Subgroups — #15689560

Order 3008.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094047	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093967	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇₅₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093965	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093963	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#10625354	—	2	1	no	—
9	D₄×D₄₇	—	2	1	no	—
10	Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₄₇	C₂²	1	1	yes	characteristic
12	#10625336	—	2	1	no	—
13	#10625334	—	2	1	no	—
14	D₃₇₆	C₂²	1	1	yes	characteristic
15	D₃₇₆	C₂²	1	1	yes	characteristic, complemented
16	C₈×D₄₇	C₂²	1	1	yes	characteristic
17	C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
18	C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄₇	—	4	1	no	—
20	Q₈×C₄₇	—	2	1	no	—
21	D₄×C₄₇	—	2	1	no	—
22	C₂²⋊D₄₇	—	4	1	no	—
23	D₁₈₈	—	2	1	no	—
24	D₁₈₈	—	2	1	no	—
25	D₁₈₈	—	4	1	no	—
26	C₄×D₄₇	—	4	1	no	—
27	C₄×D₄₇	D₄	1	1	yes	characteristic
28	C₈×C₄₇	C₂³	1	1	yes	characteristic
29	C₄₇⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₄₇	—	4	1	no	—
31	C₂×D₄₇	—	4	1	no	—
32	C₂×D₄₇	—	4	1	no	—
33	C₂×D₄₇	—	8	2	no	—
34	C₂×D₄₇	D₈	1	1	yes	characteristic
35	C₄×C₄₇	—	4	1	no	—
36	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	Dic₄₇	D₈	1	1	yes	characteristic
38	C₂×C₄₇	—	8	1	no	—
39	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
40	D₄₇	—	2	1	no	—
41	D₄₇	—	8	1	no	—
42	D₄₇	—	8	1	no	—
43	#509	—	47	1	no	maximal, Sylow
44	C₄₇	#509	1	1	yes	characteristic, complemented, Sylow
45	#135	—	47	1	no	—
46	C₂×D₈	—	47	1	no	—
47	SD₃₂	—	47	1	no	—
48	SD₃₂	D₄₇	1	1	yes	characteristic, complemented
49	D₁₆	—	47	1	no	—
50	D₁₆	—	47	1	no	—
51	M₃₂	—	47	1	no	—
52	#41	—	94	1	no	—
53	C₂×D₄	—	94	1	no	—
54	Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
55	SD₁₆	—	94	1	no	—
56	D₈	—	47	1	no	—
57	D₈	—	47	1	no	—
58	D₈	—	94	1	no	—
59	D₈	C₂×D₄₇	1	1	yes	characteristic
60	C₂×C₈	—	47	1	no	—
61	C₁₆	—	47	1	no	—
62	C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
63	C₂³	—	188	1	no	—
64	Q₈	—	2	1	no	—
65	D₄	—	2	1	no	—
66	D₄	—	94	1	no	—
67	D₄	—	94	1	no	—
68	D₄	—	188	1	no	—
69	D₄	—	188	1	no	—
70	C₂×C₄	—	47	1	no	—
71	C₂×C₄	—	188	1	no	—
72	C₈	—	47	1	no	—
73	C₈	C₂²×D₄₇	1	1	yes	characteristic
74	C₂²	—	4	1	no	—
75	C₂²	—	47	1	no	—
76	C₂²	—	376	2	no	—
77	C₂²	—	188	1	no	—
78	C₂²	—	188	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	47	1	no	—
81	C₄	D₄×D₄₇	1	1	yes	characteristic
82	C₂	—	8	1	no	—
83	C₂	—	94	1	no	—
84	C₂	—	376	1	no	—
85	C₂	—	376	1	no	—
86	C₂	D₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₇
commutator, cosocle	C₈×C₄₇	C₂³
Frattini	C₈	C₂²×D₄₇
Fitting	SD₃₂×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₈
hypercenter	SD₃₂	D₄₇
hypocenter	C₄₇	#509
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. #13094047	C₂	semidirect
2. D₈×D₄₇	C₂	semidirect
3. #13093967	C₂	semidirect
4. D₇₅₂	C₂	semidirect
5. #13093965	C₂	semidirect
6. #13093963	C₂	semidirect
7. SD₃₂×C₄₇	C₂	semidirect
10. Q₁₆×C₄₇	C₂²	semidirect
15. D₃₇₆	C₂²	semidirect
17. C₁₆×C₄₇	C₂²	semidirect
18. C₄₇⋊C₁₆	C₂²	semidirect
44. C₄₇	#509	semidirect
48. SD₃₂	D₄₇	semidirect
54. Q₁₆	C₂×D₄₇	semidirect
62. C₁₆	C₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094047	2
D₈×D₄₇	2
#13093967	2
D₇₅₂	2
#13093965	2
#13093963	2
SD₃₂×C₄₇	2
#509	47