#17986056C2211yescharacteristic, complemented
24#17986052C2211yescharacteristic
25#17986052C2211yescharacteristic
26#17986052C2211yescharacteristic, complemented
27#17986052C2211yescharacteristic, complemented
28#17986052C2211yescharacteristic, complemented
29#17986023C2211yescharacteristic, complemented
30C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
31#17985966—21no—
32#17985955—21no—
33C4×#11765849C2211yescharacteristic
34C4×#11765849C2211yescharacteristic, complemented
35C2×C4×C71⋊C8C2211yescharacteristic, complemented
36Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
37Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
38Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
39Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
40Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
41Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
42Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
43Q8⋊(C71⋊C8)C2211yescharacteristic, complemented
44D4⋊(C71⋊C8)C2211yescharacteristic
45D4⋊(C71⋊C8)C2211yescharacteristic
46D4⋊(C71⋊C8)C2211yescharacteristic
47D4⋊(C71⋊C8)C2211yescharacteristic
48D4⋊(C71⋊C8)C2211yescharacteristic
49D4⋊(C71⋊C8)C2211yescharacteristic
50D4⋊(C71⋊C8)C2211yescharacteristic
51D4⋊(C71⋊C8)C2211yescharacteristic
52#556×C71C411yescharacteristic
53#555×C71C411yescharacteristic
54#554×C71C411yescharacteristic
55#553×C71—21no—
56#552×C71—21no—
57#552×C71C411yescharacteristic
58#552×C71C411yescharacteristic
59#551×C71—21no—
60#551×C71—21no—
61#547×C71C411yescharacteristic
62#546×C71C411yescharacteristic
63#546×C71C411yescharacteristic
64#533×C71C2211yescharacteristic
65#529×C71—21no—
66#529×C71—21no—
67#529×C71C2211yescharacteristic
68#529×C71C2211yescharacteristic
69#525×C71—21no—
70C4×#41×C71C2211yescharacteristic
71C4×#41×C71C2211yescharacteristic
72C4×#41×C71C2211yescharacteristic
73C2×C4×D4×C71C2211yescharacteristic
74C2×#117×C71—21no—
75C2×#11765849—21no—
76C2×#11765849—21no—
77C2×#11765849—21no—
78C22×C71⋊C8—21no—
79C22×C71⋊C8—21no—
80C4⋊(C71⋊C8)—21no—
81C4⋊(C71⋊C8)—21no—
82C4⋊(C71⋊C8)—21no—
83C4⋊(C71⋊C8)—21no—
84C4⋊(C71⋊C8)—21no—
85C4⋊(C71⋊C8)C2311yescharacteristic
86C4⋊(C71⋊C8)C2311yescharacteristic
87C4⋊(C71⋊C8)C2311yescharacteristic
88C4⋊(C71⋊C8)C2311yescharacteristic
89C22⋊(C71⋊C8)—21no—
90C22⋊(C71⋊C8)—21no—
91C22⋊(C71⋊C8)—21no—
92C22⋊(C71⋊C8)—21no—
93C22⋊(C71⋊C8)—21no—
94C22⋊(C71⋊C8)—21no—
95C22⋊(C71⋊C8)—21no—
96#14556039—21no—
97#14556039—21no—
98#14556039—21no—
99#14556039—21no—
100C4×C71⋊C8—21no—
101C4×C71⋊C8—21no—
102C4×C71⋊C8—21no—
103C4×C71⋊C8C2311yescharacteristic
104C4×C71⋊C8C2311yescharacteristic
105C4×C71⋊C8C2311yescharacteristic
106C4×C71⋊C8C2311yescharacteristic
107C2×#41×C71C2×C411yescharacteristic
108C2×#41×C71C2×C411yescharacteristic
109C2×#41×C71D411yescharacteristic
110C22×D4×C71C2×C411yescharacteristic
111C23×C4×C71—21no—
112C4⋊Q8×C71C2×C411yescharacteristic
113C4⋊Q8×C71C2×C411yescharacteristic
114#126×C71—21no—
115#126×C71—21no—
116#126×C71—21no—
117#126×C71—21no—
118#126×C71—21no—
119#126×C71—21no—
120#125×C71—21no—
121#125×C71—21no—
122#125×C71—21no—
123#125×C71C2×C411yescharacteristic
124#125×C71C2×C411yescharacteristic
125#124×C71—21no—
126#124×C71—21no—
127#124×C71C2×C411yescharacteristic
128#124×C71C2×C411yescharacteristic
129#123×C71—21no—
130#123×C71—21no—
131#123×C71—21no—
132#123×C71—21no—
133#123×C71—21no—
134#123×C71—21no—
135#123×C71—21no—
136#123×C71—21no—
137C22⋊Q8×C71—21no—
138C22⋊Q8×C71—21no—
139C22⋊Q8×C71—21no—
140C22⋊Q8×C71—21no—
141C22⋊Q8×C71—21no—
142C22⋊Q8×C71C2×C411yescharacteristic
143C22⋊Q8×C71C2×C411yescharacteristic
144C22⋊Q8×C71C2×C411yescharacteristic
145C22⋊Q8×C71C2×C411yescharacteristic
146#121×C71—21no—
147#121×C71—21no—
148#121×C71—21no—
149#121×C71—21no—
150#121×C71C2×C411yescharacteristic
151#121×C71C2×C411yescharacteristic
152#120×C71—21no—
153#120×C71—21no—
154C4×Q8×C71—21no—
155C4×Q8×C71C2×C411yescharacteristic
156C4×Q8×C71C2×C411yescharacteristic
157C4×Q8×C71C2×C411yescharacteristic
158C4×Q8×C71D411yescharacteristic
159C4×Q8×C71C2311yescharacteristic
160C4×Q8×C71C2311yescharacteristic
161C4×D4×C71—21no—
162C4×D4×C71—21no—
163C4×D4×C71—21no—
164C4×D4×C71—21no—
165C4×D4×C71—21no—
166C4×D4×C71—21no—
167C4×D4×C71—21no—
168C4×D4×C71—21no—
169C4×D4×C71C2×C411yescharacteristic
170C4×D4×C71C2×C411yescharacteristic
171C4×D4×C71C2×C411yescharacteristic
172C4×D4×C71C2×C411yescharacteristic
173C4×D4×C71C2×C411yescharacteristic
174C4×D4×C71C2×C411yescharacteristic
175C4×D4×C71C2×C411yescharacteristic
176C4×D4×C71D411yescharacteristic
177C4×D4×C71D411yescharacteristic
178C4×D4×C71D411yescharacteristic
179C4×D4×C71C2311yescharacteristic
180C4×D4×C71C2311yescharacteristic
181#117×C71—21no—
182#117×C71—21no—
183#117×C71—21no—
184#117×C71—21no—
185#117×C71—21no—
186#117×C71—21no—
187#117×C71—21no—
188#117×C71—21no—
189#117×C71—21no—
190#117×C71C2×C411yescharacteristic
191#117×C71C2×C411yescharacteristic
192#117×C71D411yescharacteristic
193#117×C71D411yescharacteristic
194#117×C71D411yescharacteristic
195C2×C4⋊C4×C71—21no—
196C2×C4⋊C4×C71—21no—
197C2×C4⋊C4×C71C2×C411yescharacteristic
198C2×C22⋊C4×C71—21no—
199C2×C22⋊C4×C71—21no—
200C2×C22⋊C4×C71—21no—
201C2×C42×C71—21no—
202C2×C42×C71—21no—
203C2×C42×C71C2311yescharacteristic
204C2×C42×C71C2311yescharacteristic
205C2×C42×C71C2311yescharacteristic
206#11765849—42no—
207#11765849—42no—
208#11765849—42no—
209C2×C71⋊C8—21no—
210C2×C71⋊C8—21no—
211C2×C71⋊C8—21no—
212C2×C71⋊C8—21no—
213C2×C71⋊C8—21no—
214C2×C71⋊C8—21no—
215C2×C71⋊C8—21no—
216C2×C71⋊C8—21no—
217C2×C71⋊C8—42no—
218C2×C71⋊C8—42no—
219C24×C71—21no—
220#41×C71—22no—
221#41×C71—22no—
222#41×C71—41no—
223#41×C71—41no—
224#41×C71—41no—
225#41×C71—41no—
226C2×Q8×C71—21no—
227C2×Q8×C71C22⋊C411yescharacteristic
228C2×Q8×C71C22×C411yescharacteristic
229C2×Q8×C71C22×C411yescharacteristic
230C2×D4×C71—22no—
231C2×D4×C71—21no—
232C2×D4×C71—21no—
233C2×D4×C71—21no—
234C2×D4×C71—21no—
235C2×D4×C71—21no—
236C2×D4×C71—41no—
237C2×D4×C71C22⋊C411yescharacteristic
238C2×D4×C71C22⋊C411yescharacteristic
239C2×D4×C71C22⋊C411yescharacteristic
240C2×D4×C71C22×C411yescharacteristic
241C2×D4×C71C22×C411yescharacteristic
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—42no—
252C22×C4×C71—42no—
253C22×C4×C71C22×C411yescharacteristic
254C22×C4×C71C22×C411yescharacteristic
255C22×C4×C71C22×C411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71—21no—
270C4⋊C4×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71C22⋊C411yescharacteristic
279C4⋊C4×C71C22⋊C411yescharacteristic
280C4⋊C4×C71C22⋊C411yescharacteristic
281C4⋊C4×C71C22⋊C411yescharacteristic
282C4⋊C4×C71C22⋊C411yescharacteristic
283C4⋊C4×C71C22⋊C411yescharacteristic
284C4⋊C4×C71C22×C411yescharacteristic
285C4⋊C4×C71C22×C411yescharacteristic
286C4⋊C4×C71C22×C411yescharacteristic
287C4⋊C4×C71C22×C411yescharacteristic
288C22⋊C4×C71—21no—
289C22⋊C4×C71—21no—
290C22⋊C4×C71—21no—
291C22⋊C4×C71—21no—
292C22⋊C4×C71—21no—
293C22⋊C4×C71—21no—
294C22⋊C4×C71—21no—
295C22⋊C4×C71—21no—
296C22⋊C4×C71—21no—
297C22⋊C4×C71—21no—
298C22⋊C4×C71—21no—
299C22⋊C4×C71—21no—
300C22⋊C4×C71—21no—
301C22⋊C4×C71—21no—
302C22⋊C4×C71—21no—
303C22⋊C4×C71—21no—
304C22⋊C4×C71—21no—
305C22⋊C4×C71—21no—
306C22⋊C4×C71C22⋊C411yescharacteristic
307C22⋊C4×C71C22⋊C411yescharacteristic
308C22⋊C4×C71C22⋊C411yescharacteristic
309C22⋊C4×C71C22⋊C411yescharacteristic
310C22⋊C4×C71C22⋊C411yescharacteristic
311C22⋊C4×C71C22⋊C411yescharacteristic
312C42×C71—21no—
313C42×C71—21no—
314C42×C71—21no—
315C42×C71—21no—
316C42×C71—21no—
317C42×C71—21no—
318C42×C71C22×C411yescharacteristic
319C42×C71C22×C411yescharacteristic
320C42×C71C22×C411yescharacteristic
321C42×C71C2×D411yescharacteristic
322C42×C71C2×D411yescharacteristic
323C42×C71C2×D411yescharacteristic
324C42×C71C2×D411yescharacteristic
325C42×C71C2×D411yescharacteristic
326C42×C71C2×D411yescharacteristic
327C42×C71C2411yescharacteristic
328C23×C71—21no—
329C23×C71—21no—
330C23×C71—42no—
331C23×C71—42no—
332C23×C71—81no—
333C23×C71C2×C22⋊C411yescharacteristic
334C23×C71C2×C22⋊C411yescharacteristic
335C23×C71C2×C22⋊C411yescharacteristic
336Q8×C71—21no—
337Q8×C71—21no—
338Q8×C71—21no—
339Q8×C71—21no—
340Q8×C71—41no—
341Q8×C71—81no—
342D4×C71—21no—
343D4×C71—21no—
344D4×C71—21no—
345D4×C71—41no—
346D4×C71—41no—
347D4×C71—41no—
348D4×C71—42no—
349D4×C71—42no—
350D4×C71—42no—
351D4×C71—81no—
352D4×C71—81no—
353D4×C71#13112yes—
354C2×C4×C71—21no—
355C2×C4×C71—21no—
356C2×C4×C71—21no—
357C2×C4×C71—21no—
358C2×C4×C71—21no—
359C2×C4×C71—21no—
360C2×C4×C71—21no—
361C2×C4×C71—21no—
362C2×C4×C71—21no—
363C2×C4×C71—21no—
364C2×C4×C71—21no—
365C2×C4×C71—21no—
366C2×C4×C71—21no—
367C2×C4×C71—21no—
368C2×C4×C71—21no—
369C2×C4×C71—21no—
370C2×C4×C71—21no—
371C2×C4×C71—21no—
372C2×C4×C71—41no—
373C2×C4×C71—41no—
374C2×C4×C71—41no—
375C2×C4×C71—42no—
376C2×C4×C71—42no—
377C2×C4×C71—42no—
378C2×C4×C71—42no—
379C2×C4×C71—42no—
380C2×C4×C71—41no—
381C2×C4×C71—41no—
382C2×C4×C71—41no—
383C2×C4×C71—41no—
384C2×C4×C71—81no—
385C2×C4×C71—81no—
386C2×C4×C71C2×C22⋊C411yescharacteristic
387C2×C4×C71C2×C22⋊C411yescharacteristic
388C2×C4×C71C2×C22⋊C411yescharacteristic
389C2×C4×C71C2×C22⋊C411yescharacteristic
390C2×C4×C71C2×C22⋊C411yescharacteristic
391C2×C4×C71C2×C22⋊C411yescharacteristic
392C2×C4×C71C2×C22⋊C411yescharacteristic
393C2×C4×C71C2×C22⋊C411yescharacteristic
394C2×C4×C71C2×C22⋊C411yescharacteristic
395C2×C4×C71C23×C411yescharacteristic
396C2×C4×C71C22×D411yescharacteristic
397C2×C4×C71C22×D411yescharacteristic
398C71⋊C8—22no—
399C71⋊C8—41no—
400C71⋊C8—41no—
401C71⋊C8—41no—
402C71⋊C8—41no—
403C71⋊C8—41no—
404C71⋊C8—41no—
405C71⋊C8—41no—
406C22×C71—21no—
407C22×C71—21no—
408C22×C71—21no—
409C22×C71—22no—
410C22×C71—21no—
411C22×C71—21no—
412C22×C71—21no—
413C22×C71—21no—
414C22×C71—21no—
415C22×C71—21no—
416C22×C71—41no—
417C22×C71—41no—
418C22×C71—41no—
419C22×C71—41no—
420C22×C71—41no—
421C22×C71—84no—
422C22×C71C22×C22⋊C411yescharacteristic
423C4×C71—21no—
424C4×C71—21no—
425C4×C71—21no—
426C4×C71—21no—
427C4×C71—21no—
428C4×C71—21no—
429C4×C71—21no—
430C4×C71—21no—
431C4×C71—21no—
432C4×C71—21no—
433C4×C71—41no—
434C4×C71—41no—
435C4×C71—41no—
436C4×C71—41no—
437C4×C71—41no—
438C4×C71—41no—
439C4×C71C2×#13111yescharacteristic
440C4×C71#56811yescharacteristic
441C4×C71#57511yescharacteristic
442C4×C71#57511yescharacteristic
443#17513—711nomaximal, Sylow
444C2×C71—41no—
445C2×C71—41no—
446C2×C71—41no—
447C2×C71—42no—
448C2×C71—81no—
449C2×C71#288011yescharacteristic
450C2×C71#289611yescharacteristic
451C2×C71#290111yescharacteristic
452#3475D7111yescharacteristic
453#2965—711no—
454#2925—711no—
455#1497—711no—
456#1495—711no—
457#1494—711no—
458#1490—711no—
459#1489—711no—
460#1488—711no—
461#1485—711no—
462#1483—711no—
463#1482—711no—
464#1478—711no—
465#1477—711no—
466#1476—711no—
467C71#1751311yescharacteristic, complemented, Sylow
468#556Dic7111yescharacteristic
469#555Dic7111yescharacteristic
470#554Dic7111yescharacteristic
471#553—21no—
472#552—21no—
473#552Dic7111yescharacteristic
474#552Dic7111yescharacteristic
475#551—21no—
476#551—21no—
477#547Dic7111yescharacteristic
478#546Dic7111yescharacteristic
479#546Dic7111yescharacteristic
480#533C2×D7111yescharacteristic
481#529—21no—
482#529—21no—
483#529C2×D7111yescharacteristic
484#529C2×D7111yescharacteristic
485#525—21no—
486C4×#41C2×D7111yescharacteristic
487C4×#41C2×D7111yescharacteristic
488C4×#41C2×D7111yescharacteristic
489C2×C4×D4C2×D7111yescharacteristic
490C2×#117—21no—
491#446—1421no—
492#436—1421no—
493#435—1421no—
494#435—1421no—
495#433—1421no—
496#433—1421no—
497#432—711no—
498#432—711no—
499#431—711no—
500#431—711no—
501#431—711no—
502#431—711no—
503#431—711no—
504#423—711no—
505C2×C4⋊C8—711no—
506#408—1421no—
507#405—1421no—
508C4×M16—711no—
509C4×M16—711no—
510C2×C4×C8—711no—
511Q8⋊C8—711no—
512Q8⋊C8—711no—
513Q8⋊C8—711no—
514Q8⋊C8—711no—
515Q8⋊C8—711no—
516Q8⋊C8—711no—
517Q8⋊C8—711no—
518Q8⋊C8—711no—
519D4⋊C8—711no—
520D4⋊C8—711no—
521D4⋊C8—711no—
522D4⋊C8—711no—
523D4⋊C8—711no—
524D4⋊C8—711no—
525D4⋊C8—711no—
526D4⋊C8—711no—
527C2×#41C2×Dic7111yescharacteristic
528C2×#41C2×Dic7111yescharacteristic
529C2×#41C22⋊D7111yescharacteristic
530C22×D4C2×Dic7111yescharacteristic
531C23×C4—21no—
532C2×M16—1421no—
533C2×M16—1421no—
534C2×M16—1421no—
535C22×C8—1421no—
536C22×C8—1421no—
537C4⋊Q8C2×Dic7111yescharacteristic
538C4⋊Q8C2×Dic7111yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#125—21no—
546#125—21no—
547#125—21no—
548#125C2×Dic7111yescharacteristic
549#125C2×Dic7111yescharacteristic
550#124—21no—
551#124—21no—
552#124C2×Dic7111yescharacteristic
553#124C2×Dic7111yescharacteristic
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8C2×Dic7111yescharacteristic
568C22⋊Q8C2×Dic7111yescharacteristic
569C22⋊Q8C2×Dic7111yescharacteristic
570C22⋊Q8C2×Dic7111yescharacteristic
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121C2×Dic7111yescharacteristic
576#121C2×Dic7111yescharacteristic
577#120—21no—
578#120—21no—
579C4×Q8—21no—
580C4×Q8C2×Dic7111yescharacteristic
581C4×Q8C2×Dic7111yescharacteristic
582C4×Q8C2×Dic7111yescharacteristic
583C4×Q8C22⋊D7111yescharacteristic
584C4×Q8C22×D7111yescharacteristic
585C4×Q8C22×D7111yescharacteristic
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4C2×Dic7111yescharacteristic
595C4×D4C2×Dic7111yescharacteristic
596C4×D4C2×Dic7111yescharacteristic
597C4×D4C2×Dic7111yescharacteristic
598C4×D4C2×Dic7111yescharacteristic
599C4×D4C2×Dic7111yescharacteristic
600C4×D4C2×Dic7111yescharacteristic
601C4×D4C22⋊D7111yescharacteristic
602C4×D4C22⋊D7111yescharacteristic
603C4×D4C22⋊D7111yescharacteristic
604C4×D4C22×D7111yescharacteristic
605C4×D4C22×D7111yescharacteristic
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117C2×Dic7111yescharacteristic
616#117C2×Dic7111yescharacteristic
617#117C22⋊D7111yescharacteristic
618#117C22⋊D7111yescharacteristic
619#117C22⋊D7111yescharacteristic
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4C2×Dic7111yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42C22×D7111yescharacteristic
629C2×C42C22×D7111yescharacteristic
630C2×C42C22×D7111yescharacteristic
631C4⋊C8—711no—
632C4⋊C8—711no—
633C4⋊C8—711no—
634C4⋊C8—711no—
635C4⋊C8—1421no—
636C4⋊C8—1421no—
637C4⋊C8—1421no—
638C4⋊C8—1421no—
639C4⋊C8—1421no—
640C22⋊C8—1421no—
641C22⋊C8—1421no—
642C22⋊C8—1421no—
643C22⋊C8—1421no—
644C22⋊C8—1421no—
645C22⋊C8—1421no—
646C22⋊C8—1421no—
647#97—1421no—
648#97—1421no—
649#97—1421no—
650#97—1421no—
651C4×C8—711no—
652C4×C8—711no—
653C4×C8—711no—
654C4×C8—711no—
655C4×C8—1421no—
656C4×C8—1421no—
657C4×C8—1421no—
658C24—21no—
659#41—22no—
660#41—22no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665C2×Q8—21no—
666C2×Q8C22⋊Dic7111yescharacteristic
667C2×Q8C22×Dic7111yescharacteristic
668C2×Q8C22×Dic7111yescharacteristic
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—41no—
676C2×D4C22⋊Dic7111yescharacteristic
677C2×D4C22⋊Dic7111yescharacteristic
678C2×D4C22⋊Dic7111yescharacteristic
679C2×D4C22×Dic7111yescharacteristic
680C2×D4C22×Dic7111yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4C22×Dic7111yescharacteristic
693C22×C4C22×Dic7111yescharacteristic
694C22×C4C22×Dic7111yescharacteristic
695C22×C4C2×C22⋊D7111yescharacteristic
696C22×C4C2×C22⋊D7111yescharacteristic
697C22×C4C2×C22⋊D7111yescharacteristic
698C22×C4C2×C22⋊D7111yescharacteristic
699C22×C4C2×C22⋊D7111yescharacteristic
700C22×C4C2×C22⋊D7111yescharacteristic
701M16—2842no—
702M16—2842no—
703M16—2842no—
704C2×C8—2842no—
705C2×C8—2842no—
706C2×C8—1421no—
707C2×C8—1421no—
708C2×C8—1421no—
709C2×C8—1421no—
710C2×C8—1421no—
711C2×C8—1421no—
712C2×C8—1421no—
713C2×C8—1421no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C22⋊Dic7111yescharacteristic
731C4⋊C4C22⋊Dic7111yescharacteristic
732C4⋊C4C22⋊Dic7111yescharacteristic
733C4⋊C4C22⋊Dic7111yescharacteristic
734C4⋊C4C22⋊Dic7111yescharacteristic
735C4⋊C4C22⋊Dic7111yescharacteristic
736C4⋊C4C22×Dic7111yescharacteristic
737C4⋊C4C22×Dic7111yescharacteristic
738C4⋊C4C22×Dic7111yescharacteristic
739C4⋊C4C22×Dic7111yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4C22⋊Dic7111yescharacteristic
759C22⋊C4C22⋊Dic7111yescharacteristic
760C22⋊C4C22⋊Dic7111yescharacteristic
761C22⋊C4C22⋊Dic7111yescharacteristic
762C22⋊C4C22⋊Dic7111yescharacteristic
763C22⋊C4C22⋊Dic7111yescharacteristic
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42C22×Dic7111yescharacteristic
771C42C22×Dic7111yescharacteristic
772C42C22×Dic7111yescharacteristic
773C42C2×C22⋊D7111yescharacteristic
774C42C2×C22⋊D7111yescharacteristic
775C42C2×C22⋊D7111yescharacteristic
776C42C2×C22⋊D7111yescharacteristic
777C42C2×C22⋊D7111yescharacteristic
778C42C2×C22⋊D7111yescharacteristic
779C42C23×D7111yescharacteristic
780C23—21no—
781C23—21no—
782C23—42no—
783C23—42no—
784C23—81no—
785C23C2×C22⋊Dic7111yescharacteristic
786C23C2×C22⋊Dic7111yescharacteristic
787C23C2×C22⋊Dic7111yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—41no—
793Q8—81no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4#1455613512yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C2×C22⋊Dic7111yescharacteristic
839C2×C4C2×C22⋊Dic7111yescharacteristic
840C2×C4C2×C22⋊Dic7111yescharacteristic
841C2×C4C2×C22⋊Dic7111yescharacteristic
842C2×C4C2×C22⋊Dic7111yescharacteristic
843C2×C4C2×C22⋊Dic7111yescharacteristic
844C2×C4C2×C22⋊Dic7111yescharacteristic
845C2×C4C2×C22⋊Dic7111yescharacteristic
846C2×C4C2×C22⋊Dic7111yescharacteristic
847C2×C4C23×Dic7111yescharacteristic
848C2×C4C22×C22⋊D7111yescharacteristic
849C2×C4C22×C22⋊D7111yescharacteristic
850C8—2841no—
851C8—2841no—
852C8—2841no—
853C8—2841no—
854C8—2841no—
855C8—2841no—
856C8—2841no—
857C8—1422no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—22no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—84no—
874C22C22×C22⋊Dic7111yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4C2×#1455613511yescharacteristic
892C4#1798676611yescharacteristic
893C4#1798679711yescharacteristic
894C4#1798679711yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—42no—
899C2—81no—
900C2#2259678911yescharacteristic
901C2#2259685911yescharacteristic
902C2#2259688711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC42C23×D71
Fitting, prime radicalC71×#3475C2
socleC22×C71C22×C22⋊C4
cosocleC42×C71C24
hypercenter#3475D71
hypocenterC71#17513
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #22597307C2semidirect
2. #22597006C2semidirect
3. #22586813C2semidirect
4. #22586805C2semidirect
5. #22586800C2semidirect
6. #22586783C2semidirect
7. #22586779C2semidirect
8. #22586774C2semidirect
9. #22586761C2semidirect
10. #22586753C2semidirect
11. #22586748C2semidirect
12. #22586731C2semidirect
13. #22586727C2semidirect
14. #22586722C2semidirect
23. #17986056C22semidirect
26. #17986052C22semidirect
27. #17986052C22semidirect
28. #17986052C22semidirect
29. #17986023C22semidirect
30. C2×C4⋊(C71⋊C8)C22semidirect
34. C4×#11765849C22semidirect
35. C2×C4×C71⋊C8C22semidirect
36. Q8⋊(C71⋊C8)C22semidirect
37. Q8⋊(C71⋊C8)C22semidirect
38. Q8⋊(C71⋊C8)C22semidirect
39. Q8⋊(C71⋊C8)C22semidirect
40. Q8⋊(C71⋊C8)C22semidirect
41. Q8⋊(C71⋊C8)C22semidirect
42. Q8⋊(C71⋊C8)C22semidirect
43. Q8⋊(C71⋊C8)C22semidirect
467. C71#17513semidirect

Maximal subgroups

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

subgroupindex
#225973072
#225970062
#225868132
#225868052
#225868002
#225867832
#225867792
#225867742
#225867612
#225867532
#225867482
#225867312
#225867272
#225867222
C71×#34752
#1751371