Subgroups — #15688932

Order 3008.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094046	C₂	1	1	yes	maximal, characteristic
2	#13093964	C₂	1	1	yes	maximal, characteristic, complemented
3	#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625350	—	2	1	no	—
5	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
6	C₄⋊C₄×C₄₇	—	2	1	no	—
7	Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
8	D₃₇₆	C₄	1	1	yes	characteristic, complemented
9	#10625325	—	2	1	no	—
10	C₄₇⋊C₁₆	—	2	1	no	—
11	C₂×C₄×C₄₇	—	4	1	no	—
12	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
13	C₂²⋊D₄₇	—	4	1	no	—
14	D₁₈₈	—	2	1	no	—
15	C₄×D₄₇	—	4	1	no	—
16	Dic₉₄	—	2	1	no	—
17	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₈×C₄₇	D₄	1	1	yes	characteristic
19	C₂²×C₄₇	D₈	1	1	yes	characteristic
20	C₂×D₄₇	—	4	1	no	—
21	C₄×C₄₇	—	8	1	no	—
22	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₄₇	SD₁₆	1	1	yes	characteristic
24	Dic₄₇	—	4	1	no	—
25	C₂×C₄₇	—	2	1	no	—
26	C₂×C₄₇	#102	1	1	yes	characteristic
27	D₄₇	—	8	1	no	—
28	#360	—	47	1	no	maximal, Sylow
29	C₄₇	#360	1	1	yes	characteristic, complemented, Sylow
30	#135	—	47	1	no	—
31	M₃₂	—	47	1	no	—
32	#106	D₄₇	1	1	yes	characteristic, complemented
33	#41	—	94	1	no	—
34	Q₁₆	—	47	1	no	—
35	SD₁₆	—	94	1	no	—
36	D₈	—	47	1	no	—
37	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
38	C₄⋊C₄	—	2	1	no	—
39	C₁₆	—	94	1	no	—
40	Q₈	—	94	1	no	—
41	D₄	—	94	1	no	—
42	D₄	—	188	1	no	—
43	C₂×C₄	—	4	1	no	—
44	C₂×C₄	—	188	1	no	—
45	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
46	C₈	C₄×D₄₇	1	1	yes	characteristic
47	C₈	D₁₈₈	1	1	yes	characteristic
48	C₂²	—	188	1	no	—
49	C₂²	#10625334	1	1	yes	characteristic
50	C₄	—	8	1	no	—
51	C₄	—	188	1	no	—
52	C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
53	C₄	#10625336	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	376	1	no	—
56	C₂	#13093944	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093944
commutator	C₈×C₄₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₇
Fitting	#106×C₄₇	C₂
socle	C₂×C₄₇	#102
prime radical	#13094046	C₂
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	#106	D₄₇
hypocenter	C₄₇	#360
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
2. #13093964	C₂	semidirect
3. #106×C₄₇	C₂	semidirect
7. Dic₁₈₈	C₄	semidirect
8. D₃₇₆	C₄	semidirect
29. C₄₇	#360	semidirect
32. #106	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094046	2
#13093964	2
#106×C₄₇	2
#360	47