Subgroups — #28356891

Order 13851.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	2	yes	maximal, complemented
2	C₃²×#10587020	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊#10587020	C₃	1	9	yes	maximal, complemented
4	C₃×#13095331	C₃	1	1	yes	maximal, characteristic
5	#13095342	—	3	6	no	—
6	C₃×#10587020	—	3	3	no	—
7	C₃×#10587020	C₃²	1	3	yes	—
8	C₃×#10587020	C₃²	1	6	yes	—
9	#13095331	—	3	3	no	—
10	#13095331	—	3	6	no	—
11	C₃×#10587025	C₉	1	2	yes	—
12	C₃×#10587025	C₉	1	6	yes	—
13	C₃²×#4294	C₃²	1	3	yes	—
14	C₃²×#4294	C₃²	1	1	yes	characteristic
15	C₃×C₁₉×H(3,𝔽₃)	C₉	1	1	yes	characteristic
16	#10624684	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	C₃×C₉	1	3	yes	—
18	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
19	C₁₉×H(3,𝔽₃)	—	3	3	no	—
20	#10587025	—	3	6	no	—
21	#10587025	—	3	18	no	—
22	C₃×#4294	—	3	3	no	—
23	C₃×#4294	—	3	6	no	—
24	C₃×#4294	C₃×C₉	1	6	yes	—
25	C₃×#4294	C₃×C₉	1	2	yes	—
26	C₃×#4294	H(3,𝔽₃)	1	3	yes	—
27	C₃×#4294	3₋¹⁺²	1	6	yes	—
28	C₃×#4294	C₃³	1	1	yes	characteristic
29	#10587020	—	3	3	no	—
30	#10587020	—	3	6	no	—
31	C₃×#737	—	19	1	no	—
32	C₃×C₂₇⋊C₃	—	19	2	no	—
33	C₃²×C₂₇	—	19	1	no	—
34	C₃²⋊C₂₇	—	19	9	no	—
35	C₃²×C₁₉	—	3	3	no	—
36	C₃²×C₁₉	—	3	3	no	—
37	C₃²×C₁₉	—	3	9	no	—
38	C₃²×C₁₉	C₃²⋊C₉	1	3	yes	—
39	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
40	#4294	—	3	6	no	—
41	#4294	C₃²⋊C₉	1	6	yes	—
42	#4294	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	#4294	C₃×3₋¹⁺²	1	2	yes	—
44	#737	—	57	3	no	—
45	#737	—	57	6	no	—
46	C₃×3₋¹⁺²	—	19	6	no	—
47	C₃×3₋¹⁺²	—	19	2	no	—
48	C₃×H(3,𝔽₃)	#4296	1	1	yes	characteristic
49	C₃²×C₉	—	19	1	no	—
50	C₃²×C₉	—	19	3	no	—
51	C₂₇⋊C₃	—	57	6	no	—
52	C₃×C₂₇	—	19	3	no	—
53	C₃×C₂₇	—	19	6	no	—
54	C₃×C₂₇	—	57	3	no	—
55	C₃×C₁₉	—	3	3	no	—
56	C₃×C₁₉	—	9	3	no	—
57	C₃×C₁₉	C₃×C₃²⋊C₉	1	1	yes	characteristic
58	C₃×C₁₉	#6903	1	3	yes	—
59	C₃³	C₃×#4296	1	3	yes	—
60	C₃³	C₃×#4296	1	1	yes	characteristic
61	3₋¹⁺²	—	57	18	no	—
62	3₋¹⁺²	—	57	6	no	—
63	H(3,𝔽₃)	—	3	3	no	—
64	C₃×C₉	—	19	3	no	—
65	C₃×C₉	—	19	6	no	—
66	C₃×C₉	—	19	2	no	—
67	C₃×C₉	—	19	1	no	—
68	C₃×C₉	—	19	6	no	—
69	C₃×C₉	—	57	3	no	—
70	C₃×C₉	—	57	6	no	—
71	C₂₇	—	57	3	no	—
72	C₂₇	—	57	6	no	—
73	C₁₉	#10624684	1	1	yes	characteristic, complemented, Sylow
74	C₃²	—	3	3	no	—
75	C₃²	—	3	3	no	—
76	C₃²	—	3	9	no	—
77	C₃²	C₃²⋊#4296	1	3	yes	—
78	C₃²	C₃²×#4296	1	1	yes	characteristic
79	C₉	—	19	1	no	—
80	C₉	—	19	2	no	—
81	C₉	—	19	6	no	—
82	C₉	—	57	6	no	—
83	C₃	—	3	3	no	—
84	C₃	—	9	3	no	—
85	C₃	C₃×C₃²⋊#4296	1	1	yes	characteristic
86	C₃	#17987598	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator, socle	C₃²×C₁₉	C₃²×C₉
Fitting, prime radical	C₃×C₁₉×H(3,𝔽₃)	C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃×H(3,𝔽₃)	#4296
hypocenter	C₁₉	#10624684
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

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
3. C₃²⋊#10587020	C₃	semidirect
73. C₁₉	#10624684	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
C₃²⋊#10587020	3
C₃×#13095331	3
#10624684	19