Subgroups — #38785923

Order 25664.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165759	C₂	1	1	yes	maximal, characteristic
2	#27165677	C₂	1	1	yes	maximal, characteristic, complemented
3	#106×C₄₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#20264366	—	2	1	no	—
5	Dic₁₆₀₄	C₄	1	1	yes	characteristic, complemented
6	#20264355	—	2	1	no	—
7	D₃₂₀₈	C₄	1	1	yes	characteristic, complemented
8	#20264341	—	2	1	no	—
9	C₂×C₈×C₄₀₁	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₀₁	—	2	1	no	—
11	Dic₈₀₂	—	2	1	no	—
12	D₁₆₀₄	—	2	1	no	—
13	C₂²⋊D₄₀₁	—	4	1	no	—
14	C₄×D₄₀₁	—	4	1	no	—
15	C₂×C₄×C₄₀₁	—	4	1	no	—
16	C₂×C₄×C₄₀₁	D₄	1	1	yes	characteristic
17	C₈×C₄₀₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₄₀₁	D₄	1	1	yes	characteristic
19	C₂²×C₄₀₁	D₈	1	1	yes	characteristic
20	C₂×D₄₀₁	—	4	1	no	—
21	C₄×C₄₀₁	—	8	1	no	—
22	C₄×C₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₄₀₁	SD₁₆	1	1	yes	characteristic
24	Dic₄₀₁	—	4	1	no	—
25	C₂×C₄₀₁	—	2	1	no	—
26	C₂×C₄₀₁	#102	1	1	yes	characteristic
27	D₄₀₁	—	8	1	no	—
28	C₄₀₁	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	401	1	no	maximal, Sylow
30	#135	—	401	1	no	—
31	M₃₂	—	401	1	no	—
32	#106	D₄₀₁	1	1	yes	characteristic, complemented
33	#41	—	802	1	no	—
34	Q₁₆	—	401	1	no	—
35	SD₁₆	—	802	1	no	—
36	D₈	—	401	1	no	—
37	C₂×C₈	C₂×D₄₀₁	1	1	yes	characteristic
38	C₄⋊C₄	—	2	1	no	—
39	C₁₆	—	802	1	no	—
40	Q₈	—	802	1	no	—
41	D₄	—	802	1	no	—
42	D₄	—	1604	1	no	—
43	C₂×C₄	—	4	1	no	—
44	C₂×C₄	—	1604	1	no	—
45	C₂×C₄	C₂²⋊D₄₀₁	1	1	yes	characteristic
46	C₈	C₄×D₄₀₁	1	1	yes	characteristic
47	C₈	D₁₆₀₄	1	1	yes	characteristic
48	C₂²	—	1604	1	no	—
49	C₂²	#20264351	1	1	yes	characteristic
50	C₄	—	8	1	no	—
51	C₄	—	1604	1	no	—
52	C₄	#20264343	1	1	yes	characteristic
53	C₄	#20264353	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	3208	1	no	—
56	C₂	#27165657	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27165657
commutator	C₈×C₄₀₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₀₁
Fitting	#106×C₄₀₁	C₂
socle	C₂×C₄₀₁	#102
prime radical	#27165759	C₂
cosocle	C₂×C₈×C₄₀₁	C₂²
hypercenter	#106	D₄₀₁
hypocenter	C₄₀₁	#360
LCS	G ▷ C₈×C₄₀₁ ▷ C₄×C₄₀₁ ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
2. #27165677	C₂	semidirect
3. #106×C₄₀₁	C₂	semidirect
5. Dic₁₆₀₄	C₄	semidirect
7. D₃₂₀₈	C₄	semidirect
28. C₄₀₁	#360	semidirect
32. #106	D₄₀₁	semidirect

Maximal subgroups

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

subgroup	index
#27165759	2
#27165677	2
#106×C₄₀₁	2
#360	401