Subgroups — #45685199

Order 33248.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₁₀₃₉	C₂	1	2	yes	maximal
2	Dic₁₀₃₉⋊C₄	C₂	1	4	yes	maximal
3	C₄²×C₁₀₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₃₉	C₂²	1	4	yes	—
5	C₂×C₄×C₁₀₃₉	C₂²	1	2	yes	—
6	C₂×C₄×C₁₀₃₉	C₂²	1	1	yes	characteristic
7	C₂²×C₁₀₃₉	C₂³	1	1	yes	characteristic
8	C₄×C₁₀₃₉	—	2	2	no	—
9	C₄×C₁₀₃₉	Q₈	1	2	yes	—
10	Dic₁₀₃₉	—	2	4	no	—
11	C₂×C₁₀₃₉	C₂×Q₈	1	1	yes	characteristic
12	C₂×C₁₀₃₉	#41	1	2	yes	—
13	C₁₀₃₉	#125	1	1	yes	characteristic, complemented, Sylow
14	#125	—	1039	1	no	maximal, Sylow
15	C₄⋊C₄	—	1039	4	no	—
16	C₄⋊C₄	—	1039	2	no	—
17	C₄²	D₁₀₃₉	1	1	yes	characteristic
18	C₂×C₄	—	1039	4	no	—
19	C₂×C₄	C₂×D₁₀₃₉	1	2	yes	—
20	C₂×C₄	C₂×D₁₀₃₉	1	1	yes	characteristic
21	C₂²	C₂²×D₁₀₃₉	1	1	yes	characteristic
22	C₄	—	2	2	no	—
23	C₄	—	2078	4	no	—
24	C₄	Dic₂₀₇₈	1	2	yes	—
25	C₂	C₂×Dic₂₀₇₈	1	1	yes	characteristic
26	C₂	#30659027	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₀₃₉
commutator, socle, prime radical, cosocle	C₂²×C₁₀₃₉	C₂³
Fitting	C₄²×C₁₀₃₉	C₂
hypercenter	C₄²	D₁₀₃₉
hypocenter	C₁₀₃₉	#125
LCS	G ▷ C₂²×C₁₀₃₉ ▷ C₁₀₃₉
UCS	C₁ ◁ C₂² ◁ C₄²

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

N	H ≅ G/N	type
13. C₁₀₃₉	#125	semidirect

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