Subgroups — #28356887

Order 13851.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	3	yes	maximal, complemented
2	C₃²⋊#10587020	C₃	1	9	yes	maximal, complemented
3	C₃³×#4294	C₃	1	1	yes	maximal, characteristic
4	#13095342	—	3	9	no	—
5	C₃×#10587020	C₃²	1	9	yes	complemented
6	C₃²×#4294	—	3	3	no	—
7	C₃²×#4294	—	3	6	no	—
8	C₃²×#4294	C₉	1	2	yes	—
9	C₃²×#4294	C₉	1	6	yes	—
10	C₃²×#4294	C₃²	1	3	yes	—
11	C₃²×#4294	C₃²	1	1	yes	characteristic
12	C₃⁴×C₁₉	C₉	1	1	yes	characteristic
13	#10624683	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	—	3	3	no	—
15	C₃³×C₁₉	—	3	9	no	—
16	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
17	C₃³×C₁₉	C₃×C₉	1	3	yes	—
18	C₃×#4294	—	3	6	no	—
19	C₃×#4294	—	3	18	no	—
20	C₃×#4294	—	3	3	no	—
21	C₃×#4294	—	3	6	no	—
22	C₃×#4294	C₃×C₉	1	6	yes	—
23	C₃×#4294	C₃×C₉	1	2	yes	—
24	C₃×#4294	H(3,𝔽₃)	1	3	yes	—
25	C₃×#4294	3₋¹⁺²	1	6	yes	—
26	C₃×#4294	C₃³	1	1	yes	characteristic
27	#10587020	—	3	9	no	—
28	C₃³×C₉	—	19	1	no	—
29	C₃×C₂₇⋊C₃	—	19	3	no	—
30	C₃²⋊C₂₇	—	19	9	no	—
31	C₃²×C₁₉	—	3	27	no	—
32	C₃²×C₁₉	—	3	3	no	—
33	C₃²×C₁₉	—	3	3	no	—
34	C₃²×C₁₉	—	3	6	no	—
35	C₃²×C₁₉	C₃²⋊C₉	1	3	yes	—
36	C₃²×C₁₉	C₂₇⋊C₃	1	9	yes	complemented
37	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
38	#4294	—	3	6	no	—
39	#4294	C₃²⋊C₉	1	6	yes	—
40	#4294	C₃×H(3,𝔽₃)	1	1	yes	characteristic
41	#4294	C₃×3₋¹⁺²	1	2	yes	—
42	C₃⁴	#4296	1	1	yes	characteristic
43	C₃²×C₉	—	19	1	no	—
44	C₃²×C₉	—	19	6	no	—
45	C₃²×C₉	—	19	2	no	—
46	C₃²×C₉	—	19	3	no	—
47	C₃²×C₉	—	57	3	no	—
48	C₃²×C₉	—	57	6	no	—
49	C₂₇⋊C₃	—	57	9	no	—
50	C₃×C₂₇	—	19	9	no	—
51	C₃×C₁₉	—	3	3	no	—
52	C₃×C₁₉	—	3	9	no	—
53	C₃×C₁₉	C₃×C₃²⋊C₉	1	1	yes	characteristic
54	C₃×C₁₉	C₃×C₂₇⋊C₃	1	3	yes	—
55	C₃³	—	3	3	no	—
56	C₃³	—	3	9	no	—
57	C₃³	C₃×#4296	1	1	yes	characteristic
58	C₃³	C₃×#4296	1	3	yes	—
59	C₃×C₉	—	19	3	no	—
60	C₃×C₉	—	19	6	no	—
61	C₃×C₉	—	19	2	no	—
62	C₃×C₉	—	19	1	no	—
63	C₃×C₉	—	19	6	no	—
64	C₃×C₉	—	57	3	no	—
65	C₃×C₉	—	57	18	no	—
66	C₃×C₉	—	57	6	no	—
67	C₃×C₉	—	57	6	no	—
68	C₂₇	—	57	9	no	—
69	C₁₉	#10624683	1	1	yes	characteristic, complemented, Sylow
70	C₃²	—	3	27	no	—
71	C₃²	—	3	3	no	—
72	C₃²	—	3	3	no	—
73	C₃²	—	3	6	no	—
74	C₃²	C₃²⋊#4296	1	3	yes	—
75	C₃²	#13095342	1	9	yes	complemented
76	C₃²	C₃²×#4296	1	1	yes	characteristic
77	C₉	—	19	1	no	—
78	C₉	—	19	6	no	—
79	C₉	—	19	2	no	—
80	C₉	—	57	6	no	—
81	C₃	—	3	3	no	—
82	C₃	—	3	9	no	—
83	C₃	C₃×C₃²⋊#4296	1	1	yes	characteristic
84	C₃	C₃×#13095342	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator, socle	C₃²×C₁₉	C₃²×C₉
Fitting, prime radical	C₃⁴×C₁₉	C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃⁴	#4296
hypocenter	C₁₉	#10624683
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃⁴

Complements

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

N	H ≅ G/N	type
1. C₃×#13095342	C₃	semidirect
2. C₃²⋊#10587020	C₃	semidirect
5. C₃×#10587020	C₃²	semidirect
36. C₃²×C₁₉	C₂₇⋊C₃	semidirect
69. C₁₉	#10624683	semidirect
75. C₃²	#13095342	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
C₃³×#4294	3
#10624683	19