Subgroups — #34094530

Order 20032.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#19097551	C₂	1	2	yes	maximal
3	#23756495	C₂	1	2	yes	maximal
4	C₈×Dic₃₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₃₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₆₂₆	C₂²	1	2	yes	—
7	Dic₁₂₅₂	—	2	2	no	—
8	#19097551	—	2	4	no	—
9	C₂×#14578809	C₂²	1	1	yes	characteristic
10	#19097540	—	2	4	no	—
11	C₄×Dic₃₁₃	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₃₁₃	C₂²	1	2	yes	—
13	Q₁₆×C₃₁₃	—	2	2	no	—
14	C₂×C₈×C₃₁₃	C₂²	1	1	yes	characteristic
15	Dic₆₂₆	—	2	2	no	—
16	Dic₆₂₆	—	2	2	no	—
17	C₂×Dic₃₁₃	—	2	2	no	—
18	C₂×Dic₃₁₃	D₄	1	2	yes	—
19	#14578809	D₄	1	2	yes	—
20	Q₈×C₃₁₃	—	2	2	no	—
21	Q₈×C₃₁₃	—	2	2	no	—
22	C₂×C₄×C₃₁₃	—	2	2	no	—
23	C₂×C₄×C₃₁₃	C₂³	1	1	yes	characteristic
24	C₈×C₃₁₃	D₄	1	2	yes	—
25	C₂²×C₃₁₃	C₂×D₄	1	1	yes	characteristic
26	C₄×C₃₁₃	—	4	2	no	—
27	C₄×C₃₁₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₃₁₃	C₂×D₄	1	1	yes	characteristic
29	Dic₃₁₃	—	4	2	no	—
30	Dic₃₁₃	Q₁₆	1	4	yes	complemented
31	C₂×C₃₁₃	#127	1	1	yes	characteristic
32	C₂×C₃₁₃	C₂×Q₁₆	1	2	yes	—
33	C₃₁₃	#494	1	1	yes	characteristic, complemented, Sylow
34	#494	—	313	1	no	maximal, Sylow
35	C₂×Q₁₆	—	313	2	no	—
36	C₂×Q₁₆	—	313	1	no	—
37	C₂×Q₁₆	D₃₁₃	1	1	yes	characteristic
38	C₄⋊Q₈	—	313	2	no	—
39	C₄×C₈	—	313	1	no	—
40	C₂×Q₈	—	313	2	no	—
41	C₂×Q₈	C₂×D₃₁₃	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	626	4	no	—
44	Q₁₆	—	626	2	no	—
45	C₂×C₈	—	313	1	no	—
46	C₂×C₈	C₂×D₃₁₃	1	1	yes	characteristic
47	C₄⋊C₄	—	626	4	no	—
48	C₄²	—	313	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	626	2	no	—
52	Q₈	—	626	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	313	2	no	—
55	C₂×C₄	—	626	2	no	—
56	C₂×C₄	C₂²×D₃₁₃	1	1	yes	characteristic
57	C₈	—	313	2	no	—
58	C₈	C₂²⋊D₃₁₃	1	2	yes	—
59	C₂²	D₄×D₃₁₃	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	313	4	no	—
62	C₄	—	1252	2	no	—
63	C₄	D₄×D₃₁₃	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₃₁₃	1	1	yes	characteristic
65	C₂	#23756493	1	1	yes	characteristic
66	C₂	Q₁₆×D₃₁₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₃₁₃
commutator, cosocle	C₂×C₄×C₃₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₁₃
Fitting	C₂×Q₁₆×C₃₁₃	C₂
socle, prime radical	C₂²×C₃₁₃	C₂×D₄
hypercenter	C₂×Q₁₆	D₃₁₃
hypocenter	C₃₁₃	#494
LCS	G ▷ C₂×C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
30. Dic₃₁₃	Q₁₆	semidirect
33. C₃₁₃	#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₂₅₂	2
C₂×#19097551	2
#23756495	2
C₈×Dic₃₁₃	2
C₂×Q₁₆×C₃₁₃	2
#494	313