Finite Group Databasebeta

← #30611270

Subgroups — #30611270

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462676C211yesmaximal, characteristic, complemented
2#21462302C211yesmaximal, characteristic, complemented
3#21461255C211yesmaximal, characteristic, complemented
4#21461254C211yesmaximal, characteristic, complemented
5#21461246C211yesmaximal, characteristic, complemented
6#21461245C211yesmaximal, characteristic, complemented
7#21461237C211yesmaximal, characteristic, complemented
8#21461234C211yesmaximal, characteristic, complemented
9#21461225C211yesmaximal, characteristic, complemented
10#21461224C211yesmaximal, characteristic, complemented
11#21461220C211yesmaximal, characteristic, complemented
12#21461209C211yesmaximal, characteristic, complemented
13#21461198C211yesmaximal, characteristic, complemented
14#21461191C211yesmaximal, characteristic, complemented
15#21459848C211yesmaximal, characteristic
16#16840795—21no—
17#16840793—21no—
18#16840792—21no—
19#16840789—21no—
20#16840785C2211yescharacteristic, complemented
21#16840780C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic, complemented
23#16840733C2211yescharacteristic, complemented
24C2×#14519834C2211yescharacteristic, complemented
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840714—21no—
27#16840713—21no—
28#16840712—21no—
29#16840712—21no—
30#16840705C2211yescharacteristic, complemented
31#16840705C2211yescharacteristic, complemented
32#16840704C2211yescharacteristic, complemented
33#16840704C2211yescharacteristic, complemented
34C4×C4⋊#6923C2211yescharacteristic, complemented
35#16840698C2211yescharacteristic, complemented
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic, complemented
41#16840614C2211yescharacteristic, complemented
42#16840614C2211yescharacteristic, complemented
43#16840614C2211yescharacteristic, complemented
44#16840613C2211yescharacteristic
45#16840613C2211yescharacteristic
46#16840613C2211yescharacteristic
47#16840613C2211yescharacteristic
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840476C411yescharacteristic, complemented
53#16840470C411yescharacteristic, complemented
54#16840462C411yescharacteristic, complemented
55#16840458C411yescharacteristic, complemented
56#16840457—21no—
57#16840431C411yescharacteristic, complemented
58#16840409—21no—
59#16840405C411yescharacteristic, complemented
60#16840402—21no—
61D4×C22⋊D61C411yescharacteristic, complemented
62#16840394—21no—
63#16840362—21no—
64#16840348—21no—
65#16840347—21no—
66#16840309C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519748C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840235—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#546C411yescharacteristic, complemented
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88#14519844—21no—
89#14519844—21no—
90#14519834—21no—
91#14519834—21no—
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98#14519832—21no—
99C4×#92420—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×#11758226C2×C411yescharacteristic
108C2×#11758222—21no—
109C22×C22⋊D61—21no—
110C22×C22⋊D61—21no—
111C2×D4×D61—21no—
112C2×D4×D61C2×C411yescharacteristic
113C2×D4×D61D411yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116#14519776C2×C411yescharacteristic
117#14519773—21no—
118#14519773C2×C411yescharacteristic
119#14519772—21no—
120#14519770—21no—
121#14519770—21no—
122#14519769C2×C411yescharacteristic
123#14519767—21no—
124#14519764—21no—
125#14519763—21no—
126#14519763—21no—
127#14519762—21no—
128#14519760—21no—
129#14519759—21no—
130#14519759—21no—
131#14519759—21no—
132#14519758—21no—
133#14519757—21no—
134#14519754—21no—
135#14519753C2×C411yescharacteristic
136#14519753C2311yescharacteristic
137#14519752C2311yescharacteristic
138#14519751—21no—
139#14519751C2×C411yescharacteristic
140#14519751C2×C411yescharacteristic
141#14519750—21no—
142#14519750—21no—
143#14519750—21no—
144#14519750—21no—
145#14519749—21no—
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748—21no—
152#14519748C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic
154#14519748C2×C411yescharacteristic
155#14519748C2311yescharacteristic
156#14519748C2311yescharacteristic
157#14519747—21no—
158#14519747—21no—
159#14519746—21no—
160#14519745—21no—
161#14519745—21no—
162Q8×Dic61C2×C411yescharacteristic
163C4×D244C2×C411yescharacteristic
164C4×D244C2×C411yescharacteristic
165D4×Dic61C2×C411yescharacteristic
166D4×Dic61D411yescharacteristic
167#14519739—21no—
168#14519739D411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519736C2×C411yescharacteristic
183#14519735C2×C411yescharacteristic
184#14519733—21no—
185#14519733—21no—
186C2×C4⋊Dic61C2×C411yescharacteristic
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61D411yescharacteristic
189C2×C22⋊Dic61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#124×C61C2×C411yescharacteristic
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#120×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C22⋊C4×C61—21no—
206C24×C61—21no—
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214#41×C61—81no—
215C2×Q8×C61C22×C411yescharacteristic
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—81no—
220C2×D4×C61C22⋊C411yescharacteristic
221C2×D4×C61C22×C411yescharacteristic
222C2×D4×C61C22×C411yescharacteristic
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—44no—
238C2×C22⋊D61—81no—
239C2×C22⋊D61—81no—
240C2×C22⋊D61C22⋊C411yescharacteristic
241C2×C22⋊D61C22⋊C411yescharacteristic
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246#11758226—81no—
247D4×D61—42no—
248D4×D61—81no—
249D4×D61—81no—
250D4×D61—81no—
251#11758222—81no—
252#11758222—81no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244C22⋊C411yescharacteristic
256C2×D244C22×C411yescharacteristic
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—81no—
261C2×C4×D61—81no—
262C2×C4×D61C22×C411yescharacteristic
263C2×C4×D61C22×C411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2411yescharacteristic
271C2×Dic122—21no—
272C22⋊#6923—81no—
273C22⋊#6923—81no—
274C22⋊#6923—81no—
275C22⋊#6923—81no—
276#11758217—81no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—81no—
282C4⋊#6923—42no—
283C4⋊#6923—81no—
284C4⋊#6923—81no—
285C4×#6923—42no—
286C4×#6923—81no—
287#11758213—81no—
288D61⋊C8—81no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C22⋊C411yescharacteristic
291C4⋊C4×C61C22×C411yescharacteristic
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61C22⋊C411yescharacteristic
298C22⋊C4×C61C22⋊C411yescharacteristic
299C42×C61C22×C411yescharacteristic
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61C22⋊C411yescharacteristic
308C22⋊Dic61C22⋊C411yescharacteristic
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318#11758198C22⋊C411yescharacteristic
319#11758198C22⋊C411yescharacteristic
320C4⋊Dic61—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61C22⋊C411yescharacteristic
323C4⋊Dic61C22×C411yescharacteristic
324C4⋊Dic61C22×C411yescharacteristic
325C4⋊Dic61C22×C411yescharacteristic
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—42no—
343C23×C61—81no—
344C23×C61—81no—
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—42no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C22×D411yescharacteristic
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—
373C2×#6923—41no—
374Q8×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—81no—
379D4×C61—81no—
380D4×C61—81no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—81no—
386C2×C4×C61—81no—
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C23×C411yescharacteristic
392C22⋊D61—22no—
393C22⋊D61—22no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—42no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C22⋊D61—81no—
405C22⋊D61—81no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—42no—
412C2×Dic61—81no—
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C22×D411yescharacteristic
418D244—41no—
419D244—41no—
420D244—41no—
421D244—41no—
422D244—81no—
423C4×D61—21no—
424C4×D61—21no—
425C4×D61—22no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—81no—
436Dic122—81no—
437#92420—41no—
438#92420—41no—
439#92420—41no—
440#92420—41no—
441#17599—611nomaximal, Sylow
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—162no—
455C22×C61C22×C22⋊C411yescharacteristic
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—81no—
468C2×D61—81no—
469C2×D61—81no—
470C2×D61—81no—
471C2×D61—162no—
472C2×D61#57611yescharacteristic
473C2×D61#57711yescharacteristic
474#6923—81no—
475#6923—81no—
476#6923—81no—
477#6923—81no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—41no—
484C4×C61—41no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492Dic61#42112yes—
493#3519—611no—
494#2974—611no—
495#2319—611no—
496#1519—611no—
497#1519—611no—
498#1516—611no—
499#1516—611no—
500#1513—611no—
501#1513—611no—
502#1510—611no—
503#1510—611no—
504#1509—611no—
505#1505—611no—
506#1502—611no—
507#1500—611no—
508C2×C61—41no—
509C2×C61—41no—
510C2×C61—81no—
511C2×C61—81no—
512C2×C61#288311yescharacteristic
513C2×C61#289711yescharacteristic
514C2×C61C2×#42111yescharacteristic
515D61—21no—
516D61—21no—
517D61—41no—
518D61—41no—
519D61—81no—
520#555—611no—
521#554—611no—
522#553—611no—
523#553—611no—
524#553—1221no—
525#550—611no—
526#546—611no—
527#546—1221no—
528#546—1221no—
529#546#692311yescharacteristic, complemented
530D42—611no—
531D42—1221no—
532#540—1221no—
533#538—1221no—
534#538—1221no—
535#532—611no—
536#529—611no—
537#525—611no—
538#525—611no—
539C2×#121—611no—
540C2×#121—611no—
541#518—1221no—
542C2×C4×D4—611no—
543#436—1221no—
544#435—1221no—
545#435—1221no—
546C8×D4—1221no—
547#432—611no—
548#431—611no—
549#407—611no—
550#407—611no—
551C2×C22⋊C8—611no—
552C2×C22⋊C8—611no—
553#390—1221no—
554#389—1221no—
555#388—1221no—
556#388—1221no—
557#381—611no—
558#381—611no—
559#380—611no—
560#380—611no—
561C4×C4⋊C4—611no—
562#376—611no—
563#328—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#327—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579C61#1759911yescharacteristic, complemented, Sylow
580C2×#41—611no—
581C2×#41—1221no—
582C2×#41C2×#692311yescharacteristic
583C22×D4—611no—
584C22×D4—611no—
585C22×D4—1221no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4C2×#692311yescharacteristic
589C23×C4—611no—
590C23×C4—611no—
591C2×M16—1221no—
592C2×M16—1221no—
593C22×C8—1221no—
594C22×C8—1221no—
595C4⋊Q8—611no—
596#127—611no—
597#127—1221no—
598#126—1221no—
599#126—1221no—
600#126—1221no—
601#125—611no—
602#125—1221no—
603#124—1221no—
604#124—1221no—
605#124—1221no—
606#124C2×#692311yescharacteristic
607#123—21no—
608#123—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614C22⋊Q8—611no—
615C22⋊Q8—611no—
616C22⋊Q8—1221no—
617C22⋊Q8—1221no—
618C22⋊Q8C2×#692311yescharacteristic
619#121—21no—
620#121—611no—
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—1221no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121C2×#692311yescharacteristic
641#120—21no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647C4×Q8—611no—
648C4×D4—611no—
649C4×D4—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4C2×#692311yescharacteristic
668C4×D4C2×#692311yescharacteristic
669#117—611no—
670#117—611no—
671#117—1221no—
672#117—1221no—
673C2×C4⋊C4—611no—
674C2×C4⋊C4—611no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4—1221no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—611no—
690C2×C42—1221no—
691C2×C42—1221no—
692C4⋊C8—1221no—
693C4⋊C8—1221no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—611no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701C22⋊C8—1221no—
702#97—1221no—
703C4×C8—1221no—
704#95—611no—
705#95—611no—
706#95—611no—
707#95—611no—
708#95—1221no—
709#95—1221no—
710#95—1221no—
711C24—21no—
712C24—611no—
713C24—611no—
714C24—1221no—
715#41—81no—
716#41—4881no—
717#41—4881no—
718#41—4881no—
719C2×Q8—1221no—
720C2×Q8C22×#692311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—81no—
725C2×D4—611no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—611no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—4881no—
742C2×D4—4881no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—2442no—
747C2×D4—2444no—
748C2×D4C22⋊#692311yescharacteristic
749C2×D4C22×#692311yescharacteristic
750C2×D4C22×#692311yescharacteristic
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—4881no—
774C22×C4—4881no—
775C22×C4C22×#692311yescharacteristic
776C22×C4C22×#692311yescharacteristic
777M16—4881no—
778M16—4881no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8—1221no—
783C2×C8—4881no—
784C2×C8—4881no—
785C4⋊C4—21no—
786C4⋊C4—611no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
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—4881no—
801C4⋊C4—4881no—
802C4⋊C4—2442no—
803C4⋊C4C22⋊#692311yescharacteristic
804C4⋊C4C22×#692311yescharacteristic
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—611no—
811C22⋊C4—611no—
812C22⋊C4—611no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—4881no—
831C22⋊C4—4881no—
832C22⋊C4—4881no—
833C22⋊C4—4881no—
834C22⋊C4C22⋊#692311yescharacteristic
835C22⋊C4C22⋊#692311yescharacteristic
836C42—611no—
837C42—611no—
838C42—611no—
839C42—1221no—
840C42—1221no—
841C42—1221no—
842C42—4881no—
843C42—2442no—
844C42C22×#692311yescharacteristic
845C23—21no—
846C23—21no—
847C23—42no—
848C23—81no—
849C23—81no—
850C23—611no—
851C23—611no—
852C23—611no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—1221no—
858C23—4881no—
859C23—4881no—
860C23—2441no—
861C23—2441no—
862C23—2441no—
863C23—2441no—
864C23—2442no—
865C23C2×C22⋊#692311yescharacteristic
866C23C2×C22⋊#692311yescharacteristic
867Q8—41no—
868Q8—4881no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—81no—
873D4—81no—
874D4—81no—
875D4—1222no—
876D4—1222no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—2441no—
884D4—2441no—
885D4—2441no—
886D4—2441no—
887D4—2442no—
888D4—2442no—
889D4—2441no—
890D4—2441no—
891D4—2441no—
892D4—2441no—
893D4—2442no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—611no—
901C2×C4—611no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—1222no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—4881no—
914C2×C4—4881no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2442no—
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×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4C2×C22⋊#692311yescharacteristic
938C2×C4C2×C22⋊#692311yescharacteristic
939C2×C4C2×C22⋊#692311yescharacteristic
940C2×C4C2×C22⋊#692311yescharacteristic
941C2×C4C23×#692311yescharacteristic
942C8—2441no—
943C8—2441no—
944C8—2441no—
945C8—2441no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—162no—
959C22—611no—
960C22—611no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—1221no—
968C22—1221no—
969C22—9762no—
970C22—4881no—
971C22—4881no—
972C22—4881no—
973C22—4881no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22C22×C22⋊#692311yescharacteristic
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—41no—
984C4—41no—
985C4—612no—
986C4—1221no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—4881no—
991C4—4881no—
992C4—4881no—
993C4—4881no—
994C4—2441no—
995C4—2441no—
996C4—2441no—
997C2—41no—
998C2—41no—
999C2—81no—
1000C2—81no—
1001C2—1221no—
1002C2—1221no—
1003C2—4881no—
1004C2—2441no—
1005C2—2441no—
1006C2#2146241811yescharacteristic
1007C2#2146244011yescharacteristic
1008C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459848C2
cosocleC2×C4×D61C24
hypercenter#546#6923
hypocenterC61#17599
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462676C2semidirect
2. #21462302C2semidirect
3. #21461255C2semidirect
4. #21461254C2semidirect
5. #21461246C2semidirect
6. #21461245C2semidirect
7. #21461237C2semidirect
8. #21461234C2semidirect
9. #21461225C2semidirect
10. #21461224C2semidirect
11. #21461220C2semidirect
12. #21461209C2semidirect
13. #21461198C2semidirect
14. #21461191C2semidirect
20. #16840785C22semidirect
21. #16840780C22semidirect
22. #16840734C22semidirect
23. #16840733C22semidirect
24. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
30. #16840705C22semidirect
31. #16840705C22semidirect
32. #16840704C22semidirect
33. #16840704C22semidirect
34. C4×C4⋊#6923C22semidirect
35. #16840698C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840614C22semidirect
41. #16840614C22semidirect
42. #16840614C22semidirect
43. #16840614C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
52. #16840476C4semidirect
53. #16840470C4semidirect
54. #16840462C4semidirect
55. #16840458C4semidirect
57. #16840431C4semidirect
59. #16840405C4semidirect
61. D4×C22⋊D61C4semidirect
74. C61×#546C4semidirect
529. #546#6923semidirect
579. C61#17599semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214623022
#214612552
#214612542
#214612462
#214612452
#214612372
#214612342
#214612252
#214612242
#214612202
#214612092
#214611982
#214611912
#214598482
#1759961