Subgroups — #15689161

Order 3008.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093983	C₂	1	2	yes	maximal
2	#13093958	C₂	1	2	yes	maximal, complemented
3	#13093956	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₇	C₄	1	4	yes	complemented
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²⋊Dic₄₇	—	2	2	no	—
10	C₄⋊Dic₄₇	C₂²	1	4	yes	—
11	C₄×Dic₄₇	—	2	2	no	—
12	C₂³×C₄₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	Q₈	1	2	yes	—
16	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₇	—	2	4	no	—
18	C₈×C₄₇	C₂×C₄	1	2	yes	—
19	C₈×C₄₇	C₂×C₄	1	2	yes	—
20	C₂²×C₄₇	—	2	2	no	—
21	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
22	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
23	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
24	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
26	Dic₄₇	—	4	4	no	—
27	C₂×C₄₇	—	2	2	no	—
28	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄₇	#135	1	2	yes	—
30	#427	—	47	1	no	maximal, Sylow
31	C₄₇	#427	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₈	D₄₇	1	1	yes	characteristic
33	#117	—	47	2	no	—
34	#107	—	47	2	no	—
35	#106	—	47	2	no	—
36	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
37	C₂×C₈	Dic₄₇	1	4	yes	complemented
38	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
39	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
40	C₄⋊C₄	—	47	4	no	—
41	C₂²⋊C₄	—	94	2	no	—
42	C₄²	—	94	2	no	—
43	C₂³	D₁₈₈	1	1	yes	characteristic
44	C₂×C₄	—	94	4	no	—
45	C₂×C₄	Dic₉₄	1	2	yes	—
46	C₂×C₄	D₁₈₈	1	1	yes	characteristic
47	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
48	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
49	C₈	C₂×Dic₄₇	1	2	yes	—
50	C₈	C₂×Dic₄₇	1	2	yes	—
51	C₂²	—	2	2	no	—
52	C₂²	C₄⋊Dic₄₇	1	2	yes	—
53	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
54	C₄	—	188	4	no	—
55	C₄	C₄⋊Dic₄₇	1	2	yes	—
56	C₄	C₂×Dic₉₄	1	1	yes	characteristic
57	C₄	C₂²×Dic₄₇	1	1	yes	characteristic
58	C₂	—	2	2	no	—
59	C₂	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
60	C₂	#13094046	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₁₈₈
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂²×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂³×C₄₇	D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂²×C₈	D₄₇
hypocenter	C₄₇	#427
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #13093958	C₂	semidirect
3. #13093956	C₂	semidirect
6. C₂×C₈×C₄₇	C₄	semidirect
31. C₄₇	#427	semidirect
37. 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
#13093958	2
#13093956	2
C₂²×C₈×C₄₇	2
#427	47