Finite Group Databasebeta

← #29648868

Subgroups — #29648868

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459696C211yesmaximal, characteristic
2#21454946C211yesmaximal, characteristic, complemented
3#21454941C211yesmaximal, characteristic, complemented
4#21444540C211yesmaximal, characteristic, complemented
5#21444540C211yesmaximal, characteristic, complemented
6#21444532C211yesmaximal, characteristic, complemented
7#21444523C211yesmaximal, characteristic, complemented
8#21444523C211yesmaximal, characteristic, complemented
9#21444519C211yesmaximal, characteristic, complemented
10#21444495C211yesmaximal, characteristic, complemented
11#21444495C211yesmaximal, characteristic, complemented
12#21444467C211yesmaximal, characteristic, complemented
13#21444467C211yesmaximal, characteristic, complemented
14C2×#16839505C211yesmaximal, characteristic, complemented
15C61×#1552C211yesmaximal, characteristic, complemented
16#16840497—21no—
17#16840497—21no—
18#16840434—21no—
19#16840434—21no—
20#16840403—21no—
21#16840403—21no—
22#16840403—21no—
23#16840403—21no—
24#16840368C412yes—
25#16840368C412yes—
26#16840331C412yes—
27#16840313C2211yescharacteristic
28#16840313C2211yescharacteristic
29#16840313C2211yescharacteristic
30#16840313C2211yescharacteristic
31C2×#14519774C2211yescharacteristic
32#16840236C412yes—
33C4×#11758222C2211yescharacteristic
34#16839891—21no—
35#16839890—21no—
36#16839835—21no—
37#16839833—21no—
38#16839832—21no—
39#16839830—21no—
40C8×C22⋊D61—21no—
41#16839825—21no—
42#16839819C2211yescharacteristic
43#16839818C2211yescharacteristic, complemented
44#16839818C2211yescharacteristic, complemented
45#16839814C2211yescharacteristic, complemented
46#16839814C2211yescharacteristic, complemented
47#16839784C2211yescharacteristic, complemented
48#16839784C2211yescharacteristic, complemented
49C2×C4⋊#92418C2211yescharacteristic
50C4⋊C8×D61C2211yescharacteristic, complemented
51C4⋊C8×D61C2211yescharacteristic, complemented
52#16839508C2211yescharacteristic, complemented
53#16839508C2211yescharacteristic, complemented
54#16839508C2211yescharacteristic, complemented
55#16839508C2211yescharacteristic, complemented
56#16839505C2211yescharacteristic
57#16839505C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60#16839505C2211yescharacteristic
61#16839505C2211yescharacteristic
62#16839505C2211yescharacteristic
63#16839505C2211yescharacteristic
64C61×#533C2211yescharacteristic
65C61×#432C2211yescharacteristic
66C2×C4⋊C8×C61C2211yescharacteristic
67C61×#332C2211yescharacteristic, complemented
68C61×#332C2211yescharacteristic, complemented
69C61×#332C2211yescharacteristic, complemented
70C61×#332C2211yescharacteristic, complemented
71C2×#11758226—21no—
72C2×#11758226—21no—
73C2×#11758226—21no—
74C2×#11758226—21no—
75C2×#11758222C2×C411yescharacteristic
76C22×D244—21no—
77C22×D244—21no—
78C22×D244C2×C412yes—
79C2×#11758189—21no—
80C2×#11758189—21no—
81C22×#92418—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84#14519774—22no—
85#14519774—21no—
86#14519774—21no—
87#14519774C2×C412yes—
88#14519774C2311yescharacteristic
89#14519774C2311yescharacteristic
90#14519766—21no—
91#14519766—21no—
92#14519766—21no—
93#14519766—21no—
94#14519765—22no—
95#14519762—22no—
96#14519762—22no—
97#14519762—22no—
98#14519762—22no—
99#14519752—21no—
100#14519752—21no—
101#14519752—21no—
102#14519752—21no—
103#14519752—22no—
104#14519752—22no—
105#14519752—22no—
106#14519752—22no—
107#14519752C2×C412yes—
108#14519752C2×C412yes—
109#14519752C2×C412yes—
110#14519752C2×C412yes—
111#14519747—22no—
112#14519747—22no—
113C4×Dic122D411yescharacteristic
114C4×Dic122D411yescharacteristic
115C4×D244—22no—
116C4×D244—22no—
117C4×D244D411yescharacteristic
118C4×D244D411yescharacteristic
119#14519739—21no—
120#14519739—21no—
121#14519739—21no—
122#14519739—21no—
123#14519739C2×C412yes—
124#14519739C2×C412yes—
125#14519739C2×C412yes—
126#14519739C2×C412yes—
127C4×C22⋊D61D411yescharacteristic
128C4×C22⋊D61D411yescharacteristic
129C4×C22⋊D61D411yescharacteristic
130C4×C22⋊D61D411yescharacteristic
131#14519736C2×C411yescharacteristic
132#14519734C2×C411yescharacteristic
133#14519734C2×C411yescharacteristic
134C22⋊C4×D61—22no—
135C22⋊C4×D61—22no—
136C42×D61C2311yescharacteristic
137C42×D61C2311yescharacteristic
138C4⋊#92418—21no—
139C4⋊#92418C2311yescharacteristic
140C4⋊#92418C2311yescharacteristic
141C4⋊#92418C2311yescharacteristic
142C4⋊#92418C2311yescharacteristic
143#14519706—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147C22⋊#92418—21no—
148#14519689—21no—
149#14519689—21no—
150#14519689—21no—
151#14519689—21no—
152#14519688—21no—
153#14519687—21no—
154#14519687—21no—
155C8×Dic61—21no—
156C8×Dic61—21no—
157C22×C8×C61—21no—
158C4⋊Q8×C61C2311yescharacteristic
159C4⋊Q8×C61C2311yescharacteristic
160#125×C61C2×C412yes—
161C22⋊Q8×C61—21no—
162C22⋊Q8×C61—21no—
163C4×Q8×C61—21no—
164C4×Q8×C61—21no—
165#117×C61C2×C412yes—
166C2×C42×C61C2311yescharacteristic
167C4⋊C8×C61—21no—
168C4⋊C8×C61C2311yescharacteristic
169C4⋊C8×C61C2311yescharacteristic
170C4⋊C8×C61C2311yescharacteristic
171C4⋊C8×C61C2311yescharacteristic
172C22⋊C8×C61—21no—
173#97×C61—21no—
174C23×D61—22no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C2×C22⋊D61C22⋊C411yescharacteristic
181C2×C22⋊D61C22⋊C411yescharacteristic
182#11758226—81no—
183#11758226—81no—
184#11758226—81no—
185#11758226—81no—
186#11758226—81no—
187#11758226—81no—
188#11758226—81no—
189#11758226—81no—
190#11758222—42no—
191C2×D244—22no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—22no—
202C2×D244—44no—
203C2×D244—81no—
204C2×D244—81no—
205C2×D244—81no—
206C2×D244—81no—
207C2×D244C22⋊C411yescharacteristic
208C2×D244C22×C412yes—
209C2×D244C22×C412yes—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61C22×C411yescharacteristic
215C2×C4×D61C22×C411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×Dic122C22⋊C411yescharacteristic
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—81no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C22×C412yes—
231C4⋊C4×C61C22×C412yes—
232C22⋊C4×C61—22no—
233C42×C61—22no—
234C42×C61C22×C411yescharacteristic
235C42×C61C2×D411yescharacteristic
236C42×C61C2×D411yescharacteristic
237C42×C61C2411yescharacteristic
238C22⋊Dic61C22⋊C411yescharacteristic
239C22⋊Dic61C22⋊C411yescharacteristic
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—22no—
248#11758198C22⋊C411yescharacteristic
249#11758198C22⋊C411yescharacteristic
250#11758198C22⋊C411yescharacteristic
251#11758198C22⋊C411yescharacteristic
252C4⋊Dic61C22⋊C411yescharacteristic
253C4⋊Dic61C22⋊C411yescharacteristic
254#11758196C22⋊C411yescharacteristic
255#11758196C22⋊C411yescharacteristic
256#11758196C22⋊C411yescharacteristic
257#11758196C22⋊C411yescharacteristic
258C4×Dic61C22×C411yescharacteristic
259C4×Dic61C22×C411yescharacteristic
260C4×Dic61C2×D411yescharacteristic
261C4×Dic61C2×D411yescharacteristic
262C4×Dic61C2×D411yescharacteristic
263C4×Dic61C2×D411yescharacteristic
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—81no—
269#11758189—81no—
270#11758189—81no—
271C8×D61—81no—
272C8×D61—81no—
273C23×C61C2×C22⋊C411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—44no—
277C22×D61—82no—
278C22×D61—82no—
279C22×D61C2×C22⋊C411yescharacteristic
280C22×D61C2×C22⋊C411yescharacteristic
281Q8×C61—41no—
282Q8×C61—41no—
283Q8×C61—41no—
284Q8×C61—41no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C23×C411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C22⋊D61—22no—
299C22⋊D61—22no—
300C2×Dic61C2×C22⋊C411yescharacteristic
301C2×Dic61C2×C22⋊C411yescharacteristic
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C411yescharacteristic
304C2×Dic61C2×C22⋊C411yescharacteristic
305C2×Dic61C2×C22⋊C411yescharacteristic
306D244—41no—
307D244—42no—
308D244—42no—
309D244—44no—
310D244—41no—
311D244—41no—
312D244—41no—
313D244—41no—
314D244—41no—
315D244—41no—
316D244—41no—
317D244—41no—
318D244—82no—
319D244—82no—
320D244—82no—
321D244—82no—
322D244—82no—
323D244—82no—
324C4×D61—21no—
325C4×D61—21no—
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×D61—82no—
337C4×D61—82no—
338Dic122—41no—
339C8×C61—41no—
340C8×C61—41no—
341C8×C61—41no—
342C8×C61—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#17771—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61#41312yes—
351C22×C61C22×C22⋊C411yescharacteristic
352C2×D61—21no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—164no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61#57611yescharacteristic
372C4×C61#57611yescharacteristic
373C4×C61#57711yescharacteristic
374C4×C61#57711yescharacteristic
375Dic61—21no—
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—21no—
380Dic61—21no—
381#3508—611no—
382#2990—611no—
383#2990—611no—
384#1557—611no—
385#1557—611no—
386#1555—611no—
387#1553—611no—
388#1553—611no—
389#1552—611no—
390#1552D6111yescharacteristic, complemented
391#1547—611no—
392#1547—611no—
393#1540—611no—
394#1540—611no—
395C2×#331—611no—
396C2×C61—22no—
397C2×C61C2×#41311yescharacteristic
398C2×C61#289711yescharacteristic
399C2×C61#289711yescharacteristic
400D61—41no—
401D61—41no—
402D61—82no—
403D61—82no—
404#559—1221no—
405#559—1221no—
406#550—1221no—
407#550—1221no—
408#546—1221no—
409#546—1221no—
410#546—1221no—
411#546—1221no—
412#540—612no—
413#540—612no—
414#535—612no—
415#533C2×D6111yescharacteristic
416#532—611no—
417#532—611no—
418#532—611no—
419#532—611no—
420C2×#127—611no—
421#518—612no—
422C4×#41—611no—
423#446—1221no—
424#446—1221no—
425#435—1221no—
426#435—1221no—
427#435—1221no—
428#435—1221no—
429C8×D4—1221no—
430C8×D4—1221no—
431#432—611no—
432#432—611no—
433#432—611no—
434#432C2×D6111yescharacteristic
435#431—611no—
436#431—611no—
437#423—611no—
438#423—611no—
439C2×C4⋊C8—611no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C4⋊C8C2×D6111yescharacteristic
443#332—611no—
444#332—611no—
445#332—611no—
446#332—611no—
447#332C2×D6111yescharacteristic, complemented
448#332C2×D6111yescharacteristic, complemented
449#332C2×D6111yescharacteristic, complemented
450#332C2×D6111yescharacteristic, complemented
451#331—611no—
452#331—611no—
453#331—611no—
454#331—611no—
455#331—611no—
456#331—611no—
457#331—611no—
458#331—611no—
459C61#1777111yescharacteristic, complemented, Sylow
460C2×#41—611no—
461C2×#41—1221no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—1221no—
465C22×D4—612no—
466C22×D4—1221no—
467C22×D4—1221no—
468C2×M16—1221no—
469C2×M16—1221no—
470C22×C8—21no—
471C22×C8—1221no—
472C22×C8—1221no—
473C22×C8—1221no—
474C4⋊Q8C22×D6111yescharacteristic
475C4⋊Q8C22×D6111yescharacteristic
476#127—612no—
477#127—611no—
478#127—611no—
479#127—1222no—
480#127—1221no—
481#127—1221no—
482#125C4×D6112yes—
483#124—1222no—
484#124—1221no—
485#124—1221no—
486#124—1221no—
487#124—1221no—
488#123—1222no—
489#123—1222no—
490#123—1222no—
491#123—1222no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—612no—
495#121—612no—
496#121—612no—
497#121—612no—
498#121—1222no—
499#121—1222no—
500#121—1222no—
501#121—1222no—
502#121—1221no—
503#121—1221no—
504#121—1221no—
505#121—1221no—
506#120—1222no—
507#120—1222no—
508C4×Q8—21no—
509C4×Q8—21no—
510C4×Q8—611no—
511C4×Q8—611no—
512C4×D4—611no—
513C4×D4—611no—
514C4×D4—611no—
515C4×D4—611no—
516C4×D4—612no—
517C4×D4—612no—
518C4×D4—612no—
519C4×D4—612no—
520C4×D4—611no—
521C4×D4—611no—
522C4×D4—1222no—
523C4×D4—1222no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528#117—611no—
529#117—611no—
530#117—611no—
531#117C4×D6112yes—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1222no—
534C2×C42—611no—
535C2×C42—611no—
536C2×C42C22×D6111yescharacteristic
537C4⋊C8—21no—
538C4⋊C8—611no—
539C4⋊C8—611no—
540C4⋊C8—611no—
541C4⋊C8—611no—
542C4⋊C8—1221no—
543C4⋊C8—1221no—
544C4⋊C8—1221no—
545C4⋊C8—1221no—
546C4⋊C8—1221no—
547C4⋊C8C22×D6111yescharacteristic
548C4⋊C8C22×D6111yescharacteristic
549C4⋊C8C22×D6111yescharacteristic
550C4⋊C8C22×D6111yescharacteristic
551C22⋊C8—21no—
552C22⋊C8—1221no—
553C22⋊C8—1221no—
554C22⋊C8—1221no—
555C22⋊C8—1221no—
556C22⋊C8—1221no—
557#97—21no—
558#97—1221no—
559#97—1221no—
560#97—1221no—
561C4×C8—1221no—
562C4×C8—1221no—
563C24—1222no—
564#41—4881no—
565#41—4881no—
566#41—4881no—
567#41—4881no—
568#41—4881no—
569#41—4881no—
570#41—4881no—
571#41—4881no—
572#41—2442no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—611no—
576C2×D4—611no—
577C2×D4—611no—
578C2×D4—612no—
579C2×D4—612no—
580C2×D4—611no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—4881no—
593C2×D4—4881no—
594C2×D4—4881no—
595C2×D4—4881no—
596C2×D4—2444no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610M16—4881no—
611M16—4881no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—81no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—4881no—
622C2×C8—4881no—
623C2×C8—4881no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—611no—
629C4⋊C4—611no—
630C4⋊C4—611no—
631C4⋊C4—611no—
632C4⋊C4—611no—
633C4⋊C4—611no—
634C4⋊C4C2×C4×D6112yes—
635C4⋊C4C2×C4×D6112yes—
636C22⋊C4—22no—
637C22⋊C4—611no—
638C22⋊C4—611no—
639C22⋊C4—611no—
640C22⋊C4—611no—
641C22⋊C4—611no—
642C22⋊C4—611no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C42—22no—
652C42—611no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42—611no—
657C42—611no—
658C42C2×C4×D6111yescharacteristic
659C42D4×D6111yescharacteristic
660C42D4×D6111yescharacteristic
661C42C23×D6111yescharacteristic
662C23—611no—
663C23—611no—
664C23—1222no—
665C23—1222no—
666C23—4882no—
667C23—4882no—
668C23—2444no—
669C23C22⋊C4×D6111yescharacteristic
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—2441no—
675D4—1222no—
676D4—1222no—
677D4—4882no—
678D4—4882no—
679D4—4882no—
680D4—4882no—
681D4—4882no—
682D4—4882no—
683D4—2441no—
684D4—2442no—
685D4—2442no—
686D4—2444no—
687D4—2441no—
688D4—2441no—
689D4—2441no—
690D4—2441no—
691D4—2441no—
692D4—2441no—
693D4—2441no—
694D4—2441no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—4882no—
717C2×C4—4882no—
718C2×C4—4882no—
719C2×C4—4882no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4C22⋊C4×D6111yescharacteristic
723C2×C4C22⋊C4×D6111yescharacteristic
724C2×C4C22⋊C4×D6111yescharacteristic
725C2×C4C22×C4×D6111yescharacteristic
726C2×C4C2×D4×D6111yescharacteristic
727C2×C4C2×D4×D6111yescharacteristic
728C8—41no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—2441no—
733C8—2441no—
734C8—2441no—
735C8—2441no—
736C22—21no—
737C22—21no—
738C22—1221no—
739C22—1221no—
740C22—1221no—
741C22—1221no—
742C22—1221no—
743C22—1221no—
744C22—9764no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22#1683974512yes—
752C22C2×C22⋊C4×D6111yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—42no—
759C4—1221no—
760C4—1221no—
761C4—1221no—
762C4—1221no—
763C4—1221no—
764C4—1221no—
765C4#1684056411yescharacteristic
766C4#1684056611yescharacteristic
767C4#1684056911yescharacteristic
768C4#1684057111yescharacteristic
769C2—22no—
770C2—4882no—
771C2—4882no—
772C2—2441no—
773C2—2441no—
774C2C2×#1683974511yescharacteristic
775C2#2145434111yescharacteristic
776C2#2145434311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1552C2
socleC22×C61C22×C22⋊C4
prime radical#21459696C2
cosocleC42×C61C24
hypercenter#1552D61
hypocenterC61#17771
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
2. #21454946C2semidirect
3. #21454941C2semidirect
4. #21444540C2semidirect
5. #21444540C2semidirect
6. #21444532C2semidirect
7. #21444523C2semidirect
8. #21444523C2semidirect
9. #21444519C2semidirect
10. #21444495C2semidirect
11. #21444495C2semidirect
12. #21444467C2semidirect
13. #21444467C2semidirect
14. C2×#16839505C2semidirect
15. C61×#1552C2semidirect
43. #16839818C22semidirect
44. #16839818C22semidirect
45. #16839814C22semidirect
46. #16839814C22semidirect
47. #16839784C22semidirect
48. #16839784C22semidirect
50. C4⋊C8×D61C22semidirect
51. C4⋊C8×D61C22semidirect
52. #16839508C22semidirect
53. #16839508C22semidirect
54. #16839508C22semidirect
55. #16839508C22semidirect
67. C61×#332C22semidirect
68. C61×#332C22semidirect
69. C61×#332C22semidirect
70. C61×#332C22semidirect
390. #1552D61semidirect
447. #332C2×D61semidirect
448. #332C2×D61semidirect
449. #332C2×D61semidirect
450. #332C2×D61semidirect
459. C61#17771semidirect

Maximal subgroups

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

subgroupindex
#214596962
#214549462
#214549412
#214445402
#214445322
#214445232
#214445192
#214444952
#214444672
C2×#168395052
C61×#15522
#1777161