Subgroups — C₂×C₄²×Dic₄₇ #20245710

Order 6016.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Dic₄₇	C₂	1	6	yes	maximal
2	C₄²×Dic₄₇	C₂	1	8	yes	maximal, direct product factor
3	C₂²×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₄₇	C₂²	1	4	yes	—
5	C₂×C₄×Dic₄₇	C₄	1	48	yes	direct product factor
6	C₂×C₄×Dic₄₇	C₂²	1	24	yes	—
7	C₂³×C₄×C₄₇	C₂²	1	3	yes	—
8	C₂×C₄²×C₄₇	C₄	1	8	yes	complemented
9	C₂×C₄²×C₄₇	C₂²	1	4	yes	—
10	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
11	C₂²×C₄×C₄₇	C₂×C₄	1	24	yes	—
12	C₂²×C₄×C₄₇	C₂×C₄	1	12	yes	—
13	C₂²×C₄×C₄₇	C₂³	1	6	yes	—
14	C₂²×Dic₄₇	C₂×C₄	1	48	yes	—
15	C₂²×Dic₄₇	C₂³	1	8	yes	—
16	C₄²×C₄₇	C₂×C₄	1	16	yes	complemented
17	C₄×Dic₄₇	C₂×C₄	1	96	yes	direct product factor
18	C₂³×C₄₇	C₂²×C₄	1	12	yes	—
19	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
20	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
21	C₂×C₄×C₄₇	C₄²	1	48	yes	complemented
22	C₂×C₄×C₄₇	C₂²×C₄	1	24	yes	—
23	C₂×C₄×C₄₇	C₂²×C₄	1	12	yes	—
24	C₂×Dic₄₇	C₄²	1	64	yes	direct product factor
25	C₂×Dic₄₇	C₂²×C₄	1	48	yes	—
26	C₂²×C₄₇	C₂×C₄²	1	16	yes	—
27	C₂²×C₄₇	C₂×C₄²	1	12	yes	—
28	C₂²×C₄₇	C₂³×C₄	1	6	yes	—
29	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
30	C₄×C₄₇	C₂×C₄²	1	24	yes	complemented
31	Dic₄₇	C₂×C₄²	1	32	yes	direct product factor
32	C₂×C₄³	—	47	1	no	maximal, Sylow
33	C₂×C₄₇	C₄³	1	8	yes	complemented
34	C₂×C₄₇	C₂²×C₄²	1	4	yes	—
35	C₂×C₄₇	C₂²×C₄²	1	3	yes	—
36	C₂²×C₄²	—	47	6	no	—
37	C₂²×C₄²	D₄₇	1	1	yes	characteristic
38	C₄³	—	47	8	no	—
39	C₄₇	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
40	C₂³×C₄	—	47	4	no	—
41	C₂³×C₄	C₂×D₄₇	1	3	yes	—
42	C₂×C₄²	—	47	48	no	—
43	C₂×C₄²	—	47	24	no	—
44	C₂×C₄²	Dic₄₇	1	8	yes	direct product factor
45	C₂×C₄²	C₂×D₄₇	1	4	yes	—
46	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
47	C₂²×C₄	—	47	48	no	—
48	C₂²×C₄	—	47	8	no	—
49	C₂²×C₄	C₄×D₄₇	1	24	yes	—
50	C₂²×C₄	C₂×Dic₄₇	1	12	yes	—
51	C₂²×C₄	C₂²×D₄₇	1	6	yes	—
52	C₄²	—	47	96	no	—
53	C₄²	C₂×Dic₄₇	1	16	yes	direct product factor
54	C₂³	C₂×C₄×D₄₇	1	12	yes	—
55	C₂³	C₂²×Dic₄₇	1	2	yes	—
56	C₂³	C₂³×D₄₇	1	1	yes	characteristic
57	C₂×C₄	—	47	64	no	—
58	C₂×C₄	—	47	48	no	—
59	C₂×C₄	C₄×Dic₄₇	1	48	yes	direct product factor
60	C₂×C₄	C₂×C₄×D₄₇	1	24	yes	—
61	C₂×C₄	C₂²×Dic₄₇	1	12	yes	—
62	C₂²	C₄²×D₄₇	1	16	yes	—
63	C₂²	C₂×C₄×Dic₄₇	1	12	yes	—
64	C₂²	C₂²×C₄×D₄₇	1	6	yes	—
65	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
66	C₄	—	47	32	no	—
67	C₄	C₂×C₄×Dic₄₇	1	24	yes	direct product factor
68	C₂	C₄²×Dic₄₇	1	8	yes	direct product factor
69	C₂	C₂×C₄²×D₄₇	1	4	yes	—
70	C₂	C₂²×C₄×Dic₄₇	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂²×C₄²	D₄₇
commutator, hypocenter	C₄₇	C₂×C₄³
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂²×C₄²×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×Dic₄₇	C₂	direct (N × H)
5. C₂×C₄×Dic₄₇	C₄	direct (N × H)
8. C₂×C₄²×C₄₇	C₄	semidirect
16. C₄²×C₄₇	C₂×C₄	semidirect
17. C₄×Dic₄₇	C₂×C₄	direct (N × H)
21. C₂×C₄×C₄₇	C₄²	semidirect
24. C₂×Dic₄₇	C₄²	direct (N × H)
30. C₄×C₄₇	C₂×C₄²	semidirect
31. Dic₄₇	C₂×C₄²	direct (N × H)
33. C₂×C₄₇	C₄³	semidirect
39. C₄₇	C₂×C₄³	semidirect
44. C₂×C₄²	Dic₄₇	direct (N × H)
53. C₄²	C₂×Dic₄₇	direct (N × H)
59. C₂×C₄	C₄×Dic₄₇	direct (N × H)
67. C₄	C₂×C₄×Dic₄₇	direct (N × H)
68. C₂	C₄²×Dic₄₇	direct (N × H)

Subgroups — C2×C42×Dic47 #20245710

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄²×Dic₄₇ #20245710