Subgroups — #20245703

Order 6016.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₇₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688962	C₂	1	2	yes	maximal, complemented
4	D₁₅₀₄	C₂	1	2	yes	maximal, complemented
5	C₄₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094046	—	2	1	no	—
7	C₂×D₃₇₆	—	2	1	no	—
8	Dic₃₇₆	C₂²	1	1	yes	characteristic, complemented
9	#13093969	—	2	1	no	—
10	D₇₅₂	—	2	1	no	—
11	D₇₅₂	C₂²	1	2	yes	—
12	D₇₅₂	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₃₂×C₄₇	C₂²	1	2	yes	complemented
15	#10625350	—	4	1	no	—
16	C₂×D₁₈₈	—	4	1	no	—
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	Dic₁₈₈	—	2	1	no	—
19	D₃₇₆	—	2	2	no	—
20	D₃₇₆	—	2	1	no	—
21	D₃₇₆	—	4	1	no	—
22	#10625325	—	4	1	no	—
23	C₁₆×C₄₇	D₄	1	1	yes	characteristic
24	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×D₄₇	—	8	1	no	—
26	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
27	C₂²⋊D₄₇	—	8	1	no	—
28	D₁₈₈	—	4	1	no	—
29	D₁₈₈	—	4	2	no	—
30	D₁₈₈	—	8	1	no	—
31	C₄×D₄₇	—	8	1	no	—
32	Dic₉₄	—	4	1	no	—
33	C₈×C₄₇	D₈	1	1	yes	characteristic
34	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄₇	D₁₆	1	1	yes	characteristic
36	C₂×D₄₇	—	8	1	no	—
37	C₂×D₄₇	—	8	2	no	—
38	C₂×D₄₇	—	16	2	no	—
39	C₄×C₄₇	D₁₆	1	1	yes	characteristic
40	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
41	Dic₄₇	—	8	1	no	—
42	#2263	—	47	1	no	maximal, Sylow
43	C₂×C₄₇	—	2	1	no	—
44	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
45	D₄₇	—	16	1	no	—
46	D₄₇	—	16	2	no	—
47	#508	—	47	1	no	—
48	C₂×D₁₆	—	47	1	no	—
49	SD₆₄	—	47	2	no	—
50	D₃₂	—	47	2	no	—
51	M₆₄	D₄₇	1	1	yes	characteristic, complemented
52	C₄₇	#2263	1	1	yes	characteristic, complemented, Sylow
53	#135	—	94	1	no	—
54	C₂×D₈	—	94	1	no	—
55	Q₃₂	—	47	1	no	—
56	SD₃₂	—	94	1	no	—
57	D₁₆	—	47	2	no	—
58	D₁₆	—	47	1	no	—
59	D₁₆	—	94	1	no	—
60	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
61	C₃₂	C₂×D₄₇	1	2	yes	complemented
62	#41	—	188	1	no	—
63	C₂×D₄	—	188	1	no	—
64	Q₁₆	—	94	1	no	—
65	SD₁₆	—	188	1	no	—
66	D₈	—	94	2	no	—
67	D₈	—	94	1	no	—
68	D₈	—	188	1	no	—
69	C₂×C₈	D₁₈₈	1	1	yes	characteristic
70	C₁₆	D₁₈₈	1	1	yes	characteristic
71	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
72	C₂³	—	376	1	no	—
73	Q₈	—	188	1	no	—
74	D₄	—	376	1	no	—
75	D₄	—	376	1	no	—
76	D₄	—	188	2	no	—
77	D₄	—	188	1	no	—
78	C₂×C₄	—	376	1	no	—
79	C₂×C₄	D₃₇₆	1	1	yes	characteristic
80	C₈	D₃₇₆	1	1	yes	characteristic
81	C₈	C₂×D₁₈₈	1	1	yes	characteristic
82	C₂²	—	376	1	no	—
83	C₂²	—	376	2	no	—
84	C₂²	—	752	2	no	—
85	C₂²	D₇₅₂	1	1	yes	characteristic
86	C₄	—	376	1	no	—
87	C₄	D₇₅₂	1	1	yes	characteristic
88	C₄	C₂×D₃₇₆	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	752	2	no	—
91	C₂	—	752	1	no	—
92	C₂	C₂×D₇₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₇₅₂
commutator	C₁₆×C₄₇	C₂³
Frattini	C₁₆	C₂²×D₄₇
Fitting	C₄₇×M₆₄	C₂
socle	C₂×C₄₇	C₂×D₁₆
hypercenter	M₆₄	D₄₇
hypocenter	C₄₇	#2263
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
1. #15689555	C₂	semidirect
2. C₂×D₇₅₂	C₂	semidirect
3. #15688962	C₂	semidirect
4. D₁₅₀₄	C₂	semidirect
5. C₄₇×M₆₄	C₂	semidirect
8. Dic₃₇₆	C₂²	semidirect
12. D₇₅₂	C₂²	semidirect
14. C₃₂×C₄₇	C₂²	semidirect
51. M₆₄	D₄₇	semidirect
52. C₄₇	#2263	semidirect
61. C₃₂	C₂×D₄₇	semidirect