Finite Group Databasebeta

← C11×#2480 #13065318

Subgroups — C11×#2480 #13065318

Order 1408.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#126C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊C4C211yesmaximal, characteristic
3C11×#397C211yesmaximal, characteristic, complemented
4C11×#397C211yesmaximal, characteristic, complemented
5C11×#397C211yesmaximal, characteristic, complemented
6C11×#396C211yesmaximal, characteristic, complemented
7C11×#388C211yesmaximal, characteristic, complemented
8C11×#388C211yesmaximal, characteristic, complemented
9C11×#388C211yesmaximal, characteristic, complemented
10C11×#385C211yesmaximal, characteristic, complemented
11C11×#385C211yesmaximal, characteristic, complemented
12C11×#380C211yesmaximal, characteristic, complemented
13C11×#379C211yesmaximal, characteristic
14C11×#379C211yesmaximal, characteristic
15C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C11×#126—24no—
20C2×C11×C4⋊C4C2211yescharacteristic, complemented
21C2×C11×C4⋊C4C2211yescharacteristic, complemented
22C2×C11×C4⋊C4C2211yescharacteristic, complemented
23C2×C11×C4⋊C4C2211yescharacteristic, complemented
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C4⋊C4C2211yescharacteristic, complemented
26C2×C11×C22⋊C4—24no—
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C11×C22⋊C4C2211yescharacteristic
37C2×C11×C22⋊C4C2211yescharacteristic
38C2×C11×C22⋊C4C2211yescharacteristic
39C2×C11×C22⋊C4C2211yescharacteristic
40C2×C11×C22⋊C4C2211yescharacteristic
41C2×C11×C22⋊C4C2211yescharacteristic
42C2×C11×C22⋊C4C2211yescharacteristic
43C2×C42×C11C2211yescharacteristic, complemented
44C2×C42×C11C2211yescharacteristic, complemented
45C11×#95C2211yescharacteristic, complemented
46C11×#95C2211yescharacteristic, complemented
47C11×#95C2211yescharacteristic, complemented
48C11×#95C2211yescharacteristic, complemented
49C11×#95C2211yescharacteristic, complemented
50C11×#95C2211yescharacteristic, complemented
51C11×#95C2211yescharacteristic, complemented
52C11×#95C2211yescharacteristic, complemented
53C24×C11—22no—
54C24×C11—22no—
55C24×C11—22no—
56C24×C11—22no—
57C24×C11—22no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11C2311yescharacteristic
61C24×C11C2311yescharacteristic
62C24×C11C2311yescharacteristic
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4D414yes—
103C42×C11—22no—
104C42×C11—41no—
105#2480C1111yesmaximal, characteristic, direct product factor, Sylow
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—28no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—44no—
124C23×C11—44no—
125C23×C11—44no—
126C23×C11—44no—
127C23×C11—44no—
128C23×C11—44no—
129C23×C11C2×D412yes—
130C23×C11#4112yes—
131C23×C11#4112yes—
132C23×C11#4112yes—
133C23×C11#4112yes—
134C23×C11C2411yescharacteristic
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×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—44no—
170C2×C4×C11—44no—
171C2×C4×C11C2×D412yes—
172C2×C4×C11C2×D412yes—
173C2×#126C2×C1111yescharacteristic, complemented
174C22×C22⋊C4C2×C1111yescharacteristic
175#397C2×C1111yescharacteristic, complemented
176#397C2×C1111yescharacteristic, complemented
177#397C2×C1111yescharacteristic, complemented
178#396C2×C1111yescharacteristic, complemented
179#388C2×C1111yescharacteristic, complemented
180#388C2×C1111yescharacteristic, complemented
181#388C2×C1111yescharacteristic, complemented
182#385C2×C1111yescharacteristic, complemented
183#385C2×C1111yescharacteristic, complemented
184#380C2×C1111yescharacteristic, complemented
185#379C2×C1111yescharacteristic
186#379C2×C1111yescharacteristic
187C4×C22⋊C4C2×C1111yescharacteristic, complemented
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—416no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11#12614yescomplemented
210C22×C11C22×D411yescharacteristic
211C22×C11C2×#4111yescharacteristic
212C22×C11C2×#4111yescharacteristic
213C22×C11C2×#4111yescharacteristic
214C22×C11C2×#4111yescharacteristic
215C22×C11H(5,𝔽2)11yescharacteristic
216C22×C11H(5,𝔽2)11yescharacteristic
217C4×C11—22no—
218C4×C11—22no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—41no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—41no—
229C25C22×C1111yescharacteristic
230C23×C4C22×C1111yescharacteristic
231C23×C4C22×C1111yescharacteristic
232#126—24no—
233C2×C4⋊C4C22×C1111yescharacteristic, complemented
234C2×C4⋊C4C22×C1111yescharacteristic, complemented
235C2×C4⋊C4C22×C1111yescharacteristic, complemented
236C2×C4⋊C4C22×C1111yescharacteristic, complemented
237C2×C4⋊C4C22×C1111yescharacteristic, complemented
238C2×C4⋊C4C22×C1111yescharacteristic, complemented
239C2×C22⋊C4—24no—
240C2×C22⋊C4C22×C1111yescharacteristic
241C2×C22⋊C4C22×C1111yescharacteristic
242C2×C22⋊C4C22×C1111yescharacteristic
243C2×C22⋊C4C22×C1111yescharacteristic
244C2×C22⋊C4C22×C1111yescharacteristic
245C2×C22⋊C4C22×C1111yescharacteristic
246C2×C22⋊C4C22×C1111yescharacteristic
247C2×C22⋊C4C22×C1111yescharacteristic
248C2×C22⋊C4C22×C1111yescharacteristic
249C2×C22⋊C4C22×C1111yescharacteristic
250C2×C22⋊C4C22×C1111yescharacteristic
251C2×C22⋊C4C22×C1111yescharacteristic
252C2×C22⋊C4C22×C1111yescharacteristic
253C2×C22⋊C4C22×C1111yescharacteristic
254C2×C22⋊C4C22×C1111yescharacteristic
255C2×C22⋊C4C22×C1111yescharacteristic
256C2×C42C22×C1111yescharacteristic, complemented
257C2×C42C22×C1111yescharacteristic, complemented
258#95C22×C1111yescharacteristic, complemented
259#95C22×C1111yescharacteristic, complemented
260#95C22×C1111yescharacteristic, complemented
261#95C22×C1111yescharacteristic, complemented
262#95C22×C1111yescharacteristic, complemented
263#95C22×C1111yescharacteristic, complemented
264#95C22×C1111yescharacteristic, complemented
265#95C22×C1111yescharacteristic, complemented
266C2×C11—24no—
267C2×C11—42no—
268C2×C11—42no—
269C2×C11#52511yescharacteristic
270C2×C11C2×#12611yescharacteristic
271C2×C11#53811yescharacteristic
272C2×C11#54611yescharacteristic
273C2×C11#54611yescharacteristic
274C2×C11#55111yescharacteristic
275C2×C11#55111yescharacteristic
276C24—22no—
277C24—22no—
278C24—22no—
279C24—22no—
280C24—22no—
281C24—41no—
282C24—41no—
283C24C23×C1111yescharacteristic
284C24C23×C1111yescharacteristic
285C24C23×C1111yescharacteristic
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4C23×C1111yescharacteristic
293C22×C4C23×C1111yescharacteristic
294C22×C4C23×C1111yescharacteristic
295C22×C4C23×C1111yescharacteristic
296C22×C4C23×C1111yescharacteristic
297C22×C4C23×C1111yescharacteristic
298C22×C4C23×C1111yescharacteristic
299C22×C4C23×C1111yescharacteristic
300C22×C4C23×C1111yescharacteristic
301C22×C4C23×C1111yescharacteristic
302C22×C4C23×C1111yescharacteristic
303C22×C4C23×C1111yescharacteristic
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4D4×C1114yes—
326C42—22no—
327C42—41no—
328C11#248011yescharacteristic, direct product factor, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—28no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—44no—
347C23—44no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23—44no—
352C23C2×D4×C1112yes—
353C23C11×#4112yes—
354C23C11×#4112yes—
355C23C11×#4112yes—
356C23C11×#4112yes—
357C23C24×C1111yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4C2×D4×C1112yes—
395C2×C4C2×D4×C1112yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—416no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22C11×#12614yescomplemented
418C22C22×D4×C1111yescharacteristic
419C22C2×C11×#4111yescharacteristic
420C22C2×C11×#4111yescharacteristic
421C22C2×C11×#4111yescharacteristic
422C22C2×C11×#4111yescharacteristic
423C22C11×H(5,𝔽2)11yescharacteristic
424C22C11×H(5,𝔽2)11yescharacteristic
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—41no—
437C2—24no—
438C2—42no—
439C2—42no—
440C2C11×#52511yescharacteristic
441C2C2×C11×#12611yescharacteristic
442C2C11×#53811yescharacteristic
443C2C11×#54611yescharacteristic
444C2C11×#54611yescharacteristic
445C2C11×#55111yescharacteristic
446C2C11×#55111yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC25×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#126C2semidirect
3. C11×#397C2semidirect
4. C11×#397C2semidirect
5. C11×#397C2semidirect
6. C11×#396C2semidirect
7. C11×#388C2semidirect
8. C11×#388C2semidirect
9. C11×#388C2semidirect
10. C11×#385C2semidirect
11. C11×#385C2semidirect
12. C11×#380C2semidirect
15. C4×C11×C22⋊C4C2semidirect
20. C2×C11×C4⋊C4C22semidirect
21. C2×C11×C4⋊C4C22semidirect
22. C2×C11×C4⋊C4C22semidirect
23. C2×C11×C4⋊C4C22semidirect
24. C2×C11×C4⋊C4C22semidirect
25. C2×C11×C4⋊C4C22semidirect
43. C2×C42×C11C22semidirect
44. C2×C42×C11C22semidirect
45. C11×#95C22semidirect
46. C11×#95C22semidirect
47. C11×#95C22semidirect
48. C11×#95C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11×#95C22semidirect
52. C11×#95C22semidirect
105. #2480C11direct (N × H)
173. C2×#126C2×C11semidirect
175. #397C2×C11semidirect
176. #397C2×C11semidirect
177. #397C2×C11semidirect
178. #396C2×C11semidirect
179. #388C2×C11semidirect
180. #388C2×C11semidirect
181. #388C2×C11semidirect
182. #385C2×C11semidirect
183. #385C2×C11semidirect
184. #380C2×C11semidirect
187. C4×C22⋊C4C2×C11semidirect
209. C22×C11#126semidirect
233. C2×C4⋊C4C22×C11semidirect
234. C2×C4⋊C4C22×C11semidirect
235. C2×C4⋊C4C22×C11semidirect
236. C2×C4⋊C4C22×C11semidirect
237. C2×C4⋊C4C22×C11semidirect
238. C2×C4⋊C4C22×C11semidirect
256. C2×C42C22×C11semidirect
257. C2×C42C22×C11semidirect
258. #95C22×C11semidirect
259. #95C22×C11semidirect
260. #95C22×C11semidirect
261. #95C22×C11semidirect
262. #95C22×C11semidirect
263. #95C22×C11semidirect
264. #95C22×C11semidirect
265. #95C22×C11semidirect
328. C11#2480direct (N × H)
417. C22C11×#126semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C22×C11×C22⋊C42
C11×#3972
C11×#3962
C11×#3882
C11×#3852
C11×#3802
C11×#3792
C4×C11×C22⋊C42
#248011