Subgroups — #34094531

Order 20032.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19097551	C₂	1	4	yes	maximal
2	#23756497	C₂	1	1	yes	maximal, characteristic
3	C₄×#14578809	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₃₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₆₂₆	C₂²	1	2	yes	—
6	#19097551	—	2	8	no	—
7	C₂×#14578809	C₂²	1	2	yes	—
8	C₄⋊Dic₃₁₃	—	2	2	no	—
9	C₂×Q₈×C₃₁₃	C₂²	1	2	yes	—
10	C₄⋊C₄×C₃₁₃	—	2	2	no	—
11	C₄²×C₃₁₃	C₂²	1	1	yes	characteristic
12	Dic₆₂₆	—	2	4	no	—
13	C₂×Dic₃₁₃	—	2	2	no	—
14	#14578809	D₄	1	4	yes	—
15	Q₈×C₃₁₃	—	2	4	no	—
16	C₂×C₄×C₃₁₃	—	2	2	no	—
17	C₂×C₄×C₃₁₃	D₄	1	2	yes	—
18	C₂×C₄×C₃₁₃	C₂³	1	1	yes	characteristic
19	C₂²×C₃₁₃	C₂×D₄	1	1	yes	characteristic
20	C₄×C₃₁₃	—	4	2	no	—
21	C₄×C₃₁₃	Q₁₆	1	4	yes	complemented
22	C₄×C₃₁₃	C₂×D₄	1	2	yes	—
23	Dic₃₁₃	—	4	2	no	—
24	C₂×C₃₁₃	#127	1	1	yes	characteristic
25	C₂×C₃₁₃	C₂×Q₁₆	1	2	yes	—
26	C₃₁₃	#494	1	1	yes	characteristic, complemented, Sylow
27	#494	—	313	1	no	maximal, Sylow
28	C₂×Q₁₆	—	313	4	no	—
29	C₄⋊Q₈	—	313	1	no	—
30	C₄⋊Q₈	D₃₁₃	1	1	yes	characteristic
31	C₄×C₈	—	313	1	no	—
32	C₂×Q₈	—	313	2	no	—
33	C₂×Q₈	C₂×D₃₁₃	1	2	yes	—
34	Q₁₆	—	626	8	no	—
35	C₂×C₈	—	313	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	626	2	no	—
38	C₄²	C₂×D₃₁₃	1	1	yes	characteristic
39	Q₈	—	2	4	no	—
40	Q₈	—	626	4	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	626	2	no	—
43	C₂×C₄	C₂²⋊D₃₁₃	1	2	yes	—
44	C₂×C₄	C₂²×D₃₁₃	1	1	yes	characteristic
45	C₈	—	313	4	no	—
46	C₂²	C₂×C₂²⋊D₃₁₃	1	1	yes	characteristic
47	C₄	—	4	2	no	—
48	C₄	—	1252	2	no	—
49	C₄	#19097551	1	4	yes	complemented
50	C₄	D₄×D₃₁₃	1	2	yes	—
51	C₂	#23756493	1	1	yes	characteristic
52	C₂	C₂×#19097551	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁₃
commutator, cosocle	C₂×C₄×C₃₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₁₃
Fitting	C₄⋊Q₈×C₃₁₃	C₂
socle, prime radical	C₂²×C₃₁₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₃₁₃
hypocenter	C₃₁₃	#494
LCS	G ▷ C₂×C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
21. C₄×C₃₁₃	Q₁₆	semidirect
26. C₃₁₃	#494	semidirect
49. C₄	#19097551	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19097551	2
#23756497	2
C₄×#14578809	2
C₄⋊Q₈×C₃₁₃	2
#494	313