Subgroups — #20241463

Order 6016.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688944	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#364	C₂	1	1	yes	maximal, characteristic
4	#13093964	—	2	1	no	—
5	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
7	M₃₂×C₄₇	—	2	1	no	—
8	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
11	C₄²×C₄₇	Q₈	1	1	yes	characteristic
12	C₁₆×C₄₇	—	4	1	no	—
13	C₄₇⋊C₁₆	—	2	1	no	—
14	C₄₇⋊C₁₆	—	4	1	no	—
15	C₄₇⋊C₁₆	C₈	1	2	yes	—
16	C₂×C₄×C₄₇	—	2	1	no	—
17	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
19	C₈×C₄₇	M₁₆	1	1	yes	characteristic
20	C₈×C₄₇	D₈	1	1	yes	characteristic
21	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
22	C₂²×C₄₇	#108	1	1	yes	characteristic
23	C₄×C₄₇	—	2	2	no	—
24	C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₄₇	#107	1	1	yes	characteristic
26	#1373	—	47	1	no	maximal, Sylow
27	C₂×C₄₇	—	2	1	no	—
28	C₂×C₄₇	#335	1	1	yes	characteristic
29	#364	—	47	1	no	—
30	#364	D₄₇	1	1	yes	characteristic
31	C₄×C₁₆	—	47	1	no	—
32	C₄₇	#1373	1	1	yes	characteristic, complemented, Sylow
33	M₃₂	—	2	1	no	—
34	M₃₂	—	94	1	no	—
35	C₂×C₁₆	—	47	1	no	—
36	C₂×C₁₆	—	47	1	no	—
37	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
38	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
40	C₄²	Dic₉₄	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	47	2	no	—
43	C₁₆	—	94	1	no	—
44	C₁₆	—	188	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
47	C₈	C₈×D₄₇	1	1	yes	characteristic
48	C₈	#10625324	1	1	yes	characteristic
49	C₈	#10625334	1	1	yes	characteristic
50	C₈	#10625337	1	1	yes	characteristic
51	C₂²	#13093959	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	Dic₄₇⋊C₈	1	1	yes	characteristic
54	C₄	#13093957	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#15688875	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10625334
commutator	C₈×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#364	C₂
socle	C₂×C₄₇	#335
hypercenter	#364	D₄₇
hypocenter	C₄₇	#1373
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
32. C₄₇	#1373	semidirect