Subgroups — #44529460

Order 31168.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29510215	C₂	1	1	yes	maximal, characteristic
2	#29510148	C₂	1	2	yes	maximal
3	#29510146	C₂	1	2	yes	maximal
4	#29510126	C₂	1	1	yes	maximal, characteristic
5	#125×C₄₈₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₇₄	—	2	1	no	—
7	C₂×C₄₈₇⋊C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₄₈₇	—	2	1	no	—
9	C₄⋊Dic₄₈₇	C₂²	1	2	yes	—
10	C₄⋊C₄×C₄₈₇	—	2	1	no	—
11	C₄⋊C₄×C₄₈₇	—	2	1	no	—
12	C₄⋊C₄×C₄₈₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₄₈₇	C₂²	1	1	yes	characteristic
14	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
15	Dic₉₇₄	—	4	2	no	—
16	C₂×Dic₄₈₇	—	2	2	no	—
17	C₄₈₇⋊C₈	Q₈	1	4	yes	complemented
18	C₂×C₄×C₄₈₇	—	2	1	no	—
19	C₂×C₄×C₄₈₇	—	2	1	no	—
20	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
23	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₈₇	—	2	1	no	—
25	C₄×C₄₈₇	—	2	1	no	—
26	C₄×C₄₈₇	—	4	1	no	—
27	C₄×C₄₈₇	—	4	1	no	—
28	C₄×C₄₈₇	C₂×Q₈	1	2	yes	—
29	Dic₄₈₇	—	4	2	no	—
30	C₂×C₄₈₇	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₄₈₇	AGL(1,ℤ/8)	1	1	yes	characteristic
32	C₂×C₄₈₇	#137	1	1	yes	characteristic
33	C₄₈₇	#501	1	1	yes	characteristic, complemented, Sylow
34	#501	—	487	1	no	maximal, Sylow
35	C₄⋊Q₈	—	487	1	no	—
36	#125	D₄₈₇	1	1	yes	characteristic
37	#107	—	487	2	no	—
38	#106	—	487	2	no	—
39	#97	—	487	1	no	—
40	C₂×Q₈	—	974	1	no	—
41	C₂×C₈	—	487	2	no	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	974	1	no	—
45	C₄⋊C₄	—	487	2	no	—
46	C₄⋊C₄	C₂×D₄₈₇	1	1	yes	characteristic
47	C₄⋊C₄	C₂×D₄₈₇	1	1	yes	characteristic
48	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
49	Q₈	—	1948	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	974	2	no	—
53	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
54	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
56	C₈	—	487	4	no	—
57	C₂²	C₂×C₂²⋊D₄₈₇	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	1948	2	no	—
63	C₄	Q₈×D₄₈₇	1	2	yes	—
64	C₂	#29510213	1	1	yes	characteristic
65	C₂	#29510240	1	1	yes	characteristic
66	C₂	#29510245	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₈₇
commutator, cosocle	C₂×C₄×C₄₈₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	#125×C₄₈₇	C₂
socle, prime radical	C₂²×C₄₈₇	C₂×D₄
hypercenter	#125	D₄₈₇
hypocenter	C₄₈₇	#501
LCS	G ▷ C₂×C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
17. C₄₈₇⋊C₈	Q₈	semidirect
33. C₄₈₇	#501	semidirect

Maximal subgroups

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

subgroup	index
#29510215	2
#29510148	2
#29510146	2
#29510126	2
#125×C₄₈₇	2
#501	487