Subgroups — C₇×C₁₉×C₁₁⋊D₁₁ #44565686

Order 32186.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₁₁⋊D₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₉×D₁₁	—	11	12	no	maximal
4	C₁₁²×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁⋊D₁₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₁×C₁₉	D₁₁	1	12	yes	complemented
7	C₇×C₁₁²	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₁₉×D₁₁	—	11	12	no	—
9	C₂×C₇×C₁₉	—	121	1	no	Hall
10	C₁₁⋊D₁₁	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×C₁₉	C₇×D₁₁	1	12	yes	complemented
12	C₇×D₁₁	—	11	12	no	—
13	C₇×C₁₉	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁²	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
15	C₇×C₁₁	C₁₉×D₁₁	1	12	yes	complemented
16	C₂×C₁₉	—	121	1	no	Hall
17	D₁₁	—	11	12	no	—
18	C₁₉	C₇×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	—	121	1	no	Hall
20	C₁₁	C₇×C₁₉×D₁₁	1	12	yes	complemented
21	C₇	C₁₉×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	121	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₉	C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₁₁²	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₁²×C₁₉	C₂
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₇×C₁₉

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.