Finite Group Databasebeta

← #30620441

Subgroups — #30620441

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#446C211yesmaximal, characteristic, complemented
2#21462338C211yesmaximal, characteristic, complemented
3#21462003C211yesmaximal, characteristic, complemented
4#21462002C211yesmaximal, characteristic, complemented
5#21462001C211yesmaximal, characteristic, complemented
6#21461999C211yesmaximal, characteristic, complemented
7#21461999C211yesmaximal, characteristic, complemented
8#21461998C211yesmaximal, characteristic, complemented
9#21461689C211yesmaximal, characteristic
10#21461689C211yesmaximal, characteristic
11#21461687C211yesmaximal, characteristic
12#21461589C211yesmaximal, characteristic
13#21461589C211yesmaximal, characteristic
14C4×#14519839C211yesmaximal, characteristic
15#554×D61C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19#16840812—21no—
20D61⋊(C4⋊C8)C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22D61⋊(C4⋊C8)C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27#16840721C2211yescharacteristic
28#16840721C2211yescharacteristic
29C4×D61⋊C8C2211yescharacteristic
30(C2×#6923)⋊Q8—21no—
31#16840711—21no—
32#16840711—21no—
33#16840708C2211yescharacteristic
34#16840706C2211yescharacteristic
35#16840706C2211yescharacteristic
36C4⋊C4×#6923—21no—
37C4×C4⋊#6923C2211yescharacteristic
38C4×C4⋊#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840473C411yescharacteristic, complemented
53#16840472C411yescharacteristic, complemented
54#16840471C411yescharacteristic, complemented
55#16840471C411yescharacteristic, complemented
56#16840470—21no—
57#16840469C411yescharacteristic, complemented
58#16840468C411yescharacteristic, complemented
59#16840468C411yescharacteristic, complemented
60#16840467—21no—
61#16840466—21no—
62#16840466—21no—
63C4⋊Q8×D61C2211yescharacteristic
64#125×D61C2211yescharacteristic
65#125×D61C2211yescharacteristic
66C22⋊Q8×D61—21no—
67C22⋊Q8×D61—21no—
68C22⋊Q8×D61—21no—
69C4×Q8×D61C2211yescharacteristic
70C4×D4×D61C2211yescharacteristic
71C4×D4×D61C2211yescharacteristic
72C4×D4×D61C2211yescharacteristic
73C2×C4⋊C4×D61—21no—
74C61×#554C411yescharacteristic, complemented
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94#14519839—22no—
95#14519839—22no—
96#14519839—22no—
97#14519839Q814yescomplemented
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101#14519832—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111C2×Q8×D61—21no—
112C2×Q8×D61D411yescharacteristic
113C2×D4×D61C2311yescharacteristic
114C22×C4×D61—21no—
115C22×C4×D61—21no—
116C22×C4×D61—21no—
117#14519777C2×C411yescharacteristic
118#14519776—21no—
119#14519776C2×C411yescharacteristic
120#14519776C2×C411yescharacteristic
121#14519775—21no—
122#14519769C2×C411yescharacteristic
123#14519769C2×C411yescharacteristic
124#14519768C2×C411yescharacteristic
125#14519768C2×C411yescharacteristic
126#14519768C2×C411yescharacteristic
127#14519768C2×C411yescharacteristic
128#14519767—21no—
129#14519767—21no—
130#14519767—21no—
131#14519767—21no—
132#14519757—21no—
133#14519757—21no—
134#14519757—21no—
135#14519756—21no—
136#14519756—21no—
137#14519756—21no—
138#14519755—21no—
139#14519755—21no—
140#14519755—21no—
141#14519755—21no—
142#14519755—21no—
143#14519755—21no—
144#14519754—21no—
145#14519754—21no—
146#14519754—21no—
147#14519754—21no—
148#14519754—21no—
149#14519754—21no—
150#14519753—21no—
151#14519753—21no—
152#14519753—21no—
153Q8×Dic61D411yescharacteristic
154C4×Dic122C2×C411yescharacteristic
155C4×Dic122C2×C411yescharacteristic
156C4×Dic122C2×C411yescharacteristic
157#14519742D411yescharacteristic
158#14519742D411yescharacteristic
159#14519742D411yescharacteristic
160C4×D244C2×C411yescharacteristic
161C4×D244C2×C411yescharacteristic
162C4×D244C2×C411yescharacteristic
163D4×Dic61C2×C411yescharacteristic
164D4×Dic61C2×C411yescharacteristic
165D4×Dic61C2×C411yescharacteristic
166#14519739C2×C411yescharacteristic
167#14519739C2×C411yescharacteristic
168#14519739C2×C411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172#14519737—21no—
173#14519737—21no—
174#14519737—21no—
175C2×C4⋊Dic61—21no—
176C2×#11758196—21no—
177C2×#11758196—21no—
178C4⋊C4×D61—21no—
179C4⋊C4×D61—21no—
180C4⋊C4×D61—21no—
181C4⋊C4×D61—21no—
182C4⋊C4×D61—21no—
183C4⋊C4×D61—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61D411yescharacteristic
188C4⋊C4×D61D411yescharacteristic
189C4⋊C4×D61D411yescharacteristic
190C4⋊C4×D61C2311yescharacteristic
191C4⋊C4×D61C2311yescharacteristic
192C4⋊C4×D61C2311yescharacteristic
193C22⋊C4×D61—21no—
194C22⋊C4×D61—21no—
195C22⋊C4×D61—21no—
196C42×D61C2311yescharacteristic
197C42×D61C2311yescharacteristic
198C42×D61C2311yescharacteristic
199C4⋊Q8×C61C2×C411yescharacteristic
200#125×C61C2×C411yescharacteristic
201#125×C61C2×C411yescharacteristic
202C22⋊Q8×C61—21no—
203C22⋊Q8×C61—21no—
204C22⋊Q8×C61—21no—
205C4×Q8×C61C2×C411yescharacteristic
206C4×D4×C61C2×C411yescharacteristic
207C4×D4×C61C2×C411yescharacteristic
208C4×D4×C61C2×C411yescharacteristic
209C2×C4⋊C4×C61—21no—
210C23×D61—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61C22⋊C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C2×C22⋊D61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225Q8×D61—41no—
226Q8×D61—41no—
227Q8×D61—81no—
228Q8×D61—81no—
229D4×D61—21no—
230D4×D61—21no—
231D4×D61C2×Q812yes—
232D4×D61#4112yes—
233C2×D244C22×C411yescharacteristic
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—42no—
244C2×C4×D61—42no—
245C2×C4×D61—81no—
246C2×C4×D61—81no—
247C2×C4×D61—81no—
248C2×C4×D61—81no—
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2411yescharacteristic
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122C22⋊C411yescharacteristic
260C2×Dic122C22⋊C411yescharacteristic
261C2×Dic122C22⋊C411yescharacteristic
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C4⋊#6923—21no—
267C4⋊#6923—21no—
268C4⋊#6923—21no—
269C4⋊#6923—21no—
270C4⋊#6923—21no—
271C4⋊#6923—21no—
272C4⋊#6923—21no—
273C4⋊#6923—42no—
274C4⋊#6923—81no—
275C4⋊#6923C2×Q812yes—
276C4×#6923—42no—
277C4×#6923—81no—
278C4×#6923—81no—
279D61⋊C8—21no—
280D61⋊C8—21no—
281D61⋊C8—21no—
282D61⋊C8—21no—
283D61⋊C8—21no—
284D61⋊C8—21no—
285D61⋊C8—21no—
286D61⋊C8C2×Q812yes—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61C22⋊C411yescharacteristic
293C4⋊C4×C61C22⋊C411yescharacteristic
294C4⋊C4×C61C22⋊C411yescharacteristic
295C4⋊C4×C61C22×C411yescharacteristic
296C4⋊C4×C61C22×C411yescharacteristic
297C4⋊C4×C61C22×C411yescharacteristic
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C42×C61C22×C411yescharacteristic
302C42×C61C22×C411yescharacteristic
303C42×C61C22×C411yescharacteristic
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61C22⋊C411yescharacteristic
319C4⋊Dic61C22⋊C411yescharacteristic
320C4⋊Dic61C22⋊C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323C4⋊Dic61C22×C411yescharacteristic
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196C22⋊C411yescharacteristic
338#11758196C22⋊C411yescharacteristic
339#11758196C22⋊C411yescharacteristic
340#11758196C22⋊C411yescharacteristic
341#11758196C22⋊C411yescharacteristic
342#11758196C22⋊C411yescharacteristic
343C4×Dic61C22×C411yescharacteristic
344C4×Dic61C22×C411yescharacteristic
345C4×Dic61C22×C411yescharacteristic
346C4×Dic61C2×D411yescharacteristic
347C4×Dic61C2×D411yescharacteristic
348C4×Dic61C2×D411yescharacteristic
349C4×Dic61C2×D411yescharacteristic
350C4×Dic61C2×D411yescharacteristic
351C4×Dic61C2×D411yescharacteristic
352C23×C61—21no—
353C22×D61—21no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61C22×D411yescharacteristic
361C2×#6923—22no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923—41no—
369C2×#6923—41no—
370C2×#6923—41no—
371C2×#6923—41no—
372C2×#6923—41no—
373Q8×C61—41no—
374Q8×C61—81no—
375D4×C61—21no—
376D4×C61C4×Q812yes—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—42no—
381C2×C4×C61—81no—
382C2×C4×C61—81no—
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C23×C411yescharacteristic
390C22⋊D61—22no—
391C22⋊D61—22no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—42no—
396C2×Dic61—81no—
397C2×Dic61—81no—
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C22×D411yescharacteristic
405D244—21no—
406D244C4×Q812yes—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—21no—
411C4×D61—21no—
412C4×D61—21no—
413C4×D61—21no—
414C4×D61—21no—
415C4×D61—21no—
416C4×D61—21no—
417C4×D61—21no—
418C4×D61—21no—
419C4×D61—42no—
420C4×D61—42no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—81no—
428C4×D61—81no—
429C4×D61—81no—
430C4×D61—81no—
431C4×D61C22×Q811yescharacteristic
432C4×D61C2×#4111yescharacteristic
433C4×D612−1+411yescharacteristic
434C4×D612−1+411yescharacteristic
435Dic122—41no—
436Dic122—41no—
437Dic122—41no—
438Dic122—81no—
439Dic122—81no—
440Dic122—81no—
441#92420—22no—
442#92420—41no—
443#92420—41no—
444#92420—41no—
445#22526—611nomaximal, Sylow
446C22×C61—22no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61C22×C22⋊C411yescharacteristic
450C2×D61—22no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—42no—
457C2×D61#54811yescharacteristic
458C2×D61D4×Q811yescharacteristic
459C2×D61#57511yescharacteristic
460C2×D61#57511yescharacteristic
461C2×D61#57611yescharacteristic
462C2×D61#57711yescharacteristic
463#6923—42no—
464#6923—81no—
465#6923—81no—
466#6923—81no—
467C4×C61—21no—
468C4×C61—21no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—41no—
474C4×C61—41no—
475C4×C61—41no—
476C4×C61C2×C4×Q811yescharacteristic
477C4×C61#51911yescharacteristic
478Dic61—21no—
479Dic61—21no—
480Dic61—21no—
481Dic61—21no—
482Dic61—21no—
483Dic61—21no—
484Dic61—41no—
485Dic61—41no—
486Dic61—41no—
487Dic61#54811yescharacteristic
488Dic61D4×Q811yescharacteristic
489C2×#554—611no—
490C2×#446—611no—
491#2355—611no—
492#1993—611no—
493#1992—611no—
494#1991—611no—
495#1989—611no—
496#1989—611no—
497#1988—611no—
498#1804—611no—
499#1804—611no—
500#1802—611no—
501#1762—611no—
502#1762—611no—
503C4×#102—611no—
504C2×C61—42no—
505C2×C61Q8×C22⋊C411yescharacteristic
506C2×C61#289611yescharacteristic
507C2×C61#289711yescharacteristic
508D61—42no—
509D61#337011yescharacteristic
510D61#337611yescharacteristic
511D61#338811yescharacteristic
512D61#338911yescharacteristic
513#554—611no—
514#554—611no—
515#554—611no—
516#554—611no—
517#554—611no—
518#554—611no—
519#554—611no—
520#554—1221no—
521#554—1221no—
522#554—1221no—
523#554—1221no—
524#554#692311yescharacteristic, complemented
525C2×C4⋊Q8—611no—
526C2×#125—611no—
527C2×#125—611no—
528C2×C22⋊Q8—1221no—
529C2×C22⋊Q8—1221no—
530C2×C22⋊Q8—1221no—
531C2×C4×Q8—611no—
532C2×C4×D4—611no—
533C2×C4×D4—611no—
534C2×C4×D4—611no—
535C22×C4⋊C4—1221no—
536#446—1221no—
537#446—1221no—
538#446—1221no—
539#446—1221no—
540C2×C4⋊C8—611no—
541C2×C4⋊C8—611no—
542C2×C4⋊C8—611no—
543C2×#102—611no—
544C2×#102—611no—
545C2×#102—611no—
546C2×#102—611no—
547C2×#97—611no—
548C2×#97—611no—
549C2×C4×C8—611no—
550#391—1221no—
551#387—1221no—
552#387—1221no—
553#384—611no—
554#382—611no—
555#382—611no—
556C4×C4⋊C4—611no—
557C4×C4⋊C4—611no—
558C4×C4⋊C4—611no—
559C4×C4⋊C4—1221no—
560#340—611no—
561#340—611no—
562#340—611no—
563#340—611no—
564#340—611no—
565#340—611no—
566#340—611no—
567#340—611no—
568#340—611no—
569#340—611no—
570#340—611no—
571#340—611no—
572C61#2252611yescharacteristic, complemented, Sylow
573C22×Q8—611no—
574C22×Q8—1221no—
575C22×D4—611no—
576C23×C4—1221no—
577C23×C4—1221no—
578C23×C4—1221no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—611no—
583C4⋊Q8—611no—
584C4⋊Q8—611no—
585C4⋊Q8—611no—
586C4⋊Q8—1221no—
587C4⋊Q8—1221no—
588C4⋊Q8C2×#692311yescharacteristic
589#125—611no—
590#125—611no—
591#125—611no—
592#125—611no—
593#125—611no—
594#125—611no—
595#125—1221no—
596#125—1221no—
597#125—1221no—
598#125—1221no—
599#125C2×#692311yescharacteristic
600#125C2×#692311yescharacteristic
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8—1221no—
616C22⋊Q8—1221no—
617C22⋊Q8—1221no—
618C22⋊Q8—1221no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8—1221no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625C4×Q8—611no—
626C4×Q8—611no—
627C4×Q8—611no—
628C4×Q8—611no—
629C4×Q8—611no—
630C4×Q8—611no—
631C4×Q8—611no—
632C4×Q8C2×#692311yescharacteristic
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4C2×#692311yescharacteristic
649C4×D4C2×#692311yescharacteristic
650C4×D4C2×#692311yescharacteristic
651C2×C4⋊C4—21no—
652C2×C4⋊C4—611no—
653C2×C4⋊C4—611no—
654C2×C4⋊C4—611no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—1221no—
663C2×C4⋊C4—1221no—
664C2×C4⋊C4—1221no—
665C2×C4⋊C4—1221no—
666C2×C4⋊C4—1221no—
667C2×C4⋊C4—1221no—
668C2×C4⋊C4—1221no—
669C2×C4⋊C4—1221no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4—1221no—
672C2×C4⋊C4—1221no—
673C2×C4⋊C4—1221no—
674C2×C4⋊C4—1221no—
675C2×C4⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C22⋊C4—1221no—
679C2×C42—611no—
680C2×C42—611no—
681C2×C42—611no—
682C2×C42—1221no—
683C2×C42—1221no—
684C2×C42—1221no—
685C4⋊C8—1221no—
686C4⋊C8—1221no—
687C4⋊C8—1221no—
688C4⋊C8—1221no—
689C4⋊C8—1221no—
690C4⋊C8—1221no—
691#102—614no—
692#102—1222no—
693#102—1222no—
694#102—1222no—
695#97—1221no—
696#97—1221no—
697#97—1221no—
698#97—1221no—
699C4×C8—1221no—
700C4×C8—1221no—
701#95—1221no—
702#95—1221no—
703#95—1221no—
704#95—1221no—
705#95—1221no—
706#95—1221no—
707#95—1221no—
708C24—1221no—
709C2×Q8—21no—
710C2×Q8—611no—
711C2×Q8—611no—
712C2×Q8—611no—
713C2×Q8—1221no—
714C2×Q8—1221no—
715C2×Q8—1221no—
716C2×Q8—4881no—
717C2×Q8—4881no—
718C2×Q8—2441no—
719C2×Q8—2441no—
720C2×Q8C22⋊#692311yescharacteristic
721C2×D4—612no—
722C2×D4—612no—
723C2×D4—611no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4C22×#692311yescharacteristic
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—4881no—
755C22×C4—4881no—
756C22×C4—4881no—
757C22×C4—4881no—
758C22×C4—2442no—
759C22×C4—2442no—
760C2×C8—612no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—611no—
778C4⋊C4—611no—
779C4⋊C4—611no—
780C4⋊C4—611no—
781C4⋊C4—611no—
782C4⋊C4—611no—
783C4⋊C4—611no—
784C4⋊C4—611no—
785C4⋊C4—611no—
786C4⋊C4—612no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—611no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—1221no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1221no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—4881no—
816C4⋊C4—2442no—
817C4⋊C4C22⋊#692311yescharacteristic
818C4⋊C4C22⋊#692311yescharacteristic
819C4⋊C4C22⋊#692311yescharacteristic
820C4⋊C4C22×#692311yescharacteristic
821C4⋊C4C22×#692311yescharacteristic
822C4⋊C4C22×#692311yescharacteristic
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C42—611no—
836C42—611no—
837C42—611no—
838C42—611no—
839C42—611no—
840C42—611no—
841C42—611no—
842C42—611no—
843C42—611no—
844C42—4881no—
845C42—4881no—
846C42—2442no—
847C42C22×#692311yescharacteristic
848C42C22×#692311yescharacteristic
849C42C22×#692311yescharacteristic
850C23—21no—
851C23—611no—
852C23—1222no—
853C23—1222no—
854C23—1221no—
855C23—2441no—
856C23—2441no—
857C23—2441no—
858C23—2441no—
859Q8—41no—
860Q8—81no—
861Q8—4881no—
862Q8—4881no—
863Q8—4881no—
864Q8—2441no—
865Q8—2441no—
866Q8—2441no—
867D4—21no—
868D4—612no—
869D4—1222no—
870D4—1222no—
871D4—1221no—
872D4Q8×#692312yes—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—42no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—611no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1221no—
901C2×C4—1221no—
902C2×C4—1222no—
903C2×C4—1221no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—4881no—
907C2×C4—4881no—
908C2×C4—4881no—
909C2×C4—4881no—
910C2×C4—4881no—
911C2×C4—4881no—
912C2×C4—2442no—
913C2×C4—2442no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2442no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4C2×C22⋊#692311yescharacteristic
933C2×C4C2×C22⋊#692311yescharacteristic
934C2×C4C2×C22⋊#692311yescharacteristic
935C2×C4C2×C22⋊#692311yescharacteristic
936C2×C4C2×C22⋊#692311yescharacteristic
937C2×C4C2×C22⋊#692311yescharacteristic
938C2×C4C23×#692311yescharacteristic
939C8—1222no—
940C8—2441no—
941C8—2441no—
942C8—2441no—
943C22—22no—
944C22—41no—
945C22—41no—
946C22—611no—
947C22—611no—
948C22—611no—
949C22—611no—
950C22—611no—
951C22—611no—
952C22—1222no—
953C22—2442no—
954C22—2442no—
955C22—2442no—
956C22—2442no—
957C22—2441no—
958C22—2441no—
959C22C22×C22⋊#692311yescharacteristic
960C4—21no—
961C4—21no—
962C4—21no—
963C4—21no—
964C4—21no—
965C4—21no—
966C4—41no—
967C4—41no—
968C4—41no—
969C4—611no—
970C4—611no—
971C4—1221no—
972C4—1221no—
973C4—1221no—
974C4—1221no—
975C4—1221no—
976C4—1221no—
977C4—4881no—
978C4—4881no—
979C4—4881no—
980C4—2442no—
981C4—2441no—
982C4—2441no—
983C4—2441no—
984C4C2×Q8×#692311yescharacteristic
985C4#1684083011yescharacteristic
986C2—42no—
987C2—611no—
988C2—611no—
989C2—611no—
990C2—611no—
991C2—2442no—
992C2Q8×C22⋊#692311yescharacteristic
993C2#2146243911yescharacteristic
994C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#554#6923
hypocenterC61#22526
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. D61⋊#446C2semidirect
2. #21462338C2semidirect
3. #21462003C2semidirect
4. #21462002C2semidirect
5. #21462001C2semidirect
6. #21461999C2semidirect
7. #21461999C2semidirect
8. #21461998C2semidirect
52. #16840473C4semidirect
53. #16840472C4semidirect
54. #16840471C4semidirect
55. #16840471C4semidirect
57. #16840469C4semidirect
58. #16840468C4semidirect
59. #16840468C4semidirect
74. C61×#554C4semidirect
97. #14519839Q8semidirect
524. #554#6923semidirect
572. C61#22526semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4462
#214623382
#214620032
#214620022
#214620012
#214619992
#214619982
#214616892
#214616872
#214615892
C4×#145198392
#554×D612
#2252661