Subgroups — C₄₃⋊C₃×#6862 #44532455

Order 31347.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊C₉×C₄₃⋊C₃	C₃	1	4	yes	maximal
2	C₄₃⋊#6862	C₃	1	8	yes	maximal, complemented
3	C₄₃×#6862	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₄₃⋊C₃	—	3	4	no	—
6	C₃²⋊(C₄₃⋊C₉)	C₃²	1	8	yes	—
7	(C₃×C₄₃⋊C₃)⋊C₉	—	3	8	no	—
8	C₄₃×C₃²⋊C₉	C₃²	1	4	yes	—
9	C₃²×C₄₃⋊C₃	—	3	12	no	—
10	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	2	yes	—
11	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₄₃⋊C₉	—	3	8	no	—
13	C₉×C₄₃⋊C₃	—	9	12	no	—
14	C₃³×C₄₃	C₃³	1	1	yes	characteristic
15	C₃×C₉×C₄₃	—	3	4	no	—
16	C₃×#6862	—	43	1	no	maximal, Sylow
17	C₃²×C₄₃	—	3	4	no	—
18	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₄₃⋊C₃	—	3	8	no	—
20	C₃×C₄₃⋊C₃	—	9	9	no	—
21	C₃×C₄₃⋊C₃	#731	1	12	yes	—
22	C₉×C₄₃	—	9	4	no	—
23	C₄₃⋊C₉	—	9	8	no	—
24	C₃×C₃²⋊C₉	—	43	4	no	—
25	#6862	—	43	8	no	—
26	#6862	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
27	C₃×C₄₃	—	9	1	no	—
28	C₃×C₄₃	C₃×#731	1	4	yes	—
29	C₄₃⋊C₃	—	9	2	no	—
30	C₄₃⋊C₃	#6862	1	9	yes	direct product factor
31	C₃⁴	—	43	1	no	—
32	C₃²×C₉	—	129	4	no	—
33	C₃²⋊C₉	—	43	8	no	—
34	C₃²⋊C₉	—	129	8	no	—
35	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	4	yes	—
36	C₄₃	C₃×#6862	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	43	1	no	—
38	C₃³	—	43	2	no	—
39	C₃³	—	129	12	no	—
40	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
41	C₃×C₉	—	3	4	no	—
42	C₃×C₉	—	129	8	no	—
43	C₃×C₉	—	387	12	no	—
44	C₃²	—	3	4	no	—
45	C₃²	—	43	12	no	—
46	C₃²	—	129	8	no	—
47	C₃²	—	387	9	no	—
48	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
49	C₉	—	9	4	no	—
50	C₉	—	387	8	no	—
51	C₃	—	9	1	no	—
52	C₃	—	43	9	no	—
53	C₃	—	387	2	no	—
54	C₃	#731×C₄₃⋊C₃	1	4	yes	—

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₄₃⋊C₃
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6862	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃³×C₄₃⋊C₃	C₃²
hypercenter	#6862	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#6862
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ #6862

Complements

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

N	H ≅ G/N	type
2. C₄₃⋊#6862	C₃	semidirect
3. C₄₃×#6862	C₃	semidirect
26. #6862	C₄₃⋊C₃	direct (N × H)
30. C₄₃⋊C₃	#6862	direct (N × H)
36. C₄₃	C₃×#6862	semidirect

Maximal subgroups

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

subgroup	index
C₃²⋊C₉×C₄₃⋊C₃	3
C₄₃⋊#6862	3
C₄₃×#6862	3
C₃×#6862	43

Subgroups — C43⋊C3×#6862 #44532455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃⋊C₃×#6862 #44532455