Subgroups — #44531996

Order 31347.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812513	C₃	1	2	yes	maximal, complemented
2	C₄₃⋊#6855	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#6868	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
5	C₃²×C₄₃⋊C₉	—	3	1	no	—
6	#16812513	—	3	6	no	—
7	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₃²⋊C₉	—	3	1	no	—
9	C₃²×C₄₃⋊C₃	—	9	2	no	—
10	C₃²⋊(C₄₃⋊C₃)	—	3	6	no	—
11	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
12	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
13	C₃×C₄₃⋊C₉	—	3	3	no	—
14	C₃×C₄₃⋊C₉	—	9	1	no	—
15	C₃×C₄₃⋊C₉	—	9	1	no	—
16	C₃×C₄₃⋊C₉	—	9	1	no	—
17	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₉×C₄₃	—	3	2	no	—
19	C₃×C₉×C₄₃	—	3	1	no	—
20	C₃×C₉×C₄₃	—	3	1	no	—
21	C₃×C₉×C₄₃	—	9	1	no	—
22	#10624480	—	43	1	no	maximal, Sylow
23	C₃²×C₄₃	—	3	1	no	—
24	C₃²×C₄₃	—	3	1	no	—
25	C₃²×C₄₃	—	3	1	no	—
26	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	2	yes	—
27	C₃²×C₄₃	#732	1	1	yes	characteristic
28	C₃²×C₄₃	#732	1	1	yes	characteristic
29	C₃×C₄₃⋊C₃	—	9	6	no	—
30	C₃×C₄₃⋊C₃	—	27	2	no	—
31	C₃×C₄₃⋊C₃	—	27	2	no	—
32	C₃×C₄₃⋊C₃	—	27	2	no	—
33	C₉×C₄₃	—	9	1	no	—
34	C₉×C₄₃	—	27	1	no	—
35	C₄₃⋊C₉	—	9	3	no	—
36	C₃×#732	—	43	2	no	—
37	#6868	C₄₃⋊C₃	1	1	yes	characteristic, complemented
38	#6855	—	43	1	no	—
39	C₃×C₄₃	—	3	1	no	—
40	C₃×C₄₃	—	3	2	no	—
41	C₃×C₄₃	#6856	1	1	yes	characteristic
42	C₃×C₄₃	#6879	1	1	yes	characteristic
43	C₃×C₄₃	#6881	1	1	yes	characteristic
44	C₃×C₄₃	#6881	1	1	yes	characteristic
45	C₄₃⋊C₃	—	27	6	no	—
46	C₃×H(3,𝔽₃)	—	129	2	no	—
47	C₃²×C₉	—	129	1	no	—
48	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
49	#732	—	129	6	no	—
50	C₃²⋊C₉	—	3	1	no	—
51	C₄₃	#10624480	1	1	yes	characteristic, complemented, Sylow
52	C₃³	—	387	2	no	—
53	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
54	H(3,𝔽₃)	—	129	6	no	—
55	H(3,𝔽₃)	—	387	2	no	—
56	H(3,𝔽₃)	—	387	2	no	—
57	C₃×C₉	—	3	2	no	—
58	C₃×C₉	—	3	1	no	—
59	C₃×C₉	—	3	1	no	—
60	C₃×C₉	—	9	1	no	—
61	C₃×C₉	—	129	3	no	—
62	C₃×C₉	—	387	1	no	—
63	C₃×C₉	—	387	1	no	—
64	C₃×C₉	—	387	1	no	—
65	C₃²	—	3	1	no	—
66	C₃²	—	3	1	no	—
67	C₃²	—	3	1	no	—
68	C₃²	—	387	6	no	—
69	C₃²	—	1161	2	no	—
70	C₃²	—	1161	2	no	—
71	C₃²	—	1161	2	no	—
72	C₃²	#16812508	1	2	yes	—
73	C₃²	#16812512	1	1	yes	characteristic
74	C₃²	#16812513	1	1	yes	characteristic
75	C₉	—	9	1	no	—
76	C₉	—	27	1	no	—
77	C₉	—	387	3	no	—
78	C₃	—	3	1	no	—
79	C₃	—	3	2	no	—
80	C₃	—	1161	6	no	—
81	C₃	#23782687	1	1	yes	characteristic
82	C₃	#23782750	1	1	yes	characteristic
83	C₃	#23782758	1	1	yes	characteristic
84	C₃	#23782759	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#16812512
commutator, cosocle	C₃²×C₉×C₄₃	C₃²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6868	C₃
socle	C₃²×C₄₃	#732
hypercenter	#6868	C₄₃⋊C₃
hypocenter	C₄₃	#10624480
LCS	G ▷ C₃²×C₉×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ #6868

Complements

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

N	H ≅ G/N	type
1. C₃×#16812513	C₃	semidirect
2. C₄₃⋊#6855	C₃	semidirect
3. C₄₃×#6868	C₃	semidirect
37. #6868	C₄₃⋊C₃	semidirect
51. C₄₃	#10624480	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
C₄₃⋊#6855	3
C₄₃×#6868	3
#10624480	43