Subgroups — #34095196

Order 20032.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23756585	C₂	1	2	yes	maximal, complemented
2	#23756568	C₂	1	1	yes	maximal, characteristic, complemented
3	#23756562	C₂	1	2	yes	maximal, complemented
4	C₈×#11929411	C₂	1	1	yes	maximal, characteristic, complemented
5	#23756520	C₂	1	1	yes	maximal, characteristic
6	#19097571	—	2	2	no	—
7	#19097571	C₂²	1	2	yes	—
8	#19097569	—	2	2	no	—
9	#19097569	C₂²	1	1	yes	characteristic
10	C₄×#11929411	C₂²	1	1	yes	characteristic
11	#19097562	C₂²	1	2	yes	—
12	#19097548	C₄	1	2	yes	complemented
13	D₂₅₀₄	C₄	1	1	yes	characteristic, complemented
14	C₈×D₃₁₃	C₂²	1	1	yes	characteristic
15	Q₁₆×C₃₁₃	C₄	1	1	yes	characteristic, complemented
16	C₂×#11929411	—	2	1	no	—
17	#14578816	—	2	2	no	—
18	#14578816	D₄	1	1	yes	characteristic
19	#14578816	D₄	1	1	yes	characteristic
20	D₁₂₅₂	—	2	2	no	—
21	D₁₂₅₂	C₂×C₄	1	2	yes	—
22	C₄×D₃₁₃	—	2	2	no	—
23	C₄×D₃₁₃	C₂³	1	1	yes	characteristic
24	#14578809	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₃₁₃	C₂×C₄	1	2	yes	—
26	C₈×C₃₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×D₃₁₃	—	2	2	no	—
28	C₂×D₃₁₃	#41	1	1	yes	characteristic
29	#11929411	—	2	2	no	—
30	C₄×C₃₁₃	—	2	2	no	—
31	C₄×C₃₁₃	C₂²×C₄	1	1	yes	characteristic
32	Dic₃₁₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₃₁₃	C₄×D₄	1	1	yes	characteristic
34	D₃₁₃	—	2	1	no	—
35	D₃₁₃	—	4	2	no	—
36	C₃₁₃	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	313	1	no	maximal, Sylow
38	#135	—	313	1	no	—
39	#131	—	313	2	no	—
40	#108	—	313	1	no	—
41	#104	—	313	2	no	—
42	C₄×C₈	—	313	1	no	—
43	#41	—	313	2	no	—
44	Q₁₆	#11929411	1	1	yes	characteristic, complemented
45	SD₁₆	—	313	2	no	—
46	D₈	—	313	1	no	—
47	M₁₆	—	313	2	no	—
48	M₁₆	—	626	2	no	—
49	C₂×C₈	—	313	1	no	—
50	C₂×C₈	—	313	1	no	—
51	C₂×C₈	—	626	2	no	—
52	C₄²	—	313	1	no	—
53	Q₈	C₂×#11929411	1	2	yes	—
54	D₄	—	313	2	no	—
55	D₄	—	626	2	no	—
56	C₂×C₄	—	313	1	no	—
57	C₂×C₄	—	626	2	no	—
58	C₂×C₄	—	626	1	no	—
59	C₈	—	313	1	no	—
60	C₈	—	313	1	no	—
61	C₈	—	313	1	no	—
62	C₈	—	626	2	no	—
63	C₈	C₂×#11929411	1	1	yes	characteristic
64	C₂²	—	313	1	no	—
65	C₂²	—	626	2	no	—
66	C₄	—	2	2	no	—
67	C₄	—	313	1	no	—
68	C₄	—	626	2	no	—
69	C₄	C₂²×#11929411	1	1	yes	characteristic
70	C₂	—	626	1	no	—
71	C₂	—	1252	2	no	—
72	C₂	D₄×#11929411	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#11929411
commutator	C₄×C₃₁₃	C₂²×C₄
Frattini	C₄	C₂²×#11929411
Fitting	Q₁₆×C₃₁₃	C₄
socle	C₂×C₃₁₃	C₄×D₄
prime radical	#23756520	C₂
cosocle	C₄×D₃₁₃	C₂³
hypercenter	Q₁₆	#11929411
hypocenter	C₃₁₃	#443
LCS	G ▷ C₄×C₃₁₃ ▷ C₂×C₃₁₃ ▷ C₃₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #23756585	C₂	semidirect
2. #23756568	C₂	semidirect
3. #23756562	C₂	semidirect
4. C₈×#11929411	C₂	semidirect
12. #19097548	C₄	semidirect
13. D₂₅₀₄	C₄	semidirect
15. Q₁₆×C₃₁₃	C₄	semidirect
36. C₃₁₃	#443	semidirect
44. Q₁₆	#11929411	semidirect

Maximal subgroups

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

subgroup	index
#23756585	2
#23756568	2
#23756562	2
C₈×#11929411	2
#23756520	2
#443	313