Finite Group Databasebeta

← #13078242

Subgroups — #13078242

Order 1408.

496 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66995C211yesmaximal, characteristic, complemented
3#10623322C211yesmaximal, characteristic
4C22×#4318C211yesmaximal, characteristic, complemented
5#10622838C211yesmaximal, characteristic, complemented
6#10622665C212yesmaximal, complemented
7#10622664C212yesmaximal, complemented
8#10622662C212yesmaximal, complemented
9#10622661C212yesmaximal, complemented
10#10622579C211yesmaximal, characteristic, complemented
11#10622577C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C11×C22⋊Q8—21no—
16C11×C22⋊Q8—21no—
17C11×C22⋊Q8C2212yes—
18C11×C22⋊Q8C2212yes—
19C2×C11×C4⋊C4—21no—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4—21no—
22#67006—21no—
23C2×#4326C2212yescomplemented
24#66995—24no—
25C2×#4325C2212yescomplemented
26#66983C2211yescharacteristic
27#66983C2211yescharacteristic
28#66982—21no—
29C4×C22⋊D11—21no—
30C4×C22⋊D11—21no—
31#66979C2211yescharacteristic
32#66977C2211yescharacteristic
33#66977C2211yescharacteristic
34C2×#4318—24no—
35C2×#4318C2211yescharacteristic
36C2×#4318C2212yes—
37C2×#4318C2211yescharacteristic
38C22×C11⋊C8C2212yes—
39#66899C2212yescomplemented
40#66899C2212yescomplemented
41#66874C2212yescomplemented
42#66873C2212yescomplemented
43#66872C2212yescomplemented
44#66871C2212yescomplemented
45C24×C11D411yescharacteristic
46C2×Q8×C11—21no—
47C2×Q8×C11—22no—
48C2×Q8×C11—22no—
49C2×Q8×C11C2312yes—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11D411yescharacteristic
55C22×C4×C11D411yescharacteristic
56C22×C4×C11D411yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C2×C22⋊D11—21no—
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63#4339—22no—
64#4339—22no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×Dic22C2311yescharacteristic
68C11×C4⋊C4—22no—
69C11×C4⋊C4—22no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2312yes—
72C11×C22⋊C4—22no—
73C11×C22⋊C4—22no—
74C22⋊Dic11—21no—
75C22⋊Dic11—21no—
76C22⋊Dic11—21no—
77#4326—24no—
78#4325—24no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81C4⋊Dic11C2311yescharacteristic
82C4⋊Dic11C2311yescharacteristic
83Dic11⋊C4—21no—
84Dic11⋊C4—21no—
85C4×Dic11—21no—
86#4318—24no—
87#4318—22no—
88#4318D414yescomplemented
89C2×C11⋊C8—24no—
90C2×C11⋊C8C2312yes—
91C2×C11⋊C8C2312yes—
92#3056—111nomaximal, Sylow
93C23×C11—22no—
94C23×C11—22no—
95C23×C11—41no—
96C23×C11C2×D411yescharacteristic
97C23×C11C2×D411yescharacteristic
98C23×C11C2×D411yescharacteristic
99C22×D11—21no—
100Q8×C11—22no—
101Q8×C11—22no—
102Q8×C11—42no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11C2×D412yes—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11#4112yes—
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—42no—
121C22⋊D11—42no—
122C22⋊D11—42no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126D44—21no—
127D44—21no—
128C4×D11—42no—
129Dic22—21no—
130Dic22—21no—
131C11⋊C8—22no—
132C11⋊C8C2×D414yes—
133C2×#137—111no—
134C22×M16—111no—
135#525—111no—
136C2×C22⋊Q8D1111yescharacteristic, complemented
137#470—112no—
138#468—112no—
139#467—112no—
140#465—112no—
141#428—111no—
142#419—111no—
143#417—111no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—44no—
152C22×C11#12112yes—
153C22×C11#13712yescomplemented
154C22×C11C22×D411yescharacteristic
155C2×D11—41no—
156C2×D11—41no—
157C2×D11—41no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—42no—
161C4×C11—42no—
162C4×C11#12112yes—
163C4×C11C22×D411yescharacteristic
164C4×C11C2×#4111yescharacteristic
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168C2×#41—111no—
169C22×Q8C2×D1111yescharacteristic
170C23×C4C2×D1111yescharacteristic
171#137—224no—
172C2×Q16—112no—
173C2×SD16—112no—
174C2×M16—111no—
175C2×M16—111no—
176C2×M16—112no—
177C2×M16—224no—
178C22×C8—112no—
179#123—221no—
180C22⋊Q8—21no—
181C22⋊Q8—21no—
182C22⋊Q8—111no—
183C22⋊Q8—111no—
184C22⋊Q8C2×D1112yes—
185C22⋊Q8C2×D1112yes—
186#121—111no—
187#121—111no—
188#120—221no—
189C4×D4—221no—
190C4×D4—221no—
191#117—111no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×D1111yescharacteristic
194C2×C22⋊C4—21no—
195#107—112no—
196#106—112no—
197#103—112no—
198#103—112no—
199#103—112no—
200#102—112no—
201C2×C11—22no—
202C2×C11—22no—
203C2×C11—41no—
204C2×C11C2×#12111yescharacteristic
205C2×C11C2×#13711yescharacteristic
206C2×C11#57511yescharacteristic
207D11—81no—
208C24C22⋊D1111yescharacteristic
209#41—222no—
210#41—222no—
211C2×Q8—21no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—111no—
215C2×Q8C22×D1112yes—
216C2×D4—111no—
217C2×D4—221no—
218C2×D4—221no—
219C2×D4—221no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—221no—
225C22×C4C22⋊D1111yescharacteristic
226C22×C4C22⋊D1111yescharacteristic
227C22×C4C22⋊D1111yescharacteristic
228C22×C4C22×D1111yescharacteristic
229C22×C4C22×D1111yescharacteristic
230C22×C4C22×D1111yescharacteristic
231Q16—224no—
232SD16—224no—
233M16—114no—
234M16—224no—
235M16—222no—
236C2×C8—112no—
237C2×C8—112no—
238C2×C8—224no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—21no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4C22×D1112yes—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—221no—
250C22⋊C4—221no—
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C42—221no—
255C11#305611yescharacteristic, complemented, Sylow
256C23—22no—
257C23—22no—
258C23—41no—
259C23—221no—
260C23C2×C22⋊D1111yescharacteristic
261C23C2×C22⋊D1111yescharacteristic
262C23C2×C22⋊D1111yescharacteristic
263Q8—22no—
264Q8—22no—
265Q8—42no—
266Q8—221no—
267Q8—221no—
268D4—221no—
269D4—221no—
270D4—442no—
271D4—442no—
272D4—442no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—442no—
288C2×C4D4×D1112yes—
289C2×C4#434112yes—
290C2×C4C2×C22⋊D1111yescharacteristic
291C2×C4C2×C22⋊D1111yescharacteristic
292C2×C4C2×C22⋊D1111yescharacteristic
293C2×C4C23×D1111yescharacteristic
294C8—114no—
295C8—222no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—44no—
304C22—441no—
305C22—441no—
306C22—441no—
307C22#6699212yes—
308C22#6699512yescomplemented
309C22C22×C22⋊D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—42no—
313C4—42no—
314C4—441no—
315C4—441no—
316C4—441no—
317C4#6699212yes—
318C4C2×D4×D1111yescharacteristic
319C4C2×#434111yescharacteristic
320C2—22no—
321C2—22no—
322C2—41no—
323C2—881no—
324C2C2×#6699211yescharacteristic
325C2C2×#6699511yescharacteristic
326C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×C22⋊Q8C2
socleC22×C11C22×D4
prime radical#10623322C2
hypercenterC2×C22⋊Q8D11
hypocenterC11#3056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
2. C2×#66995C2semidirect
4. C22×#4318C2semidirect
5. #10622838C2semidirect
6. #10622665C2semidirect
7. #10622664C2semidirect
8. #10622662C2semidirect
9. #10622661C2semidirect
10. #10622579C2semidirect
11. #10622577C2semidirect
23. C2×#4326C22semidirect
25. C2×#4325C22semidirect
39. #66899C22semidirect
40. #66899C22semidirect
41. #66874C22semidirect
42. #66873C22semidirect
43. #66872C22semidirect
44. #66871C22semidirect
88. #4318D4semidirect
136. C2×C22⋊Q8D11semidirect
153. C22×C11#137semidirect
255. C11#3056semidirect
308. C22#66995semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669952
#106233222
C22×#43182
#106228382
#106226652
#106226642
#106226622
#106226612
#106225792
#106225772
#305611