Finite Group Databasebeta

← #29648752

Subgroups — #29648752

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459688C211yesmaximal, characteristic
2#21454933C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic, complemented
4#21444553C211yesmaximal, characteristic, complemented
5#21444539C211yesmaximal, characteristic, complemented
6#21444538C211yesmaximal, characteristic, complemented
7#21444514C211yesmaximal, characteristic, complemented
8#21444513C211yesmaximal, characteristic, complemented
9#21444506C211yesmaximal, characteristic, complemented
10#21444497C211yesmaximal, characteristic, complemented
11#21444493C211yesmaximal, characteristic, complemented
12#21444485C211yesmaximal, characteristic, complemented
13#21444473C211yesmaximal, characteristic, complemented
14#331×D61C211yesmaximal, characteristic, complemented
15C61×#1560C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840495—21no—
18#16840494C412yes—
19#16840431C412yes—
20#16840430—21no—
21#16840409—21no—
22#16840407—21no—
23#16840405C412yes—
24#16840400C412yes—
25#16840365—21no—
26#16840363—21no—
27#16840328—21no—
28#16840317C2211yescharacteristic
29#16840313C2211yescharacteristic
30#16840312C2211yescharacteristic
31#16840310C2211yescharacteristic
32#127×D61C2211yescharacteristic
33#16840234—21no—
34C4×#11758222C2211yescharacteristic
35#16839891—21no—
36#16839838—21no—
37#16839832—21no—
38#16839831—21no—
39#16839819C2211yescharacteristic, complemented
40#16839818C2211yescharacteristic, complemented
41#16839814C2211yescharacteristic
42#16839790—21no—
43#16839787—21no—
44#16839787—21no—
45#16839784C2211yescharacteristic
46#16839784C2211yescharacteristic, complemented
47#16839784C2211yescharacteristic, complemented
48C2×C4⋊#92418C2211yescharacteristic, complemented
49C4⋊C8×D61C2211yescharacteristic
50C4⋊C8×D61C2211yescharacteristic
51C4⋊C8×D61C2211yescharacteristic, complemented
52#16839511C2211yescharacteristic, complemented
53#16839511C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839509C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839507C2211yescharacteristic, complemented
58#16839506C2211yescharacteristic
59#16839506C2211yescharacteristic
60#16839505C2211yescharacteristic
61#16839505C2211yescharacteristic
62#16839505C2211yescharacteristic
63#16839505C2211yescharacteristic
64C61×#532C2211yescharacteristic
65C61×#423C2211yescharacteristic, complemented
66C61×#423C2211yescharacteristic, complemented
67C61×#333C2211yescharacteristic, complemented
68C61×#333C2211yescharacteristic, complemented
69C61×#331C2211yescharacteristic
70C61×#331C2211yescharacteristic
71C2×#11758226C2×C412yes—
72C2×#11758222—21no—
73C2×#11758222D411yescharacteristic
74C2×#11758224—21no—
75C2×D4×D61—21no—
76C2×D4×D61—21no—
77C2×D4×D61C2×C412yes—
78#14519785—44no—
79C2×#11758189—21no—
80C2×#11758189—21no—
81C2×#11758189—21no—
82C22×#92418—21no—
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86#14519777C2311yescharacteristic
87#14519774C2311yescharacteristic
88#14519773—22no—
89#14519773—21no—
90#14519773—21no—
91#14519773C2×C412yes—
92#14519768—21no—
93#14519766C2×C412yes—
94#14519765—21no—
95#14519764—21no—
96#14519763—22no—
97#14519761—22no—
98#14519760—22no—
99#14519759—22no—
100#14519759—22no—
101#14519757—21no—
102#14519753C2×C412yes—
103#14519752—21no—
104#14519752—21no—
105#14519751—21no—
106#14519751—22no—
107#14519751C2×C412yes—
108#14519750—22no—
109#14519749—22no—
110#14519748—21no—
111#14519748—22no—
112#14519748C2×C412yes—
113#14519747—22no—
114#14519745—22no—
115Q8×Dic61C2×C412yes—
116C4×Dic122C2×C411yescharacteristic
117C4×Dic122D411yescharacteristic
118#14519742—21no—
119C4×D244—21no—
120C4×D244C2×C411yescharacteristic
121C4×D244C2×C412yes—
122C4×D244D411yescharacteristic
123D4×Dic61—21no—
124D4×Dic61C2×C412yes—
125#14519739—21no—
126#14519739—21no—
127C4×C22⋊D61—22no—
128C4×C22⋊D61C2×C411yescharacteristic
129C4×C22⋊D61C2×C411yescharacteristic
130C4×C22⋊D61D411yescharacteristic
131C4×C22⋊D61D411yescharacteristic
132#14519737—22no—
133#14519736D411yescharacteristic
134#14519735—21no—
135#14519734D411yescharacteristic
136#14519734D411yescharacteristic
137C2×#11758198—22no—
138C22⋊C4×D61—22no—
139C42×D61C2311yescharacteristic
140C42×D61C2311yescharacteristic
141C4⋊#92418—21no—
142C4⋊#92418C2311yescharacteristic
143C4⋊#92418C2311yescharacteristic
144C4⋊#92418C2311yescharacteristic
145C4⋊#92418C2311yescharacteristic
146#14519706—21no—
147#14519706—21no—
148#14519706—21no—
149#14519706—21no—
150#14519706—21no—
151#14519706—21no—
152C22⋊#92418—21no—
153#14519689—21no—
154#14519689—21no—
155#14519688—21no—
156#14519687—21no—
157C8×Dic61—21no—
158C2×#41×C61C2×C412yes—
159C2×M16×C61—21no—
160C2×M16×C61—21no—
161C4⋊Q8×C61C2311yescharacteristic
162#127×C61C2311yescharacteristic
163#124×C61C2×C412yes—
164#121×C61—21no—
165#121×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C2×C42×C61C2311yescharacteristic
169C4⋊C8×C61—21no—
170C4⋊C8×C61—21no—
171C4⋊C8×C61C2311yescharacteristic
172C4⋊C8×C61C2311yescharacteristic
173C4⋊C8×C61C2311yescharacteristic
174C4⋊C8×C61C2311yescharacteristic
175C23×D61—22no—
176#41×C61—82no—
177C2×Q8×C61C22×C412yes—
178C2×D4×C61—22no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61C22×C412yes—
182C22×C4×C61—22no—
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61C22⋊C411yescharacteristic
192C2×C22⋊D61C22⋊C411yescharacteristic
193C22×Dic61—22no—
194#11758226—82no—
195#11758224—81no—
196#11758224—81no—
197D4×D61—42no—
198D4×D61—42no—
199D4×D61—81no—
200D4×D61—81no—
201D4×D61—82no—
202#11758222—22no—
203#11758222—22no—
204#11758222—81no—
205#11758222—81no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—22no—
209C2×D244C22⋊C411yescharacteristic
210C2×D244C22×C412yes—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61C22×C411yescharacteristic
214C2×C4×D61C22×C411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×Dic122—21no—
220C2×Dic122C22⋊C411yescharacteristic
221M16×C61—42no—
222M16×C61—81no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C42×C61C22×C411yescharacteristic
232C42×C61C2×D411yescharacteristic
233C42×C61C2×D411yescharacteristic
234C42×C61C2411yescharacteristic
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237C22⋊Dic61C22⋊C411yescharacteristic
238C22⋊Dic61C22⋊C411yescharacteristic
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198C22⋊C411yescharacteristic
245#11758198C22⋊C411yescharacteristic
246#11758198C22⋊C411yescharacteristic
247#11758198C22⋊C411yescharacteristic
248C4⋊Dic61—21no—
249C4⋊Dic61—22no—
250C4⋊Dic61C22⋊C411yescharacteristic
251C4⋊Dic61C22⋊C411yescharacteristic
252C4⋊Dic61C22×C412yes—
253#11758196—22no—
254#11758196C22⋊C411yescharacteristic
255#11758196C22⋊C411yescharacteristic
256#11758196C22⋊C411yescharacteristic
257#11758196C22⋊C411yescharacteristic
258C4×Dic61—22no—
259C4×Dic61C22×C411yescharacteristic
260C4×Dic61C22×C411yescharacteristic
261C4×Dic61C2×D411yescharacteristic
262C4×Dic61C2×D411yescharacteristic
263C4×Dic61C2×D411yescharacteristic
264C4×Dic61C2×D411yescharacteristic
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—42no—
270#11758189—42no—
271#11758189—42no—
272#11758189—81no—
273C8×D61—42no—
274C8×D61—42no—
275C8×D61—81no—
276C23×C61—22no—
277C23×C61C2×C22⋊C411yescharacteristic
278C22×D61—22no—
279C22×D61—44no—
280C22×D61—82no—
281C22×D61—82no—
282C22×D61C2×C22⋊C411yescharacteristic
283C22×D61C2×C22⋊C411yescharacteristic
284Q8×C61—42no—
285D4×C61—42no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—82no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—41no—
297C2×C4×C61—82no—
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C22⋊D61—22no—
305C22⋊D61—22no—
306C22⋊D61—44no—
307C22⋊D61—82no—
308C22⋊D61—82no—
309C22⋊D61—82no—
310C22⋊D61—82no—
311C2×Dic61—22no—
312C2×Dic61—82no—
313C2×Dic61C2×C22⋊C411yescharacteristic
314C2×Dic61C2×C22⋊C411yescharacteristic
315C2×Dic61C2×C22⋊C411yescharacteristic
316C2×Dic61C2×C22⋊C411yescharacteristic
317C2×Dic61C2×C22⋊C411yescharacteristic
318C2×Dic61C2×C22⋊C411yescharacteristic
319D244—22no—
320D244—42no—
321D244—41no—
322D244—41no—
323D244—41no—
324D244—41no—
325D244—82no—
326C4×D61—21no—
327C4×D61—21no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—21no—
331C4×D61—21no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—82no—
335C4×D61—82no—
336C4×D61AGL(1,ℤ/8)12yes—
337C4×D61#13712yes—
338Dic122—22no—
339Dic122—41no—
340Dic122—41no—
341C8×C61—41no—
342C8×C61—41no—
343C8×C61—41no—
344C8×C61—41no—
345#92418—41no—
346#92418—41no—
347#92418—41no—
348#92418—41no—
349#17762—611nomaximal, Sylow
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61C22×C22⋊C411yescharacteristic
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—164no—
366C2×D61#41712yes—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—42no—
372C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
373C4×C61C2×#13711yescharacteristic
374C4×C61#57611yescharacteristic
375C4×C61#57711yescharacteristic
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—21no—
380Dic61—21no—
381Dic61—42no—
382Dic61#41712yes—
383#3508—611no—
384#2989—611no—
385#2906—611no—
386#1560—611no—
387#1560D6111yescharacteristic, complemented
388#1557—611no—
389#1557—611no—
390#1551—611no—
391#1551—611no—
392#1550—611no—
393#1547—611no—
394#1547—611no—
395#1545—611no—
396#1542—611no—
397C2×#331—611no—
398C2×C61—41no—
399C2×C61—82no—
400C2×C61#288811yescharacteristic
401C2×C61C2×#41711yescharacteristic
402C2×C61#289711yescharacteristic
403D61—22no—
404D61—41no—
405D61—82no—
406C2×#131—1221no—
407#559—612no—
408#559—1221no—
409#550—612no—
410#550—1221no—
411#546—612no—
412#546—612no—
413#546—1221no—
414#546—1221no—
415#540—1221no—
416#540—1221no—
417#535—1221no—
418#533—611no—
419#532—611no—
420#532—611no—
421#532—611no—
422#532C2×D6111yescharacteristic
423C2×#127—611no—
424#518—1221no—
425C4×#41—611no—
426#446—1221no—
427#436—1221no—
428#435—1221no—
429#435—1221no—
430#432—611no—
431#432—611no—
432#431—611no—
433#424—1221no—
434#424—1221no—
435#424—1221no—
436#423—611no—
437#423—611no—
438#423—611no—
439#423C2×D6111yescharacteristic, complemented
440#423C2×D6111yescharacteristic, complemented
441C2×C4⋊C8—611no—
442C2×C4⋊C8—611no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445#333—611no—
446#333—611no—
447#333C2×D6111yescharacteristic, complemented
448#333C2×D6111yescharacteristic, complemented
449#332—611no—
450#332—611no—
451#332—611no—
452#332—611no—
453#331—611no—
454#331—611no—
455#331—611no—
456#331—611no—
457#331—611no—
458#331—611no—
459#331C2×D6111yescharacteristic
460#331C2×D6111yescharacteristic
461C61#1776211yescharacteristic, complemented, Sylow
462C2×#41—611no—
463C2×#41—612no—
464C2×#41—1221no—
465C2×#41—1221no—
466C2×#41C4×D6112yes—
467C22×D4—612no—
468C22×D4—1221no—
469C22×D4—1221no—
470#131—2444no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—1221no—
474C2×M16—1221no—
475C2×M16—1221no—
476C22×C8—1221no—
477C22×C8—1221no—
478C22×C8—1221no—
479C22×C8—1221no—
480C4⋊Q8—611no—
481C4⋊Q8C22×D6111yescharacteristic
482#127—612no—
483#127—611no—
484#127—1221no—
485#127—1221no—
486#127—1222no—
487#127C22×D6111yescharacteristic
488#125—1221no—
489#124—612no—
490#124—1221no—
491#124—1222no—
492#124—1221no—
493#124C4×D6112yes—
494#123—1222no—
495#123—1222no—
496#123—1222no—
497#123—1222no—
498C22⋊Q8—612no—
499C22⋊Q8—1221no—
500#121—21no—
501#121—21no—
502#121—612no—
503#121—612no—
504#121—1222no—
505#121—1222no—
506#121—1222no—
507#121—1222no—
508#121—1221no—
509#121—1221no—
510#121—1221no—
511#121—1221no—
512#120—1222no—
513#120—1222no—
514C4×Q8—611no—
515C4×Q8—611no—
516C4×Q8—612no—
517C4×Q8—1221no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—611no—
521C4×D4—611no—
522C4×D4—611no—
523C4×D4—611no—
524C4×D4—612no—
525C4×D4—611no—
526C4×D4—612no—
527C4×D4—611no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4—1221no—
534#117—611no—
535#117—611no—
536#117—611no—
537#117—1221no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1222no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42C22×D6111yescharacteristic
543C4⋊C8—21no—
544C4⋊C8—21no—
545C4⋊C8—611no—
546C4⋊C8—611no—
547C4⋊C8—611no—
548C4⋊C8—611no—
549C4⋊C8—1221no—
550C4⋊C8—1221no—
551C4⋊C8—1221no—
552C4⋊C8—1221no—
553C4⋊C8—1221no—
554C4⋊C8—1221no—
555C4⋊C8—1221no—
556C4⋊C8C22×D6111yescharacteristic
557C4⋊C8C22×D6111yescharacteristic
558C4⋊C8C22×D6111yescharacteristic
559C4⋊C8C22×D6111yescharacteristic
560C22⋊C8—1221no—
561C22⋊C8—1221no—
562C22⋊C8—1221no—
563#97—1221no—
564#97—1221no—
565C4×C8—1221no—
566C24—1222no—
567#41—82no—
568#41—1222no—
569#41—1222no—
570#41—4881no—
571#41—4881no—
572#41—4881no—
573#41—4881no—
574#41—4882no—
575C2×Q8—611no—
576C2×Q8—1221no—
577C2×Q8C2×C4×D6112yes—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—611no—
582C2×D4—611no—
583C2×D4—612no—
584C2×D4—611no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—4881no—
594C2×D4—4881no—
595C2×D4—4882no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4C2×C4×D6112yes—
599C22×C4—22no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4C2×C4×D6111yescharacteristic
610C22×C4D4×D6111yescharacteristic
611C22×C4D4×D6111yescharacteristic
612M16—42no—
613M16—81no—
614M16—4881no—
615M16—2442no—
616M16—2442no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—4881no—
626C2×C8—2442no—
627C2×C8—2442no—
628C2×C8—2442no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—611no—
632C4⋊C4—611no—
633C4⋊C4—611no—
634C4⋊C4—611no—
635C4⋊C4—611no—
636C4⋊C4—611no—
637C4⋊C4—612no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1221no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—611no—
644C22⋊C4—611no—
645C22⋊C4—611no—
646C22⋊C4—611no—
647C22⋊C4—611no—
648C22⋊C4—611no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C42—611no—
657C42—611no—
658C42—611no—
659C42—611no—
660C42—611no—
661C42—611no—
662C42—1222no—
663C42C2×C4×D6111yescharacteristic
664C42D4×D6111yescharacteristic
665C42D4×D6111yescharacteristic
666C42C23×D6111yescharacteristic
667C23—22no—
668C23—611no—
669C23—611no—
670C23—1222no—
671C23—4882no—
672C23—4882no—
673C23—2444no—
674C23C22⋊C4×D6111yescharacteristic
675Q8—42no—
676Q8—1222no—
677Q8—2441no—
678Q8—2441no—
679D4—42no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—82no—
685D4—1222no—
686D4—1222no—
687D4—1222no—
688D4—4882no—
689D4—4882no—
690D4—4882no—
691D4—4882no—
692D4—4882no—
693D4—2442no—
694D4—2444no—
695D4—2441no—
696D4—2441no—
697D4—2441no—
698D4—2441no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—82no—
706C2×C4—611no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1222no—
721C2×C4—4882no—
722C2×C4—4882no—
723C2×C4—4882no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4C22⋊C4×D6111yescharacteristic
727C2×C4C22⋊C4×D6111yescharacteristic
728C2×C4C22⋊C4×D6111yescharacteristic
729C2×C4C22×C4×D6111yescharacteristic
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—2441no—
737C8—2441no—
738C8—2441no—
739C8—2441no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—612no—
747C22—1221no—
748C22—1221no—
749C22—1221no—
750C22—1221no—
751C22—1221no—
752C22—9764no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22C2×C22⋊C4×D6111yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—42no—
762C4—612no—
763C4—1221no—
764C4—1221no—
765C4—1221no—
766C4—1221no—
767C4—1221no—
768C4—2442no—
769C4AGL(1,ℤ/8)×D6111yescharacteristic
770C4#137×D6111yescharacteristic
771C4#1684056611yescharacteristic
772C4#1684057111yescharacteristic
773C2—41no—
774C2—82no—
775C2—1222no—
776C2—4882no—
777C2—2441no—
778C2#2145429511yescharacteristic
779C2#417×D6111yescharacteristic
780C2#2145434311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1560C2
socleC22×C61C22×C22⋊C4
prime radical#21459688C2
cosocleC42×C61C24
hypercenter#1560D61
hypocenterC61#17762
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1560

Complements

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

NH ≅ G/Ntype
2. #21454933C2semidirect
3. #21454388C2semidirect
4. #21444553C2semidirect
5. #21444539C2semidirect
6. #21444538C2semidirect
7. #21444514C2semidirect
8. #21444513C2semidirect
9. #21444506C2semidirect
10. #21444497C2semidirect
11. #21444493C2semidirect
12. #21444485C2semidirect
13. #21444473C2semidirect
14. #331×D61C2semidirect
15. C61×#1560C2semidirect
39. #16839819C22semidirect
40. #16839818C22semidirect
46. #16839784C22semidirect
47. #16839784C22semidirect
48. C2×C4⋊#92418C22semidirect
51. C4⋊C8×D61C22semidirect
52. #16839511C22semidirect
53. #16839511C22semidirect
54. #16839509C22semidirect
55. #16839509C22semidirect
56. #16839507C22semidirect
57. #16839507C22semidirect
65. C61×#423C22semidirect
66. C61×#423C22semidirect
67. C61×#333C22semidirect
68. C61×#333C22semidirect
387. #1560D61semidirect
439. #423C2×D61semidirect
440. #423C2×D61semidirect
447. #333C2×D61semidirect
448. #333C2×D61semidirect
461. C61#17762semidirect

Maximal subgroups

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

subgroupindex
#214596882
#214549332
#214543882
#214445532
#214445392
#214445382
#214445142
#214445132
#214445062
#214444972
#214444932
#214444852
#214444732
#331×D612
C61×#15602
#1776261