Finite Group Databasebeta

← #30617204

Subgroups — #30617204

Order 15616.

844 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462306C211yesmaximal, characteristic
2#21462256C211yesmaximal, characteristic
3#21461899C211yesmaximal, characteristic, complemented
4#21461899C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461804C211yesmaximal, characteristic
8#21461768C211yesmaximal, characteristic
9#21461724C211yesmaximal, characteristic
10#21461635C211yesmaximal, characteristic, complemented
11#107×#6923C211yesmaximal, characteristic, complemented
12#21461592C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic
15#485×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×#14519856C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519846C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23D61⋊(C22⋊C8)C2211yescharacteristic
24C2×#14519831C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26(C2×#6923)⋊Q8C2211yescharacteristic
27#16840713—21no—
28#16840713C2211yescharacteristic
29#16840712—21no—
30#16840712—21no—
31#16840711—21no—
32#16840704C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4×C4⋊#6923—21no—
39C4×C4⋊#6923—21no—
40C22⋊C4×#6923—21no—
41C22⋊C4×#6923—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C22⋊Q8×D61C2211yescharacteristic
53#117×D61C2211yescharacteristic
54#16840106C411yescharacteristic, complemented
55#16840105C411yescharacteristic, complemented
56#16840104C411yescharacteristic, complemented
57#16840103C411yescharacteristic, complemented
58#16840102C411yescharacteristic, complemented
59#16840101C411yescharacteristic, complemented
60#16840100C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65C22⋊C8×D61C2211yescharacteristic
66C61×#485C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—22no—
72#14519856—22no—
73#14519856—22no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—22no—
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923D411yescharacteristic
80C2×C4⋊#6923D411yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923D411yescharacteristic
87C2×C22⋊#6923D411yescharacteristic
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—22no—
97#14519846—22no—
98#14519840—22no—
99#14519840—22no—
100#14519834—21no—
101C22⋊#92420—21no—
102#14519831—22no—
103C8×#6923—22no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113C2×Q8×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C2×C8×D61C2311yescharacteristic
116C2×C8×D61C2311yescharacteristic
117#14519757C2×C411yescharacteristic
118#14519756C2×C411yescharacteristic
119#14519755—21no—
120#14519754—21no—
121#14519753C2×C411yescharacteristic
122#14519736C2×C411yescharacteristic
123#14519735C2×C411yescharacteristic
124#14519735C2×C411yescharacteristic
125#14519734—21no—
126#14519733—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C22⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C42×D61—21no—
134#14519711C2×C411yescharacteristic, complemented
135#14519710C2×C411yescharacteristic, complemented
136#14519710C2×C411yescharacteristic, complemented
137#14519709C2×C411yescharacteristic, complemented
138#14519708C2×C411yescharacteristic, complemented
139#14519708C2×C411yescharacteristic, complemented
140#14519702C2×C411yescharacteristic, complemented
141#14519702C2×C411yescharacteristic, complemented
142#14519701C2×C411yescharacteristic, complemented
143#14519701C2×C411yescharacteristic, complemented
144#14519700C2×C411yescharacteristic, complemented
145#14519700C2×C411yescharacteristic, complemented
146C22⋊#92418C2×C411yescharacteristic
147#14519689C2×C411yescharacteristic
148#14519689C2×C411yescharacteristic
149C22⋊Q8×C61C2×C411yescharacteristic
150#117×C61C2×C411yescharacteristic
151#107×C61C2×C411yescharacteristic, complemented
152#106×C61C2×C411yescharacteristic, complemented
153#103×C61C2×C411yescharacteristic, complemented
154#103×C61C2×C411yescharacteristic, complemented
155C22⋊C8×C61C2×C411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—24no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—81no—
163C22×#6923—81no—
164C22×#6923C2×D411yescharacteristic
165C22×#6923C2×D411yescharacteristic
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C2×Q8×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×Dic61#4111yescharacteristic
171Q8×D61—21no—
172Q8×D61—21no—
173Q8×D61—21no—
174Q8×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61C22×C411yescharacteristic
184C2×C4×D61C2×D411yescharacteristic
185C2×C4×D61#4111yescharacteristic
186C2×C4×D61C2411yescharacteristic
187C2×Dic122—21no—
188C2×Dic122C22×C411yescharacteristic
189C22⋊#6923—22no—
190C22⋊#6923—22no—
191C22⋊#6923—81no—
192C2×#92420—21no—
193C2×#92420—21no—
194C4⋊#6923—24no—
195C4⋊#6923—22no—
196C4⋊#6923—22no—
197C4⋊#6923—21no—
198C4⋊#6923—21no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—42no—
204C4⋊#6923—81no—
205C4⋊#6923#4112yes—
206C4⋊#6923#4112yes—
207C4×#6923—21no—
208C4×#6923—21no—
209C4×#6923—42no—
210C4×#6923—81no—
211C4×#6923—81no—
212C4×#6923—81no—
213C4×#6923—81no—
214C4×#6923—81no—
215C4×#6923#4112yes—
216C4×#6923#4112yes—
217D61⋊C8—21no—
218D61⋊C8—21no—
219D61⋊C8—21no—
220D61⋊C8—21no—
221C2×C8×C61C22×C411yescharacteristic
222C2×C8×C61C22×C411yescharacteristic
223C4⋊C4×C61—21no—
224C4⋊C4×C61C22×C411yescharacteristic
225C4⋊C4×C61C22×C411yescharacteristic
226C4⋊C4×C61C22×C411yescharacteristic
227C22⋊C4×C61—21no—
228C22⋊C4×C61—21no—
229C42×C61—21no—
230C22⋊Dic61—21no—
231C22⋊Dic61—21no—
232#11758198—21no—
233#11758198—21no—
234#11758198—21no—
235#11758198—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61C22×C411yescharacteristic
238C4⋊Dic61C22×C411yescharacteristic
239C4⋊Dic61C22×C411yescharacteristic
240#11758196—21no—
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244#11758196—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C2×#92418C22×C411yescharacteristic
249C2×#92418C22×C411yescharacteristic
250C8×D61—21no—
251C8×D61—21no—
252C8×D61—21no—
253C8×D61—21no—
254C23×C61C4×D411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61C4×D411yescharacteristic
262C22×D61C22×D411yescharacteristic
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—22no—
270C2×#6923—22no—
271C2×#6923—21no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—84no—
286C2×#6923#12312yes—
287C2×#6923#12312yes—
288Q8×C61—21no—
289Q8×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61C4×D411yescharacteristic
305C2×Dic61C2×#4111yescharacteristic
306C4×D61—21no—
307C4×D61—21no—
308C4×D61—21no—
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61C2×#4111yescharacteristic
321C4×D61C2×#4111yescharacteristic
322C4×D61C2×#4111yescharacteristic
323C4×D61C2×#4111yescharacteristic
324Dic122—21no—
325Dic122—21no—
326Dic122—41no—
327Dic122—41no—
328#92420—41no—
329#92420—41no—
330C8×C61—21no—
331C8×C61—21no—
332#92418—21no—
333#92418—21no—
334#21589—611nomaximal, Sylow
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61C2×C4×D411yescharacteristic
339C2×D61—21no—
340C2×D61—21no—
341C2×D61—21no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61C2×#12311yescharacteristic
347C2×D61#52511yescharacteristic
348C2×D61#57611yescharacteristic
349C2×D61#57711yescharacteristic
350C2×D61#57811yescharacteristic
351C2×D61#57811yescharacteristic
352#6923—22no—
353#6923—22no—
354#6923—41no—
355#6923—41no—
356#6923—42no—
357#6923—42no—
358#6923—81no—
359#6923—81no—
360C4×C61—21no—
361C4×C61—41no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61C4×#4111yescharacteristic
366C4×C61C4×#4111yescharacteristic
367Dic61—21no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61#52911yescharacteristic
373Dic61#52911yescharacteristic
374C2×#485—611no—
375#2323—611no—
376#2274—611no—
377#1928—611no—
378#1928—611no—
379#1920—611no—
380#1918—611no—
381#1872—611no—
382#1852—611no—
383#1825—611no—
384#1776—611no—
385C4×#107—611no—
386#1763—611no—
387C4×#103—611no—
388#1750—611no—
389C2×C61—41no—
390C2×C61C4×#12311yescharacteristic
391C2×C61#294711yescharacteristic
392C2×C61#295111yescharacteristic
393D61—41no—
394D61#309711yescharacteristic
395D61#309811yescharacteristic
396D61#311811yescharacteristic
397D61#312711yescharacteristic
398C2×C22⋊Q8—611no—
399C2×C4×Q8—611no—
400C2×#117—611no—
401C2×#117—611no—
402C22×C4⋊C4—611no—
403#485—611no—
404#485—611no—
405#485—611no—
406#485—611no—
407#485—611no—
408#485—611no—
409#485—611no—
410#485#692311yescharacteristic, complemented
411C2×#107—611no—
412C2×#107—611no—
413C2×#107—611no—
414C2×#106—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×#97—611no—
422C2×C4×C8—611no—
423#391—611no—
424#389—611no—
425#389—1221no—
426#388—1221no—
427#388—1221no—
428#387—1221no—
429#380—611no—
430C4×C4⋊C4—611no—
431C4×C4⋊C4—611no—
432C4×C4⋊C4—611no—
433C4×C4⋊C4—611no—
434C4×C4⋊C4—611no—
435C4×C4⋊C4—1221no—
436C4×C4⋊C4—1221no—
437C4×C22⋊C4—1221no—
438C4×C22⋊C4—1221no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2158911yescharacteristic, complemented, Sylow
450C22×Q8—611no—
451C23×C4—611no—
452C23×C4—1221no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22⋊Q8—611no—
458C22⋊Q8—611no—
459C22⋊Q8—611no—
460C22⋊Q8—1221no—
461C22⋊Q8—1221no—
462C22⋊Q8C2×#692311yescharacteristic
463C4×Q8—1222no—
464C4×Q8—1222no—
465#117—611no—
466#117—611no—
467#117—611no—
468#117—1221no—
469#117—1222no—
470#117—1222no—
471#117—1221no—
472#117C2×#692311yescharacteristic
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—1221no—
496C2×C42—1221no—
497C2×C42—1221no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42—1221no—
502#107—611no—
503#107—611no—
504#107—611no—
505#107—1222no—
506#107—1222no—
507#107C2×#692311yescharacteristic, complemented
508#106—611no—
509#106—611no—
510#106—611no—
511#106C2×#692311yescharacteristic, complemented
512#103—611no—
513#103—611no—
514#103—611no—
515#103—611no—
516#103—611no—
517#103—611no—
518#103—1222no—
519#103—1222no—
520#103C2×#692311yescharacteristic, complemented
521#103C2×#692311yescharacteristic, complemented
522C22⋊C8—611no—
523C22⋊C8—611no—
524C22⋊C8—611no—
525C22⋊C8—1221no—
526C22⋊C8—1221no—
527C22⋊C8C2×#692311yescharacteristic
528#97—1222no—
529C4×C8—1222no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—611no—
540C2×Q8—611no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8C22×#692311yescharacteristic
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1224no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—4881no—
571C22×C4C22×#692311yescharacteristic
572C2×C8—611no—
573C2×C8—611no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8C22×#692311yescharacteristic
585C2×C8C22×#692311yescharacteristic
586C4⋊C4—21no—
587C4⋊C4—612no—
588C4⋊C4—612no—
589C4⋊C4—611no—
590C4⋊C4—611no—
591C4⋊C4—611no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1224no—
606C4⋊C4—1221no—
607C4⋊C4—4881no—
608C4⋊C4—2442no—
609C4⋊C4C22×#692311yescharacteristic
610C4⋊C4C22×#692311yescharacteristic
611C4⋊C4C22×#692311yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—1221no—
615C22⋊C4—1221no—
616C22⋊C4—1221no—
617C22⋊C4—1221no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1221no—
621C22⋊C4—1221no—
622C22⋊C4—4881no—
623C42—21no—
624C42—612no—
625C42—612no—
626C42—1221no—
627C42—1221no—
628C42—1221no—
629C42—1221no—
630C42—1221no—
631C42—4881no—
632C42—4881no—
633C42—4881no—
634C42—4881no—
635C42—4881no—
636C42—2442no—
637C23—611no—
638C23—611no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23D4×#692311yescharacteristic
646Q8—21no—
647Q8—21no—
648Q8—1221no—
649Q8—1221no—
650Q8—2441no—
651Q8—2441no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—611no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—4884no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4D4×#692311yescharacteristic
710C2×C4C23×#692311yescharacteristic
711C8—21no—
712C8—21no—
713C8—1221no—
714C8—1221no—
715C8—2441no—
716C8—2441no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—611no—
721C22—611no—
722C22—611no—
723C22—611no—
724C22—611no—
725C22—611no—
726C22—1221no—
727C22—1221no—
728C22—1221no—
729C22—2441no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22C2×D4×#692311yescharacteristic
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—611no—
740C4—611no—
741C4—1222no—
742C4—1222no—
743C4—1221no—
744C4—4881no—
745C4—4881no—
746C4—2441no—
747C4—2441no—
748C4—2442no—
749C4—2442no—
750C4—2441no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C4#41×#692311yescharacteristic
755C4#41×#692311yescharacteristic
756C2—41no—
757C2—611no—
758C2—611no—
759C2—611no—
760C2—611no—
761C2—2441no—
762C2#123×#692311yescharacteristic
763C2#2146257711yescharacteristic
764C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#485C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#485#6923
hypocenterC61#21589
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #21461899C2semidirect
4. #21461899C2semidirect
5. #21461882C2semidirect
6. #21461880C2semidirect
10. #21461635C2semidirect
11. #107×#6923C2semidirect
12. #21461592C2semidirect
13. #103×#6923C2semidirect
54. #16840106C4semidirect
55. #16840105C4semidirect
56. #16840104C4semidirect
57. #16840103C4semidirect
58. #16840102C4semidirect
59. #16840101C4semidirect
60. #16840100C4semidirect
66. C61×#485C4semidirect
134. #14519711C2×C4semidirect
135. #14519710C2×C4semidirect
136. #14519710C2×C4semidirect
137. #14519709C2×C4semidirect
138. #14519708C2×C4semidirect
139. #14519708C2×C4semidirect
140. #14519702C2×C4semidirect
141. #14519702C2×C4semidirect
142. #14519701C2×C4semidirect
143. #14519701C2×C4semidirect
144. #14519700C2×C4semidirect
145. #14519700C2×C4semidirect
151. #107×C61C2×C4semidirect
152. #106×C61C2×C4semidirect
153. #103×C61C2×C4semidirect
154. #103×C61C2×C4semidirect
410. #485#6923semidirect
449. C61#21589semidirect
507. #107C2×#6923semidirect
511. #106C2×#6923semidirect
520. #103C2×#6923semidirect
521. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623062
#214622562
#214618992
#214618822
#214618802
#214618042
#214617682
#214617242
#214616352
#107×#69232
#214615922
#103×#69232
#214615502
#485×D612
#2158961