Finite Group Databasebeta

← C11×#19051 #14596244

Subgroups — C11×#19051 #14596244

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3545C211yesmaximal, characteristic
2C11×#3238C212yesmaximal, complemented
3C2×C11×#497C211yesmaximal, characteristic, complemented
4C11×#1661C214yesmaximal, complemented
5C11×#1660C212yesmaximal, complemented
6C11×#1659C212yesmaximal, complemented
7C11×#1533C211yesmaximal, characteristic, complemented
8C11×#1532C212yesmaximal, complemented
9C22×C11×Q16—21no—
10C22×C11×SD16—21no—
11C11×#563C2211yescharacteristic
12C11×#562C2212yes—
13C11×H(3,𝔽4)C2211yescharacteristic
14C11×#555—21no—
15C11×#551—21no—
16C11×#551—22no—
17C11×#546—22no—
18C11×#542—22no—
19C11×#538—22no—
20C11×#536—21no—
21C11×#534—21no—
22C2×C11×C4⋊Q8C2211yescharacteristic, complemented
23C11×#529C2212yes—
24C2×C11×#124C2211yescharacteristic
25C11×#501C2214yescomplemented
26C11×#497—21no—
27C11×#497—21no—
28C11×#497C2212yes—
29C11×#497C2212yescomplemented
30C11×#489C2214yescomplemented
31C11×#483—22no—
32C11×#480—22no—
33C11×#477—22no—
34C11×#476—22no—
35C11×#432C2212yescomplemented
36C2×C11×#97C2211yescharacteristic, complemented
37C11×#330C2214yescomplemented
38C11×#329C2212yes—
39C11×#329C2214yescomplemented
40C11×#329C2212yescomplemented
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11D411yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16—44no—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×SD16—44no—
52C22×C8×C11—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2312yes—
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125C2312yes—
62C11×#124—21no—
63C11×#124—22no—
64C11×#124—21no—
65C11×#124—22no—
66C11×#124—22no—
67C11×#124D411yescharacteristic
68C11×#124D411yescharacteristic
69C11×#124C2312yes—
70C11×#124C2311yescharacteristic
71C11×#124C2311yescharacteristic
72C11×#123—21no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—21no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8D412yes—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121D412yes—
89C11×#120—21no—
90C11×#120—22no—
91C11×#120—21no—
92C11×#120—22no—
93C4×Q8×C11D412yes—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11D412yes—
98C11×#117—21no—
99C11×#117—22no—
100C11×#117—22no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C42×C11C2311yescharacteristic
106C11×#107—24no—
107C11×#106—24no—
108C11×C4⋊C8—22no—
109C11×#103—24no—
110C11×#102—24no—
111C11×C22⋊C8—22no—
112C11×#97—21no—
113C11×#97C2314yes—
114C11×#97C2312yes—
115#19051C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C24×C11—21no—
118C11×#41—82no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—22no—
122C2×Q8×C11—42no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C2×Q8×C11—41no—
126C2×Q8×C11C2×D412yes—
127C2×Q8×C11C2×D411yescharacteristic
128C2×Q8×C11C2×D411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—42no—
136C2×D4×C11—82no—
137C2×D4×C11C2×D412yes—
138C2×D4×C11C2×D411yescharacteristic
139C2×D4×C11C2×D411yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—41no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C11×Q16—44no—
149C11×Q16—44no—
150C11×SD16—44no—
151C11×SD16—44no—
152C2×C8×C11—24no—
153C2×C8×C11—22no—
154C2×C8×C11—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—22no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D412yes—
186C42×C11C2411yescharacteristic
187#3545C2×C1111yescharacteristic
188#3238C2×C1112yescomplemented
189C2×#497C2×C1111yescharacteristic, complemented
190#1661C2×C1114yescomplemented
191#1660C2×C1112yescomplemented
192#1659C2×C1112yescomplemented
193#1533C2×C1111yescharacteristic, complemented
194#1532C2×C1112yescomplemented
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—42no—
199C23×C11—82no—
200C23×C11—81no—
201C23×C11—82no—
202C23×C11#12011yescharacteristic
203Q8×C11—41no—
204Q8×C11—41no—
205Q8×C11—42no—
206Q8×C11—42no—
207Q8×C11—42no—
208Q8×C11—81no—
209Q8×C11—82no—
210Q8×C11—81no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—42no—
214D4×C11—44no—
215D4×C11—81no—
216D4×C11—82no—
217D4×C11—82no—
218D4×C11—82no—
219D4×C11—81no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—82no—
230C2×C4×C11—82no—
231C2×C4×C11—81no—
232C2×C4×C11—82no—
233C2×C4×C11—82no—
234C2×C4×C11#12012yes—
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D411yescharacteristic
238C8×C11—24no—
239C8×C11—44no—
240C22×Q16—21no—
241C22×SD16—21no—
242#563C22×C1111yescharacteristic
243#562C22×C1112yes—
244H(3,𝔽4)C22×C1111yescharacteristic
245#555—21no—
246#551—21no—
247#551—22no—
248#546—22no—
249#542—22no—
250#538—22no—
251#536—21no—
252#534—21no—
253C2×C4⋊Q8C22×C1111yescharacteristic, complemented
254#529C22×C1112yes—
255C2×#124C22×C1111yescharacteristic
256#501C22×C1114yescomplemented
257#497—21no—
258#497—21no—
259#497C22×C1112yes—
260#497C22×C1112yescomplemented
261#489C22×C1114yescomplemented
262#483—22no—
263#480—22no—
264#477—22no—
265#476—22no—
266#432C22×C1112yescomplemented
267C2×#97C22×C1111yescharacteristic, complemented
268#330C22×C1114yescomplemented
269#329C22×C1112yes—
270#329C22×C1114yescomplemented
271#329C22×C1112yescomplemented
272C22×C11—22no—
273C22×C11—42no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—162no—
281C22×C11—162no—
282C22×C11#45312yes—
283C22×C11C2×#12011yescharacteristic
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—41no—
289C4×C11—41no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—82no—
294C2×#41—21no—
295C22×Q8—21no—
296C22×Q8D4×C1111yescharacteristic
297C22×D4—21no—
298C22×D4D4×C1111yescharacteristic
299C2×Q16—22no—
300C2×Q16—22no—
301C2×Q16—44no—
302C2×SD16—22no—
303C2×SD16—22no—
304C2×SD16—44no—
305C22×C8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—22no—
309C4⋊Q8—21no—
310C4⋊Q8C23×C1112yes—
311#126—22no—
312#126—22no—
313#126—22no—
314#125C23×C1112yes—
315#124—21no—
316#124—22no—
317#124—21no—
318#124—22no—
319#124—22no—
320#124D4×C1111yescharacteristic
321#124D4×C1111yescharacteristic
322#124C23×C1111yescharacteristic
323#124C23×C1111yescharacteristic
324#124C23×C1112yes—
325#123—21no—
326#123—22no—
327#123—22no—
328#123—21no—
329#123—22no—
330#123—22no—
331#123—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8D4×C1112yes—
337#121—22no—
338#121—22no—
339#121—22no—
340#121—22no—
341#121D4×C1112yes—
342#120—21no—
343#120—22no—
344#120—21no—
345#120—22no—
346C4×Q8D4×C1112yes—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4D4×C1112yes—
351#117—21no—
352#117—22no—
353#117—22no—
354C2×C4⋊C4—22no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C42C23×C1111yescharacteristic
359#107—24no—
360#106—24no—
361C4⋊C8—22no—
362#103—24no—
363#102—24no—
364C22⋊C8—22no—
365#97—21no—
366#97C23×C1114yes—
367#97C23×C1112yes—
368C2×C11—22no—
369C2×C11—82no—
370C2×C11—81no—
371C2×C11—81no—
372C2×C11C2×#45311yescharacteristic
373C2×C11#302212yes—
374C24—21no—
375C24—21no—
376#41—82no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×Q8—42no—
383C2×Q8—41no—
384C2×Q8C2×D4×C1112yes—
385C2×Q8C2×D4×C1111yescharacteristic
386C2×Q8C2×D4×C1111yescharacteristic
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4—82no—
395C2×D4C2×D4×C1112yes—
396C2×D4C2×D4×C1111yescharacteristic
397C2×D4C2×D4×C1111yescharacteristic
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C2×D4×C1112yes—
406Q16—44no—
407Q16—44no—
408SD16—44no—
409SD16—44no—
410C2×C8—24no—
411C2×C8—22no—
412C2×C8—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—24no—
421C4⋊C4—42no—
422C4⋊C4C2×D4×C1112yes—
423C4⋊C4C2×D4×C1112yes—
424C22⋊C4—22no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C42—21no—
440C42—21no—
441C42—22no—
442C42C2×D4×C1111yescharacteristic
443C42C2×D4×C1112yes—
444C42C24×C1111yescharacteristic
445C11#1905111yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—22no—
448C23—21no—
449C23—42no—
450C23—82no—
451C23—81no—
452C23—82no—
453C23C11×#12011yescharacteristic
454Q8—41no—
455Q8—41no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—81no—
460Q8—82no—
461Q8—81no—
462D4—41no—
463D4—41no—
464D4—42no—
465D4—44no—
466D4—81no—
467D4—82no—
468D4—82no—
469D4—82no—
470D4—81no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—81no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4C11×#12012yes—
486C2×C4C11×#12011yescharacteristic
487C2×C4C22×D4×C1112yes—
488C2×C4C22×D4×C1111yescharacteristic
489C8—24no—
490C8—44no—
491C22—22no—
492C22—42no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—162no—
500C22—162no—
501C22C11×#45312yes—
502C22C2×C11×#12011yescharacteristic
503C4—21no—
504C4—21no—
505C4—22no—
506C4—22no—
507C4—41no—
508C4—41no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—82no—
513C2—22no—
514C2—81no—
515C2—82no—
516C2—81no—
517C2C2×C11×#45311yescharacteristic
518C2C11×#302212yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3545C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3238C2semidirect
3. C2×C11×#497C2semidirect
4. C11×#1661C2semidirect
5. C11×#1660C2semidirect
6. C11×#1659C2semidirect
7. C11×#1533C2semidirect
8. C11×#1532C2semidirect
22. C2×C11×C4⋊Q8C22semidirect
25. C11×#501C22semidirect
29. C11×#497C22semidirect
30. C11×#489C22semidirect
35. C11×#432C22semidirect
36. C2×C11×#97C22semidirect
37. C11×#330C22semidirect
39. C11×#329C22semidirect
40. C11×#329C22semidirect
115. #19051C11direct (N × H)
188. #3238C2×C11semidirect
189. C2×#497C2×C11semidirect
190. #1661C2×C11semidirect
191. #1660C2×C11semidirect
192. #1659C2×C11semidirect
193. #1533C2×C11semidirect
194. #1532C2×C11semidirect
253. C2×C4⋊Q8C22×C11semidirect
256. #501C22×C11semidirect
260. #497C22×C11semidirect
261. #489C22×C11semidirect
266. #432C22×C11semidirect
267. C2×#97C22×C11semidirect
268. #330C22×C11semidirect
270. #329C22×C11semidirect
271. #329C22×C11semidirect
445. C11#19051direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35452
C11×#32382
C2×C11×#4972
C11×#16612
C11×#16602
C11×#16592
C11×#15332
C11×#15322
#1905111