Subgroups — C₁₁⋊#14559030 #40998259

Order 26598.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#11925882	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₄₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#14559030	—	11	1	no	maximal, Hall
5	C₁₁⋊(D₃₁⋊C₃)	—	13	1	no	maximal, Hall
6	#11925882	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₃₁⋊C₃	—	13	1	no	Hall
8	C₁₁⋊(D₁₃⋊C₃)	—	31	1	no	maximal, Hall
9	D₄₀₃	—	11	1	no	Hall
10	D₃₄₁	—	13	1	no	Hall
11	C₁₁×C₁₃⋊C₃	—	31	1	no	Hall
12	C₁₃×C₃₁	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	D₁₄₃	—	31	1	no	Hall
15	D₃₁⋊C₃	—	143	1	no	Hall
16	C₁₁×C₁₃	D₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃₁⋊C₃	—	13	1	no	Hall
18	D₁₃⋊C₃	—	341	1	no	Hall
19	C₃×D₁₁	—	403	1	no	Hall
20	D₃₁	—	143	1	no	Hall
21	C₁₃⋊C₃	—	31	1	no	Hall
22	C₃×C₁₁	—	403	1	no	Hall
23	C₃₁	C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
24	D₁₃	—	341	1	no	Hall
25	D₁₁	—	403	1	no	Hall
26	C₁₃	C₁₁⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	#14559030	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	4433	1	no	Hall
29	C₃	—	403	1	no	Sylow
30	C₂	—	4433	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₃₁	C₂×C₃
LCS	G ▷ C₁₁×C₁₃×C₃₁
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.