Finite Group Databasebeta

← #30613401

Subgroups — #30613401

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462770C211yesmaximal, characteristic, complemented
2#21462751C211yesmaximal, characteristic, complemented
3#21461462C211yesmaximal, characteristic, complemented
4#21461450C211yesmaximal, characteristic, complemented
5#21461448C211yesmaximal, characteristic, complemented
6#21461446C211yesmaximal, characteristic, complemented
7#21461432C211yesmaximal, characteristic, complemented
8#21461421C211yesmaximal, characteristic, complemented
9#21461409C211yesmaximal, characteristic, complemented
10Q16×#92420C211yesmaximal, characteristic, complemented
11#21461388C211yesmaximal, characteristic, complemented
12#21461176C211yesmaximal, characteristic, complemented
13#21461114C211yesmaximal, characteristic, complemented
14#21461040C211yesmaximal, characteristic, complemented
15#21455838C211yesmaximal, characteristic
16#16840813C2211yescharacteristic
17Q8×#92420C2211yescharacteristic
18Q8×#92420C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840797—21no—
21#16840797—21no—
22#16840797C2211yescharacteristic
23#16840797C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840791—21no—
26#16840790C2211yescharacteristic
27#16840789—21no—
28#16840787—21no—
29#16840779—21no—
30#16840779C2211yescharacteristic
31#16840778C2211yescharacteristic
32#16840769—21no—
33#16840765—21no—
34#16840765C2211yescharacteristic
35C2×C4⋊#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840625C2211yescharacteristic
39#16840625C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840298C2211yescharacteristic
53#41×Dic61C2211yescharacteristic
54#16840100C411yescharacteristic
55#16840087C411yescharacteristic
56#16840067C411yescharacteristic
57#16840060C411yescharacteristic
58#16839986C411yescharacteristic
59#16839979C411yescharacteristic
60#16839907C411yescharacteristic
61Q16×Dic61C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63#16839847C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#452C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73#14519844—21no—
74#14519844—21no—
75#14519844D411yescharacteristic
76#14519844D411yescharacteristic
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420—21no—
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86#14519834—21no—
87#14519834—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420D411yescharacteristic
92C22⋊#92420D411yescharacteristic
93#14519832—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758201C2×C411yescharacteristic
102C2×#11758199C2×C411yescharacteristic
103#14519772—21no—
104#14519768C2×C411yescharacteristic
105#14519766C2×C411yescharacteristic
106#14519761—21no—
107#14519751C2×C411yescharacteristic
108Q8×Dic61C2×C411yescharacteristic
109Q8×Dic61C2311yescharacteristic
110Q8×Dic61C2311yescharacteristic
111D4×Dic61—21no—
112D4×Dic61—21no—
113D4×Dic61C2×C411yescharacteristic
114D4×Dic61C2311yescharacteristic
115#14519739C2311yescharacteristic
116#14519737—21no—
117#14519736—21no—
118#14519736C2×C411yescharacteristic
119#14519735—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519710C2×C411yescharacteristic
124#14519709C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519701C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×#41×C61C2×C411yescharacteristic
138C2×Q16×C61C2×C411yescharacteristic
139C2×SD16×C61C2×C411yescharacteristic
140C22⋊Q8×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144#41×C61—22no—
145#41×C61—41no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×Q8×C61C22×C411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61#4111yescharacteristic
157C2×D244C22×C411yescharacteristic
158C2×C4×D61—21no—
159#11758217—81no—
160#11758217—81no—
161#11758217—81no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—81no—
169C2×#92420C2×D411yescharacteristic
170C2×#92420C2×D411yescharacteristic
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173#11758213—81no—
174D61⋊C8—81no—
175Q16×C61—22no—
176SD16×C61—41no—
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊Dic61—21no—
183C22⋊Dic61—21no—
184C22⋊Dic61—21no—
185#11758201—22no—
186#11758199—41no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C22×C411yescharacteristic
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198#11758196—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61C22×C411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C4×Dic61C2411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C23×C61—21no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61#13112yes—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—42no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—42no—
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C22⋊D61—42no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—41no—
234C2×Dic61—42no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61C4×D411yescharacteristic
238C2×Dic61C4×D411yescharacteristic
239C2×Dic61C22×D411yescharacteristic
240C2×Dic61C2×#4111yescharacteristic
241D244—21no—
242D244—21no—
243C4×D61—41no—
244C4×D61—41no—
245#92420—21no—
246#92420—21no—
247#92420—21no—
248#92420—21no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420—41no—
253#92420—41no—
254#92420—41no—
255C8×C61—21no—
256C8×C61—21no—
257#92418—21no—
258#92418—21no—
259#18033—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C4×C61—21no—
271C4×C61—22no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61C2×#13111yescharacteristic
275C4×C61#56811yescharacteristic
276Dic61—21no—
277Dic61—21no—
278Dic61—21no—
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282Dic61#57611yescharacteristic
283Dic61#57811yescharacteristic
284#3102—611no—
285#2994—611no—
286#2991—611no—
287#1592—611no—
288#1589—611no—
289#1588—611no—
290#1588—611no—
291#1584—611no—
292#1581—611no—
293SD16⋊C8—611no—
294C8×Q16—611no—
295#1571—611no—
296#1495—611no—
297#1477—611no—
298#1454—611no—
299C2×C61—41no—
300C2×C61—81no—
301C2×C61#293311yescharacteristic
302C2×C61#295111yescharacteristic
303C2×C61#295511yescharacteristic
304D61—81no—
305#529—611no—
306C4×#41—611no—
307#485—611no—
308#482—611no—
309#479—611no—
310#478—611no—
311#464—611no—
312#463—611no—
313#452#692311yescharacteristic
314#449—611no—
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8—611no—
323#436—611no—
324#436—611no—
325#436—611no—
326#436—1221no—
327#436—1221no—
328#435—1221no—
329C8×D4—611no—
330C8×D4—1221no—
331#433—1221no—
332#431—611no—
333#431—611no—
334#431—611no—
335#431—1221no—
336#424—1221no—
337#423—611no—
338#423—1221no—
339C2×C4⋊C8—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#335—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352#322—611no—
353#322—611no—
354#322—611no—
355C82—611no—
356C61#1803311yescharacteristic, complemented, Sylow
357C2×#41C2×#692311yescharacteristic
358C2×Q16C2×#692311yescharacteristic
359C2×SD16—611no—
360C2×SD16C2×#692311yescharacteristic
361C2×D8—611no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368#126—1221no—
369#125—611no—
370#124—611no—
371#123—1221no—
372C22⋊Q8C2×#692311yescharacteristic
373#121—611no—
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—611no—
377C4×D4—611no—
378C4×D4—611no—
379C4×D4—611no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4—1221no—
383#117—611no—
384#117—1221no—
385#117—1221no—
386C2×C42—611no—
387C2×C42—1221no—
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407#103—611no—
408#103—611no—
409#103—611no—
410#103C2×#692311yescharacteristic
411#102—611no—
412#102—611no—
413#102—611no—
414#102C2×#692311yescharacteristic
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8C2×#692311yescharacteristic
424#97—1221no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—1221no—
432C4×C8—1221no—
433C4×C8—1221no—
434#41—22no—
435#41—41no—
436C2×Q8C22×#692311yescharacteristic
437C2×Q8C22×#692311yescharacteristic
438C2×D4—21no—
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4C22×#692311yescharacteristic
442C22×C4—21no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4C22×#692311yescharacteristic
449Q16—22no—
450SD16—41no—
451SD16—1222no—
452D8—2441no—
453M16—4881no—
454M16—4881no—
455M16—4881no—
456M16—4881no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—4881no—
470C2×C8—4881no—
471C2×C8C22×#692311yescharacteristic
472C2×C8C22×#692311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C22×#692311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C23—21no—
500C23—1221no—
501C23D4×#692311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8#1451986412yes—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—1221no—
510D4—1221no—
511D4—2442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—42no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2442no—
533C2×C4D4×#692311yescharacteristic
534C2×C4C23×#692311yescharacteristic
535C8—21no—
536C8—21no—
537C8—1221no—
538C8—1221no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22C2×D4×#692311yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—611no—
564C4—611no—
565C4—1221no—
566C4—1221no—
567C4—1221no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4C2×#1451986411yescharacteristic
572C4#1684084011yescharacteristic
573C2—41no—
574C2—81no—
575C2—4881no—
576C2#2146255111yescharacteristic
577C2#2146258111yescharacteristic
578C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#452C4
socleC22×C61C2×C4×D4
prime radical#16839907C4
cosocleC4×Dic61C24
hypercenter#452#6923
hypocenterC61#18033
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #21462770C2semidirect
2. #21462751C2semidirect
3. #21461462C2semidirect
4. #21461450C2semidirect
5. #21461448C2semidirect
6. #21461446C2semidirect
7. #21461432C2semidirect
8. #21461421C2semidirect
9. #21461409C2semidirect
10. Q16×#92420C2semidirect
11. #21461388C2semidirect
12. #21461176C2semidirect
13. #21461114C2semidirect
14. #21461040C2semidirect
356. C61#18033semidirect

Maximal subgroups

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

subgroupindex
#214627702
#214627512
#214614622
#214614502
#214614482
#214614462
#214614322
#214614212
#214614092
Q16×#924202
#214613882
#214611762
#214611142
#214610402
#214558382
#1803361