Finite Group Databasebeta

← #28400670

Subgroups — #28400670

Order 14464.

444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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#20299150C211yesmaximal, characteristic, complemented
2C2×#16813584C211yesmaximal, characteristic
3#20298933C211yesmaximal, characteristic, complemented
4#20298877C212yesmaximal, complemented
5#20298802C212yesmaximal, complemented
6#20298751C211yesmaximal, characteristic
7#20298748C211yesmaximal, characteristic
8#20298701C212yesmaximal, complemented
9#20298697C212yesmaximal, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#484×C113C211yesmaximal, characteristic, complemented
12C22×D452C2211yescharacteristic
13C22×C4×D113—21no—
14C2×#14268636C2212yes—
15C2×#14268634C2212yes—
16#16813621C2211yescharacteristic, complemented
17#16813620C2211yescharacteristic, complemented
18#16813612—21no—
19#16813601C2211yescharacteristic
20#16813599—21no—
21Q8×Dic113C2211yescharacteristic, complemented
22#16813587—21no—
23#16813587C2211yescharacteristic, complemented
24#16813584—21no—
25#16813584—21no—
26#16813584C2212yes—
27#16813584C2212yes—
28#16813578—21no—
29C2×#14268624—21no—
30C2×C4×Dic113C2211yescharacteristic
31#16813555C2212yescomplemented
32#16813551C2212yescomplemented
33#16813545C2212yescomplemented
34#16813544C2212yes—
35#16813542C2212yes—
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yescomplemented
38C22⋊Q8×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#107×C113C2212yescomplemented
41#103×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113—21no—
44C2×Dic226—21no—
45C2×Dic226C2311yescharacteristic
46C2×D452—21no—
47C2×D452—24no—
48C2×D452C2312yes—
49C22×Dic113D411yescharacteristic
50C22×Dic113D411yescharacteristic
51C2×C4×D113—22no—
52C2×C4×D113—22no—
53C2×C4×D113—44no—
54#14268636—24no—
55#14268634—24no—
56C2×#11744751C2312yes—
57C4⋊Dic113—21no—
58C4⋊Dic113C2311yescharacteristic
59#14268626—21no—
60#14268626—21no—
61#14268626—21no—
62#14268626—21no—
63#14268626—21no—
64C22⋊Dic113—21no—
65#14268624—22no—
66#14268624—22no—
67C4×Dic113—21no—
68C4×Dic113—21no—
69C4×Dic113D411yescharacteristic
70C4×Dic113D411yescharacteristic
71C4×Dic113C2311yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×Q8×C113C2311yescharacteristic
74C22×C4×C113—21no—
75C22×C4×C113C2311yescharacteristic
76C2×C8×C113C2312yes—
77C4⋊C4×C113—21no—
78C4⋊C4×C113—21no—
79C4⋊C4×C113C2312yes—
80C4⋊C4×C113C2311yescharacteristic
81C22⋊C4×C113—21no—
82C23×C113C2×D411yescharacteristic
83C22×D113—24no—
84C22×D113—22no—
85C22×D113—42no—
86C22×D113—42no—
87Q8×C113—22no—
88C2×C4×C113—22no—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—22no—
92C2×C4×C113—42no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2411yescharacteristic
95C2×Dic113—22no—
96C2×Dic113—22no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113C2×D411yescharacteristic
100C2×Dic113C2×D411yescharacteristic
101C2×Dic113C2×D411yescharacteristic
102C2×Dic113C2×D411yescharacteristic
103D452—24no—
104D452—22no—
105D452#4114yes—
106C4×D113—44no—
107C4×D113—44no—
108Dic226—22no—
109Dic226—42no—
110C8×C113—22no—
111#11744751—22no—
112C22×C113—21no—
113C22×C113—21no—
114C22×C113#13712yes—
115C22×C113C22×D411yescharacteristic
116C2×D113—24no—
117C2×D113—48no—
118C2×D113—42no—
119C2×D113—42no—
120C4×C113—21no—
121C4×C113—41no—
122C4×C113—41no—
123C4×C113—42no—
124C4×C113C2×#4112yes—
125Dic113—21no—
126Dic113—21no—
127Dic113—21no—
128Dic113—41no—
129Dic113—41no—
130Dic113AGL(1,ℤ/8)12yes—
131C2×C113—22no—
132C2×C113#52511yescharacteristic
133C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C113C2×#13711yescharacteristic
135D113—44no—
136#3110—1131nomaximal, Sylow
137C113#311011yescharacteristic, complemented, Sylow
138#533—1131no—
139C2×C4×D4—1131no—
140#484—1131no—
141#484D11311yescharacteristic, complemented
142#474—1132no—
143#461—1132no—
144#450—1131no—
145#450—1131no—
146#440—1132no—
147#440—1132no—
148#432—1131no—
149C22×D4—1131no—
150C23×C4—2261no—
151C2×SD16—1132no—
152C2×SD16—1132no—
153C4⋊Q8—1131no—
154C4⋊Q8—1131no—
155#125—2261no—
156C22⋊Q8—1131no—
157C22⋊Q8—2261no—
158C22⋊Q8C2×D11311yescharacteristic
159C4×Q8—1131no—
160C4×Q8—1131no—
161C4×Q8—2261no—
162C4×D4—1132no—
163C4×D4—1132no—
164C4×D4—2261no—
165C4×D4—2261no—
166#117—2261no—
167C2×C4⋊C4C2×D11311yescharacteristic
168C2×C22⋊C4—2261no—
169C2×C42—1131no—
170#107—1132no—
171#107C2×D11312yescomplemented
172C4⋊C8—1132no—
173#103—1132no—
174#103C2×D11312yescomplemented
175#102—1132no—
176#102—1132no—
177C22⋊C8—1131no—
178C22⋊C8C2×D11311yescharacteristic
179#97—1132no—
180C24—2261no—
181C2×Q8—1131no—
182C2×Q8—2261no—
183C2×Q8C22×D11311yescharacteristic
184C2×D4—1132no—
185C2×D4—2264no—
186C2×D4—2261no—
187C22×C4—21no—
188C22×C4—1131no—
189C22×C4—1131no—
190C22×C4—4524no—
191C22×C4—2262no—
192C22×C4—2262no—
193C22×C4C22×D11311yescharacteristic
194SD16—2264no—
195SD16—2264no—
196C2×C8—1132no—
197C2×C8C22×D11312yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—1131no—
201C4⋊C4—2261no—
202C4⋊C4—2261no—
203C4⋊C4—2261no—
204C4⋊C4—2261no—
205C4⋊C4—2261no—
206C4⋊C4—2261no—
207C4⋊C4C22×D11311yescharacteristic
208C4⋊C4C22×D11312yes—
209C22⋊C4—21no—
210C22⋊C4—2262no—
211C22⋊C4—2262no—
212C22⋊C4—2261no—
213C42—1131no—
214C42—1131no—
215C42—1131no—
216C42—1131no—
217C42—2261no—
218C42—2261no—
219C23—4522no—
220C23—4522no—
221C23—2264no—
222C23—2262no—
223C23D4×D11311yescharacteristic
224Q8—22no—
225Q8—4522no—
226Q8—2262no—
227D4—1134no—
228D4—2264no—
229D4—2262no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—1131no—
236C2×C4—1131no—
237C2×C4—1131no—
238C2×C4—1131no—
239C2×C4—4524no—
240C2×C4—4524no—
241C2×C4—2262no—
242C2×C4—2261no—
243C2×C4—2261no—
244C2×C4—2262no—
245C2×C4D4×D11311yescharacteristic
246C2×C4C23×D11311yescharacteristic
247C8—22no—
248C8—2262no—
249C22—21no—
250C22—21no—
251C22—4528no—
252C22—4522no—
253C22—4522no—
254C22—2264no—
255C22#1681365412yes—
256C22C2×D4×D11311yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—1132no—
262C4—4521no—
263C4—4521no—
264C4—2261no—
265C4—2261no—
266C4—2261no—
267C4#41×D11312yes—
268C2—22no—
269C2—4524no—
270C2#2029910611yescharacteristic
271C2AGL(1,ℤ/8)×D11311yescharacteristic
272C2C2×#1681365411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#484×C113C2
socleC22×C113C22×D4
prime radicalC22×D452C22
hypercenter#484D113
hypocenterC113#3110
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #20299150C2semidirect
3. #20298933C2semidirect
4. #20298877C2semidirect
5. #20298802C2semidirect
8. #20298701C2semidirect
9. #20298697C2semidirect
10. #20298652C2semidirect
11. #484×C113C2semidirect
16. #16813621C22semidirect
17. #16813620C22semidirect
21. Q8×Dic113C22semidirect
23. #16813587C22semidirect
31. #16813555C22semidirect
32. #16813551C22semidirect
33. #16813545C22semidirect
37. #16813532C22semidirect
40. #107×C113C22semidirect
41. #103×C113C22semidirect
137. C113#3110semidirect
141. #484D113semidirect
171. #107C2×D113semidirect
174. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991502
C2×#168135842
#202989332
#202988772
#202988022
#202987512
#202987482
#202987012
#202986972
#202986522
#484×C1132
#3110113