Finite Group Databasebeta

← C11×#2472 #13065310

Subgroups — C11×#2472 #13065310

Order 1408.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#124C211yesmaximal, characteristic, complemented
2C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C11×#120C211yesmaximal, characteristic
4C22×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#397C211yesmaximal, characteristic, complemented
6C11×#394C211yesmaximal, characteristic, complemented
7C11×#394C211yesmaximal, characteristic, complemented
8C11×#393C211yesmaximal, characteristic, complemented
9C11×#390C211yesmaximal, characteristic, complemented
10C11×#388C211yesmaximal, characteristic, complemented
11C11×#388C211yesmaximal, characteristic, complemented
12C11×#386C211yesmaximal, characteristic, complemented
13C11×#386C211yesmaximal, characteristic, complemented
14C11×#379C211yesmaximal, characteristic, complemented
15C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic, complemented
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C22×D4×C11C2211yescharacteristic
21C23×C4×C11C2211yescharacteristic
22C23×C4×C11C2211yescharacteristic
23C11×#124—24no—
24C11×C22⋊Q8—24no—
25C11×#120—24no—
26C2×C11×C4⋊C4C2211yescharacteristic, complemented
27C2×C11×C4⋊C4C2211yescharacteristic, complemented
28C2×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×C11×C22⋊C4—24no—
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×C11×C22⋊C4C2211yescharacteristic, complemented
44C2×C11×C22⋊C4C2211yescharacteristic, complemented
45C2×C11×C22⋊C4C2211yescharacteristic, complemented
46C2×C11×C22⋊C4C2211yescharacteristic, complemented
47C2×C42×C11C2211yescharacteristic, complemented
48C2×C42×C11C2211yescharacteristic, complemented
49C11×#95C2211yescharacteristic, complemented
50C11×#95C2211yescharacteristic, complemented
51C11×#95C2211yescharacteristic, complemented
52C11×#95C2211yescharacteristic, complemented
53C11×#95C2211yescharacteristic, complemented
54C11×#95C2211yescharacteristic, complemented
55C24×C11—22no—
56C24×C11—22no—
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—22no—
60C24×C11—41no—
61C24×C11—41no—
62C24×C11C2311yescharacteristic
63C24×C11C2311yescharacteristic
64C24×C11C2311yescharacteristic
65C24×C11C2311yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2311yescharacteristic
85C22×C4×C11C2311yescharacteristic
86C22×C4×C11C2311yescharacteristic
87C22×C4×C11C2311yescharacteristic
88C22×C4×C11C2311yescharacteristic
89C22×C4×C11C2311yescharacteristic
90C22×C4×C11C2311yescharacteristic
91C22×C4×C11C2311yescharacteristic
92C22×C4×C11C2311yescharacteristic
93C22×C4×C11C2311yescharacteristic
94C22×C4×C11C2311yescharacteristic
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4D414yes—
114C11×C22⋊C4D414yescomplemented
115C42×C11—22no—
116C42×C11—41no—
117#2472C1111yesmaximal, characteristic, direct product factor, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—28no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11—44no—
145C23×C11—44no—
146C23×C11—44no—
147C23×C11—44no—
148C23×C11C2×D412yes—
149C23×C11C2×D412yes—
150C23×C11#4112yes—
151C23×C11#4112yes—
152C23×C11#4112yes—
153C23×C11C2411yescharacteristic
154Q8×C11—44no—
155D4×C11—44no—
156D4×C11—44no—
157D4×C11—44no—
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—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—44no—
188C2×C4×C11—44no—
189C2×C4×C11C2×D412yes—
190C2×C4×C11C2×D412yes—
191C2×C4×C11C2×D412yes—
192C2×C4×C11C2×D412yes—
193C2×#124C2×C1111yescharacteristic, complemented
194C2×C22⋊Q8C2×C1111yescharacteristic, complemented
195C2×#120C2×C1111yescharacteristic
196C22×C22⋊C4C2×C1111yescharacteristic, complemented
197#397C2×C1111yescharacteristic, complemented
198#394C2×C1111yescharacteristic, complemented
199#394C2×C1111yescharacteristic, complemented
200#393C2×C1111yescharacteristic, complemented
201#390C2×C1111yescharacteristic, complemented
202#388C2×C1111yescharacteristic, complemented
203#388C2×C1111yescharacteristic, complemented
204#386C2×C1111yescharacteristic, complemented
205#386C2×C1111yescharacteristic, complemented
206#379C2×C1111yescharacteristic, complemented
207C4×C22⋊C4C2×C1111yescharacteristic, complemented
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—416no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11#12414yescomplemented
237C22×C11C22×D411yescharacteristic
238C22×C11C22×D411yescharacteristic
239C22×C11C2×#4111yescharacteristic
240C22×C11C2×#4111yescharacteristic
241C22×C11C2×#4111yescharacteristic
242C22×C11H(5,𝔽2)11yescharacteristic
243C22×C11H(5,𝔽2)11yescharacteristic
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—41no—
249C4×C11—41no—
250C4×C11—41no—
251C4×C11—41no—
252C4×C11—41no—
253C4×C11—41no—
254C4×C11—41no—
255C25C22×C1111yescharacteristic
256C22×Q8C22×C1111yescharacteristic, complemented
257C22×D4C22×C1111yescharacteristic
258C22×D4C22×C1111yescharacteristic
259C22×D4C22×C1111yescharacteristic
260C23×C4C22×C1111yescharacteristic
261C23×C4C22×C1111yescharacteristic
262#124—24no—
263C22⋊Q8—24no—
264#120—24no—
265C2×C4⋊C4C22×C1111yescharacteristic, complemented
266C2×C4⋊C4C22×C1111yescharacteristic, complemented
267C2×C4⋊C4C22×C1111yescharacteristic, complemented
268C2×C22⋊C4—24no—
269C2×C22⋊C4C22×C1111yescharacteristic
270C2×C22⋊C4C22×C1111yescharacteristic
271C2×C22⋊C4C22×C1111yescharacteristic
272C2×C22⋊C4C22×C1111yescharacteristic
273C2×C22⋊C4C22×C1111yescharacteristic
274C2×C22⋊C4C22×C1111yescharacteristic
275C2×C22⋊C4C22×C1111yescharacteristic
276C2×C22⋊C4C22×C1111yescharacteristic
277C2×C22⋊C4C22×C1111yescharacteristic
278C2×C22⋊C4C22×C1111yescharacteristic
279C2×C22⋊C4C22×C1111yescharacteristic
280C2×C22⋊C4C22×C1111yescharacteristic
281C2×C22⋊C4C22×C1111yescharacteristic
282C2×C22⋊C4C22×C1111yescharacteristic, complemented
283C2×C22⋊C4C22×C1111yescharacteristic, complemented
284C2×C22⋊C4C22×C1111yescharacteristic, complemented
285C2×C22⋊C4C22×C1111yescharacteristic, complemented
286C2×C42C22×C1111yescharacteristic, complemented
287C2×C42C22×C1111yescharacteristic, complemented
288#95C22×C1111yescharacteristic, complemented
289#95C22×C1111yescharacteristic, complemented
290#95C22×C1111yescharacteristic, complemented
291#95C22×C1111yescharacteristic, complemented
292#95C22×C1111yescharacteristic, complemented
293#95C22×C1111yescharacteristic, complemented
294C2×C11—24no—
295C2×C11—42no—
296C2×C11—42no—
297C2×C11—81no—
298C2×C11#52511yescharacteristic
299C2×C11C2×#12411yescharacteristic
300C2×C11#53811yescharacteristic
301C2×C11D4211yescharacteristic
302C2×C11#54611yescharacteristic
303C2×C11#54611yescharacteristic
304C2×C11#55111yescharacteristic
305C24—22no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—41no—
311C24—41no—
312C24C23×C1111yescharacteristic
313C24C23×C1111yescharacteristic
314C24C23×C1111yescharacteristic
315C24C23×C1111yescharacteristic
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—41no—
327C2×D4—41no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C23×C1111yescharacteristic
335C22×C4C23×C1111yescharacteristic
336C22×C4C23×C1111yescharacteristic
337C22×C4C23×C1111yescharacteristic
338C22×C4C23×C1111yescharacteristic
339C22×C4C23×C1111yescharacteristic
340C22×C4C23×C1111yescharacteristic
341C22×C4C23×C1111yescharacteristic
342C22×C4C23×C1111yescharacteristic
343C22×C4C23×C1111yescharacteristic
344C22×C4C23×C1111yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4D4×C1114yes—
364C22⋊C4D4×C1114yescomplemented
365C42—22no—
366C42—41no—
367C11#247211yescharacteristic, direct product factor, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23—44no—
398C23C2×D4×C1112yes—
399C23C2×D4×C1112yes—
400C23C11×#4112yes—
401C23C11×#4112yes—
402C23C11×#4112yes—
403C23C24×C1111yescharacteristic
404Q8—44no—
405D4—44no—
406D4—44no—
407D4—44no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4C2×D4×C1112yes—
440C2×C4C2×D4×C1112yes—
441C2×C4C2×D4×C1112yes—
442C2×C4C2×D4×C1112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22C11×#12414yescomplemented
472C22C22×D4×C1111yescharacteristic
473C22C22×D4×C1111yescharacteristic
474C22C2×C11×#4111yescharacteristic
475C22C2×C11×#4111yescharacteristic
476C22C2×C11×#4111yescharacteristic
477C22C11×H(5,𝔽2)11yescharacteristic
478C22C11×H(5,𝔽2)11yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—22no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—41no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—81no—
494C2C11×#52511yescharacteristic
495C2C2×C11×#12411yescharacteristic
496C2C11×#53811yescharacteristic
497C2D42×C1111yescharacteristic
498C2C11×#54611yescharacteristic
499C2C11×#54611yescharacteristic
500C2C11×#55111yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC2×C11×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×C11×C22⋊Q8C2semidirect
4. C22×C11×C22⋊C4C2semidirect
5. C11×#397C2semidirect
6. C11×#394C2semidirect
7. C11×#394C2semidirect
8. C11×#393C2semidirect
9. C11×#390C2semidirect
10. C11×#388C2semidirect
11. C11×#388C2semidirect
12. C11×#386C2semidirect
13. C11×#386C2semidirect
14. C11×#379C2semidirect
15. C4×C11×C22⋊C4C2semidirect
17. C22×Q8×C11C22semidirect
26. C2×C11×C4⋊C4C22semidirect
27. C2×C11×C4⋊C4C22semidirect
28. C2×C11×C4⋊C4C22semidirect
43. C2×C11×C22⋊C4C22semidirect
44. C2×C11×C22⋊C4C22semidirect
45. C2×C11×C22⋊C4C22semidirect
46. C2×C11×C22⋊C4C22semidirect
47. C2×C42×C11C22semidirect
48. C2×C42×C11C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11×#95C22semidirect
52. C11×#95C22semidirect
53. C11×#95C22semidirect
54. C11×#95C22semidirect
114. C11×C22⋊C4D4semidirect
117. #2472C11direct (N × H)
193. C2×#124C2×C11semidirect
194. C2×C22⋊Q8C2×C11semidirect
196. C22×C22⋊C4C2×C11semidirect
197. #397C2×C11semidirect
198. #394C2×C11semidirect
199. #394C2×C11semidirect
200. #393C2×C11semidirect
201. #390C2×C11semidirect
202. #388C2×C11semidirect
203. #388C2×C11semidirect
204. #386C2×C11semidirect
205. #386C2×C11semidirect
206. #379C2×C11semidirect
207. C4×C22⋊C4C2×C11semidirect
236. C22×C11#124semidirect
256. C22×Q8C22×C11semidirect
265. C2×C4⋊C4C22×C11semidirect
266. C2×C4⋊C4C22×C11semidirect
267. C2×C4⋊C4C22×C11semidirect
282. C2×C22⋊C4C22×C11semidirect
283. C2×C22⋊C4C22×C11semidirect
284. C2×C22⋊C4C22×C11semidirect
285. C2×C22⋊C4C22×C11semidirect
286. C2×C42C22×C11semidirect
287. C2×C42C22×C11semidirect
288. #95C22×C11semidirect
289. #95C22×C11semidirect
290. #95C22×C11semidirect
291. #95C22×C11semidirect
292. #95C22×C11semidirect
293. #95C22×C11semidirect
364. C22⋊C4D4×C11semidirect
367. C11#2472direct (N × H)
471. C22C11×#124semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×C11×C22⋊Q82
C2×C11×#1202
C22×C11×C22⋊C42
C11×#3972
C11×#3942
C11×#3932
C11×#3902
C11×#3882
C11×#3862
C11×#3792
C4×C11×C22⋊C42
#247211