Subgroups — (C₂×D₄₇)⋊C₁₆ #15688902

Order 3008.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₄₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₈×D₄₇	—	2	1	no	—
8	C₈×D₄₇	—	2	1	no	—
9	C₁₆×C₄₇	—	2	1	no	—
10	C₄₇⋊C₁₆	—	2	1	no	—
11	C₂²×D₄₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₄₇	C₈	1	1	yes	characteristic
14	C₄×D₄₇	—	2	1	no	—
15	C₄×D₄₇	—	2	1	no	—
16	C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₄₇⋊C₈	—	2	1	no	—
19	C₂²×C₄₇	C₂×C₈	1	1	yes	characteristic
20	C₂×D₄₇	—	2	1	no	—
21	C₂×D₄₇	—	2	1	no	—
22	C₂×D₄₇	C₁₆	1	2	yes	complemented
23	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₄₇	M₁₆	1	1	yes	characteristic
25	Dic₄₇	—	2	1	no	—
26	C₂×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
27	C₂×C₄₇	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₄₇	M₃₂	1	1	yes	characteristic
29	D₄₇	—	2	2	no	—
30	C₂²⋊C₁₆	—	47	1	no	maximal, Sylow
31	C₄₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₈	—	47	1	no	—
33	C₂×C₁₆	—	47	1	no	—
34	C₂×C₁₆	D₄₇	1	1	yes	characteristic, complemented
35	C₂²×C₄	—	47	1	no	—
36	C₂×C₈	—	47	1	no	—
37	C₂×C₈	—	94	1	no	—
38	C₂×C₈	—	94	1	no	—
39	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	—	94	1	no	—
42	C₂³	—	47	1	no	—
43	C₂×C₄	—	47	1	no	—
44	C₂×C₄	—	94	1	no	—
45	C₂×C₄	—	94	1	no	—
46	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
47	C₈	—	94	1	no	—
48	C₈	D₁₈₈	1	1	yes	characteristic
49	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
50	C₂²	—	47	2	no	—
51	C₂²	—	94	1	no	—
52	C₂²	—	94	1	no	—
53	C₂²	C₈×D₄₇	1	1	yes	characteristic
54	C₄	—	94	1	no	—
55	C₄	#10625324	1	1	yes	characteristic
56	C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
57	C₂	—	94	2	no	—
58	C₂	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
59	C₂	C₁₆×D₄₇	1	1	yes	characteristic
60	C₂	#13093963	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₁₆
Fitting	C₂×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₈
prime radical	C₂²×D₄₇	C₈
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	C₂×C₁₆	D₄₇
hypocenter	C₄₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇⋊C₁₆	C₂	semidirect
3. C₂×C₁₆×C₄₇	C₂	semidirect
22. C₂×D₄₇	C₁₆	semidirect
31. C₄₇	C₂²⋊C₁₆	semidirect
34. C₂×C₁₆	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄₇	2
C₂×C₄₇⋊C₁₆	2
C₂×C₁₆×C₄₇	2
C₂²⋊C₁₆	47

Subgroups — (C2×D47)⋊C16 #15688902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₄₇)⋊C₁₆ #15688902