Subgroups — C₃⋊(C₁₁⋊D₄₀₇) #41001766

Order 26862.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁⋊D₄₀₇	—	3	1	no	maximal, Hall
3	C₁₁²×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₁₂₂₁	—	11	12	no	maximal
5	C₃×C₁₁×C₃₇	D₁₁	1	12	yes	complemented
6	D₄₀₇	—	33	12	no	—
7	C₃⋊(C₁₁⋊D₁₁)	—	37	1	no	maximal, Hall
8	C₁₁×C₃₇	D₃₃	1	12	yes	complemented
9	C₃×C₁₁²	D₃₇	1	1	yes	characteristic, complemented, Hall
10	C₁₁⋊D₁₁	—	111	1	no	Hall
11	D₁₁₁	—	121	1	no	Hall
12	C₁₁²	D₁₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₇	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
14	D₃₇	—	363	1	no	Hall
15	D₃₃	—	407	12	no	—
16	C₃₇	C₃⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	D₄₀₇	1	12	yes	complemented
18	D₁₁	—	1221	12	no	—
19	C₁₁	D₁₂₂₁	1	12	yes	complemented
20	D₃	—	4477	1	no	Hall
21	C₃	C₁₁⋊D₄₀₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	13431	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁²×C₃₇	C₂
LCS	G ▷ C₃×C₁₁²×C₃₇
UCS	C₁

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

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