Subgroups — #15688989

Order 3008.

154 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	C₄₇⋊#95	C₂	1	4	yes	maximal
3	C₂×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₇	C₂²	1	2	yes	—
5	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×Dic₄₇	C₂²	1	4	yes	—
7	C₄²×C₄₇	C₄	1	4	yes	complemented
8	C₄⋊Dic₄₇	—	2	4	no	—
9	C₂³×C₄₇	C₂³	1	1	yes	characteristic
10	C₂×C₄×C₄₇	—	2	4	no	—
11	C₂×C₄×C₄₇	C₂×C₄	1	4	yes	—
12	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₄₇	D₄	1	2	yes	—
14	C₂×C₄×C₄₇	Q₈	1	2	yes	—
15	C₂×Dic₄₇	—	2	4	no	—
16	C₂×Dic₄₇	—	2	8	no	—
17	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
19	C₂²×C₄₇	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₄₇	#41	1	4	yes	—
21	C₄×C₄₇	—	2	4	no	—
22	C₄×C₄₇	C₄⋊C₄	1	4	yes	—
23	Dic₄₇	—	4	4	no	—
24	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄₇	#117	1	2	yes	—
26	C₂×C₄₇	#124	1	2	yes	—
27	C₂×C₄₇	#125	1	2	yes	—
28	#382	—	47	1	no	maximal, Sylow
29	C₄₇	#382	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₄⋊C₄	—	47	2	no	—
31	C₂×C₄²	D₄₇	1	1	yes	characteristic
32	#95	—	47	4	no	—
33	C₂²×C₄	—	47	4	no	—
34	C₂²×C₄	C₂×D₄₇	1	2	yes	—
35	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
36	C₄⋊C₄	—	94	4	no	—
37	C₄²	Dic₄₇	1	4	yes	complemented
38	C₂³	C₂²×D₄₇	1	1	yes	characteristic
39	C₂×C₄	—	2	4	no	—
40	C₂×C₄	—	94	4	no	—
41	C₂×C₄	—	94	8	no	—
42	C₂×C₄	Dic₉₄	1	2	yes	—
43	C₂×C₄	D₁₈₈	1	2	yes	—
44	C₂×C₄	C₂×Dic₄₇	1	4	yes	—
45	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
46	C₂²	C₂×Dic₉₄	1	1	yes	characteristic
47	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
48	C₂²	#10625350	1	4	yes	—
49	C₂²	C₂²×Dic₄₇	1	1	yes	characteristic
50	C₄	—	2	4	no	—
51	C₄	—	188	4	no	—
52	C₄	C₄⋊Dic₄₇	1	4	yes	—
53	C₂	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
54	C₂	#13093983	1	2	yes	—
55	C₂	#13094012	1	2	yes	—
56	C₂	#13094016	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄
Fitting	C₂×C₄²×C₄₇	C₂
socle, prime radical, cosocle	C₂³×C₄₇	C₂³
hypercenter	C₂×C₄²	D₄₇
hypocenter	C₄₇	#382
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. C₄²×C₄₇	C₄	semidirect
29. C₄₇	#382	semidirect
37. C₄²	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
C₄₇⋊#95	2
C₂×C₄²×C₄₇	2
#382	47