Group #28353510 — subgroups

Subgroups — #28353510

Order 13851.

554 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095307	C₃	1	3	yes	maximal, complemented
2	C₃×C₃²⋊#4294	C₃	1	3	yes	maximal
3	#17987308	C₃	1	6	yes	maximal, complemented
4	C₃³×C₉×C₁₉	C₃	1	1	yes	maximal, characteristic
5	C₃²×#4294	C₃²	1	9	yes	—
6	#13095307	—	3	9	no	—
7	C₃²⋊#4294	—	3	9	no	—
8	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
9	C₃²×C₉×C₁₉	—	3	3	no	—
10	C₃²×C₉×C₁₉	—	3	6	no	—
11	C₃²×C₉×C₁₉	C₉	1	9	yes	complemented
12	C₃²×C₉×C₁₉	C₃²	1	2	yes	—
13	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
14	#10624548	—	19	1	no	maximal, Sylow
15	C₃³×C₁₉	—	3	1	no	—
16	C₃³×C₁₉	—	3	2	no	—
17	C₃³×C₁₉	—	3	6	no	—
18	C₃³×C₁₉	C₃×C₉	1	3	yes	—
19	C₃³×C₁₉	3₋¹⁺²	1	9	yes	—
20	C₃³×C₁₉	C₃³	1	1	yes	characteristic
21	C₃×C₉×C₁₉	—	3	2	no	—
22	C₃×C₉×C₁₉	—	3	4	no	—
23	C₃×C₉×C₁₉	—	3	27	no	—
24	C₃×C₉×C₁₉	C₃×C₉	1	6	yes	—
25	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
26	C₃×C₉×C₁₉	H(3,𝔽₃)	1	3	yes	—
27	C₃×C₉×C₁₉	3₋¹⁺²	1	6	yes	—
28	C₃×#4294	—	3	9	no	—
29	C₃×#4294	—	3	9	no	—
30	C₃×#4294	—	3	18	no	—
31	C₃³×C₉	C₁₉⋊C₃	1	1	yes	characteristic
32	C₃×C₉⋊C₉	—	19	3	no	—
33	C₃×C₃²⋊C₉	—	19	3	no	—
34	#6855	—	19	6	no	—
35	C₃²×C₁₉	—	3	3	no	—
36	C₃²×C₁₉	—	3	6	no	—
37	C₃²×C₁₉	—	3	9	no	—
38	C₃²×C₁₉	—	3	18	no	—
39	C₃²×C₁₉	C₉⋊C₉	1	9	yes	complemented
40	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
41	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
43	C₃²×C₁₉	C₃×3₋¹⁺²	1	2	yes	—
44	C₃²×C₁₉	#737	1	6	yes	—
45	C₉×C₁₉	—	3	6	no	—
46	C₉×C₁₉	C₃²⋊C₉	1	9	yes	complemented
47	#4294	—	9	9	no	—
48	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
49	C₃²×C₉	—	3	6	no	—
50	C₃²×C₉	—	3	3	no	—
51	C₃²×C₉	—	19	9	no	—
52	C₃²×C₉	#4294	1	9	yes	complemented
53	C₃²×C₉	C₃×C₁₉⋊C₃	1	2	yes	—
54	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
55	C₉⋊C₉	—	57	9	no	—
56	C₃²⋊C₉	—	57	9	no	—
57	C₃×C₁₉	—	3	9	no	—
58	C₃×C₁₉	C₃×C₃²⋊C₉	1	1	yes	characteristic
59	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
60	C₃×C₁₉	#6887	1	2	yes	—
61	C₃×C₁₉	C₉⋊H(3,𝔽₃)	1	3	yes	—
62	C₃×C₁₉	#6894	1	6	yes	—
63	C₃³	—	3	1	no	—
64	C₃³	—	3	2	no	—
65	C₃³	—	3	6	no	—
66	C₃³	#10587023	1	9	yes	—
67	C₃³	C₃×#4294	1	3	yes	—
68	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
69	C₃×C₉	—	3	2	no	—
70	C₃×C₉	—	3	4	no	—
71	C₃×C₉	—	3	27	no	—
72	C₃×C₉	—	57	9	no	—
73	C₃×C₉	—	57	9	no	—
74	C₃×C₉	—	57	18	no	—
75	C₃×C₉	C₃×#4294	1	6	yes	—
76	C₃×C₉	C₃×#4294	1	3	yes	—
77	C₃×C₉	#10587025	1	6	yes	—
78	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
79	C₁₉	#10624548	1	1	yes	characteristic, complemented, Sylow
80	C₃²	—	3	3	no	—
81	C₃²	—	3	6	no	—
82	C₃²	—	3	9	no	—
83	C₃²	—	3	18	no	—
84	C₃²	#13095307	1	9	yes	complemented
85	C₃²	C₃²×#4294	1	1	yes	characteristic
86	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
87	C₃²	C₃×#10587023	1	3	yes	—
88	C₃²	C₃×#10587025	1	2	yes	—
89	C₃²	#13095332	1	6	yes	—
90	C₉	—	3	6	no	—
91	C₉	—	171	9	no	—
92	C₉	C₃²⋊#4294	1	9	yes	complemented
93	C₃	—	3	9	no	—
94	C₃	C₃×C₃²⋊#4294	1	1	yes	characteristic
95	C₃	C₃×#13095307	1	1	yes	characteristic
96	C₃	#17987405	1	2	yes	—
97	C₃	#17987426	1	3	yes	—
98	C₃	#17987439	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#13095307

C₃

yes

maximal, complemented

C₃×C₃²⋊#4294

C₃

yes

maximal

#17987308

C₃

yes

maximal, complemented

C₃³×C₉×C₁₉

C₃

yes

maximal, characteristic

C₃²×#4294

C₃²

yes

—

#13095307

—

C₃²⋊#4294

—

C₃⁴×C₁₉

C₃²

yes

characteristic

C₃²×C₉×C₁₉

—

C₃²×C₉×C₁₉

—

C₃²×C₉×C₁₉

C₉

yes

complemented

C₃²×C₉×C₁₉

C₃²

yes

—

C₃²×C₉×C₁₉

C₃²

yes

characteristic

#10624548

—

maximal, Sylow

C₃³×C₁₉

—

C₃³×C₁₉

—

C₃³×C₁₉

—

C₃³×C₁₉

C₃×C₉

yes

—

C₃³×C₁₉

3₋¹⁺²

yes

—

C₃³×C₁₉

C₃³

yes

characteristic

C₃×C₉×C₁₉

—

C₃×C₉×C₁₉

—

C₃×C₉×C₁₉

—

C₃×C₉×C₁₉

C₃×C₉

yes

—

C₃×C₉×C₁₉

C₃×C₉

yes

—

C₃×C₉×C₁₉

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₉

3₋¹⁺²

yes

—

C₃×#4294

—

C₃×#4294

—

C₃×#4294

—

C₃³×C₉

C₁₉⋊C₃

yes

characteristic

C₃×C₉⋊C₉

—

C₃×C₃²⋊C₉

—

#6855

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

C₉⋊C₉

yes

complemented

C₃²×C₁₉

C₃²×C₉

yes

characteristic

C₃²×C₁₉

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

#737

yes

—

C₉×C₁₉

—

C₉×C₁₉

C₃²⋊C₉

yes

complemented

#4294

—

C₃⁴

C₃×C₁₉⋊C₃

yes

characteristic

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

#4294

yes

complemented

C₃²×C₉

C₃×C₁₉⋊C₃

yes

—

C₃²×C₉

C₃×C₁₉⋊C₃

yes

characteristic

C₉⋊C₉

—

C₃²⋊C₉

—

C₃×C₁₉

—

C₃×C₁₉

C₃×C₃²⋊C₉

yes

characteristic

C₃×C₁₉

C₃×C₉⋊C₉

yes

characteristic

C₃×C₁₉

#6887

yes

—

C₃×C₁₉

C₉⋊H(3,𝔽₃)

yes

—

C₃×C₁₉

#6894

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

#10587023

yes

—

C₃³

C₃×#4294

yes

—

C₃³

C₃²×C₁₉⋊C₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×#4294

yes

—

C₃×C₉

C₃×#4294

yes

—

C₃×C₉

#10587025

yes

—

C₃×C₉

C₃²⋊(C₁₉⋊C₃)

yes

—

C₁₉

#10624548

yes

characteristic, complemented, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

#13095307

yes

complemented

C₃²

C₃²×#4294

yes

characteristic

C₃²

C₃×C₃²⋊(C₁₉⋊C₃)

yes

characteristic

C₃²

C₃×#10587023

yes

—

C₃²

C₃×#10587025

yes

—

C₃²

#13095332

yes

—

C₉

—

C₉

—

171

—

C₉

C₃²⋊#4294

yes

complemented

C₃

—

C₃

C₃×C₃²⋊#4294

yes

C₃

yes

C₃

yes

—

C₃

#17987426

yes

—

C₃

#17987439

yes

—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₁₉⋊C₃
commutator	C₃²×C₁₉	C₃²×C₉
Fitting	C₃³×C₉×C₁₉	C₃
socle, cosocle	C₃³×C₁₉	C₃³
prime radical	C₃⁴×C₁₉	C₃²
hypercenter	C₃³×C₉	C₁₉⋊C₃
hypocenter	C₁₉	#10624548
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃³×C₉

subgroup

G/H

center, Frattini

C₃³

C₃²×C₁₉⋊C₃

commutator

C₃²×C₁₉

C₃²×C₉

Fitting

C₃³×C₉×C₁₉

C₃

socle, cosocle

C₃³×C₁₉

C₃³

prime radical

C₃⁴×C₁₉

C₃²

hypercenter

C₃³×C₉

C₁₉⋊C₃

C₁₉

G ▷ C₃²×C₁₉ ▷ C₁₉

C₁ ◁ C₃³ ◁ C₃³×C₉

N	H ≅ G/N	type
1. C₃×#13095307	C₃	semidirect
3. #17987308	C₃	semidirect
11. C₃²×C₉×C₁₉	C₉	semidirect
39. C₃²×C₁₉	C₉⋊C₉	semidirect
46. C₉×C₁₉	C₃²⋊C₉	semidirect
52. C₃²×C₉	#4294	semidirect
79. C₁₉	#10624548	semidirect
84. C₃²	#13095307	semidirect
92. C₉	C₃²⋊#4294	semidirect

H ≅ G/N

type

1. C₃×#13095307

C₃

semidirect

3. #17987308

C₃

semidirect

11. C₃²×C₉×C₁₉

C₉

semidirect

39. C₃²×C₁₉

C₉⋊C₉

semidirect

46. C₉×C₁₉

C₃²⋊C₉

semidirect

52. C₃²×C₉

#4294

semidirect

79. C₁₉

#10624548

semidirect

84. C₃²

#13095307

semidirect

92. C₉

C₃²⋊#4294

semidirect

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

subgroup	index
C₃×#13095307	3
C₃×C₃²⋊#4294	3
#17987308	3
C₃³×C₉×C₁₉	3
#10624548	19

subgroup

index

C₃×#13095307

C₃×C₃²⋊#4294

#17987308

C₃³×C₉×C₁₉

#10624548

Subgroups — #28353510

Conjugacy classes of subgroups

Complements

Maximal subgroups