Group #11786330 — subgroups

Subgroups — #11786330

Order 1152.

318 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 182 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×C₉×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×#63372	C₂	1	4	yes	maximal
3	#10588604	C₂	1	2	yes	maximal
4	#69842	—	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	C₉×#97	C₄	1	4	yes	—
9	#63372	—	2	8	no	—
10	C₄⋊(C₉⋊C₈)	—	2	4	no	—
11	C₂×C₃×#97	D₃	1	1	yes	characteristic
12	C₂×#819	—	3	4	no	—
13	#4924	—	3	2	no	—
14	C₂²×C₄×C₉	Q₈	1	2	yes	—
15	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
16	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₉	D₄	1	4	yes	—
18	C₂×C₈×C₉	Q₈	1	4	yes	—
19	C₄²×C₉	C₂×C₄	1	2	yes	—
20	C₄²×C₉	D₄	1	2	yes	—
21	#3667	—	2	8	no	—
22	C₂×C₉⋊C₈	—	2	4	no	—
23	#1849	—	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×#97	Dic₃	1	4	yes	—
28	#819	—	6	8	no	—
29	C₄⋊(C₃⋊C₈)	—	6	4	no	—
30	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₉	—	4	2	no	—
32	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
33	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
37	C₈×C₉	C₄⋊C₄	1	8	yes	—
38	C₉⋊C₈	—	4	4	no	—
39	C₂×#108	—	9	4	no	—
40	#423	—	9	2	no	—
41	C₂×#97	D₉	1	1	yes	characteristic
42	C₂²×C₃×C₄	Dic₆	1	2	yes	—
43	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
44	C₂×C₃×C₈	Dic₆	1	4	yes	—
45	C₂×C₃×C₈	D₁₂	1	4	yes	—
46	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
47	C₃×C₄²	D₁₂	1	2	yes	—
48	C₃×C₄²	C₂×Dic₃	1	2	yes	—
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	C₄⋊Q₈	1	2	yes	—
54	C₄×C₉	—	2	4	no	—
55	C₄×C₉	C₂×C₄⋊C₄	1	2	yes	—
56	C₄×C₉	#127	1	1	yes	characteristic
57	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
58	C₂×M₁₆	—	9	4	no	—
59	C₂²×C₈	C₂×D₉	1	2	yes	—
60	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
61	#108	—	18	8	no	—
62	C₄⋊C₈	—	18	4	no	—
63	#97	Dic₉	1	4	yes	—
64	C₂³×C₃	C₂×Dic₆	1	1	yes	characteristic
65	C₂×C₃×C₄	—	4	2	no	—
66	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
67	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
68	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
69	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
70	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
71	C₃×C₈	C₄⋊Dic₃	1	8	yes	—
72	C₃⋊C₈	—	12	4	no	—
73	C₂×C₉	—	2	2	no	—
74	C₂×C₉	#384	1	1	yes	characteristic
75	C₂×C₉	#430	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	—	18	4	no	—
80	C₂×C₈	Dic₁₈	1	4	yes	—
81	C₂×C₈	D₃₆	1	4	yes	—
82	C₂×C₈	C₂×Dic₉	1	4	yes	—
83	C₄²	D₃₆	1	2	yes	—
84	C₄²	C₂×Dic₉	1	2	yes	—
85	C₂²×C₃	—	2	2	no	—
86	C₂²×C₃	#869	1	2	yes	—
87	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
88	C₃×C₄	—	2	4	no	—
89	C₃×C₄	#869	1	1	yes	characteristic
90	C₃×C₄	#874	1	1	yes	characteristic
91	C₃×C₄	C₂×C₄⋊Dic₃	1	2	yes	—
92	C₉	#1849	1	1	yes	characteristic, complemented, Sylow
93	C₂³	C₂×Dic₁₈	1	1	yes	characteristic
94	C₂×C₄	—	4	2	no	—
95	C₂×C₄	C₄⋊Dic₉	1	4	yes	—
96	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
97	C₂×C₄	C₂×D₃₆	1	2	yes	—
98	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
99	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
100	C₈	—	36	4	no	—
101	C₈	C₄⋊Dic₉	1	8	yes	—
102	C₂×C₃	—	2	2	no	—
103	C₂×C₃	#4935	1	1	yes	characteristic
104	C₂×C₃	#5125	1	2	yes	—
105	C₂²	—	2	2	no	—
106	C₂²	#63431	1	2	yes	—
107	C₂²	C₂×C₄⋊Dic₉	1	1	yes	characteristic
108	C₄	—	2	4	no	—
109	C₄	#63431	1	1	yes	characteristic
110	C₄	#63436	1	1	yes	characteristic
111	C₄	C₂×C₄⋊Dic₉	1	2	yes	—
112	C₃	#69842	1	1	yes	characteristic
113	C₂	—	2	2	no	—
114	C₂	#10588615	1	1	yes	characteristic
115	C₂	#10588800	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#97

C₂

yes

maximal, characteristic

C₂×#63372

C₂

yes

maximal

#10588604

C₂

yes

maximal

#69842

—

maximal

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×#3667

C₂²

yes

—

C₉×#97

C₄

yes

—

#63372

—

C₄⋊(C₉⋊C₈)

—

C₂×C₃×#97

D₃

yes

characteristic

C₂×#819

—

#4924

—

C₂²×C₄×C₉

Q₈

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂×C₈×C₉

C₂×C₄

yes

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

Q₈

yes

—

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

D₄

yes

—

#3667

—

C₂×C₉⋊C₈

—

#1849

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×#208

—

C₃×#97

Dic₃

yes

—

#819

—

C₄⋊(C₃⋊C₈)

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

—

C₈×C₉

C₄⋊C₄

yes

—

C₉⋊C₈

—

C₂×#108

—

#423

—

C₂×#97

D₉

yes

characteristic

C₂²×C₃×C₄

Dic₆

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×C₈

Dic₆

yes

—

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃×C₈

C₂×Dic₃

yes

—

C₃×C₄²

D₁₂

yes

—

C₃×C₄²

C₂×Dic₃

yes

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₉

C₄⋊Q₈

yes

—

C₄×C₉

—

C₄×C₉

C₂×C₄⋊C₄

yes

—

C₄×C₉

#127

yes

characteristic

C₄×C₉

C₄⋊Q₈

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂×D₉

yes

—

C₂×C₄²

C₂×D₉

yes

characteristic

#108

—

C₄⋊C₈

—

#97

Dic₉

yes

—

C₂³×C₃

C₂×Dic₆

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄⋊Dic₃

yes

—

C₂×C₃×C₄

C₂×Dic₆

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

C₂×C₃×C₄

C₂²×Dic₃

yes

characteristic

C₃×C₈

C₄⋊Dic₃

yes

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#384

yes

characteristic

C₂×C₉

#430

yes

—

C₂²×C₄

Dic₁₈

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₁₈

yes

—

C₂×C₈

D₃₆

yes

—

C₂×C₈

C₂×Dic₉

yes

—

C₄²

D₃₆

yes

—

C₄²

C₂×Dic₉

yes

—

C₂²×C₃

—

C₂²×C₃

#869

yes

—

C₂²×C₃

C₂×C₄⋊Dic₃

yes

characteristic

C₃×C₄

—

C₃×C₄

yes

C₃×C₄

yes

C₃×C₄

C₂×C₄⋊Dic₃

yes

—

C₉

#1849

yes

characteristic, complemented, Sylow

C₂³

C₂×Dic₁₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄⋊Dic₉

yes

—

C₂×C₄

C₂×Dic₁₈

yes

—

C₂×C₄

C₂×D₃₆

yes

—

C₂×C₄

C₂×D₃₆

yes

characteristic

C₂×C₄

C₂²×Dic₉

yes

characteristic

100

C₈

—

101

C₈

C₄⋊Dic₉

yes

—

102

C₂×C₃

—

103

C₂×C₃

#4935

yes

characteristic

104

C₂×C₃

#5125

yes

—

105

C₂²

—

106

C₂²

#63431

yes

—

107

C₂²

C₂×C₄⋊Dic₉

yes

characteristic

108

C₄

—

109

C₄

#63431

yes

characteristic

110

C₄

#63436

yes

characteristic

111

C₄

C₂×C₄⋊Dic₉

yes

—

112

C₃

#69842

yes

characteristic

113

C₂

—

114

C₂

#10588615

yes

characteristic

115

C₂

#10588800

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₃₆
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#97	C₂
socle	C₂²×C₃	C₂×C₄⋊Dic₃
prime radical	C₂³×C₃	C₂×Dic₆
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#97	D₉
hypocenter	C₉	#1849
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

C₂×D₃₆

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#97

C₂

socle

C₂²×C₃

C₂×C₄⋊Dic₃

prime radical

C₂³×C₃

C₂×Dic₆

cosocle

C₂²×C₄×C₉

C₂³

hypercenter

C₂×#97

D₉

hypocenter

C₉

#1849

LCS

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
92. C₉	#1849	semidirect

H ≅ G/N

type

92. C₉

#1849

semidirect

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

subgroup	index
C₂×C₉×#97	2
C₂×#63372	2
#10588604	2
#69842	3

subgroup

index

C₂×C₉×#97

C₂×#63372

#10588604

#69842

Subgroups — #11786330

Conjugacy classes of subgroups

Complements

Maximal subgroups