Subgroups — C₂²⋊(C₅²⋊(C₁₁²⋊C₃)) #49137809

Order 36300.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₁²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²⋊(C₁₁²⋊C₃)	—	4	1	no	maximal, Hall
3	C₂×C₅²×C₁₁²	—	3	1	no	—
4	C₅²×C₁₁²	A₄	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₅×C₁₁²	—	3	2	no	—
6	C₂²⋊(C₁₁²⋊C₃)	—	25	1	no	maximal, Hall
7	C₂×C₅×C₁₁²	—	3	6	no	—
8	C₂²×C₅²×C₁₁	—	3	4	no	—
9	C₅×C₁₁²	—	3	2	no	—
10	C₂×C₅²×C₁₁	—	3	12	no	—
11	C₂²×C₁₁²	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₁₁²⋊C₃	—	100	1	no	Hall
13	C₂²⋊(C₅²⋊C₃)	—	121	1	no	maximal, Hall
14	C₅²×C₁₁	—	3	4	no	—
15	C₂×C₁₁²	—	3	1	no	—
16	C₂²×C₅×C₁₁	—	3	24	no	—
17	C₁₁²	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×C₁₁	—	3	72	no	—
19	C₂²×C₅²	C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₅²⋊C₃	—	484	1	no	Hall
21	C₅×C₁₁	—	3	24	no	—
22	C₂×C₅²	—	3	1	no	—
23	C₂²×C₁₁	—	3	4	no	—
24	C₅²	C₂²⋊(C₁₁²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₁	—	3	12	no	—
26	C₂²×C₅	—	3	2	no	—
27	A₄	—	3025	1	no	Hall
28	C₁₁	—	3	4	no	—
29	C₂×C₅	—	3	6	no	—
30	C₅	—	3	2	no	—
31	C₂²	C₅²⋊(C₁₁²⋊C₃)	1	1	yes	characteristic, complemented, Sylow
32	C₃	—	12100	1	no	Sylow
33	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₅²×C₁₁²	C₃
LCS	G ▷ C₂²×C₅²×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.