Subgroups — #44531962

Order 31347.

170 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	C₃×C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₄₃⋊C₉	—	3	1	no	—
5	#16812505	—	3	2	no	—
6	#16812505	—	3	2	no	—
7	#16812505	C₉	1	6	yes	complemented
8	C₃×C₄₃⋊C₂₇	—	3	2	no	—
9	#16812499	—	3	1	no	—
10	#16812499	—	3	1	no	—
11	#16812499	C₉	1	3	yes	—
12	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₄₃×C₂₇⋊C₃	—	3	1	no	—
14	C₄₃×C₂₇⋊C₃	—	3	2	no	—
15	C₃×C₂₇×C₄₃	C₉	1	3	yes	complemented
16	C₃×C₄₃⋊C₉	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	9	3	no	—
18	C₄₃⋊C₂₇	—	3	6	no	—
19	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
20	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
23	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
25	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
26	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
27	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
28	C₂₇×C₄₃	—	3	3	no	—
29	#10624472	—	43	1	no	maximal, Sylow
30	C₃²×C₄₃	—	3	3	no	—
31	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
32	C₃²×C₄₃	C₉⋊C₉	1	2	yes	—
33	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
34	C₉×C₄₃	C₉²	1	1	yes	characteristic
35	C₉×C₄₃	C₃²⋊C₉	1	2	yes	—
36	C₉×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
37	C₉×C₄₃	C₉⋊C₉	1	2	yes	—
38	C₉×C₄₃	C₉⋊C₉	1	2	yes	—
39	C₉×C₄₃	C₉⋊C₉	1	1	yes	characteristic
40	C₄₃⋊C₉	—	9	3	no	—
41	C₃×C₂₇⋊C₃	—	43	2	no	—
42	C₃×C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic
43	C₃×C₉⋊C₉	—	43	1	no	—
44	C₃×C₄₃	—	3	1	no	—
45	C₃×C₄₃	—	3	2	no	—
46	C₃×C₄₃	#6855	1	1	yes	characteristic
47	C₃×C₄₃	#6875	1	3	yes	—
48	C₃²×C₉	—	129	1	no	—
49	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
50	C₂₇⋊C₃	—	3	1	no	—
51	C₂₇⋊C₃	—	3	2	no	—
52	C₂₇⋊C₃	—	43	6	no	—
53	C₂₇⋊C₃	—	129	2	no	—
54	C₂₇⋊C₃	—	129	2	no	—
55	C₃×C₂₇	—	129	2	no	—
56	C₃×C₂₇	C₄₃⋊C₉	1	3	yes	complemented
57	C₉⋊C₉	—	43	3	no	—
58	C₉⋊C₉	—	129	1	no	—
59	C₉⋊C₉	—	129	1	no	—
60	C₄₃	#10624472	1	1	yes	characteristic, complemented, Sylow
61	C₃³	#11923957	1	1	yes	characteristic
62	C₃×C₉	—	129	3	no	—
63	C₃×C₉	—	387	3	no	—
64	C₃×C₉	C₉×C₄₃⋊C₃	1	2	yes	—
65	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
66	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
67	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
68	C₃×C₉	#11923956	1	2	yes	—
69	C₃×C₉	#11923956	1	1	yes	characteristic
70	C₃×C₉	#11923957	1	2	yes	—
71	C₃×C₉	#11923958	1	2	yes	—
72	C₂₇	—	3	3	no	—
73	C₂₇	—	129	6	no	—
74	C₃²	—	3	3	no	—
75	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
76	C₃²	(C₄₃⋊C₉)⋊C₉	1	2	yes	—
77	C₃²	#16812499	1	1	yes	characteristic
78	C₉	—	387	3	no	—
79	C₉	C₉×C₄₃⋊C₉	1	1	yes	characteristic
80	C₉	(C₃×C₄₃⋊C₃)⋊C₉	1	2	yes	—
81	C₉	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
82	C₉	(C₄₃⋊C₉)⋊C₉	1	2	yes	—
83	C₉	(C₄₃⋊C₉)⋊C₉	1	2	yes	—
84	C₉	#16812500	1	1	yes	characteristic
85	C₃	—	3	1	no	—
86	C₃	—	3	2	no	—
87	C₃	C₄₃⋊#6855	1	1	yes	characteristic
88	C₃	#23782736	1	3	yes	—

	subgroup	G/H
center	C₃²	#16812499
commutator	C₉×C₄₃	C₉²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₂₇⋊C₃	C₃
socle	C₃²×C₄₃	C₉⋊C₉
prime radical	C₃³×C₄₃	3₋¹⁺²
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₂₇⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	#10624472
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
7. #16812505	C₉	semidirect
15. C₃×C₂₇×C₄₃	C₉	semidirect
56. C₃×C₂₇	C₄₃⋊C₉	semidirect
60. C₄₃	#10624472	semidirect

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
C₃×C₄₃×C₂₇⋊C₃	3
#10624472	43