Subgroups — C₄₃×#10624391 #44530200

Order 31218.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₁₁×C₄₃	—	3	1	no	maximal, Hall
3	C₁₁²×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₄₃	—	33	1	no	—
5	D₁₁×C₄₃	—	3	1	no	—
6	#10624391	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×C₄₃	—	3	1	no	—
8	C₁₁×C₄₃	—	3	1	no	—
9	C₁₁×C₄₃	—	6	1	no	—
10	C₁₁²⋊C₃	C₂×C₄₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₄₃	—	121	1	no	maximal, Hall
12	C₁₁×D₁₁	—	3	1	no	Hall
13	C₃×C₄₃	—	121	1	no	Hall
14	C₁₁²	D₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄₃	—	33	1	no	Hall
16	C₄₃	#10624391	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₁	—	33	1	no	—
18	D₁₁	—	3	1	no	—
19	C₁₁	—	3	1	no	—
20	C₁₁	—	3	1	no	—
21	C₁₁	—	6	1	no	—
22	D₃	—	121	1	no	Hall
23	C₃	—	121	1	no	Sylow
24	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₃	#10624391
commutator, cosocle, hypocenter	C₁₁²⋊C₃	C₂×C₄₃
Frattini	C₁	G
Fitting, socle	C₁₁²×C₄₃	D₃
LCS	G ▷ C₁₁²⋊C₃
UCS	C₁ ◁ C₄₃

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.