Subgroups — #15689235

Order 3008.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#13093956	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093945	C₂	1	2	yes	maximal, complemented
4	#13093934	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×C₄₇	C₂²	1	2	yes	—
7	C₂²×Dic₄₇	—	2	2	no	—
8	D₈×C₄₇	C₄	1	4	yes	complemented
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₄₇	—	2	2	no	—
11	C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇	—	2	2	no	—
15	D₄×C₄₇	—	2	2	no	—
16	D₄×C₄₇	C₂×C₄	1	4	yes	complemented
17	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₇	—	2	2	no	—
19	C₂×Dic₄₇	—	4	4	no	—
20	C₂×Dic₄₇	D₄	1	2	yes	—
21	C₈×C₄₇	C₂×C₄	1	2	yes	complemented
22	C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇	—	2	4	no	—
24	C₂²×C₄₇	—	4	2	no	—
25	C₂²×C₄₇	—	4	2	no	—
26	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
27	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₄₇	#41	1	1	yes	characteristic
29	Dic₄₇	—	2	2	no	—
30	Dic₄₇	—	4	2	no	—
31	C₂×C₄₇	—	4	4	no	—
32	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
33	C₂×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
34	#442	—	47	1	no	maximal, Sylow
35	C₄₇	#442	1	1	yes	characteristic, complemented, Sylow
36	C₂×D₈	D₄₇	1	1	yes	characteristic
37	C₄×D₄	—	47	2	no	—
38	#106	—	47	1	no	—
39	#102	—	47	2	no	—
40	#97	—	47	1	no	—
41	C₂×D₄	C₂×D₄₇	1	2	yes	—
42	C₂²×C₄	—	94	2	no	—
43	D₈	Dic₄₇	1	4	yes	complemented
44	C₂×C₈	—	47	1	no	—
45	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
46	C₄⋊C₄	—	47	2	no	—
47	C₂²⋊C₄	—	94	2	no	—
48	C₄²	—	47	1	no	—
49	C₂³	—	2	2	no	—
50	D₄	—	2	2	no	—
51	D₄	C₂×Dic₄₇	1	4	yes	complemented
52	C₂×C₄	—	47	2	no	—
53	C₂×C₄	—	94	2	no	—
54	C₂×C₄	—	188	4	no	—
55	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
56	C₈	—	94	1	no	—
57	C₈	C₂×Dic₄₇	1	2	yes	complemented
58	C₂²	—	2	4	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	D₄×D₄₇	1	1	yes	characteristic
62	C₄	—	94	2	no	—
63	C₄	—	188	2	no	—
64	C₄	#10625352	1	1	yes	characteristic
65	C₄	C₂²×Dic₄₇	1	1	yes	characteristic
66	C₂	—	4	4	no	—
67	C₂	D₄×Dic₄₇	1	1	yes	characteristic
68	C₂	#13094048	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting, prime radical	C₂×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×D₈	D₄₇
hypocenter	C₄₇	#442
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×Dic₄₇	C₂	semidirect
2. #13093956	C₂	semidirect
3. #13093945	C₂	semidirect
4. #13093934	C₂	semidirect
8. D₈×C₄₇	C₄	semidirect
16. D₄×C₄₇	C₂×C₄	semidirect
21. C₈×C₄₇	C₂×C₄	semidirect
35. C₄₇	#442	semidirect
43. D₈	Dic₄₇	semidirect
51. D₄	C₂×Dic₄₇	semidirect
57. C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₄₇	2
#13093956	2
#13093945	2
#13093934	2
C₂×D₈×C₄₇	2
#442	47