Finite Group Databasebeta

← C11×#22504 #14599697

Subgroups — C11×#22504 #14599697

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C11×#436C211yesmaximal, characteristic
3D4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1988C211yesmaximal, characteristic, complemented
6C11×#1894C212yesmaximal, complemented
7C11×#1872C212yesmaximal, complemented
8C11×#1825C212yesmaximal, complemented
9C11×#1803C211yesmaximal, characteristic, complemented
10C4×C11×#103C211yesmaximal, characteristic, complemented
11C11×#1736C212yesmaximal, complemented
12C22×C11×M16C2212yes—
13C11×#556—24no—
14C11×#556C418yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2212yes—
24C22×C11×C4⋊C4C2212yes—
25C11×#436—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#389—21no—
33C11×#385—22no—
34C11×#384C2211yescharacteristic
35C11×#380C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11C2312yes—
49C2×C11×M16—24no—
50C2×C11×M16—24no—
51C2×C11×M16—42no—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8C2×C414yescomplemented
57C11×#126—216no—
58C11×#124—28no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8C2×C418yescomplemented
61C4×Q8×C11—28no—
62C4×Q8×C11—22no—
63C4×Q8×C11C2×C414yescomplemented
64C4×D4×C11—44no—
65C4×D4×C11C2×C414yes—
66C4×D4×C11D414yes—
67C11×#117—24no—
68C11×#117C2×C418yescomplemented
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—42no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—22no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C11×C4⋊C8—22no—
92C11×#103—22no—
93C11×#103—22no—
94C11×#103—42no—
95C11×C22⋊C8—24no—
96C4×C8×C11—22no—
97C11×#95—21no—
98C11×#95—22no—
99#22504C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2×D412yes—
101C2×Q8×C11—24no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11C22×C412yes—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22⋊C414yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—44no—
124C22×C4×C11—44no—
125C22×C4×C11—82no—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C11×M16—48no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11#4112yes—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—81no—
155C11×C4⋊C4C22⋊C414yes—
156C11×C4⋊C4C22×C412yes—
157C11×C4⋊C4C22×C414yes—
158C11×C4⋊C4#4112yes—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4C22⋊C418yes—
163C42×C11—28no—
164C42×C11—24no—
165C42×C11—42no—
166C42×C11C22×C412yes—
167C42×C11C2×D412yes—
168C2×#556C2×C1111yescharacteristic
169C2×#436C2×C1111yescharacteristic
170D4×C4⋊C4C2×C1111yescharacteristic
171#1990C2×C1111yescharacteristic, complemented
172#1988C2×C1111yescharacteristic, complemented
173#1894C2×C1112yescomplemented
174#1872C2×C1112yescomplemented
175#1825C2×C1112yescomplemented
176#1803C2×C1111yescharacteristic, complemented
177C4×#103C2×C1111yescharacteristic, complemented
178#1736C2×C1112yescomplemented
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11C2×C22⋊C414yes—
186C23×C11C22×D411yescharacteristic
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11—48no—
192D4×C11—28no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—88no—
220C2×C4×C11C2×C22⋊C414yes—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C8×C11—22no—
232C8×C11—42no—
233C8×C11—41no—
234C22×M16C22×C1112yes—
235#556—24no—
236#556C4×C1118yescomplemented
237C2×C4⋊Q8C22×C1111yescharacteristic
238C2×#126—22no—
239C2×#124—21no—
240C2×C22⋊Q8C22×C1112yes—
241C2×C4×Q8—21no—
242C2×C4×Q8C22×C1111yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4C22×C1111yescharacteristic
245C2×#117C22×C1112yes—
246C22×C4⋊C4C22×C1112yes—
247#436—24no—
248C2×C4⋊C8C22×C1111yescharacteristic
249C2×#103C22×C1111yescharacteristic
250C2×#103C22×C1111yescharacteristic
251C2×#103C22×C1112yes—
252C2×C22⋊C8C22×C1112yes—
253C2×C4×C8C22×C1111yescharacteristic
254#389—21no—
255#385—22no—
256#384C22×C1111yescharacteristic
257#380C22×C1112yes—
258C4×C4⋊C4C22×C1111yescharacteristic
259#340C22×C1112yes—
260#340C22×C1111yescharacteristic
261#340C22×C1112yes—
262#340C22×C1112yes—
263#340C22×C1112yes—
264#340C22×C1112yes—
265#340C22×C1111yescharacteristic
266C22×C11—24no—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11C22×C22⋊C411yescharacteristic
274C22×C11#54611yescharacteristic
275C22×C11#54711yescharacteristic
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11C2×#13711yescharacteristic
278C22×C11#57711yescharacteristic
279C22×C11#57811yescharacteristic
280C4×C11—24no—
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—81no—
287C4×C11—82no—
288C4×C11#41714yes—
289C4×C11C4×#4111yescharacteristic
290C4×C11#52011yescharacteristic
291C4×C11#54611yescharacteristic
292C4×C11#54711yescharacteristic
293C22×Q8—21no—
294C22×Q8C23×C1111yescharacteristic
295C22×D4D4×C1111yescharacteristic
296C23×C4—22no—
297C23×C4C23×C1112yes—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16—42no—
301C22×C8C23×C1112yes—
302C22×C8C23×C1111yescharacteristic
303C22×C8C23×C1111yescharacteristic
304C4⋊Q8—22no—
305C4⋊Q8C2×C4×C1114yescomplemented
306#126—216no—
307#124—28no—
308C22⋊Q8—24no—
309C22⋊Q8C2×C4×C1118yescomplemented
310C4×Q8—28no—
311C4×Q8—22no—
312C4×Q8C2×C4×C1114yescomplemented
313C4×D4—44no—
314C4×D4C2×C4×C1114yes—
315C4×D4D4×C1114yes—
316#117—24no—
317#117C2×C4×C1118yescomplemented
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4D4×C1111yescharacteristic
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C4⋊C4C23×C1112yes—
331C2×C4⋊C4C23×C1111yescharacteristic
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4D4×C1112yes—
336C2×C42—22no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42C23×C1111yescharacteristic
340C4⋊C8—22no—
341#103—22no—
342#103—22no—
343#103—42no—
344C22⋊C8—24no—
345C4×C8—22no—
346#95—21no—
347#95—22no—
348C2×C11—44no—
349C2×C11#233911yescharacteristic
350C2×C11C2×#41711yescharacteristic
351C2×C11#289811yescharacteristic
352C2×C11#332411yescharacteristic
353C2×C11#332811yescharacteristic
354C2×C11#335311yescharacteristic
355C2×C11#335611yescharacteristic
356C24C2×D4×C1112yes—
357C2×Q8—24no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×Q8C22×C4×C1112yes—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4C11×C22⋊C414yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—44no—
380C22×C4—44no—
381C22×C4—82no—
382C22×C4C22×C4×C1114yes—
383C22×C4C2×D4×C1112yes—
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1114yes—
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C24×C1111yescharacteristic
388M16—48no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—22no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—21no—
397C2×C8C11×#4112yes—
398C4⋊C4—28no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—44no—
409C4⋊C4—42no—
410C4⋊C4—81no—
411C4⋊C4C11×C22⋊C414yes—
412C4⋊C4C22×C4×C1112yes—
413C4⋊C4C22×C4×C1114yes—
414C4⋊C4C11×#4112yes—
415C22⋊C4—28no—
416C22⋊C4—28no—
417C22⋊C4—44no—
418C22⋊C4C11×C22⋊C418yes—
419C42—28no—
420C42—24no—
421C42—42no—
422C42C22×C4×C1112yes—
423C42C2×D4×C1112yes—
424C11#2250411yescharacteristic, direct product factor, Sylow
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23C2×C11×C22⋊C414yes—
432C23C22×D4×C1111yescharacteristic
433Q8—22no—
434Q8—22no—
435Q8—41no—
436Q8—41no—
437Q8—48no—
438D4—28no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—88no—
466C2×C4C2×C11×C22⋊C414yes—
467C2×C4C2×C11×C22⋊C412yes—
468C2×C4C2×C11×C22⋊C412yes—
469C2×C4C11×AGL(1,ℤ/8)12yes—
470C2×C4C11×#13712yes—
471C2×C4C23×C4×C1111yescharacteristic
472C2×C4C22×D4×C1111yescharacteristic
473C2×C4C2×C11×#4111yescharacteristic
474C2×C4C2×C11×#4111yescharacteristic
475C2×C4C11×H(5,𝔽2)11yescharacteristic
476C2×C4C11×2−1+411yescharacteristic
477C8—22no—
478C8—42no—
479C8—41no—
480C22—24no—
481C22—24no—
482C22—24no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22C22×C11×C22⋊C411yescharacteristic
488C22C11×#54611yescharacteristic
489C22C11×#54711yescharacteristic
490C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
491C22C2×C11×#13711yescharacteristic
492C22C11×#57711yescharacteristic
493C22C11×#57811yescharacteristic
494C4—22no—
495C4—24no—
496C4—44no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—82no—
501C4—81no—
502C4C11×#41714yes—
503C4C4×C11×#4111yescharacteristic
504C4C11×#52011yescharacteristic
505C4C11×#54611yescharacteristic
506C4C11×#54711yescharacteristic
507C2—44no—
508C2C11×#233911yescharacteristic
509C2C2×C11×#41711yescharacteristic
510C2C11×#289811yescharacteristic
511C2C11×#332411yescharacteristic
512C2C11×#332811yescharacteristic
513C2C11×#335311yescharacteristic
514C2C11×#335611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1990C2semidirect
5. C11×#1988C2semidirect
6. C11×#1894C2semidirect
7. C11×#1872C2semidirect
8. C11×#1825C2semidirect
9. C11×#1803C2semidirect
10. C4×C11×#103C2semidirect
11. C11×#1736C2semidirect
14. C11×#556C4semidirect
56. C11×C4⋊Q8C2×C4semidirect
60. C11×C22⋊Q8C2×C4semidirect
63. C4×Q8×C11C2×C4semidirect
68. C11×#117C2×C4semidirect
99. #22504C11direct (N × H)
171. #1990C2×C11semidirect
172. #1988C2×C11semidirect
173. #1894C2×C11semidirect
174. #1872C2×C11semidirect
175. #1825C2×C11semidirect
176. #1803C2×C11semidirect
177. C4×#103C2×C11semidirect
178. #1736C2×C11semidirect
236. #556C4×C11semidirect
305. C4⋊Q8C2×C4×C11semidirect
309. C22⋊Q8C2×C4×C11semidirect
312. C4×Q8C2×C4×C11semidirect
317. #117C2×C4×C11semidirect
424. C11#22504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4362
D4×C11×C4⋊C42
C11×#19902
C11×#19882
C11×#18942
C11×#18722
C11×#18252
C11×#18032
C4×C11×#1032
C11×#17362
#2250411