Subgroups — #20241351

Order 6016.

98 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	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₈₈	C₄	1	1	yes	characteristic
5	C₄×Dic₉₄	—	2	1	no	—
6	C₂×C₄₇⋊C₁₆	—	2	1	no	—
7	#13093958	C₄	1	1	yes	characteristic
8	#13093949	—	2	1	no	—
9	C₄⋊C₈×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₉₄	—	2	1	no	—
12	C₂×C₈×C₄₇	—	4	1	no	—
13	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₄²×C₄₇	D₄	1	1	yes	characteristic
16	C₄⋊Dic₄₇	—	2	1	no	—
17	Dic₄₇⋊C₄	—	4	1	no	—
18	C₄×Dic₄₇	—	4	1	no	—
19	Dic₁₈₈	—	2	1	no	—
20	Dic₁₈₈	C₈	1	2	yes	complemented
21	C₄₇⋊C₁₆	—	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	—	8	1	no	—
31	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₄₇	M₁₆	1	1	yes	characteristic
33	C₂²×C₄₇	#102	1	1	yes	characteristic
34	C₄×C₄₇	—	2	1	no	—
35	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₄₇	#104	1	1	yes	characteristic
37	C₄×C₄₇	SD₃₂	1	1	yes	characteristic
38	C₄×C₄₇	Q₃₂	1	1	yes	characteristic
39	Dic₄₇	—	4	2	no	—
40	Dic₄₇	—	8	1	no	—
41	#1332	—	47	1	no	maximal, Sylow
42	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
43	C₂×C₄₇	#358	1	1	yes	characteristic
44	C₂×C₄₇	#359	1	1	yes	characteristic
45	C₄×Q₁₆	—	47	1	no	—
46	C₄×C₁₆	—	47	1	no	—
47	#335	D₄₇	1	1	yes	characteristic
48	C₄₇	#1332	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₁₆	—	47	1	no	—
50	C₄×Q₈	—	94	1	no	—
51	C₂×C₁₆	—	94	1	no	—
52	#107	—	47	1	no	—
53	C₄⋊C₈	—	2	1	no	—
54	#103	—	94	1	no	—
55	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₂×Q₈	—	94	1	no	—
57	Q₁₆	—	47	2	no	—
58	Q₁₆	—	94	1	no	—
59	C₂×C₈	—	4	1	no	—
60	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
61	C₂×C₈	D₁₈₈	1	1	yes	characteristic
62	C₄⋊C₄	—	94	1	no	—
63	C₄⋊C₄	—	188	1	no	—
64	C₄²	—	188	1	no	—
65	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
66	C₁₆	—	94	2	no	—
67	Q₈	—	94	2	no	—
68	Q₈	—	188	1	no	—
69	C₂×C₄	—	188	1	no	—
70	C₂×C₄	—	188	1	no	—
71	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
72	C₂×C₄	#10625334	1	1	yes	characteristic
73	C₂×C₄	#10625336	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	8	1	no	—
76	C₈	C₈×D₄₇	1	1	yes	characteristic
77	C₈	#10625324	1	1	yes	characteristic
78	C₂²	#13093944	1	1	yes	characteristic
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	#13093950	1	1	yes	characteristic
84	C₄	#13093968	1	1	yes	characteristic
85	C₄	#13093970	1	1	yes	characteristic
86	C₂	#15688850	1	1	yes	characteristic
87	C₂	#15688926	1	1	yes	characteristic
88	C₂	#15688929	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10625334
commutator	C₈×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#335	C₂
socle	C₂²×C₄₇	#102
hypercenter	#335	D₄₇
hypocenter	C₄₇	#1332
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
20. Dic₁₈₈	C₈	semidirect
48. C₄₇	#1332	semidirect