Subgroups — #38786173

Order 25664.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165694	C₂	1	1	yes	maximal, characteristic
2	#27165666	C₂	1	2	yes	maximal, complemented
3	#27165649	C₂	1	2	yes	maximal
4	#27165648	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₄₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
7	C₂×#15691999	C₂²	1	2	yes	—
8	#20264345	C₄	1	2	yes	—
9	#20264343	C₄	1	2	yes	—
10	C₄×Dic₄₀₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₀₁	C₂²	1	2	yes	—
12	C₄²×C₄₀₁	C₂²	1	1	yes	characteristic
13	C₂²×D₄₀₁	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₄₀₁	C₂×C₄	1	2	yes	—
15	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
16	C₄×D₄₀₁	—	2	2	no	—
17	#15691999	—	2	2	no	—
18	C₂×C₄×C₄₀₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₀₁	C₂³	1	1	yes	characteristic
20	C₈×C₄₀₁	—	2	2	no	—
21	C₂²×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
22	C₂×D₄₀₁	—	2	1	no	—
23	C₂×D₄₀₁	—	2	2	no	—
24	C₄×C₄₀₁	—	2	2	no	—
25	C₄×C₄₀₁	#41	1	2	yes	—
26	Dic₄₀₁	—	2	1	no	—
27	Dic₄₀₁	—	2	2	no	—
28	C₂×C₄₀₁	#117	1	1	yes	characteristic
29	C₂×C₄₀₁	#131	1	2	yes	—
30	D₄₀₁	—	4	1	no	—
31	C₄₀₁	#433	1	1	yes	characteristic, complemented, Sylow
32	#433	—	401	1	no	maximal, Sylow
33	#117	—	401	1	no	—
34	C₄⋊C₈	—	401	2	no	—
35	C₂²⋊C₈	—	401	2	no	—
36	#97	—	401	1	no	—
37	C₄×C₈	D₄₀₁	1	1	yes	characteristic, complemented
38	C₂²×C₄	—	401	1	no	—
39	C₂×C₈	—	401	2	no	—
40	C₂×C₈	C₂×D₄₀₁	1	2	yes	—
41	C₄⋊C₄	—	401	2	no	—
42	C₂²⋊C₄	—	401	2	no	—
43	C₄²	—	401	1	no	—
44	C₄²	C₂×D₄₀₁	1	1	yes	characteristic
45	C₂³	—	401	1	no	—
46	C₂×C₄	—	802	2	no	—
47	C₂×C₄	—	401	2	no	—
48	C₂×C₄	—	401	1	no	—
49	C₂×C₄	C₄×D₄₀₁	1	2	yes	—
50	C₂×C₄	C₂²×D₄₀₁	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	802	2	no	—
53	C₂²	—	802	2	no	—
54	C₂²	—	802	1	no	—
55	C₂²	C₂×C₄×D₄₀₁	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	802	2	no	—
58	C₄	—	802	1	no	—
59	C₄	#20264366	1	2	yes	—
60	C₂	—	1604	1	no	—
61	C₂	#27165694	1	1	yes	characteristic
62	C₂	#27165743	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₀₁
commutator, socle	C₂²×C₄₀₁	C₂²×C₄
Fitting	C₄×C₈×C₄₀₁	C₂
prime radical	C₂²×D₄₀₁	C₂×C₄
cosocle	C₂×C₄×C₄₀₁	C₂³
hypercenter	C₄×C₈	D₄₀₁
hypocenter	C₄₀₁	#433
LCS	G ▷ C₂²×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #27165666	C₂	semidirect
4. #27165648	C₂	semidirect
5. C₄×C₈×C₄₀₁	C₂	semidirect
31. C₄₀₁	#433	semidirect
37. C₄×C₈	D₄₀₁	semidirect

Maximal subgroups

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

subgroup	index
#27165694	2
#27165666	2
#27165649	2
#27165648	2
C₄×C₈×C₄₀₁	2
#433	401