Subgroups — C₂×C₈×C₄₇⋊C₈ #20241661

Order 6016.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal
2	C₈×C₄₇⋊C₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₇⋊C₈	C₄	1	4	yes	—
5	C₄×C₄₇⋊C₈	C₄	1	4	yes	—
6	C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
7	C₂²×C₈×C₄₇	C₄	1	2	yes	—
8	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₄₇	C₄	1	2	yes	—
10	C₄×C₈×C₄₇	C₂²	1	2	yes	—
11	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₄₇	C₈	1	8	yes	complemented
14	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
15	C₄²×C₄₇	C₂×C₄	1	2	yes	—
16	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₄₇	C₂³	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	C₈	1	16	yes	direct product factor
19	C₂×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
20	C₂³×C₄₇	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₄₇	C₄²	1	2	yes	—
22	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₄₇	C₂×C₈	1	8	yes	—
24	C₂×C₄×C₄₇	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
26	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₈×C₄₇	C₂×C₈	1	8	yes	complemented
28	C₄₇⋊C₈	C₂×C₈	1	16	yes	direct product factor
29	C₂²×C₄₇	C₄×C₈	1	4	yes	—
30	C₂²×C₄₇	C₄×C₈	1	2	yes	—
31	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
32	C₄×C₄₇	C₄×C₈	1	4	yes	—
33	C₄×C₄₇	C₄×C₈	1	2	yes	—
34	C₄×C₄₇	C₂²×C₈	1	4	yes	—
35	C₄×C₄₇	C₂²×C₈	1	2	yes	—
36	C₂×C₈²	—	47	1	no	maximal, Sylow
37	C₂×C₄₇	C₈²	1	4	yes	complemented
38	C₂×C₄₇	C₂×C₄×C₈	1	2	yes	—
39	C₂×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
40	C₂×C₄×C₈	—	47	2	no	—
41	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
42	C₈²	—	47	4	no	—
43	C₄₇	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₈	—	47	4	no	—
45	C₂²×C₈	Dic₄₇	1	2	yes	—
46	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
47	C₄×C₈	—	47	4	no	—
48	C₄×C₈	—	47	4	no	—
49	C₄×C₈	Dic₄₇	1	2	yes	—
50	C₄×C₈	C₂×D₄₇	1	2	yes	—
51	C₂²×C₄	C₄×D₄₇	1	2	yes	—
52	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
53	C₂×C₈	—	47	16	no	—
54	C₂×C₈	—	47	8	no	—
55	C₂×C₈	C₄₇⋊C₈	1	8	yes	direct product factor
56	C₂×C₈	C₂×Dic₄₇	1	4	yes	—
57	C₄²	C₄×D₄₇	1	2	yes	—
58	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
59	C₄²	C₂²×D₄₇	1	1	yes	characteristic
60	C₂³	C₄×Dic₄₇	1	1	yes	characteristic
61	C₂×C₄	C₈×D₄₇	1	8	yes	—
62	C₂×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
63	C₂×C₄	C₄×Dic₄₇	1	2	yes	—
64	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
65	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
66	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
67	C₈	—	47	16	no	—
68	C₈	C₂×C₄₇⋊C₈	1	8	yes	direct product factor
69	C₂²	C₈×Dic₄₇	1	4	yes	—
70	C₂²	C₄×C₄₇⋊C₈	1	2	yes	—
71	C₂²	C₂×C₄×Dic₄₇	1	1	yes	characteristic
72	C₄	C₈×Dic₄₇	1	4	yes	—
73	C₄	C₄×C₄₇⋊C₈	1	2	yes	—
74	C₄	C₂×C₈×D₄₇	1	4	yes	—
75	C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
76	C₂	C₈×C₄₇⋊C₈	1	4	yes	direct product factor
77	C₂	C₂×C₈×Dic₄₇	1	2	yes	—
78	C₂	C₂×C₄×C₄₇⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₈	D₄₇
commutator, hypocenter	C₄₇	C₂×C₈²
Frattini	C₄²	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₄²
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×C₄₇⋊C₈	C₂	direct (N × H)
13. C₂×C₈×C₄₇	C₈	semidirect
18. C₂×C₄₇⋊C₈	C₈	direct (N × H)
27. C₈×C₄₇	C₂×C₈	semidirect
28. C₄₇⋊C₈	C₂×C₈	direct (N × H)
37. C₂×C₄₇	C₈²	semidirect
43. C₄₇	C₂×C₈²	semidirect
55. C₂×C₈	C₄₇⋊C₈	direct (N × H)
68. C₈	C₂×C₄₇⋊C₈	direct (N × H)
76. C₂	C₈×C₄₇⋊C₈	direct (N × H)

Subgroups — C2×C8×C47⋊C8 #20241661

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₈×C₄₇⋊C₈ #20241661