Subgroups — C₁₁×#13095537 #30685331

Order 17094.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#11715913	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₃₇⋊C₃	—	7	1	no	maximal, Hall
5	#13095537	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₃₇⋊C₃	—	7	1	no	Hall
7	C₁₁×D₃₇	—	7	1	no	Hall
8	#11715913	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	D₂₅₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×AGL(1,𝔽₇)	—	37	1	no	maximal, Hall
11	C₁₁×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
12	C₇×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×ΓL(1,𝔽₈)	—	37	1	no	Hall
14	D₃₇⋊C₃	—	7	1	no	Hall
15	C₁₁×D₇	—	37	1	no	Hall
16	C₃₇⋊C₃	—	7	1	no	Hall
17	C₇×C₁₁	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
18	D₃₇	—	7	1	no	Hall
19	C₂×C₃×C₁₁	—	259	1	no	Hall
20	AGL(1,𝔽₇)	—	37	1	no	Hall
21	C₃₇	C₁₁×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₁	—	259	1	no	Hall
23	C₂×C₁₁	—	259	1	no	Hall
24	ΓL(1,𝔽₈)	—	37	1	no	Hall
25	D₇	—	37	1	no	Hall
26	C₁₁	#13095537	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₁₁×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	259	1	no	Hall
29	C₃	—	259	1	no	Sylow
30	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	#13095537
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₁₁

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.