Subgroups — #44567900

Order 32288.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30633332	C₂	1	1	yes	maximal, characteristic
2	#30633322	C₂	1	2	yes	maximal, complemented
3	#30633319	C₂	1	2	yes	maximal, complemented
4	#30633316	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₁₀₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₂₀₁₈	C₂²	1	1	yes	characteristic
7	D₄₀₃₆	C₂²	1	1	yes	characteristic
8	C₂²⋊D₁₀₀₉	—	2	1	no	—
9	C₄×D₁₀₀₉	—	2	1	no	—
10	#22549047	C₂²	1	2	yes	—
11	Q₈×C₁₀₀₉	—	2	1	no	—
12	Q₈×C₁₀₀₉	C₂²	1	2	yes	—
13	C₂×C₄×C₁₀₀₉	—	2	1	no	—
14	C₂×C₄×C₁₀₀₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₀₀₉	D₄	1	1	yes	characteristic
16	C₂×D₁₀₀₉	—	2	1	no	—
17	C₄×C₁₀₀₉	—	2	2	no	—
18	C₄×C₁₀₀₉	D₄	1	1	yes	characteristic
19	C₄×C₁₀₀₉	C₂³	1	1	yes	characteristic
20	Dic₁₀₀₉	—	2	1	no	—
21	C₂×C₁₀₀₉	—	2	1	no	—
22	C₂×C₁₀₀₉	C₂×D₄	1	1	yes	characteristic
23	D₁₀₀₉	—	4	1	no	—
24	C₁₀₀₉	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	1009	1	no	maximal, Sylow
26	#41	—	1009	1	no	—
27	C₂×Q₈	D₁₀₀₉	1	1	yes	characteristic, complemented
28	Q₁₆	—	1009	2	no	—
29	SD₁₆	—	1009	2	no	—
30	M₁₆	—	1009	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	1009	1	no	—
33	Q₈	C₂×D₁₀₀₉	1	2	yes	—
34	D₄	—	2018	1	no	—
35	D₄	—	1009	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2018	1	no	—
38	C₂×C₄	C₂×D₁₀₀₉	1	1	yes	characteristic
39	C₈	—	1009	2	no	—
40	C₂²	—	2018	1	no	—
41	C₂²	C₂²⋊D₁₀₀₉	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	2018	1	no	—
44	C₄	C₂²⋊D₁₀₀₉	1	1	yes	characteristic
45	C₄	C₂²×D₁₀₀₉	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4036	1	no	—
48	C₂	C₂×C₂²⋊D₁₀₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₁₀₀₉
commutator, cosocle	C₄×C₁₀₀₉	C₂³
Frattini	C₄	C₂²×D₁₀₀₉
Fitting	C₂×Q₈×C₁₀₀₉	C₂
socle	C₂×C₁₀₀₉	C₂×D₄
prime radical	#30633332	C₂
hypercenter	C₂×Q₈	D₁₀₀₉
hypocenter	C₁₀₀₉	#137
LCS	G ▷ C₄×C₁₀₀₉ ▷ C₂×C₁₀₀₉ ▷ C₁₀₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #30633322	C₂	semidirect
3. #30633319	C₂	semidirect
4. #30633316	C₂	semidirect
5. C₂×Q₈×C₁₀₀₉	C₂	semidirect
24. C₁₀₀₉	#137	semidirect
27. C₂×Q₈	D₁₀₀₉	semidirect

Maximal subgroups

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

subgroup	index
#30633332	2
#30633322	2
#30633319	2
#30633316	2
C₂×Q₈×C₁₀₀₉	2
#137	1009