Subgroups — C₄₃×C₂₇⋊H(3,𝔽₃) #44531652

Order 31347.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
2	C₃²×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₉×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₄₃×C₃²⋊C₂₇	C₃	1	6	yes	maximal, complemented
5	C₄₃×C₃²⋊C₂₇	C₃	1	2	yes	maximal, complemented
6	C₃×H(3,𝔽₃)×C₄₃	C₉	1	1	yes	characteristic
7	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
9	C₄₃×C₂₇⋊C₃	—	3	9	no	—
10	C₃×C₂₇×C₄₃	—	3	3	no	—
11	C₃×C₂₇×C₄₃	C₃²	1	2	yes	—
12	C₃×C₂₇×C₄₃	C₃²	1	6	yes	—
13	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
14	C₄₃×C₃²⋊C₉	C₉	1	6	yes	—
15	C₄₃×C₃²⋊C₉	C₉	1	2	yes	—
16	C₃³×C₄₃	C₃×C₉	1	3	yes	—
17	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
18	H(3,𝔽₃)×C₄₃	—	3	3	no	—
19	C₃×C₉×C₄₃	—	3	1	no	—
20	C₃×C₉×C₄₃	—	3	3	no	—
21	C₃×C₉×C₄₃	—	3	2	no	—
22	C₃×C₉×C₄₃	—	3	6	no	—
23	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₄₃	C₃×C₉	1	6	yes	—
25	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
26	C₂₇×C₄₃	—	3	2	no	—
27	C₂₇×C₄₃	—	3	6	no	—
28	C₂₇×C₄₃	H(3,𝔽₃)	1	3	yes	complemented
29	C₂₇⋊H(3,𝔽₃)	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₃²×C₄₃	—	3	1	no	—
31	C₃²×C₄₃	—	3	2	no	—
32	C₃²×C₄₃	—	3	3	no	—
33	C₃²×C₄₃	—	3	3	no	—
34	C₃²×C₄₃	—	3	6	no	—
35	C₃²×C₄₃	C₂₇⋊C₃	1	3	yes	complemented
36	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
37	C₉×C₄₃	—	3	2	no	—
38	C₉×C₄₃	—	3	6	no	—
39	C₉×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₉×C₄₃	#737	1	2	yes	—
41	C₃×C₂₇⋊C₃	C₃×C₄₃	1	3	yes	complemented
42	C₃²×C₂₇	C₃×C₄₃	1	1	yes	characteristic, complemented
43	C₉×H(3,𝔽₃)	C₃×C₄₃	1	1	yes	characteristic
44	C₃²⋊C₂₇	C₃×C₄₃	1	6	yes	complemented
45	C₃²⋊C₂₇	C₃×C₄₃	1	2	yes	complemented
46	C₃×C₄₃	—	3	3	no	—
47	C₃×C₄₃	—	9	3	no	—
48	C₃×C₄₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃×C₄₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic
50	C₃×C₄₃	#6903	1	2	yes	—
51	C₃×H(3,𝔽₃)	C₉×C₄₃	1	1	yes	characteristic
52	C₃²×C₉	C₃²×C₄₃	1	1	yes	characteristic
53	C₃²×C₉	C₃²×C₄₃	1	3	yes	—
54	C₂₇⋊C₃	—	3	9	no	—
55	C₃×C₂₇	—	3	3	no	—
56	C₃×C₂₇	C₃²×C₄₃	1	2	yes	—
57	C₃×C₂₇	C₃²×C₄₃	1	6	yes	—
58	C₃×C₂₇	C₃²×C₄₃	1	1	yes	characteristic
59	C₃²⋊C₉	C₉×C₄₃	1	6	yes	—
60	C₃²⋊C₉	C₉×C₄₃	1	2	yes	—
61	C₄₃	C₂₇⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
62	C₃³	C₃×C₉×C₄₃	1	3	yes	—
63	C₃³	C₃×C₉×C₄₃	1	1	yes	characteristic
64	H(3,𝔽₃)	—	3	3	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	2	no	—
68	C₃×C₉	—	3	6	no	—
69	C₃×C₉	C₃×C₉×C₄₃	1	2	yes	—
70	C₃×C₉	C₃×C₉×C₄₃	1	6	yes	—
71	C₃×C₉	C₃³×C₄₃	1	1	yes	characteristic
72	C₂₇	—	3	2	no	—
73	C₂₇	—	3	6	no	—
74	C₂₇	H(3,𝔽₃)×C₄₃	1	3	yes	complemented
75	C₃²	—	3	2	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	3	no	—
78	C₃²	—	3	6	no	—
79	C₃²	—	3	3	no	—
80	C₃²	C₄₃×C₂₇⋊C₃	1	3	yes	complemented
81	C₃²	C₃²×C₉×C₄₃	1	1	yes	characteristic
82	C₉	—	3	2	no	—
83	C₉	—	3	6	no	—
84	C₉	C₃×H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
85	C₉	C₄₃×#737	1	2	yes	—
86	C₃	—	3	3	no	—
87	C₃	—	9	3	no	—
88	C₃	C₉×H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
89	C₃	C₃×C₄₃×C₂₇⋊C₃	1	1	yes	characteristic
90	C₃	C₄₃×#6903	1	2	yes	—

	subgroup	G/H
center	C₃×C₉×C₄₃	C₃³
commutator	C₃²	C₃²×C₉×C₄₃
Frattini, cosocle	C₃×C₉	C₃³×C₄₃
socle	C₃²×C₄₃	C₃²×C₉
prime radical	C₃×H(3,𝔽₃)×C₄₃	C₉
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₃×C₂₇⋊C₃	C₃	semidirect
2. C₃²×C₂₇×C₄₃	C₃	semidirect
4. C₄₃×C₃²⋊C₂₇	C₃	semidirect
5. C₄₃×C₃²⋊C₂₇	C₃	semidirect
28. C₂₇×C₄₃	H(3,𝔽₃)	semidirect
29. C₂₇⋊H(3,𝔽₃)	C₄₃	direct (N × H)
35. C₃²×C₄₃	C₂₇⋊C₃	semidirect
41. C₃×C₂₇⋊C₃	C₃×C₄₃	semidirect
42. C₃²×C₂₇	C₃×C₄₃	semidirect
44. C₃²⋊C₂₇	C₃×C₄₃	semidirect
45. C₃²⋊C₂₇	C₃×C₄₃	semidirect
61. C₄₃	C₂₇⋊H(3,𝔽₃)	direct (N × H)
74. C₂₇	H(3,𝔽₃)×C₄₃	semidirect
80. C₃²	C₄₃×C₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₃×C₂₇⋊C₃	3
C₃²×C₂₇×C₄₃	3
C₉×H(3,𝔽₃)×C₄₃	3
C₄₃×C₃²⋊C₂₇	3
C₂₇⋊H(3,𝔽₃)	43

Subgroups — C43×C27⋊H(3,𝔽3) #44531652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×C₂₇⋊H(3,𝔽₃) #44531652