Subgroups — #15689477

Order 3008.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094016	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093948	C₂	1	2	yes	maximal, complemented
3	#13093945	C₂	1	2	yes	maximal
4	C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²⋊C₄×C₄₇	—	2	2	no	—
9	C₄²×C₄₇	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	Dic₄₇⋊C₄	—	2	2	no	—
12	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₄₇	—	2	1	no	—
14	Q₈×C₄₇	—	2	2	no	—
15	D₄×C₄₇	—	2	2	no	—
16	C₂×C₄×C₄₇	—	2	1	no	—
17	C₂×C₄×C₄₇	D₄	1	2	yes	—
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₇	—	2	2	no	—
20	C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇	—	4	1	no	—
22	C₂²×C₄₇	—	4	2	no	—
23	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₇	—	2	2	no	—
25	C₄×C₄₇	—	4	1	no	—
26	C₄×C₄₇	#41	1	2	yes	—
27	Dic₄₇	—	4	2	no	—
28	C₂×C₄₇	—	8	1	no	—
29	C₂×C₄₇	#124	1	1	yes	characteristic
30	C₂×C₄₇	#135	1	2	yes	—
31	#488	—	47	1	no	maximal, Sylow
32	C₄₇	#488	1	1	yes	characteristic, complemented, Sylow
33	#125	—	47	1	no	—
34	#124	D₄₇	1	1	yes	characteristic
35	#103	—	47	2	no	—
36	#102	—	47	2	no	—
37	C₄×C₈	—	47	1	no	—
38	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
39	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
40	C₂×C₈	—	47	2	no	—
41	C₄⋊C₄	—	47	2	no	—
42	C₄⋊C₄	—	94	2	no	—
43	C₂²⋊C₄	—	2	2	no	—
44	C₄²	C₂×D₄₇	1	1	yes	characteristic
45	C₂³	—	2	1	no	—
46	Q₈	—	2	2	no	—
47	D₄	—	2	2	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	94	2	no	—
50	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
51	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
52	C₈	—	94	2	no	—
53	C₂²	—	4	1	no	—
54	C₂²	—	4	2	no	—
55	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	4	1	no	—
58	C₄	—	188	2	no	—
59	C₄	#10625352	1	2	yes	—
60	C₂	—	8	1	no	—
61	C₂	#13094011	1	1	yes	characteristic
62	C₂	#13094044	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#124×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂×D₄×C₄₇	C₂²
hypercenter	#124	D₄₇
hypocenter	C₄₇	#488
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. #13094016	C₂	semidirect
2. #13093948	C₂	semidirect
4. C₄×C₄₇⋊C₈	C₂	semidirect
32. C₄₇	#488	semidirect

Maximal subgroups

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

subgroup	index
#13094016	2
#13093948	2
#13093945	2
C₄×C₄₇⋊C₈	2
#124×C₄₇	2
#488	47