Subgroups — #38786931

Order 25664.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165784	C₂	1	2	yes	maximal, complemented
2	#27165770	C₂	1	6	yes	maximal, complemented
3	#27165759	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₁₆₀₄	C₂	1	3	yes	maximal, complemented
5	#131×C₄₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#20264366	C₂²	1	6	yes	—
7	#20264365	—	2	6	no	—
8	C₂×Dic₈₀₂	C₂²	1	6	yes	—
9	Q₈×D₄₀₁	—	2	2	no	—
10	Dic₁₆₀₄	C₂²	1	3	yes	—
11	Dic₁₆₀₄	C₂²	1	6	yes	—
12	#20264355	C₂²	1	6	yes	—
13	D₃₂₀₈	C₂²	1	1	yes	characteristic
14	#41×C₄₀₁	C₂²	1	1	yes	characteristic
15	M₁₆×C₄₀₁	C₂²	1	3	yes	—
16	C₂×C₈×C₄₀₁	C₂²	1	3	yes	—
17	Dic₈₀₂	—	2	6	no	—
18	Dic₈₀₂	C₂³	1	6	yes	—
19	D₁₆₀₄	C₂³	1	2	yes	—
20	C₂²⋊D₄₀₁	—	2	6	no	—
21	C₂×Dic₄₀₁	—	2	6	no	—
22	C₄×D₄₀₁	—	2	6	no	—
23	Q₈×C₄₀₁	D₄	1	1	yes	characteristic
24	D₄×C₄₀₁	D₄	1	3	yes	—
25	C₂×C₄×C₄₀₁	C₂³	1	3	yes	—
26	C₈×C₄₀₁	C₂³	1	1	yes	characteristic
27	C₈×C₄₀₁	C₂³	1	3	yes	—
28	C₂²×C₄₀₁	C₂×D₄	1	3	yes	—
29	C₂×D₄₀₁	—	2	2	no	—
30	C₄×C₄₀₁	C₂×D₄	1	3	yes	—
31	C₄×C₄₀₁	C₂⁴	1	1	yes	characteristic
32	Dic₄₀₁	—	2	6	no	—
33	C₂×C₄₀₁	—	2	3	no	—
34	C₂×C₄₀₁	C₂²×D₄	1	1	yes	characteristic
35	D₄₀₁	—	4	2	no	—
36	C₄₀₁	#578	1	1	yes	characteristic, complemented, Sylow
37	#578	—	401	1	no	maximal, Sylow
38	2₋¹⁺⁴	—	401	2	no	—
39	#137	—	401	6	no	—
40	#135	—	401	3	no	—
41	C₂×Q₁₆	—	401	3	no	—
42	#131	D₄₀₁	1	1	yes	characteristic, complemented
43	#41	—	802	6	no	—
44	#41	—	401	6	no	—
45	#41	C₂×D₄₀₁	1	1	yes	characteristic
46	C₂×Q₈	—	802	2	no	—
47	C₂×Q₈	—	401	6	no	—
48	Q₁₆	—	401	3	no	—
49	Q₁₆	—	401	6	no	—
50	SD₁₆	—	401	6	no	—
51	D₈	—	401	1	no	—
52	M₁₆	C₂×D₄₀₁	1	3	yes	—
53	C₂×C₈	C₂×D₄₀₁	1	3	yes	—
54	Q₈	—	802	6	no	—
55	Q₈	—	401	6	no	—
56	Q₈	D₁₆₀₄	1	1	yes	characteristic
57	D₄	—	802	6	no	—
58	D₄	—	401	2	no	—
59	D₄	D₁₆₀₄	1	3	yes	—
60	C₂×C₄	—	802	6	no	—
61	C₂×C₄	—	802	6	no	—
62	C₂×C₄	C₂²×D₄₀₁	1	3	yes	—
63	C₈	C₂²×D₄₀₁	1	1	yes	characteristic
64	C₈	C₂²×D₄₀₁	1	3	yes	—
65	C₂²	—	802	2	no	—
66	C₂²	C₂×D₁₆₀₄	1	3	yes	—
67	C₄	—	802	6	no	—
68	C₄	C₂×D₁₆₀₄	1	3	yes	—
69	C₄	C₂³×D₄₀₁	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	1604	2	no	—
72	C₂	C₂²×D₁₆₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₁₆₀₄
commutator, cosocle	C₄×C₄₀₁	C₂⁴
Frattini	C₄	C₂³×D₄₀₁
Fitting	#131×C₄₀₁	C₂
socle	C₂×C₄₀₁	C₂²×D₄
hypercenter	#131	D₄₀₁
hypocenter	C₄₀₁	#578
LCS	G ▷ C₄×C₄₀₁ ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #27165784	C₂	semidirect
2. #27165770	C₂	semidirect
3. #27165759	C₂	semidirect
4. C₂×Dic₁₆₀₄	C₂	semidirect
5. #131×C₄₀₁	C₂	semidirect
36. C₄₀₁	#578	semidirect
42. #131	D₄₀₁	semidirect

Maximal subgroups

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

subgroup	index
#27165784	2
#27165770	2
#27165759	2
C₂×Dic₁₆₀₄	2
#131×C₄₀₁	2
#578	401