Finite Group Databasebeta

← #28401401

Subgroups — #28401401

Order 14464.

414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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#20299108C211yesmaximal, characteristic
2C2×#16813598C211yesmaximal, characteristic, complemented
3#20298938C212yesmaximal, complemented
4#20298934C211yesmaximal, characteristic, complemented
5#20298914C211yesmaximal, characteristic, complemented
6#20298855C212yesmaximal, complemented
7#20298841C212yesmaximal, complemented
8#20298757C212yesmaximal, complemented
9#20298754C211yesmaximal, characteristic, complemented
10#20298560C211yesmaximal, characteristic, complemented
11#448×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic
13C22×C4×D113C2211yescharacteristic
14C2×#14268637C2212yescomplemented
15C2×#14268630C2212yes—
16#16813604—21no—
17#16813602C2211yescharacteristic
18#16813601C2211yescharacteristic
19#16813598—21no—
20#16813598—21no—
21#16813598C2212yes—
22#16813598C2212yes—
23#16813593C2211yescharacteristic
24#16813590—21no—
25D4×Dic113—21no—
26#16813582—21no—
27#16813580C2211yescharacteristic
28C2×C4⋊Dic113C2211yescharacteristic
29C2×#14268626—21no—
30C2×#14268624—21no—
31#16813556C2212yescomplemented
32#16813553C2212yescomplemented
33#16813547C2212yescomplemented
34#16813546C2212yescomplemented
35#16813543C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813534C2212yes—
38C22×Q8×C113C2211yescharacteristic
39C2×SD16×C113C2212yescomplemented
40#121×C113C2211yescharacteristic
41#103×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113D411yescharacteristic
44#14268646—42no—
45C2×Dic226C2311yescharacteristic
46C2×C22⋊D113—21no—
47C2×C22⋊D113—21no—
48C22×Dic113—21no—
49C22×Dic113—21no—
50C22×Dic113D411yescharacteristic
51C2×C4×D113—42no—
52C2×C4×D113D411yescharacteristic
53C2×C4×D113D411yescharacteristic
54C2×C4×D113C2311yescharacteristic
55C2×C4×D113C2311yescharacteristic
56#14268637—42no—
57#14268630—42no—
58C2×#11744751C2312yes—
59C4⋊Dic113—21no—
60C4⋊Dic113—21no—
61C4⋊Dic113C2312yes—
62C4⋊Dic113C2311yescharacteristic
63#14268626—21no—
64#14268626—22no—
65#14268626—22no—
66C22⋊Dic113—21no—
67C22⋊Dic113—21no—
68#14268624—22no—
69#14268624—22no—
70#14268624—21no—
71#14268624—21no—
72C4×Dic113—21no—
73C2×Q8×C113—21no—
74C2×Q8×C113—42no—
75C2×Q8×C113C2312yes—
76C2×D4×C113—21no—
77C2×D4×C113C2311yescharacteristic
78C22×C4×C113—21no—
79C22×C4×C113C2311yescharacteristic
80SD16×C113—42no—
81C2×C8×C113C2312yes—
82C4⋊C4×C113C2311yescharacteristic
83C22⋊C4×C113—21no—
84C23×C113—21no—
85C23×C113C2×D411yescharacteristic
86C22×D113—22no—
87C22×D113—41no—
88C22×D113—41no—
89C22×D113C2×D411yescharacteristic
90C22×D113C2×D411yescharacteristic
91Q8×C113—22no—
92Q8×C113—22no—
93Q8×C113—42no—
94D4×C113—22no—
95D4×C113—42no—
96C2×C4×C113—22no—
97C2×C4×C113—21no—
98C2×C4×C113—22no—
99C2×C4×C113—42no—
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2411yescharacteristic
102C22⋊D113—42no—
103C22⋊D113—42no—
104C2×Dic113—21no—
105C2×Dic113—22no—
106C2×Dic113—21no—
107C2×Dic113—41no—
108C2×Dic113—42no—
109C2×Dic113—42no—
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112C4×D113—22no—
113C4×D113—22no—
114C4×D113—41no—
115C4×D113—41no—
116Dic226—22no—
117C8×C113—22no—
118#11744751—22no—
119C22×C113—21no—
120C22×C113—21no—
121C22×C113—41no—
122C22×C113—41no—
123C22×C113—41no—
124C22×C113#13712yes—
125C22×C113C22×D411yescharacteristic
126C2×D113—21no—
127C2×D113—21no—
128C2×D113—21no—
129C2×D113—21no—
130C2×D113—21no—
131C2×D113—21no—
132C2×D113—44no—
133C4×C113—21no—
134C4×C113—42no—
135C4×C113—41no—
136C4×C113H(5,𝔽2)12yes—
137Dic113—21no—
138Dic113—21no—
139Dic113—41no—
140Dic113—42no—
141Dic113—41no—
142C2×C113—22no—
143C2×C113—81no—
144C2×C113#53411yescharacteristic
145C2×C113C2×#13711yescharacteristic
146C2×C113#57511yescharacteristic
147D113—41no—
148D113—41no—
149#3196—1131nomaximal, Sylow
150C113#319611yescharacteristic, complemented, Sylow
151#525—1131no—
152C2×C22⋊Q8—1131no—
153#485—1132no—
154#484—1131no—
155#481—1131no—
156#470—1132no—
157#468—1132no—
158#452—1132no—
159#451—1131no—
160#448D11311yescharacteristic, complemented
161#407—1131no—
162C2×#41—1131no—
163C22×Q8C2×D11311yescharacteristic
164C23×C4—1131no—
165C2×Q16—1132no—
166C2×SD16C2×D11312yescomplemented
167C2×M16—1132no—
168#123—2261no—
169C22⋊Q8—1132no—
170C22⋊Q8—1132no—
171C22⋊Q8—1131no—
172C22⋊Q8—1131no—
173C22⋊Q8—2261no—
174C22⋊Q8—2261no—
175#121—1131no—
176#121C2×D11311yescharacteristic
177#120—2261no—
178C4×D4—2261no—
179C4×D4—2261no—
180#117—1131no—
181C2×C4⋊C4—1131no—
182C2×C4⋊C4—2261no—
183C2×C22⋊C4—2261no—
184#107—1132no—
185#106—1132no—
186#103—1132no—
187#103—1132no—
188#103C2×D11312yescomplemented
189#102—1132no—
190C22⋊C8—1131no—
191C22⋊C8—1132no—
192C22⋊C8C2×D11311yescharacteristic
193C24—1131no—
194#41—4522no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8—1131no—
198C2×Q8C22×D11312yes—
199C2×D4—21no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4C22×D11311yescharacteristic
203C22×C4—21no—
204C22×C4—1131no—
205C22×C4—1131no—
206C22×C4—1131no—
207C22×C4—1131no—
208C22×C4—1131no—
209C22×C4—4522no—
210C22×C4—2261no—
211C22×C4—2261no—
212C22×C4C22×D11311yescharacteristic
213Q16—4522no—
214SD16—42no—
215M16—4522no—
216C2×C8—1132no—
217C2×C8C22×D11312yes—
218C4⋊C4—1132no—
219C4⋊C4—1131no—
220C4⋊C4—2262no—
221C4⋊C4—2262no—
222C4⋊C4—2261no—
223C4⋊C4—2261no—
224C4⋊C4—2261no—
225C4⋊C4C22×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2262no—
228C22⋊C4—2262no—
229C22⋊C4—2261no—
230C22⋊C4—2261no—
231C22⋊C4—2261no—
232C22⋊C4—2261no—
233C42—2261no—
234C23—21no—
235C23—1131no—
236C23—1131no—
237C23—4521no—
238C23—4521no—
239C23—2262no—
240C23D4×D11311yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—2262no—
245D4—22no—
246D4—42no—
247D4—4522no—
248D4—4522no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—1131no—
254C2×C4—1131no—
255C2×C4—4521no—
256C2×C4—4521no—
257C2×C4—4522no—
258C2×C4—4522no—
259C2×C4—4521no—
260C2×C4—2261no—
261C2×C4—2262no—
262C2×C4—2261no—
263C2×C4—2262no—
264C2×C4—2262no—
265C2×C4D4×D11311yescharacteristic
266C2×C4C23×D11311yescharacteristic
267C8—22no—
268C8—2262no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—4524no—
275C22—2261no—
276C22—2261no—
277C22—2261no—
278C22—2261no—
279C22—2261no—
280C22—2261no—
281C22#1681365112yes—
282C22C2×D4×D11311yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—4522no—
287C4—4521no—
288C4—4521no—
289C4—2261no—
290C4—2261no—
291C4#1681366712yes—
292C2—22no—
293C2—81no—
294C2—4521no—
295C2—4521no—
296C2#2029915811yescharacteristic
297C2C2×#1681365111yescharacteristic
298C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#448×C113C2
socleC22×C113C22×D4
prime radical#20299108C2
hypercenter#448D113
hypocenterC113#3196
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×#16813598C2semidirect
3. #20298938C2semidirect
4. #20298934C2semidirect
5. #20298914C2semidirect
6. #20298855C2semidirect
7. #20298841C2semidirect
8. #20298757C2semidirect
9. #20298754C2semidirect
10. #20298560C2semidirect
11. #448×C113C2semidirect
14. C2×#14268637C22semidirect
31. #16813556C22semidirect
32. #16813553C22semidirect
33. #16813547C22semidirect
34. #16813546C22semidirect
35. #16813543C22semidirect
39. C2×SD16×C113C22semidirect
41. #103×C113C22semidirect
150. C113#3196semidirect
160. #448D113semidirect
166. C2×SD16C2×D113semidirect
188. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991082
C2×#168135982
#202989382
#202989342
#202989142
#202988552
#202988412
#202987572
#202987542
#202985602
#448×C1132
#3196113