Subgroups — #20245629

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	#15688924	C₂	1	4	yes	maximal, complemented
3	#15688899	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#493	C₂	1	1	yes	maximal, characteristic
5	#13094016	—	2	1	no	—
6	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
7	#13093958	C₂²	1	2	yes	—
8	#13093956	—	2	1	no	—
9	C₂×D₈×C₄₇	—	2	1	no	—
10	C₂×D₈×C₄₇	C₂²	1	2	yes	—
11	#127×C₄₇	—	2	1	no	—
12	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₄₇	—	2	2	no	—
14	C₂×D₄×C₄₇	—	4	2	no	—
15	D₈×C₄₇	—	2	4	no	—
16	D₈×C₄₇	—	4	2	no	—
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄²×C₄₇	D₄	1	1	yes	characteristic
20	C₄⋊Dic₄₇	—	2	2	no	—
21	Dic₄₇⋊C₄	—	4	2	no	—
22	C₄₇⋊C₁₆	—	2	2	no	—
23	C₂³×C₄₇	—	4	2	no	—
24	D₄×C₄₇	—	4	2	no	—
25	D₄×C₄₇	—	4	2	no	—
26	D₄×C₄₇	—	8	4	no	—
27	C₂×C₄×C₄₇	D₈	1	2	yes	—
28	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₄₇	—	4	2	no	—
30	C₈×C₄₇	SD₁₆	1	2	yes	—
31	C₈×C₄₇	#41	1	2	yes	—
32	C₂²×C₄₇	—	8	2	no	—
33	C₂²×C₄₇	—	8	4	no	—
34	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
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	—	16	2	no	—
41	C₂×C₄₇	#486	1	1	yes	characteristic
42	C₂×C₄₇	#509	1	2	yes	—
43	#499	—	47	1	no	—
44	#493	D₄₇	1	1	yes	characteristic
45	#357	—	47	4	no	—
46	#346	—	47	1	no	—
47	C₄₇	#2244	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	C₂×D₄₇	1	2	yes	—
50	#127	—	2	1	no	—
51	#125	—	94	1	no	—
52	C₂×C₁₆	—	47	2	no	—
53	#107	—	47	2	no	—
54	#106	—	94	1	no	—
55	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	—	4	2	no	—
58	D₈	—	2	4	no	—
59	D₈	—	4	2	no	—
60	C₂×C₈	C₂²⋊D₄₇	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	C₂²⋊D₄₇	1	1	yes	characteristic
65	C₁₆	—	94	2	no	—
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	188	2	no	—
71	C₂×C₄	#10625334	1	2	yes	—
72	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
73	C₈	#10625335	1	2	yes	—
74	C₈	#10625352	1	2	yes	—
75	C₂²	—	8	4	no	—
76	C₂²	—	8	2	no	—
77	C₂²	C₂×#10625334	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	376	2	no	—
80	C₄	#13094011	1	1	yes	characteristic
81	C₄	C₂×#10625335	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	#15689469	1	1	yes	characteristic
84	C₂	#15689559	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#493	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#493	D₄₇
hypocenter	C₄₇	#2244
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. #15689525	C₂	semidirect
2. #15688924	C₂	semidirect
3. #15688899	C₂	semidirect
47. C₄₇	#2244	semidirect