Subgroups — C₃⋊#21462844 #37552909

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16840847	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#21462844	—	3	1	no	maximal, Hall
3	D₃₃×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	#16840847	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₃×C₇₁⋊C₅	—	11	1	no	maximal, Hall
7	D₁₁×C₇₁	—	3	1	no	Hall
8	C₃×C₇₁⋊C₅	—	11	1	no	Hall
9	C₁₁×C₇₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇₁⋊C₅	—	33	1	no	Hall
11	D₃×C₇₁	—	11	1	no	Hall
12	C₇₁⋊C₅	—	11	1	no	Hall
13	C₃⋊AGL(1,𝔽₁₁)	—	71	1	no	maximal, Hall
14	C₃×C₇₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁⋊C₅	—	71	1	no	Hall
16	C₂×C₇₁	—	165	1	no	Hall
17	AGL(1,𝔽₁₁)	—	213	1	no	Hall
18	C₇₁	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
19	D₃₃	C₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
20	C₁₁⋊C₅	—	71	1	no	Hall
21	C₃×C₁₁	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	781	1	no	Hall
23	D₁₁	—	3	1	no	Hall
24	C₃×C₅	—	781	1	no	Hall
25	C₁₁	D₃×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	2343	1	no	Hall
27	D₃	—	55	1	no	Hall
28	C₅	—	781	1	no	Sylow
29	C₃	#21462844	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₇₁	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₇₁
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.