Subgroups — #34094445

Order 20032.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23756496	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₃₁₃	C₂	1	1	yes	maximal, characteristic
3	#23756431	C₂	1	1	yes	maximal, characteristic
4	#23756430	C₂	1	1	yes	maximal, characteristic
5	#23756426	C₂	1	1	yes	maximal, characteristic
6	#23756421	C₂	1	1	yes	maximal, characteristic
7	#103×C₃₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₆₂₆	—	2	1	no	—
9	C₂×#14578809	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃₁₃	—	2	1	no	—
11	C₄⋊Dic₃₁₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃₁₃	C₂²	1	1	yes	characteristic
13	#19097540	—	2	1	no	—
14	C₄×Dic₃₁₃	—	2	1	no	—
15	C₄×Dic₃₁₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₃₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₃₁₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₃₁₃	C₂²	1	1	yes	characteristic
19	Dic₆₂₆	—	4	2	no	—
20	C₂×Dic₃₁₃	—	2	1	no	—
21	C₂×Dic₃₁₃	—	2	1	no	—
22	C₂×Dic₃₁₃	D₄	1	1	yes	characteristic
23	C₂×Dic₃₁₃	D₄	1	1	yes	characteristic
24	#14578809	—	2	1	no	—
25	Q₈×C₃₁₃	—	2	1	no	—
26	Q₈×C₃₁₃	Q₈	1	2	yes	complemented
27	C₂×C₄×C₃₁₃	—	2	1	no	—
28	C₂×C₄×C₃₁₃	—	2	1	no	—
29	C₂×C₄×C₃₁₃	C₂³	1	1	yes	characteristic
30	C₈×C₃₁₃	—	2	1	no	—
31	C₂²×C₃₁₃	C₂×D₄	1	1	yes	characteristic
32	C₄×C₃₁₃	—	2	2	no	—
33	C₄×C₃₁₃	—	4	1	no	—
34	C₄×C₃₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₃₁₃	#41	1	1	yes	characteristic
36	Dic₃₁₃	—	2	1	no	—
37	Dic₃₁₃	—	4	1	no	—
38	Dic₃₁₃	—	4	1	no	—
39	Dic₃₁₃	Q₁₆	1	2	yes	—
40	C₂×C₃₁₃	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₃₁₃	C₂×Q₁₆	1	1	yes	characteristic
42	C₂×C₃₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₃₁₃	#477	1	1	yes	characteristic, complemented, Sylow
44	#477	—	313	1	no	maximal, Sylow
45	C₄⋊Q₈	—	313	1	no	—
46	C₄×Q₈	—	313	1	no	—
47	#107	—	313	1	no	—
48	#107	—	313	1	no	—
49	C₄⋊C₈	—	313	1	no	—
50	#103	—	313	1	no	—
51	#103	D₃₁₃	1	1	yes	characteristic
52	C₂×Q₈	—	626	1	no	—
53	C₂×Q₈	C₂×D₃₁₃	1	1	yes	characteristic
54	C₂×C₈	—	313	1	no	—
55	C₂×C₈	C₂×D₃₁₃	1	1	yes	characteristic
56	C₄⋊C₄	—	313	1	no	—
57	C₄⋊C₄	—	313	1	no	—
58	C₄⋊C₄	—	626	1	no	—
59	C₄⋊C₄	—	626	1	no	—
60	C₄⋊C₄	C₂×D₃₁₃	1	1	yes	characteristic
61	C₄²	—	313	1	no	—
62	C₄²	—	626	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	1252	2	no	—
65	Q₈	Dic₆₂₆	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	313	1	no	—
69	C₂×C₄	—	313	1	no	—
70	C₂×C₄	—	626	1	no	—
71	C₂×C₄	—	626	1	no	—
72	C₂×C₄	C₂²×D₃₁₃	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	626	1	no	—
75	C₂²	D₄×D₃₁₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	313	2	no	—
79	C₄	—	626	1	no	—
80	C₄	—	1252	1	no	—
81	C₄	—	1252	1	no	—
82	C₄	C₂×Dic₆₂₆	1	1	yes	characteristic
83	C₄	#19097560	1	1	yes	characteristic
84	C₂	#23756474	1	1	yes	characteristic
85	C₂	Q₁₆×D₃₁₃	1	1	yes	characteristic
86	C₂	#23756524	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁₃
commutator, cosocle	C₂×C₄×C₃₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₃₁₃
Fitting	#103×C₃₁₃	C₂
socle, prime radical	C₂²×C₃₁₃	C₂×D₄
hypercenter	#103	D₃₁₃
hypocenter	C₃₁₃	#477
LCS	G ▷ C₂×C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
26. Q₈×C₃₁₃	Q₈	semidirect
43. C₃₁₃	#477	semidirect
65. Q₈	Dic₆₂₆	semidirect

Maximal subgroups

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

subgroup	index
#23756496	2
Q₈×Dic₃₁₃	2
#23756431	2
#23756430	2
#23756426	2
#23756421	2
#103×C₃₁₃	2
#477	313