Subgroups — #20241595

Order 6016.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688957	C₂	1	1	yes	maximal, characteristic
2	#15688951	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#368	C₂	1	1	yes	maximal, characteristic
4	#13093958	—	2	1	no	—
5	C₄₇⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
7	#108×C₄₇	—	2	1	no	—
8	M₁₆×C₄₇	—	4	1	no	—
9	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
10	C₄⋊Dic₄₇	—	4	1	no	—
11	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₄₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
14	C₂×Dic₄₇	—	8	1	no	—
15	C₈×C₄₇	—	8	1	no	—
16	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
18	C₂²×C₄₇	SD₃₂	1	1	yes	characteristic
19	C₄×C₄₇	#107	1	1	yes	characteristic
20	C₄×C₄₇	SD₃₂	1	1	yes	characteristic
21	Dic₄₇	—	16	1	no	—
22	#1426	—	47	1	no	maximal, Sylow
23	C₂×C₄₇	—	2	1	no	—
24	C₂×C₄₇	#367	1	1	yes	characteristic
25	M₆₄	—	47	1	no	—
26	#368	D₄₇	1	1	yes	characteristic
27	#367	—	47	1	no	—
28	C₄₇	#1426	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
30	#108	—	2	1	no	—
31	#107	—	94	1	no	—
32	C₃₂	—	47	2	no	—
33	M₁₆	—	4	1	no	—
34	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
35	C₄⋊C₄	—	188	1	no	—
36	C₁₆	Dic₉₄	1	1	yes	characteristic
37	C₁₆	C₄×D₄₇	1	1	yes	characteristic
38	C₂×C₄	—	376	1	no	—
39	C₂×C₄	#10625334	1	1	yes	characteristic
40	C₈	—	8	1	no	—
41	C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
42	C₈	#10625337	1	1	yes	characteristic
43	C₂²	#13093967	1	1	yes	characteristic
44	C₄	—	752	1	no	—
45	C₄	#13093957	1	1	yes	characteristic
46	C₄	#13093968	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#15688950	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688950
commutator	C₁₆×C₄₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₄₇×#368	C₂
socle	C₂×C₄₇	#367
hypercenter	#368	D₄₇
hypocenter	C₄₇	#1426
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
5. C₄₇⋊C₃₂	C₄	semidirect
28. C₄₇	#1426	semidirect