Subgroups — C₂×C₄⋊(C₄₇⋊C₈) #15689144

Order 3008.

138 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
2	C₄⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₇	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₄₇	C₄	1	1	yes	characteristic
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₄²×C₄₇	C₄	1	2	yes	—
8	C₄²×C₄₇	C₂²	1	2	yes	—
9	C₂×C₄₇⋊C₈	—	2	4	no	—
10	C₂×C₄₇⋊C₈	C₂²	1	4	yes	—
11	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₇	—	2	2	no	—
13	C₂×C₄×C₄₇	C₈	1	4	yes	complemented
14	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₄₇	D₄	1	2	yes	—
18	C₂×C₄×C₄₇	Q₈	1	2	yes	—
19	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
20	C₄₇⋊C₈	—	2	4	no	—
21	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
22	C₂²×C₄₇	C₂×C₈	1	2	yes	—
23	C₂²×C₄₇	M₁₆	1	2	yes	—
24	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₇	—	2	2	no	—
26	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
27	C₄×C₄₇	C₂×C₈	1	4	yes	complemented
28	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄₇	C₄⋊C₈	1	4	yes	complemented
31	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄₇	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₄₇	C₂×M₁₆	1	1	yes	characteristic
34	C₂×C₄⋊C₈	—	47	1	no	maximal, Sylow
35	C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	47	2	no	—
37	C₂×C₄²	D₄₇	1	1	yes	characteristic
38	C₄⋊C₈	—	47	4	no	—
39	C₂²×C₄	Dic₄₇	1	1	yes	characteristic
40	C₂²×C₄	Dic₄₇	1	1	yes	characteristic
41	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
42	C₂×C₈	—	47	4	no	—
43	C₂×C₈	—	94	4	no	—
44	C₄²	Dic₄₇	1	2	yes	—
45	C₄²	C₂×D₄₇	1	2	yes	—
46	C₂³	C₂×Dic₄₇	1	1	yes	characteristic
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	C₄₇⋊C₈	1	4	yes	complemented
49	C₂×C₄	Dic₉₄	1	2	yes	—
50	C₂×C₄	D₁₈₈	1	2	yes	—
51	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
52	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
53	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
54	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
55	C₈	—	94	4	no	—
56	C₂²	C₂×C₄₇⋊C₈	1	2	yes	—
57	C₂²	#10625329	1	2	yes	—
58	C₂²	C₄⋊Dic₄₇	1	2	yes	—
59	C₂²	C₂²×Dic₄₇	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	C₂×C₄₇⋊C₈	1	4	yes	complemented
62	C₄	C₄⋊Dic₄₇	1	2	yes	—
63	C₄	C₂×Dic₉₄	1	1	yes	characteristic
64	C₄	C₂×D₁₈₈	1	1	yes	characteristic
65	C₂	C₄⋊(C₄₇⋊C₈)	1	4	yes	direct product factor
66	C₂	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
67	C₂	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
68	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	C₂×C₄²×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×C₄²	D₄₇
hypocenter	C₄₇	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊(C₄₇⋊C₈)	C₂	direct (N × H)
13. C₂×C₄×C₄₇	C₈	semidirect
27. C₄×C₄₇	C₂×C₈	semidirect
30. C₂×C₄₇	C₄⋊C₈	semidirect
35. C₄₇	C₂×C₄⋊C₈	semidirect
48. C₂×C₄	C₄₇⋊C₈	semidirect
61. C₄	C₂×C₄₇⋊C₈	semidirect
65. C₂	C₄⋊(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
C₄⋊(C₄₇⋊C₈)	2
C₂×C₄²×C₄₇	2
C₂×C₄⋊C₈	47

Subgroups — C2×C4⋊(C47⋊C8) #15689144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊(C₄₇⋊C₈) #15689144