Subgroups — C₃×C₁₁²×C₃₁⋊C₃ #46798255

Order 33759.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₃₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₁₁²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₁²×C₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×C₃₁⋊C₃	C₁₁	1	12	yes	maximal, direct product factor
5	C₃²×C₁₁²	—	31	1	no	maximal, Hall
6	C₃×C₁₁×C₃₁	C₃×C₁₁	1	12	yes	complemented
7	C₁₁×C₃₁⋊C₃	C₃×C₁₁	1	36	yes	direct product factor
8	C₃×C₁₁²	—	31	3	no	—
9	C₃×C₁₁²	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
10	C₁₁×C₃₁	C₃²×C₁₁	1	12	yes	complemented
11	C₃×C₃₁⋊C₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁²	C₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²×C₁₁	—	31	12	no	—
14	C₃×C₃₁	C₃×C₁₁²	1	1	yes	characteristic, complemented
15	C₃₁⋊C₃	C₃×C₁₁²	1	3	yes	direct product factor
16	C₃×C₁₁	—	31	36	no	—
17	C₃×C₁₁	C₁₁×C₃₁⋊C₃	1	12	yes	direct product factor
18	C₃₁	C₃²×C₁₁²	1	1	yes	characteristic, complemented, Sylow
19	C₁₁	C₃×C₁₁×C₃₁⋊C₃	1	12	yes	direct product factor
20	C₃²	—	31	1	no	Sylow
21	C₃	—	31	3	no	—
22	C₃	C₁₁²×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₁₁²	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃²×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×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.