Subgroups — #20245682

Order 6016.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688957	C₂	1	3	yes	maximal, complemented
2	C₂×C₄₇⋊C₃₂	C₂	1	3	yes	maximal, complemented
3	C₄₇×#504	C₂	1	1	yes	maximal, characteristic
4	C₄₇⋊C₃₂	C₂²	1	1	yes	characteristic
5	C₄₇⋊C₃₂	C₂²	1	3	yes	—
6	#131×C₄₇	C₄	1	1	yes	characteristic
7	M₃₂×C₄₇	C₄	1	3	yes	—
8	C₂×C₁₆×C₄₇	C₂²	1	3	yes	—
9	#41×C₄₇	C₈	1	1	yes	characteristic
10	M₁₆×C₄₇	C₈	1	3	yes	—
11	C₂×C₈×C₄₇	C₂×C₄	1	3	yes	—
12	C₁₆×C₄₇	C₂×C₄	1	3	yes	—
13	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
14	Q₈×C₄₇	C₁₆	1	1	yes	characteristic
15	D₄×C₄₇	C₁₆	1	3	yes	—
16	C₂×C₄×C₄₇	C₂×C₈	1	3	yes	—
17	C₈×C₄₇	C₂×C₈	1	3	yes	—
18	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₄₇	C₂×C₁₆	1	3	yes	—
20	C₄×C₄₇	C₂×C₁₆	1	3	yes	—
21	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
22	#2258	—	47	1	no	maximal, Sylow
23	C₂×C₄₇	—	2	3	no	—
24	C₂×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
25	#504	D₄₇	1	1	yes	characteristic
26	M₆₄	—	47	3	no	—
27	C₂×C₃₂	—	47	3	no	—
28	C₄₇	#2258	1	1	yes	characteristic, complemented, Sylow
29	#131	Dic₄₇	1	1	yes	characteristic
30	M₃₂	Dic₄₇	1	3	yes	—
31	C₂×C₁₆	C₂×D₄₇	1	3	yes	—
32	C₃₂	—	47	1	no	—
33	C₃₂	—	47	3	no	—
34	#41	C₄₇⋊C₈	1	1	yes	characteristic
35	M₁₆	C₄₇⋊C₈	1	3	yes	—
36	C₂×C₈	C₂×Dic₄₇	1	3	yes	—
37	C₁₆	C₂×Dic₄₇	1	3	yes	—
38	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
39	Q₈	C₄₇⋊C₁₆	1	1	yes	characteristic
40	D₄	C₄₇⋊C₁₆	1	3	yes	—
41	C₂×C₄	C₂×C₄₇⋊C₈	1	3	yes	—
42	C₈	C₂×C₄₇⋊C₈	1	3	yes	—
43	C₈	C₂²×Dic₄₇	1	1	yes	characteristic
44	C₂²	C₂×C₄₇⋊C₁₆	1	3	yes	—
45	C₄	C₂×C₄₇⋊C₁₆	1	3	yes	—
46	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×C₄₇⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₄₇
commutator, socle	C₂×C₄₇	C₂²×C₁₆
Fitting	C₄₇×#504	C₂
hypercenter	#504	D₄₇
hypocenter	C₄₇	#2258
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #15688957	C₂	semidirect
2. C₂×C₄₇⋊C₃₂	C₂	semidirect
28. C₄₇	#2258	semidirect