Subgroups — #44531971

Order 31347.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782794	C₃	1	2	yes	maximal, complemented
2	#23782712	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#6866	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	6	no	—
5	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	2	no	—
6	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
7	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₃²⋊C₉	—	3	1	no	—
9	C₃²×C₄₃⋊C₃	—	3	6	no	—
10	C₃²⋊(C₄₃⋊C₃)	—	9	18	no	—
11	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
12	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
13	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
14	C₃×C₄₃⋊C₉	—	9	1	no	—
15	C₃³×C₄₃	—	3	2	no	—
16	C₃³×C₄₃	—	3	1	no	—
17	C₃³×C₄₃	—	3	1	no	—
18	C₃³×C₄₃	—	9	3	no	—
19	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×C₉×C₄₃	—	9	1	no	—
21	#10624474	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	—	3	6	no	—
23	C₃²×C₄₃	—	9	1	no	—
24	C₃²×C₄₃	—	9	4	no	—
25	C₃²×C₄₃	—	9	3	no	—
26	C₃²×C₄₃	—	9	3	no	—
27	C₃²×C₄₃	—	9	1	no	—
28	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	2	yes	—
29	C₃²×C₄₃	#732	1	1	yes	characteristic
30	C₃²×C₄₃	#732	1	1	yes	characteristic
31	C₃×C₄₃⋊C₃	—	9	18	no	—
32	C₃×C₄₃⋊C₃	—	9	6	no	—
33	C₉×C₄₃	—	27	1	no	—
34	C₄₃⋊C₉	—	27	1	no	—
35	C₃²⋊H(3,𝔽₃)	—	43	2	no	—
36	#6866	—	43	1	no	—
37	#6866	C₄₃⋊C₃	1	1	yes	characteristic, complemented
38	C₃×C₄₃	—	3	1	no	—
39	C₃×C₄₃	—	3	1	no	—
40	C₃×C₄₃	—	3	2	no	—
41	C₃×C₄₃	—	9	3	no	—
42	C₃×C₄₃	#6856	1	1	yes	characteristic
43	C₄₃⋊C₃	—	27	6	no	—
44	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
45	C₃×H(3,𝔽₃)	—	129	6	no	—
46	C₃×H(3,𝔽₃)	—	129	2	no	—
47	C₃²⋊C₉	—	3	1	no	—
48	C₃²⋊C₉	—	129	1	no	—
49	C₄₃	#10624474	1	1	yes	characteristic, complemented, Sylow
50	C₃³	—	3	2	no	—
51	C₃³	—	3	1	no	—
52	C₃³	—	3	1	no	—
53	C₃³	—	9	3	no	—
54	C₃³	—	129	6	no	—
55	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
56	H(3,𝔽₃)	—	387	18	no	—
57	H(3,𝔽₃)	—	387	2	no	—
58	H(3,𝔽₃)	—	387	2	no	—
59	H(3,𝔽₃)	—	387	2	no	—
60	C₃×C₉	—	9	1	no	—
61	C₃×C₉	—	387	1	no	—
62	C₃²	—	3	6	no	—
63	C₃²	—	9	1	no	—
64	C₃²	—	9	3	no	—
65	C₃²	—	9	3	no	—
66	C₃²	—	9	4	no	—
67	C₃²	—	9	1	no	—
68	C₃²	—	387	18	no	—
69	C₃²	—	387	6	no	—
70	C₃²	#16812508	1	2	yes	—
71	C₃²	#16812512	1	1	yes	characteristic
72	C₃²	#16812513	1	1	yes	characteristic
73	C₉	—	27	1	no	—
74	C₉	—	1161	1	no	—
75	C₃	—	3	1	no	—
76	C₃	—	3	1	no	—
77	C₃	—	3	2	no	—
78	C₃	—	9	3	no	—
79	C₃	—	1161	6	no	—
80	C₃	#23782687	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782687
commutator, cosocle	C₃⁴×C₄₃	C₃²
Frattini	C₃⁴	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6866	C₃
socle	C₃×C₄₃	#6856
hypercenter	#6866	C₄₃⋊C₃
hypocenter	C₄₃	#10624474
LCS	G ▷ C₃⁴×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃⁴ ◁ #6866

Complements

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

N	H ≅ G/N	type
1. #23782794	C₃	semidirect
2. #23782712	C₃	semidirect
3. C₄₃×#6866	C₃	semidirect
37. #6866	C₄₃⋊C₃	semidirect
49. C₄₃	#10624474	semidirect

Maximal subgroups

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

subgroup	index
#23782794	3
#23782712	3
C₄₃×#6866	3
#10624474	43