Subgroups — C₃×A₄×#10597245 #36345176

Order 21780.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#10597245	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×#10597245	C₃	1	3	yes	maximal, direct product factor
3	C₃²×#10597245	—	4	1	no	maximal, Hall
4	C₃×C₁₁²×A₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×#10597245	—	3	1	no	—
6	C₂²×#10597245	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×A₄×C₁₁⋊C₅	—	11	2	no	maximal
8	C₃×#10597245	—	4	3	no	—
9	C₃×#10597245	A₄	1	1	yes	characteristic, direct product factor
10	C₂²×C₃×C₁₁²	C₃×C₅	1	1	yes	characteristic, complemented
11	C₁₁²×A₄	C₃×C₅	1	3	yes	complemented
12	C₂×#10597245	—	3	1	no	—
13	C₃²×C₁₁²	—	4	1	no	Hall
14	C₂×C₃×C₁₁²	—	3	1	no	—
15	C₂²×C₃×C₁₁⋊C₅	—	11	2	no	—
16	A₄×C₁₁⋊C₅	—	11	6	no	—
17	#10597245	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₁₁⋊C₅	—	44	2	no	—
19	C₂²×C₁₁²	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×A₄	—	5	2	no	—
21	C₃×C₁₁×A₄	C₁₁⋊C₅	1	2	yes	complemented
22	C₃×C₁₁²	—	4	3	no	—
23	C₃×C₁₁²	C₅×A₄	1	1	yes	characteristic, complemented
24	C₂×C₃×C₁₁⋊C₅	—	33	2	no	—
25	C₂×C₁₁²	—	3	1	no	—
26	C₂²×C₁₁⋊C₅	—	11	2	no	—
27	C₃×C₅×A₄	—	121	1	no	Hall
28	C₃×C₁₁⋊C₅	—	11	2	no	—
29	C₃×C₁₁⋊C₅	—	44	6	no	—
30	C₂²×C₃×C₁₁	—	5	2	no	—
31	C₂²×C₃×C₁₁	C₃×C₁₁⋊C₅	1	2	yes	complemented
32	C₁₁×A₄	—	5	6	no	—
33	C₁₁×A₄	C₃×C₁₁⋊C₅	1	6	yes	complemented
34	C₁₁²	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₁₁⋊C₅	—	33	2	no	—
36	C₃²×C₁₁	—	4	2	no	—
37	C₃²×C₁₁	—	20	2	no	—
38	C₂×C₃×C₁₁	—	3	2	no	—
39	C₂×C₃×C₁₁	—	15	2	no	—
40	C₂²×C₃×C₅	—	121	1	no	—
41	C₅×A₄	—	121	3	no	—
42	C₁₁⋊C₅	—	11	2	no	—
43	C₃²×C₅	—	484	1	no	Hall
44	C₂²×C₁₁	—	5	2	no	—
45	C₂²×C₁₁	C₃²×C₁₁⋊C₅	1	2	yes	complemented
46	C₃×A₄	#10597245	1	1	yes	characteristic, direct product factor, Hall
47	C₃×C₁₁	—	4	6	no	—
48	C₃×C₁₁	—	5	2	no	—
49	C₃×C₁₁	—	20	6	no	—
50	C₃×C₁₁	A₄×C₁₁⋊C₅	1	2	yes	complemented
51	C₂×C₃×C₅	—	363	1	no	—
52	C₂×C₁₁	—	3	2	no	—
53	C₂×C₁₁	—	15	2	no	—
54	C₂²×C₅	—	121	1	no	Hall
55	C₃×C₅	—	121	1	no	—
56	C₃×C₅	—	484	3	no	—
57	C₂²×C₃	C₃×#10597245	1	1	yes	characteristic, complemented
58	A₄	C₃×#10597245	1	3	yes	direct product factor
59	C₁₁	—	5	2	no	—
60	C₁₁	C₃×A₄×C₁₁⋊C₅	1	2	yes	complemented
61	C₂×C₅	—	363	1	no	—
62	C₃²	—	4	1	no	Sylow
63	C₂×C₃	—	3	1	no	—
64	C₅	—	121	1	no	Sylow
65	C₂²	C₃²×#10597245	1	1	yes	characteristic, complemented, Sylow
66	C₃	—	4	3	no	—
67	C₃	A₄×#10597245	1	1	yes	characteristic, direct product factor
68	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	A₄×#10597245
commutator, cosocle, hypocenter	C₂²×C₁₁²	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₁²	C₃×C₅
LCS	G ▷ C₂²×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#10597245	C₃	semidirect
2. A₄×#10597245	C₃	direct (N × H)
4. C₃×C₁₁²×A₄	C₅	semidirect
6. C₂²×#10597245	C₃²	semidirect
9. C₃×#10597245	A₄	direct (N × H)
10. C₂²×C₃×C₁₁²	C₃×C₅	semidirect
11. C₁₁²×A₄	C₃×C₅	semidirect
17. #10597245	C₃×A₄	direct (N × H)
19. C₂²×C₁₁²	C₃²×C₅	semidirect
21. C₃×C₁₁×A₄	C₁₁⋊C₅	semidirect
23. C₃×C₁₁²	C₅×A₄	semidirect
31. C₂²×C₃×C₁₁	C₃×C₁₁⋊C₅	semidirect
33. C₁₁×A₄	C₃×C₁₁⋊C₅	semidirect
34. C₁₁²	C₃×C₅×A₄	semidirect
45. C₂²×C₁₁	C₃²×C₁₁⋊C₅	semidirect
46. C₃×A₄	#10597245	direct (N × H)
50. C₃×C₁₁	A₄×C₁₁⋊C₅	semidirect
57. C₂²×C₃	C₃×#10597245	semidirect
58. A₄	C₃×#10597245	direct (N × H)
60. C₁₁	C₃×A₄×C₁₁⋊C₅	semidirect
65. C₂²	C₃²×#10597245	semidirect
67. C₃	A₄×#10597245	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#10597245	3
A₄×#10597245	3
C₃²×#10597245	4
C₃×C₁₁²×A₄	5
C₃×A₄×C₁₁⋊C₅	11

Subgroups — C3×A4×#10597245 #36345176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×A₄×#10597245 #36345176