Subgroups — C₂×Dic₄₇⋊C₈ #15689143

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	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	Dic₄₇⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×Dic₄₇	C₄	1	1	yes	characteristic
7	C₂²×Dic₄₇	C₄	1	1	yes	characteristic
8	C₂×C₈×C₄₇	—	2	2	no	—
9	C₂×C₈×C₄₇	C₂²	1	2	yes	—
10	C₄×Dic₄₇	C₄	1	2	yes	—
11	C₄×Dic₄₇	C₂²	1	2	yes	—
12	C₂×C₄₇⋊C₈	—	2	2	no	—
13	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₇	D₄	1	2	yes	—
17	C₂×C₄×C₄₇	Q₈	1	2	yes	—
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₇	—	2	2	no	—
20	C₂×Dic₄₇	C₈	1	4	yes	complemented
21	C₂×Dic₄₇	C₂×C₄	1	2	yes	—
22	C₂×Dic₄₇	C₂×C₄	1	2	yes	—
23	C₈×C₄₇	—	2	2	no	—
24	C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
26	C₂²×C₄₇	C₂×C₈	1	2	yes	—
27	C₂²×C₄₇	M₁₆	1	2	yes	—
28	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
30	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
32	Dic₄₇	—	2	2	no	—
33	Dic₄₇	C₂×C₈	1	4	yes	complemented
34	C₂×C₄₇	C₄⋊C₈	1	4	yes	complemented
35	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄₇	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₄₇	C₂×M₁₆	1	1	yes	characteristic
38	C₂×C₄⋊C₈	—	47	1	no	maximal, Sylow
39	C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₈	—	47	1	no	—
41	C₂²×C₈	D₄₇	1	1	yes	characteristic
42	C₂×C₄²	—	47	1	no	—
43	C₄⋊C₈	—	47	4	no	—
44	C₂²×C₄	—	47	1	no	—
45	C₂²×C₄	—	47	1	no	—
46	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
47	C₂×C₈	—	2	2	no	—
48	C₂×C₈	—	47	2	no	—
49	C₂×C₈	—	94	2	no	—
50	C₂×C₈	C₂×D₄₇	1	2	yes	—
51	C₄²	—	47	2	no	—
52	C₄²	—	47	2	no	—
53	C₂³	C₄×D₄₇	1	1	yes	characteristic
54	C₂×C₄	—	47	4	no	—
55	C₂×C₄	—	47	2	no	—
56	C₂×C₄	—	47	2	no	—
57	C₂×C₄	—	94	2	no	—
58	C₂×C₄	Dic₉₄	1	2	yes	—
59	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
60	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
61	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₈	—	94	2	no	—
64	C₂²	C₈×D₄₇	1	2	yes	—
65	C₂²	#10625324	1	2	yes	—
66	C₂²	Dic₄₇⋊C₄	1	2	yes	—
67	C₂²	C₂×C₄×D₄₇	1	1	yes	characteristic
68	C₄	—	47	4	no	—
69	C₄	—	94	2	no	—
70	C₄	Dic₄₇⋊C₄	1	2	yes	—
71	C₄	C₂×Dic₉₄	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
73	C₂	Dic₄₇⋊C₈	1	4	yes	direct product factor
74	C₂	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
75	C₂	C₂×C₈×D₄₇	1	1	yes	characteristic
76	C₂	C₂×#10625324	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. Dic₄₇⋊C₈	C₂	direct (N × H)
20. C₂×Dic₄₇	C₈	semidirect
33. Dic₄₇	C₂×C₈	semidirect
34. C₂×C₄₇	C₄⋊C₈	semidirect
39. C₄₇	C₂×C₄⋊C₈	semidirect
73. C₂	Dic₄₇⋊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
C₂×C₄×Dic₄₇	2
Dic₄₇⋊C₈	2
C₂²×C₈×C₄₇	2
C₂×C₄⋊C₈	47

Subgroups — C2×Dic47⋊C8 #15689143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₄₇⋊C₈ #15689143