Subgroups — #15688880

Order 3008.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093983	C₂	1	2	yes	maximal
2	C₂×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
4	M₁₆×C₄₇	—	2	2	no	—
5	C₂×C₈×C₄₇	C₄	1	2	yes	complemented
6	C₂²⋊Dic₄₇	—	2	2	no	—
7	C₄⋊Dic₄₇	—	2	2	no	—
8	C₄×Dic₄₇	C₄	1	4	yes	complemented
9	C₂³×C₄₇	D₄	1	1	yes	characteristic
10	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₇	D₄	1	2	yes	—
13	C₂×C₄×C₄₇	Q₈	1	1	yes	characteristic
14	C₂×Dic₄₇	—	2	4	no	—
15	C₈×C₄₇	—	2	2	no	—
16	C₂²×C₄₇	—	4	1	no	—
17	C₂²×C₄₇	C₂²⋊C₄	1	2	yes	—
18	C₂²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₄₇	C₄²	1	1	yes	characteristic
20	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
22	Dic₄₇	—	4	4	no	—
23	C₂×C₄₇	—	2	2	no	—
24	C₂×C₄₇	—	2	1	no	—
25	C₂×C₄₇	#95	1	1	yes	characteristic
26	H(3,ℤ/4)	—	47	1	no	maximal, Sylow
27	C₄₇	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
28	C₂×M₁₆	D₄₇	1	1	yes	characteristic
29	#117	—	47	2	no	—
30	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
31	M₁₆	—	2	2	no	—
32	C₂×C₈	Dic₄₇	1	2	yes	complemented
33	C₄⋊C₄	—	94	2	no	—
34	C₂²⋊C₄	—	94	2	no	—
35	C₄²	—	47	4	no	—
36	C₂³	D₁₈₈	1	1	yes	characteristic
37	C₂×C₄	—	94	4	no	—
38	C₂×C₄	Dic₉₄	1	1	yes	characteristic
39	C₂×C₄	C₄×D₄₇	1	2	yes	—
40	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
41	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
42	C₈	—	2	2	no	—
43	C₂²	—	4	1	no	—
44	C₂²	C₄⋊Dic₄₇	1	1	yes	characteristic
45	C₂²	(C₂×D₄₇)⋊C₄	1	2	yes	—
46	C₄	—	188	4	no	—
47	C₄	C₄×Dic₄₇	1	1	yes	characteristic
48	C₄	Dic₄₇⋊C₄	1	2	yes	—
49	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₄₇⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₄₇
commutator	C₄×C₄₇	C₄²
Frattini	C₂²×C₄	C₂×D₄₇
Fitting	C₂×M₁₆×C₄₇	C₂
socle	C₂×C₄₇	#95
prime radical	C₂³×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂²
hypercenter	C₂×M₁₆	D₄₇
hypocenter	C₄₇	H(3,ℤ/4)
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
5. C₂×C₈×C₄₇	C₄	semidirect
8. C₄×Dic₄₇	C₄	semidirect
27. C₄₇	H(3,ℤ/4)	semidirect
32. C₂×C₈	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13093983	2
C₂×M₁₆×C₄₇	2
H(3,ℤ/4)	47