Subgroups — C₁₁²×C₂²⋊(C₁₃⋊C₃) #34038470

Order 18876.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁²×C₁₃⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₁₁²×C₁₃	—	3	1	no	—
4	C₁₁×C₂²⋊(C₁₃⋊C₃)	C₁₁	1	12	yes	maximal, direct product factor
5	C₁₁²×C₁₃	A₄	1	1	yes	characteristic, complemented, Hall
6	C₁₁²×A₄	—	13	1	no	maximal, Hall
7	C₂²×C₁₁×C₁₃	C₃×C₁₁	1	12	yes	complemented
8	C₂²×C₁₁²	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₁₃⋊C₃	—	4	12	no	—
10	C₃×C₁₁²	—	52	1	no	Hall
11	C₂×C₁₁×C₁₃	—	3	12	no	—
12	C₂×C₁₁²	—	3	1	no	—
13	C₂²⋊(C₁₃⋊C₃)	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁×C₁₃	C₁₁×A₄	1	12	yes	complemented
15	C₁₁×A₄	—	13	12	no	—
16	C₁₁²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
17	C₂²×C₁₃	C₃×C₁₁²	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₁₁	C₁₁×C₁₃⋊C₃	1	12	yes	complemented
19	C₁₃⋊C₃	—	4	1	no	Hall
20	C₃×C₁₁	—	52	12	no	—
21	C₂×C₁₃	—	3	1	no	—
22	C₂×C₁₁	—	3	12	no	—
23	C₁₃	C₁₁²×A₄	1	1	yes	characteristic, complemented, Sylow
24	A₄	—	13	1	no	Hall
25	C₁₁	C₁₁×C₂²⋊(C₁₃⋊C₃)	1	12	yes	direct product factor
26	C₂²	C₁₁²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	52	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁²	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃×C₁₁²
Frattini	C₁	G
Fitting, socle	C₂²×C₁₁²×C₁₃	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₁₁²

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.