Finite Group Databasebeta

← C11×#32905 #14610098

Subgroups — C11×#32905 #14610098

Order 2816.

1868 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C211yesmaximal, characteristic
2C2×C11×#461C212yesmaximal, complemented
3C2×C11×#450C212yesmaximal
4C11×#2857C211yesmaximal, characteristic, complemented
5C11×#1877C214yesmaximal, complemented
6C11×#1872C212yesmaximal, complemented
7C11×#1802C212yesmaximal, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11—21no—
11C22×C11×SD16C2214yes—
12C2×C11×C4⋊Q8C2211yescharacteristic, complemented
13C2×C11×C22⋊Q8C2212yes—
14C2×C4×D4×C11—28no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4—21no—
21C22×C42×C11C2211yescharacteristic
22C11×#461—28no—
23C11×#450—28no—
24C2×C11×C4⋊C8C2212yescomplemented
25C2×C11×#103C2214yescomplemented
26C2×C11×#102C2214yes—
27C2×C11×C22⋊C8C2212yes—
28C11×#391C2212yescomplemented
29C11×#389—21no—
30C11×#389—21no—
31C11×#384C2211yescharacteristic, complemented
32C11×#380—21no—
33C11×#380—21no—
34C11×#340C2214yescomplemented
35C11×#336C2212yescomplemented
36C25×C11—21no—
37C22×Q8×C11C2312yes—
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11D414yes—
43C22×D4×C11C2312yes—
44C23×C4×C11—28no—
45C23×C4×C11—21no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—44no—
49C23×C4×C11—44no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×SD16—28no—
54C2×C11×SD16—28no—
55C2×C11×SD16—28no—
56C22×C8×C11C2314yes—
57C11×C4⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—24no—
60C4×D4×C11—28no—
61C4×D4×C11—28no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C4×D4×C11D418yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—28no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11—24no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C11×C4⋊C8—24no—
85C11×#103—28no—
86C11×#102—28no—
87C11×C22⋊C8—24no—
88C11×#95—22no—
89C11×#95—22no—
90#32905C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—24no—
94C24×C11—22no—
95C24×C11—42no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11C2×D411yescharacteristic
100C2×Q8×C11—24no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—216no—
107C2×D4×C11—216no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C2×D414yes—
113C2×D4×C11C2×D414yes—
114C2×D4×C11#4114yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—28no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—41no—
128C22×C4×C11—44no—
129C22×C4×C11—432no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11—44no—
135C22×C4×C11SD1614yescomplemented
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C11×SD16—416no—
145C2×C8×C11—24no—
146C2×C8×C11—24no—
147C2×C8×C11—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—44no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4C2×D414yes—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—44no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11C2×D414yes—
165C22×C4×D4C2×C1111yescharacteristic
166C2×#461C2×C1112yescomplemented
167C2×#450C2×C1112yes—
168#2857C2×C1111yescharacteristic, complemented
169#1877C2×C1114yescomplemented
170#1872C2×C1112yescomplemented
171#1802C2×C1112yescomplemented
172#1797C2×C1111yescharacteristic, complemented
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—216no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—48no—
182C23×C11—48no—
183C23×C11—48no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—48no—
191C23×C11#12112yes—
192C23×C11C2×SD1612yes—
193C23×C11#13712yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—44no—
196Q8×C11—44no—
197D4×C11—216no—
198D4×C11—24no—
199D4×C11—24no—
200D4×C11—24no—
201D4×C11#12118yes—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—28no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—44no—
216C2×C4×C11—416no—
217C2×C4×C11—48no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—416no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11#12112yes—
230C2×C4×C11C2×SD1612yes—
231C2×C4×C11C2×SD1612yes—
232C2×C4×C11AGL(1,ℤ/8)12yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C11C2×#4111yescharacteristic
237C8×C11—44no—
238C23×D4C22×C1111yescharacteristic
239C24×C4—21no—
240C22×SD16C22×C1114yes—
241C2×C4⋊Q8C22×C1111yescharacteristic, complemented
242C2×C22⋊Q8C22×C1112yes—
243C2×C4×D4—28no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C22×C1112yes—
247C2×C4×D4C22×C1112yes—
248C22×C4⋊C4C22×C1111yescharacteristic
249C22×C22⋊C4—21no—
250C22×C42C22×C1111yescharacteristic
251#461—28no—
252#450—28no—
253C2×C4⋊C8C22×C1112yescomplemented
254C2×#103C22×C1114yescomplemented
255C2×#102C22×C1114yes—
256C2×C22⋊C8C22×C1112yes—
257#391C22×C1112yescomplemented
258#389—21no—
259#389—21no—
260#384C22×C1111yescharacteristic, complemented
261#380—21no—
262#380—21no—
263#340C22×C1114yescomplemented
264#336C22×C1112yescomplemented
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—28no—
272C22×C11—432no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11#46114yescomplemented
280C22×C11C2×#12011yescharacteristic
281C22×C11C2×#12111yescharacteristic
282C22×C11#52511yescharacteristic
283C22×C11C22×SD1611yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11#57511yescharacteristic
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—44no—
291C4×C11—41no—
292C4×C11—82no—
293C4×C11—82no—
294C4×C11#45014yescomplemented
295C4×C11C2×#12112yes—
296C4×C11#52512yes—
297C25—21no—
298C22×Q8C23×C1112yes—
299C22×D4—24no—
300C22×D4—24no—
301C22×D4—21no—
302C22×D4—22no—
303C22×D4D4×C1114yes—
304C22×D4C23×C1112yes—
305C23×C4—28no—
306C23×C4—21no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—44no—
310C23×C4—44no—
311C23×C4D4×C1111yescharacteristic
312C23×C4D4×C1111yescharacteristic
313C23×C4C23×C1111yescharacteristic
314C2×SD16—28no—
315C2×SD16—28no—
316C2×SD16—28no—
317C22×C8C23×C1114yes—
318C4⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C4×D4—28no—
322C4×D4—28no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4D4×C1118yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4C23×C1112yes—
335C2×C4⋊C4C23×C1112yes—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C42—24no—
341C2×C42D4×C1111yescharacteristic
342C2×C42D4×C1111yescharacteristic
343C2×C42C23×C1111yescharacteristic
344C2×C42C23×C1111yescharacteristic
345C4⋊C8—24no—
346#103—28no—
347#102—28no—
348C22⋊C8—24no—
349#95—22no—
350#95—22no—
351C2×C11—24no—
352C2×C11—48no—
353C2×C11#284711yescharacteristic
354C2×C11C2×#45011yescharacteristic
355C2×C11#300711yescharacteristic
356C2×C11C2×#46111yescharacteristic
357C2×C11#303611yescharacteristic
358C2×C11#310111yescharacteristic
359C2×C11#311011yescharacteristic
360C24—24no—
361C24—24no—
362C24—24no—
363C24—22no—
364C24—42no—
365C24—42no—
366C24—42no—
367C24—42no—
368C24C2×D4×C1111yescharacteristic
369C2×Q8—24no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—24no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—216no—
376C2×D4—216no—
377C2×D4—24no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4C2×D4×C1114yes—
382C2×D4C2×D4×C1114yes—
383C2×D4C11×#4114yes—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—28no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—28no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—44no—
398C22×C4—432no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4C11×SD1614yescomplemented
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1112yes—
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C11×#4112yes—
412C22×C4C24×C1111yescharacteristic
413SD16—416no—
414C2×C8—24no—
415C2×C8—24no—
416C2×C8—24no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—44no—
425C4⋊C4—42no—
426C4⋊C4C2×D4×C1114yes—
427C22⋊C4—28no—
428C22⋊C4—28no—
429C22⋊C4—44no—
430C42—22no—
431C42—22no—
432C42—22no—
433C42C2×D4×C1114yes—
434C11#3290511yescharacteristic, direct product factor, Sylow
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—216no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—48no—
444C23—48no—
445C23—48no—
446C23—48no—
447C23—48no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—48no—
453C23C11×#12112yes—
454C23C2×C11×SD1612yes—
455C23C11×#13712yes—
456C23C22×D4×C1111yescharacteristic
457Q8—44no—
458Q8—44no—
459D4—216no—
460D4—24no—
461D4—24no—
462D4—24no—
463D4C11×#12118yes—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—28no—
473C2×C4—21no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—44no—
478C2×C4—416no—
479C2×C4—48no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—416no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4C11×#12012yes—
490C2×C4C11×#12012yes—
491C2×C4C11×#12112yes—
492C2×C4C2×C11×SD1612yes—
493C2×C4C2×C11×SD1612yes—
494C2×C4C11×AGL(1,ℤ/8)12yes—
495C2×C4C22×D4×C1111yescharacteristic
496C2×C4C22×D4×C1112yes—
497C2×C4C2×C11×#4112yes—
498C2×C4C2×C11×#4111yescharacteristic
499C8—44no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—28no—
507C22—432no—
508C22—44no—
509C22—44no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22C11×#46114yescomplemented
515C22C2×C11×#12011yescharacteristic
516C22C2×C11×#12111yescharacteristic
517C22C11×#52511yescharacteristic
518C22C22×C11×SD1611yescharacteristic
519C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
520C22C2×C11×#13711yescharacteristic
521C22C11×#57511yescharacteristic
522C4—22no—
523C4—22no—
524C4—22no—
525C4—44no—
526C4—41no—
527C4—82no—
528C4—82no—
529C4C11×#45014yescomplemented
530C4C2×C11×#12112yes—
531C4C11×#52512yes—
532C2—24no—
533C2—48no—
534C2C11×#284711yescharacteristic
535C2C2×C11×#45011yescharacteristic
536C2C11×#300711yescharacteristic
537C2C2×C11×#46111yescharacteristic
538C2C11×#303611yescharacteristic
539C2C11×#310111yescharacteristic
540C2C11×#311011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#461C2semidirect
4. C11×#2857C2semidirect
5. C11×#1877C2semidirect
6. C11×#1872C2semidirect
7. C11×#1802C2semidirect
8. C11×#1797C2semidirect
12. C2×C11×C4⋊Q8C22semidirect
24. C2×C11×C4⋊C8C22semidirect
25. C2×C11×#103C22semidirect
28. C11×#391C22semidirect
31. C11×#384C22semidirect
34. C11×#340C22semidirect
35. C11×#336C22semidirect
90. #32905C11direct (N × H)
135. C22×C4×C11SD16semidirect
166. C2×#461C2×C11semidirect
168. #2857C2×C11semidirect
169. #1877C2×C11semidirect
170. #1872C2×C11semidirect
171. #1802C2×C11semidirect
172. #1797C2×C11semidirect
241. C2×C4⋊Q8C22×C11semidirect
253. C2×C4⋊C8C22×C11semidirect
254. C2×#103C22×C11semidirect
257. #391C22×C11semidirect
260. #384C22×C11semidirect
263. #340C22×C11semidirect
264. #336C22×C11semidirect
279. C22×C11#461semidirect
294. C4×C11#450semidirect
404. C22×C4C11×SD16semidirect
434. C11#32905direct (N × H)
514. C22C11×#461semidirect
529. C4C11×#450semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C112
C2×C11×#4612
C2×C11×#4502
C11×#28572
C11×#18772
C11×#18722
C11×#18022
C11×#17972
#3290511