Subgroups — C₃×C₄₃×#6861 #44531521

Order 31347.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₄₃×C₃²⋊C₉	C₃	1	3	yes	maximal
3	C₄₃×#6861	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
5	C₃²×C₉×C₄₃	—	3	1	no	—
6	C₃²×C₉×C₄₃	—	3	3	no	—
7	C₄₃×C₃²⋊C₉	—	3	2	no	—
8	C₄₃×C₃²⋊C₉	—	3	6	no	—
9	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
10	C₄₃×C₃²⋊C₉	C₃²	1	9	yes	—
11	C₃³×C₄₃	—	3	3	no	—
12	C₃³×C₄₃	—	3	3	no	—
13	C₃³×C₄₃	—	3	6	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	2	yes	—
15	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃³×C₄₃	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₄₃	—	3	3	no	—
18	C₃×C₉×C₄₃	—	3	9	no	—
19	C₃×C₉×C₄₃	—	9	3	no	—
20	C₃×C₉×C₄₃	—	9	9	no	—
21	C₃×#6861	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃²×C₄₃	—	3	2	no	—
23	C₃²×C₄₃	—	3	1	no	—
24	C₃²×C₄₃	—	3	2	no	—
25	C₃²×C₄₃	—	3	1	no	—
26	C₃²×C₄₃	—	3	4	no	—
27	C₃²×C₄₃	—	3	2	no	—
28	C₃²×C₄₃	—	9	9	no	—
29	C₃²×C₄₃	#731	1	3	yes	—
30	C₃²×C₄₃	#732	1	3	yes	—
31	C₃²×C₄₃	#733	1	6	yes	—
32	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₉×C₄₃	—	9	3	no	—
34	C₉×C₄₃	—	9	9	no	—
35	C₃×C₃²⋊C₉	C₃×C₄₃	1	1	yes	characteristic
36	C₃×C₃²⋊C₉	C₃×C₄₃	1	3	yes	—
37	#6861	C₃×C₄₃	1	9	yes	direct product factor
38	C₃×C₄₃	—	9	2	no	—
39	C₃×C₄₃	—	9	1	no	—
40	C₃×C₄₃	#6861	1	9	yes	direct product factor
41	C₃×C₄₃	C₃×#731	1	1	yes	characteristic
42	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
43	C₃×C₄₃	C₃×#733	1	2	yes	—
44	C₃⁴	C₃²×C₄₃	1	1	yes	characteristic
45	C₃²×C₉	—	3	1	no	—
46	C₃²×C₉	—	3	3	no	—
47	C₃²⋊C₉	—	3	2	no	—
48	C₃²⋊C₉	—	3	6	no	—
49	C₃²⋊C₉	C₃²×C₄₃	1	3	yes	—
50	C₃²⋊C₉	C₃²×C₄₃	1	9	yes	—
51	C₄₃	C₃×#6861	1	1	yes	characteristic, direct product factor, Sylow
52	C₃³	—	3	3	no	—
53	C₃³	—	3	3	no	—
54	C₃³	—	3	6	no	—
55	C₃³	H(3,𝔽₃)×C₄₃	1	2	yes	—
56	C₃³	H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
57	C₃³	C₃³×C₄₃	1	1	yes	characteristic
58	C₃×C₉	—	3	3	no	—
59	C₃×C₉	—	3	9	no	—
60	C₃×C₉	—	9	3	no	—
61	C₃×C₉	—	9	9	no	—
62	C₃²	—	3	2	no	—
63	C₃²	—	3	1	no	—
64	C₃²	—	3	2	no	—
65	C₃²	—	3	1	no	—
66	C₃²	—	3	4	no	—
67	C₃²	—	3	2	no	—
68	C₃²	—	9	9	no	—
69	C₃²	C₄₃×#731	1	3	yes	—
70	C₃²	C₄₃×#732	1	3	yes	—
71	C₃²	C₄₃×#733	1	6	yes	—
72	C₃²	C₃×H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
73	C₉	—	9	3	no	—
74	C₉	—	9	9	no	—
75	C₃	—	9	2	no	—
76	C₃	—	9	1	no	—
77	C₃	C₄₃×#6861	1	9	yes	direct product factor
78	C₃	C₃×C₄₃×#731	1	1	yes	characteristic
79	C₃	C₃×C₄₃×#732	1	1	yes	characteristic
80	C₃	C₃×C₄₃×#733	1	2	yes	—

	subgroup	G/H
center, socle	C₃³×C₄₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₄₃
prime radical	C₃⁴×C₄₃	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₄₃ ◁ C₃⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#6861	C₃	direct (N × H)
21. C₃×#6861	C₄₃	direct (N × H)
37. #6861	C₃×C₄₃	direct (N × H)
40. C₃×C₄₃	#6861	direct (N × H)
51. C₄₃	C₃×#6861	direct (N × H)
77. C₃	C₄₃×#6861	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₃×C₃²⋊C₉	3
C₄₃×#6861	3
C₃×#6861	43

Subgroups — C3×C43×#6861 #44531521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×#6861 #44531521