Subgroups — #28356696

Order 13851.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊#10587020	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊#10587020	C₃	1	1	yes	maximal, characteristic
4	3₋¹⁺²×#4294	C₃	1	1	yes	maximal, characteristic
5	#13095342	—	3	3	no	—
6	C₃×#10587020	—	3	1	no	—
7	C₃×#10587020	—	3	1	no	—
8	C₃×#10587020	—	3	1	no	—
9	C₃²×#4294	C₃²	1	1	yes	characteristic
10	#13095307	—	3	1	no	—
11	#13095306	—	3	1	no	—
12	C₃²⋊#4294	C₉	1	1	yes	characteristic
13	C₃²⋊#4294	C₉	1	1	yes	characteristic
14	C₉×#4294	—	3	1	no	—
15	C₃×C₁₉×3₋¹⁺²	C₉	1	1	yes	characteristic
16	#10624455	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
18	C₁₉×3₋¹⁺²	—	3	3	no	—
19	C₃×C₉×C₁₉	—	3	1	no	—
20	C₃×#4294	—	3	1	no	—
21	C₃×#4294	—	3	1	no	—
22	C₃×#4294	—	3	1	no	—
23	C₃×#4294	—	3	1	no	—
24	C₃×#4294	—	3	1	no	—
25	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
27	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
28	#10587020	—	3	3	no	—
29	#10587020	—	9	1	no	—
30	#10587020	—	9	1	no	—
31	C₃×C₂₇⋊C₃	—	19	1	no	—
32	C₉×3₋¹⁺²	—	19	1	no	—
33	C₃²⋊C₂₇	—	19	1	no	—
34	C₃²⋊C₂₇	—	19	1	no	—
35	C₃²×C₁₉	—	3	1	no	—
36	C₃²×C₁₉	—	3	1	no	—
37	C₃²×C₁₉	—	3	1	no	—
38	C₃²×C₁₉	—	3	1	no	—
39	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
40	C₉×C₁₉	—	3	3	no	—
41	#4294	—	3	1	no	—
42	#4294	—	3	1	no	—
43	#4294	—	9	1	no	—
44	#4294	—	9	1	no	—
45	#4294	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
46	#4294	#731	1	1	yes	characteristic
47	#4294	#733	1	1	yes	characteristic
48	C₃×3₋¹⁺²	#4296	1	1	yes	characteristic
49	C₃²×C₉	—	19	1	no	—
50	C₂₇⋊C₃	—	57	3	no	—
51	C₃×C₂₇	—	57	1	no	—
52	C₃×C₂₇	—	57	1	no	—
53	C₃×C₂₇	—	57	1	no	—
54	C₉⋊C₉	—	57	1	no	—
55	C₉⋊C₉	—	57	1	no	—
56	C₃²⋊C₉	—	19	1	no	—
57	C₃²⋊C₉	—	19	1	no	—
58	C₉²	—	57	1	no	—
59	C₃×C₁₉	—	9	1	no	—
60	C₃×C₁₉	#6869	1	1	yes	characteristic
61	C₃×C₁₉	3₋¹⁺²⋊C₉	1	1	yes	characteristic
62	C₃×C₁₉	#6872	1	1	yes	characteristic
63	C₃×C₁₉	#6873	1	1	yes	characteristic
64	C₃³	C₃×#4296	1	1	yes	characteristic
65	3₋¹⁺²	—	3	3	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	19	1	no	—
68	C₃×C₉	—	19	1	no	—
69	C₃×C₉	—	19	1	no	—
70	C₃×C₉	—	57	1	no	—
71	C₃×C₉	—	57	1	no	—
72	C₃×C₉	—	57	1	no	—
73	C₃×C₉	—	57	1	no	—
74	C₃×C₉	—	57	1	no	—
75	C₂₇	—	57	3	no	—
76	C₂₇	—	171	1	no	—
77	C₂₇	—	171	1	no	—
78	C₁₉	#10624455	1	1	yes	characteristic, complemented, Sylow
79	C₃²	—	3	1	no	—
80	C₃²	—	3	1	no	—
81	C₃²	—	3	1	no	—
82	C₃²	—	3	1	no	—
83	C₃²	C₃²⋊#4296	1	1	yes	characteristic
84	C₉	—	3	3	no	—
85	C₉	—	19	1	no	—
86	C₉	—	19	1	no	—
87	C₉	—	19	1	no	—
88	C₉	—	57	1	no	—
89	C₉	—	57	1	no	—
90	C₉	—	171	1	no	—
91	C₉	—	171	1	no	—
92	C₃	—	9	1	no	—
93	C₃	#17987561	1	1	yes	characteristic
94	C₃	3₋¹⁺²⋊#4296	1	1	yes	characteristic
95	C₃	#17987567	1	1	yes	characteristic
96	C₃	#17987569	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊#4296
commutator, prime radical	C₃³×C₁₉	C₃×C₉
Frattini	C₃³	C₃×#4296
Fitting	C₃×C₁₉×3₋¹⁺²	C₉
socle	C₃²×C₁₉	C₃²⋊C₉
cosocle	C₃²×#4294	C₃²
hypercenter	C₃×3₋¹⁺²	#4296
hypocenter	C₁₉	#10624455
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
78. C₁₉	#10624455	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095342	3
C₃²⋊#10587020	3
3₋¹⁺²×#4294	3
#10624455	19