Finite Group Databasebeta

← #13078231

Subgroups — #13078231

Order 1408.

548 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66985C211yesmaximal, characteristic, complemented
3#10623322C211yesmaximal, characteristic, complemented
4C22×#4318C211yesmaximal, characteristic, complemented
5#10622828C211yesmaximal, characteristic, complemented
6#10622655C212yesmaximal, complemented
7#10622654C212yesmaximal, complemented
8#10622652C212yesmaximal, complemented
9#10622651C212yesmaximal, complemented
10#10622579C211yesmaximal, characteristic, complemented
11#10622577C211yesmaximal, characteristic, complemented
12C22×D4×C11—21no—
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C2×#4339C2211yescharacteristic
16C11×#121—21no—
17C11×#121—21no—
18C11×#121C2212yes—
19C11×#121C2212yes—
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4—21no—
22#67006—21no—
23C2×#4324C2212yescomplemented
24#66985—24no—
25C2×#4323C2212yescomplemented
26#66983C2211yescharacteristic, complemented
27#66983C2211yescharacteristic, complemented
28#66982—21no—
29C4×C22⋊D11—21no—
30C4×C22⋊D11—21no—
31#66979C2211yescharacteristic
32#66977C2211yescharacteristic, complemented
33#66977C2211yescharacteristic, complemented
34C2×#4318—24no—
35C2×#4318C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37C2×#4318C2212yescomplemented
38C22×C11⋊C8C2212yescomplemented
39#66896C2212yescomplemented
40#66896C2212yescomplemented
41#66874C2212yescomplemented
42#66873C2212yescomplemented
43#66872C2212yescomplemented
44#66871C2212yescomplemented
45C24×C11—21no—
46C24×C11D411yescharacteristic
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11—21no—
51C2×D4×C11—22no—
52C2×D4×C11—44no—
53C2×D4×C11C2312yes—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—21no—
57C22×C4×C11D411yescharacteristic
58C22×C4×C11D411yescharacteristic
59C22×C4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66#4339—22no—
67#4339—22no—
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×Dic22C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2312yes—
73C11×C22⋊C4—22no—
74C11×C22⋊C4—22no—
75C22⋊Dic11—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78#4324—24no—
79#4323—24no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82C4⋊Dic11C2311yescharacteristic
83C4⋊Dic11C2311yescharacteristic
84Dic11⋊C4—21no—
85Dic11⋊C4—21no—
86C4×Dic11—21no—
87#4318—24no—
88#4318—22no—
89#4318D414yescomplemented
90C2×C11⋊C8—24no—
91C2×C11⋊C8C2312yes—
92C2×C11⋊C8C2312yes—
93#3055—111nomaximal, Sylow
94C23×C11—22no—
95C23×C11—22no—
96C23×C11—22no—
97C23×C11—41no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11C2×D411yescharacteristic
102C23×C11C2×D411yescharacteristic
103C23×C11C2×D411yescharacteristic
104C22×D11—21no—
105D4×C11—22no—
106D4×C11—22no—
107D4×C11—44no—
108D4×C11—44no—
109D4×C11—42no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—42no—
119C2×C4×C11C2×D412yes—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11#4112yes—
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—42no—
126C22⋊D11—42no—
127C22⋊D11—42no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131D44—21no—
132D44—21no—
133C4×D11—42no—
134Dic22—21no—
135Dic22—21no—
136C11⋊C8—22no—
137C11⋊C8C2×D414yescomplemented
138C2×AGL(1,ℤ/8)—111no—
139C22×M16—111no—
140#525—111no—
141C2×#121D1111yescharacteristic, complemented
142#469—112no—
143#468—112no—
144#466—112no—
145#465—112no—
146#428—111no—
147#418—111no—
148#417—111no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—44no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—84no—
161C22×C11#12112yes—
162C22×C11AGL(1,ℤ/8)12yescomplemented
163C22×C11C22×D411yescharacteristic
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—42no—
170C4×C11#12112yes—
171C4×C11C22×D411yescharacteristic
172C4×C11C2×#4111yescharacteristic
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176C2×#41—111no—
177C22×D4—21no—
178C22×D4C2×D1111yescharacteristic
179C23×C4C2×D1111yescharacteristic
180AGL(1,ℤ/8)—224no—
181C2×SD16—112no—
182C2×D8—112no—
183C2×M16—111no—
184C2×M16—111no—
185C2×M16—112no—
186C2×M16—224no—
187C22×C8—112no—
188#123—221no—
189C22⋊Q8—111no—
190C22⋊Q8—111no—
191#121—21no—
192#121—21no—
193#121—111no—
194#121—111no—
195#121C2×D1112yes—
196#121C2×D1112yes—
197#120—221no—
198C4×D4—221no—
199C4×D4—221no—
200#117—111no—
201C2×C4⋊C4C2×D1111yescharacteristic
202C2×C22⋊C4—21no—
203#107—112no—
204#106—112no—
205#103—112no—
206#102—112no—
207#102—112no—
208#102—112no—
209C2×C11—22no—
210C2×C11—22no—
211C2×C11—41no—
212C2×C11—82no—
213C2×C11C2×#12111yescharacteristic
214C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C11#57511yescharacteristic
216D11—81no—
217C24—21no—
218C24C22⋊D1111yescharacteristic
219#41—222no—
220#41—222no—
221C2×Q8—111no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—21no—
227C2×D4—44no—
228C2×D4—111no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4—221no—
232C2×D4C22×D1112yes—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—221no—
237C22×C4C22⋊D1111yescharacteristic
238C22×C4C22⋊D1111yescharacteristic
239C22×C4C22⋊D1111yescharacteristic
240C22×C4C22×D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242C22×C4C22×D1111yescharacteristic
243SD16—224no—
244D8—224no—
245M16—114no—
246M16—224no—
247M16—222no—
248C2×C8—112no—
249C2×C8—112no—
250C2×C8—224no—
251C4⋊C4—21no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4C22×D1112yes—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—221no—
265C11#305511yescharacteristic, complemented, Sylow
266C23—22no—
267C23—22no—
268C23—22no—
269C23—41no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23—221no—
274C23C2×C22⋊D1111yescharacteristic
275C23C2×C22⋊D1111yescharacteristic
276C23C2×C22⋊D1111yescharacteristic
277Q8—221no—
278Q8—221no—
279D4—22no—
280D4—22no—
281D4—44no—
282D4—44no—
283D4—42no—
284D4—221no—
285D4—221no—
286D4—442no—
287D4—442no—
288D4—442no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—42no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—442no—
302C2×C4D4×D1112yes—
303C2×C4#434112yes—
304C2×C4C2×C22⋊D1111yescharacteristic
305C2×C4C2×C22⋊D1111yescharacteristic
306C2×C4C2×C22⋊D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—114no—
309C8—222no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—44no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—84no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22#6698512yescomplemented
326C22#6699212yes—
327C22C22×C22⋊D1111yescharacteristic
328C4—21no—
329C4—21no—
330C4—42no—
331C4—441no—
332C4—441no—
333C4—441no—
334C4#6699212yes—
335C4C2×D4×D1111yescharacteristic
336C4C2×#434111yescharacteristic
337C2—22no—
338C2—22no—
339C2—41no—
340C2—82no—
341C2—881no—
342C2C2×#6698511yescharacteristic
343C2C2×#6699211yescharacteristic
344C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#121C2
socleC22×C11C22×D4
hypercenterC2×#121D11
hypocenterC11#3055
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66985C2semidirect
3. #10623322C2semidirect
4. C22×#4318C2semidirect
5. #10622828C2semidirect
6. #10622655C2semidirect
7. #10622654C2semidirect
8. #10622652C2semidirect
9. #10622651C2semidirect
10. #10622579C2semidirect
11. #10622577C2semidirect
23. C2×#4324C22semidirect
25. C2×#4323C22semidirect
26. #66983C22semidirect
27. #66983C22semidirect
32. #66977C22semidirect
33. #66977C22semidirect
37. C2×#4318C22semidirect
38. C22×C11⋊C8C22semidirect
39. #66896C22semidirect
40. #66896C22semidirect
41. #66874C22semidirect
42. #66873C22semidirect
43. #66872C22semidirect
44. #66871C22semidirect
89. #4318D4semidirect
137. C11⋊C8C2×D4semidirect
141. C2×#121D11semidirect
162. C22×C11AGL(1,ℤ/8)semidirect
265. C11#3055semidirect
325. C22#66985semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669852
#106233222
C22×#43182
#106228282
#106226552
#106226542
#106226522
#106226512
#106225792
#106225772
#305511