Subgroups — #44476274

Order 30304.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29502984	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₉₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#29502974	C₂	1	1	yes	maximal, characteristic, complemented
4	#29502973	C₂	1	1	yes	maximal, characteristic, complemented
5	#29502970	C₂	1	1	yes	maximal, characteristic, complemented
6	#29502968	C₂	1	1	yes	maximal, characteristic, complemented
7	D₈×C₉₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₉₄₇	—	2	1	no	—
9	Dic₁₈₉₄	C₂²	1	1	yes	characteristic, complemented
10	D₃₇₈₈	C₂²	1	1	yes	characteristic
11	C₂²⋊D₉₄₇	—	2	1	no	—
12	C₂²⋊D₉₄₇	—	2	1	no	—
13	C₂×Dic₉₄₇	—	2	1	no	—
14	C₄×D₉₄₇	C₂²	1	1	yes	characteristic
15	C₉₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
16	D₄×C₉₄₇	C₂²	1	1	yes	characteristic
17	D₄×C₉₄₇	C₂²	1	1	yes	characteristic, complemented
18	C₈×C₉₄₇	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₉₄₇	—	2	1	no	—
20	C₂²×C₉₄₇	—	2	1	no	—
21	C₂×D₉₄₇	—	2	1	no	—
22	C₂×D₉₄₇	—	4	2	no	—
23	C₂×D₉₄₇	D₄	1	1	yes	characteristic
24	C₄×C₉₄₇	C₂³	1	1	yes	characteristic
25	Dic₉₄₇	—	2	1	no	—
26	Dic₉₄₇	D₄	1	1	yes	characteristic
27	C₂×C₉₄₇	—	4	1	no	—
28	C₂×C₉₄₇	—	4	1	no	—
29	C₂×C₉₄₇	C₂×D₄	1	1	yes	characteristic
30	D₉₄₇	—	2	1	no	—
31	D₉₄₇	—	4	1	no	—
32	C₉₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
33	AGL(1,ℤ/8)	—	947	1	no	maximal, Sylow
34	#41	—	947	1	no	—
35	C₂×D₄	—	947	1	no	—
36	SD₁₆	—	947	1	no	—
37	SD₁₆	—	947	1	no	—
38	D₈	—	947	1	no	—
39	D₈	D₉₄₇	1	1	yes	characteristic, complemented
40	M₁₆	—	947	1	no	—
41	C₂³	—	1894	1	no	—
42	Q₈	—	947	1	no	—
43	D₄	—	1894	1	no	—
44	D₄	—	1894	1	no	—
45	D₄	—	947	1	no	—
46	D₄	C₂×D₉₄₇	1	1	yes	characteristic
47	D₄	C₂×D₉₄₇	1	1	yes	characteristic, complemented
48	C₂×C₄	—	1894	1	no	—
49	C₂×C₄	—	947	1	no	—
50	C₈	—	947	1	no	—
51	C₈	C₂×D₉₄₇	1	1	yes	characteristic, complemented
52	C₂²	—	2	1	no	—
53	C₂²	—	2	1	no	—
54	C₂²	—	1894	1	no	—
55	C₂²	—	947	1	no	—
56	C₂²	—	3788	2	no	—
57	C₄	—	1894	1	no	—
58	C₄	—	947	1	no	—
59	C₄	C₂²×D₉₄₇	1	1	yes	characteristic
60	C₂	—	4	1	no	—
61	C₂	—	4	1	no	—
62	C₂	—	1894	1	no	—
63	C₂	—	3788	1	no	—
64	C₂	D₄×D₉₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₉₄₇
commutator, cosocle	C₄×C₉₄₇	C₂³
Frattini	C₄	C₂²×D₉₄₇
Fitting	D₈×C₉₄₇	C₂
socle	C₂×C₉₄₇	C₂×D₄
hypercenter	D₈	D₉₄₇
hypocenter	C₉₄₇	AGL(1,ℤ/8)
LCS	G ▷ C₄×C₉₄₇ ▷ C₂×C₉₄₇ ▷ C₉₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #29502984	C₂	semidirect
2. D₄×D₉₄₇	C₂	semidirect
3. #29502974	C₂	semidirect
4. #29502973	C₂	semidirect
5. #29502970	C₂	semidirect
6. #29502968	C₂	semidirect
7. D₈×C₉₄₇	C₂	semidirect
9. Dic₁₈₉₄	C₂²	semidirect
15. C₉₄₇⋊C₈	C₂²	semidirect
17. D₄×C₉₄₇	C₂²	semidirect
18. C₈×C₉₄₇	C₂²	semidirect
32. C₉₄₇	AGL(1,ℤ/8)	semidirect
39. D₈	D₉₄₇	semidirect
47. D₄	C₂×D₉₄₇	semidirect
51. C₈	C₂×D₉₄₇	semidirect

Maximal subgroups

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

subgroup	index
#29502984	2
D₄×D₉₄₇	2
#29502974	2
#29502973	2
#29502970	2
#29502968	2
D₈×C₉₄₇	2
AGL(1,ℤ/8)	947