Subgroups — #44537072

Order 31424.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30628337	C₂	1	1	yes	maximal, characteristic, complemented
2	#30628334	C₂	1	1	yes	maximal, characteristic
3	#30628259	C₂	1	4	yes	maximal, complemented
4	C₄×C₈×C₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₉₈₂	—	2	1	no	—
6	C₂×D₁₉₆₄	—	2	1	no	—
7	C₂×D₁₉₆₄	—	2	1	no	—
8	C₂×D₁₉₆₄	C₂²	1	2	yes	—
9	C₄⋊Dic₄₉₁	—	2	1	no	—
10	C₄⋊Dic₄₉₁	C₂²	1	2	yes	—
11	C₂×C₈×C₄₉₁	C₂²	1	2	yes	—
12	C₄²×C₄₉₁	C₂²	1	1	yes	characteristic
13	C₂²×D₄₉₁	—	2	2	no	—
14	Dic₉₈₂	—	4	2	no	—
15	D₁₉₆₄	—	2	4	no	—
16	D₁₉₆₄	—	4	2	no	—
17	D₁₉₆₄	—	4	2	no	—
18	C₂×Dic₄₉₁	—	2	2	no	—
19	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₉₁	C₂³	1	1	yes	characteristic
22	C₈×C₄₉₁	—	2	2	no	—
23	C₂²×C₄₉₁	C₂×D₄	1	1	yes	characteristic
24	C₂×D₄₉₁	—	4	2	no	—
25	C₂×D₄₉₁	—	4	2	no	—
26	C₂×D₄₉₁	—	4	2	no	—
27	C₄×C₄₉₁	D₈	1	2	yes	—
28	C₄×C₄₉₁	SD₁₆	1	2	yes	—
29	C₄×C₄₉₁	#41	1	2	yes	—
30	Dic₄₉₁	—	4	2	no	—
31	C₂×C₄₉₁	#124	1	1	yes	characteristic
32	C₂×C₄₉₁	C₂×D₈	1	1	yes	characteristic
33	C₂×C₄₉₁	C₂×SD₁₆	1	1	yes	characteristic
34	D₄₉₁	—	8	2	no	—
35	C₄₉₁	#486	1	1	yes	characteristic, complemented, Sylow
36	#486	—	491	1	no	maximal, Sylow
37	C₄⋊Q₈	—	491	1	no	—
38	#127	—	491	1	no	—
39	#102	—	491	4	no	—
40	C₄×C₈	D₄₉₁	1	1	yes	characteristic, complemented
41	C₂×Q₈	—	982	1	no	—
42	C₂×D₄	—	982	1	no	—
43	C₂×D₄	—	982	1	no	—
44	C₂×D₄	—	491	2	no	—
45	C₂×C₈	C₂×D₄₉₁	1	2	yes	—
46	C₄⋊C₄	—	982	1	no	—
47	C₄⋊C₄	—	491	2	no	—
48	C₄²	C₂×D₄₉₁	1	1	yes	characteristic
49	C₂³	—	982	2	no	—
50	Q₈	—	1964	2	no	—
51	D₄	—	1964	2	no	—
52	D₄	—	1964	2	no	—
53	D₄	—	982	4	no	—
54	C₂×C₄	—	982	2	no	—
55	C₂×C₄	D₁₉₆₄	1	1	yes	characteristic
56	C₂×C₄	D₁₉₆₄	1	1	yes	characteristic
57	C₂×C₄	C₂²×D₄₉₁	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₂²	—	1964	2	no	—
60	C₂²	—	1964	2	no	—
61	C₂²	—	1964	2	no	—
62	C₂²	C₂×D₁₉₆₄	1	1	yes	characteristic
63	C₄	—	1964	2	no	—
64	C₄	D₃₉₂₈	1	2	yes	—
65	C₄	#21463317	1	2	yes	—
66	C₄	#21463328	1	2	yes	—
67	C₂	—	3928	2	no	—
68	C₂	#30628325	1	1	yes	characteristic
69	C₂	C₂×D₃₉₂₈	1	1	yes	characteristic
70	C₂	C₂×#21463317	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₉₆₄
commutator, cosocle	C₂×C₄×C₄₉₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₉₁
Fitting	C₄×C₈×C₄₉₁	C₂
socle	C₂²×C₄₉₁	C₂×D₄
prime radical	#30628334	C₂
hypercenter	C₄×C₈	D₄₉₁
hypocenter	C₄₉₁	#486
LCS	G ▷ C₂×C₄×C₄₉₁ ▷ C₂×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #30628337	C₂	semidirect
3. #30628259	C₂	semidirect
4. C₄×C₈×C₄₉₁	C₂	semidirect
35. C₄₉₁	#486	semidirect
40. C₄×C₈	D₄₉₁	semidirect

Maximal subgroups

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

subgroup	index
#30628337	2
#30628334	2
#30628259	2
C₄×C₈×C₄₉₁	2
#486	491