Subgroups — #20241587

Order 6016.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#15688949	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#366	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	#107×C₄₇	—	2	1	no	—
8	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
9	C₄⋊C₄×C₄₇	—	4	1	no	—
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	—	8	1	no	—
14	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
15	C₂×Dic₄₇	—	8	1	no	—
16	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
18	C₂²×C₄₇	D₁₆	1	1	yes	characteristic
19	C₄×C₄₇	—	16	1	no	—
20	C₄×C₄₇	#107	1	1	yes	characteristic
21	C₄×C₄₇	Q₃₂	1	1	yes	characteristic
22	Dic₄₇	—	16	1	no	—
23	#1423	—	47	1	no	maximal, Sylow
24	C₂×C₄₇	#366	1	1	yes	characteristic
25	C₂×C₄₇	D₃₂	1	1	yes	characteristic
26	C₂×C₄₇	Q₆₄	1	1	yes	characteristic
27	C₂×C₃₂	—	47	1	no	—
28	#366	—	47	1	no	—
29	#366	D₄₇	1	1	yes	characteristic
30	C₄₇	#1423	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	94	1	no	—
34	C₃₂	—	47	2	no	—
35	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	188	1	no	—
38	C₁₆	Dic₉₄	1	1	yes	characteristic
39	C₁₆	C₄×D₄₇	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	376	1	no	—
42	C₂×C₄	#10625334	1	1	yes	characteristic
43	C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
44	C₈	#10625337	1	1	yes	characteristic
45	C₂²	#13093965	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	752	1	no	—
48	C₄	#13093957	1	1	yes	characteristic
49	C₄	#13093970	1	1	yes	characteristic
50	C₂	#15688948	1	1	yes	characteristic
51	C₂	#15688958	1	1	yes	characteristic
52	C₂	#15688963	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13093965
commutator	C₁₆×C₄₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₄₇×#366	C₂
socle	C₂²×C₄₇	D₁₆
hypercenter	#366	D₄₇
hypocenter	C₄₇	#1423
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₄₇⋊C₃₂	C₄	semidirect
30. C₄₇	#1423	semidirect