Subgroups — #28356768

Order 13851.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987582	C₃	1	3	yes	maximal, complemented
2	C₃×C₂₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#13095335	—	3	3	no	—
4	C₃×C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
5	C₃×#10587018	C₉	1	1	yes	characteristic
6	C₃×#10587018	C₃²	1	1	yes	characteristic
7	C₂₇×C₁₉⋊C₃	—	3	1	no	—
8	C₂₇×C₁₉⋊C₃	—	3	2	no	—
9	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
10	#10624502	—	19	1	no	maximal, Sylow
11	C₃²×C₁₉⋊C₃	C₂₇	1	1	yes	characteristic
12	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
13	C₃×#4294	C₂₇	1	2	yes	—
14	C₉×C₁₉⋊C₃	—	3	1	no	—
15	C₉×C₁₉⋊C₃	—	3	1	no	—
16	C₉×C₁₉⋊C₃	—	3	1	no	—
17	C₁₉×C₂₇	—	3	1	no	—
18	#10587018	—	3	1	no	—
19	#10587018	H(3,𝔽₃)	1	1	yes	characteristic
20	#10587018	3₋¹⁺²	1	2	yes	—
21	C₃²×C₂₇	—	19	1	no	—
22	C₈₁⋊C₃	—	19	3	no	—
23	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
24	C₃×C₁₉⋊C₃	—	3	1	no	—
25	C₃×C₁₉⋊C₃	—	3	3	no	—
26	C₉×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
27	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
28	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
29	#4294	—	3	2	no	—
30	C₃²×C₉	—	19	1	no	—
31	C₃×C₂₇	—	19	1	no	—
32	C₃×C₂₇	—	19	1	no	—
33	C₃×C₂₇	—	57	1	no	—
34	C₃×C₂₇	—	57	2	no	—
35	C₃×C₂₇	#4296	1	1	yes	characteristic
36	C₈₁	—	57	3	no	—
37	C₃×C₁₉	—	3	1	no	—
38	C₃×C₁₉	C₃²⋊C₂₇	1	1	yes	characteristic
39	C₁₉⋊C₃	—	3	3	no	—
40	C₃³	—	19	1	no	—
41	C₃×C₉	—	19	2	no	—
42	C₃×C₉	—	57	1	no	—
43	C₃×C₉	—	57	1	no	—
44	C₃×C₉	—	57	1	no	—
45	C₃×C₉	C₃×#4296	1	1	yes	characteristic
46	C₂₇	—	3	1	no	—
47	C₂₇	—	19	1	no	—
48	C₂₇	—	19	2	no	—
49	C₂₇	—	57	1	no	—
50	C₁₉	#10624502	1	1	yes	characteristic, complemented, Sylow
51	C₃²	—	57	3	no	—
52	C₃²	—	57	1	no	—
53	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
54	C₉	—	57	2	no	—
55	C₉	C₃²⋊#4296	1	1	yes	characteristic
56	C₉	#13095343	1	1	yes	characteristic
57	C₉	#13095344	1	1	yes	characteristic
58	C₃	—	3	1	no	—
59	C₃	—	57	3	no	—
60	C₃	#17987557	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊#4296
commutator	C₃²×C₁₉	C₃×C₂₇
Frattini	C₃×C₉	C₃×#4296
Fitting	C₃×C₁₉×C₂₇	C₉
socle	C₃×C₁₉	C₃²⋊C₂₇
prime radical	C₃²×C₁₉⋊C₃	C₂₇
cosocle	C₃×#10587018	C₃²
hypercenter	C₃×C₂₇	#4296
hypocenter	C₁₉	#10624502
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
1. #17987582	C₃	semidirect
50. C₁₉	#10624502	semidirect

Maximal subgroups

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

subgroup	index
#17987582	3
C₃×C₂₇×C₁₉⋊C₃	3
#10624502	19