Subgroups — #20241446

Order 6016.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#15688876	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#500	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
6	C₄⋊Q₈×C₄₇	—	2	1	no	—
7	#107×C₄₇	—	2	1	no	—
8	#107×C₄₇	C₄	1	2	yes	—
9	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₄₇	—	4	1	no	—
11	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
13	C₄⋊C₄×C₄₇	—	2	2	no	—
14	C₄⋊C₄×C₄₇	—	4	1	no	—
15	C₄²×C₄₇	D₄	1	1	yes	characteristic
16	C₂×C₄₇⋊C₈	—	4	1	no	—
17	C₄₇⋊C₁₆	—	4	1	no	—
18	Q₈×C₄₇	—	8	2	no	—
19	C₂×C₄×C₄₇	—	4	2	no	—
20	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
23	C₈×C₄₇	—	2	1	no	—
24	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
25	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
26	C₄₇⋊C₈	—	8	1	no	—
27	C₂²×C₄₇	#102	1	1	yes	characteristic
28	C₄×C₄₇	—	2	1	no	—
29	C₄×C₄₇	—	8	2	no	—
30	C₄×C₄₇	#101	1	1	yes	characteristic
31	C₄×C₄₇	#103	1	1	yes	characteristic
32	C₄×C₄₇	SD₃₂	1	1	yes	characteristic
33	C₄×C₄₇	Q₃₂	1	1	yes	characteristic
34	#1365	—	47	1	no	maximal, Sylow
35	C₂×C₄₇	#332	1	1	yes	characteristic
36	C₂×C₄₇	#358	1	1	yes	characteristic
37	C₂×C₄₇	#361	1	1	yes	characteristic
38	#500	D₄₇	1	1	yes	characteristic
39	C₄⋊C₁₆	—	47	1	no	—
40	#335	—	47	1	no	—
41	C₄₇	#1365	1	1	yes	characteristic, complemented, Sylow
42	C₄⋊Q₈	—	2	1	no	—
43	C₂×C₁₆	—	94	1	no	—
44	#107	—	2	1	no	—
45	#107	Dic₄₇	1	2	yes	—
46	C₄⋊C₈	—	94	1	no	—
47	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
48	C₂×Q₈	—	4	1	no	—
49	C₂×C₈	—	188	1	no	—
50	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
52	C₄⋊C₄	—	2	2	no	—
53	C₄⋊C₄	—	4	1	no	—
54	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
55	C₁₆	—	188	1	no	—
56	Q₈	—	8	2	no	—
57	C₂×C₄	—	4	2	no	—
58	C₂×C₄	#10625334	1	1	yes	characteristic
59	C₂×C₄	#10625335	1	1	yes	characteristic
60	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	376	1	no	—
63	C₈	#10625336	1	1	yes	characteristic
64	C₈	#10625337	1	1	yes	characteristic
65	C₂²	#13093945	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	8	2	no	—
68	C₄	#13093943	1	1	yes	characteristic
69	C₄	#13093948	1	1	yes	characteristic
70	C₄	#13093967	1	1	yes	characteristic
71	C₄	#13093970	1	1	yes	characteristic
72	C₂	#15688869	1	1	yes	characteristic
73	C₂	#15688927	1	1	yes	characteristic
74	C₂	#15688936	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13093945
commutator	C₂×C₈×C₄₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#500	C₂
socle	C₂²×C₄₇	#102
hypercenter	#500	D₄₇
hypocenter	C₄₇	#1365
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
41. C₄₇	#1365	semidirect