Subgroups — #20241427

Order 6016.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688944	C₂	1	2	yes	maximal
2	C₄₇×#494	C₂	1	1	yes	maximal, characteristic
3	#13093964	—	2	2	no	—
4	C₂×Q₁₆×C₄₇	—	2	2	no	—
5	C₄⋊Q₈×C₄₇	C₄	1	2	yes	—
6	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₄₇	—	2	2	no	—
8	Q₁₆×C₄₇	—	4	2	no	—
9	Q₁₆×C₄₇	—	4	2	no	—
10	C₂×C₈×C₄₇	D₄	1	2	yes	—
11	C₄⋊C₄×C₄₇	—	4	2	no	—
12	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₄₇⋊C₁₆	—	4	2	no	—
14	Q₈×C₄₇	—	4	4	no	—
15	C₂×C₄×C₄₇	—	2	1	no	—
16	C₂×C₄×C₄₇	—	4	2	no	—
17	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₈×C₄₇	D₈	1	2	yes	—
19	C₈×C₄₇	SD₁₆	1	2	yes	—
20	C₂²×C₄₇	#100	1	1	yes	characteristic
21	C₄×C₄₇	—	2	2	no	—
22	C₄×C₄₇	—	8	2	no	—
23	C₄×C₄₇	#102	1	2	yes	—
24	#1358	—	47	1	no	maximal, Sylow
25	C₂×C₄₇	—	2	1	no	—
26	C₂×C₄₇	#331	1	1	yes	characteristic
27	#494	D₄₇	1	1	yes	characteristic
28	#364	—	47	2	no	—
29	C₄₇	#1358	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₁₆	—	2	2	no	—
31	C₄⋊Q₈	Dic₄₇	1	2	yes	—
32	M₃₂	—	94	2	no	—
33	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
34	C₂×Q₈	—	2	2	no	—
35	Q₁₆	—	4	2	no	—
36	Q₁₆	—	4	2	no	—
37	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
38	C₄⋊C₄	—	4	2	no	—
39	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
40	C₁₆	—	188	2	no	—
41	Q₈	—	4	4	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
45	C₈	#10625334	1	2	yes	—
46	C₈	#10625335	1	2	yes	—
47	C₂²	#13093941	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	2	no	—
50	C₄	#13093945	1	2	yes	—
51	C₂	—	2	1	no	—
52	C₂	#15688867	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688867
commutator	C₄²×C₄₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#494	C₂
socle	C₂×C₄₇	#331
hypercenter	#494	D₄₇
hypocenter	C₄₇	#1358
LCS	G ▷ C₄²×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
29. C₄₇	#1358	semidirect