Subgroups — C₁₁×D₉×C₉₇ #34063403

Order 19206.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₁×C₉₇	—	3	1	no	maximal
3	C₃×C₁₁×C₉₇	D₃	1	1	yes	characteristic
4	C₂×C₁₁×C₉₇	—	9	1	no	Hall
5	D₉×C₉₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₉₇	D₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₉₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	D₃×C₉₇	—	3	1	no	—
9	C₃×C₉₇	D₃×C₁₁	1	1	yes	characteristic
10	C₁₁×D₉	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₉₇	—	9	1	no	Hall
12	C₉×C₁₁	C₂×C₉₇	1	1	yes	characteristic, complemented, Hall
13	C₉₇	C₁₁×D₉	1	1	yes	characteristic, direct product factor, Sylow
14	D₃×C₁₁	—	3	1	no	—
15	C₃×C₁₁	D₃×C₉₇	1	1	yes	characteristic
16	C₂×C₁₁	—	9	1	no	Hall
17	D₉	C₁₁×C₉₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁	D₉×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₉	C₂×C₁₁×C₉₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3	1	no	—
21	C₃	D₃×C₁₁×C₉₇	1	1	yes	characteristic
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₉₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₁×C₉₇
Frattini	C₃	D₃×C₁₁×C₉₇
Fitting	C₉×C₁₁×C₉₇	C₂
socle	C₃×C₁₁×C₉₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₁×C₉₇

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.