Subgroups — C₃×#23782757 #44534510

Order 31347.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812515	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#16812513	C₃	1	2	yes	maximal, complemented
3	#23782757	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#11923958	—	3	1	no	—
6	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
7	#16812515	—	3	2	no	—
8	#16812515	C₃²	1	3	yes	complemented
9	#16812513	—	3	4	no	—
10	#16812513	C₃²	1	6	yes	complemented
11	C₃²×C₉×C₄₃	—	3	1	no	—
12	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₄₃×C₉⋊C₉	—	3	2	no	—
14	C₄₃×C₉⋊C₉	C₃²	1	3	yes	complemented
15	C₃²×C₄₃⋊C₃	—	9	2	no	—
16	#11923958	—	3	3	no	—
17	#11923958	—	9	2	no	—
18	C₃²⋊(C₄₃⋊C₃)	—	3	6	no	—
19	C₃²⋊(C₄₃⋊C₃)	—	9	4	no	—
20	C₃×C₄₃⋊C₉	—	9	1	no	—
21	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×C₉×C₄₃	—	3	2	no	—
23	C₃×C₉×C₄₃	—	3	1	no	—
24	C₃×C₉×C₄₃	—	3	3	no	—
25	C₃×C₉×C₄₃	—	9	3	no	—
26	C₃×C₉×C₄₃	H(3,𝔽₃)	1	2	yes	—
27	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
28	C₃×#6881	—	43	1	no	maximal, Sylow
29	C₃²×C₄₃	—	3	3	no	—
30	C₃²×C₄₃	#732	1	2	yes	—
31	C₃²×C₄₃	#732	1	1	yes	characteristic
32	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃×C₄₃⋊C₃	—	9	6	no	—
34	C₃×C₄₃⋊C₃	—	27	6	no	—
35	C₉×C₄₃	—	3	2	no	—
36	C₉×C₄₃	—	3	1	no	—
37	C₉×C₄₃	—	9	3	no	—
38	C₄₃⋊C₉	—	9	3	no	—
39	C₃×#733	—	43	1	no	—
40	C₃×#732	—	43	2	no	—
41	C₃×C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
42	#6881	—	43	9	no	—
43	C₃×C₄₃	—	3	1	no	—
44	C₃×C₄₃	—	3	2	no	—
45	C₃×C₄₃	#6881	1	3	yes	complemented
46	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
47	C₄₃⋊C₃	—	27	6	no	—
48	C₃×3₋¹⁺²	—	129	1	no	—
49	C₃×H(3,𝔽₃)	—	129	2	no	—
50	C₃²×C₉	—	3	1	no	—
51	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
52	#733	—	43	3	no	—
53	#733	—	129	2	no	—
54	#732	—	43	6	no	—
55	#732	—	129	4	no	—
56	C₉⋊C₉	—	3	2	no	—
57	C₉⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	complemented
58	C₄₃	C₃×#6881	1	1	yes	characteristic, complemented, Sylow
59	C₃³	—	387	2	no	—
60	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
61	3₋¹⁺²	—	129	3	no	—
62	3₋¹⁺²	—	387	2	no	—
63	H(3,𝔽₃)	—	129	6	no	—
64	H(3,𝔽₃)	—	387	4	no	—
65	C₃×C₉	—	3	2	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	9	3	no	—
69	C₃×C₉	—	387	1	no	—
70	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
71	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
72	C₃²	—	3	3	no	—
73	C₃²	—	387	6	no	—
74	C₃²	—	1161	6	no	—
75	C₃²	#16812513	1	2	yes	—
76	C₃²	#16812513	1	1	yes	characteristic
77	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
78	C₉	—	3	2	no	—
79	C₉	—	3	1	no	—
80	C₉	—	9	3	no	—
81	C₉	—	387	3	no	—
82	C₃	—	3	1	no	—
83	C₃	—	3	2	no	—
84	C₃	—	1161	6	no	—
85	C₃	#23782757	1	3	yes	direct product factor
86	C₃	C₃×#16812513	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#16812513
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₉⋊C₉	C₃
socle	C₃²×C₄₃	#732
hypercenter	C₃×C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#6881
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
1. C₃×#16812515	C₃	semidirect
2. C₃×#16812513	C₃	semidirect
3. #23782757	C₃	direct (N × H)
4. C₃×C₄₃×C₉⋊C₉	C₃	semidirect
8. #16812515	C₃²	semidirect
10. #16812513	C₃²	semidirect
14. C₄₃×C₉⋊C₉	C₃²	semidirect
41. C₃×C₉⋊C₉	C₄₃⋊C₃	semidirect
45. C₃×C₄₃	#6881	semidirect
57. C₉⋊C₉	C₃×C₄₃⋊C₃	semidirect
58. C₄₃	C₃×#6881	semidirect
85. C₃	#23782757	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×#16812515	3
C₃×#16812513	3
#23782757	3
C₃×C₄₃×C₉⋊C₉	3
C₃×#6881	43

Subgroups — C3×#23782757 #44534510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23782757 #44534510