Subgroups — #20245172

Order 6016.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689161	C₂	1	2	yes	maximal
2	#15688951	C₂	1	2	yes	maximal, complemented
3	#15688949	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
5	#13093983	—	2	2	no	—
6	#13093958	C₂²	1	4	yes	—
7	#13093956	—	2	2	no	—
8	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₄₇	C₄	1	4	yes	complemented
10	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₄₇	Q₈	1	2	yes	—
16	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²⋊Dic₄₇	—	4	2	no	—
18	C₄⋊Dic₄₇	—	2	4	no	—
19	C₄×Dic₄₇	—	4	2	no	—
20	C₁₆×C₄₇	C₂×C₄	1	2	yes	—
21	C₁₆×C₄₇	C₂×C₄	1	2	yes	—
22	C₂³×C₄₇	D₈	1	1	yes	characteristic
23	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
25	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
26	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₄₇	—	4	4	no	—
28	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₄₇	—	2	2	no	—
32	C₂²×C₄₇	#107	1	2	yes	—
33	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
34	C₄×C₄₇	#107	1	2	yes	—
35	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₄₇	—	8	4	no	—
38	#2158	—	47	1	no	maximal, Sylow
39	C₂×C₄₇	—	2	2	no	—
40	C₂×C₄₇	C₂×#107	1	1	yes	characteristic
41	C₂×C₄₇	#508	1	2	yes	—
42	C₂²×C₁₆	D₄₇	1	1	yes	characteristic
43	#427	—	47	2	no	—
44	#367	—	47	2	no	—
45	#366	—	47	2	no	—
46	C₄₇	#2158	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
48	#117	—	94	2	no	—
49	C₂×C₁₆	Dic₄₇	1	4	yes	complemented
50	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
51	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
52	#107	—	47	4	no	—
53	#106	—	94	2	no	—
54	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
55	C₂×C₈	Dic₉₄	1	2	yes	—
56	C₂×C₈	D₁₈₈	1	1	yes	characteristic
57	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
58	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
59	C₄⋊C₄	—	94	4	no	—
60	C₂²⋊C₄	—	188	2	no	—
61	C₄²	—	188	2	no	—
62	C₁₆	C₂×Dic₄₇	1	2	yes	—
63	C₁₆	C₂×Dic₄₇	1	2	yes	—
64	C₂³	D₃₇₆	1	1	yes	characteristic
65	C₂×C₄	—	188	4	no	—
66	C₂×C₄	D₃₇₆	1	1	yes	characteristic
67	C₂×C₄	Dic₁₈₈	1	2	yes	—
68	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
69	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
70	C₈	C₄⋊Dic₄₇	1	2	yes	—
71	C₈	C₂×Dic₉₄	1	1	yes	characteristic
72	C₈	C₂²×Dic₄₇	1	1	yes	characteristic
73	C₂²	—	2	2	no	—
74	C₂²	#13093958	1	2	yes	—
75	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
76	C₄	—	376	4	no	—
77	C₄	#13093958	1	2	yes	—
78	C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
79	C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
80	C₂	—	2	2	no	—
81	C₂	C₂×#13093958	1	1	yes	characteristic
82	C₂	#15689555	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₃₇₆
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂²×C₁₆	D₄₇
hypocenter	C₄₇	#2158
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #15688951	C₂	semidirect
3. #15688949	C₂	semidirect
9. C₂×C₁₆×C₄₇	C₄	semidirect
46. C₄₇	#2158	semidirect
49. C₂×C₁₆	Dic₄₇	semidirect