Finite Group Databasebeta

← #31964461

Subgroups — #31964461

Order 18176.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597465C211yesmaximal, characteristic, complemented
2#22596984C211yesmaximal, characteristic, complemented
3#22586809C211yesmaximal, characteristic, complemented
4#22586805C211yesmaximal, characteristic, complemented
5#22586800C211yesmaximal, characteristic, complemented
6#22586783C211yesmaximal, characteristic, complemented
7#22586774C211yesmaximal, characteristic, complemented
8#22586765C211yesmaximal, characteristic, complemented
9#22586753C211yesmaximal, characteristic, complemented
10#22586748C211yesmaximal, characteristic, complemented
11#22586739C211yesmaximal, characteristic, complemented
12#22586731C211yesmaximal, characteristic, complemented
13#22586727C211yesmaximal, characteristic, complemented
14C2×D4⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
15C71×#3481C211yesmaximal, characteristic
16#17986130—21no—
17#17986071—21no—
18#17986071—21no—
19D4×C71⋊C8—21no—
20#17986060—21no—
21#17986060—21no—
22#17986056C2211yescharacteristic, complemented
23#17986056C2211yescharacteristic, complemented
24#17986052C2211yescharacteristic, complemented
25#17986052C2211yescharacteristic, complemented
26#17986052C2211yescharacteristic, complemented
27#17986052C2211yescharacteristic, complemented
28#17986052C2211yescharacteristic, complemented
29#17986026—21no—
30#17986023C2211yescharacteristic, complemented
31C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
32C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
33#17985966—21no—
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
40D4⋊(C71⋊C8)C2211yescharacteristic
41D4⋊(C71⋊C8)C2211yescharacteristic
42D4⋊(C71⋊C8)C2211yescharacteristic
43D4⋊(C71⋊C8)C2211yescharacteristic
44D4⋊(C71⋊C8)C2211yescharacteristic, complemented
45D4⋊(C71⋊C8)C2211yescharacteristic, complemented
46D4⋊(C71⋊C8)C2211yescharacteristic, complemented
47D4⋊(C71⋊C8)C2211yescharacteristic, complemented
48D4⋊(C71⋊C8)C2211yescharacteristic, complemented
49D4⋊(C71⋊C8)C2211yescharacteristic, complemented
50D4⋊(C71⋊C8)C2211yescharacteristic, complemented
51D4⋊(C71⋊C8)C2211yescharacteristic, complemented
52#559×C71C411yescharacteristic
53#554×C71C411yescharacteristic
54#554×C71C411yescharacteristic
55#553×C71—21no—
56#553×C71C411yescharacteristic
57#553×C71C411yescharacteristic
58#551×C71—21no—
59#551×C71—21no—
60#546×C71—21no—
61#546×C71C411yescharacteristic
62#546×C71C411yescharacteristic
63D42×C71C411yescharacteristic
64#532×C71C2211yescharacteristic
65#529×C71—21no—
66#529×C71C2211yescharacteristic
67#529×C71C2211yescharacteristic
68#525×C71—21no—
69#525×C71—21no—
70C4×#41×C71C2211yescharacteristic
71C4×#41×C71C2211yescharacteristic
72C2×C4×D4×C71—21no—
73C2×C4×D4×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#11765849—21no—
76C2×#11765849—21no—
77C22×C71⋊C8—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)—21no—
86C4⋊(C71⋊C8)—21no—
87C4⋊(C71⋊C8)C2311yescharacteristic
88C4⋊(C71⋊C8)C2311yescharacteristic
89C4⋊(C71⋊C8)C2311yescharacteristic
90C4⋊(C71⋊C8)C2311yescharacteristic
91C22⋊(C71⋊C8)—21no—
92C22⋊(C71⋊C8)—21no—
93C22⋊(C71⋊C8)—21no—
94C22⋊(C71⋊C8)—21no—
95C22⋊(C71⋊C8)—21no—
96C22⋊(C71⋊C8)—21no—
97C22⋊(C71⋊C8)—21no—
98#14556039—21no—
99#14556039—21no—
100#14556039—21no—
101C4×C71⋊C8—21no—
102C4×C71⋊C8—21no—
103C4×C71⋊C8C2311yescharacteristic
104C4×C71⋊C8C2311yescharacteristic
105C4×C71⋊C8C2311yescharacteristic
106C4×C71⋊C8C2311yescharacteristic
107C2×#41×C71—21no—
108C2×#41×C71C2×C411yescharacteristic
109C2×#41×C71D411yescharacteristic
110C22×D4×C71—21no—
111C22×D4×C71C2×C411yescharacteristic
112C22×D4×C71C2×C411yescharacteristic
113C23×C4×C71—21no—
114C23×C4×C71—21no—
115C4⋊Q8×C71C2×C411yescharacteristic
116#127×C71C2×C411yescharacteristic
117#126×C71—21no—
118#126×C71—21no—
119#126×C71—21no—
120#126×C71—21no—
121#125×C71—21no—
122#125×C71C2×C411yescharacteristic
123#125×C71C2×C411yescharacteristic
124#124×C71—21no—
125#124×C71—21no—
126#124×C71C2×C411yescharacteristic
127#124×C71C2×C411yescharacteristic
128#123×C71—21no—
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—
136C22⋊Q8×C71—21no—
137C22⋊Q8×C71—21no—
138C22⋊Q8×C71—21no—
139C22⋊Q8×C71—21no—
140C22⋊Q8×C71—21no—
141C22⋊Q8×C71C2×C411yescharacteristic
142C22⋊Q8×C71C2×C411yescharacteristic
143#121×C71—21no—
144#121×C71—21no—
145#121×C71—21no—
146#121×C71—21no—
147#121×C71—21no—
148#121×C71—21no—
149#121×C71C2×C411yescharacteristic
150#121×C71C2×C411yescharacteristic
151#121×C71C2×C411yescharacteristic
152#121×C71C2×C411yescharacteristic
153#120×C71—21no—
154#120×C71—21no—
155#120×C71—21no—
156#120×C71—21no—
157C4×Q8×C71C2×C411yescharacteristic
158C4×Q8×C71C2×C411yescharacteristic
159C4×Q8×C71D411yescharacteristic
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×C71—21no—
170C4×D4×C71—21no—
171C4×D4×C71—21no—
172C4×D4×C71—21no—
173C4×D4×C71—21no—
174C4×D4×C71C2×C411yescharacteristic
175C4×D4×C71C2×C411yescharacteristic
176C4×D4×C71C2×C411yescharacteristic
177C4×D4×C71C2×C411yescharacteristic
178C4×D4×C71C2×C411yescharacteristic
179C4×D4×C71C2×C411yescharacteristic
180C4×D4×C71C2×C411yescharacteristic
181C4×D4×C71C2×C411yescharacteristic
182C4×D4×C71D411yescharacteristic
183C4×D4×C71D411yescharacteristic
184C4×D4×C71D411yescharacteristic
185C4×D4×C71C2311yescharacteristic
186C4×D4×C71C2311yescharacteristic
187C4×D4×C71C2311yescharacteristic
188#117×C71—21no—
189#117×C71—21no—
190#117×C71—21no—
191#117×C71C2×C411yescharacteristic
192#117×C71D411yescharacteristic
193#117×C71D411yescharacteristic
194#117×C71D411yescharacteristic
195C2×C4⋊C4×C71—21no—
196C2×C4⋊C4×C71C2×C411yescharacteristic
197C2×C4⋊C4×C71C2×C411yescharacteristic
198C2×C22⋊C4×C71—21no—
199C2×C22⋊C4×C71—21no—
200C2×C22⋊C4×C71—21no—
201C2×C22⋊C4×C71—21no—
202C2×C42×C71—21no—
203C2×C42×C71C2311yescharacteristic
204C2×C42×C71C2311yescharacteristic
205C2×C42×C71C2311yescharacteristic
206#11765849—42no—
207#11765849—81no—
208C2×C71⋊C8—21no—
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—42no—
217C2×C71⋊C8—81no—
218C2×C71⋊C8—81no—
219C24×C71—21no—
220C24×C71—21no—
221#41×C71—22no—
222#41×C71—42no—
223#41×C71—41no—
224#41×C71—81no—
225#41×C71—81no—
226C2×Q8×C71—21no—
227C2×Q8×C71C22⋊C411yescharacteristic
228C2×Q8×C71C22×C411yescharacteristic
229C2×D4×C71—22no—
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—21no—
237C2×D4×C71—21no—
238C2×D4×C71—21no—
239C2×D4×C71—21no—
240C2×D4×C71—41no—
241C2×D4×C71—41no—
242C2×D4×C71—44no—
243C2×D4×C71C22⋊C411yescharacteristic
244C2×D4×C71C22⋊C411yescharacteristic
245C2×D4×C71C22⋊C411yescharacteristic
246C2×D4×C71C22×C411yescharacteristic
247C2×D4×C71C22×C411yescharacteristic
248C2×D4×C71C22×C411yescharacteristic
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—81no—
261C22×C4×C71—81no—
262C22×C4×C71—81no—
263C22×C4×C71—81no—
264C22×C4×C71C22×C411yescharacteristic
265C22×C4×C71C22×C411yescharacteristic
266C22×C4×C71C22×C411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D411yescharacteristic
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71—21no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71C22⋊C411yescharacteristic
285C4⋊C4×C71C22⋊C411yescharacteristic
286C4⋊C4×C71C22⋊C411yescharacteristic
287C4⋊C4×C71C22⋊C411yescharacteristic
288C4⋊C4×C71C22⋊C411yescharacteristic
289C4⋊C4×C71C22⋊C411yescharacteristic
290C4⋊C4×C71C22×C411yescharacteristic
291C4⋊C4×C71C22×C411yescharacteristic
292C4⋊C4×C71C22×C411yescharacteristic
293C4⋊C4×C71C22×C411yescharacteristic
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×C71—21no—
307C22⋊C4×C71—21no—
308C22⋊C4×C71—21no—
309C22⋊C4×C71—21no—
310C22⋊C4×C71—21no—
311C22⋊C4×C71—21no—
312C22⋊C4×C71—21no—
313C22⋊C4×C71C22⋊C411yescharacteristic
314C22⋊C4×C71C22⋊C411yescharacteristic
315C22⋊C4×C71C22⋊C411yescharacteristic
316C22⋊C4×C71C22⋊C411yescharacteristic
317C22⋊C4×C71C22⋊C411yescharacteristic
318C22⋊C4×C71C22⋊C411yescharacteristic
319C42×C71—21no—
320C42×C71—21no—
321C42×C71—21no—
322C42×C71C22×C411yescharacteristic
323C42×C71C22×C411yescharacteristic
324C42×C71C22×C411yescharacteristic
325C42×C71C2×D411yescharacteristic
326C42×C71C2×D411yescharacteristic
327C42×C71C2×D411yescharacteristic
328C42×C71C2×D411yescharacteristic
329C42×C71C2×D411yescharacteristic
330C42×C71C2×D411yescharacteristic
331C42×C71C2411yescharacteristic
332C23×C71—21no—
333C23×C71—21no—
334C23×C71—21no—
335C23×C71—42no—
336C23×C71—42no—
337C23×C71—42no—
338C23×C71—42no—
339C23×C71—81no—
340C23×C71—81no—
341C23×C71C2×C22⋊C411yescharacteristic
342C23×C71C2×C22⋊C411yescharacteristic
343C23×C71C2×C22⋊C411yescharacteristic
344Q8×C71—21no—
345Q8×C71—21no—
346Q8×C71—41no—
347Q8×C71—81no—
348D4×C71—22no—
349D4×C71—22no—
350D4×C71—21no—
351D4×C71—21no—
352D4×C71—21no—
353D4×C71—21no—
354D4×C71—21no—
355D4×C71—41no—
356D4×C71—42no—
357D4×C71—42no—
358D4×C71—42no—
359D4×C71—42no—
360D4×C71—42no—
361D4×C71—42no—
362D4×C71—81no—
363D4×C71—81no—
364D4×C71—81no—
365D4×C71#13112yes—
366C2×C4×C71—22no—
367C2×C4×C71—21no—
368C2×C4×C71—21no—
369C2×C4×C71—21no—
370C2×C4×C71—21no—
371C2×C4×C71—21no—
372C2×C4×C71—21no—
373C2×C4×C71—21no—
374C2×C4×C71—21no—
375C2×C4×C71—21no—
376C2×C4×C71—21no—
377C2×C4×C71—21no—
378C2×C4×C71—21no—
379C2×C4×C71—21no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—21no—
383C2×C4×C71—21no—
384C2×C4×C71—41no—
385C2×C4×C71—41no—
386C2×C4×C71—42no—
387C2×C4×C71—42no—
388C2×C4×C71—41no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—41no—
393C2×C4×C71—41no—
394C2×C4×C71—81no—
395C2×C4×C71—81no—
396C2×C4×C71—81no—
397C2×C4×C71—81no—
398C2×C4×C71—81no—
399C2×C4×C71—81no—
400C2×C4×C71C2×C22⋊C411yescharacteristic
401C2×C4×C71C2×C22⋊C411yescharacteristic
402C2×C4×C71C2×C22⋊C411yescharacteristic
403C2×C4×C71C2×C22⋊C411yescharacteristic
404C2×C4×C71C2×C22⋊C411yescharacteristic
405C2×C4×C71C2×C22⋊C411yescharacteristic
406C2×C4×C71C2×C22⋊C411yescharacteristic
407C2×C4×C71C2×C22⋊C411yescharacteristic
408C2×C4×C71C2×C22⋊C411yescharacteristic
409C2×C4×C71C23×C411yescharacteristic
410C2×C4×C71C22×D411yescharacteristic
411C2×C4×C71C22×D411yescharacteristic
412C71⋊C8—41no—
413C71⋊C8—41no—
414C71⋊C8—41no—
415C71⋊C8—41no—
416C71⋊C8—41no—
417C71⋊C8—41no—
418C71⋊C8—41no—
419C71⋊C8—41no—
420C22×C71—21no—
421C22×C71—21no—
422C22×C71—21no—
423C22×C71—21no—
424C22×C71—22no—
425C22×C71—21no—
426C22×C71—21no—
427C22×C71—21no—
428C22×C71—21no—
429C22×C71—41no—
430C22×C71—41no—
431C22×C71—41no—
432C22×C71—41no—
433C22×C71—41no—
434C22×C71—41no—
435C22×C71—41no—
436C22×C71—41no—
437C22×C71—84no—
438C22×C71—84no—
439C22×C71#42112yes—
440C22×C71C22×C22⋊C411yescharacteristic
441C4×C71—21no—
442C4×C71—21no—
443C4×C71—21no—
444C4×C71—21no—
445C4×C71—21no—
446C4×C71—21no—
447C4×C71—21no—
448C4×C71—21no—
449C4×C71—21no—
450C4×C71—21no—
451C4×C71—41no—
452C4×C71—41no—
453C4×C71—41no—
454C4×C71—41no—
455C4×C71—41no—
456C4×C71C2×#13111yescharacteristic
457C4×C71#56811yescharacteristic
458C4×C71#57611yescharacteristic
459C4×C71#57711yescharacteristic
460#17521—711nomaximal, Sylow
461C2×C71—22no—
462C2×C71—41no—
463C2×C71—41no—
464C2×C71—42no—
465C2×C71—81no—
466C2×C71—81no—
467C2×C71#288011yescharacteristic
468C2×C71#289711yescharacteristic
469C2×C71C2×#42111yescharacteristic
470#3481D7111yescharacteristic
471#2990—711no—
472#2922—711no—
473#1496—711no—
474#1495—711no—
475#1494—711no—
476#1490—711no—
477#1488—711no—
478#1486—711no—
479#1483—711no—
480#1482—711no—
481#1480—711no—
482#1478—711no—
483#1477—711no—
484C2×D4⋊C8—711no—
485C71#1752111yescharacteristic, complemented, Sylow
486#559Dic7111yescharacteristic
487#554Dic7111yescharacteristic
488#554Dic7111yescharacteristic
489#553—21no—
490#553Dic7111yescharacteristic
491#553Dic7111yescharacteristic
492#551—21no—
493#551—21no—
494#546—21no—
495#546Dic7111yescharacteristic
496#546Dic7111yescharacteristic
497D42Dic7111yescharacteristic
498#532C2×D7111yescharacteristic
499#529—21no—
500#529C2×D7111yescharacteristic
501#529C2×D7111yescharacteristic
502#525—21no—
503#525—21no—
504C4×#41C2×D7111yescharacteristic
505C4×#41C2×D7111yescharacteristic
506C2×C4×D4—21no—
507C2×C4×D4C2×D7111yescharacteristic
508C2×C4×D4C2×D7111yescharacteristic
509#446—1421no—
510#435—1421no—
511#435—1421no—
512C8×D4—1421no—
513#433—1421no—
514#433—1421no—
515#432—711no—
516#432—711no—
517#431—711no—
518#431—711no—
519#431—711no—
520#431—711no—
521#431—711no—
522#424—1421no—
523#423—711no—
524C2×C4⋊C8—711no—
525C2×C4⋊C8—711no—
526#408—1421no—
527C4×M16—711no—
528C2×C4×C8—711no—
529Q8⋊C8—711no—
530Q8⋊C8—711no—
531Q8⋊C8—711no—
532Q8⋊C8—711no—
533D4⋊C8—711no—
534D4⋊C8—711no—
535D4⋊C8—711no—
536D4⋊C8—711no—
537D4⋊C8—711no—
538D4⋊C8—711no—
539D4⋊C8—711no—
540D4⋊C8—711no—
541D4⋊C8—711no—
542D4⋊C8—711no—
543D4⋊C8—711no—
544D4⋊C8—711no—
545C2×#41—21no—
546C2×#41C2×Dic7111yescharacteristic
547C2×#41C22⋊D7111yescharacteristic
548C22×D4—21no—
549C22×D4C2×Dic7111yescharacteristic
550C22×D4C2×Dic7111yescharacteristic
551C23×C4—21no—
552C23×C4—21no—
553C2×M16—1421no—
554C2×M16—1421no—
555C22×C8—1421no—
556C22×C8—1421no—
557C22×C8—1421no—
558C4⋊Q8C2×Dic7111yescharacteristic
559#127C2×Dic7111yescharacteristic
560#126—21no—
561#126—21no—
562#126—21no—
563#126—21no—
564#125—21no—
565#125C2×Dic7111yescharacteristic
566#125C2×Dic7111yescharacteristic
567#124—21no—
568#124—21no—
569#124C2×Dic7111yescharacteristic
570#124C2×Dic7111yescharacteristic
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8C2×Dic7111yescharacteristic
585C22⋊Q8C2×Dic7111yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121C2×Dic7111yescharacteristic
593#121C2×Dic7111yescharacteristic
594#121C2×Dic7111yescharacteristic
595#121C2×Dic7111yescharacteristic
596#120—21no—
597#120—21no—
598#120—21no—
599#120—21no—
600C4×Q8C2×Dic7111yescharacteristic
601C4×Q8C2×Dic7111yescharacteristic
602C4×Q8C22⋊D7111yescharacteristic
603C4×Q8C22×D7111yescharacteristic
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4C2×Dic7111yescharacteristic
618C4×D4C2×Dic7111yescharacteristic
619C4×D4C2×Dic7111yescharacteristic
620C4×D4C2×Dic7111yescharacteristic
621C4×D4C2×Dic7111yescharacteristic
622C4×D4C2×Dic7111yescharacteristic
623C4×D4C2×Dic7111yescharacteristic
624C4×D4C2×Dic7111yescharacteristic
625C4×D4C22⋊D7111yescharacteristic
626C4×D4C22⋊D7111yescharacteristic
627C4×D4C22⋊D7111yescharacteristic
628C4×D4C22×D7111yescharacteristic
629C4×D4C22×D7111yescharacteristic
630C4×D4C22×D7111yescharacteristic
631#117—21no—
632#117—21no—
633#117—21no—
634#117C2×Dic7111yescharacteristic
635#117C22⋊D7111yescharacteristic
636#117C22⋊D7111yescharacteristic
637#117C22⋊D7111yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4C2×Dic7111yescharacteristic
640C2×C4⋊C4C2×Dic7111yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C42—21no—
646C2×C42C22×D7111yescharacteristic
647C2×C42C22×D7111yescharacteristic
648C2×C42C22×D7111yescharacteristic
649C4⋊C8—711no—
650C4⋊C8—711no—
651C4⋊C8—711no—
652C4⋊C8—711no—
653C4⋊C8—1421no—
654C4⋊C8—1421no—
655C4⋊C8—1421no—
656C4⋊C8—1421no—
657C4⋊C8—1421no—
658C4⋊C8—1421no—
659C4⋊C8—1421no—
660C22⋊C8—1421no—
661C22⋊C8—1421no—
662C22⋊C8—1421no—
663C22⋊C8—1421no—
664C22⋊C8—1421no—
665C22⋊C8—1421no—
666C22⋊C8—1421no—
667#97—1421no—
668#97—1421no—
669#97—1421no—
670C4×C8—711no—
671C4×C8—711no—
672C4×C8—711no—
673C4×C8—711no—
674C4×C8—1421no—
675C4×C8—1421no—
676C24—21no—
677C24—21no—
678#41—22no—
679#41—42no—
680#41—41no—
681#41—81no—
682#41—81no—
683C2×Q8—21no—
684C2×Q8C22⋊Dic7111yescharacteristic
685C2×Q8C22×Dic7111yescharacteristic
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—44no—
700C2×D4C22⋊Dic7111yescharacteristic
701C2×D4C22⋊Dic7111yescharacteristic
702C2×D4C22⋊Dic7111yescharacteristic
703C2×D4C22×Dic7111yescharacteristic
704C2×D4C22×Dic7111yescharacteristic
705C2×D4C22×Dic7111yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4—81no—
721C22×C4C22×Dic7111yescharacteristic
722C22×C4C22×Dic7111yescharacteristic
723C22×C4C22×Dic7111yescharacteristic
724C22×C4C2×C22⋊D7111yescharacteristic
725C22×C4C2×C22⋊D7111yescharacteristic
726C22×C4C2×C22⋊D7111yescharacteristic
727C22×C4C2×C22⋊D7111yescharacteristic
728C22×C4C2×C22⋊D7111yescharacteristic
729C22×C4C2×C22⋊D7111yescharacteristic
730M16—2842no—
731M16—5681no—
732C2×C8—2842no—
733C2×C8—5681no—
734C2×C8—5681no—
735C2×C8—1421no—
736C2×C8—1421no—
737C2×C8—1421no—
738C2×C8—1421no—
739C2×C8—1421no—
740C2×C8—1421no—
741C2×C8—1421no—
742C2×C8—1421no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4C22⋊Dic7111yescharacteristic
755C4⋊C4C22⋊Dic7111yescharacteristic
756C4⋊C4C22⋊Dic7111yescharacteristic
757C4⋊C4C22⋊Dic7111yescharacteristic
758C4⋊C4C22⋊Dic7111yescharacteristic
759C4⋊C4C22⋊Dic7111yescharacteristic
760C4⋊C4C22×Dic7111yescharacteristic
761C4⋊C4C22×Dic7111yescharacteristic
762C4⋊C4C22×Dic7111yescharacteristic
763C4⋊C4C22×Dic7111yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4C22⋊Dic7111yescharacteristic
784C22⋊C4C22⋊Dic7111yescharacteristic
785C22⋊C4C22⋊Dic7111yescharacteristic
786C22⋊C4C22⋊Dic7111yescharacteristic
787C22⋊C4C22⋊Dic7111yescharacteristic
788C22⋊C4C22⋊Dic7111yescharacteristic
789C42—21no—
790C42—21no—
791C42—21no—
792C42C22×Dic7111yescharacteristic
793C42C22×Dic7111yescharacteristic
794C42C22×Dic7111yescharacteristic
795C42C2×C22⋊D7111yescharacteristic
796C42C2×C22⋊D7111yescharacteristic
797C42C2×C22⋊D7111yescharacteristic
798C42C2×C22⋊D7111yescharacteristic
799C42C2×C22⋊D7111yescharacteristic
800C42C2×C22⋊D7111yescharacteristic
801C42C23×D7111yescharacteristic
802C23—21no—
803C23—21no—
804C23—21no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23C2×C22⋊Dic7111yescharacteristic
812C23C2×C22⋊Dic7111yescharacteristic
813C23C2×C22⋊Dic7111yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—41no—
817Q8—81no—
818D4—22no—
819D4—22no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—21no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—42no—
831D4—42no—
832D4—81no—
833D4—81no—
834D4—81no—
835D4#1455613512yes—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4C2×C22⋊Dic7111yescharacteristic
871C2×C4C2×C22⋊Dic7111yescharacteristic
872C2×C4C2×C22⋊Dic7111yescharacteristic
873C2×C4C2×C22⋊Dic7111yescharacteristic
874C2×C4C2×C22⋊Dic7111yescharacteristic
875C2×C4C2×C22⋊Dic7111yescharacteristic
876C2×C4C2×C22⋊Dic7111yescharacteristic
877C2×C4C2×C22⋊Dic7111yescharacteristic
878C2×C4C2×C22⋊Dic7111yescharacteristic
879C2×C4C23×Dic7111yescharacteristic
880C2×C4C22×C22⋊D7111yescharacteristic
881C2×C4C22×C22⋊D7111yescharacteristic
882C8—2841no—
883C8—2841no—
884C8—2841no—
885C8—2841no—
886C8—2841no—
887C8—2841no—
888C8—2841no—
889C8—2841no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—84no—
908C22—84no—
909C22#1798601612yes—
910C22C22×C22⋊Dic7111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—41no—
926C4C2×#1455613511yescharacteristic
927C4#1798676611yescharacteristic
928C4#1798680211yescharacteristic
929C4#1798681011yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—42no—
934C2—81no—
935C2—81no—
936C2#2259678911yescharacteristic
937C2#2259686611yescharacteristic
938C2C2×#1798601611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC42C23×D71
Fitting, prime radicalC71×#3481C2
socleC22×C71C22×C22⋊C4
cosocleC42×C71C24
hypercenter#3481D71
hypocenterC71#17521
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #22597465C2semidirect
2. #22596984C2semidirect
3. #22586809C2semidirect
4. #22586805C2semidirect
5. #22586800C2semidirect
6. #22586783C2semidirect
7. #22586774C2semidirect
8. #22586765C2semidirect
9. #22586753C2semidirect
10. #22586748C2semidirect
11. #22586739C2semidirect
12. #22586731C2semidirect
13. #22586727C2semidirect
14. C2×D4⋊(C71⋊C8)C2semidirect
22. #17986056C22semidirect
23. #17986056C22semidirect
24. #17986052C22semidirect
25. #17986052C22semidirect
26. #17986052C22semidirect
27. #17986052C22semidirect
28. #17986052C22semidirect
30. #17986023C22semidirect
31. C2×C4⋊(C71⋊C8)C22semidirect
32. 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
44. D4⋊(C71⋊C8)C22semidirect
45. D4⋊(C71⋊C8)C22semidirect
46. D4⋊(C71⋊C8)C22semidirect
47. D4⋊(C71⋊C8)C22semidirect
48. D4⋊(C71⋊C8)C22semidirect
49. D4⋊(C71⋊C8)C22semidirect
50. D4⋊(C71⋊C8)C22semidirect
51. D4⋊(C71⋊C8)C22semidirect
485. C71#17521semidirect

Maximal subgroups

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

subgroupindex
#225974652
#225969842
#225868092
#225868052
#225868002
#225867832
#225867742
#225867652
#225867532
#225867482
#225867392
#225867312
#225867272
C2×D4⋊(C71⋊C8)2
C71×#34812
#1752171