Group #21419328 — subgroups

Subgroups — #21419328

Order 7533.

124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 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×#11719686	C₃	1	1	yes	maximal, characteristic
2	C₃×C₉×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#14578887	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₃₁⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
5	(C₃₁⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	(C₃₁⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	(C₃₁⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	(C₃₁⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	(C₃₁⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	(C₃₁⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
11	(C₃×C₃₁⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
12	(C₃×C₃₁⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
13	C₃₁×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
14	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
15	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
19	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
20	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
21	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
22	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
23	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
24	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
25	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
26	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
27	#11719686	—	3	3	no	—
28	C₉×C₃₁⋊C₃	—	3	3	no	—
29	C₃²×C₃₁	C₃³	1	1	yes	characteristic
30	C₃×C₃₁⋊C₃	—	3	1	no	—
31	C₃×C₃₁⋊C₃	—	3	1	no	—
32	C₃×C₃₁⋊C₃	—	3	1	no	—
33	C₃×C₃₁⋊C₃	3₋¹⁺²	1	3	yes	—
34	C₉×C₃₁	—	3	1	no	—
35	C₉×C₃₁	—	3	1	no	—
36	C₉×C₃₁	—	3	1	no	—
37	C₉×C₃₁	—	3	1	no	—
38	C₃₁⋊C₉	—	3	1	no	—
39	C₃₁⋊C₉	—	3	1	no	—
40	C₃₁⋊C₉	—	3	1	no	—
41	C₃₁⋊C₉	—	3	1	no	—
42	C₃₁⋊C₉	—	3	1	no	—
43	C₃₁⋊C₉	—	3	1	no	—
44	C₃₁⋊C₉	—	3	1	no	—
45	C₃₁⋊C₉	3₋¹⁺²	1	3	yes	complemented
46	#6894	—	31	1	no	maximal, Sylow
47	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
48	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
49	C₃×C₃₁	#737	1	1	yes	characteristic
50	C₃×C₃₁	#737	1	1	yes	characteristic
51	C₃₁⋊C₃	—	3	3	no	—
52	C₃×3₋¹⁺²	—	31	1	no	—
53	C₃²×C₉	—	31	1	no	—
54	C₉⋊C₉	—	31	1	no	—
55	C₉⋊C₉	—	31	1	no	—
56	C₉⋊C₉	—	31	1	no	—
57	C₉⋊C₉	—	31	1	no	—
58	C₉⋊C₉	—	31	1	no	—
59	C₉⋊C₉	—	31	1	no	—
60	C₉⋊C₉	—	31	1	no	—
61	C₉⋊C₉	—	31	1	no	—
62	C₉⋊C₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
63	C₃²⋊C₉	—	31	1	no	—
64	C₃²⋊C₉	—	31	1	no	—
65	C₃₁	#6894	1	1	yes	characteristic, complemented, Sylow
66	C₃³	—	31	1	no	—
67	3₋¹⁺²	—	93	3	no	—
68	C₃×C₉	—	31	1	no	—
69	C₃×C₉	—	31	1	no	—
70	C₃×C₉	—	31	1	no	—
71	C₃×C₉	—	31	1	no	—
72	C₃×C₉	—	31	1	no	—
73	C₃×C₉	—	31	1	no	—
74	C₃×C₉	—	31	1	no	—
75	C₃×C₉	—	31	1	no	—
76	C₃×C₉	—	93	3	no	—
77	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
78	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
79	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
80	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
81	C₃²	—	31	3	no	—
82	C₃²	—	93	1	no	—
83	C₃²	—	93	1	no	—
84	C₃²	—	93	1	no	—
85	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	3	1	no	—
89	C₉	—	3	1	no	—
90	C₉	—	31	3	no	—
91	C₉	—	93	1	no	—
92	C₉	—	93	1	no	—
93	C₉	—	93	1	no	—
94	C₉	—	93	1	no	—
95	C₉	—	93	1	no	—
96	C₉	—	93	1	no	—
97	C₉	—	93	1	no	—
98	C₃	—	93	3	no	—
99	C₃	3₋¹⁺²×C₃₁⋊C₃	1	1	yes	characteristic
100	C₃	3₋¹⁺²×C₃₁⋊C₃	1	1	yes	characteristic
101	C₃	#14578912	1	1	yes	characteristic
102	C₃	#14578913	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#11719686

C₃

yes

maximal, characteristic

C₃×C₉×C₃₁⋊C₃

C₃

yes

maximal, characteristic

#14578887

C₃

yes

maximal, characteristic, complemented

(C₃₁⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃₁⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃₁⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃₁⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃₁⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃₁⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃₁⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃×C₃₁⋊C₃)⋊C₉

C₃

yes

maximal, characteristic

(C₃×C₃₁⋊C₃)⋊C₉

C₃

yes

maximal, characteristic

C₃₁×C₉⋊C₉

C₃

yes

maximal, characteristic, complemented

C₃²×C₃₁⋊C₃

C₃²

yes

characteristic

C₃×C₉×C₃₁

C₃²

yes

characteristic

C₃×C₉×C₃₁

C₃²

yes

characteristic

C₃×C₉×C₃₁

C₃²

yes

characteristic

C₃×C₉×C₃₁

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

C₃×C₃₁⋊C₉

C₃²

yes

characteristic

#11719686

—

C₉×C₃₁⋊C₃

—

C₃²×C₃₁

C₃³

yes

characteristic

C₃×C₃₁⋊C₃

—

C₃×C₃₁⋊C₃

—

C₃×C₃₁⋊C₃

—

C₃×C₃₁⋊C₃

3₋¹⁺²

yes

—

C₉×C₃₁

—

C₉×C₃₁

—

C₉×C₃₁

—

C₉×C₃₁

—

C₃₁⋊C₉

—

C₃₁⋊C₉

—

C₃₁⋊C₉

—

C₃₁⋊C₉

—

C₃₁⋊C₉

—

C₃₁⋊C₉

—

C₃₁⋊C₉

—

C₃₁⋊C₉

3₋¹⁺²

yes

complemented

#6894

—

maximal, Sylow

C₃×C₃₁

C₃×3₋¹⁺²

yes

characteristic

C₃×C₃₁

C₃×3₋¹⁺²

yes

C₃×C₃₁

yes

C₃×C₃₁

yes

C₃₁⋊C₃

—

C₃×3₋¹⁺²

—

C₃²×C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

C₃₁⋊C₃

yes

characteristic, complemented

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃₁

#6894

yes

characteristic, complemented, Sylow

C₃³

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₃₁⋊C₃

yes

characteristic

C₃×C₉

C₃×C₃₁⋊C₃

yes

characteristic

C₃×C₉

C₃×C₃₁⋊C₃

yes

characteristic

C₃×C₉

C₃×C₃₁⋊C₃

yes

characteristic

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²×C₃₁⋊C₃

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

C₃

—

C₃

3₋¹⁺²×C₃₁⋊C₃

yes

characteristic

100

C₃

3₋¹⁺²×C₃₁⋊C₃

yes

characteristic

101

C₃

#14578912

yes

characteristic

102

C₃

#14578913

yes

characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator, socle	C₃²×C₃₁	C₃³
Fitting	C₃₁×C₉⋊C₉	C₃
hypercenter	C₉⋊C₉	C₃₁⋊C₃
hypocenter	C₃₁	#6894
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

subgroup

G/H

center, Frattini

C₃²

C₃²×C₃₁⋊C₃

commutator, socle

C₃²×C₃₁

C₃³

Fitting

C₃₁×C₉⋊C₉

C₃

hypercenter

C₉⋊C₉

C₃₁⋊C₃

C₃₁

G ▷ C₃²×C₃₁ ▷ C₃₁

C₁ ◁ C₃² ◁ C₉⋊C₉

N	H ≅ G/N	type
3. #14578887	C₃	semidirect
4. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
5. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
6. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
7. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
8. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
9. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
10. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
13. C₃₁×C₉⋊C₉	C₃	semidirect
45. C₃₁⋊C₉	3₋¹⁺²	semidirect
62. C₉⋊C₉	C₃₁⋊C₃	semidirect
65. C₃₁	#6894	semidirect

H ≅ G/N

type

3. #14578887

C₃

semidirect

4. (C₃₁⋊C₉)⋊C₉

C₃

semidirect

5. (C₃₁⋊C₉)⋊C₉

C₃

semidirect

6. (C₃₁⋊C₉)⋊C₉

C₃

semidirect

7. (C₃₁⋊C₉)⋊C₉

C₃

semidirect

8. (C₃₁⋊C₉)⋊C₉

C₃

semidirect

9. (C₃₁⋊C₉)⋊C₉

C₃

semidirect

10. (C₃₁⋊C₉)⋊C₉

C₃

semidirect

13. C₃₁×C₉⋊C₉

C₃

semidirect

45. C₃₁⋊C₉

3₋¹⁺²

semidirect

62. C₉⋊C₉

C₃₁⋊C₃

semidirect

65. C₃₁

#6894

semidirect

Subgroups — #21419328

Conjugacy classes of subgroups

Complements