Finite Group Databasebeta

← #13076265

Subgroups — #13076265

Order 1408.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#390C211yesmaximal, characteristic
2#10622833C211yesmaximal, characteristic
3#10622833C211yesmaximal, characteristic
4#10622599C211yesmaximal, characteristic, complemented
5#10622597C211yesmaximal, characteristic, complemented
6#10622563C211yesmaximal, characteristic, complemented
7#10622563C211yesmaximal, characteristic, complemented
8#10622562C211yesmaximal, characteristic, complemented
9#10622561C211yesmaximal, characteristic, complemented
10#10622561C211yesmaximal, characteristic, complemented
11#10622561C211yesmaximal, characteristic, complemented
12#10622559C211yesmaximal, characteristic, complemented
13#10622555C211yesmaximal, characteristic, complemented
14#10622546C211yesmaximal, characteristic, complemented
15#10622541C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C42×C11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C24×C11C2311yescharacteristic
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11Q814yes—
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×Dic11—22no—
62C22×Dic11—41no—
63C22×Dic11—41no—
64C22×Dic11—41no—
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C11×C4⋊C4—41no—
76C11×C22⋊C4—22no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C42×C11—41no—
81C22⋊Dic11—22no—
82C22⋊Dic11—41no—
83C22⋊Dic11—41no—
84C22⋊Dic11—41no—
85C22⋊Dic11—41no—
86C22⋊Dic11—41no—
87C4⋊Dic11—22no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—22no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97#2780—111nomaximal, Sylow
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11C2×Q812yes—
111C23×C11C2×Q812yes—
112C23×C11C2411yescharacteristic
113D4×C11—44no—
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×C11C2×Q812yes—
128C2×C4×C11#4112yes—
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—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—44no—
153C2×Dic11—44no—
154C2×Dic11#4112yes—
155#400—111no—
156#399—111no—
157#398—111no—
158#396—111no—
159#396—111no—
160#396—111no—
161#390D1111yescharacteristic
162#389—111no—
163#387—111no—
164#386—111no—
165#386—111no—
166#385—111no—
167#385—111no—
168#385—111no—
169#380—111no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11C22×Q811yescharacteristic
185C22×C11C2×#4111yescharacteristic
186C22×C11C2×#4111yescharacteristic
187C22×C11H(5,𝔽2)11yescharacteristic
188C22×C11H(5,𝔽2)11yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196Dic11—22no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204C22×D4C2×D1111yescharacteristic
205C23×C4—111no—
206C23×C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4C2×D1111yescharacteristic
218C2×C22⋊C4—111no—
219C2×C22⋊C4—111no—
220C2×C22⋊C4—111no—
221C2×C22⋊C4—111no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4—111no—
224C2×C22⋊C4C2×D1111yescharacteristic
225C2×C22⋊C4C2×D1111yescharacteristic
226C2×C22⋊C4C2×D1111yescharacteristic
227C2×C22⋊C4C2×D1111yescharacteristic
228C2×C42C2×D1111yescharacteristic
229#95—111no—
230#95—111no—
231#95—111no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—111no—
236#95—111no—
237#95—111no—
238#95—111no—
239C2×C11—42no—
240C2×C11—42no—
241C2×C11#53811yescharacteristic
242C2×C11#54011yescharacteristic
243C2×C11#54311yescharacteristic
244C2×C11#55311yescharacteristic
245C2×C11#55411yescharacteristic
246C2×C11#55411yescharacteristic
247C2×C11#56011yescharacteristic
248C24C22×D1111yescharacteristic
249C24C22×D1111yescharacteristic
250C2×D4—41no—
251C2×D4—41no—
252C2×D4Dic2214yes—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—222no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4C22×D1111yescharacteristic
268C22×C4C22×D1111yescharacteristic
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C4⋊C4—41no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—222no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C22⋊C4—441no—
293C42—41no—
294C11#278011yescharacteristic, complemented, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23C2×Dic2212yes—
308C23C2×Dic2212yes—
309C23C23×D1111yescharacteristic
310D4—44no—
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—21no—
323C2×C4—21no—
324C2×C4—112no—
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—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—444no—
349C2×C4—444no—
350C2×C4C2×Dic2212yes—
351C2×C4#434112yes—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22C22×Dic2211yescharacteristic
367C22C2×#434111yescharacteristic
368C22#6703711yescharacteristic
369C22#6703711yescharacteristic
370C22#6703711yescharacteristic
371C22#41×D1111yescharacteristic
372C22#6704211yescharacteristic
373C4—22no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—222no—
379C4—441no—
380C4—441no—
381C4—441no—
382C4—441no—
383C4—441no—
384C4—441no—
385C4—441no—
386C2—42no—
387C2—42no—
388C2#1062301411yescharacteristic
389C2#1062307011yescharacteristic
390C2#1062307411yescharacteristic
391C2#1062313211yescharacteristic
392C2#1062315111yescharacteristic
393C2#1062320911yescharacteristic
394C2#1062325011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2780
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
4. #10622599C2semidirect
5. #10622597C2semidirect
6. #10622563C2semidirect
7. #10622563C2semidirect
8. #10622562C2semidirect
9. #10622561C2semidirect
10. #10622561C2semidirect
11. #10622561C2semidirect
12. #10622559C2semidirect
13. #10622555C2semidirect
14. #10622546C2semidirect
15. #10622541C2semidirect
294. C11#2780semidirect

Maximal subgroups

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

subgroupindex
C11×#3902
#106228332
#106225992
#106225972
#106225632
#106225622
#106225612
#106225592
#106225552
#106225462
#106225412
#278011