Subgroups — #15689502

Order 3008.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625337	C₂	1	4	yes	maximal
2	#13094024	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₄₇	C₂²	1	2	yes	—
6	C₂×Dic₉₄	C₂²	1	2	yes	—
7	C₄⋊C₄×C₄₇	—	2	2	no	—
8	C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	#10625337	—	2	8	no	—
10	C₄⋊Dic₄₇	—	2	2	no	—
11	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
12	Q₈×C₄₇	—	2	4	no	—
13	C₂×C₄×C₄₇	—	2	2	no	—
14	C₂×C₄×C₄₇	D₄	1	2	yes	—
15	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₇	—	2	2	no	—
17	Dic₉₄	—	2	4	no	—
18	C₄₇⋊C₈	D₄	1	4	yes	—
19	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
20	C₄×C₄₇	—	4	2	no	—
21	C₄×C₄₇	Q₁₆	1	4	yes	complemented
22	C₄×C₄₇	C₂×D₄	1	2	yes	—
23	Dic₄₇	—	4	2	no	—
24	C₂×C₄₇	#127	1	1	yes	characteristic
25	C₂×C₄₇	C₂×Q₁₆	1	2	yes	—
26	#494	—	47	1	no	maximal, Sylow
27	C₄₇	#494	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₁₆	—	47	4	no	—
29	C₄⋊Q₈	—	47	1	no	—
30	C₄⋊Q₈	D₄₇	1	1	yes	characteristic
31	C₄×C₈	—	47	1	no	—
32	C₂×Q₈	—	47	2	no	—
33	C₂×Q₈	C₂×D₄₇	1	2	yes	—
34	Q₁₆	—	94	8	no	—
35	C₂×C₈	—	47	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	94	2	no	—
38	C₄²	C₂×D₄₇	1	1	yes	characteristic
39	Q₈	—	2	4	no	—
40	Q₈	—	94	4	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	94	2	no	—
43	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
44	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
45	C₈	—	47	4	no	—
46	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
47	C₄	—	4	2	no	—
48	C₄	—	188	2	no	—
49	C₄	#10625337	1	4	yes	complemented
50	C₄	D₄×D₄₇	1	2	yes	—
51	C₂	#13094020	1	1	yes	characteristic
52	C₂	C₂×#10625337	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₄⋊Q₈×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
hypercenter	C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#494
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
21. C₄×C₄₇	Q₁₆	semidirect
27. C₄₇	#494	semidirect
49. C₄	#10625337	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625337	2
#13094024	2
C₄×C₄₇⋊C₈	2
C₄⋊Q₈×C₄₇	2
#494	47