Subgroups — #20241340

Order 6016.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689151	C₂	1	1	yes	maximal, characteristic
2	#15688905	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#349	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₇⋊C₈	C₄	1	1	yes	characteristic
5	#13093983	C₄	1	1	yes	characteristic
6	#13093964	—	2	1	no	—
7	Dic₄₇⋊C₈	—	2	1	no	—
8	Dic₄₇⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	M₃₂×C₄₇	—	2	1	no	—
11	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	M₁₆×C₄₇	—	4	1	no	—
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₂²⋊Dic₄₇	C₈	1	2	yes	—
16	C₄⋊Dic₄₇	—	2	1	no	—
17	C₄×Dic₄₇	—	2	1	no	—
18	C₂×C₄₇⋊C₈	—	2	1	no	—
19	C₂×C₄₇⋊C₈	—	4	1	no	—
20	C₁₆×C₄₇	—	4	1	no	—
21	C₄₇⋊C₁₆	—	4	1	no	—
22	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₄₇	—	2	1	no	—
24	C₂×C₄×C₄₇	—	2	1	no	—
25	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
27	C₂×Dic₄₇	—	2	2	no	—
28	C₈×C₄₇	—	2	1	no	—
29	C₈×C₄₇	—	2	1	no	—
30	C₄₇⋊C₈	—	4	1	no	—
31	C₂²×C₄₇	—	2	1	no	—
32	C₂²×C₄₇	—	4	1	no	—
33	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₄₇	—	2	1	no	—
35	C₄×C₄₇	#99	1	1	yes	characteristic
36	C₄×C₄₇	#101	1	1	yes	characteristic
37	Dic₄₇	—	4	2	no	—
38	#1328	—	47	1	no	maximal, Sylow
39	C₂×C₄₇	—	2	1	no	—
40	C₂×C₄₇	—	4	1	no	—
41	C₂×C₄₇	#324	1	1	yes	characteristic
42	#424	—	47	1	no	—
43	#349	—	47	1	no	—
44	#349	D₄₇	1	1	yes	characteristic
45	C₄₇	#1328	1	1	yes	characteristic, complemented, Sylow
46	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
47	C₂²×C₈	—	47	1	no	—
48	#117	—	47	1	no	—
49	M₃₂	—	2	1	no	—
50	M₃₂	—	94	1	no	—
51	C₄⋊C₈	—	94	1	no	—
52	C₄⋊C₈	—	94	1	no	—
53	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
54	M₁₆	—	4	1	no	—
55	C₂×C₈	—	94	1	no	—
56	C₂×C₈	—	188	1	no	—
57	C₂×C₈	D₁₈₈	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
59	C₄⋊C₄	—	94	1	no	—
60	C₂²⋊C₄	—	47	2	no	—
61	C₄²	—	94	1	no	—
62	C₁₆	—	4	1	no	—
63	C₁₆	—	188	1	no	—
64	C₂³	C₈×D₄₇	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	94	2	no	—
68	C₂×C₄	#10625324	1	1	yes	characteristic
69	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₈	—	188	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	188	2	no	—
78	C₄	#13093938	1	1	yes	characteristic
79	C₄	#13093942	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#15688848	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13093938
commutator	C₂³×C₄₇	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₄₇
Fitting	C₄₇×#349	C₂
socle	C₂×C₄₇	#324
hypercenter	#349	D₄₇
hypocenter	C₄₇	#1328
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
45. C₄₇	#1328	semidirect