Finite Group Databasebeta

← #30616400

Subgroups — #30616400

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462278C211yesmaximal, characteristic, complemented
2#21462276C211yesmaximal, characteristic
3#21461969C211yesmaximal, characteristic
4#21461964C211yesmaximal, characteristic
5#21461924C211yesmaximal, characteristic, complemented
6#21461923C211yesmaximal, characteristic, complemented
7#21461911C211yesmaximal, characteristic
8#21461910C211yesmaximal, characteristic, complemented
9#21461909C211yesmaximal, characteristic
10#21461908C211yesmaximal, characteristic, complemented
11#21461633C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic
14#97×#6923C211yesmaximal, characteristic, complemented
15#440×D61C211yesmaximal, characteristic
16C2×#14519856—21no—
17C2×#14519846C2211yescharacteristic
18C2×#14519845C2211yescharacteristic
19C2×#14519840C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23#16840721C2211yescharacteristic
24C2×#14519831C2211yescharacteristic
25C2×#14519831C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28(C2×#6923)⋊Q8C2211yescharacteristic
29(C2×#6923)⋊Q8C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840714C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840713C2211yescharacteristic
34#16840713C2211yescharacteristic
35#16840713C2211yescharacteristic
36#16840712—21no—
37#16840712—21no—
38#16840711—21no—
39#16840711—21no—
40C4×C4⋊#6923—21no—
41C4×C4⋊#6923C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C4×C22⋊#6923—21no—
44#16840698—21no—
45C42×#6923C2211yescharacteristic
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839865C411yescharacteristic, complemented
56#16839864C411yescharacteristic, complemented
57#16839863C411yescharacteristic, complemented
58#16839862C411yescharacteristic, complemented
59#16839861C411yescharacteristic, complemented
60#16839860C411yescharacteristic, complemented
61#16839859C411yescharacteristic, complemented
62#107×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#440C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69#14519856—44no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—21no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923C2311yescharacteristic
75C2×C4⋊#6923C2311yescharacteristic
76C2×C4⋊#6923C2311yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C22⋊#6923—21no—
79C2×C22⋊#6923—21no—
80C2×C22⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923D411yescharacteristic
85C2×C4×#6923D411yescharacteristic
86C2×C4×#6923D411yescharacteristic
87C2×C4×#6923D411yescharacteristic
88C2×C4×#6923C2311yescharacteristic
89C2×C4×#6923C2311yescharacteristic
90#14519846—22no—
91#14519845—22no—
92#14519840—22no—
93#14519840—22no—
94#14519839—22no—
95#14519839—22no—
96#14519832—21no—
97#14519832—21no—
98#14519831—22no—
99#14519831—22no—
100C8×#6923—22no—
101C8×#6923—22no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
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—
112C2×Q8×D61C2311yescharacteristic
113C2×D4×D61C2311yescharacteristic
114C22×C4×D61—21no—
115C2×#11758190C2×C411yescharacteristic
116C2×#11758200C2×C411yescharacteristic
117C2×#11758201C2×C411yescharacteristic
118SD16×D61—22no—
119SD16×D61—22no—
120C2×C8×D61C2311yescharacteristic
121C2×C8×D61C2311yescharacteristic
122Q8×Dic61C2×C411yescharacteristic
123C4×Dic122—21no—
124C4×Dic122C2×C411yescharacteristic
125#14519742—21no—
126#14519742C2×C411yescharacteristic
127C4×D244C2×C411yescharacteristic
128D4×Dic61C2×C411yescharacteristic
129#14519739C2×C411yescharacteristic
130C4×C22⋊D61—21no—
131#14519737—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61C2311yescharacteristic
134C4⋊C4×D61C2311yescharacteristic
135C22⋊C4×D61—21no—
136C42×D61—21no—
137C42×D61C2311yescharacteristic
138#14519711C2×C411yescharacteristic
139#14519710C2×C411yescharacteristic
140#14519710C2×C411yescharacteristic
141#14519702C2×C411yescharacteristic
142#14519701C2×C411yescharacteristic
143#14519700C2×C411yescharacteristic
144#14519699C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#14519688C2×C411yescharacteristic
148#14519687C2×C411yescharacteristic
149#14519687C2×C411yescharacteristic
150C2×SD16×C61C2×C411yescharacteristic
151C4×Q8×C61C2×C411yescharacteristic
152C4×D4×C61C2×C411yescharacteristic
153#107×C61C2×C411yescharacteristic
154#103×C61C2×C411yescharacteristic
155#102×C61C2×C411yescharacteristic
156#97×C61C2×C411yescharacteristic
157C23×D61—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923C2×D411yescharacteristic
163C22×#6923C2×D411yescharacteristic
164C22×#6923C2×D411yescharacteristic
165C22×#6923C2×D411yescharacteristic
166C2×Q8×C61C22×C411yescharacteristic
167C2×D4×C61C22×C411yescharacteristic
168C22×C4×C61—21no—
169C2×C22⋊D61—21no—
170C22×Dic61—21no—
171Q8×D61—21no—
172Q8×D61—21no—
173Q8×D61—21no—
174Q8×D61—21no—
175D4×D61—21no—
176D4×D61—21no—
177D4×D61—21no—
178D4×D61—21no—
179C2×D244C22×C411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2411yescharacteristic
190C2×Dic122—21no—
191C2×Dic122C22×C411yescharacteristic
192C22⋊#6923—42no—
193C22⋊#6923—42no—
194C22⋊#6923—42no—
195C22⋊#6923—42no—
196C2×#92420—21no—
197C2×#92420—21no—
198C4⋊#6923—21no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—42no—
207C4⋊#6923—42no—
208C4⋊#6923—42no—
209C4⋊#6923—42no—
210C4×#6923—22no—
211C4×#6923—22no—
212C4×#6923—21no—
213C4×#6923—21no—
214C4×#6923—21no—
215C4×#6923—21no—
216C4×#6923—41no—
217C4×#6923—41no—
218C4×#6923—42no—
219C4×#6923—42no—
220D61⋊C8—21no—
221D61⋊C8—21no—
222D61⋊C8#4112yes—
223D61⋊C8#4112yes—
224SD16×C61—22no—
225C2×C8×C61C22×C411yescharacteristic
226C2×C8×C61C22×C411yescharacteristic
227C4⋊C4×C61—21no—
228C4⋊C4×C61C22×C411yescharacteristic
229C4⋊C4×C61C22×C411yescharacteristic
230C22⋊C4×C61—21no—
231C42×C61—21no—
232C42×C61C22×C411yescharacteristic
233C22⋊Dic61—21no—
234#11758201—22no—
235#11758200—22no—
236#11758198—21no—
237#11758198—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61C22×C411yescharacteristic
240C4⋊Dic61C22×C411yescharacteristic
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244#11758196—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61C22×C411yescharacteristic
249C4×Dic61#4111yescharacteristic
250C4×Dic61#4111yescharacteristic
251C2×#92418C22×C411yescharacteristic
252C2×#92418C22×C411yescharacteristic
253#11758190—22no—
254C8×D61—21no—
255C8×D61—21no—
256C8×D61#4112yes—
257C8×D61#4112yes—
258C23×C61—21no—
259C22×D61—21no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61C22×D411yescharacteristic
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—21no—
271C2×#6923—21no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—21no—
276C2×#6923—21no—
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—41no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—41no—
289C2×#6923AGL(1,ℤ/8)12yes—
290C2×#6923#13712yes—
291Q8×C61—21no—
292Q8×C61—21no—
293D4×C61—21no—
294D4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—42no—
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C23×C411yescharacteristic
302C22⋊D61—41no—
303C22⋊D61—41no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—42no—
308C2×Dic61C4×D411yescharacteristic
309C2×Dic61C4×D411yescharacteristic
310C2×Dic61C2×#4111yescharacteristic
311D244—21no—
312D244—21no—
313C4×D61—21no—
314C4×D61—21no—
315C4×D61—21no—
316C4×D61—21no—
317C4×D61—42no—
318C4×D61—42no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324C4×D61—41no—
325C4×D61C2×#4111yescharacteristic
326C4×D61C2×#4111yescharacteristic
327C4×D61C2×#4111yescharacteristic
328C4×D61C2×#4111yescharacteristic
329Dic122—21no—
330Dic122—21no—
331Dic122—41no—
332Dic122—41no—
333#92420—22no—
334#92420—22no—
335C8×C61—21no—
336C8×C61#11712yescomplemented
337#92418—21no—
338#92418#11712yescomplemented
339#21288—611nomaximal, Sylow
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61C2×C4×D411yescharacteristic
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61#53211yescharacteristic
352C2×D61#53211yescharacteristic
353C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
354C2×D61C2×#13711yescharacteristic
355C2×D61#57511yescharacteristic
356C2×D61#57511yescharacteristic
357#6923—22no—
358#6923—22no—
359#6923—41no—
360#6923—41no—
361#6923—81no—
362#6923—81no—
363#6923—81no—
364#6923—81no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61C2×#11711yescharacteristic
371C4×C61C4×#4111yescharacteristic
372Dic61—21no—
373Dic61—21no—
374Dic61—41no—
375Dic61—41no—
376Dic61—41no—
377Dic61#52911yescharacteristic
378Dic61#52911yescharacteristic
379C2×#440—611no—
380#2295—611no—
381#2293—611no—
382#1973—611no—
383#1968—611no—
384#1943—611no—
385#1942—611no—
386#1936—611no—
387#1935—611no—
388#1934—611no—
389#1933—611no—
390#1776—611no—
391#1763—611no—
392#1762—611no—
393C4×#97—611no—
394C2×C61—81no—
395C2×C61#229311yescharacteristic
396C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
397C2×C61C4×#13711yescharacteristic
398D61—81no—
399D61#318011yescharacteristic
400D61#318111yescharacteristic
401D61#318211yescharacteristic
402D61#318311yescharacteristic
403C22×SD16—611no—
404C2×C4×Q8—611no—
405C2×C4×D4—611no—
406C2×#117—1221no—
407#440—611no—
408#440—611no—
409#440—611no—
410#440—611no—
411#440—611no—
412#440—611no—
413#440—611no—
414#440#692311yescharacteristic, complemented
415C2×#107—611no—
416C2×#107—611no—
417C2×#106—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#97—611no—
425C2×#97—611no—
426C2×#97—611no—
427C2×#97—611no—
428C2×C4×C8—611no—
429C2×C4×C8—611no—
430#391—611no—
431#391—611no—
432#390—611no—
433#390—611no—
434#389—611no—
435#389—611no—
436#389—611no—
437#389—611no—
438#388—1221no—
439#388—1221no—
440#387—1221no—
441#387—1221no—
442C4×C4⋊C4—611no—
443C4×C4⋊C4—611no—
444C4×C4⋊C4—1221no—
445C4×C22⋊C4—1221no—
446#376—1221no—
447C43—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454C61#2128811yescharacteristic, complemented, Sylow
455C22×Q8—611no—
456C22×D4—611no—
457C23×C4—1221no—
458C2×SD16—611no—
459C2×SD16—611no—
460C2×SD16—611no—
461C2×SD16—1222no—
462C2×SD16—1222no—
463C2×SD16C2×#692311yescharacteristic
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C4×Q8—611no—
469C4×Q8—611no—
470C4×Q8—611no—
471C4×Q8—1221no—
472C4×Q8—1221no—
473C4×Q8C2×#692311yescharacteristic
474C4×D4—611no—
475C4×D4—611no—
476C4×D4—611no—
477C4×D4—1221no—
478C4×D4—1221no—
479C4×D4C2×#692311yescharacteristic
480#117—2444no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C42—611no—
498C2×C42—611no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—611no—
503C2×C42—611no—
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42—1221no—
507#107—611no—
508#107—611no—
509#107—611no—
510#107—1222no—
511#107C2×#692311yescharacteristic
512#106—1222no—
513#103—611no—
514#103—611no—
515#103—611no—
516#103—1222no—
517#103—1222no—
518#103C2×#692311yescharacteristic
519#102—611no—
520#102—611no—
521#102—611no—
522#102—1222no—
523#102—1222no—
524#102C2×#692311yescharacteristic
525#97—611no—
526#97—611no—
527#97—611no—
528#97—1221no—
529#97—1221no—
530#97—1222no—
531#97—1222no—
532#97C2×#692311yescharacteristic
533C4×C8—1222no—
534C4×C8—1222no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544#95—1221no—
545C24—1221no—
546C2×Q8—611no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8C22×#692311yescharacteristic
553C2×D4—611no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4C22×#692311yescharacteristic
560C22×C4—21no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—2442no—
579C22×C4—2442no—
580SD16—22no—
581SD16—1222no—
582SD16—1222no—
583SD16—1222no—
584C2×C8—611no—
585C2×C8—612no—
586C2×C8—612no—
587C2×C8—612no—
588C2×C8—612no—
589C2×C8—611no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8C22×#692311yescharacteristic
597C2×C8C22×#692311yescharacteristic
598C4⋊C4—21no—
599C4⋊C4—611no—
600C4⋊C4—611no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C4⋊C4C22×#692311yescharacteristic
619C4⋊C4C22×#692311yescharacteristic
620C22⋊C4—21no—
621C22⋊C4—1221no—
622C22⋊C4—1221no—
623C22⋊C4—1221no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C42—21no—
629C42—611no—
630C42—611no—
631C42—611no—
632C42—1221no—
633C42—1221no—
634C42—1221no—
635C42—1221no—
636C42—1221no—
637C42—1221no—
638C42—1222no—
639C42—1222no—
640C42—1221no—
641C42—2441no—
642C42—2441no—
643C42—2442no—
644C42—2442no—
645C42C22×#692311yescharacteristic
646C23—21no—
647C23—611no—
648C23—1221no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655Q8—21no—
656Q8—21no—
657Q8—1221no—
658Q8—1221no—
659Q8—2441no—
660Q8—2441no—
661D4—21no—
662D4—21no—
663D4—1221no—
664D4—1221no—
665D4—2441no—
666D4—2441no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—42no—
671C2×C4—611no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—611no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—611no—
679C2×C4—611no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2442no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4D4×#692311yescharacteristic
719C2×C4D4×#692311yescharacteristic
720C2×C4C23×#692311yescharacteristic
721C8—21no—
722C8—612no—
723C8—1222no—
724C8—1222no—
725C8—1221no—
726C8#1451985612yescomplemented
727C22—41no—
728C22—41no—
729C22—41no—
730C22—611no—
731C22—611no—
732C22—611no—
733C22—611no—
734C22—611no—
735C22—611no—
736C22—4881no—
737C22—4881no—
738C22—4881no—
739C22—4881no—
740C22—2441no—
741C22—2441no—
742C22—2441no—
743C22C2×D4×#692311yescharacteristic
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—611no—
750C4—611no—
751C4—1222no—
752C4—1222no—
753C4—1221no—
754C4—1221no—
755C4—4881no—
756C4—4881no—
757C4—4881no—
758C4—4881no—
759C4—2441no—
760C4—2441no—
761C4—2441no—
762C4—2441no—
763C4—2441no—
764C4C2×#1451985611yescharacteristic
765C4#41×#692311yescharacteristic
766C2—81no—
767C2—611no—
768C2—611no—
769C2—611no—
770C2—611no—
771C2—4881no—
772C2#2146227611yescharacteristic
773C2AGL(1,ℤ/8)×#692311yescharacteristic
774C2#137×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#440#6923
hypocenterC61#21288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #21462278C2semidirect
5. #21461924C2semidirect
6. #21461923C2semidirect
8. #21461910C2semidirect
10. #21461908C2semidirect
11. #21461633C2semidirect
12. #21461591C2semidirect
14. #97×#6923C2semidirect
55. #16839865C4semidirect
56. #16839864C4semidirect
57. #16839863C4semidirect
58. #16839862C4semidirect
59. #16839861C4semidirect
60. #16839860C4semidirect
61. #16839859C4semidirect
66. C61×#440C4semidirect
336. C8×C61#117semidirect
338. #92418#117semidirect
414. #440#6923semidirect
454. C61#21288semidirect
726. C8#14519856semidirect

Maximal subgroups

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

subgroupindex
#214622782
#214622762
#214619692
#214619642
#214619242
#214619232
#214619112
#214619102
#214619092
#214619082
#214616332
#214615912
#214615892
#97×#69232
#440×D612
#2128861