Subgroups — #20241577

Order 6016.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₅₂	C₂	1	1	yes	maximal, characteristic
2	#15688957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₇₆	—	2	1	no	—
5	D₇₅₂	—	2	1	no	—
6	D₇₅₂	C₄	1	2	yes	—
7	C₄₇⋊C₃₂	—	2	1	no	—
8	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
9	#108×C₄₇	—	2	1	no	—
10	C₂×D₁₈₈	—	4	1	no	—
11	M₁₆×C₄₇	—	4	1	no	—
12	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
13	D₃₇₆	—	2	2	no	—
14	D₃₇₆	—	4	1	no	—
15	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×D₄₇	—	8	1	no	—
18	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
19	D₁₈₈	—	4	2	no	—
20	D₁₈₈	—	8	1	no	—
21	C₈×C₄₇	—	8	1	no	—
22	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
24	C₂²×C₄₇	SD₃₂	1	1	yes	characteristic
25	C₂×D₄₇	—	8	2	no	—
26	C₂×D₄₇	—	16	2	no	—
27	C₄×C₄₇	#102	1	1	yes	characteristic
28	C₄×C₄₇	D₁₆	1	1	yes	characteristic
29	#1419	—	47	1	no	maximal, Sylow
30	C₂×C₄₇	—	2	1	no	—
31	C₂×C₄₇	#357	1	1	yes	characteristic
32	D₄₇	—	16	2	no	—
33	C₂×D₁₆	—	47	1	no	—
34	M₆₄	—	47	1	no	—
35	#368	D₄₇	1	1	yes	characteristic, complemented
36	C₄₇	#1419	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₈	—	94	1	no	—
38	D₁₆	—	47	2	no	—
39	D₁₆	—	94	1	no	—
40	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
41	#108	—	2	1	no	—
42	C₃₂	—	94	1	no	—
43	C₂×D₄	—	188	1	no	—
44	D₈	—	94	2	no	—
45	D₈	—	188	1	no	—
46	M₁₆	—	4	1	no	—
47	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
48	C₁₆	C₄×D₄₇	1	1	yes	characteristic
49	C₁₆	D₁₈₈	1	1	yes	characteristic
50	C₂³	—	376	1	no	—
51	D₄	—	376	1	no	—
52	D₄	—	188	2	no	—
53	C₂×C₄	#10625334	1	1	yes	characteristic
54	C₈	—	8	1	no	—
55	C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
56	C₈	#10625336	1	1	yes	characteristic
57	C₂²	—	376	2	no	—
58	C₂²	—	752	2	no	—
59	C₂²	#13093967	1	1	yes	characteristic
60	C₄	#13093944	1	1	yes	characteristic
61	C₄	#13093965	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	752	2	no	—
64	C₂	#15688923	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688923
commutator	C₁₆×C₄₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₄₇×#368	C₂
socle	C₂×C₄₇	#357
hypercenter	#368	D₄₇
hypocenter	C₄₇	#1419
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #15688957	C₂	semidirect
3. C₄₇×#368	C₂	semidirect
35. #368	D₄₇	semidirect
36. C₄₇	#1419	semidirect