Subgroups — #15689042

Order 3008.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₇⋊C₄	C₂	1	3	yes	maximal
2	C₄₇⋊#95	C₂	1	3	yes	maximal
3	C₂²×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₄₇	—	2	6	no	—
5	C₂²×C₄×C₄₇	C₂²	1	3	yes	—
6	C₂²×Dic₄₇	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₇	C₂²	1	3	yes	—
8	Dic₄₇⋊C₄	—	2	6	no	—
9	C₂³×C₄₇	C₂³	1	1	yes	characteristic
10	Q₈×C₄₇	—	2	8	no	—
11	C₂×C₄×C₄₇	—	2	6	no	—
12	C₂×C₄×C₄₇	D₄	1	6	yes	—
13	C₂×Dic₄₇	—	2	3	no	—
14	C₂×Dic₄₇	—	2	3	no	—
15	C₂×Dic₄₇	—	2	3	no	—
16	C₂×Dic₄₇	Q₈	1	6	yes	complemented
17	C₂²×C₄₇	C₂×D₄	1	3	yes	—
18	C₂²×C₄₇	C₂×Q₈	1	3	yes	—
19	C₂²×C₄₇	#41	1	1	yes	characteristic
20	C₄×C₄₇	—	2	6	no	—
21	Dic₄₇	—	2	6	no	—
22	Dic₄₇	—	4	1	no	—
23	C₂×C₄₇	#120	1	1	yes	characteristic
24	C₂×C₄₇	C₂²⋊Q₈	1	3	yes	—
25	C₂×C₄₇	C₄⋊Q₈	1	3	yes	—
26	#395	—	47	1	no	maximal, Sylow
27	C₄₇	#395	1	1	yes	characteristic, complemented, Sylow
28	C₂²×Q₈	D₄₇	1	1	yes	characteristic
29	C₂×C₄⋊C₄	—	47	3	no	—
30	#95	—	47	3	no	—
31	C₂×Q₈	—	2	6	no	—
32	C₂²×C₄	—	47	3	no	—
33	C₂²×C₄	—	47	1	no	—
34	C₂²×C₄	C₂×D₄₇	1	3	yes	—
35	C₄⋊C₄	—	94	6	no	—
36	C₂³	C₂²×D₄₇	1	1	yes	characteristic
37	Q₈	—	2	8	no	—
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	47	6	no	—
40	C₂×C₄	—	94	3	no	—
41	C₂×C₄	—	94	3	no	—
42	C₂×C₄	—	94	3	no	—
43	C₂×C₄	C₂²⋊D₄₇	1	6	yes	—
44	C₂²	Q₈×D₄₇	1	3	yes	—
45	C₂²	#10625354	1	1	yes	characteristic
46	C₂²	C₂×C₂²⋊D₄₇	1	3	yes	—
47	C₄	—	2	6	no	—
48	C₄	—	94	6	no	—
49	C₄	—	188	1	no	—
50	C₂	#13093993	1	1	yes	characteristic
51	C₂	#13094000	1	3	yes	—
52	C₂	#13094022	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₇
commutator, socle, prime radical, cosocle	C₂³×C₄₇	C₂³
Fitting	C₂²×Q₈×C₄₇	C₂
hypercenter	C₂²×Q₈	D₄₇
hypocenter	C₄₇	#395
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
16. C₂×Dic₄₇	Q₈	semidirect
27. C₄₇	#395	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₄₇⋊C₄	2
C₄₇⋊#95	2
C₂²×Q₈×C₄₇	2
#395	47