Finite Group Databasebeta

← #31964285

Subgroups — #31964285

Order 18176.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597457C211yesmaximal, characteristic, complemented
2#22597307C211yesmaximal, characteristic, complemented
3#22586809C211yesmaximal, characteristic, complemented
4#22586805C211yesmaximal, characteristic, complemented
5#22586800C211yesmaximal, characteristic, complemented
6#22586791C211yesmaximal, characteristic, complemented
7#22586783C211yesmaximal, characteristic, complemented
8#22586779C211yesmaximal, characteristic, complemented
9#22586774C211yesmaximal, characteristic, complemented
10#22586765C211yesmaximal, characteristic, complemented
11#22586757C211yesmaximal, characteristic, complemented
12#22586753C211yesmaximal, characteristic, complemented
13#22586748C211yesmaximal, characteristic, complemented
14#22586739C211yesmaximal, characteristic, complemented
15C71×#3460C211yesmaximal, characteristic
16#17986130—21no—
17#17986130—21no—
18#17986077—21no—
19#17986077—21no—
20#17986071—21no—
21#17986071—21no—
22#17986071—21no—
23#17986071—21no—
24#17986056C2211yescharacteristic
25#17986056C2211yescharacteristic, complemented
26#17986052C2211yescharacteristic
27#17986052C2211yescharacteristic, complemented
28#17986052C2211yescharacteristic, complemented
29#17986052C2211yescharacteristic, complemented
30#17986023C2211yescharacteristic
31#17986023C2211yescharacteristic, complemented
32C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
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
40D4⋊(C71⋊C8)C2211yescharacteristic
41D4⋊(C71⋊C8)C2211yescharacteristic
42D4⋊(C71⋊C8)C2211yescharacteristic
43D4⋊(C71⋊C8)C2211yescharacteristic
44D4⋊(C71⋊C8)C2211yescharacteristic
45D4⋊(C71⋊C8)C2211yescharacteristic
46D4⋊(C71⋊C8)C2211yescharacteristic
47D4⋊(C71⋊C8)C2211yescharacteristic
48D4⋊(C71⋊C8)C2211yescharacteristic, complemented
49D4⋊(C71⋊C8)C2211yescharacteristic, complemented
50D4⋊(C71⋊C8)C2211yescharacteristic, complemented
51D4⋊(C71⋊C8)C2211yescharacteristic, complemented
52#544×C71C411yescharacteristic
53#542×C71—21no—
54#542×C71C411yescharacteristic
55#542×C71C411yescharacteristic
56#540×C71—21no—
57#540×C71C411yescharacteristic
58#540×C71C411yescharacteristic
59#538×C71—21no—
60#538×C71—21no—
61#537×C71C411yescharacteristic
62#535×C71C411yescharacteristic
63#535×C71C411yescharacteristic
64#532×C71—21no—
65#532×C71C2211yescharacteristic
66#532×C71C2211yescharacteristic
67#529×C71—21no—
68#529×C71C2211yescharacteristic
69#529×C71C2211yescharacteristic
70#525×C71—21no—
71#525×C71—21no—
72C4×#41×C71C2211yescharacteristic
73C4×#41×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#11765849—21no—
76C2×#11765849—21no—
77C2×#11765849—21no—
78C2×#11765849—21no—
79C22×C71⋊C8—21no—
80C22×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—
97#14556039—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×C71—21no—
109C2×#41×C71C2×C411yescharacteristic
110C2×#41×C71C2×C411yescharacteristic
111C22×D4×C71C2×C411yescharacteristic
112C23×C4×C71—21no—
113C4⋊Q8×C71—21no—
114C4⋊Q8×C71C2×C411yescharacteristic
115C4⋊Q8×C71C2×C411yescharacteristic
116#127×C71—21no—
117#127×C71C2×C411yescharacteristic
118#127×C71C2×C411yescharacteristic
119#126×C71—21no—
120#126×C71—21no—
121#126×C71—21no—
122#126×C71—21no—
123#125×C71—21no—
124#125×C71C2×C411yescharacteristic
125#125×C71C2×C411yescharacteristic
126#124×C71—21no—
127#124×C71—21no—
128#124×C71—21no—
129#124×C71—21no—
130#124×C71—21no—
131#124×C71C2×C411yescharacteristic
132#124×C71C2×C411yescharacteristic
133#123×C71—21no—
134#123×C71—21no—
135#123×C71—21no—
136#123×C71—21no—
137#123×C71—21no—
138#123×C71—21no—
139#123×C71—21no—
140#123×C71—21no—
141C22⋊Q8×C71—21no—
142C22⋊Q8×C71—21no—
143C22⋊Q8×C71—21no—
144C22⋊Q8×C71—21no—
145C22⋊Q8×C71—21no—
146C22⋊Q8×C71C2×C411yescharacteristic
147C22⋊Q8×C71C2×C411yescharacteristic
148#121×C71—21no—
149#121×C71—21no—
150#121×C71—21no—
151#121×C71—21no—
152#121×C71—21no—
153#121×C71—21no—
154#121×C71—21no—
155#121×C71—21no—
156#121×C71—21no—
157#121×C71—21no—
158#121×C71—21no—
159#121×C71C2×C411yescharacteristic
160#121×C71C2×C411yescharacteristic
161#121×C71C2×C411yescharacteristic
162#121×C71C2×C411yescharacteristic
163#121×C71C2×C411yescharacteristic
164#121×C71C2×C411yescharacteristic
165#120×C71—21no—
166#120×C71—21no—
167#120×C71—21no—
168#120×C71—21no—
169C4×Q8×C71C2×C411yescharacteristic
170C4×Q8×C71D411yescharacteristic
171C4×Q8×C71D411yescharacteristic
172C4×Q8×C71C2311yescharacteristic
173C4×D4×C71—21no—
174C4×D4×C71—21no—
175C4×D4×C71—21no—
176C4×D4×C71—21no—
177C4×D4×C71—21no—
178C4×D4×C71—21no—
179C4×D4×C71—21no—
180C4×D4×C71—21no—
181C4×D4×C71C2×C411yescharacteristic
182C4×D4×C71C2×C411yescharacteristic
183C4×D4×C71C2×C411yescharacteristic
184C4×D4×C71D411yescharacteristic
185C4×D4×C71D411yescharacteristic
186C4×D4×C71D411yescharacteristic
187C4×D4×C71D411yescharacteristic
188C4×D4×C71D411yescharacteristic
189C4×D4×C71D411yescharacteristic
190C4×D4×C71C2311yescharacteristic
191C4×D4×C71C2311yescharacteristic
192C4×D4×C71C2311yescharacteristic
193#117×C71—21no—
194#117×C71—21no—
195#117×C71—21no—
196#117×C71C2×C411yescharacteristic
197#117×C71C2×C411yescharacteristic
198#117×C71C2×C411yescharacteristic
199#117×C71C2×C411yescharacteristic
200C2×C4⋊C4×C71C2×C411yescharacteristic
201C2×C22⋊C4×C71—21no—
202C2×C42×C71—21no—
203C2×C42×C71C2311yescharacteristic
204C2×C42×C71C2311yescharacteristic
205C2×C42×C71C2311yescharacteristic
206#11765849—42no—
207#11765849—42no—
208#11765849—81no—
209#11765849—81no—
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—21no—
218C2×C71⋊C8—42no—
219C2×C71⋊C8—81no—
220C24×C71—21no—
221#41×C71—42no—
222#41×C71—42no—
223#41×C71—81no—
224#41×C71—81no—
225#41×C71—81no—
226#41×C71—81no—
227C2×Q8×C71—21no—
228C2×Q8×C71—21no—
229C2×Q8×C71C22⋊C411yescharacteristic
230C2×Q8×C71C22×C411yescharacteristic
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—21no—
241C2×D4×C71—21no—
242C2×D4×C71—21no—
243C2×D4×C71—42no—
244C2×D4×C71C22⋊C411yescharacteristic
245C2×D4×C71C22⋊C411yescharacteristic
246C2×D4×C71C22⋊C411yescharacteristic
247C2×D4×C71C22×C411yescharacteristic
248C2×D4×C71C22×C411yescharacteristic
249C2×D4×C71C22×C411yescharacteristic
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—81no—
259C22×C4×C71—81no—
260C22×C4×C71C22×C411yescharacteristic
261C22×C4×C71C22×C411yescharacteristic
262C22×C4×C71C22×C411yescharacteristic
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
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×C71—21no—
279C4⋊C4×C71—21no—
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
288C4⋊C4×C71C22×C411yescharacteristic
289C4⋊C4×C71C22×C411yescharacteristic
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×C71—21no—
307C22⋊C4×C71—21no—
308C22⋊C4×C71—21no—
309C22⋊C4×C71C22⋊C411yescharacteristic
310C22⋊C4×C71C22⋊C411yescharacteristic
311C22⋊C4×C71C22⋊C411yescharacteristic
312C22⋊C4×C71C22⋊C411yescharacteristic
313C22⋊C4×C71C22⋊C411yescharacteristic
314C22⋊C4×C71C22⋊C411yescharacteristic
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—21no—
331C23×C71—42no—
332C23×C71—81no—
333C23×C71—81no—
334C23×C71C2×C22⋊C411yescharacteristic
335C23×C71C2×C22⋊C411yescharacteristic
336C23×C71C2×C22⋊C411yescharacteristic
337Q8×C71—22no—
338Q8×C71—41no—
339Q8×C71—81no—
340Q8×C71—81no—
341D4×C71—22no—
342D4×C71—22no—
343D4×C71—22no—
344D4×C71—41no—
345D4×C71—41no—
346D4×C71—41no—
347D4×C71—42no—
348D4×C71—42no—
349D4×C71—81no—
350D4×C71—81no—
351D4×C71—81no—
352D4×C71—81no—
353D4×C71—81no—
354D4×C71—81no—
355D4×C71—81no—
356D4×C71—81no—
357D4×C71—81no—
358D4×C71—81no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
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—21no—
373C2×C4×C71—41no—
374C2×C4×C71—41no—
375C2×C4×C71—41no—
376C2×C4×C71—42no—
377C2×C4×C71—41no—
378C2×C4×C71—41no—
379C2×C4×C71—41no—
380C2×C4×C71—41no—
381C2×C4×C71—41no—
382C2×C4×C71—41no—
383C2×C4×C71—81no—
384C2×C4×C71—81no—
385C2×C4×C71—81no—
386C2×C4×C71—81no—
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×C71C2×C22⋊C411yescharacteristic
396C2×C4×C71C23×C411yescharacteristic
397C2×C4×C71C22×D411yescharacteristic
398C2×C4×C71C22×D411yescharacteristic
399C71⋊C8—22no—
400C71⋊C8—41no—
401C71⋊C8—41no—
402C71⋊C8—41no—
403C71⋊C8—41no—
404C71⋊C8—41no—
405C71⋊C8—41no—
406C71⋊C8—41no—
407C22×C71—21no—
408C22×C71—21no—
409C22×C71—21no—
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—41no—
422C22×C71—41no—
423C22×C71—41no—
424C22×C71—41no—
425C22×C71—84no—
426C22×C71C22×C22⋊C411yescharacteristic
427C4×C71—21no—
428C4×C71—21no—
429C4×C71—21no—
430C4×C71—21no—
431C4×C71—21no—
432C4×C71—21no—
433C4×C71—21no—
434C4×C71—21no—
435C4×C71—21no—
436C4×C71—21no—
437C4×C71—41no—
438C4×C71—41no—
439C4×C71—41no—
440C4×C71—41no—
441C4×C71—41no—
442C4×C71#56812yes—
443C4×C71#57611yescharacteristic
444C4×C71#57711yescharacteristic
445#17505—711nomaximal, Sylow
446C2×C71—41no—
447C2×C71—41no—
448C2×C71—41no—
449C2×C71—81no—
450C2×C71—81no—
451C2×C71—81no—
452C2×C71#287911yescharacteristic
453C2×C71#289711yescharacteristic
454C2×C71#290111yescharacteristic
455#3460D7111yescharacteristic
456#2989—711no—
457#2965—711no—
458#1496—711no—
459#1495—711no—
460#1494—711no—
461#1492—711no—
462#1490—711no—
463#1489—711no—
464#1488—711no—
465#1486—711no—
466#1484—711no—
467#1483—711no—
468#1482—711no—
469#1480—711no—
470C71#1750511yescharacteristic, complemented, Sylow
471#544Dic7111yescharacteristic
472#542—21no—
473#542Dic7111yescharacteristic
474#542Dic7111yescharacteristic
475#540—21no—
476#540Dic7111yescharacteristic
477#540Dic7111yescharacteristic
478#538—21no—
479#538—21no—
480#537Dic7111yescharacteristic
481#535Dic7111yescharacteristic
482#535Dic7111yescharacteristic
483#532—21no—
484#532C2×D7111yescharacteristic
485#532C2×D7111yescharacteristic
486#529—21no—
487#529C2×D7111yescharacteristic
488#529C2×D7111yescharacteristic
489#525—21no—
490#525—21no—
491C4×#41C2×D7111yescharacteristic
492C4×#41C2×D7111yescharacteristic
493C2×C4×D4C2×D7111yescharacteristic
494#446—1421no—
495#446—1421no—
496#436—1421no—
497#436—1421no—
498#435—1421no—
499#435—1421no—
500#435—1421no—
501#435—1421no—
502#432—711no—
503#432—711no—
504#431—711no—
505#431—711no—
506#431—711no—
507#431—711no—
508#423—711no—
509#423—711no—
510C2×C4⋊C8—711no—
511C4×M16—711no—
512C4×M16—711no—
513C2×C4×C8—711no—
514Q8⋊C8—711no—
515Q8⋊C8—711no—
516Q8⋊C8—711no—
517Q8⋊C8—711no—
518D4⋊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—
527D4⋊C8—711no—
528D4⋊C8—711no—
529D4⋊C8—711no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41C2×Dic7111yescharacteristic
533C2×#41C2×Dic7111yescharacteristic
534C22×D4C2×Dic7111yescharacteristic
535C23×C4—21no—
536C2×M16—1421no—
537C2×M16—1421no—
538C2×M16—1421no—
539C2×M16—1421no—
540C22×C8—1421no—
541C22×C8—1421no—
542C4⋊Q8—21no—
543C4⋊Q8C2×Dic7111yescharacteristic
544C4⋊Q8C2×Dic7111yescharacteristic
545#127—21no—
546#127C2×Dic7111yescharacteristic
547#127C2×Dic7111yescharacteristic
548#126—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#125—21no—
553#125C2×Dic7111yescharacteristic
554#125C2×Dic7111yescharacteristic
555#124—21no—
556#124—21no—
557#124—21no—
558#124—21no—
559#124—21no—
560#124C2×Dic7111yescharacteristic
561#124C2×Dic7111yescharacteristic
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8C2×Dic7111yescharacteristic
576C22⋊Q8C2×Dic7111yescharacteristic
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121C2×Dic7111yescharacteristic
589#121C2×Dic7111yescharacteristic
590#121C2×Dic7111yescharacteristic
591#121C2×Dic7111yescharacteristic
592#121C2×Dic7111yescharacteristic
593#121C2×Dic7111yescharacteristic
594#120—21no—
595#120—21no—
596#120—21no—
597#120—21no—
598C4×Q8C2×Dic7111yescharacteristic
599C4×Q8C22⋊D7111yescharacteristic
600C4×Q8C22⋊D7111yescharacteristic
601C4×Q8C22×D7111yescharacteristic
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4C2×Dic7111yescharacteristic
611C4×D4C2×Dic7111yescharacteristic
612C4×D4C2×Dic7111yescharacteristic
613C4×D4C22⋊D7111yescharacteristic
614C4×D4C22⋊D7111yescharacteristic
615C4×D4C22⋊D7111yescharacteristic
616C4×D4C22⋊D7111yescharacteristic
617C4×D4C22⋊D7111yescharacteristic
618C4×D4C22⋊D7111yescharacteristic
619C4×D4C22×D7111yescharacteristic
620C4×D4C22×D7111yescharacteristic
621C4×D4C22×D7111yescharacteristic
622#117—21no—
623#117—21no—
624#117—21no—
625#117C2×Dic7111yescharacteristic
626#117C2×Dic7111yescharacteristic
627#117C2×Dic7111yescharacteristic
628#117C2×Dic7111yescharacteristic
629C2×C4⋊C4C2×Dic7111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C42—21no—
632C2×C42C22×D7111yescharacteristic
633C2×C42C22×D7111yescharacteristic
634C2×C42C22×D7111yescharacteristic
635C4⋊C8—711no—
636C4⋊C8—711no—
637C4⋊C8—711no—
638C4⋊C8—711no—
639C4⋊C8—1421no—
640C4⋊C8—1421no—
641C4⋊C8—1421no—
642C4⋊C8—1421no—
643C4⋊C8—1421no—
644C4⋊C8—1421no—
645C22⋊C8—1421no—
646C22⋊C8—1421no—
647C22⋊C8—1421no—
648C22⋊C8—1421no—
649C22⋊C8—1421no—
650C22⋊C8—1421no—
651#97—1421no—
652#97—1421no—
653#97—1421no—
654#97—1421no—
655C4×C8—711no—
656C4×C8—711no—
657C4×C8—711no—
658C4×C8—711no—
659C4×C8—1421no—
660C4×C8—1421no—
661C24—21no—
662#41—42no—
663#41—42no—
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8C22⋊Dic7111yescharacteristic
671C2×Q8C22×Dic7111yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4C22⋊Dic7111yescharacteristic
686C2×D4C22⋊Dic7111yescharacteristic
687C2×D4C22⋊Dic7111yescharacteristic
688C2×D4C22×Dic7111yescharacteristic
689C2×D4C22×Dic7111yescharacteristic
690C2×D4C22×Dic7111yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C22×Dic7111yescharacteristic
702C22×C4C22×Dic7111yescharacteristic
703C22×C4C22×Dic7111yescharacteristic
704C22×C4C2×C22⋊D7111yescharacteristic
705C22×C4C2×C22⋊D7111yescharacteristic
706C22×C4C2×C22⋊D7111yescharacteristic
707C22×C4C2×C22⋊D7111yescharacteristic
708C22×C4C2×C22⋊D7111yescharacteristic
709C22×C4C2×C22⋊D7111yescharacteristic
710M16—2842no—
711M16—2842no—
712M16—5681no—
713M16—5681no—
714C2×C8—2842no—
715C2×C8—5681no—
716C2×C8—1421no—
717C2×C8—1421no—
718C2×C8—1421no—
719C2×C8—1421no—
720C2×C8—1421no—
721C2×C8—1421no—
722C2×C8—1421no—
723C2×C8—1421no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4C22⋊Dic7111yescharacteristic
736C4⋊C4C22⋊Dic7111yescharacteristic
737C4⋊C4C22⋊Dic7111yescharacteristic
738C4⋊C4C22⋊Dic7111yescharacteristic
739C4⋊C4C22⋊Dic7111yescharacteristic
740C4⋊C4C22⋊Dic7111yescharacteristic
741C4⋊C4C22×Dic7111yescharacteristic
742C4⋊C4C22×Dic7111yescharacteristic
743C4⋊C4C22×Dic7111yescharacteristic
744C4⋊C4C22×Dic7111yescharacteristic
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⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4C22⋊Dic7111yescharacteristic
765C22⋊C4C22⋊Dic7111yescharacteristic
766C22⋊C4C22⋊Dic7111yescharacteristic
767C22⋊C4C22⋊Dic7111yescharacteristic
768C22⋊C4C22⋊Dic7111yescharacteristic
769C22⋊C4C22⋊Dic7111yescharacteristic
770C42—21no—
771C42—21no—
772C42—21no—
773C42C22×Dic7111yescharacteristic
774C42C22×Dic7111yescharacteristic
775C42C22×Dic7111yescharacteristic
776C42C2×C22⋊D7111yescharacteristic
777C42C2×C22⋊D7111yescharacteristic
778C42C2×C22⋊D7111yescharacteristic
779C42C2×C22⋊D7111yescharacteristic
780C42C2×C22⋊D7111yescharacteristic
781C42C2×C22⋊D7111yescharacteristic
782C42C23×D7111yescharacteristic
783C23—21no—
784C23—21no—
785C23—21no—
786C23—42no—
787C23—81no—
788C23—81no—
789C23C2×C22⋊Dic7111yescharacteristic
790C23C2×C22⋊Dic7111yescharacteristic
791C23C2×C22⋊Dic7111yescharacteristic
792Q8—22no—
793Q8—41no—
794Q8—81no—
795Q8—81no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4C2×C22⋊Dic7111yescharacteristic
843C2×C4C2×C22⋊Dic7111yescharacteristic
844C2×C4C2×C22⋊Dic7111yescharacteristic
845C2×C4C2×C22⋊Dic7111yescharacteristic
846C2×C4C2×C22⋊Dic7111yescharacteristic
847C2×C4C2×C22⋊Dic7111yescharacteristic
848C2×C4C2×C22⋊Dic7111yescharacteristic
849C2×C4C2×C22⋊Dic7111yescharacteristic
850C2×C4C2×C22⋊Dic7111yescharacteristic
851C2×C4C23×Dic7111yescharacteristic
852C2×C4C22×C22⋊D7111yescharacteristic
853C2×C4C22×C22⋊D7111yescharacteristic
854C8—2841no—
855C8—2841no—
856C8—2841no—
857C8—2841no—
858C8—2841no—
859C8—2841no—
860C8—2841no—
861C8—1422no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—84no—
881C22C22×C22⋊Dic7111yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4#1798676612yes—
898C4#1798680211yescharacteristic
899C4#1798681011yescharacteristic
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—81no—
905C2—81no—
906C2#2259678511yescharacteristic
907C2#2259686611yescharacteristic
908C2#2259688711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC42C23×D71
Fitting, prime radicalC71×#3460C2
socleC22×C71C22×C22⋊C4
cosocleC42×C71C24
hypercenter#3460D71
hypocenterC71#17505
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #22597457C2semidirect
2. #22597307C2semidirect
3. #22586809C2semidirect
4. #22586805C2semidirect
5. #22586800C2semidirect
6. #22586791C2semidirect
7. #22586783C2semidirect
8. #22586779C2semidirect
9. #22586774C2semidirect
10. #22586765C2semidirect
11. #22586757C2semidirect
12. #22586753C2semidirect
13. #22586748C2semidirect
14. #22586739C2semidirect
25. #17986056C22semidirect
27. #17986052C22semidirect
28. #17986052C22semidirect
29. #17986052C22semidirect
31. #17986023C22semidirect
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
48. D4⋊(C71⋊C8)C22semidirect
49. D4⋊(C71⋊C8)C22semidirect
50. D4⋊(C71⋊C8)C22semidirect
51. D4⋊(C71⋊C8)C22semidirect
470. C71#17505semidirect

Maximal subgroups

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

subgroupindex
#225974572
#225973072
#225868092
#225868052
#225868002
#225867912
#225867832
#225867792
#225867742
#225867652
#225867572
#225867532
#225867482
#225867392
C71×#34602
#1750571