Subgroups — C₃×#4341 #10587261

Order 528.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂²⋊D₁₁	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×Dic₁₁	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#4341	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₁₁	C₂²	1	2	yes	—
8	C₂×C₃×D₁₁	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₃×Dic₁₁	C₂²	1	2	yes	—
11	C₃×Dic₁₁	C₂²	1	1	yes	characteristic
12	D₄×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²⋊D₁₁	C₂×C₃	1	2	yes	complemented
14	C₂×Dic₁₁	C₂×C₃	1	2	yes	complemented
15	C₄×D₁₁	C₂×C₃	1	1	yes	characteristic, complemented
16	Dic₂₂	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×C₃×C₁₁	—	2	2	no	—
18	C₂×C₃×C₁₁	C₂³	1	1	yes	characteristic
19	C₃×D₁₁	—	2	1	no	—
20	C₃×#41	—	11	1	no	maximal, Hall
21	C₂²×C₁₁	C₂²×C₃	1	2	yes	—
22	C₂×D₁₁	C₂²×C₃	1	1	yes	characteristic
23	C₄×C₁₁	C₂²×C₃	1	1	yes	characteristic
24	Dic₁₁	C₂²×C₃	1	2	yes	—
25	Dic₁₁	C₂²×C₃	1	1	yes	characteristic
26	C₃×C₁₁	#41	1	1	yes	characteristic, complemented, Hall
27	C₃×Q₈	—	11	1	no	—
28	C₃×D₄	—	11	2	no	—
29	C₃×D₄	D₁₁	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄	—	11	2	no	—
31	C₂×C₃×C₄	—	11	1	no	—
32	C₂×C₁₁	—	2	2	no	—
33	C₂×C₁₁	C₂³×C₃	1	1	yes	characteristic
34	D₁₁	—	2	1	no	—
35	#41	—	11	1	no	Sylow
36	C₂²×C₃	—	11	1	no	—
37	C₂²×C₃	C₂×D₁₁	1	2	yes	—
38	C₃×C₄	—	11	1	no	—
39	C₃×C₄	—	11	2	no	—
40	C₃×C₄	C₂×D₁₁	1	1	yes	characteristic
41	C₁₁	C₃×#41	1	1	yes	characteristic, complemented, Sylow
42	Q₈	—	11	1	no	—
43	D₄	—	11	2	no	—
44	D₄	C₃×D₁₁	1	1	yes	characteristic, complemented
45	C₂×C₄	—	11	2	no	—
46	C₂×C₄	—	11	1	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	—	22	1	no	—
49	C₂×C₃	C₂²×D₁₁	1	1	yes	characteristic
50	C₂²	—	11	1	no	—
51	C₂²	C₂×C₃×D₁₁	1	2	yes	—
52	C₄	—	11	1	no	—
53	C₄	—	11	2	no	—
54	C₄	C₂×C₃×D₁₁	1	1	yes	characteristic
55	C₃	#4341	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	2	2	no	—
57	C₂	—	22	1	no	—
58	C₂	C₂²×C₃×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₁₁
commutator, cosocle	C₂×C₁₁	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₁₁
Fitting	C₃×D₄×C₁₁	C₂
socle	C₂×C₃×C₁₁	C₂³
hypercenter	C₃×D₄	D₁₁
hypocenter	C₁₁	C₃×#41
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₁₁	C₂	semidirect
2. C₃×C₂²⋊D₁₁	C₂	semidirect
3. C₂×C₃×Dic₁₁	C₂	semidirect
4. C₃×C₄×D₁₁	C₂	semidirect
5. C₃×Dic₂₂	C₂	semidirect
6. #4341	C₃	direct (N × H)
12. D₄×C₁₁	C₂×C₃	semidirect
13. C₂²⋊D₁₁	C₂×C₃	semidirect
14. C₂×Dic₁₁	C₂×C₃	semidirect
15. C₄×D₁₁	C₂×C₃	semidirect
16. Dic₂₂	C₂×C₃	semidirect
26. C₃×C₁₁	#41	semidirect
29. C₃×D₄	D₁₁	semidirect
41. C₁₁	C₃×#41	semidirect
44. D₄	C₃×D₁₁	semidirect
55. C₃	#4341	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×D₄×C₁₁	2
C₃×C₂²⋊D₁₁	2
C₂×C₃×Dic₁₁	2
C₃×C₄×D₁₁	2
C₃×Dic₂₂	2
#4341	3
C₃×#41	11

Subgroups — C3×#4341 #10587261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4341 #10587261