Finite Group Databasebeta

← C11×#21766 #14598959

Subgroups — C11×#21766 #14598959

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C2×C11×#407C211yesmaximal, characteristic, complemented
3C11×#2280C211yesmaximal, characteristic, complemented
4C11×#1895C212yesmaximal, complemented
5C11×#1894C212yesmaximal, complemented
6C11×#1875C212yesmaximal, complemented
7C11×#1873C212yesmaximal, complemented
8C11×#1825C212yesmaximal, complemented
9C11×#1788C212yesmaximal, complemented
10C22×C11×#41C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C11×M16C2212yes—
13C11×#525—24no—
14C11×#525C418yescomplemented
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C11×#117C2211yescharacteristic
24C2×C11×#117C2212yes—
25C2×C11×#103C2214yescomplemented
26C2×C11×#102C2214yescomplemented
27C11×#407—24no—
28C2×C11×C22⋊C8C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C11×#381—21no—
31C11×#380C2212yes—
32C11×#380C2212yes—
33C11×#379—21no—
34C4×C11×C22⋊C4—21no—
35C4×C11×C22⋊C4—21no—
36C11×#340C2214yescomplemented
37C11×#340C2214yescomplemented
38C25×C11D411yescharacteristic
39C2×C11×#41—22no—
40C2×C11×#41—44no—
41C2×C11×#41C2×C414yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—44no—
49C23×C4×C11C2×C414yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C2×C11×M16—24no—
58C2×C11×M16—44no—
59C22×C8×C11C2314yes—
60C11×#123—28no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8C2×C414yes—
64C11×C22⋊Q8C2×C414yes—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121C2×C414yes—
68C11×#121C2×C414yes—
69C11×#120—28no—
70C4×D4×C11—28no—
71C4×D4×C11—28no—
72C11×#117—22no—
73C11×#117—44no—
74C11×#117C2×C414yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11—21no—
89C2×C42×C11—22no—
90C11×#103—44no—
91C11×#102—44no—
92C11×C22⋊C8—24no—
93C11×C22⋊C8—24no—
94C11×#95—22no—
95C11×#95—22no—
96#21766C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11C22⋊C414yes—
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D411yescharacteristic
105C11×#41—48no—
106C11×#41—48no—
107C2×Q8×C11—21no—
108C2×Q8×C11—24no—
109C2×Q8×C11C22×C412yes—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—21no—
114C2×D4×C11—24no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11C22×C412yes—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—48no—
128C22×C4×C11—48no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—44no—
133C22×C4×C11C22⋊C414yes—
134C22×C4×C11C22⋊C414yes—
135C22×C4×C11C22⋊C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C11×M16—48no—
147C2×C8×C11—24no—
148C2×C8×C11—24no—
149C2×C8×C11—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4C22×C412yes—
157C11×C4⋊C4C22×C412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4—44no—
166C42×C11—24no—
167C42×C11—44no—
168C2×#525C2×C1111yescharacteristic
169C2×#407C2×C1111yescharacteristic, complemented
170#2280C2×C1111yescharacteristic, complemented
171#1895C2×C1112yescomplemented
172#1894C2×C1112yescomplemented
173#1875C2×C1112yescomplemented
174#1873C2×C1112yescomplemented
175#1825C2×C1112yescomplemented
176#1788C2×C1112yescomplemented
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—416no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11C2×C22⋊C412yes—
195C23×C11C2×C22⋊C412yes—
196C23×C11C2×C22⋊C412yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—24no—
199Q8×C11—42no—
200D4×C11—24no—
201D4×C11—48no—
202D4×C11—48no—
203D4×C11—48no—
204D4×C11—42no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11H(5,𝔽2)14yes—
233C8×C11—44no—
234C22×#41C22×C1111yescharacteristic
235C24×C4C22×C1111yescharacteristic
236C22×M16C22×C1112yes—
237#525—24no—
238#525C4×C1118yescomplemented
239C2×#123—21no—
240C2×C22⋊Q8C22×C1111yescharacteristic
241C2×C22⋊Q8C22×C1111yescharacteristic
242C2×#121C22×C1111yescharacteristic
243C2×#121C22×C1111yescharacteristic
244C2×#120—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×#117C22×C1111yescharacteristic
248C2×#117C22×C1112yes—
249C2×#103C22×C1114yescomplemented
250C2×#102C22×C1114yescomplemented
251#407—24no—
252C2×C22⋊C8C22×C1112yes—
253C2×C22⋊C8C22×C1112yes—
254#381—21no—
255#380C22×C1112yes—
256#380C22×C1112yes—
257#379—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260#340C22×C1114yescomplemented
261#340C22×C1114yescomplemented
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—416no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—84no—
279C22×C11C22×C22⋊C411yescharacteristic
280C22×C11#53412yes—
281C22×C11#57512yes—
282C22×C11#57512yes—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—84no—
290C4×C11#51812yes—
291C4×C11#53412yes—
292C25D4×C1111yescharacteristic
293C2×#41—22no—
294C2×#41—44no—
295C2×#41C2×C4×C1114yes—
296C22×Q8C23×C1111yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C23×C1111yescharacteristic
301C23×C4—21no—
302C23×C4—44no—
303C23×C4C2×C4×C1114yes—
304C23×C4D4×C1111yescharacteristic
305C23×C4D4×C1111yescharacteristic
306C23×C4D4×C1111yescharacteristic
307C23×C4D4×C1114yes—
308C23×C4C23×C1111yescharacteristic
309C23×C4C23×C1111yescharacteristic
310C23×C4C23×C1111yescharacteristic
311C2×M16—24no—
312C2×M16—44no—
313C22×C8C23×C1114yes—
314#123—28no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8C2×C4×C1114yes—
318C22⋊Q8C2×C4×C1114yes—
319#121—22no—
320#121—22no—
321#121C2×C4×C1114yes—
322#121C2×C4×C1114yes—
323#120—28no—
324C4×D4—28no—
325C4×D4—28no—
326#117—22no—
327#117—44no—
328#117C2×C4×C1114yes—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4C23×C1114yes—
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C42—21no—
343C2×C42—22no—
344#103—44no—
345#102—44no—
346C22⋊C8—24no—
347C22⋊C8—24no—
348#95—22no—
349#95—22no—
350C2×C11—42no—
351C2×C11—42no—
352C2×C11—42no—
353C2×C11—82no—
354C2×C11#230811yescharacteristic
355C2×C11#289611yescharacteristic
356C2×C11#289611yescharacteristic
357C2×C11#319714yes—
358C24—21no—
359C24—42no—
360C24—42no—
361C24—42no—
362C24C11×C22⋊C414yes—
363C24C2×D4×C1111yescharacteristic
364C24C2×D4×C1111yescharacteristic
365C24C2×D4×C1111yescharacteristic
366#41—48no—
367#41—48no—
368C2×Q8—21no—
369C2×Q8—24no—
370C2×Q8C22×C4×C1112yes—
371C2×D4—24no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—21no—
375C2×D4—24no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—44no—
379C2×D4C22×C4×C1112yes—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—48no—
389C22×C4—48no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—44no—
394C22×C4C11×C22⋊C414yes—
395C22×C4C11×C22⋊C414yes—
396C22×C4C11×C22⋊C414yes—
397C22×C4C22×C4×C1112yes—
398C22×C4C22×C4×C1112yes—
399C22×C4C22×C4×C1112yes—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1112yes—
404C22×C4C2×D4×C1112yes—
405C22×C4C2×D4×C1112yes—
406C22×C4C24×C1111yescharacteristic
407M16—48no—
408C2×C8—24no—
409C2×C8—24no—
410C2×C8—24no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4C22×C4×C1112yes—
418C4⋊C4C22×C4×C1112yes—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—44no—
425C22⋊C4—44no—
426C22⋊C4—44no—
427C42—24no—
428C42—44no—
429C11#2176611yescharacteristic, direct product factor, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—416no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23C2×C11×C22⋊C412yes—
448C23C2×C11×C22⋊C412yes—
449C23C2×C11×C22⋊C412yes—
450C23C22×D4×C1111yescharacteristic
451Q8—24no—
452Q8—42no—
453D4—24no—
454D4—48no—
455D4—48no—
456D4—48no—
457D4—42no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4C2×C11×C22⋊C412yes—
481C2×C4C2×C11×C22⋊C412yes—
482C2×C4C2×C11×C22⋊C412yes—
483C2×C4C23×C4×C1111yescharacteristic
484C2×C4C22×D4×C1111yescharacteristic
485C2×C4C11×H(5,𝔽2)14yes—
486C8—44no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—416no—
497C22—44no—
498C22—44no—
499C22—44no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—84no—
504C22C22×C11×C22⋊C411yescharacteristic
505C22C11×#53412yes—
506C22C11×#57512yes—
507C22C11×#57512yes—
508C4—22no—
509C4—22no—
510C4—22no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—84no—
515C4C11×#51812yes—
516C4C11×#53412yes—
517C2—42no—
518C2—42no—
519C2—42no—
520C2—82no—
521C2C11×#230811yescharacteristic
522C2C11×#289611yescharacteristic
523C2C11×#289611yescharacteristic
524C2C11×#319714yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#407C2semidirect
3. C11×#2280C2semidirect
4. C11×#1895C2semidirect
5. C11×#1894C2semidirect
6. C11×#1875C2semidirect
7. C11×#1873C2semidirect
8. C11×#1825C2semidirect
9. C11×#1788C2semidirect
14. C11×#525C4semidirect
25. C2×C11×#103C22semidirect
26. C2×C11×#102C22semidirect
36. C11×#340C22semidirect
37. C11×#340C22semidirect
96. #21766C11direct (N × H)
169. C2×#407C2×C11semidirect
170. #2280C2×C11semidirect
171. #1895C2×C11semidirect
172. #1894C2×C11semidirect
173. #1875C2×C11semidirect
174. #1873C2×C11semidirect
175. #1825C2×C11semidirect
176. #1788C2×C11semidirect
238. #525C4×C11semidirect
249. C2×#103C22×C11semidirect
250. C2×#102C22×C11semidirect
260. #340C22×C11semidirect
261. #340C22×C11semidirect
429. C11#21766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C2×C11×#4072
C11×#22802
C11×#18952
C11×#18942
C11×#18752
C11×#18732
C11×#18252
C11×#17882
#2176611