Subgroups — #28353210

Order 13851.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095312	C₃	1	2	yes	maximal
2	#17987405	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
4	#13095312	—	3	2	no	—
5	#13095312	—	3	2	no	—
6	#13095312	C₉	1	6	yes	complemented
7	C₃×#10587018	—	3	2	no	—
8	#13095307	—	3	1	no	—
9	#13095306	—	3	1	no	—
10	C₃²⋊#4294	C₉	1	3	yes	—
11	C₉×#4294	—	3	1	no	—
12	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
13	C₃×C₁₉×C₂₇	—	3	1	no	—
14	C₃×C₁₉×C₂₇	—	3	2	no	—
15	C₃×C₁₉×C₂₇	C₉	1	3	yes	complemented
16	#10624469	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
19	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
22	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
23	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
24	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
25	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
26	C₃×#4294	—	3	3	no	—
27	C₁₉×C₂₇	—	3	3	no	—
28	#10587018	—	3	6	no	—
29	C₃×C₂₇⋊C₃	—	19	2	no	—
30	C₃²×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
31	#6887	—	19	1	no	—
32	C₃²×C₁₉	—	3	3	no	—
33	C₃²×C₁₉	C₉²	1	1	yes	characteristic
34	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
35	C₃²×C₁₉	C₉⋊C₉	1	2	yes	—
36	C₉×C₁₉	C₃²⋊C₉	1	2	yes	—
37	C₉×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
38	C₉×C₁₉	C₉⋊C₉	1	2	yes	—
39	C₉×C₁₉	C₉⋊C₉	1	2	yes	—
40	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
41	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
42	#4294	—	9	3	no	—
43	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
44	C₂₇⋊C₃	—	19	6	no	—
45	C₂₇⋊C₃	—	57	2	no	—
46	C₂₇⋊C₃	—	57	2	no	—
47	C₃×C₂₇	—	3	2	no	—
48	C₃×C₂₇	—	3	1	no	—
49	C₃×C₂₇	—	57	2	no	—
50	C₃×C₂₇	#4294	1	3	yes	complemented
51	C₉⋊C₉	—	57	1	no	—
52	C₉⋊C₉	—	57	1	no	—
53	C₃²⋊C₉	—	19	3	no	—
54	C₉²	—	57	1	no	—
55	C₃×C₁₉	—	3	1	no	—
56	C₃×C₁₉	—	3	2	no	—
57	C₃×C₁₉	#6855	1	1	yes	characteristic
58	C₃×C₁₉	#6872	1	3	yes	—
59	C₃³	C₉×C₁₉⋊C₃	1	1	yes	characteristic
60	C₃×C₉	—	57	3	no	—
61	C₃×C₉	C₉×C₁₉⋊C₃	1	2	yes	—
62	C₃×C₉	#10587022	1	2	yes	—
63	C₃×C₉	#10587022	1	1	yes	characteristic
64	C₃×C₉	#10587023	1	2	yes	—
65	C₃×C₉	#10587023	1	1	yes	characteristic
66	C₃×C₉	C₃×#4294	1	1	yes	characteristic
67	C₃×C₉	#10587025	1	2	yes	—
68	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
69	C₂₇	—	3	3	no	—
70	C₂₇	—	57	6	no	—
71	C₁₉	#10624469	1	1	yes	characteristic, complemented, Sylow
72	C₃²	—	3	3	no	—
73	C₃²	C₉×#4294	1	1	yes	characteristic
74	C₃²	#13095303	1	1	yes	characteristic
75	C₃²	#13095305	1	2	yes	—
76	C₉	—	171	3	no	—
77	C₉	#13095303	1	2	yes	—
78	C₉	C₃²⋊#4294	1	1	yes	characteristic
79	C₉	#13095305	1	2	yes	—
80	C₉	#13095305	1	2	yes	—
81	C₉	#13095306	1	1	yes	characteristic
82	C₉	#13095307	1	1	yes	characteristic
83	C₃	—	3	1	no	—
84	C₃	—	3	2	no	—
85	C₃	#17987308	1	1	yes	characteristic
86	C₃	#17987351	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₁₉⋊C₃)
commutator	C₃²×C₁₉	C₉²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₃²×C₁₉×C₂₇	C₃
socle	C₃²×C₁₉	C₃²⋊C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃²×C₉×C₁₉	C₃²
hypercenter	C₃²×C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	#10624469
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
6. #13095312	C₉	semidirect
15. C₃×C₁₉×C₂₇	C₉	semidirect
50. C₃×C₂₇	#4294	semidirect
71. C₁₉	#10624469	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095312	3
#17987405	3
C₃²×C₁₉×C₂₇	3
#10624469	19