Finite Group Databasebeta

← #28406554

Subgroups — #28406554

Order 14464.

408 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C22×#14268657C211yesmaximal, characteristic, complemented
2C2×#16813679C212yesmaximal, complemented
3C2×#16813679C211yesmaximal, characteristic, complemented
4#20299464C212yesmaximal, complemented
5C2×#16813584C211yesmaximal, characteristic
6C2×#14268657—24no—
7C2×#14268657—22no—
8C22×#11744753C2212yes—
9C22×#11744753C2212yes—
10#16813679—24no—
11#16813679—22no—
12C22×D452C411yescharacteristic
13C22×C4×D113C2211yescharacteristic
14C22×C4×D113C2211yescharacteristic
15#16813584—22no—
16#16813584—22no—
17C2×#14268624C411yescharacteristic
18C2×#14268624C411yescharacteristic
19C2×C4×Dic113C2211yescharacteristic
20C2×C4⋊C4×C113C411yescharacteristic
21#14268657—28no—
22C2×#11744753—22no—
23C2×#11744753—22no—
24C2×#11744753—22no—
25C2×#11744753—22no—
26C2×#11744753—22no—
27C2×#11744753D414yescomplemented
28C23×D113C2×C411yescharacteristic
29C23×D113C2×C411yescharacteristic
30C2×D452—22no—
31C2×D452—22no—
32C2×D452—22no—
33C22×Dic113C2×C411yescharacteristic
34C22×Dic113C2311yescharacteristic
35C2×C4×D113—22no—
36C2×C4×D113—22no—
37C2×C4×D113—21no—
38C2×C4×D113—21no—
39C2×C4×D113—22no—
40C2×C4×D113—22no—
41C2×C4×D113D412yes—
42C2×C4×D113D412yes—
43#14268624—22no—
44#14268624—22no—
45C4×Dic113—21no—
46C4×Dic113—21no—
47C22×C4×C113C2×C411yescharacteristic
48C22×C4×C113C2×C411yescharacteristic
49C22×C4×C113C2×C411yescharacteristic
50C4⋊C4×C113—22no—
51C23×C113C22×C411yescharacteristic
52C22×D113—21no—
53C22×D113—22no—
54C22×D113—22no—
55C22×D113—21no—
56C22×D113—21no—
57C22×D113—21no—
58C22×D113—22no—
59C22×D113—22no—
60C22×D113C22⋊C412yes—
61C22×D113M1612yescomplemented
62C2×C4×C113—21no—
63C2×C4×C113—22no—
64C2×C4×C113—21no—
65C2×C4×C113—21no—
66C2×C4×C113—22no—
67C2×C4×C113C22⋊C412yes—
68C2×C4×C113M1612yescomplemented
69C2×Dic113—21no—
70C2×Dic113—22no—
71C2×Dic113C2×D412yes—
72C2×Dic113C2×D411yescharacteristic
73C2×Dic113C2×D411yescharacteristic
74C2×Dic113#4112yes—
75D452—28no—
76C4×D113—22no—
77C4×D113—24no—
78C4×D113—22no—
79C4×D113—41no—
80C4×D113—42no—
81C4×D113—41no—
82#11744753—24no—
83#11744753—42no—
84C22×C113C2×C22⋊C411yescharacteristic
85C22×C113C4×D412yes—
86C22×C113C2×M1611yescharacteristic
87C22×C113C2×M1611yescharacteristic
88C22×C113#13112yes—
89C2×D113—22no—
90C2×D113—22no—
91C2×D113—22no—
92C2×D113—22no—
93C2×D113—24no—
94C2×D113—41no—
95C2×D113—41no—
96C2×D113—42no—
97C2×D113—42no—
98C2×D113—42no—
99C4×C113—22no—
100C4×C113—22no—
101C4×C113—41no—
102Dic113—41no—
103Dic113#12011yescharacteristic
104Dic113#12112yes—
105Dic113#12311yescharacteristic
106C2×C113#38611yescharacteristic
107C2×C113#40711yescharacteristic
108C2×C113#40811yescharacteristic
109C2×C113#43512yes—
110C2×C113#43612yes—
111D113—42no—
112D113—42no—
113#1870—1131nomaximal, Sylow
114C113#187011yescharacteristic, complemented, Sylow
115C22×M16—1131no—
116C2×C4×D4—1131no—
117C2×C22⋊C8—1132no—
118C2×C22⋊C8—1131no—
119#336—1132no—
120C22×D4—1131no—
121C23×C4—1131no—
122C23×C4—1131no—
123C2×M16—2264no—
124C2×M16—2262no—
125C22×C8—1132no—
126C22×C8—1132no—
127C4×D4—2262no—
128C4×D4—2262no—
129C2×C4⋊C4#9067311yescharacteristic
130C2×C22⋊C4—1131no—
131C2×C22⋊C4—1131no—
132C2×C42—1131no—
133C22⋊C8—2264no—
134C22⋊C8—2262no—
135C24—1131no—
136C24—1131no—
137C2×D4—2262no—
138C2×D4—2262no—
139C2×D4—2262no—
140C22×C4—1131no—
141C22×C4—1132no—
142C22×C4—1132no—
143C22×C4—1131no—
144C22×C4—2262no—
145C22×C4—2261no—
146C22×C4—2261no—
147C22×C4—2262no—
148C22×C4—2262no—
149C22×C4—2262no—
150C22×C4C2×#9067311yescharacteristic
151C22×C4C2×#9067311yescharacteristic
152C22×C4C2×#9067311yescharacteristic
153M16—2268no—
154C2×C8—1134no—
155C2×C8—2262no—
156C2×C8—2262no—
157C2×C8—2262no—
158C2×C8—2262no—
159C2×C8—2262no—
160C4⋊C4—22no—
161C22⋊C4—2262no—
162C22⋊C4—2262no—
163C42—2261no—
164C42—2261no—
165C23—1132no—
166C23—1132no—
167C23—2261no—
168C23—2262no—
169C23—2262no—
170C23—2261no—
171C23—2261no—
172C23—2261no—
173C23—2262no—
174C23—2262no—
175C23C22×#9067311yescharacteristic
176D4—2268no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—1131no—
183C2×C4—1131no—
184C2×C4—1132no—
185C2×C4—1132no—
186C2×C4—4522no—
187C2×C4—4521no—
188C2×C4—4521no—
189C2×C4—2262no—
190C2×C4—2264no—
191C2×C4—2262no—
192C2×C4—2261no—
193C2×C4—2262no—
194C2×C4C22⋊#9067312yes—
195C2×C4#1426865712yescomplemented
196C8—4522no—
197C8—2264no—
198C22—4521no—
199C22—4521no—
200C22—4522no—
201C22—4522no—
202C22—4522no—
203C22—2262no—
204C22—2262no—
205C22—2262no—
206C22—2262no—
207C22—2264no—
208C22C2×C22⋊#9067311yescharacteristic
209C22D4×#9067312yes—
210C22D113⋊M1611yescharacteristic
211C22C2×#1426865711yescharacteristic
212C22#1681371012yes—
213C4—22no—
214C4—22no—
215C4—41no—
216C4—1132no—
217C4—1131no—
218C4—1131no—
219C4—4521no—
220C2—4522no—
221C2—4522no—
222C2#2029954611yescharacteristic
223C2#2029956911yescharacteristic
224C2#2029957311yescharacteristic
225C2#2029962812yes—
226C2#2029963212yes—
subgroupG/H
center, FrattiniC23C22×#90673
commutator, socleC23×C113C22×C4
FittingC2×C4⋊C4×C113C4
prime radicalC22×D452C4
cosocleC22×Dic113C23
hypercenterC2×C4⋊C4#90673
hypocenterC113#1870
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14268657C2semidirect
2. C2×#16813679C2semidirect
3. C2×#16813679C2semidirect
4. #20299464C2semidirect
27. C2×#11744753D4semidirect
61. C22×D113M16semidirect
68. C2×C4×C113M16semidirect
114. C113#1870semidirect
195. C2×C4#14268657semidirect

Maximal subgroups

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

subgroupindex
C22×#142686572
C2×#168136792
#202994642
C2×#168135842
#1870113