Finite Group Databasebeta

← #29648924

Subgroups — #29648924

Order 15616.

988 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#21459688C211yesmaximal, characteristic
2#21454949C211yesmaximal, characteristic, complemented
3#21454941C211yesmaximal, characteristic, complemented
4#21444555C211yesmaximal, characteristic, complemented
5#21444539C211yesmaximal, characteristic, complemented
6#21444538C211yesmaximal, characteristic, complemented
7#21444524C211yesmaximal, characteristic, complemented
8#21444523C211yesmaximal, characteristic, complemented
9#21444495C211yesmaximal, characteristic, complemented
10#21444485C211yesmaximal, characteristic, complemented
11#21444485C211yesmaximal, characteristic, complemented
12#21444482C211yesmaximal, characteristic, complemented
13#21444469C211yesmaximal, characteristic, complemented
14#21444465C211yesmaximal, characteristic, complemented
15C61×#1547C211yesmaximal, characteristic, complemented
16#16840495—21no—
17#16840494—21no—
18#16840431—21no—
19#16840430—21no—
20#16840409—21no—
21#16840407—21no—
22#16840405—21no—
23#16840400—21no—
24#16840365C412yes—
25#16840363C412yes—
26#16840328C412yes—
27#16840317C2211yescharacteristic
28#16840313C2211yescharacteristic
29#16840312C2211yescharacteristic
30#16840310C2211yescharacteristic
31#127×D61C2211yescharacteristic
32#16840234C412yes—
33C4×#11758222C2211yescharacteristic
34#16839891—21no—
35#16839886—21no—
36#16839839—21no—
37#16839838—21no—
38#16839838—21no—
39#16839833—21no—
40#16839832—21no—
41C8×C22⋊D61—21no—
42#16839819C2211yescharacteristic, complemented
43#16839818C2211yescharacteristic, complemented
44#16839815C2211yescharacteristic, complemented
45#16839814C2211yescharacteristic
46#16839814C2211yescharacteristic
47#16839814C2211yescharacteristic, complemented
48#16839784C2211yescharacteristic
49#16839784C2211yescharacteristic
50#16839784C2211yescharacteristic, complemented
51C4⋊C8×D61C2211yescharacteristic, complemented
52#16839509C2211yescharacteristic, complemented
53#16839509C2211yescharacteristic, complemented
54#16839508C2211yescharacteristic, complemented
55#16839508C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839507C2211yescharacteristic, complemented
58#16839506C2211yescharacteristic
59#16839506C2211yescharacteristic
60#16839505C2211yescharacteristic
61#16839505C2211yescharacteristic
62#16839505C2211yescharacteristic
63#16839505C2211yescharacteristic
64C61×#532C2211yescharacteristic
65C61×#423C2211yescharacteristic, complemented
66C2×C4⋊C8×C61C2211yescharacteristic, complemented
67C61×#332C2211yescharacteristic, complemented
68C61×#332C2211yescharacteristic, complemented
69C61×#331C2211yescharacteristic
70C61×#331C2211yescharacteristic
71C2×#11758226—21no—
72C2×#11758222—21no—
73C2×#11758222C2×C411yescharacteristic
74C2×#11758224—21no—
75C2×D4×D61—21no—
76C2×D4×D61—21no—
77C2×D4×D61C2×C412yes—
78C2×#11758189—21no—
79C2×#11758189—21no—
80C2×#11758189—21no—
81C2×C8×D61—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519773—22no—
85#14519773—21no—
86#14519773—21no—
87#14519773C2×C412yes—
88#14519768C2×C412yes—
89#14519766—21no—
90#14519765—21no—
91#14519764—21no—
92#14519763—22no—
93#14519761—22no—
94#14519760—22no—
95#14519759—22no—
96#14519759—22no—
97#14519757—21no—
98#14519753—21no—
99#14519752—21no—
100#14519752C2×C412yes—
101#14519751—21no—
102#14519751—22no—
103#14519751C2×C412yes—
104#14519750—22no—
105#14519749—22no—
106#14519748—21no—
107#14519748—22no—
108#14519748C2×C412yes—
109#14519747—22no—
110#14519745—22no—
111Q8×Dic61—21no—
112C4×Dic122D411yescharacteristic
113C4×Dic122D411yescharacteristic
114#14519742—21no—
115C4×D244—21no—
116C4×D244C2×C412yes—
117C4×D244D411yescharacteristic
118C4×D244D411yescharacteristic
119D4×Dic61—21no—
120D4×Dic61C2×C412yes—
121#14519739—21no—
122#14519739C2×C412yes—
123C4×C22⋊D61—22no—
124C4×C22⋊D61D411yescharacteristic
125C4×C22⋊D61D411yescharacteristic
126C4×C22⋊D61D411yescharacteristic
127C4×C22⋊D61D411yescharacteristic
128#14519737—22no—
129#14519736C2×C411yescharacteristic
130#14519735C2×C412yes—
131#14519734C2×C411yescharacteristic
132#14519734C2×C411yescharacteristic
133C2×#11758198—22no—
134C22⋊C4×D61—22no—
135C42×D61C2311yescharacteristic
136C42×D61C2311yescharacteristic
137C4⋊#92418C2311yescharacteristic
138C4⋊#92418C2311yescharacteristic
139C4⋊#92418C2311yescharacteristic
140C4⋊#92418C2311yescharacteristic
141#14519706—21no—
142#14519706—21no—
143#14519706—21no—
144#14519706—21no—
145C22⋊#92418—21no—
146C22⋊#92418—21no—
147#14519689—21no—
148#14519689—21no—
149#14519689—21no—
150#14519689—21no—
151#14519688—21no—
152#14519687—21no—
153C4×#92418—21no—
154C8×Dic61—21no—
155C8×Dic61—21no—
156C8×Dic61—21no—
157C2×#41×C61—21no—
158C2×M16×C61—21no—
159C22×C8×C61—21no—
160C4⋊Q8×C61C2311yescharacteristic
161#127×C61C2311yescharacteristic
162#124×C61—21no—
163#121×C61—21no—
164#121×C61C2×C412yes—
165C4×D4×C61—21no—
166C4×D4×C61C2×C412yes—
167C2×C42×C61C2311yescharacteristic
168C4⋊C8×C61—21no—
169C4⋊C8×C61—21no—
170C4⋊C8×C61C2311yescharacteristic
171C4⋊C8×C61C2311yescharacteristic
172C4⋊C8×C61C2311yescharacteristic
173C4⋊C8×C61C2311yescharacteristic
174C23×D61—22no—
175#41×C61—81no—
176#41×C61—81no—
177C2×Q8×C61—21no—
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—81no—
195#11758226—81no—
196#11758224—81no—
197#11758224—81no—
198D4×D61—44no—
199D4×D61—81no—
200D4×D61—81no—
201D4×D61—81no—
202D4×D61—81no—
203#11758222—42no—
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—81no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—81no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61C22×C412yes—
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—
269#11758189—81no—
270#11758189—81no—
271#11758189—81no—
272C8×D61—81no—
273C23×C61—22no—
274C23×C61C2×C22⋊C411yescharacteristic
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—
283D4×C61—42no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—82no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—41no—
295C2×C4×C61—82no—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C23×C411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C22⋊D61—22no—
303C22⋊D61—41no—
304C22⋊D61—44no—
305C22⋊D61—82no—
306C22⋊D61—82no—
307C22⋊D61—82no—
308C22⋊D61—82no—
309C2×Dic61—22no—
310C2×Dic61—82no—
311C2×Dic61C2×C22⋊C411yescharacteristic
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C2×C22⋊C411yescharacteristic
314C2×Dic61C2×C22⋊C411yescharacteristic
315C2×Dic61C2×C22⋊C411yescharacteristic
316C2×Dic61C2×C22⋊C411yescharacteristic
317D244—41no—
318D244—42no—
319D244—41no—
320D244—41no—
321D244—41no—
322D244—41no—
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—22no—
333C4×D61—41no—
334C4×D61—82no—
335C4×D61—82no—
336Dic122—22no—
337Dic122—41no—
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#17776—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61C22×C22⋊C411yescharacteristic
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
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#57611yescharacteristic
371C4×C61#57611yescharacteristic
372C4×C61#57711yescharacteristic
373C4×C61#57711yescharacteristic
374Dic61—21no—
375Dic61—21no—
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—42no—
380Dic61#41312yes—
381#3508—611no—
382#2991—611no—
383#2990—611no—
384#1561—611no—
385#1557—611no—
386#1557—611no—
387#1553—611no—
388#1553—611no—
389#1547—611no—
390#1547D6111yescharacteristic, complemented
391#1545—611no—
392#1545—611no—
393#1544—611no—
394#1540—611no—
395#1540—611no—
396C2×C61—41no—
397C2×C61—82no—
398C2×C61C2×#41311yescharacteristic
399C2×C61#289711yescharacteristic
400C2×C61#289711yescharacteristic
401D61—41no—
402D61—41no—
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#533—611no—
416#532—611no—
417#532—611no—
418#532—611no—
419#532C2×D6111yescharacteristic
420C2×#127—611no—
421#518—612no—
422C4×#41—611no—
423#446—1221no—
424C8×Q8—1221no—
425#436—1221no—
426#436—1221no—
427#436—1221no—
428#435—1221no—
429#435—1221no—
430C8×D4—1221no—
431#432—611no—
432#432—611no—
433#431—611no—
434#431—611no—
435#431—611no—
436#431—611no—
437#423—611no—
438#423—611no—
439#423—611no—
440#423C2×D6111yescharacteristic, complemented
441C2×C4⋊C8—611no—
442C2×C4⋊C8C2×D6111yescharacteristic, complemented
443#332—611no—
444#332—611no—
445#332—611no—
446#332—611no—
447#332—611no—
448#332—611no—
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#331C2×D6111yescharacteristic
458#331C2×D6111yescharacteristic
459C61#1777611yescharacteristic, complemented, Sylow
460C2×#41—21no—
461C2×#41—611no—
462C2×#41—1221no—
463C2×#41—1221no—
464C2×#41—1221no—
465C22×D4—612no—
466C22×D4—1221no—
467C22×D4—1221no—
468C2×M16—21no—
469C2×M16—1221no—
470C2×M16—1221no—
471C2×M16—1221no—
472C22×C8—21no—
473C22×C8—1221no—
474C4⋊Q8—611no—
475C4⋊Q8C22×D6111yescharacteristic
476#127—612no—
477#127—611no—
478#127—1221no—
479#127—1221no—
480#127—1222no—
481#127C22×D6111yescharacteristic
482#125—612no—
483#124—21no—
484#124—1221no—
485#124—1221no—
486#124—1222no—
487#124—1221no—
488#123—1222no—
489#123—1222no—
490#123—1222no—
491#123—1222no—
492C22⋊Q8—1221no—
493C22⋊Q8—1221no—
494#121—21no—
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#121C4×D6112yes—
506#120—1222no—
507#120—1222no—
508C4×Q8—611no—
509C4×Q8—611no—
510C4×Q8—1221no—
511C4×Q8—1221no—
512C4×D4—21no—
513C4×D4—611no—
514C4×D4—611no—
515C4×D4—611no—
516C4×D4—611no—
517C4×D4—612no—
518C4×D4—612no—
519C4×D4—612no—
520C4×D4—611no—
521C4×D4—611no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1221no—
527C4×D4C4×D6112yes—
528#117—611no—
529#117—611no—
530#117—611no—
531#117—612no—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1222no—
534C2×C42—611no—
535C2×C42—611no—
536C2×C42C22×D6111yescharacteristic
537C4⋊C8—21no—
538C4⋊C8—21no—
539C4⋊C8—611no—
540C4⋊C8—611no—
541C4⋊C8—611no—
542C4⋊C8—611no—
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—1221no—
552C22⋊C8—1221no—
553C22⋊C8—1221no—
554C22⋊C8—1221no—
555C22⋊C8—1221no—
556C22⋊C8—1221no—
557#97—1221no—
558#97—1221no—
559C4×C8—1221no—
560C4×C8—1221no—
561C4×C8—1221no—
562C4×C8—1221no—
563C24—1222no—
564#41—81no—
565#41—81no—
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—611no—
575C2×Q8—1221no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—611no—
580C2×D4—611no—
581C2×D4—612no—
582C2×D4—611no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—4881no—
592C2×D4—4881no—
593C2×D4—4881no—
594C2×D4—4881no—
595C2×D4—2444no—
596C2×D4C2×C4×D6112yes—
597C22×C4—22no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610M16—81no—
611M16—4881no—
612M16—4881no—
613M16—4881no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—4881no—
624C4⋊C4—21no—
625C4⋊C4—611no—
626C4⋊C4—611no—
627C4⋊C4—611no—
628C4⋊C4—611no—
629C4⋊C4—611no—
630C4⋊C4—611no—
631C4⋊C4—612no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1221no—
635C4⋊C4C2×C4×D6112yes—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—611no—
639C22⋊C4—611no—
640C22⋊C4—611no—
641C22⋊C4—611no—
642C22⋊C4—611no—
643C22⋊C4—611no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C42—611no—
652C42—611no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42—611no—
657C42—1222no—
658C42C2×C4×D6111yescharacteristic
659C42D4×D6111yescharacteristic
660C42D4×D6111yescharacteristic
661C42C23×D6111yescharacteristic
662C23—22no—
663C23—611no—
664C23—611no—
665C23—1222no—
666C23—4882no—
667C23—4882no—
668C23—2444no—
669C23C22⋊C4×D6111yescharacteristic
670Q8—41no—
671Q8—41no—
672Q8—1222no—
673Q8—2441no—
674Q8—2441no—
675D4—42no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—1222no—
682D4—4882no—
683D4—4882no—
684D4—4882no—
685D4—4882no—
686D4—4882no—
687D4—2441no—
688D4—2442no—
689D4—2444no—
690D4—2441no—
691D4—2441no—
692D4—2441no—
693D4—2441no—
694D4—2441no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—1222no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1222no—
718C2×C4—4882no—
719C2×C4—4882no—
720C2×C4—4882no—
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—21no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—1221no—
743C22—1221no—
744C22—1221no—
745C22—1221no—
746C22—1221no—
747C22—1221no—
748C22—9764no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22C2×C22⋊C4×D6111yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—612no—
759C4—1221no—
760C4—1221no—
761C4—1221no—
762C4—1221no—
763C4—1221no—
764C4—2442no—
765C4#1684056311yescharacteristic
766C4#1684056611yescharacteristic
767C4#1684056811yescharacteristic
768C4#1684057111yescharacteristic
769C2—41no—
770C2—82no—
771C2—4882no—
772C2—2441no—
773C2—2441no—
774C2#413×D6111yescharacteristic
775C2#2145434011yescharacteristic
776C2#2145434311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1547C2
socleC22×C61C22×C22⋊C4
prime radical#21459688C2
cosocleC42×C61C24
hypercenter#1547D61
hypocenterC61#17776
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #21454949C2semidirect
3. #21454941C2semidirect
4. #21444555C2semidirect
5. #21444539C2semidirect
6. #21444538C2semidirect
7. #21444524C2semidirect
8. #21444523C2semidirect
9. #21444495C2semidirect
10. #21444485C2semidirect
11. #21444485C2semidirect
12. #21444482C2semidirect
13. #21444469C2semidirect
14. #21444465C2semidirect
15. C61×#1547C2semidirect
42. #16839819C22semidirect
43. #16839818C22semidirect
44. #16839815C22semidirect
47. #16839814C22semidirect
50. #16839784C22semidirect
51. C4⋊C8×D61C22semidirect
52. #16839509C22semidirect
53. #16839509C22semidirect
54. #16839508C22semidirect
55. #16839508C22semidirect
56. #16839507C22semidirect
57. #16839507C22semidirect
65. C61×#423C22semidirect
66. C2×C4⋊C8×C61C22semidirect
67. C61×#332C22semidirect
68. C61×#332C22semidirect
390. #1547D61semidirect
440. #423C2×D61semidirect
442. C2×C4⋊C8C2×D61semidirect
449. #332C2×D61semidirect
450. #332C2×D61semidirect
459. C61#17776semidirect

Maximal subgroups

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

subgroupindex
#214596882
#214549492
#214549412
#214445552
#214445392
#214445382
#214445242
#214445232
#214444952
#214444852
#214444822
#214444692
#214444652
C61×#15472
#1777661