Subgroups — #20245694

Order 6016.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689552	C₂	1	2	yes	maximal, complemented
2	Dic₇₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688961	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094043	—	2	2	no	—
7	Dic₃₇₆	C₂²	1	2	yes	—
8	#13093968	—	2	2	no	—
9	C₁₆×D₄₇	C₂²	1	1	yes	characteristic
10	C₄₇⋊C₃₂	C₂²	1	1	yes	characteristic
11	D₁₆×C₄₇	C₂²	1	2	yes	—
12	C₃₂×C₄₇	C₂²	1	1	yes	characteristic
13	#10625352	—	4	2	no	—
14	D₈×C₄₇	—	2	2	no	—
15	#10625335	—	4	2	no	—
16	Dic₁₈₈	—	2	2	no	—
17	C₈×D₄₇	D₄	1	1	yes	characteristic
18	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
19	C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
20	D₄×C₄₇	—	4	2	no	—
21	C₂²⋊D₄₇	—	8	2	no	—
22	C₂×Dic₄₇	—	8	2	no	—
23	C₄×D₄₇	D₈	1	1	yes	characteristic
24	Dic₉₄	—	4	2	no	—
25	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
26	C₄₇⋊C₈	D₈	1	1	yes	characteristic
27	C₂²×C₄₇	—	8	2	no	—
28	C₂×D₄₇	D₁₆	1	1	yes	characteristic
29	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
30	Dic₄₇	—	8	2	no	—
31	Dic₄₇	D₁₆	1	1	yes	characteristic
32	#2262	—	47	1	no	maximal, Sylow
33	C₂×C₄₇	—	16	2	no	—
34	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
35	D₄₇	—	2	1	no	—
36	#508	—	47	2	no	—
37	Q₆₄	—	47	1	no	—
38	SD₆₄	—	47	2	no	—
39	D₃₂	D₄₇	1	1	yes	characteristic, complemented
40	C₂×C₃₂	—	47	1	no	—
41	C₄₇	#2262	1	1	yes	characteristic, complemented, Sylow
42	#135	—	94	2	no	—
43	Q₃₂	—	47	2	no	—
44	SD₃₂	—	94	2	no	—
45	D₁₆	C₂×D₄₇	1	2	yes	—
46	C₂×C₁₆	—	47	1	no	—
47	C₃₂	—	47	1	no	—
48	C₃₂	C₂×D₄₇	1	1	yes	characteristic
49	#41	—	188	2	no	—
50	Q₁₆	—	94	2	no	—
51	SD₁₆	—	188	2	no	—
52	D₈	—	2	2	no	—
53	C₂×C₈	—	47	1	no	—
54	C₁₆	—	47	1	no	—
55	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
56	Q₈	—	188	2	no	—
57	D₄	—	4	2	no	—
58	D₄	—	376	2	no	—
59	C₂×C₄	—	47	1	no	—
60	C₂×C₄	—	376	2	no	—
61	C₈	—	47	1	no	—
62	C₈	D₄×D₄₇	1	1	yes	characteristic
63	C₂²	—	8	2	no	—
64	C₂²	—	47	1	no	—
65	C₄	—	47	1	no	—
66	C₄	—	376	2	no	—
67	C₄	D₈×D₄₇	1	1	yes	characteristic
68	C₂	—	16	2	no	—
69	C₂	—	94	1	no	—
70	C₂	D₁₆×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₄₇
commutator	C₁₆×C₄₇	C₂³
Frattini	C₁₆	C₂²×D₄₇
Fitting	C₄₇×D₃₂	C₂
socle	C₂×C₄₇	C₂×D₁₆
hypercenter	D₃₂	D₄₇
hypocenter	C₄₇	#2262
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. #15689552	C₂	semidirect
2. Dic₇₅₂	C₂	semidirect
3. #15688961	C₂	semidirect
4. C₃₂×D₄₇	C₂	semidirect
5. C₄₇×D₃₂	C₂	semidirect
39. D₃₂	D₄₇	semidirect
41. C₄₇	#2262	semidirect