Finite Group Databasebeta

← #13079963

Subgroups — #13079963

Order 1408.

360 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
1C11×#529C211yesmaximal, characteristic, complemented
2#10623010C211yesmaximal, characteristic, complemented
3#10622679C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622670C211yesmaximal, characteristic, complemented
6#10622667C211yesmaximal, characteristic, complemented
7#10622664C211yesmaximal, characteristic, complemented
8#10622661C211yesmaximal, characteristic, complemented
9#10622654C211yesmaximal, characteristic, complemented
10#10622651C211yesmaximal, characteristic
11#10622641C211yesmaximal, characteristic, complemented
12#10622635C211yesmaximal, characteristic, complemented
13#10622629C211yesmaximal, characteristic, complemented
14#10622622C211yesmaximal, characteristic, complemented
15C2×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
16C11×#126—21no—
17C11×#125C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C11×#123—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11—21no—
24C4×D4×C11C2211yescharacteristic
25C11×#117—21no—
26C2×C42×C11C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983C2211yescharacteristic
32#66982—21no—
33C4×C22⋊D11—21no—
34#66977C2211yescharacteristic
35C22×C11⋊C8C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic
37#66929—21no—
38#66928C2211yescharacteristic
39C4×D44C2211yescharacteristic
40#66925—21no—
41#66923C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66874C2211yescharacteristic
48#66874C2211yescharacteristic
49#66873C2211yescharacteristic
50#66873C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56C4⋊(C11⋊C8)C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11D411yescharacteristic
64C22×C4×C11D411yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×Dic22C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C42×C11—21no—
82C42×C11D411yescharacteristic
83C42×C11D411yescharacteristic
84C42×C11C2311yescharacteristic
85C42×C11C2311yescharacteristic
86C22⋊Dic11—21no—
87#4326—41no—
88#4325—41no—
89#4324—41no—
90#4323—41no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3250—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—42no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—42no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135D44—21no—
136D44—21no—
137C4×D11—42no—
138Dic22—21no—
139Dic22—21no—
140C11⋊C8—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144#529—111no—
145#529D1111yescharacteristic, complemented
146#479—111no—
147#479—111no—
148#478—111no—
149#478—111no—
150#467—111no—
151#466—111no—
152#465—111no—
153#465—111no—
154#464—111no—
155#464—111no—
156#463—111no—
157#463—111no—
158C2×C4⋊C8—111no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11#13512yes—
165C22×C11C22×D411yescharacteristic
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11H(5,𝔽2)11yescharacteristic
178C4×C112−1+411yescharacteristic
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×SD16—111no—
184C2×SD16—111no—
185C2×D8—111no—
186C22×C8—111no—
187C22×C8—111no—
188#126—21no—
189#126—221no—
190#125—111no—
191#125C2×D1111yescharacteristic
192#124—111no—
193#124C2×D1111yescharacteristic
194#123—21no—
195#123—221no—
196C22⋊Q8—111no—
197C22⋊Q8C2×D1111yescharacteristic
198#121—111no—
199#121C2×D1111yescharacteristic
200C4×Q8—111no—
201C4×Q8C2×D1111yescharacteristic
202C4×D4—21no—
203C4×D4—111no—
204C4×D4—221no—
205C4×D4C2×D1111yescharacteristic
206#117—21no—
207#117—221no—
208C2×C42C2×D1111yescharacteristic
209#107—111no—
210#107—111no—
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216C4⋊C8—111no—
217#103—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225C2×C11—22no—
226C2×C11—81no—
227C2×C11#53711yescharacteristic
228C2×C11C2×#13511yescharacteristic
229C2×C11#57511yescharacteristic
230D11—81no—
231C2×Q8—111no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—21no—
234C2×D4—111no—
235C2×D4—221no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—221no—
239C22×C4C22⋊D1111yescharacteristic
240C22×C4C22⋊D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242Q16—441no—
243SD16—441no—
244SD16—441no—
245D8—441no—
246C2×C8—111no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—111no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—21no—
275C42—221no—
276C42C22⋊D1111yescharacteristic
277C42C22⋊D1111yescharacteristic
278C42C22×D1111yescharacteristic
279C42C22×D1111yescharacteristic
280C11#325011yescharacteristic, complemented, Sylow
281C23—21no—
282C23—221no—
283C23C2×C22⋊D1111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—221no—
287Q8—221no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—221no—
292D4—221no—
293D4—442no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—442no—
306C2×C4C2×C22⋊D1111yescharacteristic
307C2×C4C2×C22⋊D1111yescharacteristic
308C2×C4C2×C22⋊D1111yescharacteristic
309C2×C4C2×C22⋊D1111yescharacteristic
310C2×C4C2×C22⋊D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—221no—
313C8—221no—
314C8—221no—
315C8—221no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—441no—
322C22—441no—
323C22—441no—
324C22#6700312yes—
325C22C22×C22⋊D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4#6704211yescharacteristic
338C4#6704311yescharacteristic
339C2—22no—
340C2—81no—
341C2—881no—
342C2C2×#6700311yescharacteristic
343C2#1062335311yescharacteristic
344C2#1062336411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#529C2
socleC22×C11C22×D4
prime radical#10622651C2
hypercenter#529D11
hypocenterC11#3250
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C11×#529C2semidirect
2. #10623010C2semidirect
3. #10622679C2semidirect
4. #10622676C2semidirect
5. #10622670C2semidirect
6. #10622667C2semidirect
7. #10622664C2semidirect
8. #10622661C2semidirect
9. #10622654C2semidirect
11. #10622641C2semidirect
12. #10622635C2semidirect
13. #10622629C2semidirect
14. #10622622C2semidirect
15. C2×C4⋊(C11⋊C8)C2semidirect
145. #529D11semidirect
280. C11#3250semidirect

Maximal subgroups

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

subgroupindex
C11×#5292
#106230102
#106226792
#106226762
#106226702
#106226672
#106226642
#106226612
#106226542
#106226512
#106226412
#106226352
#106226292
#106226222
C2×C4⋊(C11⋊C8)2
#325011