Subgroups — C₈²×D₄₇ #20241660

Order 6016.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×D₄₇	C₂	1	3	yes	maximal
2	C₈×C₄₇⋊C₈	C₂	1	3	yes	maximal, complemented
3	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₄₇	C₄	1	6	yes	—
5	C₄²×D₄₇	C₂²	1	1	yes	characteristic
6	C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
7	C₈×Dic₄₇	C₄	1	6	yes	—
8	C₄×C₈×C₄₇	C₂²	1	3	yes	—
9	C₂×C₄×D₄₇	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
11	C₄²×C₄₇	C₂³	1	1	yes	characteristic
12	C₄×Dic₄₇	C₂×C₄	1	3	yes	—
13	C₂×C₄₇⋊C₈	C₂×C₄	1	6	yes	—
14	C₈×D₄₇	C₈	1	24	yes	direct product factor
15	C₂²×D₄₇	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
17	C₂×Dic₄₇	C₄²	1	3	yes	—
18	C₄×D₄₇	C₂×C₈	1	12	yes	—
19	C₈×C₄₇	C₂×C₈	1	12	yes	complemented
20	C₄₇⋊C₈	C₂×C₈	1	12	yes	complemented
21	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₄₇	C₄×C₈	1	6	yes	—
23	C₄×C₄₇	C₂²×C₈	1	6	yes	—
24	Dic₄₇	C₄×C₈	1	6	yes	—
25	C₂×C₈²	—	47	1	no	maximal, Sylow
26	C₂×C₄₇	C₂×C₄×C₈	1	3	yes	—
27	D₄₇	C₈²	1	4	yes	direct product factor
28	C₂×C₄×C₈	—	47	3	no	—
29	C₈²	—	47	3	no	—
30	C₈²	D₄₇	1	1	yes	characteristic, direct product factor
31	C₄₇	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₈	—	47	6	no	—
33	C₂×C₄²	—	47	1	no	—
34	C₄×C₈	—	47	6	no	—
35	C₄×C₈	—	47	3	no	—
36	C₄×C₈	C₂×D₄₇	1	3	yes	—
37	C₂²×C₄	—	47	3	no	—
38	C₂×C₈	—	47	6	no	—
39	C₂×C₈	—	47	24	no	—
40	C₂×C₈	C₄×D₄₇	1	6	yes	—
41	C₄²	—	47	3	no	—
42	C₄²	C₂²×D₄₇	1	1	yes	characteristic
43	C₂³	—	47	1	no	—
44	C₂×C₄	—	47	3	no	—
45	C₂×C₄	—	47	12	no	—
46	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
47	C₈	—	47	12	no	—
48	C₈	C₈×D₄₇	1	12	yes	direct product factor
49	C₂²	—	47	6	no	—
50	C₂²	C₄²×D₄₇	1	1	yes	characteristic
51	C₄	—	47	6	no	—
52	C₄	C₂×C₈×D₄₇	1	6	yes	—
53	C₂	—	47	4	no	—
54	C₂	C₄×C₈×D₄₇	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₈×C₄₇⋊C₈	C₂	semidirect
3. C₈²×C₄₇	C₂	semidirect
14. C₈×D₄₇	C₈	direct (N × H)
19. C₈×C₄₇	C₂×C₈	semidirect
20. C₄₇⋊C₈	C₂×C₈	semidirect
27. D₄₇	C₈²	direct (N × H)
30. C₈²	D₄₇	direct (N × H)
31. C₄₇	C₂×C₈²	semidirect
48. C₈	C₈×D₄₇	direct (N × H)

Subgroups — C82×D47 #20241660

Conjugacy classes of subgroups

Complements

Subgroups — C₈²×D₄₇ #20241660