Subgroups — C₃×#23782736 #44533477

Order 31347.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812505	C₃	1	2	yes	maximal
2	C₃×#16812499	C₃	1	1	yes	maximal, characteristic
3	#23782736	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃²×C₄₃⋊C₉	—	3	1	no	—
6	#16812505	—	3	4	no	—
7	#16812505	C₃²	1	6	yes	—
8	C₃×C₄₃⋊C₂₇	—	3	2	no	—
9	#16812499	—	3	2	no	—
10	#16812499	C₃²	1	3	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃×C₂₇⋊C₃	C₉	1	6	yes	complemented
13	C₄₃×C₂₇⋊C₃	C₃²	1	3	yes	—
14	C₃×C₂₇×C₄₃	C₉	1	3	yes	complemented
15	C₃×C₄₃⋊C₉	—	3	3	no	—
16	C₃×C₄₃⋊C₉	—	9	3	no	—
17	C₄₃⋊C₂₇	—	3	6	no	—
18	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
19	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
22	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
23	C₃×C₉×C₄₃	3₋¹⁺²	1	4	yes	—
24	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
25	C₂₇×C₄₃	C₃×C₉	1	9	yes	complemented
26	C₃×#6875	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	—	3	3	no	—
28	C₃²×C₄₃	C₉⋊C₉	1	2	yes	—
29	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
30	C₃²×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
31	C₉×C₄₃	C₉⋊C₉	1	2	yes	—
32	C₉×C₄₃	C₉⋊C₉	1	4	yes	—
33	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
34	C₉×C₄₃	C₃×3₋¹⁺²	1	2	yes	—
35	C₄₃⋊C₉	—	9	3	no	—
36	C₃×C₂₇⋊C₃	—	43	2	no	—
37	C₃×C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic
38	C₃×C₉⋊C₉	—	43	1	no	—
39	#6875	—	43	9	no	—
40	C₃×C₄₃	—	3	1	no	—
41	C₃×C₄₃	—	3	2	no	—
42	C₃×C₄₃	#6875	1	3	yes	complemented
43	C₃×C₄₃	C₃×C₉⋊C₉	1	1	yes	characteristic
44	C₃²×C₉	—	129	1	no	—
45	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
46	C₂₇⋊C₃	—	43	6	no	—
47	C₂₇⋊C₃	—	129	4	no	—
48	C₂₇⋊C₃	C₄₃⋊C₉	1	6	yes	complemented
49	C₂₇⋊C₃	C₃×C₄₃⋊C₃	1	3	yes	—
50	C₃×C₂₇	—	129	2	no	—
51	C₃×C₂₇	C₄₃⋊C₉	1	3	yes	complemented
52	C₉⋊C₉	—	43	3	no	—
53	C₉⋊C₉	—	129	2	no	—
54	C₄₃	C₃×#6875	1	1	yes	characteristic, complemented, Sylow
55	C₃³	#11923957	1	1	yes	characteristic
56	C₃×C₉	—	129	3	no	—
57	C₃×C₉	—	387	3	no	—
58	C₃×C₉	C₃×C₄₃⋊C₉	1	2	yes	—
59	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
60	C₃×C₉	#11923957	1	2	yes	—
61	C₃×C₉	#11923957	1	4	yes	—
62	C₃×C₉	#11923957	1	2	yes	—
63	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
64	C₂₇	—	129	6	no	—
65	C₂₇	C₃×C₄₃⋊C₉	1	9	yes	complemented
66	C₃²	—	3	3	no	—
67	C₃²	#16812499	1	2	yes	—
68	C₃²	#16812499	1	1	yes	characteristic
69	C₃²	C₃×#11923957	1	1	yes	characteristic
70	C₉	—	387	3	no	—
71	C₉	#16812499	1	4	yes	—
72	C₉	#16812499	1	2	yes	—
73	C₉	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
74	C₉	C₃×#11923957	1	2	yes	—
75	C₃	—	3	1	no	—
76	C₃	—	3	2	no	—
77	C₃	#23782736	1	3	yes	direct product factor
78	C₃	C₃×#16812499	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#16812499
commutator	C₉×C₄₃	C₃²×C₉
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₂₇⋊C₃	C₃
socle	C₃²×C₄₃	C₉⋊C₉
prime radical	C₃³×C₄₃	3₋¹⁺²
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	C₃×C₂₇⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#6875
LCS	G ▷ C₉×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
3. #23782736	C₃	direct (N × H)
12. C₄₃×C₂₇⋊C₃	C₉	semidirect
14. C₃×C₂₇×C₄₃	C₉	semidirect
25. C₂₇×C₄₃	C₃×C₉	semidirect
42. C₃×C₄₃	#6875	semidirect
48. C₂₇⋊C₃	C₄₃⋊C₉	semidirect
51. C₃×C₂₇	C₄₃⋊C₉	semidirect
54. C₄₃	C₃×#6875	semidirect
65. C₂₇	C₃×C₄₃⋊C₉	semidirect
77. C₃	#23782736	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×#16812505	3
C₃×#16812499	3
#23782736	3
C₃×C₄₃×C₂₇⋊C₃	3
C₃×#6875	43

Subgroups — C3×#23782736 #44533477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23782736 #44533477