Subgroups — #20241480

Order 6016.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093958	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₄₇	—	2	2	no	—
4	#13093958	—	2	2	no	—
5	#13093958	C₄	1	4	yes	complemented
6	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₄₇	—	2	2	no	—
8	C₂×C₁₆×C₄₇	C₄	1	2	yes	complemented
9	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
10	C₂²×Dic₄₇	—	4	2	no	—
11	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₄₇	D₄	1	2	yes	—
14	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
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	C₂×Dic₄₇	—	8	2	no	—
25	C₂×Dic₄₇	—	8	2	no	—
26	C₈×C₄₇	C₄²	1	1	yes	characteristic
27	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₂²×C₄₇	#102	1	2	yes	—
30	C₂²×C₄₇	#107	1	1	yes	characteristic
31	C₂²×C₄₇	D₁₆	1	1	yes	characteristic
32	C₂²×C₄₇	SD₃₂	1	2	yes	—
33	C₂²×C₄₇	Q₃₂	1	1	yes	characteristic
34	C₄×C₄₇	#95	1	1	yes	characteristic
35	C₄×C₄₇	#103	1	2	yes	—
36	C₄×C₄₇	#106	1	1	yes	characteristic
37	Dic₄₇	—	8	4	no	—
38	#1380	—	47	1	no	maximal, Sylow
39	C₂×C₄₇	#340	1	1	yes	characteristic
40	C₂×C₄₇	#357	1	2	yes	—
41	C₂×C₄₇	#358	1	2	yes	—
42	C₂×C₄₇	#366	1	1	yes	characteristic
43	C₂×C₄₇	#367	1	1	yes	characteristic
44	C₂²×C₁₆	D₄₇	1	1	yes	characteristic
45	C₂×#107	—	47	2	no	—
46	C₄₇	#1380	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	94	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₄₇	1	2	yes	complemented
51	#107	—	47	4	no	—
52	#107	—	94	2	no	—
53	C₂²×C₄	—	188	2	no	—
54	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
55	C₂×C₈	Dic₉₄	1	1	yes	characteristic
56	C₂×C₈	C₄×D₄₇	1	2	yes	—
57	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
59	C₄⋊C₄	—	94	4	no	—
60	C₄⋊C₄	—	188	2	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₃₇₆	1	1	yes	characteristic
63	C₂×C₄	—	376	2	no	—
64	C₂×C₄	—	376	2	no	—
65	C₂×C₄	—	188	4	no	—
66	C₂×C₄	#10625325	1	2	yes	—
67	C₂×C₄	Dic₁₈₈	1	1	yes	characteristic
68	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
69	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
70	C₈	C₄×Dic₄₇	1	1	yes	characteristic
71	C₈	Dic₄₇⋊C₄	1	2	yes	—
72	C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
73	C₂²	#13093946	1	2	yes	—
74	C₂²	#13093958	1	1	yes	characteristic
75	C₂²	D₇₅₂	1	1	yes	characteristic
76	C₂²	#13093969	1	2	yes	—
77	C₂²	Dic₃₇₆	1	1	yes	characteristic
78	C₄	—	376	4	no	—
79	C₄	C₄₇⋊#95	1	1	yes	characteristic
80	C₄	#13093949	1	2	yes	—
81	C₄	#13093956	1	1	yes	characteristic
82	C₂	#15688886	1	1	yes	characteristic
83	C₂	#15688925	1	2	yes	—
84	C₂	#15688928	1	2	yes	—
85	C₂	#15688949	1	1	yes	characteristic
86	C₂	#15688951	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃₇₆
commutator	C₈×C₄₇	C₄²
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂³×C₄₇	D₈
hypercenter	C₂²×C₁₆	D₄₇
hypocenter	C₄₇	#1380
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #13093958	C₄	semidirect
8. C₂×C₁₆×C₄₇	C₄	semidirect
46. C₄₇	#1380	semidirect
50. C₂×C₁₆	Dic₄₇	semidirect