Subgroups — #44531918

Order 31347.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11923958	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₄₃⋊C₂₇)	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₄₃⋊C₂₇)	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	C₉	1	1	yes	characteristic
6	C₃×C₄₃⋊C₂₇	—	3	1	no	—
7	C₃×C₄₃⋊C₂₇	—	3	1	no	—
8	(C₄₃⋊C₉)⋊C₉	—	3	1	no	—
9	(C₄₃⋊C₉)⋊C₉	—	3	1	no	—
10	C₃²⋊(C₄₃⋊C₉)	C₉	1	1	yes	characteristic
11	C₃²⋊(C₄₃⋊C₉)	C₉	1	1	yes	characteristic
12	C₉×C₄₃⋊C₉	—	3	1	no	—
13	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
14	C₄₃×C₂₇⋊C₃	—	3	3	no	—
15	C₃×C₂₇×C₄₃	—	3	1	no	—
16	#11923958	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	3	1	no	—
18	C₃×C₄₃⋊C₉	—	3	1	no	—
19	C₃×C₄₃⋊C₉	—	3	1	no	—
20	C₄₃⋊C₂₇	—	9	1	no	—
21	C₄₃⋊C₂₇	—	9	1	no	—
22	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
23	C₃×C₉×C₄₃	—	3	1	no	—
24	C₃×C₉×C₄₃	—	3	1	no	—
25	C₃×C₉×C₄₃	—	3	1	no	—
26	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
29	C₂₇×C₄₃	—	3	3	no	—
30	#10624455	—	43	1	no	maximal, Sylow
31	C₃²×C₄₃	—	3	1	no	—
32	C₃²×C₄₃	—	3	1	no	—
33	C₃²×C₄₃	—	3	1	no	—
34	C₃²×C₄₃	—	3	1	no	—
35	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
36	C₉×C₄₃	—	3	1	no	—
37	C₉×C₄₃	—	3	1	no	—
38	C₉×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	C₉×C₄₃	#731	1	1	yes	characteristic
40	C₉×C₄₃	#733	1	1	yes	characteristic
41	C₄₃⋊C₉	—	3	3	no	—
42	C₄₃⋊C₉	—	9	1	no	—
43	C₄₃⋊C₉	—	9	1	no	—
44	C₃×C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic
45	C₉×3₋¹⁺²	—	43	1	no	—
46	C₃²⋊C₂₇	—	43	1	no	—
47	C₃²⋊C₂₇	—	43	1	no	—
48	C₃×C₄₃	—	9	1	no	—
49	C₃×C₄₃	#6869	1	1	yes	characteristic
50	C₃×C₄₃	3₋¹⁺²⋊C₉	1	1	yes	characteristic
51	C₃×C₄₃	#6872	1	1	yes	characteristic
52	C₃×C₄₃	#6873	1	1	yes	characteristic
53	C₃×3₋¹⁺²	—	43	1	no	—
54	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
55	C₂₇⋊C₃	—	3	3	no	—
56	C₃×C₂₇	—	3	1	no	—
57	C₃×C₂₇	—	129	1	no	—
58	C₃×C₂₇	—	129	1	no	—
59	C₉⋊C₉	—	129	1	no	—
60	C₉⋊C₉	—	129	1	no	—
61	C₃²⋊C₉	—	43	1	no	—
62	C₃²⋊C₉	—	43	1	no	—
63	C₉²	—	129	1	no	—
64	C₄₃	#10624455	1	1	yes	characteristic, complemented, Sylow
65	C₃³	C₉×C₄₃⋊C₃	1	1	yes	characteristic
66	3₋¹⁺²	—	129	3	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	129	1	no	—
71	C₃×C₉	—	129	1	no	—
72	C₃×C₉	—	129	1	no	—
73	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
74	C₃×C₉	#11923956	1	1	yes	characteristic
75	C₃×C₉	#11923957	1	1	yes	characteristic
76	C₂₇	—	3	3	no	—
77	C₂₇	—	387	1	no	—
78	C₂₇	—	387	1	no	—
79	C₃²	—	3	1	no	—
80	C₃²	—	3	1	no	—
81	C₃²	—	3	1	no	—
82	C₃²	—	3	1	no	—
83	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	129	3	no	—
87	C₉	—	387	1	no	—
88	C₉	—	387	1	no	—
89	C₉	#16812507	1	1	yes	characteristic
90	C₉	#16812510	1	1	yes	characteristic
91	C₉	#16812515	1	1	yes	characteristic
92	C₃	—	9	1	no	—
93	C₃	#23782717	1	1	yes	characteristic
94	C₃	#23782724	1	1	yes	characteristic
95	C₃	#23782726	1	1	yes	characteristic
96	C₃	#23782729	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator, prime radical	C₃³×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₂₇⋊C₃	C₃
socle	C₃²×C₄₃	C₃²⋊C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₂₇⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	#10624455
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
64. C₄₃	#10624455	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×#11923958	3
C₃²⋊(C₄₃⋊C₂₇)	3
C₃×C₄₃×C₂₇⋊C₃	3
#10624455	43