Subgroups — C₃×C₁₁²×#261 #34038433

Order 18876.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×#261	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁²×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₁×#261	C₁₁	1	12	yes	maximal, direct product factor
6	C₁₁²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₁₁²	—	13	1	no	maximal, Hall
8	C₃×C₁₁×D₁₃	C₂×C₁₁	1	12	yes	—
9	C₂×C₃×C₁₁²	—	13	1	no	—
10	C₁₁×#261	C₃×C₁₁	1	12	yes	direct product factor
11	C₄×C₁₁²	—	13	1	no	Hall
12	C₃×C₁₁×C₁₃	C₄×C₁₁	1	12	yes	complemented
13	C₃×C₁₁²	#261	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁×D₁₃	C₂×C₃×C₁₁	1	12	yes	—
15	C₂×C₁₁²	—	13	1	no	—
16	C₃×#261	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×C₁₃	C₃×C₄×C₁₁	1	12	yes	complemented
18	C₃×C₄×C₁₁	—	13	12	no	—
19	C₁₁²	C₃×#261	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×D₁₃	C₂×C₁₁²	1	1	yes	characteristic
21	C₂×C₃×C₁₁	—	13	12	no	—
22	#261	C₃×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
23	C₄×C₁₁	—	13	12	no	—
24	C₃×C₁₃	C₄×C₁₁²	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁	C₁₁×#261	1	12	yes	direct product factor
26	D₁₃	C₂×C₃×C₁₁²	1	1	yes	characteristic
27	C₂×C₁₁	—	13	12	no	—
28	C₁₃	C₃×C₄×C₁₁²	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	Hall
30	C₁₁	C₃×C₁₁×#261	1	12	yes	direct product factor
31	C₂×C₃	—	13	1	no	—
32	C₄	—	13	1	no	Sylow
33	C₃	C₁₁²×#261	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₁²	#261
commutator, hypocenter	C₁₃	C₃×C₄×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₁₃	C₄
prime radical	C₃×C₁₁²×D₁₃	C₂
cosocle	D₁₃	C₂×C₃×C₁₁²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₁²

Complements

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

N	H ≅ G/N	type
2. C₁₁²×#261	C₃	direct (N × H)
3. C₃×C₁₁²×C₁₃	C₄	semidirect
5. C₃×C₁₁×#261	C₁₁	direct (N × H)
6. C₁₁²×C₁₃	C₃×C₄	semidirect
10. C₁₁×#261	C₃×C₁₁	direct (N × H)
12. C₃×C₁₁×C₁₃	C₄×C₁₁	semidirect
13. C₃×C₁₁²	#261	direct (N × H)
16. C₃×#261	C₁₁²	direct (N × H)
17. C₁₁×C₁₃	C₃×C₄×C₁₁	semidirect
19. C₁₁²	C₃×#261	direct (N × H)
22. #261	C₃×C₁₁²	direct (N × H)
24. C₃×C₁₃	C₄×C₁₁²	semidirect
25. C₃×C₁₁	C₁₁×#261	direct (N × H)
28. C₁₃	C₃×C₄×C₁₁²	semidirect
30. C₁₁	C₃×C₁₁×#261	direct (N × H)
33. C₃	C₁₁²×#261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₁²×D₁₃	2
C₁₁²×#261	3
C₃×C₁₁×#261	11
C₃×C₄×C₁₁²	13

Subgroups — C3×C112×#261 #34038433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁²×#261 #34038433