Subgroups — #15688905

Order 3008.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093964	C₂	1	2	yes	maximal, complemented
2	C₂×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₇	C₄	1	1	yes	characteristic
4	M₁₆×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	—	4	1	no	—
17	C₂²×C₄₇	C₂×C₈	1	1	yes	characteristic
18	C₄×C₄₇	—	2	1	no	—
19	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₄₇	M₁₆	1	1	yes	characteristic
21	C₂×C₄₇	—	2	1	no	—
22	C₂×C₄₇	—	4	1	no	—
23	C₂×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
24	#349	—	47	1	no	maximal, Sylow
25	C₄₇	#349	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	D₄₇	1	1	yes	characteristic
27	M₃₂	—	47	2	no	—
28	C₂²×C₄	Dic₄₇	1	1	yes	characteristic
29	M₁₆	—	2	2	no	—
30	C₂×C₈	Dic₄₇	1	1	yes	characteristic
31	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
32	C₁₆	—	94	2	no	—
33	C₂³	C₄₇⋊C₈	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₄₇⋊C₈	1	1	yes	characteristic
37	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂²⋊D₄₇	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×C₄₇⋊C₈	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	#10625329	1	1	yes	characteristic
45	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₄₇
commutator	C₂²×C₄₇	C₂×C₈
Frattini	C₂×C₈	C₂×D₄₇
Fitting	C₂×M₁₆×C₄₇	C₂
socle	C₂×C₄₇	C₂²⋊C₈
prime radical	C₂³×C₄₇	C₈
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	C₂×M₁₆	D₄₇
hypocenter	C₄₇	#349
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #13093964	C₂	semidirect
25. C₄₇	#349	semidirect

Maximal subgroups

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

subgroup	index
#13093964	2
C₂×M₁₆×C₄₇	2
#349	47