Subgroups — C₁₁⋊#16809809 #49146331

Order 36894.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#13131976	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₄₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#16809809	—	11	1	no	maximal, Hall
5	C₁₁⋊(D₄₃⋊C₃)	—	13	1	no	maximal, Hall
6	#13131976	D₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₄₃⋊C₃	—	13	1	no	Hall
8	C₁₃×D₄₃	—	11	1	no	Hall
9	D₄₇₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
10	D₁₁×C₁₃⋊C₃	—	43	1	no	maximal, Hall
11	C₁₃×C₄₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₄₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₁₃⋊C₃	—	43	1	no	Hall
14	C₁₃×D₁₁	—	43	1	no	Hall
15	D₄₃⋊C₃	—	143	1	no	Hall
16	C₁₁×C₁₃	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₄₃⋊C₃	—	13	1	no	Hall
18	D₄₃	—	11	1	no	Hall
19	C₂×C₁₃⋊C₃	—	473	1	no	Hall
20	C₃×D₁₁	—	559	1	no	Hall
21	C₄₃	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₁₃⋊C₃	—	43	1	no	Hall
23	C₃×C₁₁	—	559	1	no	Hall
24	C₂×C₁₃	—	473	1	no	Hall
25	D₁₁	—	43	1	no	Hall
26	C₁₃	C₁₁⋊(D₄₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	#16809809	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	6149	1	no	Hall
29	C₃	—	559	1	no	Sylow
30	C₂	—	473	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₁₁×C₁₃×C₄₃
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.