Subgroups — #13094048

Order 1504.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625352	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625335	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625334	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625325	C₂	1	1	yes	maximal, characteristic, complemented
7	#10625324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄₇	—	2	1	no	—
9	D₄×C₄₇	C₂²	1	1	yes	characteristic
10	D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
11	C₂²⋊D₄₇	—	2	1	no	—
12	C₂²⋊D₄₇	—	2	1	no	—
13	C₂×Dic₄₇	—	2	1	no	—
14	D₁₈₈	C₂²	1	1	yes	characteristic
15	C₄×D₄₇	C₂²	1	1	yes	characteristic
16	Dic₉₄	C₂²	1	1	yes	characteristic, complemented
17	C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
18	C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₄₇	—	2	1	no	—
20	C₂²×C₄₇	—	2	1	no	—
21	C₂×D₄₇	—	2	1	no	—
22	C₂×D₄₇	—	4	2	no	—
23	C₂×D₄₇	D₄	1	1	yes	characteristic
24	C₄×C₄₇	C₂³	1	1	yes	characteristic
25	Dic₄₇	—	2	1	no	—
26	Dic₄₇	D₄	1	1	yes	characteristic
27	C₂×C₄₇	—	4	1	no	—
28	C₂×C₄₇	—	4	1	no	—
29	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
30	D₄₇	—	2	1	no	—
31	D₄₇	—	4	1	no	—
32	C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
33	AGL(1,ℤ/8)	—	47	1	no	maximal, Sylow
34	#41	—	47	1	no	—
35	C₂×D₄	—	47	1	no	—
36	SD₁₆	—	47	1	no	—
37	SD₁₆	—	47	1	no	—
38	D₈	—	47	1	no	—
39	D₈	D₄₇	1	1	yes	characteristic, complemented
40	M₁₆	—	47	1	no	—
41	C₂³	—	94	1	no	—
42	Q₈	—	47	1	no	—
43	D₄	—	47	1	no	—
44	D₄	—	94	1	no	—
45	D₄	—	94	1	no	—
46	D₄	C₂×D₄₇	1	1	yes	characteristic
47	D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
48	C₂×C₄	—	47	1	no	—
49	C₂×C₄	—	94	1	no	—
50	C₈	—	47	1	no	—
51	C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
52	C₂²	—	2	1	no	—
53	C₂²	—	2	1	no	—
54	C₂²	—	47	1	no	—
55	C₂²	—	94	1	no	—
56	C₂²	—	188	2	no	—
57	C₄	—	47	1	no	—
58	C₄	—	94	1	no	—
59	C₄	C₂²×D₄₇	1	1	yes	characteristic
60	C₂	—	4	1	no	—
61	C₂	—	4	1	no	—
62	C₂	—	94	1	no	—
63	C₂	—	188	1	no	—
64	C₂	D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₄₇
commutator, cosocle	C₄×C₄₇	C₂³
Frattini	C₄	C₂²×D₄₇
Fitting	D₈×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₄
hypercenter	D₈	D₄₇
hypocenter	C₄₇	AGL(1,ℤ/8)
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #10625352	C₂	semidirect
2. D₄×D₄₇	C₂	semidirect
3. D₈×C₄₇	C₂	semidirect
4. #10625335	C₂	semidirect
5. #10625334	C₂	semidirect
6. #10625325	C₂	semidirect
7. #10625324	C₂	semidirect
10. D₄×C₄₇	C₂²	semidirect
16. Dic₉₄	C₂²	semidirect
17. C₈×C₄₇	C₂²	semidirect
18. C₄₇⋊C₈	C₂²	semidirect
32. C₄₇	AGL(1,ℤ/8)	semidirect
39. D₈	D₄₇	semidirect
47. D₄	C₂×D₄₇	semidirect
51. C₈	C₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#10625352	2
D₄×D₄₇	2
D₈×C₄₇	2
#10625335	2
#10625334	2
#10625325	2
#10625324	2
AGL(1,ℤ/8)	47