Subgroups — D₉×#10597243 #24926107

Order 10890.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#10597243	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×#10597243	—	3	1	no	maximal
3	C₁₁²×D₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×#10597243	D₃	1	1	yes	characteristic
5	C₂×#10597243	—	9	1	no	Hall
6	C₉×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₉×C₁₁⋊C₅	—	11	12	no	maximal
8	D₃×C₁₁²	—	3	1	no	—
9	#10597243	D₉	1	1	yes	characteristic, direct product factor, Hall
10	C₉×C₁₁⋊C₅	—	11	12	no	—
11	C₃×C₁₁²	C₅×D₃	1	1	yes	characteristic
12	D₃×C₁₁⋊C₅	—	33	12	no	—
13	C₂×C₁₁²	—	9	1	no	Hall
14	C₁₁×D₉	C₁₁⋊C₅	1	12	yes	complemented
15	C₃×C₁₁⋊C₅	—	11	12	no	—
16	C₁₁²	C₅×D₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₁⋊C₅	—	99	12	no	—
18	C₉×C₁₁	C₂×C₁₁⋊C₅	1	12	yes	complemented
19	C₅×D₉	—	121	1	no	Hall
20	D₃×C₁₁	—	3	12	no	—
21	C₁₁⋊C₅	—	11	12	no	—
22	C₅×C₉	—	121	1	no	Hall
23	C₃×C₁₁	D₃×C₁₁⋊C₅	1	12	yes	—
24	C₅×D₃	—	363	1	no	—
25	C₂×C₁₁	—	9	12	no	—
26	D₉	#10597243	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₅	—	121	1	no	—
28	C₁₁	D₉×C₁₁⋊C₅	1	12	yes	complemented
29	C₂×C₅	—	1089	1	no	Hall
30	C₉	C₂×#10597243	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	1	no	—
32	C₅	—	121	1	no	Sylow
33	C₃	D₃×#10597243	1	1	yes	characteristic
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁²	C₂×C₅
Frattini	C₃	D₃×#10597243
socle	C₃×C₁₁²	C₅×D₃
LCS	G ▷ C₉×C₁₁²
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.