Subgroups — #44532365

Order 31347.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	4	yes	maximal
2	C₄₃⋊#6855	C₃	1	8	yes	maximal, complemented
3	C₄₃×#6855	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
5	C₃²×C₄₃⋊C₉	C₃²	1	8	yes	—
6	(C₃×C₄₃⋊C₃)⋊C₉	—	3	12	no	—
7	C₃²×C₉×C₄₃	C₃²	1	4	yes	—
8	C₃²×C₄₃⋊C₃	—	3	4	no	—
9	C₃²×C₄₃⋊C₃	—	3	8	no	—
10	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	3	yes	—
11	C₃×C₄₃⋊C₉	—	3	8	no	—
12	C₃×C₄₃⋊C₉	—	3	8	no	—
13	C₃×C₄₃⋊C₉	—	3	16	no	—
14	C₃³×C₄₃	C₃³	1	1	yes	characteristic
15	C₃×C₉×C₄₃	—	3	4	no	—
16	C₃×C₉×C₄₃	—	3	4	no	—
17	C₃×C₉×C₄₃	—	3	8	no	—
18	#10624568	—	43	1	no	maximal, Sylow
19	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²×C₄₃	#737	1	4	yes	—
21	C₃²×C₄₃	#737	1	8	yes	—
22	C₃×C₄₃⋊C₃	—	3	12	no	—
23	C₃×C₄₃⋊C₃	—	9	1	no	—
24	C₃×C₄₃⋊C₃	—	9	8	no	—
25	C₉×C₄₃	—	9	4	no	—
26	C₄₃⋊C₉	—	9	8	no	—
27	C₃×C₃²⋊C₉	—	43	4	no	—
28	#6855	—	43	8	no	—
29	#6855	C₄₃⋊C₃	1	1	yes	characteristic, complemented
30	C₃×C₄₃	#6893	1	4	yes	—
31	C₃×C₄₃	#6897	1	1	yes	characteristic
32	C₃×C₄₃	#6897	1	8	yes	—
33	C₄₃⋊C₃	—	9	3	no	—
34	C₃⁴	—	43	1	no	—
35	C₃²×C₉	—	43	8	no	—
36	C₃²×C₉	C₃×C₄₃⋊C₃	1	4	yes	—
37	C₃²⋊C₉	—	129	12	no	—
38	C₄₃	#10624568	1	1	yes	characteristic, complemented, Sylow
39	C₃³	—	43	3	no	—
40	C₃³	—	129	4	no	—
41	C₃³	—	129	8	no	—
42	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
43	C₃×C₉	—	3	4	no	—
44	C₃×C₉	—	3	4	no	—
45	C₃×C₉	—	3	8	no	—
46	C₃×C₉	—	129	8	no	—
47	C₃×C₉	—	129	8	no	—
48	C₃×C₉	—	129	16	no	—
49	C₃²	—	129	12	no	—
50	C₃²	—	387	1	no	—
51	C₃²	—	387	8	no	—
52	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
53	C₃²	#16812525	1	4	yes	—
54	C₃²	#16812526	1	8	yes	—
55	C₉	—	9	4	no	—
56	C₉	—	387	8	no	—
57	C₃	—	387	3	no	—
58	C₃	#23782807	1	4	yes	—
59	C₃	#23782831	1	1	yes	characteristic
60	C₃	#23782832	1	8	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃³×C₄₃	C₃³
Fitting	C₄₃×#6855	C₃
prime radical	C₃³×C₄₃⋊C₃	C₃²
hypercenter	#6855	C₄₃⋊C₃
hypocenter	C₄₃	#10624568
LCS	G ▷ C₃³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ #6855

Complements

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

N	H ≅ G/N	type
2. C₄₃⋊#6855	C₃	semidirect
3. C₄₃×#6855	C₃	semidirect
29. #6855	C₄₃⋊C₃	semidirect
38. C₄₃	#10624568	semidirect

Maximal subgroups

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

subgroup	index
C₃×(C₃×C₄₃⋊C₃)⋊C₉	3
C₄₃⋊#6855	3
C₄₃×#6855	3
#10624568	43