Finite Group Databasebeta

← #28401407

Subgroups — #28401407

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#20299111C211yesmaximal, characteristic
2C2×#16813598C211yesmaximal, characteristic, complemented
3#20298937C212yesmaximal, complemented
4#20298931C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298853C212yesmaximal, complemented
7#20298847C212yesmaximal, complemented
8#20298759C212yesmaximal, complemented
9#20298737C211yesmaximal, characteristic, complemented
10#20298560C211yesmaximal, characteristic, complemented
11#451×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C22×C4×D113C2211yescharacteristic
14C2×#14268634C2212yescomplemented
15C2×#14268630C2212yes—
16#16813607—21no—
17#16813598—21no—
18#16813598—21no—
19#16813598C2212yes—
20#16813598C2212yes—
21#16813598C2211yescharacteristic
22#16813597C2211yescharacteristic
23#16813596C2211yescharacteristic
24#16813592—21no—
25#16813584—21no—
26#16813582—21no—
27#16813580C2211yescharacteristic
28C2×C4⋊Dic113C2211yescharacteristic
29C2×#14268626—21no—
30C2×#14268624—21no—
31#16813555C2212yescomplemented
32#16813554C2212yescomplemented
33#16813546C2212yescomplemented
34#16813546C2212yescomplemented
35#16813544C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813534C2212yes—
38C22×Q8×C113C2211yescharacteristic
39C2×Q16×C113C2212yescomplemented
40C22⋊Q8×C113C2211yescharacteristic
41#103×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113D411yescharacteristic
44#14268648—42no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452C2311yescharacteristic
48C2×C22⋊D113—21no—
49C22×Dic113—21no—
50C22×Dic113D411yescharacteristic
51C2×C4×D113—21no—
52C2×C4×D113—42no—
53C2×C4×D113D411yescharacteristic
54C2×C4×D113D411yescharacteristic
55C2×C4×D113C2311yescharacteristic
56C2×C4×D113C2311yescharacteristic
57#14268634—42no—
58#14268630—42no—
59C2×#11744751C2312yes—
60C4⋊Dic113—21no—
61C4⋊Dic113C2312yes—
62C4⋊Dic113C2311yescharacteristic
63#14268626—22no—
64#14268626—22no—
65#14268626—21no—
66#14268624—22no—
67#14268624—22no—
68#14268624—21no—
69#14268624—21no—
70#14268624—21no—
71#14268624—21no—
72C4×Dic113—21no—
73C2×Q8×C113—21no—
74C2×Q8×C113—42no—
75C2×Q8×C113C2312yes—
76C2×Q8×C113C2311yescharacteristic
77C22×C4×C113—21no—
78C22×C4×C113C2311yescharacteristic
79Q16×C113—42no—
80C2×C8×C113C2312yes—
81C4⋊C4×C113—21no—
82C4⋊C4×C113C2311yescharacteristic
83C22⋊C4×C113—21no—
84C23×C113C2×D411yescharacteristic
85C22×D113—22no—
86C22×D113—21no—
87C22×D113—41no—
88C22×D113—41no—
89C22×D113C2×D411yescharacteristic
90C22×D113C2×D411yescharacteristic
91Q8×C113—22no—
92Q8×C113—22no—
93Q8×C113—22no—
94Q8×C113—42no—
95C2×C4×C113—22no—
96C2×C4×C113—21no—
97C2×C4×C113—21no—
98C2×C4×C113—22no—
99C2×C4×C113—42no—
100C2×C4×C113C2×D411yescharacteristic
101C2×C4×C113C2411yescharacteristic
102C22⋊D113—42no—
103C2×Dic113—21no—
104C2×Dic113—22no—
105C2×Dic113—41no—
106C2×Dic113—42no—
107C2×Dic113C2×D411yescharacteristic
108C2×Dic113C2×D411yescharacteristic
109D452—22no—
110D452—42no—
111D452—42no—
112C4×D113—22no—
113C4×D113—22no—
114C4×D113—41no—
115C4×D113—41no—
116C4×D113—42no—
117C8×C113—22no—
118#11744751—22no—
119C22×C113—21no—
120C22×C113—21no—
121C22×C113#13712yes—
122C22×C113C22×D411yescharacteristic
123C2×D113—21no—
124C2×D113—21no—
125C2×D113—21no—
126C2×D113—21no—
127C2×D113—21no—
128C2×D113—21no—
129C2×D113—44no—
130C2×D113—41no—
131C2×D113—41no—
132C2×D113—41no—
133C4×C113—21no—
134C4×C113—41no—
135C4×C113—42no—
136C4×C113—41no—
137C4×C113H(5,𝔽2)12yes—
138Dic113—21no—
139Dic113—21no—
140Dic113—41no—
141Dic113—42no—
142C2×C113—22no—
143C2×C113#53411yescharacteristic
144C2×C113C2×#13711yescharacteristic
145C2×C113#57511yescharacteristic
146D113—41no—
147D113—41no—
148D113—81no—
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#451D11311yescharacteristic, complemented
160#448—1131no—
161#407—1131no—
162C2×#41—1131no—
163C22×Q8C2×D11311yescharacteristic
164C23×C4—1131no—
165C2×Q16C2×D11312yescomplemented
166C2×SD16—1132no—
167C2×M16—1132no—
168#123—2261no—
169C22⋊Q8—1132no—
170C22⋊Q8—1132no—
171C22⋊Q8—1131no—
172C22⋊Q8—2261no—
173C22⋊Q8—2261no—
174C22⋊Q8C2×D11311yescharacteristic
175#121—1131no—
176#121—1131no—
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×Q8C22×D11311yescharacteristic
198C2×Q8C22×D11312yes—
199C2×D4—1131no—
200C2×D4—2261no—
201C2×D4—2261no—
202C2×D4—2261no—
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—42no—
214SD16—4522no—
215M16—4522no—
216C2×C8—1132no—
217C2×C8C22×D11312yes—
218C4⋊C4—21no—
219C4⋊C4—1132no—
220C4⋊C4—1131no—
221C4⋊C4—2262no—
222C4⋊C4—2262no—
223C4⋊C4—2261no—
224C4⋊C4—2261no—
225C4⋊C4C22×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2261no—
228C22⋊C4—2262no—
229C22⋊C4—2262no—
230C22⋊C4—2261no—
231C22⋊C4—2261no—
232C22⋊C4—2261no—
233C42—2261no—
234C23—1131no—
235C23—1131no—
236C23—4521no—
237C23—4521no—
238C23—2261no—
239C23—2262no—
240C23D4×D11311yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—22no—
244Q8—42no—
245D4—4522no—
246D4—4522no—
247D4—4522no—
248D4—2262no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—1131no—
255C2×C4—1131no—
256C2×C4—4521no—
257C2×C4—4521no—
258C2×C4—4522no—
259C2×C4—4522no—
260C2×C4—4521no—
261C2×C4—2261no—
262C2×C4—2262no—
263C2×C4—2262no—
264C2×C4—2262no—
265C2×C4D4×D11311yescharacteristic
266C2×C4C23×D11311yescharacteristic
267C8—22no—
268C8—2262no—
269C22—21no—
270C22—21no—
271C22—4524no—
272C22—4521no—
273C22—4521no—
274C22—4521no—
275C22—2261no—
276C22—2261no—
277C22—2261no—
278C22—2261no—
279C22—2261no—
280C22—2261no—
281C22#1681365412yes—
282C22C2×D4×D11311yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—41no—
287C4—4521no—
288C4—4522no—
289C4—2261no—
290C4—2261no—
291C4#1681366712yes—
292C2—22no—
293C2—9041no—
294C2—4521no—
295C2—4521no—
296C2#2029915811yescharacteristic
297C2C2×#1681365411yescharacteristic
298C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radical#20299111C2
hypercenter#451D113
hypocenterC113#3196
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#16813598C2semidirect
3. #20298937C2semidirect
4. #20298931C2semidirect
5. #20298917C2semidirect
6. #20298853C2semidirect
7. #20298847C2semidirect
8. #20298759C2semidirect
9. #20298737C2semidirect
10. #20298560C2semidirect
11. #451×C113C2semidirect
14. C2×#14268634C22semidirect
31. #16813555C22semidirect
32. #16813554C22semidirect
33. #16813546C22semidirect
34. #16813546C22semidirect
35. #16813544C22semidirect
39. C2×Q16×C113C22semidirect
41. #103×C113C22semidirect
150. C113#3196semidirect
159. #451D113semidirect
165. C2×Q16C2×D113semidirect
188. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991112
C2×#168135982
#202989372
#202989312
#202989172
#202988532
#202988472
#202987592
#202987372
#202985602
#451×C1132
#3196113