Subgroups — #44527175

Order 31072.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29509488	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₉₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#29509478	C₂	1	1	yes	maximal, characteristic, complemented
4	#29509477	C₂	1	1	yes	maximal, characteristic, complemented
5	#29509474	C₂	1	1	yes	maximal, characteristic, complemented
6	#29509472	C₂	1	1	yes	maximal, characteristic, complemented
7	D₈×C₉₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₉₇₁	—	2	1	no	—
9	Dic₁₉₄₂	C₂²	1	1	yes	characteristic, complemented
10	D₃₈₈₄	C₂²	1	1	yes	characteristic
11	C₂²⋊D₉₇₁	—	2	1	no	—
12	C₂²⋊D₉₇₁	—	2	1	no	—
13	C₂×Dic₉₇₁	—	2	1	no	—
14	C₄×D₉₇₁	C₂²	1	1	yes	characteristic
15	C₉₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
16	D₄×C₉₇₁	C₂²	1	1	yes	characteristic
17	D₄×C₉₇₁	C₂²	1	1	yes	characteristic, complemented
18	C₈×C₉₇₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₉₇₁	—	2	1	no	—
20	C₂²×C₉₇₁	—	2	1	no	—
21	C₂×D₉₇₁	—	2	1	no	—
22	C₂×D₉₇₁	—	4	2	no	—
23	C₂×D₉₇₁	D₄	1	1	yes	characteristic
24	C₄×C₉₇₁	C₂³	1	1	yes	characteristic
25	Dic₉₇₁	—	2	1	no	—
26	Dic₉₇₁	D₄	1	1	yes	characteristic
27	C₂×C₉₇₁	—	4	1	no	—
28	C₂×C₉₇₁	—	4	1	no	—
29	C₂×C₉₇₁	C₂×D₄	1	1	yes	characteristic
30	D₉₇₁	—	2	1	no	—
31	D₉₇₁	—	4	1	no	—
32	C₉₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
33	AGL(1,ℤ/8)	—	971	1	no	maximal, Sylow
34	#41	—	971	1	no	—
35	C₂×D₄	—	971	1	no	—
36	SD₁₆	—	971	1	no	—
37	SD₁₆	—	971	1	no	—
38	D₈	—	971	1	no	—
39	D₈	D₉₇₁	1	1	yes	characteristic, complemented
40	M₁₆	—	971	1	no	—
41	C₂³	—	1942	1	no	—
42	Q₈	—	971	1	no	—
43	D₄	—	1942	1	no	—
44	D₄	—	1942	1	no	—
45	D₄	—	971	1	no	—
46	D₄	C₂×D₉₇₁	1	1	yes	characteristic
47	D₄	C₂×D₉₇₁	1	1	yes	characteristic, complemented
48	C₂×C₄	—	1942	1	no	—
49	C₂×C₄	—	971	1	no	—
50	C₈	—	971	1	no	—
51	C₈	C₂×D₉₇₁	1	1	yes	characteristic, complemented
52	C₂²	—	2	1	no	—
53	C₂²	—	2	1	no	—
54	C₂²	—	3884	2	no	—
55	C₂²	—	1942	1	no	—
56	C₂²	—	971	1	no	—
57	C₄	—	1942	1	no	—
58	C₄	—	971	1	no	—
59	C₄	C₂²×D₉₇₁	1	1	yes	characteristic
60	C₂	—	4	1	no	—
61	C₂	—	4	1	no	—
62	C₂	—	3884	1	no	—
63	C₂	—	1942	1	no	—
64	C₂	D₄×D₉₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₉₇₁
commutator, cosocle	C₄×C₉₇₁	C₂³
Frattini	C₄	C₂²×D₉₇₁
Fitting	D₈×C₉₇₁	C₂
socle	C₂×C₉₇₁	C₂×D₄
hypercenter	D₈	D₉₇₁
hypocenter	C₉₇₁	AGL(1,ℤ/8)
LCS	G ▷ C₄×C₉₇₁ ▷ C₂×C₉₇₁ ▷ C₉₇₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #29509488	C₂	semidirect
2. D₄×D₉₇₁	C₂	semidirect
3. #29509478	C₂	semidirect
4. #29509477	C₂	semidirect
5. #29509474	C₂	semidirect
6. #29509472	C₂	semidirect
7. D₈×C₉₇₁	C₂	semidirect
9. Dic₁₉₄₂	C₂²	semidirect
15. C₉₇₁⋊C₈	C₂²	semidirect
17. D₄×C₉₇₁	C₂²	semidirect
18. C₈×C₉₇₁	C₂²	semidirect
32. C₉₇₁	AGL(1,ℤ/8)	semidirect
39. D₈	D₉₇₁	semidirect
47. D₄	C₂×D₉₇₁	semidirect
51. C₈	C₂×D₉₇₁	semidirect

Maximal subgroups

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

subgroup	index
#29509488	2
D₄×D₉₇₁	2
#29509478	2
#29509477	2
#29509474	2
#29509472	2
D₈×C₉₇₁	2
AGL(1,ℤ/8)	971