Subgroups — #20241573

Order 6016.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689555	C₂	1	1	yes	maximal, characteristic
2	#15688953	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094046	—	2	1	no	—
5	Dic₃₇₆	C₄	1	1	yes	characteristic
6	#13093969	—	2	1	no	—
7	D₇₅₂	C₄	1	1	yes	characteristic
8	#13093960	—	2	1	no	—
9	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	C₃₂×C₄₇	—	2	1	no	—
11	#10625350	—	4	1	no	—
12	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
13	#10625329	—	4	1	no	—
14	Dic₁₈₈	—	2	1	no	—
15	D₃₇₆	—	2	1	no	—
16	#10625325	—	4	1	no	—
17	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
20	C₂²⋊D₄₇	—	8	1	no	—
21	D₁₈₈	—	4	1	no	—
22	C₄×D₄₇	—	8	1	no	—
23	Dic₉₄	—	4	1	no	—
24	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
26	C₄₇⋊C₈	—	8	1	no	—
27	C₂²×C₄₇	SD₃₂	1	1	yes	characteristic
28	C₂×D₄₇	—	8	1	no	—
29	C₄×C₄₇	#102	1	1	yes	characteristic
30	C₄×C₄₇	D₁₆	1	1	yes	characteristic
31	Dic₄₇	—	8	1	no	—
32	#1417	—	47	1	no	maximal, Sylow
33	C₂×C₄₇	—	2	1	no	—
34	C₂×C₄₇	#357	1	1	yes	characteristic
35	D₄₇	—	16	1	no	—
36	#508	—	47	1	no	—
37	C₂×C₃₂	D₄₇	1	1	yes	characteristic, complemented
38	#368	—	47	1	no	—
39	C₄₇	#1417	1	1	yes	characteristic, complemented, Sylow
40	#135	—	94	1	no	—
41	Q₃₂	—	47	1	no	—
42	SD₃₂	—	94	1	no	—
43	D₁₆	—	47	1	no	—
44	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
45	#108	—	94	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	188	1	no	—
48	Q₁₆	—	94	1	no	—
49	SD₁₆	—	188	1	no	—
50	D₈	—	94	1	no	—
51	M₁₆	—	188	1	no	—
52	C₂×C₈	D₁₈₈	1	1	yes	characteristic
53	C₁₆	C₄×D₄₇	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
55	Q₈	—	188	1	no	—
56	D₄	—	376	1	no	—
57	D₄	—	188	1	no	—
58	C₂×C₄	—	376	1	no	—
59	C₂×C₄	D₃₇₆	1	1	yes	characteristic
60	C₈	—	376	1	no	—
61	C₈	#10625325	1	1	yes	characteristic
62	C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
63	C₂²	—	376	1	no	—
64	C₂²	#13093969	1	1	yes	characteristic
65	C₄	—	376	1	no	—
66	C₄	#13093946	1	1	yes	characteristic
67	C₄	D₇₅₂	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	752	1	no	—
70	C₂	#15688925	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₇₅₂
commutator	C₁₆×C₄₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₂×C₃₂×C₄₇	C₂
socle	C₂×C₄₇	#357
hypercenter	C₂×C₃₂	D₄₇
hypocenter	C₄₇	#1417
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #15688953	C₂	semidirect
3. C₂×C₃₂×C₄₇	C₂	semidirect
37. C₂×C₃₂	D₄₇	semidirect
39. C₄₇	#1417	semidirect