Subgroups — C₁₁²×D₄₃⋊C₃ #44530206

Order 31218.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁²×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₄₃⋊C₃	C₁₁	1	12	yes	maximal, direct product factor
5	C₁₁×C₄₃⋊C₃	C₂×C₁₁	1	12	yes	complemented
6	C₁₁×D₄₃	C₃×C₁₁	1	12	yes	complemented
7	C₂×C₃×C₁₁²	—	43	1	no	maximal, Hall
8	C₁₁×C₄₃	C₂×C₃×C₁₁	1	12	yes	complemented
9	C₃×C₁₁²	—	43	1	no	Hall
10	D₄₃⋊C₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁²	—	43	1	no	Hall
12	C₄₃⋊C₃	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
13	C₁₁²	D₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	D₄₃	C₃×C₁₁²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₁	—	43	12	no	—
16	C₄₃	C₂×C₃×C₁₁²	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	—	43	12	no	—
18	C₂×C₁₁	—	43	12	no	—
19	C₁₁	C₁₁×D₄₃⋊C₃	1	12	yes	direct product factor
20	C₂×C₃	—	43	1	no	Hall
21	C₃	—	43	1	no	Sylow
22	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁²	D₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₃×C₁₁²
Frattini	C₁	G
Fitting, socle	C₁₁²×C₄₃	C₂×C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₁₁²

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.