Subgroups — #16812749

Order 3488.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13182004	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₀₉	C₄	1	1	yes	characteristic
3	C₄×C₁₀₉	C₈	1	1	yes	characteristic
4	C₂×C₁₀₉	C₁₆	1	1	yes	characteristic
5	C₁₀₉	C₃₂	1	1	yes	characteristic, complemented, Sylow
6	C₃₂	—	109	1	no	maximal, Sylow
7	C₁₆	—	109	1	no	—
8	C₈	#89137	1	1	yes	characteristic
9	C₄	#11724786	1	1	yes	characteristic
10	C₂	#13182032	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	#89137
commutator, hypocenter	C₁₀₉	C₃₂
Fitting	C₈×C₁₀₉	C₄
socle, prime radical	C₂×C₁₀₉	C₁₆
cosocle	#13182004	C₂
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₈

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

N	H ≅ G/N	type
5. C₁₀₉	C₃₂	semidirect

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

subgroup	index
#13182004	2
C₃₂	109