Subgroups — #20256491

Order 6016.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689540	C₂	1	8	yes	maximal, complemented
2	C₂×#13093964	C₂	1	6	yes	maximal, complemented
3	C₂×#131×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093964	C₂²	1	4	yes	—
5	#13093964	C₂²	1	12	yes	complemented
6	C₂×C₄₇⋊C₁₆	C₂²	1	12	yes	complemented
7	C₂×#41×C₄₇	C₄	1	1	yes	characteristic
8	#131×C₄₇	C₄	1	4	yes	—
9	#131×C₄₇	C₂²	1	4	yes	—
10	C₂×M₁₆×C₄₇	C₄	1	3	yes	—
11	C₂²×C₈×C₄₇	C₂²	1	3	yes	—
12	#41×C₄₇	C₈	1	4	yes	—
13	#41×C₄₇	C₂×C₄	1	4	yes	—
14	C₂×Q₈×C₄₇	C₈	1	1	yes	characteristic
15	C₂×D₄×C₄₇	C₈	1	3	yes	—
16	C₂²×C₄×C₄₇	C₂×C₄	1	3	yes	—
17	M₁₆×C₄₇	C₂×C₄	1	12	yes	—
18	C₂×C₈×C₄₇	C₂×C₄	1	3	yes	—
19	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
20	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂³	1	6	yes	—
22	C₄₇⋊C₁₆	C₂³	1	8	yes	—
23	C₂³×C₄₇	C₂×C₈	1	3	yes	—
24	Q₈×C₄₇	C₂×C₈	1	4	yes	—
25	D₄×C₄₇	C₂×C₈	1	12	yes	—
26	C₂×C₄×C₄₇	C₂×C₈	1	3	yes	—
27	C₂×C₄×C₄₇	C₂×C₈	1	6	yes	—
28	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂²×C₄	1	6	yes	—
30	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₈×C₄₇	C₂²×C₄	1	6	yes	—
32	C₈×C₄₇	C₂⁴	1	1	yes	characteristic
33	C₂²×C₄₇	—	4	3	no	—
34	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
35	C₂²×C₄₇	C₂²×C₈	1	6	yes	—
36	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
37	C₄×C₄₇	C₂²×C₈	1	6	yes	—
38	C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
39	#3407	—	47	1	no	maximal, Sylow
40	C₂×C₄₇	—	2	1	no	—
41	C₂×C₄₇	—	2	6	no	—
42	C₂×C₄₇	C₂³×C₈	1	1	yes	characteristic
43	C₂×#131	D₄₇	1	1	yes	characteristic
44	#504	—	47	8	no	—
45	C₂×M₃₂	—	47	6	no	—
46	C₄₇	#3407	1	1	yes	characteristic, complemented, Sylow
47	C₂×#41	Dic₄₇	1	1	yes	characteristic
48	#131	Dic₄₇	1	4	yes	—
49	#131	C₂×D₄₇	1	4	yes	—
50	C₂×M₁₆	Dic₄₇	1	3	yes	—
51	C₂²×C₈	C₂×D₄₇	1	3	yes	—
52	M₃₂	—	47	4	no	—
53	M₃₂	—	47	12	no	—
54	C₂×C₁₆	—	47	12	no	—
55	#41	C₄₇⋊C₈	1	4	yes	—
56	#41	C₂×Dic₄₇	1	4	yes	—
57	C₂×Q₈	C₄₇⋊C₈	1	1	yes	characteristic
58	C₂×D₄	C₄₇⋊C₈	1	3	yes	—
59	C₂²×C₄	C₂×Dic₄₇	1	3	yes	—
60	M₁₆	C₂×Dic₄₇	1	12	yes	—
61	C₂×C₈	C₂×Dic₄₇	1	3	yes	—
62	C₂×C₈	C₂×Dic₄₇	1	6	yes	—
63	C₂×C₈	C₂²×D₄₇	1	6	yes	—
64	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
65	C₁₆	—	47	8	no	—
66	C₂³	C₂×C₄₇⋊C₈	1	3	yes	—
67	Q₈	C₂×C₄₇⋊C₈	1	4	yes	—
68	D₄	C₂×C₄₇⋊C₈	1	12	yes	—
69	C₂×C₄	C₂×C₄₇⋊C₈	1	3	yes	—
70	C₂×C₄	C₂×C₄₇⋊C₈	1	6	yes	—
71	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
72	C₂×C₄	C₂²×Dic₄₇	1	6	yes	—
73	C₈	C₂²×Dic₄₇	1	1	yes	characteristic
74	C₈	C₂²×Dic₄₇	1	6	yes	—
75	C₈	C₂³×D₄₇	1	1	yes	characteristic
76	C₂²	—	4	3	no	—
77	C₂²	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
78	C₂²	C₂²×C₄₇⋊C₈	1	6	yes	—
79	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
80	C₄	C₂²×C₄₇⋊C₈	1	6	yes	—
81	C₄	C₂³×Dic₄₇	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	2	6	no	—
84	C₂	C₂³×C₄₇⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂³×D₄₇
commutator, socle	C₂×C₄₇	C₂³×C₈
Fitting	C₂×#131×C₄₇	C₂
hypercenter	C₂×#131	D₄₇
hypocenter	C₄₇	#3407
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. #15689540	C₂	semidirect
2. C₂×#13093964	C₂	semidirect
5. #13093964	C₂²	semidirect
6. C₂×C₄₇⋊C₁₆	C₂²	semidirect
46. C₄₇	#3407	semidirect