Subgroups — #20241359

Order 6016.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#15688874	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#346	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₈₈	C₄	1	1	yes	characteristic
5	C₄×Dic₉₄	—	2	1	no	—
6	#13093958	C₄	1	1	yes	characteristic
7	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
8	#13093949	—	2	1	no	—
9	C₂×C₁₆×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₉₄	—	2	1	no	—
12	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₄²×C₄₇	D₄	1	1	yes	characteristic
15	C₄⋊Dic₄₇	—	2	1	no	—
16	Dic₄₇⋊C₄	—	4	1	no	—
17	C₄×Dic₄₇	—	4	1	no	—
18	C₂×C₄₇⋊C₈	—	4	1	no	—
19	Dic₁₈₈	—	2	1	no	—
20	Dic₁₈₈	C₈	1	2	yes	complemented
21	C₁₆×C₄₇	—	2	2	no	—
22	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
24	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₄₇	—	4	1	no	—
26	C₂×Dic₄₇	—	4	1	no	—
27	Dic₉₄	—	2	2	no	—
28	Dic₉₄	—	4	1	no	—
29	C₈×C₄₇	—	2	1	no	—
30	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₄₇	M₁₆	1	1	yes	characteristic
32	C₄₇⋊C₈	—	8	1	no	—
33	C₂²×C₄₇	#102	1	1	yes	characteristic
34	C₄×C₄₇	—	2	1	no	—
35	C₄×C₄₇	—	2	1	no	—
36	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₄₇	#104	1	1	yes	characteristic
38	Dic₄₇	—	4	2	no	—
39	Dic₄₇	—	8	1	no	—
40	#1334	—	47	1	no	maximal, Sylow
41	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₄₇	#360	1	1	yes	characteristic
43	C₂×C₄₇	#362	1	1	yes	characteristic
44	C₄×Q₁₆	—	47	1	no	—
45	#346	D₄₇	1	1	yes	characteristic
46	#334	—	47	1	no	—
47	C₄₇	#1334	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₁₆	—	47	1	no	—
49	C₄×Q₈	—	94	1	no	—
50	C₂×C₁₆	—	2	1	no	—
51	#107	—	47	1	no	—
52	C₄⋊C₈	—	94	1	no	—
53	#103	—	94	1	no	—
54	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
55	C₂×Q₈	—	94	1	no	—
56	Q₁₆	—	47	2	no	—
57	Q₁₆	—	94	1	no	—
58	C₂×C₈	—	188	1	no	—
59	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
60	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
61	C₄⋊C₄	—	94	1	no	—
62	C₄⋊C₄	—	188	1	no	—
63	C₄²	—	188	1	no	—
64	C₄²	D₁₈₈	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	Q₈	—	94	2	no	—
67	Q₈	—	188	1	no	—
68	C₂×C₄	—	188	1	no	—
69	C₂×C₄	—	188	1	no	—
70	C₂×C₄	#10625325	1	1	yes	characteristic
71	C₂×C₄	D₃₇₆	1	1	yes	characteristic
72	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	376	1	no	—
75	C₈	C₈×D₄₇	1	1	yes	characteristic
76	C₈	#10625324	1	1	yes	characteristic
77	C₂²	#13093946	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	376	1	no	—
81	C₄	—	188	2	no	—
82	C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
83	C₄	#13093952	1	1	yes	characteristic
84	C₂	#15688852	1	1	yes	characteristic
85	C₂	#15688934	1	1	yes	characteristic
86	C₂	#15688940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13093946
commutator	C₈×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#346	C₂
socle	C₂²×C₄₇	#102
hypercenter	#346	D₄₇
hypocenter	C₄₇	#1334
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
20. Dic₁₈₈	C₈	semidirect
47. C₄₇	#1334	semidirect