Finite Group Databasebeta

← #13073863

Subgroups — #13073863

Order 1408.

476 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#388C211yesmaximal, characteristic, complemented
2#10622603C211yesmaximal, characteristic, complemented
3#10622595C211yesmaximal, characteristic, complemented
4#10622572C211yesmaximal, characteristic
5#10622571C211yesmaximal, characteristic
6#10622569C211yesmaximal, characteristic
7#10622560C211yesmaximal, characteristic, complemented
8#10622556C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11#10622550C211yesmaximal, characteristic, complemented
12#10622286C211yesmaximal, characteristic, complemented
13#10622277C211yesmaximal, characteristic, complemented
14#10622264C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C42×C11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34C2×C4×Dic11C2211yescharacteristic
35C11×#95C2211yescharacteristic
36C11×#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C23×D11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C2×C22⋊D11—22no—
60C2×C22⋊D11—22no—
61C2×C22⋊D11—41no—
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—41no—
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C2×C4×D11—22no—
73C2×C4×D11—22no—
74C2×C4×D11—41no—
75C2×Dic22—22no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C11×C4⋊C4—41no—
79C11×C22⋊C4—22no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—41no—
82C42×C11—22no—
83C22⋊Dic11—22no—
84C22⋊Dic11—41no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—22no—
87(C2×D11)⋊C4—22no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90Dic11⋊C4—41no—
91C4×Dic11—22no—
92C4×Dic11—41no—
93#2572—111nomaximal, Sylow
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11#4112yes—
101C23×C11C2411yescharacteristic
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11#4112yes—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11#4112yes—
127C22⋊D11—44no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—44no—
148C2×Dic11#4112yes—
149C2×Dic11#4112yes—
150C4×D11—44no—
151Dic22—44no—
152#400—111no—
153#394—111no—
154#393—111no—
155#393—111no—
156#391—111no—
157#388—111no—
158#388D1111yescharacteristic, complemented
159#386—111no—
160#386—111no—
161#383—111no—
162#383—111no—
163#381—111no—
164#381—111no—
165C4×C22⋊C4—111no—
166C4×C22⋊C4—111no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—22no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C2×#4111yescharacteristic
175C22×C11C2×#4111yescharacteristic
176C22×C11C2×#4111yescharacteristic
177C22×C11C2×#4111yescharacteristic
178C22×C11C2×#4111yescharacteristic
179C22×C11H(5,𝔽2)11yescharacteristic
180C22×C11H(5,𝔽2)11yescharacteristic
181C2×D11—22no—
182C2×D11—22no—
183C2×D11—22no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C4×C11—22no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194Dic11—22no—
195Dic11—22no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200Dic11—41no—
201C22×Q8—111no—
202C22×D4—111no—
203C23×C4—111no—
204C23×C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4C2×D1111yescharacteristic
207C2×C22⋊C4—111no—
208C2×C22⋊C4—111no—
209C2×C22⋊C4—111no—
210C2×C22⋊C4—111no—
211C2×C22⋊C4—111no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4C2×D1111yescharacteristic
215C2×C22⋊C4C2×D1111yescharacteristic
216C2×C22⋊C4C2×D1111yescharacteristic
217C2×C42—111no—
218C2×C42—111no—
219C2×C42C2×D1111yescharacteristic
220#95—111no—
221#95—111no—
222#95—111no—
223#95—111no—
224#95—111no—
225#95—111no—
226#95—111no—
227#95—111no—
228#95—111no—
229#95—111no—
230#95—111no—
231#95—111no—
232#95—111no—
233#95—111no—
234#95C2×D1111yescharacteristic
235#95C2×D1111yescharacteristic
236C2×C11—42no—
237C2×C11#52911yescharacteristic
238C2×C11#52911yescharacteristic
239C2×C11#53811yescharacteristic
240C2×C11#55111yescharacteristic
241C2×C11#55111yescharacteristic
242C2×C11#55111yescharacteristic
243C2×C11#55511yescharacteristic
244D11—42no—
245C24—111no—
246C24C22×D1111yescharacteristic
247C2×Q8—222no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×D4—222no—
251C2×D4—222no—
252C2×D4—441no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—222no—
261C22×C4—222no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4C22×D1111yescharacteristic
267C22×C4C22×D1111yescharacteristic
268C22×C4C22×D1111yescharacteristic
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C4⋊C4—41no—
273C4⋊C4—441no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—222no—
278C22⋊C4—222no—
279C22⋊C4—222no—
280C22⋊C4—222no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C42—22no—
285C42—222no—
286C42—441no—
287C11#257211yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—112no—
295C23—221no—
296C23—221no—
297C23—221no—
298C23—221no—
299C23—221no—
300C23—221no—
301C23#433912yes—
302C23C23×D1111yescharacteristic
303Q8—444no—
304D4—444no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—112no—
323C2×C4—112no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—444no—
344C2×C4—444no—
345C2×C4#434112yes—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—222no—
354C22—222no—
355C22—222no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22—441no—
360C22C2×#433911yescharacteristic
361C22C2×#434111yescharacteristic
362C22#6703711yescharacteristic
363C22#41×D1111yescharacteristic
364C22#41×D1111yescharacteristic
365C22#41×D1111yescharacteristic
366C22#6704211yescharacteristic
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—222no—
374C4—222no—
375C4—441no—
376C4—441no—
377C4—441no—
378C4—441no—
379C4—441no—
380C2—42no—
381C2—442no—
382C2#1062305811yescharacteristic
383C2#1062306911yescharacteristic
384C2#1062308711yescharacteristic
385C2#1062314711yescharacteristic
386C2#1062318911yescharacteristic
387C2#1062320911yescharacteristic
388C2#1062323711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC22×C22⋊D11C22
hypercenter#388D11
hypocenterC11#2572
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C11×#388C2semidirect
2. #10622603C2semidirect
3. #10622595C2semidirect
7. #10622560C2semidirect
8. #10622556C2semidirect
9. C22⋊C4×Dic11C2semidirect
10. C4×(C2×D11)⋊C4C2semidirect
11. #10622550C2semidirect
12. #10622286C2semidirect
13. #10622277C2semidirect
14. #10622264C2semidirect
15. #10622259C2semidirect
158. #388D11semidirect
287. C11#2572semidirect

Maximal subgroups

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

subgroupindex
C11×#3882
#106226032
#106225952
#106225722
#106225712
#106225692
#106225602
#106225562
C22⋊C4×Dic112
C4×(C2×D11)⋊C42
#106225502
#106222862
#106222772
#106222642
#106222592
#257211