Subgroups — #44534450

Order 31347.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782782	C₃	1	1	yes	maximal, characteristic
2	#23782738	C₃	1	6	yes	maximal, complemented
3	#23782737	C₃	1	3	yes	maximal, complemented
4	#23782718	C₃	1	2	yes	maximal
5	C₄₃×#6869	C₃	1	1	yes	maximal, characteristic
6	#16812505	C₃²	1	6	yes	—
7	#16812500	C₃²	1	1	yes	characteristic
8	#16812500	C₃²	1	2	yes	—
9	#16812499	—	3	1	no	—
10	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
11	C₉×C₄₃⋊C₉	—	3	1	no	—
12	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₄₃×C₂₇⋊C₃	C₃²	1	3	yes	—
14	C₃×C₄₃⋊C₉	—	3	1	no	—
15	C₃×C₄₃⋊C₉	—	3	2	no	—
16	C₄₃⋊C₂₇	—	3	6	no	—
17	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
18	C₃×C₉×C₄₃	—	3	1	no	—
19	C₃×C₉×C₄₃	—	3	2	no	—
20	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
21	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
22	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
23	C₂₇×C₄₃	—	3	3	no	—
24	#10624829	—	43	1	no	maximal, Sylow
25	C₃²×C₄₃	—	3	1	no	—
26	C₃²×C₄₃	—	9	1	no	—
27	C₃²×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₉×C₄₃	—	3	1	no	—
29	C₉×C₄₃	—	3	1	no	—
30	C₉×C₄₃	#737	1	1	yes	characteristic
31	C₉×C₄₃	#737	1	2	yes	—
32	C₄₃⋊C₉	—	9	1	no	—
33	C₄₃⋊C₉	—	9	2	no	—
34	#6887	—	43	1	no	—
35	#6875	—	43	3	no	—
36	#6875	—	43	6	no	—
37	#6869	—	43	2	no	—
38	#6869	C₄₃⋊C₃	1	1	yes	characteristic
39	C₃×C₄₃	—	3	1	no	—
40	C₃×C₄₃	—	9	1	no	—
41	C₃×C₄₃	#6895	1	1	yes	characteristic
42	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
43	C₂₇⋊C₃	—	43	6	no	—
44	C₂₇⋊C₃	C₃×C₄₃⋊C₃	1	3	yes	—
45	C₉⋊C₉	—	43	1	no	—
46	C₉⋊C₉	—	43	2	no	—
47	C₉⋊C₉	—	129	1	no	—
48	C₃²⋊C₉	—	129	1	no	—
49	C₉²	—	129	1	no	—
50	C₄₃	#10624829	1	1	yes	characteristic, complemented, Sylow
51	C₃³	#11923956	1	1	yes	characteristic
52	C₃×C₉	—	3	1	no	—
53	C₃×C₉	—	3	2	no	—
54	C₃×C₉	—	129	1	no	—
55	C₃×C₉	—	129	2	no	—
56	C₃×C₉	#11923956	1	1	yes	characteristic
57	C₃×C₉	#11923956	1	1	yes	characteristic
58	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
59	C₂₇	—	3	3	no	—
60	C₂₇	—	129	6	no	—
61	C₃²	—	3	1	no	—
62	C₃²	—	9	1	no	—
63	C₃²	C₃×#11923956	1	1	yes	characteristic
64	C₉	—	3	1	no	—
65	C₉	—	3	1	no	—
66	C₉	—	387	1	no	—
67	C₉	—	387	2	no	—
68	C₉	#16812524	1	1	yes	characteristic
69	C₉	#16812526	1	2	yes	—
70	C₃	—	3	1	no	—
71	C₃	—	9	1	no	—
72	C₃	#23782819	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782819
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6869	C₃
socle	C₃×C₄₃	#6895
prime radical	C₃³×C₄₃	3₋¹⁺²
hypercenter	#6869	C₄₃⋊C₃
hypocenter	C₄₃	#10624829
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ #6869

Complements

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

N	H ≅ G/N	type
2. #23782738	C₃	semidirect
3. #23782737	C₃	semidirect
50. C₄₃	#10624829	semidirect

Maximal subgroups

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

subgroup	index
#23782782	3
#23782738	3
#23782737	3
#23782718	3
C₄₃×#6869	3
#10624829	43