Group #11786049 — subgroups

Subgroups — #11786049

Order 1152.

324 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 158 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	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	#10588616	C₂	1	2	yes	maximal
3	#10588229	C₂	1	4	yes	maximal
4	#69763	—	3	1	no	maximal
5	C₂²×C₈×C₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₉	C₂²	1	4	yes	—
8	C₄×C₈×C₉	C₄	1	4	yes	complemented
9	C₉⋊#95	—	2	4	no	—
10	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
11	#4936	—	3	2	no	—
12	#4551	—	3	4	no	—
13	C₂²×C₄×C₉	D₄	1	2	yes	—
14	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₉	—	2	4	no	—
16	C₂×C₈×C₉	—	2	4	no	—
17	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
18	C₄²×C₉	C₂×C₄	1	2	yes	—
19	C₄²×C₉	Q₈	1	2	yes	—
20	C₄⋊Dic₉	—	2	8	no	—
21	#1835	—	9	1	no	Sylow
22	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
23	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
24	C₂×C₄⋊Dic₃	—	3	4	no	—
25	C₃×C₄×C₈	Dic₃	1	4	yes	—
26	C₃⋊#95	—	6	4	no	—
27	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₉	—	2	4	no	—
29	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
30	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₉	#41	1	4	yes	—
33	C₂×Dic₉	—	4	4	no	—
34	C₂×Dic₉	—	4	8	no	—
35	C₈×C₉	—	2	4	no	—
36	C₂×C₄×C₈	D₉	1	1	yes	characteristic
37	#382	—	9	2	no	—
38	#340	—	9	4	no	—
39	C₂²×C₃×C₄	D₁₂	1	2	yes	—
40	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
41	C₂²×Dic₃	—	6	4	no	—
42	C₂×C₃×C₈	—	2	4	no	—
43	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
44	C₃×C₄²	Dic₆	1	2	yes	—
45	C₃×C₄²	C₂×Dic₃	1	2	yes	—
46	C₄⋊Dic₃	—	6	8	no	—
47	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₉	#124	1	2	yes	—
49	C₂²×C₉	#135	1	4	yes	—
50	C₄×C₉	—	2	4	no	—
51	C₄×C₉	#117	1	2	yes	—
52	C₄×C₉	#125	1	2	yes	—
53	Dic₉	—	8	4	no	—
54	C₂²×C₈	C₂×D₉	1	2	yes	—
55	C₂×C₄⋊C₄	—	9	4	no	—
56	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
57	C₄×C₈	Dic₉	1	4	yes	complemented
58	#95	—	18	4	no	—
59	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
60	C₂×C₃×C₄	—	2	4	no	—
61	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
62	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
63	C₂×C₃×C₄	#235	1	4	yes	—
64	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
65	C₂×Dic₃	—	12	4	no	—
66	C₂×Dic₃	—	12	8	no	—
67	C₃×C₈	—	2	4	no	—
68	C₂×C₉	#382	1	1	yes	characteristic
69	C₂×C₉	#427	1	2	yes	—
70	C₂×C₉	#488	1	4	yes	—
71	C₂²×C₄	—	18	4	no	—
72	C₂²×C₄	D₃₆	1	2	yes	—
73	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
74	C₂×C₈	—	2	4	no	—
75	C₂×C₈	C₂×Dic₉	1	4	yes	—
76	C₄⋊C₄	—	18	8	no	—
77	C₄²	Dic₁₈	1	2	yes	—
78	C₄²	C₂×Dic₉	1	2	yes	—
79	C₂²×C₃	#875	1	2	yes	—
80	C₂²×C₃	#904	1	4	yes	—
81	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
82	C₃×C₄	—	2	4	no	—
83	C₃×C₄	#870	1	2	yes	—
84	C₃×C₄	#926	1	2	yes	—
85	Dic₃	—	24	4	no	—
86	C₉	#1835	1	1	yes	characteristic, complemented, Sylow
87	C₂³	C₂×D₃₆	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	36	4	no	—
90	C₂×C₄	—	36	8	no	—
91	C₂×C₄	C₄⋊Dic₉	1	4	yes	—
92	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
93	C₂×C₄	#3697	1	4	yes	—
94	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
95	C₈	—	2	4	no	—
96	C₂×C₃	#4697	1	4	yes	—
97	C₂×C₃	#4936	1	1	yes	characteristic
98	C₂×C₃	#5106	1	2	yes	—
99	C₂²	#63437	1	2	yes	—
100	C₂²	#63467	1	4	yes	—
101	C₂²	C₂×C₄⋊Dic₉	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	72	4	no	—
104	C₄	#63432	1	2	yes	—
105	C₄	#63488	1	2	yes	—
106	C₃	#69763	1	1	yes	characteristic
107	C₂	#10588379	1	4	yes	—
108	C₂	#10588616	1	1	yes	characteristic
109	C₂	#10588787	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₈×C₉

C₂

yes

maximal, characteristic

#10588616

C₂

yes

maximal

#10588229

C₂

yes

maximal

#69763

—

maximal

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

C₂²

yes

—

C₄×C₈×C₉

C₄

yes

complemented

C₉⋊#95

—

C₂×C₃×C₄×C₈

D₃

yes

characteristic

#4936

—

#4551

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂×C₄

yes

—

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

Q₈

yes

—

C₄⋊Dic₉

—

#1835

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

C₃×C₄×C₈

Dic₃

yes

—

C₃⋊#95

—

C₂³×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₈×C₉

—

C₂×C₄×C₈

D₉

yes

characteristic

#382

—

#340

—

C₂²×C₃×C₄

D₁₂

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×Dic₃

yes

—

C₃×C₄²

Dic₆

yes

—

C₃×C₄²

C₂×Dic₃

yes

—

C₄⋊Dic₃

—

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₉

#124

yes

—

C₂²×C₉

#135

yes

—

C₄×C₉

—

C₄×C₉

#117

yes

—

C₄×C₉

#125

yes

—

Dic₉

—

C₂²×C₈

C₂×D₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₄×C₈

Dic₉

yes

complemented

#95

—

C₂³×C₃

C₂×D₁₂

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄⋊Dic₃

yes

—

C₂×C₃×C₄

C₂×Dic₆

yes

characteristic

C₂×C₃×C₄

#235

yes

—

C₂×C₃×C₄

C₂²×Dic₃

yes

characteristic

C₂×Dic₃

—

C₂×Dic₃

—

C₃×C₈

—

C₂×C₉

#382

yes

characteristic

C₂×C₉

#427

yes

—

C₂×C₉

#488

yes

—

C₂²×C₄

—

C₂²×C₄

D₃₆

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Dic₉

yes

—

C₄⋊C₄

—

C₄²

Dic₁₈

yes

—

C₄²

C₂×Dic₉

yes

—

C₂²×C₃

#875

yes

—

C₂²×C₃

#904

yes

—

C₂²×C₃

C₂×C₄⋊Dic₃

yes

characteristic

C₃×C₄

—

C₃×C₄

#870

yes

—

C₃×C₄

#926

yes

—

Dic₃

—

C₉

#1835

yes

characteristic, complemented, Sylow

C₂³

C₂×D₃₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊Dic₉

yes

—

C₂×C₄

C₂×Dic₁₈

yes

characteristic

C₂×C₄

#3697

yes

—

C₂×C₄

C₂²×Dic₉

yes

characteristic

C₈

—

C₂×C₃

#4697

yes

—

C₂×C₃

#4936

yes

characteristic

C₂×C₃

#5106

yes

—

C₂²

#63437

yes

—

100

C₂²

#63467

yes

—

101

C₂²

C₂×C₄⋊Dic₉

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

#63432

yes

—

105

C₄

#63488

yes

—

106

C₃

#69763

yes

characteristic

107

C₂

#10588379

yes

—

108

C₂

#10588616

yes

characteristic

109

C₂

#10588787

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₄×C₈×C₉	C₂
socle, prime radical	C₂³×C₃	C₂×D₁₂
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×C₄×C₈	D₉
hypocenter	C₉	#1835
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₃₆

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₄×C₈×C₉

C₂

socle, prime radical

C₂³×C₃

C₂×D₁₂

cosocle

C₂²×C₄×C₉

C₂³

hypercenter

C₂×C₄×C₈

D₉

hypocenter

C₉

#1835

LCS

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
8. C₄×C₈×C₉	C₄	semidirect
57. C₄×C₈	Dic₉	semidirect
86. C₉	#1835	semidirect

H ≅ G/N

type

8. C₄×C₈×C₉

C₄

semidirect

57. C₄×C₈

Dic₉

semidirect

86. C₉

#1835

semidirect

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

subgroup	index
C₂×C₄×C₈×C₉	2
#10588616	2
#10588229	2
#69763	3

subgroup

index

C₂×C₄×C₈×C₉

#10588616

#10588229

#69763

Subgroups — #11786049

Conjugacy classes of subgroups

Complements

Maximal subgroups