Finite Group Databasebeta

← #13075656

Subgroups — #13075656

Order 1408.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#397C211yesmaximal, characteristic, complemented
2#10622607C211yesmaximal, characteristic, complemented
3#10622603C211yesmaximal, characteristic, complemented
4#10622568C211yesmaximal, characteristic
5#10622568C211yesmaximal, characteristic
6#10622568C211yesmaximal, characteristic
7#10622564C211yesmaximal, characteristic, complemented
8#10622564C211yesmaximal, characteristic, complemented
9#10622561C211yesmaximal, characteristic, complemented
10#10622290C211yesmaximal, characteristic, complemented
11#10622288C211yesmaximal, characteristic, complemented
12#10622288C211yesmaximal, characteristic, complemented
13#10622283C211yesmaximal, characteristic, complemented
14#10622283C211yesmaximal, characteristic, complemented
15#10622282C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic, complemented
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×C4⋊Dic11C2211yescharacteristic, complemented
37C2×C4⋊Dic11C2211yescharacteristic, complemented
38C2×C4⋊Dic11C2211yescharacteristic, complemented
39C2×Dic11⋊C4C2211yescharacteristic, complemented
40C2×Dic11⋊C4C2211yescharacteristic, complemented
41C2×C4×Dic11C2211yescharacteristic, complemented
42C2×C4×Dic11C2211yescharacteristic, complemented
43C11×#95C2211yescharacteristic, complemented
44C11×#95C2211yescharacteristic, complemented
45C11×#95C2211yescharacteristic, complemented
46C11⋊#95C2211yescharacteristic, complemented
47C11⋊#95C2211yescharacteristic, complemented
48C11⋊#95C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C24×C11C2311yescharacteristic
52C23×D11—22no—
53C23×D11—22no—
54C23×D11—22no—
55C23×D11—41no—
56C23×D11—41no—
57C23×D11—41no—
58C23×D11—41no—
59C23×D11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C11×C4⋊C4—41no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4—41no—
77C22⋊Dic11—41no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4—22no—
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—41no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99#2735—111nomaximal, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11#4112yes—
107C23×C11C2411yescharacteristic
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—44no—
121C22×D11—44no—
122C22×D11—44no—
123C22×D11—44no—
124C22×D11—44no—
125C22×D11—44no—
126C22×D11—44no—
127C22×D11#4112yes—
128C22×D11#4112yes—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165#399—111no—
166#397—111no—
167#397—111no—
168#397D1111yescharacteristic, complemented
169#396—111no—
170#396—111no—
171#388—111no—
172#388—111no—
173#388—111no—
174#388—111no—
175#388—111no—
176#388—111no—
177#379—111no—
178#379—111no—
179#379—111no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11C2×#4111yescharacteristic
188C22×C11C2×#4111yescharacteristic
189C22×C11C2×#4111yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C22×C11H(5,𝔽2)11yescharacteristic
192C22×C11H(5,𝔽2)11yescharacteristic
193C22×C11H(5,𝔽2)11yescharacteristic
194C2×D11—22no—
195C2×D11—22no—
196C2×D11—22no—
197C2×D11—22no—
198C2×D11—22no—
199C2×D11—22no—
200C2×D11—416no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—41no—
215Dic11—41no—
216Dic11—41no—
217Dic11—41no—
218Dic11—41no—
219Dic11—41no—
220Dic11—41no—
221C25—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4C2×D1111yescharacteristic, complemented
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—111no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—111no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—111no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4C2×D1111yescharacteristic
244C2×C22⋊C4C2×D1111yescharacteristic
245C2×C22⋊C4C2×D1111yescharacteristic
246C2×C42—111no—
247C2×C42—111no—
248#95—111no—
249#95—111no—
250#95—111no—
251#95—111no—
252#95—111no—
253#95C2×D1111yescharacteristic, complemented
254#95C2×D1111yescharacteristic, complemented
255#95C2×D1111yescharacteristic, complemented
256C2×C11—42no—
257C2×C11#53811yescharacteristic
258C2×C11#53811yescharacteristic
259C2×C11#53811yescharacteristic
260C2×C11#55111yescharacteristic
261C2×C11#55111yescharacteristic
262C2×C11#55111yescharacteristic
263C2×C11#56011yescharacteristic
264D11—42no—
265D11—42no—
266C24—111no—
267C24—111no—
268C24—222no—
269C24—222no—
270C24—222no—
271C24—441no—
272C24—441no—
273C24—441no—
274C24—441no—
275C24C22×D1111yescharacteristic
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4C22×D1111yescharacteristic
283C22×C4C22×D1111yescharacteristic
284C22×C4C22×D1111yescharacteristic
285C22×C4C22×D1111yescharacteristic
286C22×C4C22×D1111yescharacteristic
287C22×C4C22×D1111yescharacteristic
288C4⋊C4—41no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C22⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C22⋊C4—441no—
312C42—441no—
313C42—441no—
314C11#273511yescharacteristic, complemented, Sylow
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—112no—
322C23—112no—
323C23—221no—
324C23—221no—
325C23—221no—
326C23—221no—
327C23—221no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—444no—
336C23—444no—
337C23—444no—
338C23—444no—
339C23—444no—
340C23—444no—
341C23—444no—
342C23#434112yes—
343C23C23×D1111yescharacteristic
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—222no—
388C22—222no—
389C22—222no—
390C22—222no—
391C22—222no—
392C22—222no—
393C22—4416no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22—441no—
398C22—441no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22C2×#434111yescharacteristic
403C22#6703711yescharacteristic
404C22#41×D1111yescharacteristic
405C22#41×D1111yescharacteristic
406C22#6704211yescharacteristic
407C22#6704211yescharacteristic
408C22#6704211yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—441no—
416C4—441no—
417C4—441no—
418C4—441no—
419C4—441no—
420C4—441no—
421C2—42no—
422C2—442no—
423C2—442no—
424C2#1062314811yescharacteristic
425C2#1062318811yescharacteristic
426C2#1062318911yescharacteristic
427C2#1062318911yescharacteristic
428C2#1062320911yescharacteristic
429C2#1062323611yescharacteristic
430C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×D11C22
hypercenter#397D11
hypocenterC11#2735
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C11×#397C2semidirect
2. #10622607C2semidirect
3. #10622603C2semidirect
7. #10622564C2semidirect
8. #10622564C2semidirect
9. #10622561C2semidirect
10. #10622290C2semidirect
11. #10622288C2semidirect
12. #10622288C2semidirect
13. #10622283C2semidirect
14. #10622283C2semidirect
15. #10622282C2semidirect
17. C2×C11×C4⋊C4C22semidirect
36. C2×C4⋊Dic11C22semidirect
37. C2×C4⋊Dic11C22semidirect
38. C2×C4⋊Dic11C22semidirect
39. C2×Dic11⋊C4C22semidirect
40. C2×Dic11⋊C4C22semidirect
41. C2×C4×Dic11C22semidirect
42. C2×C4×Dic11C22semidirect
43. C11×#95C22semidirect
44. C11×#95C22semidirect
45. C11×#95C22semidirect
46. C11⋊#95C22semidirect
47. C11⋊#95C22semidirect
48. C11⋊#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
168. #397D11semidirect
227. C2×C4⋊C4C2×D11semidirect
253. #95C2×D11semidirect
254. #95C2×D11semidirect
255. #95C2×D11semidirect
314. C11#2735semidirect

Maximal subgroups

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

subgroupindex
C11×#3972
#106226072
#106226032
#106225682
#106225642
#106225612
#106222902
#106222882
#106222832
#106222822
#273511