Subgroups — #44529004

Order 31168.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21441244	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄₈₇	C₂	1	1	yes	maximal, characteristic
3	#29510172	C₂	1	1	yes	maximal, characteristic
4	#29510126	C₂	1	1	yes	maximal, characteristic, complemented
5	#29510125	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₄₈₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₈₇	C₂²	1	1	yes	characteristic
9	#21441244	C₄	1	4	yes	complemented
10	C₂×C₄₈₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄₈₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₈×D₄₈₇	C₄	1	4	yes	complemented
13	Dic₄₈₇⋊C₄	C₄	1	2	yes	—
14	(C₂×D₄₈₇)⋊C₄	C₄	1	2	yes	—
15	C₄×Dic₄₈₇	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
18	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
19	C₂²×D₄₈₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₄₈₇	C₂×C₄	1	2	yes	—
21	C₂×Dic₄₈₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₄₈₇	C₂×C₄	1	2	yes	—
23	C₄×D₄₈₇	C₂×C₄	1	2	yes	—
24	C₄₈₇⋊C₈	C₂×C₄	1	2	yes	—
25	C₄₈₇⋊C₈	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₄₈₇	C₂×C₄	1	2	yes	—
27	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
28	C₈×C₄₈₇	C₂×C₄	1	2	yes	—
29	C₈×C₄₈₇	C₂×C₄	1	2	yes	—
30	C₂²×C₄₈₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₄₈₇	—	2	2	no	—
32	C₂×D₄₈₇	C₄²	1	2	yes	—
33	C₄×C₄₈₇	—	2	2	no	—
34	C₄×C₄₈₇	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₄₈₇	C₂²×C₄	1	1	yes	characteristic
36	Dic₄₈₇	—	2	2	no	—
37	Dic₄₈₇	C₄²	1	2	yes	—
38	C₂×C₄₈₇	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₄₈₇	#131	1	2	yes	—
40	D₄₈₇	—	2	2	no	—
41	C₄₈₇	#405	1	1	yes	characteristic, complemented, Sylow
42	#405	—	487	1	no	maximal, Sylow
43	C₂×M₁₆	—	487	1	no	—
44	C₂²×C₈	—	487	1	no	—
45	#117	—	487	1	no	—
46	#97	—	487	1	no	—
47	#97	—	487	1	no	—
48	C₄×C₈	—	487	1	no	—
49	C₄×C₈	D₄₈₇	1	1	yes	characteristic, complemented
50	C₂²×C₄	—	487	1	no	—
51	M₁₆	—	487	4	no	—
52	C₂×C₈	—	487	1	no	—
53	C₂×C₈	—	487	1	no	—
54	C₂×C₈	—	487	4	no	—
55	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
56	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
57	C₄⋊C₄	—	487	2	no	—
58	C₂²⋊C₄	—	487	2	no	—
59	C₄²	—	487	1	no	—
60	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
61	C₂³	—	487	1	no	—
62	C₂×C₄	—	487	2	no	—
63	C₂×C₄	—	487	1	no	—
64	C₂×C₄	—	487	2	no	—
65	C₂×C₄	—	487	2	no	—
66	C₂×C₄	C₄×D₄₈₇	1	2	yes	—
67	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
68	C₈	—	487	2	no	—
69	C₈	—	487	2	no	—
70	C₈	C₄×D₄₈₇	1	2	yes	—
71	C₈	C₄×D₄₈₇	1	2	yes	—
72	C₂²	—	974	2	no	—
73	C₂²	—	487	2	no	—
74	C₂²	C₂×C₄×D₄₈₇	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	974	2	no	—
77	C₄	—	487	2	no	—
78	C₄	C₂×C₄×D₄₈₇	1	1	yes	characteristic
79	C₄	C₂×C₄×D₄₈₇	1	1	yes	characteristic
80	C₂	—	974	2	no	—
81	C₂	C₄²×D₄₈₇	1	1	yes	characteristic
82	C₂	#29510221	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₄₈₇
commutator	C₂×C₄₈₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	C₄×C₈×C₄₈₇	C₂
socle	C₂²×C₄₈₇	C₂²×C₄
prime radical	C₂²×D₄₈₇	C₂×C₄
cosocle	C₂×C₄×C₄₈₇	C₂³
hypercenter	C₄×C₈	D₄₈₇
hypocenter	C₄₈₇	#405
LCS	G ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #29510126	C₂	semidirect
5. #29510125	C₂	semidirect
6. C₈×Dic₄₈₇	C₂	semidirect
7. C₄×C₈×C₄₈₇	C₂	semidirect
9. #21441244	C₄	semidirect
12. C₈×D₄₈₇	C₄	semidirect
41. C₄₈₇	#405	semidirect
49. C₄×C₈	D₄₈₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21441244	2
C₂×C₈×D₄₈₇	2
#29510172	2
#29510126	2
#29510125	2
C₈×Dic₄₈₇	2
C₄×C₈×C₄₈₇	2
#405	487