Finite Group Databasebeta

← #28390607

Subgroups — #28390607

Order 14464.

316 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813556C211yesmaximal, characteristic, complemented
2C2×#16813554C211yesmaximal, characteristic, complemented
3#20298458C212yesmaximal
4#20298361C212yesmaximal, complemented
5C22×M16×C113C211yesmaximal, characteristic
6C2×C4⋊Dic113C2212yes—
7C2×C4⋊Dic113C2212yes—
8C2×C22⋊Dic113—22no—
9#16813556—22no—
10#16813554—22no—
11#16813529—22no—
12C23×C4×C113C2211yescharacteristic
13C2×M16×C113—22no—
14C2×M16×C113—22no—
15C2×M16×C113C414yescomplemented
16C22×C8×C113C2211yescharacteristic
17C22×C8×C113C2211yescharacteristic
18C22×Dic113—22no—
19C22×Dic113—22no—
20C4⋊Dic113—22no—
21C4⋊Dic113—22no—
22C4⋊Dic113—22no—
23C4⋊Dic113—22no—
24C22⋊Dic113—44no—
25C24×C113D411yescharacteristic
26C22×C4×C113—21no—
27C22×C4×C113—21no—
28C22×C4×C113—21no—
29C22×C4×C113—21no—
30C22×C4×C113C2×C412yes—
31C22×C4×C113D411yescharacteristic
32C22×C4×C113Q812yes—
33C22×C4×C113C2311yescharacteristic
34M16×C113—28no—
35C2×C8×C113—21no—
36C2×C8×C113—21no—
37C2×C8×C113C2×C412yes—
38C2×C8×C113C2×C412yes—
39C2×C8×C113D412yes—
40C2×C8×C113D412yes—
41C23×C113—21no—
42C23×C113—21no—
43C23×C113—22no—
44C23×C113—22no—
45C23×C113C4⋊C412yes—
46C23×C113C2×D411yescharacteristic
47C2×C4×C113—21no—
48C2×C4×C113—21no—
49C2×C4×C113—22no—
50C2×C4×C113—22no—
51C2×C4×C113—22no—
52C2×C4×C113—22no—
53C2×C4×C113C4⋊C412yes—
54C2×C4×C113C22×C411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×Q811yescharacteristic
58C2×C4×C113#4111yescharacteristic
59C2×C4×C113#4111yescharacteristic
60C2×Dic113—42no—
61C2×Dic113—42no—
62C2×Dic113—42no—
63C2×Dic113—42no—
64C2×Dic113—42no—
65C2×Dic113—42no—
66C8×C113—22no—
67C8×C113C22⋊C414yescomplemented
68C22×C113—22no—
69C22×C113—24no—
70C22×C113—42no—
71C22×C113—41no—
72C22×C113—41no—
73C22×C113C2×C4⋊C411yescharacteristic
74C22×C113#12111yescharacteristic
75C22×C113#12111yescharacteristic
76C22×C113AGL(1,ℤ/8)12yes—
77C22×C113#13712yes—
78C4×C113—22no—
79C4×C113C2×C22⋊C411yescharacteristic
80C4×C113#11711yescharacteristic
81C4×C113C22⋊Q811yescharacteristic
82C4×C113C22⋊Q811yescharacteristic
83Dic113—82no—
84Dic113—82no—
85C2×C113—42no—
86C2×C113#38011yescharacteristic
87C2×C113#42812yes—
88C2×C113#46812yes—
89C2×C113#46911yescharacteristic
90C2×C113#47011yescharacteristic
91#1809—1131nomaximal, Sylow
92C113#180911yescharacteristic, complemented, Sylow
93C22×M16D11311yescharacteristic
94C2×#107—1131no—
95C2×#106—1131no—
96#380—1132no—
97#340—1132no—
98C23×C4C2×D11311yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16Dic11314yescomplemented
102C22×C8C2×D11311yescharacteristic
103C22×C8C2×D11311yescharacteristic
104C2×C4⋊C4—1132no—
105C2×C4⋊C4—1132no—
106C2×C22⋊C4—2262no—
107#107—2262no—
108#106—2262no—
109#95—2262no—
110C24D45211yescharacteristic
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—2262no—
116C22×C4—2262no—
117C22×C4Dic22612yes—
118C22×C4D45211yescharacteristic
119C22×C4C2×Dic11312yes—
120C22×C4C22×D11311yescharacteristic
121M16—28no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8C2×Dic11312yes—
125C2×C8C2×Dic11312yes—
126C2×C8C22⋊D11312yes—
127C2×C8C22⋊D11312yes—
128C4⋊C4—2262no—
129C4⋊C4—2262no—
130C4⋊C4—2262no—
131C4⋊C4—2262no—
132C22⋊C4—4524no—
133C23—21no—
134C23—21no—
135C23—22no—
136C23—22no—
137C23C4⋊Dic11312yes—
138C23C2×D45211yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—4522no—
146C2×C4—4522no—
147C2×C4—4522no—
148C2×C4—4522no—
149C2×C4—4522no—
150C2×C4—4522no—
151C2×C4C4⋊Dic11312yes—
152C2×C4C22×Dic11311yescharacteristic
153C2×C4C2×C22⋊D11311yescharacteristic
154C2×C4C2×C22⋊D11311yescharacteristic
155C2×C4C2×Dic22611yescharacteristic
156C2×C4#1426864711yescharacteristic
157C2×C4#1426864711yescharacteristic
158C8—22no—
159C8C22⋊Dic11314yescomplemented
160C22—24no—
161C22—22no—
162C22—42no—
163C22—41no—
164C22—41no—
165C22C2×C4⋊Dic11311yescharacteristic
166C22#1681359611yescharacteristic
167C22#1681359611yescharacteristic
168C22#1681365012yes—
169C22#1681365512yes—
170C4—22no—
171C4—9042no—
172C4—9042no—
173C4C2×C22⋊Dic11311yescharacteristic
174C4#1681358111yescharacteristic
175C4#1681360111yescharacteristic
176C4#1681360111yescharacteristic
177C2—42no—
178C2#2029845811yescharacteristic
179C2#2029864012yes—
180C2#2029884412yes—
181C2#2029885111yescharacteristic
182C2#2029885611yescharacteristic
subgroupG/H
centerC23C2×D452
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC22×M16×C113C2
socleC23×C113C2×D4
prime radicalC24×C113D4
cosocleC22×C4×C113C23
hypercenterC22×M16D113
hypocenterC113#1809
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16813556C2semidirect
2. C2×#16813554C2semidirect
4. #20298361C2semidirect
15. C2×M16×C113C4semidirect
67. C8×C113C22⋊C4semidirect
92. C113#1809semidirect
101. C2×M16Dic113semidirect
159. C8C22⋊Dic113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135562
C2×#168135542
#202984582
#202983612
C22×M16×C1132
#1809113