Subgroups — #44532016

Order 31347.

130 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	#23782822	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782714	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#6895	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
6	#16812513	—	3	3	no	—
7	(C₄₃⋊C₉)⋊C₉	—	3	3	no	—
8	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
9	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
10	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
11	C₄₃×C₉⋊C₉	—	3	3	no	—
12	C₄₃×C₃²⋊C₉	—	3	1	no	—
13	C₃²×C₄₃⋊C₃	—	9	1	no	—
14	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
15	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
16	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
17	C₃×C₄₃⋊C₉	—	3	3	no	—
18	C₃×C₄₃⋊C₉	—	9	1	no	—
19	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×C₉×C₄₃	—	3	3	no	—
21	C₃×C₉×C₄₃	—	3	1	no	—
22	C₃×C₉×C₄₃	—	3	1	no	—
23	C₃×C₉×C₄₃	—	3	1	no	—
24	C₃×C₉×C₄₃	—	3	1	no	—
25	#10624484	—	43	1	no	maximal, Sylow
26	C₃²×C₄₃	—	9	1	no	—
27	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
28	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
29	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
30	C₃²×C₄₃	#731	1	1	yes	characteristic
31	C₃×C₄₃⋊C₃	—	9	3	no	—
32	C₃×C₄₃⋊C₃	—	27	3	no	—
33	C₉×C₄₃	—	9	3	no	—
34	C₉×C₄₃	—	9	1	no	—
35	C₄₃⋊C₉	—	9	3	no	—
36	C₄₃⋊C₉	—	27	1	no	—
37	C₃×#732	—	43	1	no	—
38	#6895	—	43	1	no	—
39	#6895	C₄₃⋊C₃	1	1	yes	characteristic, complemented
40	#6867	—	43	1	no	—
41	C₃×C₄₃	—	3	1	no	—
42	C₃×C₄₃	—	3	1	no	—
43	C₃×C₄₃	—	3	1	no	—
44	C₃×C₄₃	—	3	1	no	—
45	C₃×C₄₃	#6857	1	1	yes	characteristic
46	C₄₃⋊C₃	—	27	3	no	—
47	C₃×H(3,𝔽₃)	—	129	1	no	—
48	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
49	#732	—	129	3	no	—
50	C₉⋊C₉	—	3	3	no	—
51	C₉⋊C₉	—	129	3	no	—
52	C₃²⋊C₉	—	3	1	no	—
53	C₃²⋊C₉	—	129	1	no	—
54	C₃²⋊C₉	—	129	1	no	—
55	C₄₃	#10624484	1	1	yes	characteristic, complemented, Sylow
56	C₃³	—	387	1	no	—
57	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
58	H(3,𝔽₃)	—	129	3	no	—
59	H(3,𝔽₃)	—	387	1	no	—
60	H(3,𝔽₃)	—	387	1	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	129	3	no	—
67	C₃×C₉	—	387	1	no	—
68	C₃²	—	9	1	no	—
69	C₃²	—	387	3	no	—
70	C₃²	—	1161	3	no	—
71	C₃²	#16812507	1	1	yes	characteristic
72	C₃²	#16812508	1	1	yes	characteristic
73	C₃²	#16812508	1	1	yes	characteristic
74	C₃²	#16812511	1	1	yes	characteristic
75	C₉	—	9	3	no	—
76	C₉	—	9	1	no	—
77	C₉	—	387	3	no	—
78	C₉	—	1161	1	no	—
79	C₃	—	3	1	no	—
80	C₃	—	3	1	no	—
81	C₃	—	3	1	no	—
82	C₃	—	3	1	no	—
83	C₃	—	1161	3	no	—
84	C₃	#23782688	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782688
commutator, cosocle	C₃²×C₉×C₄₃	C₃²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6895	C₃
socle	C₃×C₄₃	#6857
prime radical	C₃×#16812513	C₃
hypercenter	#6895	C₄₃⋊C₃
hypocenter	C₄₃	#10624484
LCS	G ▷ C₃²×C₉×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6895

Complements

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

N	H ≅ G/N	type
2. #23782822	C₃	semidirect
3. #23782714	C₃	semidirect
4. C₄₃×#6895	C₃	semidirect
39. #6895	C₄₃⋊C₃	semidirect
55. C₄₃	#10624484	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
#23782822	3
#23782714	3
C₄₃×#6895	3
#10624484	43