Subgroups — #20241490

Order 6016.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689161	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093983	—	2	2	no	—
4	#13093958	—	2	2	no	—
5	#13093956	C₄	1	4	yes	complemented
6	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	M₃₂×C₄₇	—	2	2	no	—
8	C₂×C₁₆×C₄₇	C₄	1	2	yes	complemented
9	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
10	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₄₇	D₄	1	2	yes	—
13	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
14	C₂²⋊Dic₄₇	—	4	2	no	—
15	C₄⋊Dic₄₇	—	2	4	no	—
16	C₄×Dic₄₇	—	4	2	no	—
17	C₁₆×C₄₇	—	2	2	no	—
18	C₂³×C₄₇	D₈	1	1	yes	characteristic
19	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
22	C₂×C₄×C₄₇	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₄₇	—	4	4	no	—
24	C₈×C₄₇	C₄²	1	1	yes	characteristic
25	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
27	C₂²×C₄₇	—	4	1	no	—
28	C₂²×C₄₇	#102	1	2	yes	—
29	C₂²×C₄₇	#107	1	1	yes	characteristic
30	C₄×C₄₇	#95	1	1	yes	characteristic
31	C₄×C₄₇	#103	1	2	yes	—
32	C₄×C₄₇	#106	1	1	yes	characteristic
33	Dic₄₇	—	8	4	no	—
34	#1384	—	47	1	no	maximal, Sylow
35	C₂×C₄₇	—	2	2	no	—
36	C₂×C₄₇	—	2	1	no	—
37	C₂×C₄₇	#340	1	1	yes	characteristic
38	C₂×M₃₂	D₄₇	1	1	yes	characteristic
39	#427	—	47	2	no	—
40	C₄₇	#1384	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
42	#117	—	94	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₄₇	1	2	yes	complemented
45	#107	—	94	2	no	—
46	#106	—	47	4	no	—
47	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
48	C₂×C₈	Dic₉₄	1	1	yes	characteristic
49	C₂×C₈	C₄×D₄₇	1	2	yes	—
50	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
52	C₄⋊C₄	—	94	4	no	—
53	C₂²⋊C₄	—	188	2	no	—
54	C₄²	—	188	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₃₇₆	1	1	yes	characteristic
57	C₂×C₄	—	188	4	no	—
58	C₂×C₄	#10625325	1	2	yes	—
59	C₂×C₄	Dic₁₈₈	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
61	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
62	C₈	C₄×Dic₄₇	1	1	yes	characteristic
63	C₈	Dic₄₇⋊C₄	1	2	yes	—
64	C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
65	C₂²	—	4	1	no	—
66	C₂²	#13093946	1	2	yes	—
67	C₂²	#13093958	1	1	yes	characteristic
68	C₄	—	376	4	no	—
69	C₄	C₄₇⋊#95	1	1	yes	characteristic
70	C₄	#13093949	1	2	yes	—
71	C₄	#13093956	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#15688886	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13093956
commutator	C₈×C₄₇	C₄²
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₂×M₃₂×C₄₇	C₂
socle	C₂×C₄₇	#340
hypercenter	C₂×M₃₂	D₄₇
hypocenter	C₄₇	#1384
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #13093956	C₄	semidirect
8. C₂×C₁₆×C₄₇	C₄	semidirect
40. C₄₇	#1384	semidirect
44. C₂×C₁₆	Dic₄₇	semidirect