Group #11786091 — subgroups

Subgroups — #11786091

Order 1152.

282 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 146 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	#10588604	C₂	1	2	yes	maximal
3	#10588227	C₂	1	4	yes	maximal
4	#69791	—	3	1	no	maximal
5	C₂²×C₈×C₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
7	C₂×#3667	C₂²	1	4	yes	—
8	C₄×C₈×C₉	C₄	1	2	yes	—
9	C₄×C₈×C₉	C₄	1	2	yes	—
10	C₄⋊(C₉⋊C₈)	—	2	4	no	—
11	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
12	#4924	—	3	2	no	—
13	#4552	—	3	4	no	—
14	C₂²×C₄×C₉	Q₈	1	2	yes	—
15	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
16	C₂×C₈×C₉	—	2	4	no	—
17	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
18	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₉	D₄	1	2	yes	—
21	#3667	—	2	8	no	—
22	C₂×C₉⋊C₈	—	2	4	no	—
23	#1837	—	9	1	no	Sylow
24	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
25	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
26	C₂×#208	—	3	4	no	—
27	C₃×C₄×C₈	Dic₃	1	2	yes	—
28	C₃×C₄×C₈	Dic₃	1	2	yes	—
29	C₄⋊(C₃⋊C₈)	—	6	4	no	—
30	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₉	—	2	4	no	—
32	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₉	#41	1	4	yes	—
37	C₈×C₉	—	2	4	no	—
38	C₉⋊C₈	—	4	4	no	—
39	#423	—	9	2	no	—
40	C₂×C₄×C₈	D₉	1	1	yes	characteristic
41	#341	—	9	4	no	—
42	C₂²×C₃×C₄	Dic₆	1	2	yes	—
43	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
44	C₂×C₃×C₈	—	2	4	no	—
45	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
46	C₃×C₄²	D₁₂	1	2	yes	—
47	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
48	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
49	#208	—	6	8	no	—
50	C₂×C₃⋊C₈	—	6	4	no	—
51	C₂²×C₉	—	2	2	no	—
52	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₉	#125	1	2	yes	—
54	C₄×C₉	—	2	2	no	—
55	C₄×C₉	#108	1	4	yes	—
56	C₄×C₉	#117	1	2	yes	—
57	C₄×C₉	#124	1	2	yes	—
58	C₂×M₁₆	—	9	4	no	—
59	C₂²×C₈	C₂×D₉	1	2	yes	—
60	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
61	C₄⋊C₈	—	18	4	no	—
62	C₄×C₈	Dic₉	1	2	yes	—
63	C₄×C₈	Dic₉	1	2	yes	—
64	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
65	C₂×C₃×C₄	—	2	4	no	—
66	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
67	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
68	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
69	C₂×C₃×C₄	#235	1	4	yes	—
70	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
71	C₃×C₈	—	2	4	no	—
72	C₃⋊C₈	—	12	4	no	—
73	C₂×C₉	—	2	2	no	—
74	C₂×C₉	#382	1	1	yes	characteristic
75	C₂×C₉	C₂×#108	1	2	yes	—
76	C₂²×C₄	Dic₁₈	1	2	yes	—
77	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
78	M₁₆	—	18	8	no	—
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	—	18	4	no	—
81	C₂×C₈	C₂×Dic₉	1	4	yes	—
82	C₄²	D₃₆	1	2	yes	—
83	C₄²	C₂×Dic₉	1	1	yes	characteristic
84	C₄²	C₂×Dic₉	1	1	yes	characteristic
85	C₂²×C₃	—	2	2	no	—
86	C₂²×C₃	#870	1	2	yes	—
87	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
88	C₃×C₄	—	2	2	no	—
89	C₃×C₄	#819	1	4	yes	—
90	C₃×C₄	#875	1	2	yes	—
91	C₃×C₄	#926	1	2	yes	—
92	C₉	#1837	1	1	yes	characteristic, complemented, Sylow
93	C₂³	C₂×Dic₁₈	1	1	yes	characteristic
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	C₄⋊Dic₉	1	2	yes	—
96	C₂×C₄	C₄⋊Dic₉	1	2	yes	—
97	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
98	C₂×C₄	#3697	1	4	yes	—
99	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
100	C₈	—	2	4	no	—
101	C₈	—	36	4	no	—
102	C₂×C₃	—	2	2	no	—
103	C₂×C₃	#4936	1	1	yes	characteristic
104	C₂×C₃	C₂×#819	1	2	yes	—
105	C₂²	—	2	2	no	—
106	C₂²	#63432	1	2	yes	—
107	C₂²	C₂×C₄⋊Dic₉	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	#63372	1	4	yes	—
110	C₄	#63437	1	2	yes	—
111	C₄	#63488	1	2	yes	—
112	C₃	#69791	1	1	yes	characteristic
113	C₂	—	2	2	no	—
114	C₂	#10588616	1	1	yes	characteristic
115	C₂	C₂×#63372	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₈×C₉

C₂

yes

maximal, characteristic

#10588604

C₂

yes

maximal

#10588227

C₂

yes

maximal

#69791

—

maximal

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×#3667

C₂²

yes

—

C₄×C₈×C₉

C₄

yes

—

C₄×C₈×C₉

C₄

yes

—

C₄⋊(C₉⋊C₈)

—

C₂×C₃×C₄×C₈

D₃

yes

characteristic

#4924

—

#4552

—

C₂²×C₄×C₉

Q₈

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂×C₄

yes

—

C₄²×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

D₄

yes

—

#3667

—

C₂×C₉⋊C₈

—

#1837

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×#208

—

C₃×C₄×C₈

Dic₃

yes

—

C₃×C₄×C₈

Dic₃

yes

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₈×C₉

—

C₉⋊C₈

—

#423

—

C₂×C₄×C₈

D₉

yes

characteristic

#341

—

C₂²×C₃×C₄

Dic₆

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×Dic₃

yes

—

C₃×C₄²

D₁₂

yes

—

C₃×C₄²

C₂×Dic₃

yes

characteristic

C₃×C₄²

C₂×Dic₃

yes

characteristic

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₉

#125

yes

—

C₄×C₉

—

C₄×C₉

#108

yes

—

C₄×C₉

#117

yes

—

C₄×C₉

#124

yes

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₉

yes

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

Dic₉

yes

—

C₄×C₈

Dic₉

yes

—

C₂³×C₃

C₂×Dic₆

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄⋊Dic₃

yes

—

C₂×C₃×C₄

C₄⋊Dic₃

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

C₂×C₃×C₄

#235

yes

—

C₂×C₃×C₄

C₂²×Dic₃

yes

characteristic

C₃×C₈

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#382

yes

characteristic

C₂×C₉

C₂×#108

yes

—

C₂²×C₄

Dic₁₈

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₉

yes

—

C₄²

D₃₆

yes

—

C₄²

C₂×Dic₉

yes

characteristic

C₄²

C₂×Dic₉

yes

characteristic

C₂²×C₃

—

C₂²×C₃

#870

yes

—

C₂²×C₃

C₂×C₄⋊Dic₃

yes

characteristic

C₃×C₄

—

C₃×C₄

#819

yes

—

C₃×C₄

#875

yes

—

C₃×C₄

#926

yes

—

C₉

#1837

yes

characteristic, complemented, Sylow

C₂³

C₂×Dic₁₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄⋊Dic₉

yes

—

C₂×C₄

C₄⋊Dic₉

yes

—

C₂×C₄

C₂×D₃₆

yes

characteristic

C₂×C₄

#3697

yes

—

C₂×C₄

C₂²×Dic₉

yes

characteristic

100

C₈

—

101

C₈

—

102

C₂×C₃

—

103

C₂×C₃

#4936

yes

characteristic

104

C₂×C₃

C₂×#819

yes

—

105

C₂²

—

106

C₂²

#63432

yes

—

107

C₂²

C₂×C₄⋊Dic₉

yes

characteristic

108

C₄

—

109

C₄

#63372

yes

—

110

C₄

#63437

yes

—

111

C₄

#63488

yes

—

112

C₃

#69791

yes

characteristic

113

C₂

—

114

C₂

#10588616

yes

characteristic

115

C₂

C₂×#63372

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₃₆
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₄×C₈×C₉	C₂
socle	C₂²×C₃	C₂×C₄⋊Dic₃
prime radical	C₂³×C₃	C₂×Dic₆
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×C₄×C₈	D₉
hypocenter	C₉	#1837
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

C₂×D₃₆

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₄×C₈×C₉

C₂

socle

C₂²×C₃

C₂×C₄⋊Dic₃

prime radical

C₂³×C₃

C₂×Dic₆

cosocle

C₂²×C₄×C₉

C₂³

hypercenter

C₂×C₄×C₈

D₉

hypocenter

C₉

#1837

LCS

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
92. C₉	#1837	semidirect

H ≅ G/N

type

92. C₉

#1837

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
#10588604	2
#10588227	2
#69791	3

subgroup

index

C₂×C₄×C₈×C₉

#10588604

#10588227

#69791

Subgroups — #11786091

Conjugacy classes of subgroups

Complements

Maximal subgroups