Finite Group Databasebeta

← #28400662

Subgroups — #28400662

Order 14464.

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

normal subgroups only

This group has 488 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#20299143C211yesmaximal, characteristic, complemented
2C2×#16813584C211yesmaximal, characteristic, complemented
3#20298916C211yesmaximal, characteristic, complemented
4#20298887C212yesmaximal, complemented
5#20298792C212yesmaximal, complemented
6#20298734C211yesmaximal, characteristic, complemented
7#20298731C211yesmaximal, characteristic, complemented
8#20298709C212yesmaximal, complemented
9#20298707C212yesmaximal, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#481×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—21no—
13C22×D452C2211yescharacteristic
14C22×C4×D113—21no—
15C2×D904C2212yes—
16C2×#14268632C2212yes—
17#16813621C2211yescharacteristic, complemented
18#16813618C2211yescharacteristic, complemented
19#16813608—21no—
20#16813596C2211yescharacteristic
21#16813594—21no—
22D4×Dic113C2211yescharacteristic, complemented
23#16813584—21no—
24#16813584—21no—
25#16813584C2212yes—
26#16813584C2212yes—
27#16813584C2211yescharacteristic, complemented
28#16813582—21no—
29C2×#14268624—21no—
30C2×C4×Dic113C2211yescharacteristic
31#16813553C2212yescomplemented
32#16813551C2212yescomplemented
33#16813544C2212yes—
34#16813542C2212yes—
35#16813542C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yescomplemented
38#121×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#106×C113C2212yescomplemented
41#102×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113—21no—
44#14268646—44no—
45C2×Dic226—21no—
46C2×D452—21no—
47C2×D452—24no—
48C2×D452C2311yescharacteristic
49C2×D452C2312yes—
50C2×C22⋊D113—21no—
51C2×C22⋊D113—21no—
52C2×C22⋊D113—21no—
53C22×Dic113—21no—
54C22×Dic113D411yescharacteristic
55C22×Dic113D411yescharacteristic
56C2×C4×D113—21no—
57C2×C4×D113—22no—
58C2×C4×D113—22no—
59C2×C4×D113—44no—
60D904—24no—
61#14268632—24no—
62C2×#11744751C2312yes—
63C4⋊Dic113C2311yescharacteristic
64#14268626—21no—
65C22⋊Dic113—21no—
66#14268624—21no—
67#14268624—22no—
68#14268624—22no—
69#14268624—21no—
70C4×Dic113D411yescharacteristic
71C4×Dic113D411yescharacteristic
72C4×Dic113C2311yescharacteristic
73C4×Dic113C2311yescharacteristic
74C2×D4×C113—21no—
75C2×D4×C113C2311yescharacteristic
76C22×C4×C113—21no—
77C22×C4×C113C2311yescharacteristic
78C2×C8×C113C2312yes—
79C4⋊C4×C113—21no—
80C4⋊C4×C113C2312yes—
81C4⋊C4×C113C2311yescharacteristic
82C22⋊C4×C113—21no—
83C23×C113—21no—
84C23×C113C2×D411yescharacteristic
85C22×D113—24no—
86C22×D113—22no—
87C22×D113—21no—
88C22×D113—42no—
89C22×D113—42no—
90D4×C113—22no—
91D4×C113—42no—
92C2×C4×C113—22no—
93C2×C4×C113—21no—
94C2×C4×C113—22no—
95C2×C4×C113—42no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—42no—
99C22⋊D113—42no—
100C22⋊D113—42no—
101C2×Dic113—22no—
102C2×Dic113—22no—
103C2×Dic113—21no—
104C2×Dic113—42no—
105C2×Dic113C2×D411yescharacteristic
106C2×Dic113C2×D411yescharacteristic
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109D452—24no—
110D452—22no—
111D452—22no—
112D452#4114yescomplemented
113C4×D113—44no—
114C4×D113—42no—
115C4×D113—44no—
116Dic226—42no—
117C8×C113—22no—
118#11744751—22no—
119C22×C113—21no—
120C22×C113—21no—
121C22×C113—41no—
122C22×C113—41no—
123C22×C113—41no—
124C22×C113AGL(1,ℤ/8)12yes—
125C22×C113C22×D411yescharacteristic
126C2×D113—24no—
127C2×D113—48no—
128C2×D113—42no—
129C2×D113—42no—
130C2×D113—41no—
131C2×D113—41no—
132C2×D113—41no—
133C4×C113—21no—
134C4×C113—41no—
135C4×C113—42no—
136C4×C113C2×#4112yes—
137Dic113—21no—
138Dic113—21no—
139Dic113—21no—
140Dic113—41no—
141Dic113AGL(1,ℤ/8)12yes—
142C2×C113—22no—
143C2×C113—81no—
144C2×C113#52511yescharacteristic
145C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
147D113—44no—
148D113—81no—
149#3109—1131nomaximal, Sylow
150C113#310911yescharacteristic, complemented, Sylow
151#532—1131no—
152C2×C4×D4—1131no—
153#481—1131no—
154#481D11311yescharacteristic, complemented
155#476—1132no—
156#459—1132no—
157#447—1131no—
158#447—1131no—
159#442—1132no—
160#442—1132no—
161#432—1131no—
162C2×#41—2261no—
163C22×D4—1131no—
164C23×C4—2261no—
165C2×D8—1132no—
166C2×D8—1132no—
167C4⋊Q8—1131no—
168#127—1131no—
169#124—2261no—
170#121—1131no—
171#121—2261no—
172#121C2×D11311yescharacteristic
173C4×D4—1131no—
174C4×D4—1132no—
175C4×D4—1132no—
176C4×D4—1131no—
177C4×D4—2261no—
178C4×D4—2261no—
179C4×D4—2261no—
180C2×C4⋊C4C2×D11311yescharacteristic
181C2×C22⋊C4—2261no—
182C2×C42—1131no—
183#106—1132no—
184#106C2×D11312yescomplemented
185C4⋊C8—1132no—
186#102—1132no—
187#102—1132no—
188#102—1132no—
189#102C2×D11312yescomplemented
190C22⋊C8—1131no—
191C22⋊C8C2×D11311yescharacteristic
192#97—1132no—
193C24—2261no—
194#41—4524no—
195C2×Q8—2261no—
196C2×D4—21no—
197C2×D4—1132no—
198C2×D4—1131no—
199C2×D4—2264no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4—2261no—
203C2×D4—2261no—
204C2×D4C22×D11311yescharacteristic
205C22×C4—21no—
206C22×C4—1131no—
207C22×C4—1131no—
208C22×C4—4524no—
209C22×C4—2262no—
210C22×C4—2262no—
211C22×C4—2261no—
212C22×C4—2261no—
213C22×C4C22×D11311yescharacteristic
214D8—2264no—
215D8—2264no—
216C2×C8—1132no—
217C2×C8C22×D11312yes—
218C4⋊C4—21no—
219C4⋊C4—1131no—
220C4⋊C4—2261no—
221C4⋊C4C22×D11311yescharacteristic
222C4⋊C4C22×D11312yes—
223C22⋊C4—21no—
224C22⋊C4—2262no—
225C22⋊C4—2262no—
226C22⋊C4—2261no—
227C22⋊C4—2261no—
228C22⋊C4—2261no—
229C42—1131no—
230C42—1131no—
231C42—1131no—
232C42—1131no—
233C23—21no—
234C23—4522no—
235C23—4522no—
236C23—2264no—
237C23—2261no—
238C23—2262no—
239C23D4×D11311yescharacteristic
240Q8—4522no—
241D4—22no—
242D4—42no—
243D4—1134no—
244D4—4522no—
245D4—4522no—
246D4—4522no—
247D4—2264no—
248D4—2262no—
249D4—2262no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—1131no—
255C2×C4—1131no—
256C2×C4—1131no—
257C2×C4—1131no—
258C2×C4—4524no—
259C2×C4—4524no—
260C2×C4—4522no—
261C2×C4—4522no—
262C2×C4—2262no—
263C2×C4—2261no—
264C2×C4—2262no—
265C2×C4D4×D11311yescharacteristic
266C2×C4C23×D11311yescharacteristic
267C8—22no—
268C8—2262no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—4528no—
275C22—4521no—
276C22—4521no—
277C22—4521no—
278C22—4522no—
279C22—4522no—
280C22—2264no—
281C22#1681364912yes—
282C22C2×D4×D11311yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—1132no—
287C4—4521no—
288C4—2261no—
289C4—2261no—
290C4—2261no—
291C4#41×D11312yes—
292C2—22no—
293C2—81no—
294C2—9041no—
295C2—4524no—
296C2#2029910611yescharacteristic
297C2AGL(1,ℤ/8)×D11311yescharacteristic
298C2C2×#1681364911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#481×C113C2
socleC22×C113C22×D4
hypercenter#481D113
hypocenterC113#3109
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #20299143C2semidirect
2. C2×#16813584C2semidirect
3. #20298916C2semidirect
4. #20298887C2semidirect
5. #20298792C2semidirect
6. #20298734C2semidirect
7. #20298731C2semidirect
8. #20298709C2semidirect
9. #20298707C2semidirect
10. #20298652C2semidirect
11. #481×C113C2semidirect
17. #16813621C22semidirect
18. #16813618C22semidirect
22. D4×Dic113C22semidirect
27. #16813584C22semidirect
31. #16813553C22semidirect
32. #16813551C22semidirect
35. #16813542C22semidirect
37. #16813532C22semidirect
40. #106×C113C22semidirect
41. #102×C113C22semidirect
112. D452#41semidirect
150. C113#3109semidirect
154. #481D113semidirect
184. #106C2×D113semidirect
189. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991432
C2×#168135842
#202989162
#202988872
#202987922
#202987342
#202987312
#202987092
#202987072
#202986522
#481×C1132
#3109113