Subgroups — C₂×C₂²⋊(C₄₇⋊C₈) #15689084

Order 3008.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
2	C₂²⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×C₄₇	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₄₇	—	2	4	no	—
6	C₂²×C₄×C₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₄₇	C₄	1	2	yes	—
8	C₂²×C₄×C₄₇	C₂²	1	2	yes	—
9	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₈	—	2	4	no	—
11	C₂×C₄₇⋊C₈	C₂²	1	4	yes	complemented
12	C₂³×C₄₇	—	2	2	no	—
13	C₂³×C₄₇	—	2	2	no	—
14	C₂³×C₄₇	C₈	1	4	yes	complemented
15	C₂³×C₄₇	C₂×C₄	1	2	yes	—
16	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	—	2	4	no	—
19	C₂×C₄×C₄₇	—	2	4	no	—
20	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₇	D₄	1	4	yes	—
23	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₄₇⋊C₈	—	2	4	no	—
25	C₂²×C₄₇	—	2	8	no	—
26	C₂²×C₄₇	—	2	2	no	—
27	C₂²×C₄₇	—	2	2	no	—
28	C₂²×C₄₇	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₄₇	C₂×C₈	1	2	yes	—
30	C₂²×C₄₇	C₂×C₈	1	4	yes	complemented
31	C₂²×C₄₇	M₁₆	1	2	yes	—
32	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₄₇	—	2	2	no	—
34	C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
35	C₄×C₄₇	C₂×D₄	1	2	yes	—
36	C₂×C₄₇	—	2	4	no	—
37	C₂×C₄₇	C₂²⋊C₈	1	4	yes	complemented
38	C₂×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₄₇	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₄₇	C₂×M₁₆	1	1	yes	characteristic
41	C₂×C₂²⋊C₈	—	47	1	no	maximal, Sylow
42	C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
43	C₂³×C₄	D₄₇	1	1	yes	characteristic
44	C₂²×C₈	—	47	2	no	—
45	C₂²⋊C₈	—	47	4	no	—
46	C₂⁴	Dic₄₇	1	1	yes	characteristic
47	C₂²×C₄	—	2	4	no	—
48	C₂²×C₄	Dic₄₇	1	1	yes	characteristic
49	C₂²×C₄	Dic₄₇	1	2	yes	—
50	C₂²×C₄	C₂×D₄₇	1	2	yes	—
51	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
52	C₂×C₈	—	47	4	no	—
53	C₂×C₈	—	94	4	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	2	2	no	—
56	C₂³	C₄₇⋊C₈	1	4	yes	complemented
57	C₂³	C₂×Dic₄₇	1	2	yes	—
58	C₂³	C₂×Dic₄₇	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
63	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
64	C₂×C₄	C₂²⋊D₄₇	1	4	yes	—
65	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
66	C₈	—	94	4	no	—
67	C₂²	—	2	8	no	—
68	C₂²	—	2	2	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂×C₄₇⋊C₈	1	2	yes	—
71	C₂²	C₂×C₄₇⋊C₈	1	4	yes	complemented
72	C₂²	#10625329	1	2	yes	—
73	C₂²	C₂²⋊Dic₄₇	1	2	yes	—
74	C₂²	C₂²×Dic₄₇	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	C₂²⋊Dic₄₇	1	2	yes	—
77	C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
78	C₂	—	2	4	no	—
79	C₂	C₂²⋊(C₄₇⋊C₈)	1	4	yes	direct product factor
80	C₂	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
81	C₂	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
82	C₂	C₂×#10625329	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₇
commutator	C₂×C₄₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂³×C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₄
prime radical	C₂⁴×C₄₇	C₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂³×C₄	D₄₇
hypocenter	C₄₇	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄₇⋊C₈	C₂	semidirect
2. C₂²⋊(C₄₇⋊C₈)	C₂	direct (N × H)
11. C₂×C₄₇⋊C₈	C₂²	semidirect
14. C₂³×C₄₇	C₈	semidirect
30. C₂²×C₄₇	C₂×C₈	semidirect
37. C₂×C₄₇	C₂²⋊C₈	semidirect
42. C₄₇	C₂×C₂²⋊C₈	semidirect
56. C₂³	C₄₇⋊C₈	semidirect
71. C₂²	C₂×C₄₇⋊C₈	semidirect
79. C₂	C₂²⋊(C₄₇⋊C₈)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄₇⋊C₈	2
C₂²⋊(C₄₇⋊C₈)	2
C₂³×C₄×C₄₇	2
C₂×C₂²⋊C₈	47

Subgroups — C2×C22⋊(C47⋊C8) #15689084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊(C₄₇⋊C₈) #15689084