Subgroups — #15688886

Order 3008.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₄₇	C₂	1	2	yes	maximal
2	C₂²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
4	C₂²×Dic₄₇	—	2	2	no	—
5	C₂×C₈×C₄₇	—	2	2	no	—
6	C₂×C₈×C₄₇	C₄	1	2	yes	complemented
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	C₂×Dic₄₇	—	4	2	no	—
16	C₂×Dic₄₇	—	4	2	no	—
17	C₈×C₄₇	—	2	2	no	—
18	C₂²×C₄₇	C₂²⋊C₄	1	2	yes	—
19	C₂²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
20	C₂²×C₄₇	D₈	1	1	yes	characteristic
21	C₂²×C₄₇	SD₁₆	1	2	yes	—
22	C₂²×C₄₇	Q₁₆	1	1	yes	characteristic
23	C₄×C₄₇	C₄²	1	1	yes	characteristic
24	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
26	Dic₄₇	—	4	4	no	—
27	C₂×C₄₇	#95	1	1	yes	characteristic
28	C₂×C₄₇	#102	1	2	yes	—
29	C₂×C₄₇	#103	1	2	yes	—
30	C₂×C₄₇	#106	1	1	yes	characteristic
31	C₂×C₄₇	#107	1	1	yes	characteristic
32	#340	—	47	1	no	maximal, Sylow
33	C₄₇	#340	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₈	D₄₇	1	1	yes	characteristic
35	C₂×C₄⋊C₄	—	47	2	no	—
36	C₂²×C₄	—	94	2	no	—
37	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
38	C₂×C₈	—	2	2	no	—
39	C₂×C₈	Dic₄₇	1	2	yes	complemented
40	C₄⋊C₄	—	47	4	no	—
41	C₄⋊C₄	—	94	2	no	—
42	C₂³	D₁₈₈	1	1	yes	characteristic
43	C₂×C₄	—	94	4	no	—
44	C₂×C₄	—	188	2	no	—
45	C₂×C₄	—	188	2	no	—
46	C₂×C₄	Dic₉₄	1	1	yes	characteristic
47	C₂×C₄	C₄×D₄₇	1	2	yes	—
48	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
50	C₈	—	2	2	no	—
51	C₂²	#10625325	1	2	yes	—
52	C₂²	D₃₇₆	1	1	yes	characteristic
53	C₂²	Dic₁₈₈	1	1	yes	characteristic
54	C₂²	C₄⋊Dic₄₇	1	1	yes	characteristic
55	C₂²	(C₂×D₄₇)⋊C₄	1	2	yes	—
56	C₄	—	188	4	no	—
57	C₄	C₄×Dic₄₇	1	1	yes	characteristic
58	C₄	Dic₄₇⋊C₄	1	2	yes	—
59	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
60	C₂	C₄₇⋊#95	1	1	yes	characteristic
61	C₂	#13093946	1	2	yes	—
62	C₂	#13093949	1	2	yes	—
63	C₂	#13093956	1	1	yes	characteristic
64	C₂	#13093958	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₈₈
commutator	C₄×C₄₇	C₄²
Frattini	C₂²×C₄	C₂×D₄₇
Fitting	C₂²×C₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂²
hypercenter	C₂²×C₈	D₄₇
hypocenter	C₄₇	#340
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
6. C₂×C₈×C₄₇	C₄	semidirect
8. C₄⋊Dic₄₇	C₄	semidirect
33. C₄₇	#340	semidirect
39. 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
C₂×C₄⋊Dic₄₇	2
C₂²×C₈×C₄₇	2
#340	47