Finite Group Databasebeta

← #30611256

Subgroups — #30611256

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462676C211yesmaximal, characteristic, complemented
2#21462301C211yesmaximal, characteristic, complemented
3#21461261C211yesmaximal, characteristic, complemented
4#21461254C211yesmaximal, characteristic, complemented
5#21461250C211yesmaximal, characteristic, complemented
6#21461247C211yesmaximal, characteristic, complemented
7#21461240C211yesmaximal, characteristic, complemented
8#21461236C211yesmaximal, characteristic, complemented
9#21461230C211yesmaximal, characteristic, complemented
10#21461225C211yesmaximal, characteristic, complemented
11#21461214C211yesmaximal, characteristic, complemented
12#21461207C211yesmaximal, characteristic, complemented
13#21461196C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459854C211yesmaximal, 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#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840709—21no—
30#16840707C2211yescharacteristic, complemented
31#16840706C2211yescharacteristic, complemented
32#16840705C2211yescharacteristic, complemented
33#16840704C2211yescharacteristic, complemented
34C4×C22⋊#6923C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic, complemented
41#16840614C2211yescharacteristic, complemented
42#16840614C2211yescharacteristic, complemented
43#16840614C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic, complemented
45#16840614C2211yescharacteristic, complemented
46#16840614C2211yescharacteristic, complemented
47#16840614C2211yescharacteristic, complemented
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840473C411yescharacteristic, complemented
53#16840456—21no—
54#16840456C411yescharacteristic, complemented
55#16840456C411yescharacteristic, complemented
56#16840433C411yescharacteristic, complemented
57#16840409C411yescharacteristic, complemented
58#16840409C411yescharacteristic, complemented
59#16840405—21no—
60#16840405—21no—
61D4×D244C411yescharacteristic, complemented
62#16840396—21no—
63#16840365—21no—
64#16840346—21no—
65#16840346—21no—
66#16840313C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840274C2211yescharacteristic
69#16840274C2211yescharacteristic
70#121×D61C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840236—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#555C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87#14519844—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97C4×#92420—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—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×#11758226—21no—
108C2×#11758222C2×C411yescharacteristic
109C2×#11758222C2×C411yescharacteristic, complemented
110C22×D244—21no—
111C2×D4×D61—21no—
112C2×D4×D61—21no—
113C2×D4×D61C2×C411yescharacteristic
114C2×D4×D61C2×C411yescharacteristic, complemented
115C2×D4×D61D411yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118#14519774C2×C411yescharacteristic, complemented
119#14519773—21no—
120#14519771—21no—
121#14519771—21no—
122#14519770—21no—
123#14519768—21no—
124#14519768C2×C411yescharacteristic, complemented
125#14519766—21no—
126#14519764C2×C411yescharacteristic, complemented
127#14519761—21no—
128#14519761—21no—
129#14519759—21no—
130#14519759—21no—
131#14519759—21no—
132#14519759—21no—
133#14519759—21no—
134#14519757C2×C411yescharacteristic
135#14519757C2×C411yescharacteristic, complemented
136#14519757C2311yescharacteristic
137#14519753—21no—
138#14519753—21no—
139#14519752—21no—
140#14519752C2×C411yescharacteristic
141#14519752C2×C411yescharacteristic, complemented
142#14519752C2311yescharacteristic
143#14519752C2311yescharacteristic
144#14519751—21no—
145#14519751C2×C411yescharacteristic
146#14519751C2×C411yescharacteristic, complemented
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519749—21no—
154#14519749—21no—
155#14519748—21no—
156#14519748—21no—
157#14519748C2311yescharacteristic
158#14519747—21no—
159#14519747—21no—
160#14519747—21no—
161#14519747—21no—
162#14519745—21no—
163#14519745—21no—
164C4×Dic122C2×C411yescharacteristic, complemented
165C4×D244—21no—
166C4×D244—21no—
167C4×D244—21no—
168C4×D244—21no—
169C4×D244—21no—
170C4×D244—21no—
171C4×D244C2×C411yescharacteristic
172D4×Dic61D411yescharacteristic
173#14519739—21no—
174#14519739—21no—
175#14519739—21no—
176#14519739C2×C411yescharacteristic, complemented
177#14519739C2×C411yescharacteristic, complemented
178#14519739D411yescharacteristic
179C4×C22⋊D61—21no—
180C4×C22⋊D61C2×C411yescharacteristic
181C4×C22⋊D61C2×C411yescharacteristic
182#14519737D411yescharacteristic
183#14519737D411yescharacteristic
184#14519736—21no—
185C4⋊C4×D61C2×C411yescharacteristic
186C4⋊C4×D61C2×C411yescharacteristic, complemented
187C4⋊C4×D61D411yescharacteristic
188C22⋊C4×D61—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic, complemented
196#124×C61—21no—
197#124×C61—21no—
198#121×C61—21no—
199#121×C61C2×C411yescharacteristic
200#121×C61C2×C411yescharacteristic, complemented
201C4×D4×C61C2×C411yescharacteristic
202C4×D4×C61C2×C411yescharacteristic, complemented
203#117×C61—21no—
204#117×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic, complemented
206C23×D61—21no—
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—42no—
215C22×#6923—81no—
216C22×#6923—81no—
217C2×Q8×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61C22⋊C411yescharacteristic
221C2×D4×C61C22×C411yescharacteristic
222C22×C4×C61—21no—
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236#11758226—81no—
237#11758226—81no—
238D4×D61—42no—
239D4×D61—81no—
240D4×D61—81no—
241D4×D61—81no—
242D4×D61—81no—
243D4×D61—81no—
244D4×D61—81no—
245#11758222—81no—
246#11758222—81no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—44no—
254C2×D244C22⋊C411yescharacteristic
255C2×D244C22×C411yescharacteristic
256C2×D244C22×C411yescharacteristic
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—81no—
264C2×C4×D61—81no—
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2411yescharacteristic
274C2×Dic122C22×C411yescharacteristic
275C22⋊#6923—42no—
276C22⋊#6923—81no—
277C22⋊#6923—81no—
278#11758217—81no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—21no—
283C2×#92420—81no—
284C4⋊#6923—81no—
285C4⋊#6923—81no—
286C4×#6923—81no—
287#11758213—81no—
288D61⋊C8—81no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C22⋊C411yescharacteristic
291C4⋊C4×C61C22×C411yescharacteristic
292C4⋊C4×C61C22×C411yescharacteristic
293C4⋊C4×C61C22×C411yescharacteristic
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61C22⋊C411yescharacteristic
300C22⋊C4×C61C22⋊C411yescharacteristic
301C42×C61—21no—
302C42×C61—21no—
303C42×C61C22×C411yescharacteristic
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#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198C22⋊C411yescharacteristic
321#11758198C22⋊C411yescharacteristic
322#11758198C22⋊C411yescharacteristic
323#11758198C22⋊C411yescharacteristic
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61—21no—
328C4⋊Dic61C22⋊C411yescharacteristic
329C4⋊Dic61C22×C411yescharacteristic
330#11758196—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196C22⋊C411yescharacteristic
335#11758196C22⋊C411yescharacteristic
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C23×C61—21no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—22no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—81no—
356C22×D61—81no—
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—
374C2×#6923—84no—
375Q8×C61—81no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—81no—
379D4×C61—81no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—42no—
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C23×C411yescharacteristic
391C22⋊D61—22no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—81no—
396C22⋊D61—81no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C22×D411yescharacteristic
410D244—22no—
411D244—41no—
412D244—41no—
413D244—42no—
414D244—42no—
415D244—41no—
416D244—41no—
417D244—41no—
418D244—41no—
419D244—42no—
420D244—81no—
421C4×D61—21no—
422C4×D61—21no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—81no—
432C4×D61—81no—
433C4×D61—81no—
434C4×D61—81no—
435C4×D61—81no—
436C4×D61—81no—
437Dic122—41no—
438#92420—41no—
439#92420—41no—
440#92420—41no—
441#92420—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61C22×C22⋊C411yescharacteristic
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—21no—
459C2×D61—21no—
460C2×D61—42no—
461C2×D61—42no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—81no—
469C2×D61—81no—
470C2×D61—162no—
471C2×D61—162no—
472C2×D61#42112yes—
473C2×D61#57611yescharacteristic
474C2×D61#57711yescharacteristic
475#6923—81no—
476#6923—81no—
477#6923—81no—
478#6923—81no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—41no—
493Dic61—41no—
494#3519—611no—
495#2974—611no—
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517—611no—
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327—611no—
509C2×C61—41no—
510C2×C61—41no—
511C2×C61—81no—
512C2×C61#288311yescharacteristic
513C2×C61#289711yescharacteristic
514C2×C61C2×#42111yescharacteristic
515D61—21no—
516D61—21no—
517D61—22no—
518D61—41no—
519D61—81no—
520D61—81no—
521#555#692311yescharacteristic, complemented
522#554—611no—
523#553—611no—
524#553—611no—
525#553—1221no—
526#550—611no—
527#546—611no—
528#546—611no—
529#546—1221no—
530#546—1221no—
531D42—611no—
532D42—1221no—
533#540—1221no—
534#538—1221no—
535#538—1221no—
536#532—611no—
537#529—611no—
538#525—611no—
539#525—611no—
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382—611no—
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#328—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—
579#327—611no—
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—1221no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—1221no—
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—1221no—
596C22×C8—1221no—
597C4⋊Q8C2×#692311yescharacteristic, complemented
598#127—611no—
599#127—1221no—
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#125—611no—
604#125—1221no—
605#124—21no—
606#124—21no—
607#124—611no—
608#124—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621#121—21no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
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#121—1221no—
641#121C2×#692311yescharacteristic
642#121C2×#692311yescharacteristic, complemented
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
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×D4—1221no—
668C4×D4—1221no—
669C4×D4C2×#692311yescharacteristic
670C4×D4C2×#692311yescharacteristic, complemented
671#117—21no—
672#117—1221no—
673#117C2×#692311yescharacteristic
674#117C2×#692311yescharacteristic, complemented
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
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—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—611no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—1221no—
702C4×C8—1221no—
703#95—611no—
704#95—611no—
705#95—611no—
706#95—611no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95—1221no—
711#95—1221no—
712C24—611no—
713C24—611no—
714C24—1221no—
715C24—1221no—
716#41—4881no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—21no—
721C2×Q8—611no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—611no—
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—1221no—
742C2×D4—4881no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—2444no—
749C2×D4—2442no—
750C2×D4C22⋊#692311yescharacteristic
751C2×D4C22×#692311yescharacteristic
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—1221no—
774C22×C4—4881no—
775C22×C4—4881no—
776C22×C4—4881no—
777C22×C4—4881no—
778C22×C4—2442no—
779C22×C4C22×#692311yescharacteristic
780C22×C4C22×#692311yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—21no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
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—4881no—
803C4⋊C4—4881no—
804C4⋊C4C22⋊#692311yescharacteristic
805C4⋊C4C22×#692311yescharacteristic
806C4⋊C4C22×#692311yescharacteristic
807C4⋊C4C22×#692311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—611no—
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—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—4881no—
834C22⋊C4—4881no—
835C22⋊C4—2442no—
836C22⋊C4C22⋊#692311yescharacteristic
837C22⋊C4C22⋊#692311yescharacteristic
838C42—21no—
839C42—21no—
840C42—611no—
841C42—611no—
842C42—611no—
843C42—1221no—
844C42—4881no—
845C42C22×#692311yescharacteristic
846C23—21no—
847C23—611no—
848C23—611no—
849C23—611no—
850C23—1221no—
851C23—1221no—
852C23—1222no—
853C23—1221no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—2441no—
862C23—2441no—
863C23—2441no—
864C23—2442no—
865C23—2442no—
866C23C2×C22⋊#692311yescharacteristic
867C23C2×C22⋊#692311yescharacteristic
868Q8—81no—
869Q8—2441no—
870D4—41no—
871D4—41no—
872D4—81no—
873D4—81no—
874D4—1222no—
875D4—1222no—
876D4—4881no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—2441no—
884D4—2441no—
885D4—2442no—
886D4—2441no—
887D4—2441no—
888D4—2441no—
889D4—2441no—
890D4—2442no—
891D4—2442no—
892D4—2441no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—611no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—4881no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—4881no—
914C2×C4—4881no—
915C2×C4—4881no—
916C2×C4—4884no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
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×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4C2×C22⋊#692311yescharacteristic
940C2×C4C2×C22⋊#692311yescharacteristic
941C2×C4C2×C22⋊#692311yescharacteristic
942C2×C4C2×C22⋊#692311yescharacteristic
943C2×C4C23×#692311yescharacteristic
944C8—2441no—
945C8—2441no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—611no—
958C22—611no—
959C22—612no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—9762no—
968C22—9762no—
969C22—4881no—
970C22—4881no—
971C22—2442no—
972C22—2442no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22—2441no—
978C22—2441no—
979C22C22×C22⋊#692311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—41no—
986C4—41no—
987C4—41no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—4881no—
994C4—4881no—
995C4—4881no—
996C4—4881no—
997C4—2441no—
998C4—2441no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—1221no—
1003C2—1221no—
1004C2—1222no—
1005C2—4881no—
1006C2—4881no—
1007C2—2441no—
1008C2#2146241911yescharacteristic
1009C2#2146244011yescharacteristic
1010C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#555C4
socleC22×C61C22×C22⋊C4
prime radical#21459854C2
cosocleC2×C4×D61C24
hypercenter#555#6923
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #21462676C2semidirect
2. #21462301C2semidirect
3. #21461261C2semidirect
4. #21461254C2semidirect
5. #21461250C2semidirect
6. #21461247C2semidirect
7. #21461240C2semidirect
8. #21461236C2semidirect
9. #21461230C2semidirect
10. #21461225C2semidirect
11. #21461214C2semidirect
12. #21461207C2semidirect
13. #21461196C2semidirect
14. D61⋊#327C2semidirect
20. #16840785C22semidirect
21. #16840780C22semidirect
22. #16840734C22semidirect
23. #16840733C22semidirect
24. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
30. #16840707C22semidirect
31. #16840706C22semidirect
32. #16840705C22semidirect
33. #16840704C22semidirect
34. C4×C22⋊#6923C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
40. #16840614C22semidirect
41. #16840614C22semidirect
42. #16840614C22semidirect
43. #16840614C22semidirect
44. #16840614C22semidirect
45. #16840614C22semidirect
46. #16840614C22semidirect
47. #16840614C22semidirect
52. #16840473C4semidirect
54. #16840456C4semidirect
55. #16840456C4semidirect
56. #16840433C4semidirect
57. #16840409C4semidirect
58. #16840409C4semidirect
61. D4×D244C4semidirect
74. C61×#555C4semidirect
109. C2×#11758222C2×C4semidirect
114. C2×D4×D61C2×C4semidirect
118. #14519774C2×C4semidirect
124. #14519768C2×C4semidirect
126. #14519764C2×C4semidirect
135. #14519757C2×C4semidirect
141. #14519752C2×C4semidirect
146. #14519751C2×C4semidirect
164. C4×Dic122C2×C4semidirect
176. #14519739C2×C4semidirect
177. #14519739C2×C4semidirect
186. C4⋊C4×D61C2×C4semidirect
195. C4⋊Q8×C61C2×C4semidirect
200. #121×C61C2×C4semidirect
202. C4×D4×C61C2×C4semidirect
205. #117×C61C2×C4semidirect
521. #555#6923semidirect
580. C61#17597semidirect
597. C4⋊Q8C2×#6923semidirect
642. #121C2×#6923semidirect
670. C4×D4C2×#6923semidirect
674. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214623012
#214612612
#214612542
#214612502
#214612472
#214612402
#214612362
#214612302
#214612252
#214612142
#214612072
#214611962
D61⋊#3272
#214598542
#1759761