Subgroups — Dic₂₃×C₁₁²⋊C₃ #45688984

Order 33396.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×Dic₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₃×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁²×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₁²⋊C₃	—	23	1	no	maximal, Hall
7	C₁₁×Dic₂₃	—	3	4	no	—
8	C₂×C₁₁²⋊C₃	D₂₃	1	1	yes	characteristic
9	C₂×C₁₁×C₂₃	—	3	4	no	—
10	C₄×C₁₁²	—	23	1	no	Hall
11	C₁₁²⋊C₃	Dic₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×Dic₂₃	—	121	1	no	maximal, Hall
13	C₁₁×C₂₃	—	3	4	no	—
14	C₂×C₁₁²	C₃×D₂₃	1	1	yes	characteristic
15	C₂×C₃×C₂₃	—	121	1	no	—
16	C₁₁²	C₃×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
17	Dic₂₃	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₂₃	—	121	1	no	Hall
19	C₂×C₂₃	C₂×C₁₁²⋊C₃	1	1	yes	characteristic
20	C₄×C₁₁	—	69	4	no	—
21	C₂₃	C₄×C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₁	—	3	4	no	—
23	C₃×C₄	—	2783	1	no	Hall
24	C₁₁	—	3	4	no	—
25	C₂×C₃	—	121	1	no	—
26	C₄	—	23	1	no	Sylow
27	C₃	—	121	1	no	Sylow
28	C₂	D₂₃×C₁₁²⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₃×C₁₁²⋊C₃
commutator, hypocenter	C₁₁²×C₂₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₁²×C₂₃	C₂×C₃
prime radical	C₂×C₂₃×C₁₁²⋊C₃	C₂
LCS	G ▷ C₁₁²×C₂₃
UCS	C₁ ◁ C₂

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.