Subgroups — #20245630

Order 6016.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689525	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689500	C₂	1	1	yes	maximal, characteristic
3	#15688925	C₂	1	4	yes	maximal, complemented
4	C₄₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₇₆	—	2	1	no	—
6	C₂×D₃₇₆	C₂²	1	2	yes	—
7	#13094021	—	2	1	no	—
8	#13094016	—	2	1	no	—
9	#13093958	C₂²	1	2	yes	—
10	#13093956	—	2	1	no	—
11	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
12	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×D₁₈₈	—	2	2	no	—
14	C₂×D₁₈₈	—	4	2	no	—
15	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
17	C₄²×C₄₇	D₄	1	1	yes	characteristic
18	C₄⋊Dic₄₇	—	2	2	no	—
19	Dic₄₇⋊C₄	—	4	2	no	—
20	D₃₇₆	—	2	4	no	—
21	D₃₇₆	—	4	2	no	—
22	C₁₆×C₄₇	—	2	2	no	—
23	C₂²×D₄₇	—	4	2	no	—
24	C₂×C₄×C₄₇	D₈	1	2	yes	—
25	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₄₇	—	4	2	no	—
27	D₁₈₈	—	4	2	no	—
28	D₁₈₈	—	4	2	no	—
29	D₁₈₈	—	8	4	no	—
30	C₈×C₄₇	SD₁₆	1	2	yes	—
31	C₈×C₄₇	#41	1	2	yes	—
32	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
33	C₂×D₄₇	—	8	2	no	—
34	C₂×D₄₇	—	8	4	no	—
35	C₄×C₄₇	—	2	2	no	—
36	C₄×C₄₇	#124	1	1	yes	characteristic
37	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
38	Dic₄₇	—	8	2	no	—
39	#2244	—	47	1	no	maximal, Sylow
40	C₂×C₄₇	#486	1	1	yes	characteristic
41	C₂×C₄₇	#509	1	2	yes	—
42	D₄₇	—	16	2	no	—
43	#499	—	47	1	no	—
44	#493	—	47	1	no	—
45	#357	—	47	4	no	—
46	#346	D₄₇	1	1	yes	characteristic, complemented
47	C₄₇	#2244	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₈	—	47	2	no	—
49	C₂×D₈	—	94	1	no	—
50	#127	—	94	1	no	—
51	#125	—	94	1	no	—
52	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
53	#107	—	47	2	no	—
54	#106	—	94	1	no	—
55	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₂×D₄	—	94	2	no	—
57	C₂×D₄	—	188	2	no	—
58	D₈	—	94	4	no	—
59	D₈	—	188	2	no	—
60	C₂×C₈	D₁₈₈	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
62	C₄⋊C₄	—	94	2	no	—
63	C₄⋊C₄	—	188	2	no	—
64	C₄²	D₁₈₈	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	188	2	no	—
67	D₄	—	376	4	no	—
68	D₄	—	188	2	no	—
69	D₄	—	188	2	no	—
70	C₂×C₄	—	188	2	no	—
71	C₂×C₄	D₃₇₆	1	2	yes	—
72	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
73	C₈	#10625325	1	2	yes	—
74	C₈	#10625350	1	2	yes	—
75	C₂²	—	376	4	no	—
76	C₂²	—	376	2	no	—
77	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	376	2	no	—
80	C₄	#13094012	1	1	yes	characteristic
81	C₄	C₂×#10625325	1	1	yes	characteristic
82	C₂	—	752	2	no	—
83	C₂	#15689470	1	1	yes	characteristic
84	C₂	#15689561	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#346	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#346	D₄₇
hypocenter	C₄₇	#2244
LCS	G ▷ C₂×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
1. #15689525	C₂	semidirect
3. #15688925	C₂	semidirect
4. C₄₇×#346	C₂	semidirect
46. #346	D₄₇	semidirect
47. C₄₇	#2244	semidirect