Subgroups — C₃²×C₂₃×#4223 #46800421

Order 33948.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃×D₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃×#4223	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₄₁	C₂×C₃	1	4	yes	—
5	C₂₃×#4223	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₃×C₄₁	C₃×C₄	1	4	yes	complemented
7	C₂₃×D₄₁	C₂×C₃²	1	1	yes	characteristic
8	C₃²×#4223	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂₃×C₄₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₄×C₂₃	—	41	1	no	maximal, Hall
11	C₃²×D₄₁	C₂×C₂₃	1	1	yes	characteristic
12	C₃×#4223	C₃×C₂₃	1	4	yes	direct product factor
13	C₂×C₃²×C₂₃	—	41	1	no	—
14	C₃²×C₄₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄×C₂₃	—	41	4	no	—
16	C₃×D₄₁	C₂×C₃×C₂₃	1	4	yes	—
17	C₃²×C₂₃	#4223	1	1	yes	characteristic, direct product factor, Hall
18	#4223	C₃²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₂₃	—	41	4	no	—
20	C₃×C₄₁	C₃×C₄×C₂₃	1	4	yes	complemented
21	C₄×C₂₃	—	41	1	no	Hall
22	D₄₁	C₂×C₃²×C₂₃	1	1	yes	characteristic
23	C₃×C₂₃	C₃×#4223	1	4	yes	direct product factor
24	C₂×C₂₃	—	41	1	no	—
25	C₄₁	C₃²×C₄×C₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₃²×C₄	—	41	1	no	Hall
27	C₂₃	C₃²×#4223	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃²	—	41	1	no	—
29	C₃×C₄	—	41	4	no	—
30	C₃²	C₂₃×#4223	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	41	4	no	—
32	C₄	—	41	1	no	Sylow
33	C₃	C₃×C₂₃×#4223	1	4	yes	direct product factor
34	C₂	—	41	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₂₃	#4223
commutator, hypocenter	C₄₁	C₃²×C₄×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₄₁	C₄
prime radical	C₃²×C₂₃×D₄₁	C₂
cosocle	D₄₁	C₂×C₃²×C₂₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃²×C₂₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×C₂₃×#4223	C₃	direct (N × H)
3. C₃²×C₂₃×C₄₁	C₄	semidirect
5. C₂₃×#4223	C₃²	direct (N × H)
6. C₃×C₂₃×C₄₁	C₃×C₄	semidirect
8. C₃²×#4223	C₂₃	direct (N × H)
9. C₂₃×C₄₁	C₃²×C₄	semidirect
12. C₃×#4223	C₃×C₂₃	direct (N × H)
14. C₃²×C₄₁	C₄×C₂₃	semidirect
17. C₃²×C₂₃	#4223	direct (N × H)
18. #4223	C₃²×C₂₃	direct (N × H)
20. C₃×C₄₁	C₃×C₄×C₂₃	semidirect
23. C₃×C₂₃	C₃×#4223	direct (N × H)
25. C₄₁	C₃²×C₄×C₂₃	semidirect
27. C₂₃	C₃²×#4223	direct (N × H)
30. C₃²	C₂₃×#4223	direct (N × H)
33. C₃	C₃×C₂₃×#4223	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₂₃×D₄₁	2
C₃×C₂₃×#4223	3
C₃²×#4223	23
C₃²×C₄×C₂₃	41

Subgroups — C32×C23×#4223 #46800421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₂₃×#4223 #46800421