Subgroups — SD₃₂×D₄₉₁ #44537147

Order 31424.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₄₉₁	C₂	1	1	yes	maximal, characteristic
3	#30628282	C₂	1	1	yes	maximal, characteristic, complemented
4	#30628281	C₂	1	1	yes	maximal, characteristic, complemented
5	#30628280	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×D₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₄₉₁	—	2	1	no	—
9	D₄×D₄₉₁	—	2	1	no	—
10	Dic₁₉₆₄	C₂²	1	1	yes	characteristic, complemented
11	#21463318	—	2	1	no	—
12	D₃₉₂₈	C₂²	1	1	yes	characteristic
13	#21463313	—	2	1	no	—
14	C₈×D₄₉₁	C₂²	1	1	yes	characteristic
15	C₄₉₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
16	Q₁₆×C₄₉₁	C₂²	1	1	yes	characteristic, complemented
17	D₈×C₄₉₁	C₂²	1	1	yes	characteristic
18	C₁₆×C₄₉₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄₉₁	—	4	1	no	—
20	Dic₉₈₂	—	2	1	no	—
21	Dic₉₈₂	—	4	1	no	—
22	D₁₉₆₄	—	2	1	no	—
23	C₂²⋊D₄₉₁	—	4	1	no	—
24	C₄×D₄₉₁	—	4	1	no	—
25	C₄×D₄₉₁	D₄	1	1	yes	characteristic
26	C₄₉₁⋊C₈	D₄	1	1	yes	characteristic
27	Q₈×C₄₉₁	—	2	1	no	—
28	D₄×C₄₉₁	—	2	1	no	—
29	C₈×C₄₉₁	C₂³	1	1	yes	characteristic
30	C₂²×C₄₉₁	—	4	1	no	—
31	C₂×D₄₉₁	—	4	1	no	—
32	C₂×D₄₉₁	—	8	2	no	—
33	C₂×D₄₉₁	D₈	1	1	yes	characteristic
34	C₄×C₄₉₁	—	4	1	no	—
35	C₄×C₄₉₁	C₂×D₄	1	1	yes	characteristic
36	Dic₄₉₁	—	4	1	no	—
37	Dic₄₉₁	D₈	1	1	yes	characteristic
38	C₂×C₄₉₁	—	8	1	no	—
39	C₂×C₄₉₁	C₂×D₈	1	1	yes	characteristic
40	D₄₉₁	—	8	1	no	—
41	D₄₉₁	SD₃₂	1	2	yes	direct product factor
42	C₄₉₁	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂×SD₃₂	—	491	1	no	maximal, Sylow
44	C₂×Q₁₆	—	491	1	no	—
45	C₂×D₈	—	491	1	no	—
46	SD₃₂	—	491	1	no	—
47	SD₃₂	—	491	1	no	—
48	SD₃₂	—	491	1	no	—
49	SD₃₂	D₄₉₁	1	1	yes	characteristic, direct product factor
50	C₂×C₁₆	—	491	1	no	—
51	C₂×Q₈	—	982	1	no	—
52	C₂×D₄	—	982	1	no	—
53	Q₁₆	—	982	1	no	—
54	Q₁₆	—	491	1	no	—
55	Q₁₆	C₂×D₄₉₁	1	1	yes	characteristic, complemented
56	D₈	—	982	1	no	—
57	D₈	—	491	1	no	—
58	D₈	C₂×D₄₉₁	1	1	yes	characteristic
59	C₂×C₈	—	491	1	no	—
60	C₁₆	—	491	1	no	—
61	C₁₆	C₂×D₄₉₁	1	1	yes	characteristic, complemented
62	C₂³	—	1964	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	1964	1	no	—
65	Q₈	—	982	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	1964	1	no	—
68	D₄	—	982	1	no	—
69	C₂×C₄	—	1964	1	no	—
70	C₂×C₄	—	491	1	no	—
71	C₈	—	491	1	no	—
72	C₈	C₂²×D₄₉₁	1	1	yes	characteristic
73	C₂²	—	4	1	no	—
74	C₂²	—	3928	2	no	—
75	C₂²	—	1964	1	no	—
76	C₂²	—	491	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	1964	1	no	—
79	C₄	—	491	1	no	—
80	C₄	D₄×D₄₉₁	1	1	yes	characteristic
81	C₂	—	8	1	no	—
82	C₂	—	3928	1	no	—
83	C₂	—	491	2	no	—
84	C₂	D₈×D₄₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₉₁
commutator, cosocle	C₈×C₄₉₁	C₂³
Frattini	C₈	C₂²×D₄₉₁
Fitting	SD₃₂×C₄₉₁	C₂
socle	C₂×C₄₉₁	C₂×D₈
prime radical	D₈×D₄₉₁	C₂
hypercenter	SD₃₂	D₄₉₁
hypocenter	C₄₉₁	C₂×SD₃₂
LCS	G ▷ C₈×C₄₉₁ ▷ C₄×C₄₉₁ ▷ C₂×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×D₄₉₁	C₂	semidirect
3. #30628282	C₂	semidirect
4. #30628281	C₂	semidirect
5. #30628280	C₂	semidirect
6. C₁₆×D₄₉₁	C₂	semidirect
7. SD₃₂×C₄₉₁	C₂	semidirect
10. Dic₁₉₆₄	C₂²	semidirect
15. C₄₉₁⋊C₁₆	C₂²	semidirect
16. Q₁₆×C₄₉₁	C₂²	semidirect
18. C₁₆×C₄₉₁	C₂²	semidirect
41. D₄₉₁	SD₃₂	direct (N × H)
42. C₄₉₁	C₂×SD₃₂	semidirect
49. SD₃₂	D₄₉₁	direct (N × H)
55. Q₁₆	C₂×D₄₉₁	semidirect
61. C₁₆	C₂×D₄₉₁	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×D₄₉₁	2
D₈×D₄₉₁	2
#30628282	2
#30628281	2
#30628280	2
C₁₆×D₄₉₁	2
SD₃₂×C₄₉₁	2
C₂×SD₃₂	491

Subgroups — SD32×D491 #44537147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₃₂×D₄₉₁ #44537147