Subgroups — #44532178

Order 31347.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812513	C₃	1	1	yes	maximal, characteristic
2	#23782716	C₃	1	2	yes	maximal, complemented
3	C₃×C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
5	#16812513	—	3	1	no	—
6	#16812513	—	3	1	no	—
7	#16812513	C₉	1	3	yes	complemented
8	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
9	C₃²×C₉×C₄₃	—	3	1	no	—
10	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
11	C₄₃×C₉⋊C₉	—	3	3	no	—
12	C₃²×C₄₃⋊C₃	—	9	1	no	—
13	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
14	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
15	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
16	C₃×C₄₃⋊C₉	—	9	2	no	—
17	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₉×C₄₃	—	3	1	no	—
19	C₃×C₉×C₄₃	—	3	1	no	—
20	C₃×C₉×C₄₃	—	3	1	no	—
21	C₃×C₉×C₄₃	—	3	3	no	—
22	C₃×C₉×C₄₃	—	9	2	no	—
23	C₃×C₉×C₄₃	—	9	1	no	—
24	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
25	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
26	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
27	#10624527	—	43	1	no	maximal, Sylow
28	C₃²×C₄₃	—	3	2	no	—
29	C₃²×C₄₃	—	3	1	no	—
30	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
31	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
32	C₃²×C₄₃	#731	1	1	yes	characteristic
33	C₃²×C₄₃	#732	1	1	yes	characteristic
34	C₃×C₄₃⋊C₃	—	9	3	no	—
35	C₃×C₄₃⋊C₃	—	27	2	no	—
36	C₃×C₄₃⋊C₃	—	27	1	no	—
37	C₉×C₄₃	—	3	1	no	—
38	C₉×C₄₃	—	3	1	no	—
39	C₉×C₄₃	—	3	1	no	—
40	C₉×C₄₃	—	9	3	no	—
41	C₄₃⋊C₉	—	27	2	no	—
42	C₃×#732	—	43	1	no	—
43	C₃×C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
44	#6868	—	43	2	no	—
45	C₃×C₄₃	—	3	1	no	—
46	C₃×C₄₃	—	3	1	no	—
47	C₃×C₄₃	—	3	1	no	—
48	C₃×C₄₃	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
49	C₃×C₄₃	#6881	1	2	yes	—
50	C₃×C₄₃	#6883	1	1	yes	characteristic
51	C₄₃⋊C₃	—	27	3	no	—
52	C₃×H(3,𝔽₃)	—	129	1	no	—
53	C₃²×C₉	—	3	1	no	—
54	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
55	#732	—	43	3	no	—
56	#732	—	129	1	no	—
57	#732	—	129	1	no	—
58	C₉⋊C₉	—	3	3	no	—
59	C₃²⋊C₉	—	129	2	no	—
60	C₄₃	#10624527	1	1	yes	characteristic, complemented, Sylow
61	C₃³	—	387	1	no	—
62	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
63	H(3,𝔽₃)	—	129	3	no	—
64	H(3,𝔽₃)	—	387	1	no	—
65	H(3,𝔽₃)	—	387	1	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	3	no	—
70	C₃×C₉	—	9	2	no	—
71	C₃×C₉	—	9	1	no	—
72	C₃×C₉	—	387	2	no	—
73	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
74	C₃×C₉	#11923956	1	1	yes	characteristic
75	C₃×C₉	#11923957	1	1	yes	characteristic
76	C₃²	—	3	2	no	—
77	C₃²	—	3	1	no	—
78	C₃²	—	387	3	no	—
79	C₃²	—	1161	2	no	—
80	C₃²	—	1161	1	no	—
81	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
82	C₃²	#16812507	1	1	yes	characteristic
83	C₃²	#16812510	1	1	yes	characteristic
84	C₃²	#16812513	1	1	yes	characteristic
85	C₉	—	3	1	no	—
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	9	3	no	—
89	C₉	—	1161	2	no	—
90	C₃	—	3	1	no	—
91	C₃	—	3	1	no	—
92	C₃	—	3	1	no	—
93	C₃	—	1161	3	no	—
94	C₃	#23782721	1	1	yes	characteristic
95	C₃	#23782757	1	2	yes	—
96	C₃	#23782767	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#16812513
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₉⋊C₉	C₃
socle	C₃²×C₄₃	#732
prime radical	C₃×#16812513	C₃
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#10624527
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
2. #23782716	C₃	semidirect
3. C₃×C₄₃×C₉⋊C₉	C₃	semidirect
7. #16812513	C₉	semidirect
43. C₃×C₉⋊C₉	C₄₃⋊C₃	semidirect
60. C₄₃	#10624527	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812513	3
#23782716	3
C₃×C₄₃×C₉⋊C₉	3
#10624527	43