Subgroups — C₁₁×C₇⋊(C₁₃⋊D₁₃) #39907367

Order 26026.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₃⋊D₁₃	—	7	1	no	maximal, Hall
3	C₇⋊(C₁₃⋊D₁₃)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×D₉₁	—	13	14	no	maximal
5	C₁₁×C₁₃²	D₇	1	1	yes	characteristic, complemented, Hall
6	C₇×C₁₃²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₁×C₁₃	D₁₃	1	14	yes	complemented
8	C₁₃⋊D₁₃	—	7	1	no	Hall
9	C₁₁×D₁₃	—	91	14	no	—
10	D₉₁	—	13	14	no	—
11	C₁₃²	C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
12	C₁₁×D₇	—	169	1	no	Hall
13	C₁₁×C₁₃	D₉₁	1	14	yes	complemented
14	C₇×C₁₃	C₁₁×D₁₃	1	14	yes	complemented
15	C₇×C₁₁	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
16	D₁₃	—	91	14	no	—
17	C₂×C₁₁	—	1183	1	no	Hall
18	D₇	—	169	1	no	Hall
19	C₁₃	C₁₁×D₉₁	1	14	yes	complemented
20	C₁₁	C₇⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor, Sylow
21	C₇	C₁₁×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	1183	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₇⋊(C₁₃⋊D₁₃)
commutator, cosocle, hypocenter	C₇×C₁₃²	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃²	C₂
LCS	G ▷ C₇×C₁₃²
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.