Subgroups — #44534489

Order 31347.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812515	C₃	1	2	yes	maximal, complemented
2	C₃×#16812513	C₃	1	1	yes	maximal, characteristic
3	#23782747	C₃	1	9	yes	maximal, complemented
4	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#11923958	—	3	2	no	—
6	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
7	#16812515	—	3	4	no	—
8	#16812515	C₃²	1	6	yes	complemented
9	#16812513	—	3	2	no	—
10	#16812513	C₃²	1	3	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃×C₉⋊C₉	—	3	2	no	—
13	C₄₃×C₃²⋊C₉	—	3	1	no	—
14	C₉²×C₄₃	C₃²	1	3	yes	complemented
15	C₃²×C₄₃⋊C₃	—	9	1	no	—
16	#11923958	—	3	6	no	—
17	#11923958	—	9	2	no	—
18	#11923958	—	9	2	no	—
19	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
20	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
21	C₃×C₄₃⋊C₉	—	9	2	no	—
22	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×C₉×C₄₃	—	3	2	no	—
24	C₃×C₉×C₄₃	—	3	1	no	—
25	C₃×C₉×C₄₃	—	3	3	no	—
26	C₃×C₉×C₄₃	H(3,𝔽₃)	1	2	yes	—
27	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
28	#10624838	—	43	1	no	maximal, Sylow
29	C₃²×C₄₃	—	9	1	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	3	no	—
34	C₃×C₄₃⋊C₃	—	27	3	no	—
35	C₉×C₄₃	—	3	2	no	—
36	C₉×C₄₃	—	3	1	no	—
37	C₉×C₄₃	—	9	3	no	—
38	C₄₃⋊C₉	—	9	6	no	—
39	C₃×#733	—	43	2	no	—
40	C₃×#732	—	43	1	no	—
41	#6887	C₄₃⋊C₃	1	1	yes	characteristic, complemented
42	#6878	—	43	9	no	—
43	C₃×C₄₃	—	3	1	no	—
44	C₃×C₄₃	—	3	1	no	—
45	C₃×C₄₃	—	3	2	no	—
46	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
47	C₄₃⋊C₃	—	27	3	no	—
48	C₃×3₋¹⁺²	—	129	2	no	—
49	C₃×H(3,𝔽₃)	—	129	1	no	—
50	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	#733	—	43	6	no	—
52	#733	—	129	4	no	—
53	#732	—	43	3	no	—
54	#732	—	129	2	no	—
55	C₉⋊C₉	—	3	2	no	—
56	C₃²⋊C₉	—	3	1	no	—
57	C₉²	C₃×C₄₃⋊C₃	1	3	yes	complemented
58	C₄₃	#10624838	1	1	yes	characteristic, complemented, Sylow
59	C₃³	—	387	1	no	—
60	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
61	3₋¹⁺²	—	129	6	no	—
62	3₋¹⁺²	—	387	2	no	—
63	3₋¹⁺²	—	387	2	no	—
64	H(3,𝔽₃)	—	129	3	no	—
65	H(3,𝔽₃)	—	387	2	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	3	no	—
69	C₃×C₉	—	387	2	no	—
70	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
71	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
72	C₃²	—	9	1	no	—
73	C₃²	—	387	3	no	—
74	C₃²	—	1161	3	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	6	no	—
82	C₃	—	3	1	no	—
83	C₃	—	3	1	no	—
84	C₃	—	3	2	no	—
85	C₃	—	1161	3	no	—
86	C₃	C₃×#16812513	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#16812513
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃×C₄₃	C₃×#732
prime radical	C₃×#16812513	C₃
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624838
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. C₃×#16812515	C₃	semidirect
3. #23782747	C₃	semidirect
4. C₄₃×#6887	C₃	semidirect
8. #16812515	C₃²	semidirect
14. C₉²×C₄₃	C₃²	semidirect
41. #6887	C₄₃⋊C₃	semidirect
57. C₉²	C₃×C₄₃⋊C₃	semidirect
58. C₄₃	#10624838	semidirect

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
#23782747	3
C₄₃×#6887	3
#10624838	43