Finite Group Databasebeta

← C11×#19850 #14597043

Subgroups — C11×#19850 #14597043

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3396C211yesmaximal, characteristic
2C11×#3375C211yesmaximal, characteristic, complemented
3C11×#3365C211yesmaximal, characteristic, complemented
4C11×#3363C211yesmaximal, characteristic, complemented
5C11×#1717C211yesmaximal, characteristic
6C11×#1702C211yesmaximal, characteristic, complemented
7C11×#1684C211yesmaximal, characteristic, complemented
8C11×#1678C211yesmaximal, characteristic, complemented
9C11×#1668C211yesmaximal, characteristic
10C11×#1640C211yesmaximal, characteristic, complemented
11C11×#1630C211yesmaximal, characteristic, complemented
12C11×#1626C211yesmaximal, characteristic, complemented
13C11×#1623C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16C11×#559C2211yescharacteristic
17C11×#559C2211yescharacteristic
18Q82×C11C2211yescharacteristic
19C11×#557C2211yescharacteristic
20C11×#495—21no—
21C11×#493C2211yescharacteristic
22C11×#492C2211yescharacteristic
23C11×#489—21no—
24C11×#488—21no—
25C11×#487—21no—
26C11×#487C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#486C2211yescharacteristic
30C11×#478—21no—
31C11×#477—21no—
32C11×#477C2211yescharacteristic
33C11×#477C2211yescharacteristic
34C11×#475C2211yescharacteristic
35C11×#474—21no—
36C11×#464—21no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#463—21no—
40C11×#462—21no—
41C11×#462C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#460C2211yescharacteristic
44C11×#460C2211yescharacteristic
45C11×#460C2211yescharacteristic
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C8×Q8×C11C2211yescharacteristic
50C11×#440—21no—
51C4×C11×Q16—21no—
52C4×C11×Q16C2211yescharacteristic
53C4×C11×Q16C2211yescharacteristic
54C4×C11×SD16—21no—
55C4×C11×D8—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×Q8⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×Q16—21no—
68C2×C11×Q16D411yescharacteristic
69C2×C11×Q16D411yescharacteristic
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—41no—
75C2×C11×D8—21no—
76C2×C11×D8—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8—41no—
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×#127C2311yescharacteristic
84C11×#127C2311yescharacteristic
85C11×#125—21no—
86C11×#125—41no—
87C11×#124—21no—
88C11×#124—21no—
89C11×#124—21no—
90C11×#124—21no—
91C11×#123—41no—
92C11×#123—41no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11C2311yescharacteristic
98C4×Q8×C11C2311yescharacteristic
99C4×Q8×C11C2311yescharacteristic
100C4×Q8×C11C2311yescharacteristic
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107D411yescharacteristic
108C11×#107D411yescharacteristic
109C11×#106—21no—
110C11×C4⋊C8—21no—
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×#103D411yescharacteristic
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#102—41no—
137C11×#97—21no—
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19850C1111yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C11×Q16—22no—
161C11×Q16—41no—
162C11×Q16—42no—
163C11×SD16—42no—
164C11×SD16—42no—
165C11×SD16—81no—
166C11×SD16—81no—
167C11×SD16—82no—
168C11×D8—42no—
169C11×D8—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—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—41no—
207C42×C11—41no—
208C42×C11C2411yescharacteristic
209#3396C2×C1111yescharacteristic
210#3375C2×C1111yescharacteristic, complemented
211#3365C2×C1111yescharacteristic, complemented
212#3363C2×C1111yescharacteristic, complemented
213#1717C2×C1111yescharacteristic
214#1702C2×C1111yescharacteristic, complemented
215#1684C2×C1111yescharacteristic, complemented
216#1678C2×C1111yescharacteristic, complemented
217#1668C2×C1111yescharacteristic
218#1640C2×C1111yescharacteristic, complemented
219#1630C2×C1111yescharacteristic, complemented
220#1626C2×C1111yescharacteristic, complemented
221#1623C2×C1111yescharacteristic, complemented
222#1584C2×C1111yescharacteristic, complemented
223#1579C2×C1111yescharacteristic, complemented
224C23×C11—41no—
225C23×C11—41no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—81no—
236Q8×C11—161no—
237Q8×C11#13512yes—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—81no—
247D4×C11—81no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—161no—
259C2×C4×C11—161no—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272#559C22×C1111yescharacteristic
273#559C22×C1111yescharacteristic
274Q82C22×C1111yescharacteristic
275#557C22×C1111yescharacteristic
276#495—21no—
277#493C22×C1111yescharacteristic
278#492C22×C1111yescharacteristic
279#489—21no—
280#488—21no—
281#487—21no—
282#487C22×C1111yescharacteristic
283#486C22×C1111yescharacteristic
284#486C22×C1111yescharacteristic
285#486C22×C1111yescharacteristic
286#478—21no—
287#477—21no—
288#477C22×C1111yescharacteristic
289#477C22×C1111yescharacteristic
290#475C22×C1111yescharacteristic
291#474—21no—
292#464—21no—
293#464—21no—
294#463—21no—
295#463—21no—
296#462—21no—
297#462C22×C1111yescharacteristic
298#460C22×C1111yescharacteristic
299#460C22×C1111yescharacteristic
300#460C22×C1111yescharacteristic
301#460C22×C1111yescharacteristic
302#446C22×C1111yescharacteristic
303C8×Q8C22×C1111yescharacteristic
304C8×Q8C22×C1111yescharacteristic
305C8×Q8C22×C1111yescharacteristic
306#440—21no—
307C4×Q16—21no—
308C4×Q16C22×C1111yescharacteristic
309C4×Q16C22×C1111yescharacteristic
310C4×SD16—21no—
311C4×D8—21no—
312#335C22×C1111yescharacteristic
313#334C22×C1111yescharacteristic
314#333C22×C1111yescharacteristic
315#332C22×C1111yescharacteristic
316#331C22×C1111yescharacteristic
317#331C22×C1111yescharacteristic
318Q8⋊C8C22×C1111yescharacteristic
319Q8⋊C8C22×C1111yescharacteristic
320Q8⋊C8C22×C1111yescharacteristic
321Q8⋊C8C22×C1111yescharacteristic
322#322C22×C1111yescharacteristic
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11D4211yescharacteristic
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11C2×#13511yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345C2×Q16—21no—
346C2×Q16D4×C1111yescharacteristic
347C2×Q16D4×C1111yescharacteristic
348C2×SD16—21no—
349C2×SD16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16—41no—
353C2×D8—21no—
354C2×D8—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—41no—
359C4⋊Q8C23×C1111yescharacteristic
360C4⋊Q8C23×C1111yescharacteristic
361#127C23×C1111yescharacteristic
362#127C23×C1111yescharacteristic
363#125—21no—
364#125—41no—
365#124—21no—
366#124—21no—
367#124—21no—
368#124—21no—
369#123—41no—
370#123—41no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C1111yescharacteristic
376C4×Q8C23×C1111yescharacteristic
377C4×Q8C23×C1111yescharacteristic
378C4×Q8C23×C1111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383#107—21no—
384#107—21no—
385#107D4×C1111yescharacteristic
386#107D4×C1111yescharacteristic
387#106—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8C23×C1111yescharacteristic
393C4⋊C8C23×C1111yescharacteristic
394C4⋊C8C23×C1111yescharacteristic
395C4⋊C8C23×C1111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103D4×C1111yescharacteristic
403#103D4×C1111yescharacteristic
404#103D4×C1111yescharacteristic
405#103D4×C1111yescharacteristic
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—41no—
415#97—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8C23×C1111yescharacteristic
420C4×C8C23×C1111yescharacteristic
421C4×C8C23×C1111yescharacteristic
422C2×C11—161no—
423C2×C11—161no—
424C2×C11#327111yescharacteristic
425C2×C11#328511yescharacteristic
426C2×C11#328811yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8C2×D4×C1111yescharacteristic
431C2×Q8C2×D4×C1111yescharacteristic
432C2×Q8C2×D4×C1111yescharacteristic
433C2×Q8C2×D4×C1111yescharacteristic
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C22×C4—41no—
441C22×C4—41no—
442Q16—22no—
443Q16—41no—
444Q16—42no—
445SD16—42no—
446SD16—42no—
447SD16—81no—
448SD16—81no—
449SD16—82no—
450D8—42no—
451D8—81no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8C2×D4×C1111yescharacteristic
458C2×C8C2×D4×C1111yescharacteristic
459C2×C8C2×D4×C1111yescharacteristic
460C2×C8C2×D4×C1111yescharacteristic
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⋊C4C2×D4×C1111yescharacteristic
475C4⋊C4C2×D4×C1111yescharacteristic
476C4⋊C4C2×D4×C1111yescharacteristic
477C4⋊C4C2×D4×C1111yescharacteristic
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42—41no—
490C42C24×C1111yescharacteristic
491C11#1985011yescharacteristic, direct product factor, Sylow
492C23—41no—
493C23—41no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—81no—
504Q8—161no—
505Q8C11×#13512yes—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—81no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—161no—
527C2×C4—161no—
528C2×C4C22×D4×C1111yescharacteristic
529C2×C4C22×D4×C1111yescharacteristic
530C2×C4C11×H(5,𝔽2)11yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C1111yescharacteristic
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4C2×C11×#13511yescharacteristic
559C4C11×#57511yescharacteristic
560C4C11×#57711yescharacteristic
561C4C11×#57811yescharacteristic
562C2—161no—
563C2—161no—
564C2C11×#327111yescharacteristic
565C2C11×#328511yescharacteristic
566C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#493C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3375C2semidirect
3. C11×#3365C2semidirect
4. C11×#3363C2semidirect
6. C11×#1702C2semidirect
7. C11×#1684C2semidirect
8. C11×#1678C2semidirect
10. C11×#1640C2semidirect
11. C11×#1630C2semidirect
12. C11×#1626C2semidirect
13. C11×#1623C2semidirect
14. C11×#1584C2semidirect
15. C11×#1579C2semidirect
144. #19850C11direct (N × H)
210. #3375C2×C11semidirect
211. #3365C2×C11semidirect
212. #3363C2×C11semidirect
214. #1702C2×C11semidirect
215. #1684C2×C11semidirect
216. #1678C2×C11semidirect
218. #1640C2×C11semidirect
219. #1630C2×C11semidirect
220. #1626C2×C11semidirect
221. #1623C2×C11semidirect
222. #1584C2×C11semidirect
223. #1579C2×C11semidirect
491. C11#19850direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33962
C11×#33752
C11×#33652
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