Subgroups — #15689499

Order 3008.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625334	C₂	1	4	yes	maximal, complemented
2	#13094021	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₄₇	—	2	2	no	—
6	C₂×D₄×C₄₇	C₂²	1	2	yes	—
7	C₂×D₁₈₈	—	2	2	no	—
8	C₂×D₁₈₈	C₂²	1	2	yes	—
9	C₄²×C₄₇	C₂²	1	1	yes	characteristic
10	#10625334	—	2	8	no	—
11	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
12	C₂³×C₄₇	—	2	2	no	—
13	C₂²×D₄₇	—	2	2	no	—
14	D₄×C₄₇	—	2	4	no	—
15	D₄×C₄₇	—	4	4	no	—
16	C₂×C₄×C₄₇	D₄	1	2	yes	—
17	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	D₁₈₈	—	2	4	no	—
19	D₁₈₈	—	4	4	no	—
20	C₄₇⋊C₈	D₄	1	4	yes	complemented
21	C₂²×C₄₇	—	4	2	no	—
22	C₂²×C₄₇	—	4	4	no	—
23	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
24	C₂×D₄₇	—	4	2	no	—
25	C₂×D₄₇	—	4	4	no	—
26	C₄×C₄₇	D₈	1	4	yes	complemented
27	C₄×C₄₇	C₂×D₄	1	2	yes	—
28	C₂×C₄₇	—	8	2	no	—
29	C₂×C₄₇	#127	1	1	yes	characteristic
30	C₂×C₄₇	C₂×D₈	1	2	yes	—
31	D₄₇	—	8	2	no	—
32	#493	—	47	1	no	maximal, Sylow
33	C₄₇	#493	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₈	—	47	4	no	—
35	#127	—	47	1	no	—
36	#127	D₄₇	1	1	yes	characteristic, complemented
37	C₄×C₈	—	47	1	no	—
38	C₂×D₄	—	2	2	no	—
39	C₂×D₄	—	47	2	no	—
40	C₂×D₄	—	94	2	no	—
41	C₂×D₄	C₂×D₄₇	1	2	yes	—
42	D₈	—	94	8	no	—
43	C₂×C₈	—	47	2	no	—
44	C₄²	C₂×D₄₇	1	1	yes	characteristic
45	C₂³	—	2	2	no	—
46	C₂³	—	94	2	no	—
47	D₄	—	2	4	no	—
48	D₄	—	4	4	no	—
49	D₄	—	94	4	no	—
50	D₄	—	188	4	no	—
51	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
52	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
53	C₈	—	47	4	no	—
54	C₂²	—	4	2	no	—
55	C₂²	—	4	4	no	—
56	C₂²	—	188	2	no	—
57	C₂²	—	188	4	no	—
58	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
59	C₄	#10625334	1	4	yes	complemented
60	C₄	D₄×D₄₇	1	2	yes	—
61	C₂	—	8	2	no	—
62	C₂	—	376	2	no	—
63	C₂	#13094020	1	1	yes	characteristic
64	C₂	C₂×#10625334	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#127×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	#127	D₄₇
hypocenter	C₄₇	#493
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#10625334	C₂	semidirect
2. #13094021	C₂	semidirect
3. C₄×C₄₇⋊C₈	C₂	semidirect
4. #127×C₄₇	C₂	semidirect
20. C₄₇⋊C₈	D₄	semidirect
26. C₄×C₄₇	D₈	semidirect
33. C₄₇	#493	semidirect
36. #127	D₄₇	semidirect
59. C₄	#10625334	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625334	2
#13094021	2
C₄×C₄₇⋊C₈	2
#127×C₄₇	2
#493	47