Group #23782833 — subgroups

Subgroups — #23782833

Order 10449.

100 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 44 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	#16812500	C₃	1	1	yes	maximal, characteristic, complemented
2	#16812499	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₄₃⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₄₃⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
5	(C₄₃⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	(C₄₃⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	(C₄₃⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
9	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
10	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
11	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
12	C₉×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
13	C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
14	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
15	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
16	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
17	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
18	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
19	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
20	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
21	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
22	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
23	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
24	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
25	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
26	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
27	C₃²×C₄₃	C₃³	1	1	yes	characteristic
28	C₃×C₄₃⋊C₃	—	3	1	no	—
29	C₃×C₄₃⋊C₃	—	3	1	no	—
30	C₃×C₄₃⋊C₃	—	3	1	no	—
31	C₃×C₄₃⋊C₃	—	3	1	no	—
32	C₉×C₄₃	—	3	1	no	—
33	C₉×C₄₃	—	3	1	no	—
34	C₉×C₄₃	—	3	1	no	—
35	C₉×C₄₃	—	3	1	no	—
36	C₄₃⋊C₉	—	3	1	no	—
37	C₄₃⋊C₉	—	3	1	no	—
38	C₄₃⋊C₉	—	3	1	no	—
39	C₄₃⋊C₉	—	3	1	no	—
40	C₄₃⋊C₉	—	3	1	no	—
41	C₄₃⋊C₉	—	3	1	no	—
42	C₄₃⋊C₉	—	3	1	no	—
43	C₄₃⋊C₉	—	3	1	no	—
44	#6897	—	43	1	no	maximal, Sylow
45	C₃×C₄₃	#737	1	1	yes	characteristic
46	C₃×C₄₃	#737	1	1	yes	characteristic
47	C₃×C₄₃	#737	1	1	yes	characteristic
48	C₃×C₄₃	#737	1	1	yes	characteristic
49	C₄₃⋊C₃	—	9	1	no	—
50	C₉⋊C₉	—	43	1	no	—
51	C₉⋊C₉	—	43	1	no	—
52	C₉⋊C₉	—	43	1	no	—
53	C₉⋊C₉	—	43	1	no	—
54	C₉⋊C₉	—	43	1	no	—
55	C₉⋊C₉	—	43	1	no	—
56	C₉⋊C₉	—	43	1	no	—
57	C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
58	C₃²⋊C₉	—	43	1	no	—
59	C₃²⋊C₉	—	43	1	no	—
60	C₃²⋊C₉	—	43	1	no	—
61	C₃²⋊C₉	—	43	1	no	—
62	C₉²	—	43	1	no	—
63	C₄₃	#6897	1	1	yes	characteristic, complemented, Sylow
64	C₃³	—	43	1	no	—
65	C₃×C₉	—	43	1	no	—
66	C₃×C₉	—	43	1	no	—
67	C₃×C₉	—	43	1	no	—
68	C₃×C₉	—	43	1	no	—
69	C₃×C₉	—	43	1	no	—
70	C₃×C₉	—	43	1	no	—
71	C₃×C₉	—	43	1	no	—
72	C₃×C₉	—	43	1	no	—
73	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
74	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
75	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
76	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
77	C₃²	—	129	1	no	—
78	C₃²	—	129	1	no	—
79	C₃²	—	129	1	no	—
80	C₃²	—	129	1	no	—
81	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
82	C₉	—	3	1	no	—
83	C₉	—	3	1	no	—
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	129	1	no	—
87	C₉	—	129	1	no	—
88	C₉	—	129	1	no	—
89	C₉	—	129	1	no	—
90	C₉	—	129	1	no	—
91	C₉	—	129	1	no	—
92	C₉	—	129	1	no	—
93	C₉	—	129	1	no	—
94	C₃	—	387	1	no	—
95	C₃	#16812525	1	1	yes	characteristic
96	C₃	#16812526	1	1	yes	characteristic
97	C₃	#16812526	1	1	yes	characteristic
98	C₃	#16812526	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16812500

C₃

yes

maximal, characteristic, complemented

#16812499

C₃

yes

maximal, characteristic, complemented

(C₄₃⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₄₃⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₄₃⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₄₃⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₄₃⋊C₉)⋊C₉

C₃

yes

maximal, characteristic, complemented

(C₃×C₄₃⋊C₃)⋊C₉

C₃

yes

maximal, characteristic

(C₃×C₄₃⋊C₃)⋊C₉

C₃

yes

maximal, characteristic

(C₃×C₄₃⋊C₃)⋊C₉

C₃

yes

maximal, characteristic

(C₃×C₄₃⋊C₃)⋊C₉

C₃

yes

maximal, characteristic

C₉×C₄₃⋊C₉

C₃

yes

maximal, characteristic, complemented

C₄₃×C₉⋊C₉

C₃

yes

maximal, characteristic, complemented

C₃²×C₄₃⋊C₃

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₄₃⋊C₉

C₃²

yes

characteristic

C₃×C₉×C₄₃

C₃²

yes

characteristic

C₃×C₉×C₄₃

C₃²

yes

characteristic

C₃×C₉×C₄₃

C₃²

yes

characteristic

C₃×C₉×C₄₃

C₃²

yes

characteristic

C₃²×C₄₃

C₃³

yes

characteristic

C₃×C₄₃⋊C₃

—

C₃×C₄₃⋊C₃

—

C₃×C₄₃⋊C₃

—

C₃×C₄₃⋊C₃

—

C₉×C₄₃

—

C₉×C₄₃

—

C₉×C₄₃

—

C₉×C₄₃

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

C₄₃⋊C₉

—

—

C₃×C₄₃

yes

C₃×C₄₃

yes

C₃×C₄₃

yes

C₃×C₄₃

yes

C₄₃⋊C₃

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

C₄₃⋊C₃

yes

characteristic, complemented

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₉²

—

C₄₃

#6897

yes

characteristic, complemented, Sylow

C₃³

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₄₃⋊C₃

yes

characteristic

C₃×C₉

C₃×C₄₃⋊C₃

yes

characteristic

C₃×C₉

C₃×C₄₃⋊C₃

yes

characteristic

C₃×C₉

C₃×C₄₃⋊C₃

yes

characteristic

C₃²

—

129

—

C₃²

—

129

—

C₃²

—

129

—

C₃²

—

129

—

C₃²

C₃²×C₄₃⋊C₃

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

129

—

C₉

—

129

—

C₉

—

129

—

C₉

—

129

—

C₉

—

129

—

C₉

—

129

—

C₉

—

129

—

C₉

—

129

—

C₃

—

387

—

C₃

yes

C₃

yes

C₃

yes

C₃

yes

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃³
Fitting	C₄₃×C₉⋊C₉	C₃
prime radical	C₃²×C₄₃⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#6897
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

subgroup

G/H

center, Frattini

C₃²

C₃²×C₄₃⋊C₃

commutator, socle, cosocle

C₃²×C₄₃

C₃³

Fitting

C₄₃×C₉⋊C₉

C₃

prime radical

C₃²×C₄₃⋊C₃

C₃²

hypercenter

C₉⋊C₉

C₄₃⋊C₃

C₄₃

G ▷ C₃²×C₄₃ ▷ C₄₃

C₁ ◁ C₃² ◁ C₉⋊C₉

N	H ≅ G/N	type
1. #16812500	C₃	semidirect
2. #16812499	C₃	semidirect
3. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
4. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
5. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
6. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
7. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
12. C₉×C₄₃⋊C₉	C₃	semidirect
13. C₄₃×C₉⋊C₉	C₃	semidirect
57. C₉⋊C₉	C₄₃⋊C₃	semidirect
63. C₄₃	#6897	semidirect

H ≅ G/N

type

1. #16812500

C₃

semidirect

2. #16812499

C₃

semidirect

3. (C₄₃⋊C₉)⋊C₉

C₃

semidirect

4. (C₄₃⋊C₉)⋊C₉

C₃

semidirect

5. (C₄₃⋊C₉)⋊C₉

C₃

semidirect

6. (C₄₃⋊C₉)⋊C₉

C₃

semidirect

7. (C₄₃⋊C₉)⋊C₉

C₃

semidirect

12. C₉×C₄₃⋊C₉

C₃

semidirect

13. C₄₃×C₉⋊C₉

C₃

semidirect

57. C₉⋊C₉

C₄₃⋊C₃

semidirect

63. C₄₃

#6897

semidirect

Subgroups — #23782833

Conjugacy classes of subgroups

Complements