Subgroups — #44531950

Order 31347.

164 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	C₃²×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
4	#16812505	—	3	2	no	—
5	#16812505	—	3	2	no	—
6	#16812505	C₉	1	6	yes	complemented
7	C₃×C₄₃⋊C₂₇	—	3	1	no	—
8	C₃×C₄₃⋊C₂₇	—	3	2	no	—
9	C₃×C₄₃⋊C₂₇	—	3	1	no	—
10	C₃×C₄₃⋊C₂₇	—	3	1	no	—
11	C₃×C₄₃⋊C₂₇	C₉	1	3	yes	complemented
12	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₄₃×C₉⋊C₉	—	3	2	no	—
14	C₄₃×C₃²⋊C₉	C₉	1	3	yes	—
15	C₉²×C₄₃	—	3	1	no	—
16	C₄₃⋊C₂₇	—	3	3	no	—
17	C₄₃⋊C₂₇	—	3	6	no	—
18	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
19	C₃×C₉×C₄₃	—	3	3	no	—
20	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
22	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
24	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
25	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
26	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
27	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
28	#10624469	—	43	1	no	maximal, Sylow
29	C₃²×C₄₃	—	3	3	no	—
30	C₃²×C₄₃	C₉²	1	1	yes	characteristic
31	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
32	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
33	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
34	C₉×C₄₃	—	9	3	no	—
35	C₉×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
36	C₉×C₄₃	C₃²⋊C₉	1	2	yes	—
37	C₉×C₄₃	C₉⋊C₉	1	2	yes	—
38	C₉×C₄₃	C₉⋊C₉	1	2	yes	—
39	C₉×C₄₃	C₉⋊C₉	1	2	yes	—
40	C₃×C₂₇⋊C₃	—	43	2	no	—
41	C₃²×C₂₇	—	43	1	no	—
42	#6887	C₄₃⋊C₃	1	1	yes	characteristic
43	C₃×C₄₃	—	3	1	no	—
44	C₃×C₄₃	—	3	1	no	—
45	C₃×C₄₃	—	3	1	no	—
46	C₃×C₄₃	#6855	1	1	yes	characteristic
47	C₃×C₄₃	#6872	1	3	yes	—
48	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
49	C₂₇⋊C₃	—	43	6	no	—
50	C₂₇⋊C₃	—	129	2	no	—
51	C₂₇⋊C₃	—	129	2	no	—
52	C₃×C₂₇	—	43	3	no	—
53	C₃×C₂₇	—	129	1	no	—
54	C₃×C₂₇	—	129	2	no	—
55	C₃×C₂₇	—	129	1	no	—
56	C₃×C₂₇	—	129	1	no	—
57	C₉⋊C₉	—	3	2	no	—
58	C₃²⋊C₉	C₄₃⋊C₉	1	3	yes	—
59	C₉²	—	3	1	no	—
60	C₄₃	#10624469	1	1	yes	characteristic, complemented, Sylow
61	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
64	C₃×C₉	C₉×C₄₃⋊C₃	1	2	yes	—
65	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
66	C₃×C₉	#11923956	1	1	yes	characteristic
67	C₃×C₉	#11923956	1	2	yes	—
68	C₃×C₉	#11923957	1	1	yes	characteristic
69	C₃×C₉	#11923957	1	2	yes	—
70	C₃×C₉	#11923958	1	2	yes	—
71	C₂₇	—	129	3	no	—
72	C₂₇	—	129	6	no	—
73	C₃²	—	3	3	no	—
74	C₃²	C₉×C₄₃⋊C₉	1	1	yes	characteristic
75	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
76	C₃²	#16812499	1	1	yes	characteristic
77	C₃²	#16812500	1	1	yes	characteristic
78	C₉	—	9	3	no	—
79	C₉	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
80	C₉	(C₃×C₄₃⋊C₃)⋊C₉	1	2	yes	—
81	C₉	(C₄₃⋊C₉)⋊C₉	1	2	yes	—
82	C₉	(C₄₃⋊C₉)⋊C₉	1	2	yes	—
83	C₉	(C₄₃⋊C₉)⋊C₉	1	2	yes	—
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	C₄₃⋊#6855	1	1	yes	characteristic
88	C₃	#23782727	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator	C₃²×C₄₃	C₉²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃²×C₄₃	C₃²⋊C₉
prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624469
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
6. #16812505	C₉	semidirect
11. C₃×C₄₃⋊C₂₇	C₉	semidirect
60. C₄₃	#10624469	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
C₃²×C₄₃⋊C₂₇	3
C₄₃×#6887	3
#10624469	43