Finite Group Databasebeta

← C11×#19853 #14597046

Subgroups — C11×#19853 #14597046

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3398C211yesmaximal, characteristic, complemented
2C11×#3381C211yesmaximal, characteristic, complemented
3C11×#3335C211yesmaximal, characteristic
4C11×#3302C211yesmaximal, characteristic
5C11×#1716C211yesmaximal, characteristic, complemented
6C11×#1692C211yesmaximal, characteristic, complemented
7C11×#1680C211yesmaximal, characteristic, complemented
8C11×#1671C211yesmaximal, characteristic, complemented
9C11×#1669C211yesmaximal, characteristic, complemented
10C11×#1654C211yesmaximal, characteristic
11C11×#1653C211yesmaximal, characteristic, complemented
12C11×#1644C211yesmaximal, characteristic, complemented
13C11×#1638C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic
17C11×#556C2211yescharacteristic
18C11×#554C2211yescharacteristic
19C11×#547C2211yescharacteristic
20C11×#499—21no—
21C11×#498C2211yescharacteristic
22C11×#498C2211yescharacteristic
23C11×#498C2211yescharacteristic
24C11×#497—21no—
25C11×#494C2211yescharacteristic
26C11×#487C2211yescharacteristic
27C11×#487C2211yescharacteristic
28C11×#485—21no—
29C11×#483—21no—
30C11×#481—21no—
31C11×#479—21no—
32C11×#478—21no—
33C11×#477C2211yescharacteristic
34C11×#476C2211yescharacteristic
35C11×#475C2211yescharacteristic
36C11×#474C2211yescharacteristic
37C11×#474C2211yescharacteristic
38C11×#467—21no—
39C11×#465—21no—
40C11×#464—21no—
41C11×#462—21no—
42C11×#462C2211yescharacteristic
43C11×#462C2211yescharacteristic
44C11×#461C2211yescharacteristic
45C11×#452—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C11×#441—21no—
49C4×C11×SD16—21no—
50C4×C11×SD16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C2×C11×#106—21no—
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16D411yescharacteristic
74C2×C11×SD16D411yescharacteristic
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8C2311yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#126—41no—
83C11×#125—21no—
84C11×#125—21no—
85C11×#125—41no—
86C11×#124—21no—
87C11×#123—41no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—41no—
92C11×#121—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11C2311yescharacteristic
97C4×Q8×C11C2311yescharacteristic
98C4×D4×C11—21no—
99C4×D4×C11C2311yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C11×#117—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×#106—21no—
112C11×#106—21no—
113C11×#106—41no—
114C11×#106D411yescharacteristic
115C11×#106D411yescharacteristic
116C11×C4⋊C8—21no—
117C11×C4⋊C8—21no—
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×#103—21no—
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—21no—
129C11×#103—41no—
130C11×#103D411yescharacteristic
131C11×#103D411yescharacteristic
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C11×#97—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19853C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—41no—
154C2×D4×C11C2×D411yescharacteristic
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C11×Q16—42no—
161C11×Q16—81no—
162C11×Q16—81no—
163C11×Q16—81no—
164C11×SD16—22no—
165C11×SD16—22no—
166C11×SD16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—42no—
173C2×C8×C11—81no—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—41no—
208C42×C11—41no—
209C42×C11C2411yescharacteristic
210#3398C2×C1111yescharacteristic, complemented
211#3381C2×C1111yescharacteristic, complemented
212#3335C2×C1111yescharacteristic
213#3302C2×C1111yescharacteristic
214#1716C2×C1111yescharacteristic, complemented
215#1692C2×C1111yescharacteristic, complemented
216#1680C2×C1111yescharacteristic, complemented
217#1671C2×C1111yescharacteristic, complemented
218#1669C2×C1111yescharacteristic, complemented
219#1654C2×C1111yescharacteristic
220#1653C2×C1111yescharacteristic, complemented
221#1644C2×C1111yescharacteristic, complemented
222#1638C2×C1111yescharacteristic, complemented
223#1582C2×C1111yescharacteristic, complemented
224SD16⋊C8C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—81no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—82no—
242D4×C11#13712yes—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—82no—
258C2×C4×C11—161no—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11#13512yes—
271#557C22×C1111yescharacteristic
272#556C22×C1111yescharacteristic
273#554C22×C1111yescharacteristic
274#547C22×C1111yescharacteristic
275#499—21no—
276#498C22×C1111yescharacteristic
277#498C22×C1111yescharacteristic
278#498C22×C1111yescharacteristic
279#497—21no—
280#494C22×C1111yescharacteristic
281#487C22×C1111yescharacteristic
282#487C22×C1111yescharacteristic
283#485—21no—
284#483—21no—
285#481—21no—
286#479—21no—
287#478—21no—
288#477C22×C1111yescharacteristic
289#476C22×C1111yescharacteristic
290#475C22×C1111yescharacteristic
291#474C22×C1111yescharacteristic
292#474C22×C1111yescharacteristic
293#467—21no—
294#465—21no—
295#464—21no—
296#462—21no—
297#462C22×C1111yescharacteristic
298#462C22×C1111yescharacteristic
299#461C22×C1111yescharacteristic
300#452—21no—
301#446C22×C1111yescharacteristic
302C8×Q8C22×C1111yescharacteristic
303#441—21no—
304C4×SD16—21no—
305C4×SD16C22×C1111yescharacteristic
306C4×SD16C22×C1111yescharacteristic
307C8×D4C22×C1111yescharacteristic
308C8×D4C22×C1111yescharacteristic
309C2×#106—21no—
310#416—21no—
311#335C22×C1111yescharacteristic
312#334C22×C1111yescharacteristic
313#333C22×C1111yescharacteristic
314#332C22×C1111yescharacteristic
315#332C22×C1111yescharacteristic
316#332C22×C1111yescharacteristic
317Q8⋊C8C22×C1111yescharacteristic
318Q8⋊C8C22×C1111yescharacteristic
319D4⋊C8C22×C1111yescharacteristic
320D4⋊C8C22×C1111yescharacteristic
321#322C22×C1111yescharacteristic
322C22×C11—22no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11D4211yescharacteristic
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C2×#13511yescharacteristic
341C4×C11C2×#13711yescharacteristic
342C4×C11#57711yescharacteristic
343C4×C11#57711yescharacteristic
344C2×#41—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×SD16—21no—
350C2×SD16D4×C1111yescharacteristic
351C2×SD16D4×C1111yescharacteristic
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8—21no—
355C4⋊Q8C23×C1111yescharacteristic
356C4⋊Q8C23×C1111yescharacteristic
357C4⋊Q8C23×C1111yescharacteristic
358C4⋊Q8C23×C1111yescharacteristic
359#126—41no—
360#125—21no—
361#125—21no—
362#125—41no—
363#124—21no—
364#123—41no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—41no—
369#121—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C1111yescharacteristic
374C4×Q8C23×C1111yescharacteristic
375C4×D4—21no—
376C4×D4C23×C1111yescharacteristic
377C4×D4C23×C1111yescharacteristic
378#117—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—41no—
391#106D4×C1111yescharacteristic
392#106D4×C1111yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C1111yescharacteristic
396C4⋊C8C23×C1111yescharacteristic
397C4⋊C8C23×C1111yescharacteristic
398C4⋊C8C23×C1111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—41no—
407#103D4×C1111yescharacteristic
408#103D4×C1111yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102D4×C1111yescharacteristic
413#102D4×C1111yescharacteristic
414C22⋊C8—21no—
415C22⋊C8—21no—
416#97—21no—
417C4×C8—21no—
418C4×C8C23×C1111yescharacteristic
419C4×C8C23×C1111yescharacteristic
420C4×C8C23×C1111yescharacteristic
421C2×C11—42no—
422C2×C11—81no—
423C2×C11#326611yescharacteristic
424C2×C11#328411yescharacteristic
425C2×C11#328911yescharacteristic
426#41—42no—
427#41—81no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8C2×D4×C1111yescharacteristic
433C2×Q8C2×D4×C1111yescharacteristic
434C2×D4—41no—
435C2×D4C2×D4×C1111yescharacteristic
436C2×D4C2×D4×C1111yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—41no—
440C22×C4—41no—
441Q16—42no—
442Q16—81no—
443Q16—81no—
444Q16—81no—
445SD16—22no—
446SD16—22no—
447SD16—81no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—81no—
455C2×C8C2×D4×C1111yescharacteristic
456C2×C8C2×D4×C1111yescharacteristic
457C2×C8C2×D4×C1111yescharacteristic
458C2×C8C2×D4×C1111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4C2×D4×C1111yescharacteristic
477C4⋊C4C2×D4×C1111yescharacteristic
478C4⋊C4C2×D4×C1111yescharacteristic
479C4⋊C4C2×D4×C1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42—41no—
490C42C24×C1111yescharacteristic
491C11#1985311yescharacteristic, direct product factor, Sylow
492C23—21no—
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—82no—
509D4C11×#13712yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4—161no—
526C2×C4C22×D4×C1111yescharacteristic
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C11×H(5,𝔽2)11yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8C11×#13512yes—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22D42×C1111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×C11×#13511yescharacteristic
557C4C2×C11×#13711yescharacteristic
558C4C11×#57711yescharacteristic
559C4C11×#57711yescharacteristic
560C2—42no—
561C2—81no—
562C2C11×#326611yescharacteristic
563C2C11×#328411yescharacteristic
564C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#547C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3398C2semidirect
2. C11×#3381C2semidirect
5. C11×#1716C2semidirect
6. C11×#1692C2semidirect
7. C11×#1680C2semidirect
8. C11×#1671C2semidirect
9. C11×#1669C2semidirect
11. C11×#1653C2semidirect
12. C11×#1644C2semidirect
13. C11×#1638C2semidirect
14. C11×#1582C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19853C11direct (N × H)
210. #3398C2×C11semidirect
211. #3381C2×C11semidirect
214. #1716C2×C11semidirect
215. #1692C2×C11semidirect
216. #1680C2×C11semidirect
217. #1671C2×C11semidirect
218. #1669C2×C11semidirect
220. #1653C2×C11semidirect
221. #1644C2×C11semidirect
222. #1638C2×C11semidirect
223. #1582C2×C11semidirect
224. SD16⋊C8C2×C11semidirect
491. C11#19853direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33982
C11×#33812
C11×#33352
C11×#33022
C11×#17162
C11×#16922
C11×#16802
C11×#16712
C11×#16692
C11×#16542
C11×#16532
C11×#16442
C11×#16382
C11×#15822
C11×SD16⋊C82
#1985311