Subgroups — #15688913

Order 3008.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093941	C₂	1	1	yes	maximal, characteristic
2	#13093939	C₂	1	1	yes	maximal, characteristic
3	#123×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₄₇	C₄	1	1	yes	characteristic, complemented
6	C₄⋊C₄×C₄₇	—	2	1	no	—
7	C₂²⋊C₄×C₄₇	—	2	1	no	—
8	C₂²⋊C₄×C₄₇	C₄	1	1	yes	characteristic, complemented
9	C₂²⋊Dic₄₇	—	2	1	no	—
10	#10625329	—	2	1	no	—
11	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄₇	D₄	1	1	yes	characteristic
13	D₄×C₄₇	—	4	1	no	—
14	C₂×C₄×C₄₇	—	2	1	no	—
15	C₂×C₄×C₄₇	—	2	1	no	—
16	C₂×C₄×C₄₇	—	4	1	no	—
17	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
18	C₂×Dic₄₇	—	4	1	no	—
19	C₄₇⋊C₈	—	4	1	no	—
20	C₂²×C₄₇	—	2	1	no	—
21	C₂²×C₄₇	—	2	1	no	—
22	C₂²×C₄₇	—	4	1	no	—
23	C₂²×C₄₇	—	4	1	no	—
24	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₄₇	—	2	1	no	—
26	C₄×C₄₇	—	4	1	no	—
27	C₄×C₄₇	—	4	1	no	—
28	Dic₄₇	—	8	1	no	—
29	C₂×C₄₇	—	2	1	no	—
30	C₂×C₄₇	—	4	1	no	—
31	C₂×C₄₇	—	4	1	no	—
32	C₂×C₄₇	#99	1	1	yes	characteristic
33	#352	—	47	1	no	maximal, Sylow
34	C₄₇	#352	1	1	yes	characteristic, complemented, Sylow
35	#123	D₄₇	1	1	yes	characteristic
36	#100	—	47	1	no	—
37	#99	—	47	1	no	—
38	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
39	C₂²×C₄	Dic₄₇	1	1	yes	characteristic, complemented
40	M₁₆	—	94	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₂²⋊C₄	—	2	1	no	—
43	C₂²⋊C₄	—	94	1	no	—
44	C₂²⋊C₄	Dic₄₇	1	1	yes	characteristic, complemented
45	C₂³	C₂×Dic₄₇	1	1	yes	characteristic
46	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
47	D₄	—	4	1	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	—	188	1	no	—
52	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
53	C₈	—	188	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	4	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂²⋊Dic₄₇	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	376	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	4	1	no	—
66	C₂	#13093939	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093939
commutator	C₂³×C₄₇	C₂×C₄
Frattini	C₂×D₄	C₂×D₄₇
Fitting	#123×C₄₇	C₂
socle	C₂×C₄₇	#99
prime radical, cosocle	C₂×D₄×C₄₇	C₂²
hypercenter	#123	D₄₇
hypocenter	C₄₇	#352
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #123

Complements

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

N	H ≅ G/N	type
5. C₂²×C₄×C₄₇	C₄	semidirect
8. C₂²⋊C₄×C₄₇	C₄	semidirect
34. C₄₇	#352	semidirect
39. C₂²×C₄	Dic₄₇	semidirect
44. C₂²⋊C₄	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13093941	2
#13093939	2
#123×C₄₇	2
#352	47