Subgroups — #20241450

Order 6016.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689525	C₂	1	1	yes	maximal, characteristic
2	#15688944	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#364	C₂	1	1	yes	maximal, characteristic
4	#13094016	C₄	1	2	yes	—
5	#13093964	—	2	1	no	—
6	#13093958	—	2	1	no	—
7	#13093956	—	2	1	no	—
8	M₃₂×C₄₇	—	2	1	no	—
9	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
11	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
12	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₄₇	—	2	2	no	—
14	Dic₄₇⋊C₄	—	4	2	no	—
15	C₁₆×C₄₇	—	4	1	no	—
16	C₄₇⋊C₁₆	—	4	1	no	—
17	C₂×C₄×C₄₇	—	2	1	no	—
18	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₄₇	—	4	2	no	—
20	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
21	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
22	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
23	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
24	C₂²×C₄₇	#100	1	1	yes	characteristic
25	C₄×C₄₇	—	4	1	no	—
26	C₄×C₄₇	#103	1	1	yes	characteristic
27	C₄×C₄₇	#103	1	1	yes	characteristic
28	Dic₄₇	—	8	2	no	—
29	#1366	—	47	1	no	maximal, Sylow
30	C₂×C₄₇	—	2	1	no	—
31	C₂×C₄₇	#333	1	1	yes	characteristic
32	#499	—	47	1	no	—
33	#364	—	47	1	no	—
34	#364	D₄₇	1	1	yes	characteristic
35	C₄₇	#1366	1	1	yes	characteristic, complemented, Sylow
36	#125	—	47	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	94	1	no	—
39	#107	—	94	1	no	—
40	#106	—	94	1	no	—
41	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
42	C₂×C₈	D₁₈₈	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
44	C₄⋊C₄	—	94	2	no	—
45	C₄⋊C₄	—	188	2	no	—
46	C₄²	C₄×D₄₇	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	188	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	188	2	no	—
51	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
52	C₈	#10625325	1	1	yes	characteristic
53	C₈	Dic₁₈₈	1	1	yes	characteristic
54	C₈	#10625335	1	1	yes	characteristic
55	C₈	#10625337	1	1	yes	characteristic
56	C₂²	#13093940	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	376	2	no	—
59	C₄	#13093947	1	1	yes	characteristic
60	C₄	#13093949	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#15688871	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688871
commutator	C₄²×C₄₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#364	C₂
socle	C₂×C₄₇	#333
hypercenter	#364	D₄₇
hypocenter	C₄₇	#1366
LCS	G ▷ C₄²×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
35. C₄₇	#1366	semidirect