Group #28355968 — subgroups

Subgroups — C₃×#17987435 #28355968

Order 13851.

932 conjugacy classes of subgroups; only the 346 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 346 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	C₃³×#4294	C₃	1	1	yes	maximal, characteristic
2	#17987435	C₃	1	27	yes	maximal, direct product factor
3	C₃×#13095305	C₃	1	6	yes	maximal, complemented
4	C₃×#13095305	C₃	1	3	yes	maximal, complemented
5	C₃×C₃²⋊#4294	C₃	1	2	yes	maximal
6	C₃²×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
7	C₃²×#4294	—	3	9	no	—
8	C₃²×#4294	C₃²	1	6	yes	—
9	C₃²×#4294	C₃²	1	2	yes	—
10	C₃²×#4294	C₃²	1	9	yes	—
11	C₃²×#4294	C₃²	1	1	yes	characteristic
12	#13095305	C₃²	1	54	yes	complemented
13	#13095305	C₃²	1	27	yes	complemented
14	C₃²⋊#4294	C₃²	1	18	yes	—
15	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
16	C₃×C₁₉×3₋¹⁺²	—	3	9	no	—
17	C₃×C₁₉×3₋¹⁺²	C₃²	1	9	yes	—
18	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
19	C₃×#6894	—	19	1	no	maximal, Sylow
20	C₃³×C₁₉	—	3	3	no	—
21	C₃³×C₁₉	—	3	6	no	—
22	C₃³×C₁₉	3₋¹⁺²	1	9	yes	—
23	C₃³×C₁₉	C₃³	1	3	yes	—
24	C₃³×C₁₉	C₃³	1	1	yes	characteristic
25	C₁₉×3₋¹⁺²	—	3	27	no	—
26	C₃×C₉×C₁₉	—	3	9	no	—
27	C₃×C₉×C₁₉	C₃³	1	9	yes	—
28	C₃×#4294	—	3	6	no	—
29	C₃×#4294	—	3	18	no	—
30	C₃×#4294	—	3	27	no	—
31	C₃×#4294	3₋¹⁺²	1	9	yes	complemented
32	C₃×#4294	C₃³	1	18	yes	—
33	C₃×#4294	C₃³	1	6	yes	—
34	C₃×#4294	C₃³	1	3	yes	—
35	C₃²×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
36	C₃³×C₉	—	19	1	no	—
37	#6894	—	19	27	no	—
38	C₃×C₉⋊C₉	—	19	3	no	—
39	C₃×C₉⋊C₉	—	19	6	no	—
40	C₃×C₃²⋊C₉	—	19	2	no	—
41	C₃²×C₁₉	—	3	3	no	—
42	C₃²×C₁₉	—	3	6	no	—
43	C₃²×C₁₉	—	3	27	no	—
44	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
45	C₃²×C₁₉	C₃×3₋¹⁺²	1	9	yes	—
46	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
47	C₃²×C₁₉	#737	1	6	yes	—
48	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
49	C₉×C₁₉	—	3	9	no	—
50	#4294	—	3	6	no	—
51	#4294	—	3	18	no	—
52	#4294	C₃×3₋¹⁺²	1	9	yes	complemented
53	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
54	C₃×3₋¹⁺²	—	3	9	no	—
55	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	9	yes	—
56	C₃²×C₉	—	19	1	no	—
57	C₃²×C₉	—	19	9	no	—
58	C₃²×C₉	—	19	2	no	—
59	C₃²×C₉	—	19	6	no	—
60	C₃²×C₉	—	57	9	no	—
61	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
62	C₉⋊C₉	—	19	27	no	—
63	C₉⋊C₉	—	19	54	no	—
64	C₃²⋊C₉	—	19	18	no	—
65	C₃×C₁₉	—	3	9	no	—
66	C₃×C₁₉	#6894	1	9	yes	complemented
67	C₃×C₁₉	C₃²×3₋¹⁺²	1	1	yes	characteristic
68	C₃×C₁₉	C₃²×3₋¹⁺²	1	1	yes	characteristic
69	C₃×C₁₉	C₃×#737	1	2	yes	—
70	C₃³	—	3	3	no	—
71	C₃³	—	3	6	no	—
72	C₃³	#10587025	1	9	yes	—
73	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
74	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
75	3₋¹⁺²	—	3	27	no	—
76	C₃×C₉	—	3	9	no	—
77	C₃×C₉	—	19	9	no	—
78	C₃×C₉	—	19	3	no	—
79	C₃×C₉	—	19	18	no	—
80	C₃×C₉	—	19	6	no	—
81	C₃×C₉	—	57	27	no	—
82	C₃×C₉	—	57	6	no	—
83	C₃×C₉	—	57	18	no	—
84	C₃×C₉	C₃²×C₁₉⋊C₃	1	9	yes	—
85	C₁₉	C₃×#6894	1	1	yes	characteristic, complemented, Sylow
86	C₃²	—	3	27	no	—
87	C₃²	—	3	3	no	—
88	C₃²	—	3	6	no	—
89	C₃²	3₋¹⁺²×C₁₉⋊C₃	1	3	yes	—
90	C₃²	C₃×#10587025	1	9	yes	—
91	C₃²	C₃×#10587025	1	3	yes	—
92	C₃²	#13095333	1	6	yes	—
93	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
94	C₉	—	3	9	no	—
95	C₉	—	19	9	no	—
96	C₉	—	57	6	no	—
97	C₉	—	57	18	no	—
98	C₃	—	3	9	no	—
99	C₃	#17987435	1	9	yes	direct product factor
100	C₃	C₃×3₋¹⁺²×C₁₉⋊C₃	1	1	yes	characteristic
101	C₃	C₃²×#10587025	1	1	yes	characteristic
102	C₃	C₃×#13095333	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃³×#4294

C₃

yes

maximal, characteristic

#17987435

C₃

yes

maximal, direct product factor

C₃×#13095305

C₃

yes

maximal, complemented

C₃×#13095305

C₃

yes

maximal, complemented

C₃×C₃²⋊#4294

C₃

yes

maximal

C₃²×C₁₉×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃²×#4294

—

C₃²×#4294

C₃²

yes

—

C₃²×#4294

C₃²

yes

—

C₃²×#4294

C₃²

yes

—

C₃²×#4294

C₃²

yes

characteristic

#13095305

C₃²

yes

complemented

#13095305

C₃²

yes

complemented

C₃²⋊#4294

C₃²

yes

—

C₃⁴×C₁₉

C₃²

yes

characteristic

C₃×C₁₉×3₋¹⁺²

—

C₃×C₁₉×3₋¹⁺²

C₃²

yes

—

C₃²×C₉×C₁₉

C₃²

yes

—

C₃×#6894

—

maximal, Sylow

C₃³×C₁₉

—

C₃³×C₁₉

—

C₃³×C₁₉

3₋¹⁺²

yes

—

C₃³×C₁₉

C₃³

yes

—

C₃³×C₁₉

C₃³

yes

characteristic

C₁₉×3₋¹⁺²

—

C₃×C₉×C₁₉

—

C₃×C₉×C₁₉

C₃³

yes

—

—

—

—

3₋¹⁺²

yes

complemented

C₃×#4294

C₃³

yes

—

C₃×#4294

C₃³

yes

—

C₃×#4294

C₃³

yes

—

C₃²×3₋¹⁺²

C₁₉⋊C₃

yes

characteristic

C₃³×C₉

—

#6894

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₃²⋊C₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

#737

yes

—

C₃²×C₁₉

C₃⁴

yes

characteristic

C₉×C₁₉

—

#4294

—

#4294

—

#4294

C₃×3₋¹⁺²

yes

complemented

C₃⁴

C₃×C₁₉⋊C₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃×C₁₉⋊C₃

yes

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×C₁₉⋊C₃

yes

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃×C₁₉

—

C₃×C₁₉

#6894

yes

complemented

C₃×C₁₉

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₁₉

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₁₉

C₃×#737

yes

—

C₃³

—

C₃³

—

C₃³

#10587025

yes

—

C₃³

C₃²×C₁₉⋊C₃

yes

—

C₃³

C₃²×C₁₉⋊C₃

yes

characteristic

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃²×C₁₉⋊C₃

yes

—

C₁₉

C₃×#6894

yes

characteristic, complemented, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

3₋¹⁺²×C₁₉⋊C₃

yes

—

C₃²

C₃×#10587025

yes

—

C₃²

C₃×#10587025

yes

—

C₃²

#13095333

yes

—

C₃²

C₃³×C₁₉⋊C₃

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

—

C₃

—

C₃

#17987435

yes

direct product factor

100

C₃

C₃×3₋¹⁺²×C₁₉⋊C₃

yes

characteristic

101

C₃

C₃²×#10587025

yes

characteristic

102

C₃

C₃×#13095333

yes

—

	subgroup	G/H
center	C₃³	C₃²×C₁₉⋊C₃
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₃²×C₁₉×3₋¹⁺²	C₃
socle	C₃³×C₁₉	C₃³
prime radical	C₃⁴×C₁₉	C₃²
hypercenter	C₃²×3₋¹⁺²	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6894
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃²×3₋¹⁺²

subgroup

G/H

center

C₃³

C₃²×C₁₉⋊C₃

commutator, cosocle

C₃²×C₁₉

C₃⁴

Frattini

C₃²

C₃³×C₁₉⋊C₃

Fitting

C₃²×C₁₉×3₋¹⁺²

C₃

socle

C₃³×C₁₉

C₃³

prime radical

C₃⁴×C₁₉

C₃²

hypercenter

C₃²×3₋¹⁺²

C₁₉⋊C₃

C₁₉

G ▷ C₃²×C₁₉ ▷ C₁₉

C₁ ◁ C₃³ ◁ C₃²×3₋¹⁺²

N	H ≅ G/N	type
2. #17987435	C₃	direct (N × H)
3. C₃×#13095305	C₃	semidirect
4. C₃×#13095305	C₃	semidirect
12. #13095305	C₃²	semidirect
13. #13095305	C₃²	semidirect
31. C₃×#4294	3₋¹⁺²	semidirect
52. #4294	C₃×3₋¹⁺²	semidirect
66. C₃×C₁₉	#6894	semidirect
85. C₁₉	C₃×#6894	semidirect
99. C₃	#17987435	direct (N × H)

H ≅ G/N

type

2. #17987435

C₃

direct (N × H)

3. C₃×#13095305

C₃

semidirect

4. C₃×#13095305

C₃

semidirect

12. #13095305

C₃²

semidirect

13. #13095305

C₃²

semidirect

31. C₃×#4294

3₋¹⁺²

semidirect

52. #4294

C₃×3₋¹⁺²

semidirect

66. C₃×C₁₉

#6894

semidirect

85. C₁₉

C₃×#6894

semidirect

99. C₃

#17987435

direct (N × H)

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

subgroup	index
C₃³×#4294	3
#17987435	3
C₃×#13095305	3
C₃×C₃²⋊#4294	3
C₃²×C₁₉×3₋¹⁺²	3
C₃×#6894	19

subgroup

index

C₃³×#4294

#17987435

C₃×#13095305

C₃×C₃²⋊#4294

C₃²×C₁₉×3₋¹⁺²

C₃×#6894

Subgroups — C₃×#17987435 #28355968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#17987435 #28355968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987435 #28355968