Subgroups — #44532246

Order 31347.

2150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	12	yes	maximal, complemented
2	C₃⁵×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₄₃⋊C₉	C₃²	1	9	yes	complemented
4	C₃²⋊(C₄₃⋊C₉)	—	3	36	no	—
5	C₃⁴×C₄₃	—	3	12	no	—
6	C₃⁴×C₄₃	—	3	24	no	—
7	C₃⁴×C₄₃	C₉	1	9	yes	complemented
8	C₃⁴×C₄₃	C₃²	1	4	yes	—
9	C₃×C₄₃⋊C₉	—	3	36	no	—
10	C₃³×C₄₃	—	3	27	no	—
11	C₃³×C₄₃	—	3	216	no	—
12	C₃³×C₄₃	—	3	108	no	—
13	C₃³×C₄₃	—	3	12	no	—
14	C₃³×C₄₃	—	3	24	no	—
15	C₃³×C₄₃	C₃×C₉	1	12	yes	—
16	C₃³×C₄₃	H(3,𝔽₃)	1	12	yes	—
17	C₃³×C₄₃	3₋¹⁺²	1	24	yes	—
18	C₃³×C₄₃	C₃³	1	1	yes	characteristic
19	#10624547	—	43	1	no	maximal, Sylow
20	C₃²×C₄₃	—	3	243	no	—
21	C₃²×C₄₃	—	3	36	no	—
22	C₃²×C₄₃	—	3	12	no	—
23	C₃²×C₄₃	—	3	24	no	—
24	C₃²×C₄₃	—	3	72	no	—
25	C₃²×C₄₃	C₃²⋊C₉	1	36	yes	complemented
26	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
27	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	4	yes	—
28	C₃²×C₄₃	C₃×3₋¹⁺²	1	8	yes	—
29	C₄₃⋊C₉	—	9	9	no	—
30	C₃⁵	C₄₃⋊C₃	1	1	yes	characteristic
31	C₃×C₃²⋊C₉	—	43	12	no	—
32	C₃×C₄₃	—	3	36	no	—
33	C₃×C₄₃	C₃×C₃²⋊C₉	1	4	yes	—
34	C₃×C₄₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
35	C₃×C₄₃	#6891	1	8	yes	—
36	C₃⁴	—	3	12	no	—
37	C₃⁴	—	3	24	no	—
38	C₃⁴	C₄₃⋊C₉	1	9	yes	complemented
39	C₃⁴	C₃×C₄₃⋊C₃	1	4	yes	—
40	C₃²×C₉	—	43	9	no	—
41	C₃²⋊C₉	—	129	36	no	—
42	C₄₃	#10624547	1	1	yes	characteristic, complemented, Sylow
43	C₃³	—	3	27	no	—
44	C₃³	—	3	216	no	—
45	C₃³	—	3	108	no	—
46	C₃³	—	3	12	no	—
47	C₃³	—	3	24	no	—
48	C₃³	C₃×C₄₃⋊C₉	1	12	yes	—
49	C₃³	C₃²⋊(C₄₃⋊C₃)	1	12	yes	—
50	C₃³	#11923958	1	24	yes	—
51	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
52	C₃×C₉	—	129	36	no	—
53	C₃²	—	3	243	no	—
54	C₃²	—	3	36	no	—
55	C₃²	—	3	12	no	—
56	C₃²	—	3	24	no	—
57	C₃²	—	3	72	no	—
58	C₃²	C₃²⋊(C₄₃⋊C₉)	1	36	yes	complemented
59	C₃²	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
60	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	4	yes	—
61	C₃²	C₃×#11923958	1	8	yes	—
62	C₉	—	387	9	no	—
63	C₃	—	3	36	no	—
64	C₃	C₃×C₃²⋊(C₄₃⋊C₉)	1	4	yes	—
65	C₃	#23782794	1	1	yes	characteristic
66	C₃	#23782798	1	8	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator	C₃²×C₄₃	C₃²×C₉
Fitting, prime radical	C₃⁵×C₄₃	C₃
socle, cosocle	C₃³×C₄₃	C₃³
hypercenter	C₃⁵	C₄₃⋊C₃
hypocenter	C₄₃	#10624547
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃⁵

Complements

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

N	H ≅ G/N	type
1. C₃×C₃²⋊(C₄₃⋊C₉)	C₃	semidirect
3. C₃²×C₄₃⋊C₉	C₃²	semidirect
7. C₃⁴×C₄₃	C₉	semidirect
25. C₃²×C₄₃	C₃²⋊C₉	semidirect
38. C₃⁴	C₄₃⋊C₉	semidirect
42. C₄₃	#10624547	semidirect
58. C₃²	C₃²⋊(C₄₃⋊C₉)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₃⁵×C₄₃	3
#10624547	43