Subgroups — #45683050

Order 33056.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₁₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#22551916	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×C₁₀₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₀₃₃	—	2	1	no	—
5	D₄₁₃₂	—	2	1	no	—
6	D₄₁₃₂	C₄	1	2	yes	complemented
7	#22551916	—	2	1	no	—
8	C₂×C₄×C₁₀₃₃	—	2	1	no	—
9	C₂×C₄×C₁₀₃₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₀₃₃	D₄	1	1	yes	characteristic
11	C₂×D₁₀₃₃	—	2	2	no	—
12	C₂×D₁₀₃₃	—	4	1	no	—
13	C₂×D₁₀₃₃	—	4	1	no	—
14	C₄×C₁₀₃₃	—	4	1	no	—
15	C₄×C₁₀₃₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₀₃₃	D₄	1	1	yes	characteristic
17	C₂×C₁₀₃₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₁₀₃₃	D₈	1	1	yes	characteristic
19	C₂×C₁₀₃₃	SD₁₆	1	1	yes	characteristic
20	D₁₀₃₃	—	4	2	no	—
21	C₁₀₃₃	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	1033	1	no	maximal, Sylow
23	C₂×D₄	—	1033	1	no	—
24	C₂×C₈	—	1033	1	no	—
25	C₄⋊C₄	D₁₀₃₃	1	1	yes	characteristic, complemented
26	C₂³	—	2066	1	no	—
27	D₄	—	1033	2	no	—
28	D₄	—	2066	1	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂×D₁₀₃₃	1	1	yes	characteristic
31	C₈	—	2066	1	no	—
32	C₂²	—	2066	2	no	—
33	C₂²	—	4132	1	no	—
34	C₂²	—	4132	1	no	—
35	C₂²	C₂²⋊D₁₀₃₃	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₁₀₃₃	1	1	yes	characteristic
38	C₄	D₄₁₃₂	1	1	yes	characteristic
39	C₂	—	4132	2	no	—
40	C₂	#30658302	1	1	yes	characteristic
41	C₂	#30658310	1	1	yes	characteristic
42	C₂	#30658312	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₁₀₃₃
commutator	C₄×C₁₀₃₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₁₀₃₃
Fitting	C₄⋊C₄×C₁₀₃₃	C₂
socle	C₂²×C₁₀₃₃	D₄
prime radical	C₂×D₄₁₃₂	C₂
cosocle	C₂×C₄×C₁₀₃₃	C₂²
hypercenter	C₄⋊C₄	D₁₀₃₃
hypocenter	C₁₀₃₃	#102
LCS	G ▷ C₄×C₁₀₃₃ ▷ C₂×C₁₀₃₃ ▷ C₁₀₃₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#22551916	C₂	semidirect
3. C₄⋊C₄×C₁₀₃₃	C₂	semidirect
6. D₄₁₃₂	C₄	semidirect
21. C₁₀₃₃	#102	semidirect
25. C₄⋊C₄	D₁₀₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₁₃₂	2
C₂×#22551916	2
C₄⋊C₄×C₁₀₃₃	2
#102	1033