Subgroups — #44537166

Order 31424.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30628359	C₂	1	1	yes	maximal, characteristic
2	#30628283	C₂	1	2	yes	maximal, complemented
3	#30628280	C₂	1	2	yes	maximal, complemented
4	#30628277	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#21463328	—	2	1	no	—
7	Dic₁₉₆₄	C₂²	1	1	yes	characteristic
8	#21463317	—	2	1	no	—
9	D₃₉₂₈	C₂²	1	1	yes	characteristic
10	C₄₉₁⋊C₁₆	C₂²	1	2	yes	—
11	C₂×Q₈×C₄₉₁	—	2	1	no	—
12	Q₁₆×C₄₉₁	—	2	1	no	—
13	Q₁₆×C₄₉₁	C₂²	1	2	yes	—
14	C₂×C₈×C₄₉₁	C₂²	1	1	yes	characteristic
15	Dic₉₈₂	—	2	1	no	—
16	D₁₉₆₄	—	2	1	no	—
17	C₂²⋊D₄₉₁	—	4	1	no	—
18	C₄×D₄₉₁	—	4	1	no	—
19	Q₈×C₄₉₁	—	2	2	no	—
20	Q₈×C₄₉₁	—	4	1	no	—
21	C₂×C₄×C₄₉₁	—	4	1	no	—
22	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
23	C₈×C₄₉₁	D₄	1	1	yes	characteristic
24	C₈×C₄₉₁	C₂³	1	1	yes	characteristic
25	C₂²×C₄₉₁	D₈	1	1	yes	characteristic
26	C₂×D₄₉₁	—	4	1	no	—
27	C₄×C₄₉₁	—	4	2	no	—
28	C₄×C₄₉₁	D₈	1	1	yes	characteristic
29	C₄×C₄₉₁	C₂×D₄	1	1	yes	characteristic
30	Dic₄₉₁	—	4	1	no	—
31	C₂×C₄₉₁	—	2	1	no	—
32	C₂×C₄₉₁	C₂×D₈	1	1	yes	characteristic
33	D₄₉₁	—	8	1	no	—
34	C₄₉₁	#510	1	1	yes	characteristic, complemented, Sylow
35	#510	—	491	1	no	maximal, Sylow
36	#135	—	491	1	no	—
37	C₂×Q₁₆	D₄₉₁	1	1	yes	characteristic, complemented
38	Q₃₂	—	491	2	no	—
39	SD₃₂	—	491	2	no	—
40	M₃₂	—	491	1	no	—
41	#41	—	982	1	no	—
42	C₂×Q₈	—	2	1	no	—
43	Q₁₆	—	2	1	no	—
44	Q₁₆	—	491	1	no	—
45	Q₁₆	C₂×D₄₉₁	1	2	yes	—
46	SD₁₆	—	982	1	no	—
47	D₈	—	491	1	no	—
48	C₂×C₈	C₂×D₄₉₁	1	1	yes	characteristic
49	C₁₆	—	491	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	4	1	no	—
52	Q₈	—	982	1	no	—
53	D₄	—	1964	1	no	—
54	D₄	—	982	1	no	—
55	C₂×C₄	—	4	1	no	—
56	C₂×C₄	—	1964	1	no	—
57	C₂×C₄	C₂²⋊D₄₉₁	1	1	yes	characteristic
58	C₈	C₂²⋊D₄₉₁	1	1	yes	characteristic
59	C₈	C₂²×D₄₉₁	1	1	yes	characteristic
60	C₂²	—	1964	1	no	—
61	C₂²	#21463313	1	1	yes	characteristic
62	C₄	—	4	2	no	—
63	C₄	—	1964	1	no	—
64	C₄	#21463313	1	1	yes	characteristic
65	C₄	C₂×C₂²⋊D₄₉₁	1	1	yes	characteristic
66	C₂	—	2	1	no	—
67	C₂	—	3928	1	no	—
68	C₂	C₂×#21463313	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#21463313
commutator, cosocle	C₈×C₄₉₁	C₂³
Frattini	C₈	C₂²×D₄₉₁
Fitting	C₂×Q₁₆×C₄₉₁	C₂
socle	C₂×C₄₉₁	C₂×D₈
prime radical	#30628359	C₂
hypercenter	C₂×Q₁₆	D₄₉₁
hypocenter	C₄₉₁	#510
LCS	G ▷ C₈×C₄₉₁ ▷ C₄×C₄₉₁ ▷ C₂×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #30628283	C₂	semidirect
3. #30628280	C₂	semidirect
4. #30628277	C₂	semidirect
5. C₂×Q₁₆×C₄₉₁	C₂	semidirect
34. C₄₉₁	#510	semidirect
37. C₂×Q₁₆	D₄₉₁	semidirect

Maximal subgroups

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

subgroup	index
#30628359	2
#30628283	2
#30628280	2
#30628277	2
C₂×Q₁₆×C₄₉₁	2
#510	491