Subgroups — C₁₁×D₁₅₂₁ #45689502

Order 33462.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₅₀₇	—	3	1	no	maximal
3	C₃×C₁₁×C₁₆₉	D₃	1	1	yes	characteristic
4	C₁₁×D₁₆₉	—	9	1	no	Hall
5	D₁₅₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×D₁₁₇	—	13	1	no	maximal
7	C₁₁×C₁₆₉	D₉	1	1	yes	characteristic, complemented, Hall
8	C₉×C₁₆₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₉×C₁₁×C₁₃	D₁₃	1	1	yes	characteristic
10	D₅₀₇	—	3	1	no	—
11	C₁₁×D₃₉	—	39	1	no	—
12	C₃×C₁₆₉	D₃×C₁₁	1	1	yes	characteristic
13	C₃×C₁₁×C₁₃	D₃₉	1	1	yes	characteristic
14	D₁₆₉	—	9	1	no	Hall
15	C₁₁×D₁₃	—	117	1	no	—
16	D₁₁₇	—	13	1	no	—
17	C₁₁×D₉	—	169	1	no	Hall
18	C₁₆₉	C₁₁×D₉	1	1	yes	characteristic, complemented, Sylow
19	C₁₁×C₁₃	D₁₁₇	1	1	yes	characteristic
20	C₉×C₁₃	C₁₁×D₁₃	1	1	yes	characteristic
21	C₉×C₁₁	D₁₆₉	1	1	yes	characteristic, complemented, Hall
22	D₃₉	—	39	1	no	—
23	D₃×C₁₁	—	507	1	no	—
24	C₃×C₁₃	C₁₁×D₃₉	1	1	yes	characteristic
25	C₃×C₁₁	D₅₀₇	1	1	yes	characteristic
26	D₁₃	—	117	1	no	—
27	C₂×C₁₁	—	1521	1	no	Hall
28	D₉	—	169	1	no	Hall
29	C₁₃	C₁₁×D₁₁₇	1	1	yes	characteristic
30	C₁₁	D₁₅₂₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₉	C₁₁×D₁₆₉	1	1	yes	characteristic, complemented, Sylow
32	D₃	—	507	1	no	—
33	C₃	C₁₁×D₅₀₇	1	1	yes	characteristic
34	C₂	—	1521	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₅₂₁
commutator, cosocle, hypocenter	C₉×C₁₆₉	C₂×C₁₁
Frattini	C₃×C₁₃	C₁₁×D₃₉
Fitting	C₉×C₁₁×C₁₆₉	C₂
socle	C₃×C₁₁×C₁₃	D₃₉
LCS	G ▷ C₉×C₁₆₉
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.