Finite Group Databasebeta

← #28405980

Subgroups — #28405980

Order 14464.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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#20299569C211yesmaximal, characteristic, complemented
2#20299541C211yesmaximal, characteristic, complemented
3#20299450C212yesmaximal, complemented
4#20299449C212yesmaximal, complemented
5#121×D113C211yesmaximal, characteristic
6C2×#14268657—21no—
7C2×C22⋊#90673—21no—
8#16813679C2212yescomplemented
9C22⋊#11744753—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yescomplemented
12C2×D4×D113—21no—
13C2×D4×D113C411yescharacteristic, complemented
14C22×C4×D113C2211yescharacteristic
15#16813597C2211yescharacteristic
16#16813596C411yescharacteristic, complemented
17#16813595—21no—
18#16813594—21no—
19#16813593C2211yescharacteristic
20C4⋊C4×D113C411yescharacteristic, complemented
21C22⋊C4×D113—21no—
22#121×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268657—42no—
25C2×#11744753—22no—
26C22⋊#90673—42no—
27C23×D113—21no—
28C23×D113D411yescharacteristic
29C2×D452—21no—
30C2×D452C2×C411yescharacteristic
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34D4×D113—42no—
35D4×D113—44no—
36C22×Dic113D411yescharacteristic
37C2×C4×D113—21no—
38C2×C4×D113—42no—
39C2×C4×D113C2×C411yescharacteristic
40C2×C4×D113D411yescharacteristic
41C2×C4×D113D411yescharacteristic
42C2×C4×D113C2311yescharacteristic
43C4⋊Dic113C2×C411yescharacteristic
44#14268626—21no—
45C22⋊Dic113—21no—
46#14268624—21no—
47#14268624—21no—
48C2×D4×C113—21no—
49C2×D4×C113C2×C411yescharacteristic
50C22×C4×C113C2×C411yescharacteristic
51C4⋊C4×C113C2×C411yescharacteristic
52C22⋊C4×C113—21no—
53C23×C113—21no—
54C23×C113C22⋊C411yescharacteristic
55C22×D113—22no—
56C22×D113—22no—
57C22×D113—21no—
58C22×D113—41no—
59C22×D113—42no—
60C22×D113—42no—
61C22×D113—42no—
62C22×D113C22⋊C411yescharacteristic
63C22×D113C2×D411yescharacteristic
64C2×#90673—42no—
65C2×#90673—42no—
66C2×#90673—42no—
67D4×C113—41no—
68D4×C113—42no—
69C2×C4×C113—21no—
70C2×C4×C113—41no—
71C2×C4×C113C22⋊C411yescharacteristic
72C2×C4×C113C22×C411yescharacteristic
73C22⋊D113—42no—
74C22⋊D113—42no—
75C22⋊D113—42no—
76C2×Dic113—21no—
77C2×Dic113—41no—
78C2×Dic113C22⋊C411yescharacteristic
79C2×Dic113C2×D411yescharacteristic
80D452—41no—
81D452—42no—
82C4×D113—22no—
83C4×D113—22no—
84C4×D113—41no—
85C4×D113—41no—
86C4×D113—42no—
87#11744753—42no—
88C22×C113—21no—
89C22×C113—21no—
90C22×C113—21no—
91C22×C113—41no—
92C22×C113—41no—
93C22×C113—41no—
94C22×C113C2×C22⋊C411yescharacteristic
95C2×D113—21no—
96C2×D113—21no—
97C2×D113—21no—
98C2×D113—21no—
99C2×D113—44no—
100C2×D113—41no—
101C2×D113—41no—
102C2×D113—41no—
103C2×D113—84no—
104C2×D113#9912yes—
105C2×D113AGL(1,ℤ/8)12yes—
106#90673—82no—
107C4×C113—21no—
108C4×C113—21no—
109C4×C113—41no—
110Dic113—21no—
111Dic113—21no—
112Dic113—41no—
113C2×C113—41no—
114C2×C113—81no—
115C2×C113C2×#9911yescharacteristic
116C2×C113#41811yescharacteristic
117C2×C113#42111yescharacteristic
118D113—22no—
119D113—22no—
120D113—81no—
121#1510—1131nomaximal, Sylow
122C113#151011yescharacteristic, complemented, Sylow
123C2×#121—1131no—
124#407—1131no—
125#381—1131no—
126#327—1132no—
127#327—1132no—
128C22×D4—1131no—
129C22×D4—2261no—
130C23×C4—1131no—
131C2×M16—2261no—
132#121—1131no—
133#121—1131no—
134#121—1131no—
135#121—2261no—
136#121—2261no—
137#121#9067311yescharacteristic, complemented
138C2×C4⋊C4—1131no—
139C2×C22⋊C4—2261no—
140C2×C22⋊C4—2261no—
141C22⋊C8—1132no—
142C22⋊C8—2261no—
143#95—1132no—
144#95—2261no—
145C24—1131no—
146C24—2261no—
147C2×D4—21no—
148C2×D4—1131no—
149C2×D4—4524no—
150C2×D4—4522no—
151C2×D4—2261no—
152C2×D4—2261no—
153C2×D4—2261no—
154C2×D4—2261no—
155C2×D4C2×#9067311yescharacteristic
156C22×C4—1131no—
157C22×C4—1131no—
158C22×C4—1131no—
159C22×C4—1131no—
160C22×C4—1131no—
161C22×C4—4522no—
162C22×C4—2261no—
163C22×C4—2262no—
164C22×C4C2×#9067311yescharacteristic
165M16—4522no—
166C2×C8—2262no—
167C4⋊C4—1131no—
168C4⋊C4—2261no—
169C4⋊C4C2×#9067311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—4522no—
172C22⋊C4—2261no—
173C22⋊C4—2261no—
174C22⋊C4—2261no—
175C23—21no—
176C23—1131no—
177C23—1131no—
178C23—4521no—
179C23—4522no—
180C23—4522no—
181C23—4522no—
182C23—2262no—
183C23—2262no—
184C23—2261no—
185C23C22⋊#9067311yescharacteristic
186D4—41no—
187D4—42no—
188D4—4521no—
189D4—4522no—
190D4—4522no—
191D4—4522no—
192D4—4522no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—1131no—
196C2×C4—1131no—
197C2×C4—4521no—
198C2×C4—4521no—
199C2×C4—4522no—
200C2×C4—4522no—
201C2×C4—4522no—
202C2×C4—4522no—
203C2×C4—4521no—
204C2×C4—2262no—
205C2×C4—2262no—
206C2×C4—2261no—
207C2×C4C22⋊#9067311yescharacteristic
208C2×C4C22×#9067311yescharacteristic
209C8—4522no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—1132no—
217C22—1132no—
218C22—9044no—
219C22—4524no—
220C22—4521no—
221C22—4521no—
222C22—4521no—
223C22—2261no—
224C22—2261no—
225C22—2261no—
226C22—2261no—
227C22C2×C22⋊#9067311yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—9042no—
232C4—4521no—
233C4—2261no—
234C4—2261no—
235C2—41no—
236C2—81no—
237C2—9041no—
238C2—2262no—
239C2—2262no—
240C2D113⋊#9911yescharacteristic
241C2#2029959011yescharacteristic
242C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#121×C113C4
socleC22×C113C2×C22⋊C4
prime radical#121×D113C2
cosocleC2×C4×D113C23
hypercenter#121#90673
hypocenterC113#1510
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20299569C2semidirect
2. #20299541C2semidirect
3. #20299450C2semidirect
4. #20299449C2semidirect
8. #16813679C22semidirect
11. (C2×#90673)⋊C4C22semidirect
13. C2×D4×D113C4semidirect
16. #16813596C4semidirect
20. C4⋊C4×D113C4semidirect
22. #121×C113C4semidirect
122. C113#1510semidirect
137. #121#90673semidirect

Maximal subgroups

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

subgroupindex
#202995692
#202995412
#202994502
#202994492
#121×D1132
#1510113