Group #11800173 — subgroups

Subgroups — #11800173

Order 1152.

198 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 74 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	C₉×#494	C₂	1	1	yes	maximal, characteristic
2	#10588363	C₂	1	1	yes	maximal, characteristic
3	#10588241	C₂	1	4	yes	maximal
4	#10588138	C₂	1	1	yes	maximal, characteristic
5	#71311	—	3	1	no	maximal
6	C₂×C₉×Q₁₆	—	2	1	no	—
7	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
8	C₉×C₄⋊Q₈	—	2	1	no	—
9	#63432	—	2	1	no	—
10	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
11	#63378	C₂²	1	2	yes	—
12	#63377	—	2	1	no	—
13	C₂×C₉⋊C₁₆	C₂²	1	2	yes	—
14	C₃×#494	D₃	1	1	yes	characteristic
15	#4683	—	3	1	no	—
16	#4564	—	3	4	no	—
17	#4461	—	3	1	no	—
18	C₂×Q₈×C₉	—	2	2	no	—
19	C₉×Q₁₆	—	2	4	no	—
20	C₉×Q₁₆	—	4	2	no	—
21	C₂×C₈×C₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
23	C₉×C₄⋊C₄	—	4	2	no	—
24	C₄²×C₉	D₄	1	1	yes	characteristic
25	C₄⋊Dic₉	—	2	2	no	—
26	Dic₉⋊C₄	—	4	2	no	—
27	C₉⋊C₁₆	—	2	2	no	—
28	#2245	—	9	1	no	Sylow
29	C₂×C₃×Q₁₆	—	2	1	no	—
30	C₂×C₃×Q₁₆	C₂×D₃	1	2	yes	—
31	C₃×C₄⋊Q₈	—	2	1	no	—
32	#870	—	6	1	no	—
33	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
34	#818	—	3	2	no	—
35	#817	—	6	1	no	—
36	C₂×C₃⋊C₁₆	—	3	2	no	—
37	Q₈×C₉	—	4	2	no	—
38	Q₈×C₉	—	4	2	no	—
39	C₂×C₄×C₉	—	4	2	no	—
40	C₂×C₄×C₉	D₈	1	2	yes	—
41	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₉	—	4	2	no	—
43	C₈×C₉	SD₁₆	1	2	yes	—
44	C₈×C₉	#41	1	2	yes	—
45	#499	—	9	1	no	—
46	#494	D₉	1	1	yes	characteristic
47	#358	—	9	4	no	—
48	#346	—	9	1	no	—
49	C₂×C₃×Q₈	—	2	2	no	—
50	C₃×Q₁₆	—	2	4	no	—
51	C₃×Q₁₆	—	4	2	no	—
52	C₂×C₃×C₈	#67	1	1	yes	characteristic
53	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
54	C₃×C₄⋊C₄	—	4	2	no	—
55	C₃×C₄²	#67	1	1	yes	characteristic
56	C₄⋊Dic₃	—	6	2	no	—
57	Dic₃⋊C₄	—	12	2	no	—
58	C₃⋊C₁₆	—	6	2	no	—
59	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
60	C₄×C₉	—	2	2	no	—
61	C₄×C₉	—	8	2	no	—
62	C₄×C₉	#124	1	1	yes	characteristic
63	C₄×C₉	C₂×SD₁₆	1	1	yes	characteristic
64	Dic₉	—	8	2	no	—
65	C₂×Q₁₆	—	2	1	no	—
66	C₂×Q₁₆	C₂×D₉	1	2	yes	—
67	C₄⋊Q₈	—	2	1	no	—
68	#125	—	18	1	no	—
69	C₂×C₁₆	—	9	2	no	—
70	#107	—	9	2	no	—
71	#106	—	18	1	no	—
72	C₄×C₈	C₂×D₉	1	1	yes	characteristic
73	C₃×Q₈	—	4	2	no	—
74	C₃×Q₈	—	4	2	no	—
75	C₂×C₃×C₄	—	4	2	no	—
76	C₂×C₃×C₄	#213	1	2	yes	—
77	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
78	C₂×Dic₃	—	12	2	no	—
79	C₃×C₈	#214	1	2	yes	—
80	C₃×C₈	#237	1	2	yes	—
81	C₂×C₉	#486	1	1	yes	characteristic
82	C₂×C₉	#510	1	2	yes	—
83	C₂×Q₈	—	2	2	no	—
84	Q₁₆	—	2	4	no	—
85	Q₁₆	—	4	2	no	—
86	C₂×C₈	#611	1	1	yes	characteristic
87	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
88	C₄⋊C₄	—	4	2	no	—
89	C₄⋊C₄	—	18	2	no	—
90	C₄⋊C₄	—	36	2	no	—
91	C₄²	#611	1	1	yes	characteristic
92	C₁₆	—	18	2	no	—
93	C₂²×C₃	C₂×#213	1	1	yes	characteristic
94	C₃×C₄	—	2	2	no	—
95	C₃×C₄	—	8	2	no	—
96	C₃×C₄	C₂×#214	1	1	yes	characteristic
97	C₃×C₄	#936	1	1	yes	characteristic
98	Dic₃	—	24	2	no	—
99	C₉	#2245	1	1	yes	characteristic, complemented, Sylow
100	Q₈	—	4	2	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	—	36	2	no	—
104	C₂×C₄	#3673	1	2	yes	—
105	C₂×C₄	C₂×#611	1	1	yes	characteristic
106	C₈	#3672	1	2	yes	—
107	C₈	#3699	1	2	yes	—
108	C₂×C₃	#5070	1	1	yes	characteristic
109	C₂×C₃	#5179	1	2	yes	—
110	C₂²	C₂×#3673	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	8	2	no	—
113	C₄	—	72	2	no	—
114	C₄	C₂×#3672	1	1	yes	characteristic
115	C₄	#63498	1	1	yes	characteristic
116	C₃	#71311	1	1	yes	characteristic
117	C₂	#10588750	1	1	yes	characteristic
118	C₂	#10588859	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#494

C₂

yes

maximal, characteristic

#10588363

C₂

yes

maximal, characteristic

#10588241

C₂

yes

maximal

#10588138

C₂

yes

maximal, characteristic

#71311

—

maximal

C₂×C₉×Q₁₆

—

C₂×C₉×Q₁₆

C₂²

yes

—

C₉×C₄⋊Q₈

—

#63432

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63378

C₂²

yes

—

#63377

—

C₂×C₉⋊C₁₆

C₂²

yes

—

C₃×#494

D₃

yes

—

—

—

C₂×Q₈×C₉

—

C₉×Q₁₆

—

C₉×Q₁₆

—

C₂×C₈×C₉

D₄

yes

characteristic

C₂×C₈×C₉

C₂³

yes

characteristic

C₉×C₄⋊C₄

—

C₄²×C₉

D₄

yes

characteristic

C₄⋊Dic₉

—

Dic₉⋊C₄

—

C₉⋊C₁₆

—

#2245

—

Sylow

C₂×C₃×Q₁₆

—

C₂×C₃×Q₁₆

C₂×D₃

yes

—

C₃×C₄⋊Q₈

—

#870

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#818

—

#817

—

C₂×C₃⋊C₁₆

—

Q₈×C₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

D₈

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×Dic₉

—

C₈×C₉

SD₁₆

yes

—

C₈×C₉

#41

yes

—

#499

—

#494

D₉

yes

characteristic

#358

—

#346

—

C₂×C₃×Q₈

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₂×C₃×C₈

#67

yes

characteristic

C₂×C₃×C₈

C₂²×D₃

yes

characteristic

C₃×C₄⋊C₄

—

C₃×C₄²

#67

yes

characteristic

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₃⋊C₁₆

—

C₂²×C₉

C₂×D₈

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#124

yes

characteristic

C₄×C₉

C₂×SD₁₆

yes

characteristic

Dic₉

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₉

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₁₆

—

#107

—

#106

—

C₄×C₈

C₂×D₉

yes

characteristic

C₃×Q₈

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

#213

yes

—

C₂×C₃×C₄

C₂×#67

yes

characteristic

C₂×Dic₃

—

C₃×C₈

#214

yes

—

C₃×C₈

#237

yes

—

C₂×C₉

#486

yes

characteristic

C₂×C₉

#510

yes

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

#611

yes

characteristic

C₂×C₈

C₂²×D₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#611

yes

characteristic

C₁₆

—

C₂²×C₃

C₂×#213

yes

characteristic

C₃×C₄

—

C₃×C₄

—

C₃×C₄

yes

C₃×C₄

yes

Dic₃

—

C₉

#2245

yes

characteristic, complemented, Sylow

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

#3673

yes

—

105

C₂×C₄

C₂×#611

yes

characteristic

106

C₈

#3672

yes

—

107

C₈

#3699

yes

—

108

C₂×C₃

#5070

yes

characteristic

109

C₂×C₃

#5179

yes

—

110

C₂²

C₂×#3673

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

C₂×#3672

yes

characteristic

115

C₄

#63498

yes

characteristic

116

C₃

#71311

yes

characteristic

117

C₂

#10588750

yes

characteristic

118

C₂

#10588859

yes

—

	subgroup	G/H
center	C₂²	C₂×#3673
commutator, cosocle	C₂×C₈×C₉	C₂³
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₉×#494	C₂
socle, prime radical	C₂²×C₃	C₂×#213
hypercenter	#494	D₉
hypocenter	C₉	#2245
LCS	G ▷ C₂×C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂²

C₂×#3673

commutator, cosocle

C₂×C₈×C₉

C₂³

Frattini

C₂×C₃×C₈

C₂²×D₃

C₂

C₂²×C₃

D₉

C₉

G ▷ C₂×C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
99. C₉	#2245	semidirect

H ≅ G/N

type

99. C₉

#2245

semidirect

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

subgroup	index
C₉×#494	2
#10588363	2
#10588241	2
#10588138	2
#71311	3

subgroup

index

Subgroups — #11800173

Conjugacy classes of subgroups

Complements

Maximal subgroups