Finite Group Databasebeta

← #28389090

Subgroups — #28389090

Order 14464.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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
1#20298562C211yesmaximal, characteristic, complemented
2C4×C22⋊Dic113C211yesmaximal, characteristic, complemented
3#20298332C214yesmaximal, complemented
4C2×#121×C113C211yesmaximal, characteristic
5C2×#14268631—21no—
6C2×C22⋊Dic113—21no—
7C2×C4×Dic113—21no—
8C22⋊#11744751—21no—
9C22⋊#11744751C2212yescomplemented
10#16813529C2212yescomplemented
11C22×D4×C113—21no—
12C22×D4×C113C411yescharacteristic, complemented
13C23×C4×C113C2211yescharacteristic
14#121×C113—21no—
15#121×C113—21no—
16#121×C113C412yescomplemented
17#121×C113C2212yes—
18C2×C4⋊C4×C113C411yescharacteristic, complemented
19C2×C22⋊C4×C113—21no—
20C22×Dic113—22no—
21#14268631—42no—
22C2×#11744751—22no—
23C22⋊Dic113—24no—
24C4×Dic113—42no—
25C24×C113—21no—
26C24×C113D411yescharacteristic
27C2×D4×C113—22no—
28C2×D4×C113—22no—
29C2×D4×C113—21no—
30C2×D4×C113—42no—
31C2×D4×C113—44no—
32C2×D4×C113C2×C412yes—
33C22×C4×C113—21no—
34C22×C4×C113—42no—
35C22×C4×C113C2×C411yescharacteristic
36C22×C4×C113C2×C411yescharacteristic
37C22×C4×C113D411yescharacteristic
38C22×C4×C113D411yescharacteristic
39C22×C4×C113D411yescharacteristic
40C22×C4×C113C2311yescharacteristic
41C4⋊C4×C113—21no—
42C4⋊C4×C113C2×C412yes—
43C22⋊C4×C113—22no—
44C22⋊C4×C113—22no—
45C23×C113—22no—
46C23×C113—22no—
47C23×C113—22no—
48C23×C113—41no—
49C23×C113—42no—
50C23×C113—42no—
51C23×C113—42no—
52C23×C113C22⋊C411yescharacteristic
53C23×C113C22⋊C411yescharacteristic
54C23×C113C2×D411yescharacteristic
55D4×C113—42no—
56D4×C113—44no—
57D4×C113—44no—
58D4×C113—42no—
59C2×C4×C113—22no—
60C2×C4×C113—22no—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—41no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113—42no—
67C2×C4×C113C22⋊C411yescharacteristic
68C2×C4×C113C22⋊C411yescharacteristic
69C2×C4×C113C22×C411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C2×Dic113—24no—
72C2×Dic113—42no—
73C2×Dic113—42no—
74#11744751—42no—
75C22×C113—21no—
76C22×C113—21no—
77C22×C113—21no—
78C22×C113—21no—
79C22×C113—21no—
80C22×C113—21no—
81C22×C113—21no—
82C22×C113—44no—
83C22×C113—42no—
84C22×C113—42no—
85C22×C113—42no—
86C22×C113—84no—
87C22×C113#10412yes—
88C22×C113C2×C22⋊C411yescharacteristic
89C22×C113AGL(1,ℤ/8)12yes—
90C4×C113—21no—
91C4×C113—21no—
92C4×C113—21no—
93C4×C113—42no—
94C4×C113#9912yes—
95Dic113—44no—
96C2×C113—22no—
97C2×C113—22no—
98C2×C113—41no—
99C2×C113—82no—
100C2×C113C2×#9911yescharacteristic
101C2×C113#41811yescharacteristic
102C2×C113C2×#10411yescharacteristic
103#1507—1131nomaximal, Sylow
104C113#150711yescharacteristic, complemented, Sylow
105C2×#121D11311yescharacteristic
106#407—1131no—
107C4×C22⋊C4—1131no—
108#327—1134no—
109C22×D4—21no—
110C22×D4Dic11311yescharacteristic, complemented
111C23×C4C2×D11311yescharacteristic
112C2×M16—2261no—
113#121—21no—
114#121—21no—
115#121Dic11312yescomplemented
116#121C2×D11312yes—
117C2×C4⋊C4Dic11311yescharacteristic, complemented
118C2×C22⋊C4—21no—
119C2×C22⋊C4—2261no—
120C2×C42—2261no—
121C22⋊C8—1132no—
122C22⋊C8—2261no—
123#95—1132no—
124C24—21no—
125C24C22⋊D11311yescharacteristic
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—21no—
129C2×D4—42no—
130C2×D4—44no—
131C2×D4C2×Dic11312yes—
132C22×C4—21no—
133C22×C4—42no—
134C22×C4—2262no—
135C22×C4C2×Dic11311yescharacteristic
136C22×C4C2×Dic11311yescharacteristic
137C22×C4C22⋊D11311yescharacteristic
138C22×C4C22⋊D11311yescharacteristic
139C22×C4C22⋊D11311yescharacteristic
140C22×C4C22×D11311yescharacteristic
141M16—4522no—
142C2×C8—2262no—
143C4⋊C4—21no—
144C4⋊C4C2×Dic11312yes—
145C22⋊C4—22no—
146C22⋊C4—22no—
147C22⋊C4—2264no—
148C42—4522no—
149C23—22no—
150C23—22no—
151C23—22no—
152C23—41no—
153C23—42no—
154C23—42no—
155C23—42no—
156C23C22⋊Dic11311yescharacteristic
157C23C22⋊Dic11311yescharacteristic
158C23C2×C22⋊D11311yescharacteristic
159D4—42no—
160D4—44no—
161D4—44no—
162D4—42no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—42no—
171C2×C4—4522no—
172C2×C4—4522no—
173C2×C4—2264no—
174C2×C4C22⋊Dic11311yescharacteristic
175C2×C4C22⋊Dic11311yescharacteristic
176C2×C4C22×Dic11311yescharacteristic
177C2×C4C2×C22⋊D11311yescharacteristic
178C8—4522no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—84no—
191C22#1681354912yes—
192C22C2×C22⋊Dic11311yescharacteristic
193C22#1681364812yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—4524no—
199C4#1681353712yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—82no—
204C2C2×#1681353711yescharacteristic
205C2#2029860311yescharacteristic
206C2C2×#1681354911yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting, prime radicalC2×#121×C113C2
socleC22×C113C2×C22⋊C4
cosocleC22×C4×C113C23
hypercenterC2×#121D113
hypocenterC113#1507
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #20298562C2semidirect
2. C4×C22⋊Dic113C2semidirect
3. #20298332C2semidirect
9. C22⋊#11744751C22semidirect
10. #16813529C22semidirect
12. C22×D4×C113C4semidirect
16. #121×C113C4semidirect
18. C2×C4⋊C4×C113C4semidirect
104. C113#1507semidirect
110. C22×D4Dic113semidirect
115. #121Dic113semidirect
117. C2×C4⋊C4Dic113semidirect

Maximal subgroups

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

subgroupindex
#202985622
C4×C22⋊Dic1132
#202983322
C2×#121×C1132
#1507113