Subgroups — #37588759

Order 24512.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133840	C₂	1	1	yes	maximal, characteristic
2	#27133832	C₂	1	1	yes	maximal, characteristic
3	#27133774	C₂	1	1	yes	maximal, characteristic
4	#27133773	C₂	1	1	yes	maximal, characteristic
5	#27133772	C₂	1	1	yes	maximal, characteristic
6	#27133751	C₂	1	1	yes	maximal, characteristic
7	#107×C₃₈₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₇₆₆	—	2	1	no	—
9	C₂×C₃₈₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃₈₃	—	2	1	no	—
11	C₄⋊Dic₃₈₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃₈₃	C₂²	1	1	yes	characteristic
13	Dic₃₈₃⋊C₄	—	2	1	no	—
14	Dic₃₈₃⋊C₄	—	2	1	no	—
15	C₄×Dic₃₈₃	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₃₈₃	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₃₈₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₃₈₃	C₂²	1	1	yes	characteristic
19	Dic₇₆₆	—	4	2	no	—
20	C₂×Dic₃₈₃	—	2	1	no	—
21	C₂×Dic₃₈₃	—	2	1	no	—
22	C₂×Dic₃₈₃	D₄	1	1	yes	characteristic
23	C₂×Dic₃₈₃	D₄	1	1	yes	characteristic
24	C₃₈₃⋊C₈	Q₈	1	2	yes	complemented
25	C₂×C₄×C₃₈₃	—	2	1	no	—
26	C₂×C₄×C₃₈₃	—	2	1	no	—
27	C₂×C₄×C₃₈₃	C₂³	1	1	yes	characteristic
28	C₈×C₃₈₃	Q₈	1	2	yes	complemented
29	C₂²×C₃₈₃	C₂×D₄	1	1	yes	characteristic
30	C₄×C₃₈₃	—	4	1	no	—
31	C₄×C₃₈₃	—	4	1	no	—
32	C₄×C₃₈₃	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₃₈₃	C₂×Q₈	1	1	yes	characteristic
34	Dic₃₈₃	—	2	1	no	—
35	Dic₃₈₃	—	2	1	no	—
36	Dic₃₈₃	—	4	1	no	—
37	Dic₃₈₃	—	4	1	no	—
38	C₂×C₃₈₃	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₃₈₃	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₃₈₃	#137	1	1	yes	characteristic
41	C₃₈₃	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	383	1	no	maximal, Sylow
43	C₄⋊Q₈	—	383	1	no	—
44	#125	—	383	1	no	—
45	#107	—	383	1	no	—
46	#107	D₃₈₃	1	1	yes	characteristic
47	#106	—	383	1	no	—
48	#106	—	383	1	no	—
49	#97	—	383	1	no	—
50	C₂×Q₈	—	766	1	no	—
51	C₂×C₈	—	383	1	no	—
52	C₂×C₈	C₂×D₃₈₃	1	1	yes	characteristic
53	C₄⋊C₄	—	383	1	no	—
54	C₄⋊C₄	—	383	1	no	—
55	C₄⋊C₄	—	766	1	no	—
56	C₄⋊C₄	—	766	1	no	—
57	C₄⋊C₄	—	766	1	no	—
58	C₄⋊C₄	C₂×D₃₈₃	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₃₈₃	1	1	yes	characteristic
60	C₄²	—	383	1	no	—
61	Q₈	—	1532	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	383	1	no	—
65	C₂×C₄	—	383	1	no	—
66	C₂×C₄	—	766	1	no	—
67	C₂×C₄	—	766	1	no	—
68	C₂×C₄	C₂²×D₃₈₃	1	1	yes	characteristic
69	C₈	—	383	2	no	—
70	C₈	Dic₇₆₆	1	2	yes	complemented
71	C₂²	D₄×D₃₈₃	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	1532	1	no	—
75	C₄	—	1532	1	no	—
76	C₄	—	766	1	no	—
77	C₄	—	766	1	no	—
78	C₄	Q₈×D₃₈₃	1	1	yes	characteristic
79	C₄	C₂×Dic₇₆₆	1	1	yes	characteristic
80	C₂	#27133840	1	1	yes	characteristic
81	C₂	#27133865	1	1	yes	characteristic
82	C₂	#27133873	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₈₃
commutator, cosocle	C₂×C₄×C₃₈₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₈₃
Fitting	#107×C₃₈₃	C₂
socle, prime radical	C₂²×C₃₈₃	C₂×D₄
hypercenter	#107	D₃₈₃
hypocenter	C₃₈₃	#501
LCS	G ▷ C₂×C₄×C₃₈₃ ▷ C₂×C₃₈₃ ▷ C₃₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
24. C₃₈₃⋊C₈	Q₈	semidirect
28. C₈×C₃₈₃	Q₈	semidirect
41. C₃₈₃	#501	semidirect
70. C₈	Dic₇₆₆	semidirect

Maximal subgroups

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

subgroup	index
#27133840	2
#27133832	2
#27133774	2
#27133773	2
#27133772	2
#27133751	2
#107×C₃₈₃	2
#501	383