Finite Group Databasebeta

← #30611638

Subgroups — #30611638

Order 15616.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462659C211yesmaximal, characteristic, complemented
2#21462505C211yesmaximal, characteristic, complemented
3#21461311C211yesmaximal, characteristic, complemented
4#21461306C211yesmaximal, characteristic, complemented
5#21461305C211yesmaximal, characteristic, complemented
6#21461301C211yesmaximal, characteristic, complemented
7#21461297C211yesmaximal, characteristic, complemented
8#21461296C211yesmaximal, characteristic, complemented
9#21461292C211yesmaximal, characteristic, complemented
10#21461287C211yesmaximal, characteristic, complemented
11#21461283C211yesmaximal, characteristic, complemented
12#21461281C211yesmaximal, characteristic, complemented
13#21461272C211yesmaximal, characteristic, complemented
14C2×#16840619C211yesmaximal, characteristic, complemented
15#21459798C211yesmaximal, characteristic
16#16840814—21no—
17#16840794—21no—
18#16840793—21no—
19#16840789—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic
23#16840785C2211yescharacteristic
24#16840784C2211yescharacteristic
25#16840783C2211yescharacteristic
26#16840783C2211yescharacteristic
27#16840782C2211yescharacteristic
28#16840782C2211yescharacteristic
29#16840768—21no—
30#16840735—21no—
31C4×#11758217C2211yescharacteristic
32C4×#11758217C2211yescharacteristic
33#16840721C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36#16840619C2211yescharacteristic
37#16840619C2211yescharacteristic
38#16840619C2211yescharacteristic
39#16840619C2211yescharacteristic
40#16840619C2211yescharacteristic
41#16840619C2211yescharacteristic
42#16840619C2211yescharacteristic
43#16840619C2211yescharacteristic
44#16840619C2211yescharacteristic
45#16840619C2211yescharacteristic
46#16840619C2211yescharacteristic
47#16840619C2211yescharacteristic
48#16840618C2211yescharacteristic
49#16840618C2211yescharacteristic
50#16840618C2211yescharacteristic
51#16840618C2211yescharacteristic
52#16840491C411yescharacteristic
53#16840473C411yescharacteristic
54#16840460C411yescharacteristic
55#16840460C411yescharacteristic
56#16840454—21no—
57#16840454—21no—
58#16840454C411yescharacteristic
59#16840454C411yescharacteristic
60#16840450—21no—
61#16840416—21no—
62#16840416C411yescharacteristic
63#16840375—21no—
64#16840361—21no—
65#16840361—21no—
66#16840317C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840298C2211yescharacteristic
69#16840298C2211yescharacteristic
70C2×#14519768C2211yescharacteristic
71C2×#14519768C2211yescharacteristic
72#16840241—21no—
73C4×#11758224C2211yescharacteristic
74C61×#554C411yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103#14519832C2311yescharacteristic
104#14519832C2311yescharacteristic
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758224—21no—
108C2×#11758224D411yescharacteristic
109#14519777—21no—
110#14519777C2×C411yescharacteristic
111#14519772—21no—
112#14519772—21no—
113#14519772—21no—
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519768—21no—
119#14519768—21no—
120#14519768—21no—
121#14519768—21no—
122#14519768—21no—
123#14519768—21no—
124#14519768—21no—
125#14519768—21no—
126#14519768C2×C411yescharacteristic
127#14519768C2×C411yescharacteristic
128#14519768C2×C411yescharacteristic
129#14519768C2×C411yescharacteristic
130#14519768C2311yescharacteristic
131#14519768C2311yescharacteristic
132#14519768C2311yescharacteristic
133#14519766C2311yescharacteristic
134#14519762—21no—
135#14519762—21no—
136#14519762—21no—
137#14519761—21no—
138#14519761—21no—
139#14519761—21no—
140#14519761—21no—
141#14519761—21no—
142#14519761—21no—
143#14519757—21no—
144#14519757—21no—
145#14519757—21no—
146#14519753—21no—
147#14519753—21no—
148#14519753—21no—
149#14519753C2×C411yescharacteristic
150#14519752C2×C411yescharacteristic
151#14519751—21no—
152#14519751—21no—
153#14519751C2×C411yescharacteristic
154#14519751C2×C411yescharacteristic
155Q8×Dic61—21no—
156Q8×Dic61C2×C411yescharacteristic
157Q8×Dic61C2×C411yescharacteristic
158C4×Dic122—21no—
159C4×Dic122C2×C411yescharacteristic
160#14519742—21no—
161#14519742D411yescharacteristic
162C4×D244—21no—
163C4×D244C2×C411yescharacteristic
164D4×Dic61D411yescharacteristic
165#14519739C2×C411yescharacteristic
166#14519739C2×C411yescharacteristic
167C4×C22⋊D61—21no—
168C4×C22⋊D61—21no—
169C4×C22⋊D61C2×C411yescharacteristic
170C4×C22⋊D61C2×C411yescharacteristic
171#14519737—21no—
172#14519737—21no—
173#14519737D411yescharacteristic
174#14519737D411yescharacteristic
175#14519735—21no—
176#14519735—21no—
177#14519735C2×C411yescharacteristic
178#14519735C2×C411yescharacteristic
179#14519735D411yescharacteristic
180#14519734—21no—
181#14519733—21no—
182#14519733—21no—
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C2×C4⋊Dic61—21no—
186C2×C4⋊Dic61—21no—
187C2×C4⋊Dic61C2×C411yescharacteristic
188C2×C4⋊Dic61C2×C411yescharacteristic
189C2×#11758196—21no—
190C2×#11758196—21no—
191C4⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#125×C61—21no—
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic
201C4×Q8×C61C2×C411yescharacteristic
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C2×C4⋊C4×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61C22⋊C411yescharacteristic
216C2×C22⋊D61C22⋊C411yescharacteristic
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758224—42no—
224#11758224—44no—
225C2×D244—21no—
226C2×D244C22×C411yescharacteristic
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×Dic122—21no—
234C2×Dic122C22⋊C411yescharacteristic
235#11758217—42no—
236#11758217—42no—
237C2×#92420—21no—
238C2×#92420—21no—
239C2×#92420—21no—
240C2×#92420—21no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—42no—
246C2×#92420—42no—
247D61⋊C8—42no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22⋊C411yescharacteristic
255C4⋊C4×C61C22×C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61C22⋊C411yescharacteristic
261C22⋊C4×C61C22⋊C411yescharacteristic
262C42×C61—21no—
263C42×C61C22×C411yescharacteristic
264C22⋊Dic61C22⋊C411yescharacteristic
265C22⋊Dic61C22⋊C411yescharacteristic
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198C22⋊C411yescharacteristic
278#11758198C22⋊C411yescharacteristic
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61C22⋊C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293C4⋊Dic61C22×C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61C22×C411yescharacteristic
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2411yescharacteristic
320C23×C61C2×C22⋊C411yescharacteristic
321C23×C61C2×C22⋊C411yescharacteristic
322C22×D61—21no—
323C22×D61C2×C22⋊C411yescharacteristic
324Q8×C61—41no—
325Q8×C61—81no—
326D4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—81no—
334C2×C4×C61—81no—
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C2×C4×C61C2×C22⋊C411yescharacteristic
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C23×C411yescharacteristic
340C22⋊D61—22no—
341C22⋊D61—41no—
342C22⋊D61—42no—
343C22⋊D61—42no—
344C2×Dic61—22no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C22×D411yescharacteristic
359C2×Dic61C22×D411yescharacteristic
360D244—41no—
361D244—81no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—42no—
366C4×D61—81no—
367C4×D61—81no—
368Dic122—41no—
369Dic122—42no—
370#92420—22no—
371#92420—41no—
372#92420—41no—
373#92420—41no—
374#92420—41no—
375#92420—41no—
376#92420—41no—
377#92420—41no—
378#17680—611nomaximal, Sylow
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61#42112yes—
385C22×C61C22×C22⋊C411yescharacteristic
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61—41no—
401Dic61—21no—
402Dic61—21no—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—41no—
409Dic61—41no—
410Dic61—41no—
411#3515—611no—
412#2970—611no—
413#2923—611no—
414#1537—611no—
415#1535—611no—
416#1535—611no—
417#1534—611no—
418#1532—611no—
419#1532—611no—
420#1531—611no—
421#1529—611no—
422#1528—611no—
423#1528—611no—
424#1524—611no—
425C2×#330—611no—
426C2×C61—22no—
427C2×C61—41no—
428C2×C61#288911yescharacteristic
429C2×C61C2×#42111yescharacteristic
430C2×C61#290111yescharacteristic
431D61—41no—
432D61—81no—
433#557—611no—
434#554—611no—
435#554#692311yescharacteristic
436#553—611no—
437#553—611no—
438#552—611no—
439#552—611no—
440#552—1221no—
441#552—1221no—
442#552—1221no—
443#547—611no—
444#547—1221no—
445#541—1221no—
446#539—1221no—
447#539—1221no—
448#533—611no—
449#529—611no—
450#529—611no—
451#529—611no—
452C2×#125—611no—
453C2×#125—611no—
454#520—1221no—
455C4×#41—611no—
456#446—1221no—
457#435—1221no—
458#435—1221no—
459C8×D4—1221no—
460#433—1221no—
461#433—1221no—
462#432—611no—
463#432—611no—
464#432—611no—
465#432—611no—
466#432—611no—
467#432—611no—
468#432—611no—
469#424—1221no—
470#408—1221no—
471C4×M16—611no—
472C4×M16—611no—
473C2×#97—611no—
474C2×#97—611no—
475C2×#97—611no—
476#330—611no—
477#330—611no—
478#330—611no—
479#330—611no—
480#330—611no—
481#330—611no—
482#330—611no—
483#330—611no—
484#330—611no—
485#330—611no—
486#330—611no—
487#330—611no—
488#329—611no—
489#329—611no—
490#329—611no—
491#329—611no—
492C61#1768011yescharacteristic, complemented, Sylow
493C2×#41—611no—
494C2×#41—1221no—
495C2×M16—1221no—
496C2×M16—1221no—
497C22×C8—1221no—
498C22×C8—1221no—
499C22×C8—1221no—
500C4⋊Q8—611no—
501C4⋊Q8—1221no—
502C4⋊Q8C2×#692311yescharacteristic
503#126—1221no—
504#126—1221no—
505#126—1221no—
506#126—1221no—
507#126—1221no—
508#126—1221no—
509#126—1221no—
510#125—21no—
511#125—611no—
512#125—611no—
513#125—611no—
514#125—611no—
515#125—611no—
516#125—611no—
517#125—611no—
518#125—1221no—
519#125—1221no—
520#125—1221no—
521#125—1221no—
522#125—1221no—
523#125—1221no—
524#125—1221no—
525#125—1221no—
526#124—611no—
527#123—1221no—
528#123—1221no—
529#123—1221no—
530#123—1221no—
531#123—1221no—
532#123—1221no—
533#123—1221no—
534#123—1221no—
535#123—1221no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—611no—
539C22⋊Q8—1221no—
540C22⋊Q8—1221no—
541C22⋊Q8—1221no—
542C22⋊Q8—1221no—
543C22⋊Q8—1221no—
544C22⋊Q8—1221no—
545C22⋊Q8C2×#692311yescharacteristic
546C22⋊Q8C2×#692311yescharacteristic
547#121—611no—
548#121—611no—
549#121—611no—
550#121—1221no—
551#121—1221no—
552C4×Q8—611no—
553C4×Q8—611no—
554C4×Q8—611no—
555C4×Q8—611no—
556C4×Q8—1221no—
557C4×Q8—1221no—
558C4×Q8—1221no—
559C4×Q8C2×#692311yescharacteristic
560C4×D4—21no—
561C4×D4—611no—
562C4×D4—611no—
563C4×D4—611no—
564C4×D4—611no—
565C4×D4—611no—
566C4×D4—611no—
567C4×D4—611no—
568C4×D4—611no—
569C4×D4—1221no—
570C4×D4—1221no—
571C4×D4—1221no—
572C4×D4—1221no—
573C4×D4—1221no—
574C4×D4C2×#692311yescharacteristic
575#117—611no—
576#117—611no—
577#117—611no—
578#117—611no—
579#117—611no—
580#117—1221no—
581#117—1221no—
582#117—1221no—
583#117—1221no—
584#117—1221no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4C2×#692311yescharacteristic
593C2×C4⋊C4C2×#692311yescharacteristic
594C2×C42—611no—
595C2×C42—611no—
596C2×C42—611no—
597C4⋊C8—1221no—
598C4⋊C8—1221no—
599C4⋊C8—1221no—
600C4⋊C8—1221no—
601C4⋊C8—1221no—
602C4⋊C8—1221no—
603C4⋊C8—1221no—
604C22⋊C8—1221no—
605C22⋊C8—1221no—
606C22⋊C8—1221no—
607C22⋊C8—1221no—
608C22⋊C8—1221no—
609C22⋊C8—1221no—
610C22⋊C8—1221no—
611#97—611no—
612#97—611no—
613#97—611no—
614#97—611no—
615#97—611no—
616#97—611no—
617#97—611no—
618#97—611no—
619#97—1221no—
620#97—1221no—
621#97—1221no—
622C4×C8—1221no—
623C4×C8—1221no—
624#41—2442no—
625#41—2444no—
626C2×Q8—21no—
627C2×Q8—611no—
628C2×Q8—1221no—
629C2×Q8C22×#692311yescharacteristic
630C2×D4—611no—
631C2×D4—611no—
632C2×D4—611no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4C22⋊#692311yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4C22×#692311yescharacteristic
652C22×C4C22×#692311yescharacteristic
653M16—2442no—
654M16—2442no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—2442no—
664C2×C8—2442no—
665C2×C8—2442no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—611no—
673C4⋊C4—611no—
674C4⋊C4—611no—
675C4⋊C4—611no—
676C4⋊C4—611no—
677C4⋊C4—611no—
678C4⋊C4—611no—
679C4⋊C4—611no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4C22⋊#692311yescharacteristic
701C4⋊C4C22×#692311yescharacteristic
702C4⋊C4C22×#692311yescharacteristic
703C4⋊C4C22×#692311yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—611no—
707C22⋊C4—611no—
708C22⋊C4—611no—
709C22⋊C4—611no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4C22⋊#692311yescharacteristic
722C22⋊C4C22⋊#692311yescharacteristic
723C42—21no—
724C42—611no—
725C42—611no—
726C42—611no—
727C42—611no—
728C42—611no—
729C42—611no—
730C42—611no—
731C42—611no—
732C42—611no—
733C42—1221no—
734C42—1221no—
735C42—1221no—
736C42—1221no—
737C42C22×#692311yescharacteristic
738C23—611no—
739C23—1221no—
740C23C2×C22⋊#692311yescharacteristic
741C23C2×C22⋊#692311yescharacteristic
742Q8—41no—
743Q8—81no—
744Q8—2441no—
745Q8—2442no—
746D4—22no—
747D4—1222no—
748D4—4881no—
749D4—2441no—
750D4—2441no—
751D4—2442no—
752D4—2442no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—1222no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—4881no—
773C2×C4—4881no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2442no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4C2×C22⋊#692311yescharacteristic
784C2×C4C2×C22⋊#692311yescharacteristic
785C2×C4C2×C22⋊#692311yescharacteristic
786C2×C4C2×C22⋊#692311yescharacteristic
787C2×C4C23×#692311yescharacteristic
788C8—1222no—
789C8—2441no—
790C8—2441no—
791C8—2441no—
792C8—2441no—
793C8—2441no—
794C8—2441no—
795C8—2441no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—1221no—
802C22—1221no—
803C22—1221no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22#1684076112yes—
808C22C22×C22⋊#692311yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—1221no—
819C4—1221no—
820C4—1221no—
821C4—1221no—
822C4—1221no—
823C4—1221no—
824C4—1221no—
825C4—2441no—
826C4—2441no—
827C4—2441no—
828C2—22no—
829C2—41no—
830C2—4881no—
831C2—2441no—
832C2#2146243111yescharacteristic
833C2C2×#1684076111yescharacteristic
834C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radical#21459798C2
cosocleC4×Dic61C24
hypercenter#554#6923
hypocenterC61#17680
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #21462659C2semidirect
2. #21462505C2semidirect
3. #21461311C2semidirect
4. #21461306C2semidirect
5. #21461305C2semidirect
6. #21461301C2semidirect
7. #21461297C2semidirect
8. #21461296C2semidirect
9. #21461292C2semidirect
10. #21461287C2semidirect
11. #21461283C2semidirect
12. #21461281C2semidirect
13. #21461272C2semidirect
14. C2×#16840619C2semidirect
492. C61#17680semidirect

Maximal subgroups

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

subgroupindex
#214626592
#214625052
#214613112
#214613062
#214613052
#214613012
#214612972
#214612962
#214612922
#214612872
#214612832
#214612812
#214612722
C2×#168406192
#214597982
#1768061