Finite Group Databasebeta

← #29657415

Subgroups — #29657415

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457156C211yesmaximal, characteristic, complemented
2#21456329C211yesmaximal, characteristic, complemented
3#21455918C211yesmaximal, characteristic, complemented
4#21445103C211yesmaximal, characteristic, complemented
5#21445103C211yesmaximal, characteristic, complemented
6#21445089C211yesmaximal, characteristic, complemented
7#21445082C211yesmaximal, characteristic, complemented
8#21445075C211yesmaximal, characteristic, complemented
9#21445068C211yesmaximal, characteristic, complemented
10#21445054C211yesmaximal, characteristic, complemented
11#21445054C211yesmaximal, characteristic, complemented
12#21444519C211yesmaximal, characteristic, complemented
13#21444279C211yesmaximal, characteristic, complemented
14C2×D4⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3520C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840165C2211yescharacteristic, complemented
18#16840165C2211yescharacteristic, complemented
19#16840161—22no—
20#16840158C2211yescharacteristic, complemented
21#16840158C2211yescharacteristic, complemented
22#16840097—21no—
23#16840066—21no—
24#16840047C2211yescharacteristic, complemented
25#16840042C2211yescharacteristic
26#16840042C2211yescharacteristic
27#16840042C2211yescharacteristic, complemented
28#16840001—21no—
29#16839989—21no—
30#16839981—21no—
31#16839972C2211yescharacteristic, complemented
32#16839967C2211yescharacteristic
33#16839967C2211yescharacteristic
34#16839967C2211yescharacteristic, complemented
35#16839913—21no—
36#16839862—21no—
37#16839862—21no—
38#16839819C2211yescharacteristic
39#16839798—22no—
40C2×C4⋊#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839508C2211yescharacteristic, complemented
43#16839508C2211yescharacteristic, complemented
44#16839508C2211yescharacteristic, complemented
45#16839508C2211yescharacteristic, complemented
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C61×#556C2211yescharacteristic
55C61×#554—21no—
56C61×#552—21no—
57C61×#551—22no—
58D4×Q8×C61C2211yescharacteristic
59C61×#548—21no—
60C61×#547C2211yescharacteristic
61C61×#547C2211yescharacteristic
62C61×#546—21no—
63C61×#542—21no—
64C61×#539—22no—
65C61×#533C2211yescharacteristic
66C61×#529C2211yescharacteristic
67C61×#525—21no—
68C2×C22⋊Q8×C61—21no—
69C61×#520—21no—
70C2×C4×D4×C61C2211yescharacteristic
71C2×#11758202—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C22×#92418—21no—
76C22×#92418—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519769—21no—
80#14519756—21no—
81#14519756—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84#14519736—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—22no—
89#14519710—22no—
90#14519708—21no—
91#14519708—22no—
92#14519708—22no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519700—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106C22⋊#92418—21no—
107#14519688—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C22×Q8×C61—21no—
114C22×D4×C61D411yescharacteristic
115C23×C4×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#126×C61—22no—
120#126×C61—22no—
121#126×C61—21no—
122#125×C61—22no—
123#125×C61D412yes—
124#125×C61D411yescharacteristic
125#124×C61—22no—
126#124×C61—21no—
127#124×C61D411yescharacteristic
128#123×C61—22no—
129#123×C61—22no—
130#123×C61—21no—
131#123×C61—22no—
132#123×C61—22no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—22no—
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—21no—
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61—21no—
143C22⋊Q8×C61D411yescharacteristic
144#121×C61—22no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61D411yescharacteristic
148#120×C61—22no—
149C4×Q8×C61—21no—
150C4×Q8×C61—21no—
151C4×Q8×C61—21no—
152C4×Q8×C61C2311yescharacteristic
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C4×D4×C61—22no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61D411yescharacteristic
161C4×D4×C61D411yescharacteristic
162C4×D4×C61C2311yescharacteristic
163C4×D4×C61C2311yescharacteristic
164C4×D4×C61C2311yescharacteristic
165#117×C61—22no—
166#117×C61—21no—
167#117×C61—21no—
168#117×C61D412yes—
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C24×C61—21no—
177#41×C61—42no—
178#41×C61—42no—
179#41×C61—81no—
180#41×C61—81no—
181C2×Q8×C61—22no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—81no—
185C2×Q8×C61—81no—
186C2×Q8×C61C2×D411yescharacteristic
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—41no—
193C2×D4×C61C2×D411yescharacteristic
194C2×D4×C61C2×D411yescharacteristic
195C2×D4×C61C2×D411yescharacteristic
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—81no—
206C22×C4×C61—81no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C2×Dic122—21no—
211C2×Dic122—21no—
212C4⋊C4×C61—22no—
213C4⋊C4×C61—22no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61C2×D411yescharacteristic
226C4⋊C4×C61C2×D411yescharacteristic
227C4⋊C4×C61C2×D411yescharacteristic
228C4⋊C4×C61C2×D411yescharacteristic
229C4⋊C4×C61C2×D412yes—
230C4⋊C4×C61C2×D412yes—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C42×C61—22no—
247C42×C61—22no—
248C42×C61—21no—
249C42×C61C2×D411yescharacteristic
250C42×C61C2×D411yescharacteristic
251C42×C61C2×D411yescharacteristic
252C42×C61C2411yescharacteristic
253C22⋊Dic61—41no—
254#11758202—81no—
255#11758200—42no—
256#11758200—42no—
257#11758200—81no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262#11758196—41no—
263#11758196—41no—
264C4×Dic61—41no—
265C2×#92418—24no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—81no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61—81no—
279C23×C61#12011yescharacteristic
280Q8×C61—21no—
281Q8×C61—21no—
282Q8×C61—41no—
283Q8×C61—41no—
284Q8×C61—41no—
285Q8×C61—41no—
286Q8×C61—82no—
287D4×C61—21no—
288D4×C61—21no—
289D4×C61—21no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—42no—
293D4×C61—44no—
294D4×C61—42no—
295D4×C61—82no—
296D4×C61#13512yes—
297C2×C4×C61—22no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—44no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—81no—
317C2×C4×C61—81no—
318C2×C4×C61—81no—
319C2×C4×C61—82no—
320C2×C4×C61—82no—
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×Dic61—41no—
328C2×Dic61—41no—
329Dic122—41no—
330Dic122—41no—
331Dic122—41no—
332Dic122—41no—
333#92418—22no—
334#92418—22no—
335#92418—41no—
336#92418—41no—
337#92418—41no—
338#92418—41no—
339#18648—611nomaximal, Sylow
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—22no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—84no—
352C22×C61#45612yes—
353C22×C61C2×#12011yescharacteristic
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—21no—
357C4×C61—21no—
358C4×C61—41no—
359C4×C61—42no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61—42no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61C2×#13511yescharacteristic
366C4×C61#57511yescharacteristic
367C4×C61#57611yescharacteristic
368C4×C61#57711yescharacteristic
369Dic61—81no—
370Dic61—81no—
371#3520D6111yescharacteristic
372#3248—611no—
373#3160—611no—
374#3110—611no—
375#1654—611no—
376#1654—611no—
377#1652—611no—
378#1651—611no—
379#1650—611no—
380#1649—611no—
381#1647—611no—
382#1647—611no—
383#1552—611no—
384#1494—611no—
385C2×D4⋊C8—611no—
386C2×C61—22no—
387C2×C61—42no—
388C2×C61—81no—
389C2×C61—81no—
390C2×C61#300211yescharacteristic
391C2×C61#301211yescharacteristic
392C2×C61C2×#45611yescharacteristic
393#556C2×D6111yescharacteristic
394#554—21no—
395#552—21no—
396#551—22no—
397D4×Q8C2×D6111yescharacteristic
398#548—21no—
399#547C2×D6111yescharacteristic
400#547C2×D6111yescharacteristic
401#546—21no—
402#542—21no—
403#539—22no—
404#533—611no—
405#533C2×D6111yescharacteristic
406#529C2×D6111yescharacteristic
407#525—21no—
408C2×C22⋊Q8—21no—
409#520—21no—
410C2×C4×D4C2×D6111yescharacteristic
411#500—611no—
412#500—611no—
413#499—1222no—
414#498—611no—
415#498—611no—
416#484—1221no—
417#479—1221no—
418#475—611no—
419#474—611no—
420#474—611no—
421#474—611no—
422#467—1221no—
423#465—1221no—
424#464—1221no—
425#462—611no—
426#461—611no—
427#461—611no—
428#461—611no—
429#450—1221no—
430#440—1221no—
431#440—1221no—
432#432—611no—
433#427—1222no—
434C2×C4⋊C8—611no—
435C2×C4×C8—611no—
436#332—611no—
437#332—611no—
438#332—611no—
439#332—611no—
440Q8⋊C8—611no—
441Q8⋊C8—611no—
442D4⋊C8—611no—
443D4⋊C8—611no—
444D4⋊C8—611no—
445D4⋊C8—611no—
446D4⋊C8—611no—
447D4⋊C8—611no—
448C61#1864811yescharacteristic, complemented, Sylow
449C2×#41—21no—
450C2×#41—21no—
451C22×Q8—21no—
452C22×D4C22⋊D6111yescharacteristic
453C23×C4—21no—
454C2×Q16—1221no—
455C2×SD16—1221no—
456C2×SD16—1221no—
457C2×SD16—1221no—
458C22×C8—1221no—
459C22×C8—1221no—
460C4⋊Q8—21no—
461C4⋊Q8—611no—
462C4⋊Q8—611no—
463C4⋊Q8C22×D6111yescharacteristic
464C4⋊Q8C22×D6111yescharacteristic
465#126—22no—
466#126—22no—
467#126—21no—
468#125—22no—
469#125—1221no—
470#125C22⋊D6111yescharacteristic
471#125C22⋊D6112yes—
472#124—22no—
473#124—21no—
474#124C22⋊D6111yescharacteristic
475#123—22no—
476#123—22no—
477#123—21no—
478#123—22no—
479#123—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—1221no—
491C22⋊Q8—1221no—
492C22⋊Q8C22⋊D6111yescharacteristic
493#121—22no—
494#121—21no—
495#121—21no—
496#121C22⋊D6111yescharacteristic
497#120—22no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—1221no—
502C4×Q8—1221no—
503C4×Q8C22×D6111yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4C22⋊D6111yescharacteristic
512C4×D4C22⋊D6111yescharacteristic
513C4×D4C22×D6111yescharacteristic
514C4×D4C22×D6111yescharacteristic
515C4×D4C22×D6111yescharacteristic
516#117—22no—
517#117—21no—
518#117—21no—
519#117—1221no—
520#117C22⋊D6112yes—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4C22⋊D6111yescharacteristic
525C2×C22⋊C4—22no—
526C2×C22⋊C4—21no—
527C2×C42C22×D6111yescharacteristic
528#107—1222no—
529#107—1222no—
530#107—1221no—
531#107—1221no—
532#107—1221no—
533#106—1222no—
534#106—1222no—
535#106—1221no—
536C4⋊C8—611no—
537C4⋊C8—611no—
538C4⋊C8—611no—
539C4⋊C8—611no—
540C4⋊C8—1221no—
541#103—1221no—
542#103—1221no—
543#103—1221no—
544#103—1221no—
545#103—1221no—
546#102—1221no—
547#102—1221no—
548#102—1221no—
549C22⋊C8—1221no—
550#97—1221no—
551C4×C8—611no—
552C4×C8—611no—
553C4×C8—1221no—
554C24—21no—
555#41—42no—
556#41—42no—
557#41—81no—
558#41—81no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—81no—
563C2×Q8—81no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8C2×C22⋊D6111yescharacteristic
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—41no—
573C2×D4C2×C22⋊D6111yescharacteristic
574C2×D4C2×C22⋊D6111yescharacteristic
575C2×D4C2×C22⋊D6111yescharacteristic
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C2×C22⋊D6111yescharacteristic
590Q16—4881no—
591SD16—4881no—
592SD16—2442no—
593SD16—2442no—
594C2×C8—1224no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—4881no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—2441no—
620C4⋊C4—2441no—
621C4⋊C4C2×C22⋊D6111yescharacteristic
622C4⋊C4C2×C22⋊D6111yescharacteristic
623C4⋊C4C2×C22⋊D6111yescharacteristic
624C4⋊C4C2×C22⋊D6111yescharacteristic
625C4⋊C4C2×C22⋊D6112yes—
626C4⋊C4C2×C22⋊D6112yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—2441no—
643C42—22no—
644C42—21no—
645C42—22no—
646C42—2441no—
647C42C2×C22⋊D6111yescharacteristic
648C42C2×C22⋊D6111yescharacteristic
649C42C2×C22⋊D6111yescharacteristic
650C42C23×D6111yescharacteristic
651C23—21no—
652C23—21no—
653C23—21no—
654C23—42no—
655C23—42no—
656C23—81no—
657C23#1451974611yescharacteristic
658Q8—21no—
659Q8—21no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—82no—
665Q8—2441no—
666Q8—2441no—
667Q8—2441no—
668Q8—2441no—
669D4—21no—
670D4—21no—
671D4—21no—
672D4—21no—
673D4—21no—
674D4—42no—
675D4—44no—
676D4—42no—
677D4—82no—
678D4#1451979712yes—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4#1451974611yescharacteristic
706C2×C4#1451974611yescharacteristic
707C2×C4#1451974611yescharacteristic
708C2×C4C22×C22⋊D6111yescharacteristic
709C2×C4C22×C22⋊D6111yescharacteristic
710C2×C4C22×C22⋊D6111yescharacteristic
711C8—1222no—
712C8—1222no—
713C8—2441no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C22—21no—
718C22—21no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—84no—
729C22#1683994512yes—
730C22C2×#1451974611yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—42no—
742C4—4881no—
743C4—4881no—
744C4C2×#1451979711yescharacteristic
745C4#1684056011yescharacteristic
746C4#1684056511yescharacteristic
747C4#1684057311yescharacteristic
748C2—22no—
749C2—42no—
750C2—81no—
751C2—81no—
752C2#2145503711yescharacteristic
753C2#2145512311yescharacteristic
754C2C2×#1683994511yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3520C2
socleC22×C61C2×#120
hypercenter#3520D61
hypocenterC61#18648
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #21457156C2semidirect
2. #21456329C2semidirect
3. #21455918C2semidirect
4. #21445103C2semidirect
5. #21445103C2semidirect
6. #21445089C2semidirect
7. #21445082C2semidirect
8. #21445075C2semidirect
9. #21445068C2semidirect
10. #21445054C2semidirect
11. #21445054C2semidirect
12. #21444519C2semidirect
13. #21444279C2semidirect
14. C2×D4⋊#92418C2semidirect
17. #16840165C22semidirect
18. #16840165C22semidirect
20. #16840158C22semidirect
21. #16840158C22semidirect
24. #16840047C22semidirect
27. #16840042C22semidirect
31. #16839972C22semidirect
34. #16839967C22semidirect
42. #16839508C22semidirect
43. #16839508C22semidirect
44. #16839508C22semidirect
45. #16839508C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
448. C61#18648semidirect

Maximal subgroups

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

subgroupindex
#214571562
#214563292
#214559182
#214451032
#214450892
#214450822
#214450752
#214450682
#214450542
#214445192
#214442792
C2×D4⋊#924182
C61×#35202
#1864861