Subgroups — #28356700

Order 13851.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#10587020	C₃	1	3	yes	maximal, complemented
2	C₃×#13095333	C₃	1	1	yes	maximal, characteristic
3	C₃×#10587020	—	3	3	no	—
4	#13095333	—	3	9	no	—
5	C₃×#10587025	C₉	1	1	yes	characteristic
6	C₃×#10587022	—	3	1	no	—
7	C₃×#10587023	—	3	1	no	—
8	C₃×C₃²⋊(C₁₉⋊C₃)	C₉	1	1	yes	characteristic
9	C₃²×#4294	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₁₉⋊C₃	—	3	1	no	—
11	C₃×C₁₉×3₋¹⁺²	C₉	1	1	yes	characteristic
12	#10624456	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₃²×C₁₉⋊C₃	—	3	1	no	—
15	C₁₉×3₋¹⁺²	—	3	3	no	—
16	C₃×C₉×C₁₉	—	3	1	no	—
17	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
18	#10587025	—	3	3	no	—
19	C₃×#4294	—	3	1	no	—
20	C₃×#4294	—	3	3	no	—
21	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
23	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
24	#10587023	—	3	9	no	—
25	#10587022	—	3	9	no	—
26	C₉×C₁₉⋊C₃	—	3	9	no	—
27	#10587020	—	9	3	no	—
28	C₃×#737	—	19	1	no	—
29	C₃²⋊C₂₇	—	19	3	no	—
30	C₃²×C₁₉	—	3	1	no	—
31	C₃²×C₁₉	—	3	3	no	—
32	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
33	C₃×C₁₉⋊C₃	—	3	3	no	—
34	C₃×C₁₉⋊C₃	—	9	3	no	—
35	C₉×C₁₉	—	3	3	no	—
36	#4294	—	3	3	no	—
37	#4294	—	3	1	no	—
38	#4294	—	3	1	no	—
39	#4294	AΣL(1,𝔽₂₇)	1	3	yes	—
40	#737	—	57	9	no	—
41	C₃×3₋¹⁺²	—	19	1	no	—
42	C₃×3₋¹⁺²	—	57	1	no	—
43	C₃×3₋¹⁺²	—	57	1	no	—
44	C₃×3₋¹⁺²	#4296	1	1	yes	characteristic
45	C₃×H(3,𝔽₃)	—	19	1	no	—
46	C₃²×C₉	—	19	1	no	—
47	C₃²×C₉	—	57	1	no	—
48	C₃×C₂₇	—	57	3	no	—
49	C₃×C₁₉	—	9	1	no	—
50	C₃×C₁₉	#6866	1	1	yes	characteristic
51	C₃×C₁₉	#6872	1	3	yes	—
52	C₁₉⋊C₃	—	9	3	no	—
53	C₃³	—	57	1	no	—
54	C₃³	C₃×#4296	1	1	yes	characteristic
55	3₋¹⁺²	—	3	3	no	—
56	3₋¹⁺²	—	57	9	no	—
57	3₋¹⁺²	—	57	9	no	—
58	3₋¹⁺²	—	57	3	no	—
59	H(3,𝔽₃)	—	57	3	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	19	1	no	—
62	C₃×C₉	—	19	1	no	—
63	C₃×C₉	—	19	1	no	—
64	C₃×C₉	—	57	9	no	—
65	C₃×C₉	—	57	3	no	—
66	C₃×C₉	—	57	1	no	—
67	C₂₇	—	171	3	no	—
68	C₁₉	#10624456	1	1	yes	characteristic, complemented, Sylow
69	C₃²	—	3	1	no	—
70	C₃²	—	3	3	no	—
71	C₃²	—	57	3	no	—
72	C₃²	—	171	3	no	—
73	C₃²	C₃²⋊#4296	1	1	yes	characteristic
74	C₉	—	3	3	no	—
75	C₉	—	19	3	no	—
76	C₉	—	57	1	no	—
77	C₉	—	57	1	no	—
78	C₉	—	57	3	no	—
79	C₃	—	9	1	no	—
80	C₃	—	171	3	no	—
81	C₃	#17987558	1	1	yes	characteristic
82	C₃	#17987567	1	3	yes	—

	subgroup	G/H
center	C₃²	C₃²⋊#4296
commutator	C₃³×C₁₉	C₃×C₉
Frattini	C₃³	C₃×#4296
Fitting	C₃×C₁₉×3₋¹⁺²	C₉
socle	C₃²×C₁₉	C₃²⋊C₉
prime radical	C₃×C₃²⋊(C₁₉⋊C₃)	C₉
cosocle	C₃²×#4294	C₃²
hypercenter	C₃×3₋¹⁺²	#4296
hypocenter	C₁₉	#10624456
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
1. C₃²⋊#10587020	C₃	semidirect
68. C₁₉	#10624456	semidirect

Maximal subgroups

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

subgroup	index
C₃²⋊#10587020	3
C₃×#13095333	3
#10624456	19