Finite Group Databasebeta

← #30619273

Subgroups — #30619273

Order 15616.

666 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462314C211yesmaximal, characteristic
2#21462313C211yesmaximal, characteristic
3#21462001C211yesmaximal, characteristic
4#21462000C211yesmaximal, characteristic
5#21461883C211yesmaximal, characteristic
6#21461883C211yesmaximal, characteristic
7#21461882C211yesmaximal, characteristic
8#21461882C211yesmaximal, characteristic
9#21461881C211yesmaximal, characteristic
10#21461881C211yesmaximal, characteristic
11#21461880C211yesmaximal, characteristic
12#21461880C211yesmaximal, characteristic
13#21461742C211yesmaximal, characteristic
14#21461539C211yesmaximal, characteristic
15#501×D61C211yesmaximal, characteristic
16C4×D61⋊C8C2211yescharacteristic
17(C2×#6923)⋊Q8—21no—
18(C2×#6923)⋊Q8—21no—
19#16840713—21no—
20#16840713—21no—
21#16840713C2211yescharacteristic
22#16840713C2211yescharacteristic
23#16840713C2211yescharacteristic
24#16840713C2211yescharacteristic
25#16840711—21no—
26#16840711—21no—
27#16840711—21no—
28#16840711—21no—
29#16840708C2211yescharacteristic
30#16840706C2211yescharacteristic
31C4⋊C4×#6923C2211yescharacteristic
32C4⋊C4×#6923C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35#16840698C2211yescharacteristic
36#16840636C2211yescharacteristic
37#16840636C2211yescharacteristic
38#16840636C2211yescharacteristic
39#16840636C2211yescharacteristic
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48(C2×#6923)⋊C8C2211yescharacteristic
49(C2×#6923)⋊C8C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C4⋊Q8×D61C2211yescharacteristic
53#125×D61C2211yescharacteristic
54#16840172C411yescharacteristic, complemented
55#16840171C411yescharacteristic, complemented
56#16840170C411yescharacteristic, complemented
57#16840170C411yescharacteristic, complemented
58#16840169C411yescharacteristic, complemented
59#16840169C411yescharacteristic, complemented
60#16840168C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#107×D61C2211yescharacteristic
63#106×D61C2211yescharacteristic
64#106×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#501C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69C2×C4⋊#6923—21no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—21no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923C2311yescharacteristic
76C2×C4⋊#6923C2311yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4×#6923—21no—
80C2×C4×#6923—21no—
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923C2311yescharacteristic
84C2×C4×#6923C2311yescharacteristic
85C4×#92420—21no—
86C4×#92420—21no—
87(C2×#6923)⋊C4—21no—
88(C2×#6923)⋊C4—21no—
89(C2×#6923)⋊C4—21no—
90(C2×#6923)⋊C4—21no—
91(C2×#6923)⋊C4—21no—
92(C2×#6923)⋊C4—21no—
93(C2×#6923)⋊C4—21no—
94(C2×#6923)⋊C4—21no—
95(C2×#6923)⋊C4—21no—
96(C2×#6923)⋊C4—21no—
97(C2×#6923)⋊C4D411yescharacteristic
98(C2×#6923)⋊C4D411yescharacteristic
99(C2×#6923)⋊C4D411yescharacteristic
100(C2×#6923)⋊C4D411yescharacteristic
101C2×Q8×D61—21no—
102C2×C8×D61C2311yescharacteristic
103C2×C8×D61C2311yescharacteristic
104#14519777C2×C411yescharacteristic
105#14519776—21no—
106#14519776C2×C411yescharacteristic
107#14519776C2×C411yescharacteristic
108#14519775—21no—
109#14519769C2×C411yescharacteristic
110#14519768C2×C411yescharacteristic
111#14519768C2×C411yescharacteristic
112#14519767—21no—
113#14519767—21no—
114C4⋊C4×D61—21no—
115C4⋊C4×D61—21no—
116C4⋊C4×D61—21no—
117C4⋊C4×D61C2311yescharacteristic
118C4⋊C4×D61C2311yescharacteristic
119C4⋊C4×D61C2311yescharacteristic
120C4⋊C4×D61C2311yescharacteristic
121C42×D61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519710C2×C411yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519709C2×C411yescharacteristic
129#14519709C2×C411yescharacteristic
130#14519708C2×C411yescharacteristic
131#14519708C2×C411yescharacteristic
132#14519708C2×C411yescharacteristic
133#14519708C2×C411yescharacteristic
134#14519688C2×C411yescharacteristic
135#14519687C2×C411yescharacteristic
136#14519687C2×C411yescharacteristic
137C4⋊Q8×C61C2×C411yescharacteristic
138#125×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#106×C61C2×C411yescharacteristic
143#97×C61C2×C411yescharacteristic
144C22×#6923—21no—
145C22×#6923—21no—
146C22×#6923—21no—
147C22×#6923—21no—
148C22×#6923C2×D411yescharacteristic
149C22×#6923C2×D411yescharacteristic
150C22×#6923C2×D411yescharacteristic
151C22×#6923C2×D411yescharacteristic
152C2×Q8×C61—21no—
153Q8×D61—81no—
154Q8×D61—81no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61C2411yescharacteristic
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C4⋊#6923—21no—
168C4⋊#6923—21no—
169C4⋊#6923—21no—
170C4⋊#6923—21no—
171C4⋊#6923—21no—
172C4⋊#6923—21no—
173C4⋊#6923—21no—
174C4⋊#6923—21no—
175C4⋊#6923—81no—
176C4⋊#6923—81no—
177C4⋊#6923—81no—
178C4⋊#6923—81no—
179C4⋊#6923—81no—
180C4⋊#6923—81no—
181C4×#6923—21no—
182C4×#6923—21no—
183C4×#6923—21no—
184C4×#6923—21no—
185C4×#6923—81no—
186C4×#6923—81no—
187C4×#6923—81no—
188C4×#6923—81no—
189D61⋊C8—21no—
190D61⋊C8—21no—
191D61⋊C8—21no—
192D61⋊C8—21no—
193C2×C8×C61C22×C411yescharacteristic
194C2×C8×C61C22×C411yescharacteristic
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61C22×C411yescharacteristic
199C4⋊C4×C61C22×C411yescharacteristic
200C4⋊C4×C61C22×C411yescharacteristic
201C4⋊C4×C61C22×C411yescharacteristic
202C42×C61C22×C411yescharacteristic
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208C4⋊Dic61C22×C411yescharacteristic
209C4⋊Dic61C22×C411yescharacteristic
210#11758196—21no—
211#11758196—21no—
212#11758196—21no—
213#11758196—21no—
214#11758196—21no—
215#11758196—21no—
216#11758196—21no—
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61#4111yescharacteristic
222C4×Dic61#4111yescharacteristic
223C2×#92418C22×C411yescharacteristic
224C2×#92418C22×C411yescharacteristic
225C8×D61—21no—
226C8×D61—21no—
227C8×D61—21no—
228C8×D61—21no—
229C22×D61C22×D411yescharacteristic
230C2×#6923—21no—
231C2×#6923—21no—
232C2×#6923—21no—
233C2×#6923—21no—
234C2×#6923—21no—
235C2×#6923—21no—
236C2×#6923—21no—
237C2×#6923—21no—
238C2×#6923—21no—
239C2×#6923—21no—
240C2×#6923—21no—
241C2×#6923—21no—
242C2×#6923—41no—
243C2×#6923—41no—
244C2×#6923—41no—
245C2×#6923—41no—
246C2×#6923—41no—
247C2×#6923—41no—
248C2×#6923—41no—
249C2×#6923—41no—
250C2×#6923—41no—
251C2×#6923—41no—
252C2×#6923—41no—
253C2×#6923—41no—
254Q8×C61—81no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61C4×D411yescharacteristic
260C2×C4×C61C4×D411yescharacteristic
261C2×C4×C61C23×C411yescharacteristic
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61C4×D411yescharacteristic
267C2×Dic61C4×D411yescharacteristic
268C2×Dic61C2×#4111yescharacteristic
269C4×D61—21no—
270C4×D61—21no—
271C4×D61—21no—
272C4×D61—21no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D612−1+411yescharacteristic
282C4×D612−1+411yescharacteristic
283C4×D612−1+411yescharacteristic
284C4×D612−1+411yescharacteristic
285Dic122—81no—
286Dic122—81no—
287Dic122—81no—
288#92420—41no—
289#92420—41no—
290C8×C61—21no—
291C8×C61—21no—
292#92418—21no—
293#92418—21no—
294#22255—611nomaximal, Sylow
295C22×C61C2×C4×D411yescharacteristic
296C2×D61#53611yescharacteristic
297C2×D61#53611yescharacteristic
298C2×D61#57611yescharacteristic
299C2×D61#57711yescharacteristic
300C2×D61#57711yescharacteristic
301C2×D61#57811yescharacteristic
302#6923—41no—
303#6923—41no—
304#6923—41no—
305#6923—41no—
306#6923—81no—
307#6923—81no—
308#6923—81no—
309#6923—81no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61#51911yescharacteristic
317C4×C61#51911yescharacteristic
318Dic61—21no—
319Dic61—21no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323Dic61—41no—
324Dic61#54111yescharacteristic
325Dic61#54111yescharacteristic
326C2×#501—611no—
327#2331—611no—
328#2330—611no—
329#1991—611no—
330#1990—611no—
331#1921—611no—
332#1921—611no—
333#1920—611no—
334#1920—611no—
335#1919—611no—
336#1919—611no—
337#1918—611no—
338#1918—611no—
339#1836—611no—
340#1746—611no—
341C2×C61#232711yescharacteristic
342C2×C61#294611yescharacteristic
343C2×C61#294711yescharacteristic
344D61#324111yescharacteristic
345D61#324211yescharacteristic
346D61#324311yescharacteristic
347D61#324411yescharacteristic
348C2×C4⋊Q8—611no—
349C2×#125—611no—
350#501—611no—
351#501—611no—
352#501—611no—
353#501—611no—
354#501—611no—
355#501—611no—
356#501—611no—
357#501#692311yescharacteristic, complemented
358C2×#107—611no—
359C2×#107—611no—
360C2×#106—611no—
361C2×#106—611no—
362C2×#97—611no—
363C2×C4×C8—611no—
364#391—1221no—
365#391—1221no—
366#389—611no—
367#389—611no—
368#389—611no—
369#389—611no—
370#389—1221no—
371#389—1221no—
372#387—1221no—
373#387—1221no—
374#387—1221no—
375#387—1221no—
376#384—611no—
377#382—611no—
378C4×C4⋊C4—611no—
379C4×C4⋊C4—611no—
380C4×C4⋊C4—611no—
381C4×C4⋊C4—611no—
382#376—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#340—611no—
395#336—611no—
396#336—611no—
397#336—611no—
398#336—611no—
399C61#2225511yescharacteristic, complemented, Sylow
400C22×Q8—1221no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—611no—
405C4⋊Q8—611no—
406C4⋊Q8—611no—
407C4⋊Q8—611no—
408C4⋊Q8—1221no—
409C4⋊Q8—1221no—
410C4⋊Q8C2×#692311yescharacteristic
411#125—611no—
412#125—611no—
413#125—611no—
414#125—1221no—
415#125—1221no—
416#125C2×#692311yescharacteristic
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441#107—611no—
442#107—611no—
443#107—611no—
444#107—611no—
445#107—611no—
446#107—611no—
447#107C2×#692311yescharacteristic
448#107C2×#692311yescharacteristic
449#106—611no—
450#106—611no—
451#106—611no—
452#106—611no—
453#106—611no—
454#106—611no—
455#106C2×#692311yescharacteristic
456#106C2×#692311yescharacteristic
457#97—611no—
458#97—611no—
459#97—611no—
460#97C2×#692311yescharacteristic
461C4×C8—1221no—
462C4×C8—1221no—
463#95—611no—
464#95—611no—
465#95—611no—
466#95—611no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477C2×Q8—21no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×Q8—4881no—
482C2×Q8—4881no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8C22×#692311yescharacteristic
511C2×C8C22×#692311yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—611no—
516C4⋊C4—611no—
517C4⋊C4—611no—
518C4⋊C4—611no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—4881no—
541C4⋊C4—4881no—
542C4⋊C4—4881no—
543C4⋊C4—4881no—
544C4⋊C4—4881no—
545C4⋊C4—4881no—
546C4⋊C4C22×#692311yescharacteristic
547C4⋊C4C22×#692311yescharacteristic
548C4⋊C4C22×#692311yescharacteristic
549C4⋊C4C22×#692311yescharacteristic
550C42—611no—
551C42—611no—
552C42—611no—
553C42—1221no—
554C42—1221no—
555C42—1221no—
556C42—1221no—
557C42—4881no—
558C42—4881no—
559C42—4881no—
560C42—4881no—
561C42C22×#692311yescharacteristic
562C23—611no—
563Q8—81no—
564Q8—4881no—
565Q8—4881no—
566Q8—4881no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4D4×#692311yescharacteristic
619C2×C4D4×#692311yescharacteristic
620C2×C4C23×#692311yescharacteristic
621C8—21no—
622C8—21no—
623C8—1221no—
624C8—1221no—
625C8—2441no—
626C8—2441no—
627C22—611no—
628C22—611no—
629C22—611no—
630C22—611no—
631C22—611no—
632C22—611no—
633C22C2×D4×#692311yescharacteristic
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—611no—
641C4—611no—
642C4—1221no—
643C4—1221no—
644C4—4881no—
645C4—4881no—
646C4—4881no—
647C4—4881no—
648C4—2441no—
649C4—2441no—
650C4—2441no—
651C4—2441no—
652C4—2441no—
653C4—2441no—
654C4—2441no—
655C4—2441no—
656C4#1684083011yescharacteristic
657C4#1684083011yescharacteristic
658C2—611no—
659C2—611no—
660C2—611no—
661C2—611no—
662C2#2146231011yescharacteristic
663C2#2146257611yescharacteristic
664C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#501C4
socleC22×C61C2×C4×D4
prime radicalC22×D61C22×D4
cosocleC2×C4×D61C24
hypercenter#501#6923
hypocenterC61#22255
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
54. #16840172C4semidirect
55. #16840171C4semidirect
56. #16840170C4semidirect
57. #16840170C4semidirect
58. #16840169C4semidirect
59. #16840169C4semidirect
60. #16840168C4semidirect
66. C61×#501C4semidirect
357. #501#6923semidirect
399. C61#22255semidirect

Maximal subgroups

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

subgroupindex
#214623142
#214623132
#214620012
#214620002
#214618832
#214618822
#214618812
#214618802
#214617422
#214615392
#501×D612
#2225561