Finite Group Databasebeta

← #30622573

Subgroups — #30622573

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462344C211yesmaximal, characteristic
2#21462343C211yesmaximal, characteristic, complemented
3#21461909C211yesmaximal, characteristic, complemented
4#21461908C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461815C211yesmaximal, characteristic, complemented
8#21461812C211yesmaximal, characteristic, complemented
9#21461806C211yesmaximal, characteristic
10#21461804C211yesmaximal, characteristic, complemented
11#103×#6923C211yesmaximal, characteristic, complemented
12#102×#6923C211yesmaximal, characteristic, complemented
13C8×C22⋊#6923C211yesmaximal, characteristic, complemented
14C2×#16840636C211yesmaximal, characteristic, complemented
15#465×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923—21no—
18C2×D4×#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28(C2×#6923)⋊Q8C2211yescharacteristic
29#16840714C2211yescharacteristic
30#16840713—21no—
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840712—21no—
34#16840711—21no—
35#16840710—21no—
36#16840709—21no—
37#16840709—21no—
38C4⋊C4×#6923C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C22⋊C4×#6923—21no—
41C4×C22⋊#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C22×C8×D61C2211yescharacteristic
54C22⋊Q8×D61C2211yescharacteristic
55#121×D61C2211yescharacteristic
56#16839994C411yescharacteristic, complemented
57#16839993C411yescharacteristic, complemented
58#16839992C411yescharacteristic, complemented
59#16839991C411yescharacteristic, complemented
60#16839990C411yescharacteristic, complemented
61#16839989C411yescharacteristic, complemented
62#16839988C411yescharacteristic, complemented
63#106×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#465C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C23×#6923—21no—
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72Q8×#6923—22no—
73Q8×#6923—41no—
74D4×#6923—22no—
75D4×#6923—41no—
76D4×#6923—44no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—41no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923D411yescharacteristic
94C2×C22⋊#6923D411yescharacteristic
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923C2311yescharacteristic
99C2×C4×#6923C2311yescharacteristic
100#14519840—22no—
101#14519840—41no—
102#14519839—22no—
103#14519839—41no—
104#14519834—21no—
105C22⋊#92420—21no—
106C8×#6923—41no—
107C8×#6923—41no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4D411yescharacteristic
115(C2×#6923)⋊C4D411yescharacteristic
116C2×Q8×D61C2311yescharacteristic
117C2×D4×D61—21no—
118C2×D4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C2×#11758190C2×C411yescharacteristic, complemented
121C2×#11758200C2×C411yescharacteristic, complemented
122C2×#11758201C2×C411yescharacteristic, complemented
123SD16×D61—41no—
124SD16×D61—41no—
125C22×#92418C2×C411yescharacteristic, complemented
126C2×C8×D61—41no—
127C2×C8×D61—41no—
128C2×C8×D61C2×C411yescharacteristic, complemented
129C2×C8×D61C2×C411yescharacteristic, complemented
130C2×C8×D61C2311yescharacteristic
131C2×C8×D61C2311yescharacteristic
132#14519757C2×C411yescharacteristic, complemented
133#14519756C2×C411yescharacteristic, complemented
134#14519755—21no—
135#14519754—21no—
136#14519753C2×C411yescharacteristic, complemented
137#14519752C2×C411yescharacteristic
138#14519751C2×C411yescharacteristic
139#14519750—21no—
140#14519749—21no—
141#14519748C2×C411yescharacteristic
142C4⋊C4×D61—21no—
143C4⋊C4×D61C2311yescharacteristic
144C4⋊C4×D61C2311yescharacteristic
145C22⋊C4×D61—21no—
146C22⋊C4×D61—21no—
147#14519709C2×C411yescharacteristic, complemented
148#14519708C2×C411yescharacteristic, complemented
149#14519708C2×C411yescharacteristic, complemented
150#14519702C2×C411yescharacteristic, complemented
151#14519701C2×C411yescharacteristic, complemented
152#14519700C2×C411yescharacteristic, complemented
153#14519699C2×C411yescharacteristic, complemented
154#14519698C2×C411yescharacteristic, complemented
155#14519697C2×C411yescharacteristic, complemented
156C2×SD16×C61C2×C411yescharacteristic, complemented
157C22×C8×C61C2×C411yescharacteristic, complemented
158C22⋊Q8×C61C2×C411yescharacteristic, complemented
159#121×C61C2×C411yescharacteristic
160#106×C61C2×C411yescharacteristic, complemented
161#103×C61C2×C411yescharacteristic, complemented
162#102×C61C2×C411yescharacteristic, complemented
163C23×D61—21no—
164C23×D61C2×D411yescharacteristic
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—42no—
170C22×#6923—42no—
171C22×#6923—42no—
172C22×#6923—42no—
173C22×#6923—42no—
174C22×#6923—42no—
175C22×#6923—81no—
176C22×#6923—81no—
177C22×#6923—81no—
178C22×#6923C2×D411yescharacteristic
179C22×#6923C2×D411yescharacteristic
180C22×#6923C2×D411yescharacteristic
181C22×#6923C2×D411yescharacteristic
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C22×Dic61#4111yescharacteristic
190Q8×D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193Q8×D61—21no—
194D4×D61—21no—
195D4×D61—21no—
196D4×D61—21no—
197D4×D61—21no—
198D4×D61—42no—
199D4×D61—42no—
200C2×D244—21no—
201C2×D244C22×C411yescharacteristic
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61C22×C411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61#4111yescharacteristic
212C2×C4×D61C2411yescharacteristic
213C2×Dic122—21no—
214C2×Dic122C22×C411yescharacteristic
215C22⋊#6923—22no—
216C22⋊#6923—42no—
217C22⋊#6923—42no—
218C22⋊#6923—81no—
219C22⋊#6923SD1614yescomplemented
220C2×#92420—21no—
221C2×#92420—21no—
222C4⋊#6923—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—21no—
226C4⋊#6923—21no—
227C4⋊#6923—21no—
228C4⋊#6923—42no—
229C4⋊#6923—42no—
230C4⋊#6923—42no—
231C4⋊#6923—42no—
232C4⋊#6923—81no—
233C4⋊#6923#4112yes—
234C4⋊#6923#4112yes—
235C4×#6923—21no—
236C4×#6923—21no—
237C4×#6923—21no—
238C4×#6923—21no—
239C4×#6923—42no—
240C4×#6923—42no—
241C4×#6923—81no—
242D61⋊C8—21no—
243D61⋊C8—21no—
244D61⋊C8—21no—
245D61⋊C8—21no—
246SD16×C61—41no—
247C2×C8×C61—41no—
248C2×C8×C61C22×C411yescharacteristic
249C2×C8×C61C22×C411yescharacteristic
250C4⋊C4×C61—21no—
251C4⋊C4×C61C22×C411yescharacteristic
252C4⋊C4×C61C22×C411yescharacteristic
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C22⋊Dic61—21no—
256C22⋊Dic61—21no—
257#11758201—41no—
258#11758200—41no—
259#11758198—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C411yescharacteristic
265C4⋊Dic61C22×C411yescharacteristic
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270C2×#92418—41no—
271C2×#92418C22×C411yescharacteristic
272C2×#92418C22×C411yescharacteristic
273#11758190—41no—
274C8×D61—21no—
275C8×D61—21no—
276C8×D61—21no—
277C8×D61—21no—
278C8×D61—41no—
279C8×D61—41no—
280C23×C61—21no—
281C23×C61C4×D411yescharacteristic
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61C4×D411yescharacteristic
294C22×D61C2×SD1612yes—
295C22×D61#13512yes—
296C22×D61C22×D411yescharacteristic
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—21no—
300C2×#6923—21no—
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—22no—
304C2×#6923—22no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—84no—
320C2×#6923—84no—
321C2×#6923—84no—
322C2×#6923C2×SD1612yes—
323C2×#6923C2×SD1612yes—
324Q8×C61—21no—
325Q8×C61—21no—
326D4×C61—21no—
327D4×C61—21no—
328D4×C61—42no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61C4×D411yescharacteristic
335C2×C4×C61C23×C411yescharacteristic
336C22⋊D61—42no—
337C22⋊D61—42no—
338C22⋊D61—41no—
339C22⋊D61—41no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61C4×D411yescharacteristic
346C2×Dic61C2×#4111yescharacteristic
347D244—21no—
348D244—21no—
349D244—42no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61C2×#4111yescharacteristic
363C4×D61C2×#4111yescharacteristic
364C4×D61H(5,𝔽2)11yescharacteristic
365C4×D61H(5,𝔽2)11yescharacteristic
366Dic122—21no—
367Dic122—21no—
368Dic122—41no—
369Dic122—41no—
370#92420—41no—
371#92420—41no—
372C8×C61—21no—
373C8×C61—21no—
374#92418—21no—
375#92418—21no—
376#23126—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61C4×SD1612yes—
383C22×C61C2×C4×D411yescharacteristic
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61—81no—
396C2×D61—81no—
397C2×D61C4×SD1612yes—
398C2×D61#54611yescharacteristic
399C2×D61#54611yescharacteristic
400C2×D61C22×SD1611yescharacteristic
401C2×D61C2×#13511yescharacteristic
402C2×D61#57611yescharacteristic
403C2×D61#57811yescharacteristic
404#6923—22no—
405#6923—22no—
406#6923—42no—
407#6923—41no—
408#6923—42no—
409#6923—41no—
410#6923—81no—
411#6923—81no—
412C4×C61—21no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61C4×#4111yescharacteristic
417C4×C61#51811yescharacteristic
418Dic61—21no—
419Dic61—41no—
420Dic61—41no—
421Dic61—41no—
422Dic61#55311yescharacteristic
423Dic61#55311yescharacteristic
424C2×#465—611no—
425#2361—611no—
426#2360—611no—
427#1934—611no—
428#1933—611no—
429#1920—611no—
430#1919—611no—
431#1880—611no—
432#1877—611no—
433#1874—611no—
434#1872—611no—
435C4×#103—611no—
436C4×#102—611no—
437C8×C22⋊C4—611no—
438C2×#340—611no—
439C2×C61—22no—
440C2×C61—81no—
441C2×C61#236411yescharacteristic
442C2×C61C2×C4×SD1611yescharacteristic
443C2×C61#295111yescharacteristic
444D61—22no—
445D61—81no—
446D61#329511yescharacteristic
447D61#329711yescharacteristic
448D61#329811yescharacteristic
449D61#330011yescharacteristic
450C22×SD16—611no—
451C23×C8—611no—
452C2×C22⋊Q8—611no—
453C2×#121—611no—
454C2×C4×Q8—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C22×C4⋊C4—611no—
458C22×C4⋊C4—611no—
459#465—611no—
460#465—611no—
461#465—611no—
462#465—611no—
463#465—611no—
464#465—611no—
465#465—611no—
466#465#692311yescharacteristic, complemented
467C2×#106—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×C22⋊C8—611no—
475C2×C4×C8—611no—
476C2×C4×C8—611no—
477#391—611no—
478#390—611no—
479#389—611no—
480#389—611no—
481#389—1221no—
482#388—1221no—
483#387—1221no—
484#386—1221no—
485#385—1221no—
486#385—1221no—
487C4×C4⋊C4—611no—
488C4×C4⋊C4—611no—
489C4×C22⋊C4—611no—
490C4×C22⋊C4—1221no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497#340—611no—
498#340—611no—
499#336—611no—
500#336—611no—
501C61#2312611yescharacteristic, complemented, Sylow
502C22×Q8—611no—
503C22×D4—611no—
504C22×D4—1221no—
505C23×C4—611no—
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4—1221no—
509C2×SD16—611no—
510C2×SD16—611no—
511C2×SD16—611no—
512C2×SD16—2441no—
513C2×SD16—2441no—
514C2×SD16C2×#692311yescharacteristic, complemented
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8—2441no—
523C22×C8—2441no—
524C22×C8C2×#692311yescharacteristic, complemented
525C22⋊Q8—611no—
526C22⋊Q8—611no—
527C22⋊Q8—611no—
528C22⋊Q8—1221no—
529C22⋊Q8—1221no—
530C22⋊Q8C2×#692311yescharacteristic, complemented
531#121—611no—
532#121—611no—
533#121—611no—
534#121—1221no—
535#121—1221no—
536#121C2×#692311yescharacteristic
537C4×Q8—1222no—
538C4×Q8—2441no—
539C4×D4—1222no—
540C4×D4—2441no—
541C4×D4—2444no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1222no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—2441no—
557C2×C4⋊C4—2441no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—611no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—1221no—
568C2×C42—1221no—
569C2×C42—1221no—
570#106—611no—
571#106—611no—
572#106—611no—
573#106C2×#692311yescharacteristic, complemented
574#103—611no—
575#103—611no—
576#103—611no—
577#103—1222no—
578#103—2441no—
579#103C2×#692311yescharacteristic, complemented
580#102—611no—
581#102—611no—
582#102—611no—
583#102—1222no—
584#102—2441no—
585#102C2×#692311yescharacteristic, complemented
586C22⋊C8—1221no—
587C22⋊C8—1221no—
588C4×C8—2441no—
589C4×C8—2441no—
590#95—611no—
591#95—611no—
592#95—1221no—
593#95—1221no—
594#95—1221no—
595#95—1221no—
596#95—1221no—
597#95—1221no—
598C24—611no—
599C24—1221no—
600C2×Q8—611no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8C22×#692311yescharacteristic
607C2×D4—21no—
608C2×D4—611no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—2442no—
618C2×D4—2442no—
619C2×D4C22×#692311yescharacteristic
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—4881no—
641C22×C4—4881no—
642C22×C4—4881no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4C22×#692311yescharacteristic
650SD16—41no—
651SD16—2441no—
652SD16—2441no—
653SD16—2441no—
654C2×C8—41no—
655C2×C8—611no—
656C2×C8—611no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—2441no—
668C2×C8—2441no—
669C2×C8—2441no—
670C2×C8C22×#692311yescharacteristic
671C2×C8C22×#692311yescharacteristic
672C4⋊C4—21no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—611no—
676C4⋊C4—611no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—4881no—
689C4⋊C4—2442no—
690C4⋊C4—2442no—
691C4⋊C4—2442no—
692C4⋊C4—2442no—
693C4⋊C4C22×#692311yescharacteristic
694C4⋊C4C22×#692311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—614no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1222no—
703C22⋊C4—1221no—
704C22⋊C4—1221no—
705C22⋊C4—4881no—
706C22⋊C4—2442no—
707C22⋊C4—2442no—
708C42—1221no—
709C42—1221no—
710C42—1221no—
711C42—1221no—
712C42—4881no—
713C42—2442no—
714C42—2442no—
715C23—21no—
716C23—611no—
717C23—612no—
718C23—612no—
719C23—611no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—2441no—
726C23—2441no—
727C23—2441no—
728C23—2441no—
729C23—2441no—
730C23—2441no—
731C23D4×#692311yescharacteristic
732Q8—21no—
733Q8—21no—
734Q8—1221no—
735Q8—1221no—
736Q8—2441no—
737Q8—2441no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—1221no—
742D4—1221no—
743D4—2442no—
744D4—2441no—
745D4—2441no—
746D4—2442no—
747D4—2442no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—611no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1222no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1222no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—4884no—
785C2×C4—4884no—
786C2×C4—4884no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4D4×#692311yescharacteristic
804C2×C4C23×#692311yescharacteristic
805C8—21no—
806C8—21no—
807C8—1221no—
808C8—1221no—
809C8—2441no—
810C8—2441no—
811C22—21no—
812C22—21no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—611no—
817C22—611no—
818C22—611no—
819C22—611no—
820C22—611no—
821C22—611no—
822C22—612no—
823C22—1222no—
824C22—1222no—
825C22—1222no—
826C22—1222no—
827C22—1221no—
828C22—1221no—
829C22—4881no—
830C22—4881no—
831C22—4881no—
832C22—4881no—
833C22—2441no—
834C22—2441no—
835C22—2441no—
836C22SD16×#692312yes—
837C22C2×D4×#692311yescharacteristic
838C4—21no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—611no—
843C4—611no—
844C4—1222no—
845C4—1222no—
846C4—1221no—
847C4—4881no—
848C4—4881no—
849C4—2441no—
850C4—2441no—
851C4—2442no—
852C4—2442no—
853C4—2441no—
854C4—2441no—
855C4—2441no—
856C4#41×#692311yescharacteristic
857C4#1684082911yescharacteristic
858C2—22no—
859C2—81no—
860C2—611no—
861C2—611no—
862C2—611no—
863C2—611no—
864C2—1222no—
865C2—4881no—
866C2#2146234711yescharacteristic
867C2C2×SD16×#692311yescharacteristic
868C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#465#6923
hypocenterC61#23126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. #21462343C2semidirect
3. #21461909C2semidirect
4. #21461908C2semidirect
5. #21461882C2semidirect
6. #21461881C2semidirect
7. #21461815C2semidirect
8. #21461812C2semidirect
10. #21461804C2semidirect
11. #103×#6923C2semidirect
12. #102×#6923C2semidirect
13. C8×C22⋊#6923C2semidirect
14. C2×#16840636C2semidirect
56. #16839994C4semidirect
57. #16839993C4semidirect
58. #16839992C4semidirect
59. #16839991C4semidirect
60. #16839990C4semidirect
61. #16839989C4semidirect
62. #16839988C4semidirect
66. C61×#465C4semidirect
120. C2×#11758190C2×C4semidirect
121. C2×#11758200C2×C4semidirect
122. C2×#11758201C2×C4semidirect
125. C22×#92418C2×C4semidirect
128. C2×C8×D61C2×C4semidirect
129. C2×C8×D61C2×C4semidirect
132. #14519757C2×C4semidirect
133. #14519756C2×C4semidirect
136. #14519753C2×C4semidirect
147. #14519709C2×C4semidirect
148. #14519708C2×C4semidirect
149. #14519708C2×C4semidirect
150. #14519702C2×C4semidirect
151. #14519701C2×C4semidirect
152. #14519700C2×C4semidirect
153. #14519699C2×C4semidirect
154. #14519698C2×C4semidirect
155. #14519697C2×C4semidirect
156. C2×SD16×C61C2×C4semidirect
157. C22×C8×C61C2×C4semidirect
158. C22⋊Q8×C61C2×C4semidirect
160. #106×C61C2×C4semidirect
161. #103×C61C2×C4semidirect
162. #102×C61C2×C4semidirect
219. C22⋊#6923SD16semidirect
466. #465#6923semidirect
501. C61#23126semidirect
514. C2×SD16C2×#6923semidirect
524. C22×C8C2×#6923semidirect
530. C22⋊Q8C2×#6923semidirect
573. #106C2×#6923semidirect
579. #103C2×#6923semidirect
585. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623442
#214623432
#214619092
#214619082
#214618822
#214618812
#214618152
#214618122
#214618062
#214618042
#103×#69232
#102×#69232
C8×C22⋊#69232
C2×#168406362
#465×D612
#2312661