Subgroups — C₂²⋊(C₄₇⋊C₁₆) #15688903

Order 3008.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
2	C₂²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₇	C₄	1	1	yes	characteristic
4	C₂×C₈×C₄₇	—	2	2	no	—
5	C₂×C₈×C₄₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₄₇⋊C₁₆	—	2	2	no	—
8	C₂³×C₄₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₄₇	—	2	1	no	—
10	C₂×C₄×C₄₇	—	2	1	no	—
11	C₂×C₄×C₄₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₄₇	—	2	1	no	—
14	C₈×C₄₇	D₄	1	2	yes	—
15	C₂²×C₄₇	—	2	1	no	—
16	C₂²×C₄₇	—	2	1	no	—
17	C₂²×C₄₇	C₁₆	1	2	yes	complemented
18	C₂²×C₄₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₄₇	—	2	1	no	—
20	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₇	M₁₆	1	1	yes	characteristic
22	C₂×C₄₇	—	2	2	no	—
23	C₂×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₄₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₄₇	M₃₂	1	1	yes	characteristic
26	C₂²⋊C₁₆	—	47	1	no	maximal, Sylow
27	C₄₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₈	D₄₇	1	1	yes	characteristic
29	C₂×C₁₆	—	47	2	no	—
30	C₂²×C₄	Dic₄₇	1	1	yes	characteristic
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	Dic₄₇	1	1	yes	characteristic
33	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
34	C₁₆	—	94	2	no	—
35	C₂³	C₄₇⋊C₈	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	C₄₇⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	C₂²⋊D₄₇	1	2	yes	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	C₄₇⋊C₁₆	1	2	yes	complemented
45	C₂²	C₂×C₄₇⋊C₈	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	#10625329	1	1	yes	characteristic
48	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
51	C₂	C₂×C₄₇⋊C₁₆	1	1	yes	characteristic
52	C₂	#13093964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₁₆
Fitting	C₂²×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₈
prime radical	C₂³×C₄₇	C₈
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	C₂²×C₈	D₄₇
hypocenter	C₄₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇⋊C₁₆	C₂	semidirect
17. C₂²×C₄₇	C₁₆	semidirect
27. C₄₇	C₂²⋊C₁₆	semidirect
44. C₂²	C₄₇⋊C₁₆	semidirect

Maximal subgroups

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

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

Subgroups — C22⋊(C47⋊C16) #15688903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₄₇⋊C₁₆) #15688903