Finite Group Databasebeta

← #13076291

Subgroups — #13076291

Order 1408.

448 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#385C211yesmaximal, characteristic, complemented
2#10622826C211yesmaximal, characteristic
3#10622823C211yesmaximal, characteristic, complemented
4#10622602C211yesmaximal, characteristic, complemented
5#10622602C211yesmaximal, characteristic, complemented
6#10622595C211yesmaximal, characteristic, complemented
7#10622595C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic
9#10622569C211yesmaximal, characteristic
10#10622565C211yesmaximal, characteristic, complemented
11#10622558C211yesmaximal, characteristic, complemented
12#10622288C211yesmaximal, characteristic, complemented
13#10622282C211yesmaximal, characteristic, complemented
14#10622271C211yesmaximal, characteristic, complemented
15#10622263C211yesmaximal, characteristic, complemented
16C23×C4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
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×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—22no—
63C2×C22⋊D11—22no—
64C2×C22⋊D11—41no—
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—41no—
79C22⋊Dic11—22no—
80C22⋊Dic11—22no—
81C22⋊Dic11—41no—
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—22no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92C4×Dic11—22no—
93#2782—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—21no—
127C2×C4×C11—44no—
128C22⋊D11—44no—
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—21no—
148C2×Dic11—21no—
149C2×Dic11#4112yes—
150C4×D11—44no—
151#400—111no—
152#400—111no—
153#400—111no—
154#397—111no—
155#397—111no—
156#394—111no—
157#388—111no—
158#388—111no—
159#386—111no—
160#386—111no—
161#385—111no—
162#385—111no—
163#385—111no—
164#385D1111yescharacteristic, complemented
165#382—111no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C2×#4111yescharacteristic
174C22×C11C2×#4111yescharacteristic
175C22×C11C2×#4111yescharacteristic
176C22×C11H(5,𝔽2)11yescharacteristic
177C22×C11H(5,𝔽2)11yescharacteristic
178C22×C11H(5,𝔽2)11yescharacteristic
179C22×C112−1+411yescharacteristic
180C2×D11—22no—
181C2×D11—22no—
182C2×D11—22no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193Dic11—22no—
194Dic11—41no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200C22×D4—111no—
201C23×C4—111no—
202C23×C4C2×D1111yescharacteristic
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4C2×D1111yescharacteristic
209C2×C4⋊C4C2×D1111yescharacteristic
210C2×C22⋊C4—111no—
211C2×C22⋊C4—111no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4—111no—
218C2×C22⋊C4C2×D1111yescharacteristic
219C2×C22⋊C4C2×D1111yescharacteristic
220C2×C42—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#95C2×D1111yescharacteristic
234#95C2×D1111yescharacteristic
235C2×C11—42no—
236C2×C11#53911yescharacteristic
237C2×C11#53911yescharacteristic
238C2×C11#53911yescharacteristic
239C2×C11#55111yescharacteristic
240C2×C11#55311yescharacteristic
241C2×C11#55311yescharacteristic
242C2×C11H(3,𝔽4)11yescharacteristic
243D11—42no—
244C24—111no—
245C24C22×D1111yescharacteristic
246C2×D4—222no—
247C2×D4—222no—
248C2×D4—441no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—441no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4C22×D1111yescharacteristic
263C22×C4C22×D1111yescharacteristic
264C22×C4C22×D1111yescharacteristic
265C22×C4C22×D1111yescharacteristic
266C22×C4C22×D1111yescharacteristic
267C22×C4C22×D1111yescharacteristic
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—222no—
278C22⋊C4—222no—
279C22⋊C4—222no—
280C22⋊C4—222no—
281C22⋊C4—222no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C42—222no—
286C11#278211yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—112no—
294C23—221no—
295C23—221no—
296C23—221no—
297C23—221no—
298C23—221no—
299C23—221no—
300C23#433912yes—
301C23C23×D1111yescharacteristic
302D4—444no—
303C2×C4—21no—
304C2×C4—21no—
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—44no—
322C2×C4—112no—
323C2×C4—221no—
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—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—222no—
352C22—222no—
353C22—222no—
354C22—441no—
355C22—441no—
356C22—441no—
357C22—441no—
358C22C2×#433911yescharacteristic
359C22#6703711yescharacteristic
360C22#6703711yescharacteristic
361C22#6703711yescharacteristic
362C22#6704011yescharacteristic
363C22#41×D1111yescharacteristic
364C22#41×D1111yescharacteristic
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—222no—
372C4—441no—
373C4—441no—
374C4—441no—
375C4—441no—
376C4—441no—
377C4—441no—
378C2—42no—
379C2—442no—
380C2#1062304611yescharacteristic
381C2#1062307111yescharacteristic
382C2#1062308711yescharacteristic
383C2#1062312511yescharacteristic
384C2#1062316911yescharacteristic
385C2#1062316911yescharacteristic
386C2#1062319211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radicalC22×C22⋊D11C22
hypercenter#385D11
hypocenterC11#2782
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C11×#385C2semidirect
3. #10622823C2semidirect
4. #10622602C2semidirect
5. #10622602C2semidirect
6. #10622595C2semidirect
7. #10622595C2semidirect
10. #10622565C2semidirect
11. #10622558C2semidirect
12. #10622288C2semidirect
13. #10622282C2semidirect
14. #10622271C2semidirect
15. #10622263C2semidirect
164. #385D11semidirect
286. C11#2782semidirect

Maximal subgroups

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

subgroupindex
C11×#3852
#106228262
#106228232
#106226022
#106225952
#106225722
#106225692
#106225652
#106225582
#106222882
#106222822
#106222712
#106222632
#278211