Finite Group Databasebeta

← #30611257

Subgroups — #30611257

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#21461263C211yesmaximal, characteristic, complemented
4#21461256C211yesmaximal, characteristic, complemented
5#21461250C211yesmaximal, characteristic, complemented
6#21461246C211yesmaximal, characteristic, complemented
7#21461240C211yesmaximal, characteristic, complemented
8#21461237C211yesmaximal, characteristic, complemented
9#21461232C211yesmaximal, characteristic, complemented
10#21461226C211yesmaximal, characteristic, complemented
11#21461216C211yesmaximal, characteristic, complemented
12#21461206C211yesmaximal, characteristic, complemented
13#21461197C211yesmaximal, characteristic, complemented
14C2×#16840614C211yesmaximal, characteristic, complemented
15#21459852C211yesmaximal, 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#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic
41#16840614C2211yescharacteristic
42#16840614C2211yescharacteristic
43#16840614C2211yescharacteristic
44#16840614C2211yescharacteristic, complemented
45#16840614C2211yescharacteristic, complemented
46#16840614C2211yescharacteristic, complemented
47#16840614C2211yescharacteristic, complemented
48#16840614C2211yescharacteristic, complemented
49#16840614C2211yescharacteristic, complemented
50#16840614C2211yescharacteristic, complemented
51#16840614C2211yescharacteristic, complemented
52#16840478C411yescharacteristic, complemented
53#16840465—21no—
54#16840460C411yescharacteristic, complemented
55#16840460C411yescharacteristic, complemented
56#16840434C411yescharacteristic, complemented
57#16840403—21no—
58#16840403—21no—
59#16840403C411yescharacteristic, complemented
60#16840403C411yescharacteristic, complemented
61D4×D244—21no—
62D4×D244C411yescharacteristic, complemented
63#16840368—21no—
64#16840352—21no—
65#16840352—21no—
66#16840313C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840275C2211yescharacteristic
70C2×#14519752C2211yescharacteristic
71C2×#14519752C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#554C411yescharacteristic, 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×#11758226C2×C411yescharacteristic
109C2×#11758226C2×C411yescharacteristic, complemented
110C22×D244—21no—
111C22×D244—21no—
112C22×D244C2×C411yescharacteristic
113C22×D244C2×C411yescharacteristic, complemented
114C2×D4×D61—21no—
115C2×D4×D61D411yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118#14519774—21no—
119#14519774C2×C411yescharacteristic, complemented
120#14519772—21no—
121#14519772—21no—
122#14519772—21no—
123#14519768C2×C411yescharacteristic, complemented
124#14519766—21no—
125#14519766—21no—
126#14519766—21no—
127#14519766C2×C411yescharacteristic, complemented
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519762—21no—
134#14519762—21no—
135#14519753C2311yescharacteristic
136#14519752—21no—
137#14519752—21no—
138#14519752—21no—
139#14519752—21no—
140#14519752—21no—
141#14519752—21no—
142#14519752—21no—
143#14519752—21no—
144#14519752—21no—
145#14519752—21no—
146#14519752—21no—
147#14519752C2×C411yescharacteristic
148#14519752C2×C411yescharacteristic
149#14519752C2×C411yescharacteristic, complemented
150#14519752C2×C411yescharacteristic, complemented
151#14519752C2311yescharacteristic
152#14519752C2311yescharacteristic
153#14519752C2311yescharacteristic
154#14519751—21no—
155#14519751—21no—
156#14519751C2×C411yescharacteristic
157#14519751C2×C411yescharacteristic, complemented
158#14519747—21no—
159#14519747—21no—
160#14519747—21no—
161#14519747—21no—
162#14519747—21no—
163#14519747—21no—
164C4×D244—21no—
165C4×D244—21no—
166C4×D244C2×C411yescharacteristic
167C4×D244C2×C411yescharacteristic, complemented
168D4×Dic61D411yescharacteristic
169#14519739—21no—
170#14519739—21no—
171#14519739—21no—
172#14519739C2×C411yescharacteristic, complemented
173#14519739C2×C411yescharacteristic, complemented
174#14519739D411yescharacteristic
175C4×C22⋊D61—21no—
176C4×C22⋊D61—21no—
177C4×C22⋊D61C2×C411yescharacteristic
178C4×C22⋊D61C2×C411yescharacteristic
179#14519737—21no—
180#14519737—21no—
181#14519737D411yescharacteristic
182#14519737D411yescharacteristic
183#14519735—21no—
184#14519735C2×C411yescharacteristic
185#14519735C2×C411yescharacteristic, complemented
186#14519734—21no—
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic, complemented
196#125×C61—21no—
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic, complemented
201C4×Q8×C61C2×C411yescharacteristic, complemented
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C2×C4⋊C4×C61C2×C411yescharacteristic
205C2×C4⋊C4×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×Q8×C61C22×C411yescharacteristic
219C2×D4×C61C22⋊C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61C22⋊C411yescharacteristic
227C2×C22⋊D61C22⋊C411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230#11758226—81no—
231#11758226—81no—
232#11758226—81no—
233#11758226—81no—
234D4×D61—42no—
235D4×D61—44no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—81no—
250C2×D244—81no—
251C2×D244—81no—
252C2×D244—81no—
253C2×D244—81no—
254C2×D244—81no—
255C2×D244C22⋊C411yescharacteristic
256C2×D244C22×C411yescharacteristic
257C2×D244C22×C411yescharacteristic
258C2×D244C22×C411yescharacteristic
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—81no—
265C2×C4×D61—81no—
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2411yescharacteristic
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×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61C22⋊C411yescharacteristic
296C4⋊C4×C61C22×C411yescharacteristic
297C4⋊C4×C61C22×C411yescharacteristic
298C4⋊C4×C61C22×C411yescharacteristic
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61C22⋊C411yescharacteristic
302C22⋊C4×C61C22⋊C411yescharacteristic
303C42×C61—21no—
304C42×C61C22×C411yescharacteristic
305C22⋊Dic61C22⋊C411yescharacteristic
306C22⋊Dic61C22⋊C411yescharacteristic
307#11758198—21no—
308#11758198—21no—
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#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198C22⋊C411yescharacteristic
325#11758198C22⋊C411yescharacteristic
326#11758198C22⋊C411yescharacteristic
327#11758198C22⋊C411yescharacteristic
328C4⋊Dic61—21no—
329C4⋊Dic61C22⋊C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331#11758196—21no—
332#11758196—21no—
333#11758196C22⋊C411yescharacteristic
334#11758196C22⋊C411yescharacteristic
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C23×C61C2×C22⋊C411yescharacteristic
341C23×C61C2×C22⋊C411yescharacteristic
342C22×D61—22no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
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—41no—
376Q8×C61—81no—
377D4×C61—22no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
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—42no—
394C22⋊D61—42no—
395C2×Dic61—21no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C22×D411yescharacteristic
403D244—41no—
404D244—41no—
405D244—41no—
406D244—41no—
407D244—42no—
408D244—41no—
409D244—41no—
410D244—41no—
411D244—41no—
412D244—41no—
413D244—41no—
414D244—81no—
415D244—81no—
416D244—81no—
417D244—81no—
418D244—81no—
419D244—81no—
420D244—81no—
421D244—81no—
422D244—81no—
423C4×D61—21no—
424C4×D61—21no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—42no—
434C4×D61—81no—
435C4×D61—81no—
436C4×D61—81no—
437C4×D61—81no—
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#42112yes—
449C22×C61C22×C22⋊C411yescharacteristic
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—42no—
459C2×D61—42no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—81no—
470C2×D61—81no—
471C2×D61—162no—
472C2×D61—162no—
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—
487C4×C61—41no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—21no—
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—22no—
510C2×C61—41no—
511C2×C61#288311yescharacteristic
512C2×C61#289711yescharacteristic
513C2×C61C2×#42111yescharacteristic
514D61—21no—
515D61—21no—
516D61—41no—
517D61—41no—
518D61—81no—
519D61—81no—
520D61—81no—
521#555—611no—
522#554#692311yescharacteristic, complemented
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—21no—
604#125—611no—
605#124—611no—
606#124—1221no—
607#124—1221no—
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—21no—
617C22⋊Q8—21no—
618C22⋊Q8—611no—
619C22⋊Q8C2×#692311yescharacteristic
620C22⋊Q8C2×#692311yescharacteristic, complemented
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—611no—
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#121—1221no—
642#121—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8C2×#692311yescharacteristic, complemented
650C4×D4—21no—
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—611no—
660C4×D4—611no—
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×D4—1221no—
670C4×D4C2×#692311yescharacteristic
671#117—611no—
672#117—611no—
673#117—1221no—
674#117—1221no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4C2×#692311yescharacteristic
679C2×C4⋊C4C2×#692311yescharacteristic, complemented
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×Q8C22×#692311yescharacteristic
722C2×D4—611no—
723C2×D4—611no—
724C2×D4—611no—
725C2×D4—611no—
726C2×D4—611no—
727C2×D4—611no—
728C2×D4—1221no—
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—1221no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—4881no—
748C2×D4—4881no—
749C2×D4—2442no—
750C2×D4—2444no—
751C2×D4C22⋊#692311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
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—611no—
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—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—611no—
798C4⋊C4—611no—
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—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—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—611no—
840C42—611no—
841C42—611no—
842C42—1221no—
843C42—1221no—
844C42—4881no—
845C42C22×#692311yescharacteristic
846C23—611no—
847C23—611no—
848C23—611no—
849C23—1221no—
850C23—1221no—
851C23—1221no—
852C23—1221no—
853C23—1222no—
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—41no—
869Q8—81no—
870D4—22no—
871D4—1222no—
872D4—4881no—
873D4—4881no—
874D4—4881no—
875D4—4881no—
876D4—4881no—
877D4—4881no—
878D4—4881no—
879D4—4881no—
880D4—4881no—
881D4—2441no—
882D4—2441no—
883D4—2441no—
884D4—2441no—
885D4—2442no—
886D4—2441no—
887D4—2441no—
888D4—2441no—
889D4—2441no—
890D4—2441no—
891D4—2441no—
892D4—2441no—
893D4—2442no—
894D4—2442no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—4881no—
914C2×C4—4881no—
915C2×C4—4884no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2442no—
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—611no—
954C22—611no—
955C22—1221no—
956C22—1221no—
957C22—1221no—
958C22—1221no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1221no—
963C22—9762no—
964C22—9762no—
965C22—4881no—
966C22—4881no—
967C22—2442no—
968C22—2442no—
969C22—2441no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22—2441no—
978C22#1684076112yes—
979C22C22×C22⋊#692311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—41no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—4881no—
995C4—4881no—
996C4—4881no—
997C4—4881no—
998C4—2441no—
999C2—22no—
1000C2—41no—
1001C2—1221no—
1002C2—1221no—
1003C2—4881no—
1004C2—4881no—
1005C2—4881no—
1006C2—2441no—
1007C2—2441no—
1008C2#2146241911yescharacteristic
1009C2#2146244011yescharacteristic
1010C2C2×#1684076111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radical#21459852C2
cosocleC2×C4×D61C24
hypercenter#554#6923
hypocenterC61#17597
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. #21462676C2semidirect
2. #21462301C2semidirect
3. #21461263C2semidirect
4. #21461256C2semidirect
5. #21461250C2semidirect
6. #21461246C2semidirect
7. #21461240C2semidirect
8. #21461237C2semidirect
9. #21461232C2semidirect
10. #21461226C2semidirect
11. #21461216C2semidirect
12. #21461206C2semidirect
13. #21461197C2semidirect
14. C2×#16840614C2semidirect
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. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
44. #16840614C22semidirect
45. #16840614C22semidirect
46. #16840614C22semidirect
47. #16840614C22semidirect
48. #16840614C22semidirect
49. #16840614C22semidirect
50. #16840614C22semidirect
51. #16840614C22semidirect
52. #16840478C4semidirect
54. #16840460C4semidirect
55. #16840460C4semidirect
56. #16840434C4semidirect
59. #16840403C4semidirect
60. #16840403C4semidirect
62. D4×D244C4semidirect
74. C61×#554C4semidirect
109. C2×#11758226C2×C4semidirect
113. C22×D244C2×C4semidirect
119. #14519774C2×C4semidirect
123. #14519768C2×C4semidirect
127. #14519766C2×C4semidirect
149. #14519752C2×C4semidirect
150. #14519752C2×C4semidirect
157. #14519751C2×C4semidirect
167. C4×D244C2×C4semidirect
172. #14519739C2×C4semidirect
173. #14519739C2×C4semidirect
185. #14519735C2×C4semidirect
195. C4⋊Q8×C61C2×C4semidirect
200. C22⋊Q8×C61C2×C4semidirect
201. C4×Q8×C61C2×C4semidirect
205. C2×C4⋊C4×C61C2×C4semidirect
522. #554#6923semidirect
580. C61#17597semidirect
597. C4⋊Q8C2×#6923semidirect
620. C22⋊Q8C2×#6923semidirect
649. C4×Q8C2×#6923semidirect
679. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214623012
#214612632
#214612562
#214612502
#214612462
#214612402
#214612372
#214612322
#214612262
#214612162
#214612062
#214611972
C2×#168406142
#214598522
#1759761