Subgroups — #20245265

Order 6016.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₅₂	C₂	1	1	yes	maximal, characteristic
2	C₄×D₃₇₆	C₂	1	2	yes	maximal, complemented
3	#15688951	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688925	C₂	1	2	yes	maximal, complemented
5	C₄₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₇₆	C₂²	1	2	yes	—
7	C₄×D₁₈₈	—	2	2	no	—
8	D₇₅₂	C₄	1	4	yes	complemented
9	#13093958	C₂²	1	2	yes	—
10	#13093946	—	2	2	no	—
11	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×D₁₈₈	—	2	2	no	—
15	C₂×C₄×D₄₇	—	4	2	no	—
16	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
18	C₄²×C₄₇	D₄	1	1	yes	characteristic
19	(C₂×D₄₇)⋊C₄	—	4	2	no	—
20	C₄⋊Dic₄₇	—	2	2	no	—
21	D₃₇₆	—	2	2	no	—
22	D₃₇₆	C₂×C₄	1	4	yes	complemented
23	C₁₆×C₄₇	—	2	1	no	—
24	C₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
25	C₂²×D₄₇	—	4	2	no	—
26	C₂×C₄×C₄₇	D₈	1	2	yes	—
27	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₄₇	—	4	2	no	—
29	D₁₈₈	—	2	4	no	—
30	D₁₈₈	—	4	2	no	—
31	C₄×D₄₇	—	8	4	no	—
32	C₈×C₄₇	—	2	1	no	—
33	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₄₇	#41	1	1	yes	characteristic
35	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
36	C₂×D₄₇	—	4	4	no	—
37	C₂×D₄₇	—	8	2	no	—
38	C₂×D₄₇	—	8	2	no	—
39	C₄×C₄₇	—	2	2	no	—
40	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
41	C₄×C₄₇	#135	1	1	yes	characteristic
42	Dic₄₇	—	8	2	no	—
43	#2177	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	C₄×D₈	1	1	yes	characteristic
45	C₂×C₄₇	#509	1	2	yes	—
46	D₄₇	—	8	4	no	—
47	C₂×D₁₆	—	47	1	no	—
48	C₄×D₈	—	47	2	no	—
49	#367	—	47	1	no	—
50	#357	—	47	2	no	—
51	#346	D₄₇	1	1	yes	characteristic, complemented
52	C₄₇	#2177	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₈	—	47	2	no	—
54	C₄×D₄	—	94	2	no	—
55	D₁₆	—	47	4	no	—
56	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
57	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
58	#107	—	47	2	no	—
59	#102	—	94	2	no	—
60	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
61	C₂×D₄	—	94	2	no	—
62	C₂²×C₄	—	188	2	no	—
63	D₈	—	47	4	no	—
64	D₈	—	94	2	no	—
65	C₂×C₈	D₁₈₈	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
67	C₄⋊C₄	—	94	2	no	—
68	C₂²⋊C₄	—	188	2	no	—
69	C₄²	D₁₈₈	1	1	yes	characteristic
70	C₁₆	—	2	1	no	—
71	C₁₆	C₄×D₄₇	1	2	yes	complemented
72	C₂³	—	188	2	no	—
73	D₄	—	94	4	no	—
74	D₄	—	188	2	no	—
75	C₂×C₄	—	376	4	no	—
76	C₂×C₄	—	188	2	no	—
77	C₂×C₄	D₃₇₆	1	2	yes	—
78	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
79	C₈	—	2	1	no	—
80	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
81	C₈	#10625350	1	1	yes	characteristic
82	C₂²	—	376	2	no	—
83	C₂²	—	376	2	no	—
84	C₂²	—	188	4	no	—
85	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	376	2	no	—
88	C₄	C₄×D₁₈₈	1	1	yes	characteristic
89	C₄	#13094046	1	1	yes	characteristic
90	C₂	—	376	4	no	—
91	C₂	C₄×D₃₇₆	1	1	yes	characteristic
92	C₂	#15689561	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#346	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#346	D₄₇
hypocenter	C₄₇	#2177
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
2. C₄×D₃₇₆	C₂	semidirect
3. #15688951	C₂	semidirect
4. #15688925	C₂	semidirect
5. C₄₇×#346	C₂	semidirect
8. D₇₅₂	C₄	semidirect
22. D₃₇₆	C₂×C₄	semidirect
24. C₁₆×C₄₇	C₂×C₄	semidirect
51. #346	D₄₇	semidirect
52. C₄₇	#2177	semidirect
71. C₁₆	C₄×D₄₇	semidirect