Subgroups — C₃²⋊#13095301 #28353352

Order 13851.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095301	C₃	1	3	yes	maximal, complemented
2	C₃²×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
3	#13095301	—	3	3	no	—
4	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
5	C₃×C₁₉×C₂₇	—	3	1	no	—
6	C₃×C₁₉×C₂₇	—	3	2	no	—
7	C₃×C₁₉×C₂₇	C₉	1	2	yes	—
8	C₃×C₁₉×C₂₇	C₃²	1	1	yes	characteristic
9	C₃²⋊C₈₁	—	19	1	no	maximal, Sylow
10	C₃³×C₁₉	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₁₉	—	3	1	no	—
12	C₃×C₉×C₁₉	—	3	2	no	—
13	C₃×C₉×C₁₉	C₂₇	1	2	yes	—
14	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₁₉×C₂₇	—	3	2	no	—
16	C₁₉×C₂₇	H(3,𝔽₃)	1	1	yes	characteristic
17	C₁₉×C₂₇	3₋¹⁺²	1	2	yes	—
18	C₃²×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
19	C₃×C₈₁	—	19	3	no	—
20	C₃²×C₁₉	—	3	1	no	—
21	C₃²×C₁₉	—	3	2	no	—
22	C₃²×C₁₉	C₈₁	1	3	yes	complemented
23	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
24	C₉×C₁₉	—	3	2	no	—
25	C₉×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
26	C₉×C₁₉	C₂₇⋊C₃	1	2	yes	—
27	C₃²×C₉	#4294	1	1	yes	characteristic
28	C₃×C₂₇	—	3	2	no	—
29	C₃×C₂₇	—	3	1	no	—
30	C₃×C₂₇	#4294	1	2	yes	—
31	C₃×C₂₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic
32	C₈₁	—	57	3	no	—
33	C₃×C₁₉	—	3	3	no	—
34	C₃×C₁₉	C₃²⋊C₂₇	1	1	yes	characteristic
35	C₃×C₁₉	C₃×C₈₁	1	1	yes	characteristic
36	C₃×C₁₉	C₈₁⋊C₃	1	2	yes	—
37	C₃³	#10587018	1	1	yes	characteristic
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	—	3	2	no	—
40	C₃×C₉	#10587018	1	2	yes	—
41	C₃×C₉	C₃×#4294	1	1	yes	characteristic
42	C₂₇	—	3	2	no	—
43	C₂₇	#10587025	1	2	yes	—
44	C₂₇	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
45	C₁₉	C₃²⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
46	C₃²	—	3	1	no	—
47	C₃²	—	3	2	no	—
48	C₃²	#13095301	1	3	yes	complemented
49	C₃²	C₃×#10587018	1	1	yes	characteristic
50	C₉	—	3	2	no	—
51	C₉	C₃²⋊#4294	1	1	yes	characteristic
52	C₉	#13095312	1	2	yes	—
53	C₃	—	3	3	no	—
54	C₃	C₃²⋊#10587018	1	1	yes	characteristic
55	C₃	C₃×#13095301	1	1	yes	characteristic
56	C₃	#17987367	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃×C₂₇	C₃×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃×C₈₁
Fitting	C₃²×C₁₉×C₂₇	C₃
socle	C₃²×C₁₉	C₃×C₂₇
prime radical	C₃³×C₁₉	C₂₇
cosocle	C₃×C₁₉×C₂₇	C₃²
hypercenter	C₃²×C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	C₃²⋊C₈₁
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×#13095301	C₃	semidirect
22. C₃²×C₁₉	C₈₁	semidirect
45. C₁₉	C₃²⋊C₈₁	semidirect
48. C₃²	#13095301	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095301	3
C₃²×C₁₉×C₂₇	3
C₃²⋊C₈₁	19

Subgroups — C32⋊#13095301 #28353352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²⋊#13095301 #28353352