Subgroups — #15688924

Order 3008.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093958	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₄₇	—	2	1	no	—
5	D₈×C₄₇	—	2	1	no	—
6	D₈×C₄₇	C₄	1	2	yes	complemented
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₇	—	2	1	no	—
9	C₄₇⋊C₁₆	—	2	1	no	—
10	C₂³×C₄₇	—	4	1	no	—
11	D₄×C₄₇	—	2	2	no	—
12	D₄×C₄₇	—	4	1	no	—
13	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
14	C₂×Dic₄₇	—	4	1	no	—
15	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×C₄₇	—	4	2	no	—
18	C₂²×C₄₇	—	8	1	no	—
19	C₂²×C₄₇	—	8	1	no	—
20	C₂²×C₄₇	D₈	1	1	yes	characteristic
21	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₄₇	SD₁₆	1	1	yes	characteristic
23	Dic₄₇	—	8	1	no	—
24	C₂×C₄₇	—	8	2	no	—
25	C₂×C₄₇	#102	1	1	yes	characteristic
26	C₂×C₄₇	D₁₆	1	1	yes	characteristic
27	C₂×C₄₇	SD₃₂	1	1	yes	characteristic
28	#357	—	47	1	no	maximal, Sylow
29	C₄₇	#357	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₈	D₄₇	1	1	yes	characteristic
31	C₂×C₁₆	—	47	1	no	—
32	#107	—	47	1	no	—
33	C₂×D₄	—	2	1	no	—
34	D₈	—	2	1	no	—
35	D₈	Dic₄₇	1	2	yes	complemented
36	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
37	C₄⋊C₄	—	94	1	no	—
38	C₁₆	—	94	1	no	—
39	C₂³	—	4	1	no	—
40	D₄	—	2	2	no	—
41	D₄	—	4	1	no	—
42	C₂×C₄	—	188	1	no	—
43	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
44	C₈	C₂×Dic₄₇	1	1	yes	characteristic
45	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
46	C₂²	—	4	2	no	—
47	C₂²	—	8	1	no	—
48	C₂²	—	8	1	no	—
49	C₂²	#10625334	1	1	yes	characteristic
50	C₄	—	376	1	no	—
51	C₄	#10625335	1	1	yes	characteristic
52	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
53	C₂	—	8	2	no	—
54	C₂	#13093945	1	1	yes	characteristic
55	C₂	#13093965	1	1	yes	characteristic
56	C₂	#13093968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10625334
commutator	C₈×C₄₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₇
Fitting, prime radical	C₂×D₈×C₄₇	C₂
socle	C₂²×C₄₇	D₈
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	C₂×D₈	D₄₇
hypocenter	C₄₇	#357
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇⋊C₁₆	C₂	semidirect
2. #13093958	C₂	semidirect
6. D₈×C₄₇	C₄	semidirect
29. C₄₇	#357	semidirect
35. D₈	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇⋊C₁₆	2
#13093958	2
C₂×D₈×C₄₇	2
#357	47