Finite Group Databasebeta

← C11×#19829 #14597022

Subgroups — C11×#19829 #14597022

Order 2816.

590 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×#3381C211yesmaximal, characteristic, complemented
2C11×#3363C211yesmaximal, characteristic, complemented
3C11×#3362C211yesmaximal, characteristic
4C11×#3333C211yesmaximal, characteristic
5C11×#1720C211yesmaximal, characteristic, complemented
6C11×#1703C211yesmaximal, characteristic, complemented
7C11×#1678C211yesmaximal, characteristic, complemented
8C11×#1678C211yesmaximal, characteristic, complemented
9C11×#1672C211yesmaximal, characteristic, complemented
10C11×#1641C211yesmaximal, characteristic
11C11×#1633C211yesmaximal, characteristic, complemented
12C11×#1632C211yesmaximal, characteristic, complemented
13C11×#1626C211yesmaximal, characteristic, complemented
14C11×#1583C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic
17C11×#557C2211yescharacteristic
18C11×#554C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#499—21no—
21C11×#498C2211yescharacteristic
22C11×#494C2211yescharacteristic
23C11×#487—21no—
24C11×#487C2211yescharacteristic
25C11×#486—21no—
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#480—21no—
30C11×#479—21no—
31C11×#478—21no—
32C11×#477—21no—
33C11×#477C2211yescharacteristic
34C11×#477C2211yescharacteristic
35C11×#477C2211yescharacteristic
36C11×#476—21no—
37C11×#476C2211yescharacteristic
38C11×#474C2211yescharacteristic
39C11×#468—21no—
40C11×#462—21no—
41C11×#462C2211yescharacteristic
42C11×#460—21no—
43C11×#460C2211yescharacteristic
44C11×#460C2211yescharacteristic
45C11×#452—21no—
46C8×Q8×C11C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C4×C11×Q16—21no—
50C4×C11×Q16C2211yescharacteristic
51C4×C11×SD16—21no—
52C4×C11×SD16—21no—
53C4×C11×SD16C2211yescharacteristic
54C11×#436C2211yescharacteristic
55C11×#417—21no—
56C11×#334C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—41no—
70C2×C11×Q16D411yescharacteristic
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16D411yescharacteristic
74C2×C11×M16—21no—
75C11×C4⋊Q8—21no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—41no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127—21no—
83C11×#127C2311yescharacteristic
84C11×#125—21no—
85C11×#125—21no—
86C11×#125—41no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—41no—
89C11×#121—21no—
90C11×#121—41no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11C2311yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×Q8×C11C2311yescharacteristic
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11C2311yescharacteristic
101C2×C11×C4⋊C4—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107D411yescharacteristic
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106D411yescharacteristic
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×#103—21no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#103D411yescharacteristic
125C11×#103D411yescharacteristic
126C11×#103D411yescharacteristic
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—41no—
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19829C1111yesmaximal, 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—41no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11C2×D411yescharacteristic
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11—41no—
163C11×Q16—22no—
164C11×Q16—42no—
165C11×Q16—82no—
166C11×SD16—22no—
167C11×SD16—42no—
168C11×SD16—81no—
169C11×M16—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
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—41no—
201C11×C22⋊C4—41no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—41no—
206C42×C11—41no—
207C42×C11C2411yescharacteristic
208#3381C2×C1111yescharacteristic, complemented
209#3363C2×C1111yescharacteristic, complemented
210#3362C2×C1111yescharacteristic
211#3333C2×C1111yescharacteristic
212#1720C2×C1111yescharacteristic, complemented
213#1703C2×C1111yescharacteristic, complemented
214#1678C2×C1111yescharacteristic, complemented
215#1678C2×C1111yescharacteristic, complemented
216#1672C2×C1111yescharacteristic, complemented
217#1641C2×C1111yescharacteristic
218#1633C2×C1111yescharacteristic, complemented
219#1632C2×C1111yescharacteristic, complemented
220#1626C2×C1111yescharacteristic, complemented
221#1583C2×C1111yescharacteristic, complemented
222#1579C2×C1111yescharacteristic, complemented
223C23×C11—21no—
224C23×C11—41no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—81no—
232Q8×C11—81no—
233Q8×C11—161no—
234Q8×C11#13512yes—
235Q8×C11#13712yes—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—82no—
243D4×C11—81no—
244D4×C11—161no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
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—21no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271Q82C22×C1111yescharacteristic
272#557C22×C1111yescharacteristic
273#554C22×C1111yescharacteristic
274#550C22×C1111yescharacteristic
275#499—21no—
276#498C22×C1111yescharacteristic
277#494C22×C1111yescharacteristic
278#487—21no—
279#487C22×C1111yescharacteristic
280#486—21no—
281#486C22×C1111yescharacteristic
282#486C22×C1111yescharacteristic
283#486C22×C1111yescharacteristic
284#480—21no—
285#479—21no—
286#478—21no—
287#477—21no—
288#477C22×C1111yescharacteristic
289#477C22×C1111yescharacteristic
290#477C22×C1111yescharacteristic
291#476—21no—
292#476C22×C1111yescharacteristic
293#474C22×C1111yescharacteristic
294#468—21no—
295#462—21no—
296#462C22×C1111yescharacteristic
297#460—21no—
298#460C22×C1111yescharacteristic
299#460C22×C1111yescharacteristic
300#452—21no—
301C8×Q8C22×C1111yescharacteristic
302C8×Q8C22×C1111yescharacteristic
303C8×Q8C22×C1111yescharacteristic
304C4×Q16—21no—
305C4×Q16C22×C1111yescharacteristic
306C4×SD16—21no—
307C4×SD16—21no—
308C4×SD16C22×C1111yescharacteristic
309#436C22×C1111yescharacteristic
310#417—21no—
311#334C22×C1111yescharacteristic
312#334C22×C1111yescharacteristic
313#333C22×C1111yescharacteristic
314#333C22×C1111yescharacteristic
315#332C22×C1111yescharacteristic
316#331C22×C1111yescharacteristic
317Q8⋊C8C22×C1111yescharacteristic
318Q8⋊C8C22×C1111yescharacteristic
319Q8⋊C8C22×C1111yescharacteristic
320D4⋊C8C22×C1111yescharacteristic
321#322C22×C1111yescharacteristic
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11D4211yescharacteristic
329C4×C11—22no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C2×#13511yescharacteristic
341C4×C11C2×#13711yescharacteristic
342C4×C11#57711yescharacteristic
343C4×C11#57811yescharacteristic
344C2×#41—21no—
345C2×Q16—21no—
346C2×Q16—41no—
347C2×Q16D4×C1111yescharacteristic
348C2×SD16—21no—
349C2×SD16—21no—
350C2×SD16D4×C1111yescharacteristic
351C2×M16—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—41no—
356C4⋊Q8C23×C1111yescharacteristic
357C4⋊Q8C23×C1111yescharacteristic
358C4⋊Q8C23×C1111yescharacteristic
359#127—21no—
360#127C23×C1111yescharacteristic
361#125—21no—
362#125—21no—
363#125—41no—
364C22⋊Q8—21no—
365C22⋊Q8—41no—
366#121—21no—
367#121—41no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C1111yescharacteristic
373C4×Q8C23×C1111yescharacteristic
374C4×Q8C23×C1111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4C23×C1111yescharacteristic
378C2×C4⋊C4—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107D4×C1111yescharacteristic
384#106—21no—
385#106—21no—
386#106—21no—
387#106D4×C1111yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C1111yescharacteristic
392C4⋊C8C23×C1111yescharacteristic
393C4⋊C8C23×C1111yescharacteristic
394C4⋊C8C23×C1111yescharacteristic
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103D4×C1111yescharacteristic
402#103D4×C1111yescharacteristic
403#103D4×C1111yescharacteristic
404#102—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—41no—
413#102D4×C1111yescharacteristic
414C22⋊C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C1111yescharacteristic
419C4×C8C23×C1111yescharacteristic
420C4×C8C23×C1111yescharacteristic
421C2×C11—81no—
422C2×C11—161no—
423C2×C11#327011yescharacteristic
424C2×C11#328211yescharacteristic
425C2×C11#328811yescharacteristic
426#41—42no—
427#41—81no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8C2×D4×C1111yescharacteristic
433C2×Q8C2×D4×C1111yescharacteristic
434C2×Q8C2×D4×C1111yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C2×D4×C1111yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444Q16—22no—
445Q16—42no—
446Q16—82no—
447SD16—22no—
448SD16—42no—
449SD16—81no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8C2×D4×C1111yescharacteristic
457C2×C8C2×D4×C1111yescharacteristic
458C2×C8C2×D4×C1111yescharacteristic
459C2×C8C2×D4×C1111yescharacteristic
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—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42—41no—
488C42C24×C1111yescharacteristic
489C11#1982911yescharacteristic, direct product factor, Sylow
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500Q8—161no—
501Q8C11×#13512yes—
502Q8C11×#13712yes—
503D4—21no—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—82no—
510D4—81no—
511D4—161no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
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—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C1111yescharacteristic
545C4—22no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×C11×#13511yescharacteristic
557C4C2×C11×#13711yescharacteristic
558C4C11×#57711yescharacteristic
559C4C11×#57811yescharacteristic
560C2—81no—
561C2—161no—
562C2C11×#327011yescharacteristic
563C2C11×#328211yescharacteristic
564C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#550C22
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×#3381C2semidirect
2. C11×#3363C2semidirect
5. C11×#1720C2semidirect
6. C11×#1703C2semidirect
7. C11×#1678C2semidirect
8. C11×#1678C2semidirect
9. C11×#1672C2semidirect
11. C11×#1633C2semidirect
12. C11×#1632C2semidirect
13. C11×#1626C2semidirect
14. C11×#1583C2semidirect
15. C11×#1579C2semidirect
144. #19829C11direct (N × H)
208. #3381C2×C11semidirect
209. #3363C2×C11semidirect
212. #1720C2×C11semidirect
213. #1703C2×C11semidirect
214. #1678C2×C11semidirect
215. #1678C2×C11semidirect
216. #1672C2×C11semidirect
218. #1633C2×C11semidirect
219. #1632C2×C11semidirect
220. #1626C2×C11semidirect
221. #1583C2×C11semidirect
222. #1579C2×C11semidirect
489. C11#19829direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33812
C11×#33632
C11×#33622
C11×#33332
C11×#17202
C11×#17032
C11×#16782
C11×#16722
C11×#16412
C11×#16332
C11×#16322
C11×#16262
C11×#15832
C11×#15792
#1982911