Finite Group Databasebeta

← C11×#19847 #14597040

Subgroups — C11×#19847 #14597040

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3395C211yesmaximal, characteristic, complemented
2C11×#3368C211yesmaximal, characteristic
3C11×#3364C211yesmaximal, characteristic, complemented
4C11×#3304C211yesmaximal, characteristic
5C11×#1720C211yesmaximal, characteristic, complemented
6C11×#1700C211yesmaximal, characteristic, complemented
7C11×#1682C211yesmaximal, characteristic, complemented
8C11×#1682C211yesmaximal, characteristic, complemented
9C11×#1669C211yesmaximal, characteristic, complemented
10C11×#1653C211yesmaximal, characteristic, complemented
11C11×#1652C211yesmaximal, characteristic, complemented
12C11×#1641C211yesmaximal, characteristic
13C11×#1626C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic
17C11×#557C2211yescharacteristic
18C11×#556C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#494—21no—
22C11×#494C2211yescharacteristic
23C11×#490—21no—
24C11×#488—21no—
25C11×#487C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#482—21no—
30C11×#479—21no—
31C11×#478—21no—
32C11×#475C2211yescharacteristic
33C11×#474C2211yescharacteristic
34C11×#474C2211yescharacteristic
35C11×#465—21no—
36C11×#464—21no—
37C11×#462—21no—
38C11×#462—21no—
39C11×#462C2211yescharacteristic
40C11×#462C2211yescharacteristic
41C11×#462C2211yescharacteristic
42C11×#460—21no—
43C11×#460C2211yescharacteristic
44C11×#460C2211yescharacteristic
45C11×#452—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C11×#440—21no—
50C4×C11×Q16—21no—
51C4×C11×Q16—21no—
52C4×C11×Q16C2211yescharacteristic
53C4×C11×SD16C2211yescharacteristic
54C8×D4×C11C2211yescharacteristic
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#335C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#332C2211yescharacteristic
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—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16—21no—
72C2×C11×Q16—21no—
73C2×C11×Q16D411yescharacteristic
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16D411yescharacteristic
77C22×C8×C11—21no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×#127—21no—
84C11×#127C2311yescharacteristic
85C11×#126—41no—
86C11×#125—21no—
87C11×#125—21no—
88C11×#125—41no—
89C11×#125—41no—
90C11×#124—21no—
91C11×C22⋊Q8—21no—
92C11×#121—21no—
93C11×#121—41no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11C2311yescharacteristic
100C4×Q8×C11C2311yescharacteristic
101C4×Q8×C11C2311yescharacteristic
102C4×D4×C11—21no—
103C4×D4×C11C2311yescharacteristic
104C11×#117—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107D411yescharacteristic
108C11×#106—21no—
109C11×#106—41no—
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—
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19847C1111yesmaximal, 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×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C11×Q16—41no—
162C11×Q16—42no—
163C11×Q16—42no—
164C11×Q16—81no—
165C11×Q16—81no—
166C11×Q16—81no—
167C11×SD16—22no—
168C11×SD16—42no—
169C11×SD16—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—81no—
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
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—21no—
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⋊C4—41no—
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—41no—
208C42×C11—41no—
209C42×C11—41no—
210C42×C11C2411yescharacteristic
211#3395C2×C1111yescharacteristic, complemented
212#3368C2×C1111yescharacteristic
213#3364C2×C1111yescharacteristic, complemented
214#3304C2×C1111yescharacteristic
215#1720C2×C1111yescharacteristic, complemented
216#1700C2×C1111yescharacteristic, complemented
217#1682C2×C1111yescharacteristic, complemented
218#1682C2×C1111yescharacteristic, complemented
219#1669C2×C1111yescharacteristic, complemented
220#1653C2×C1111yescharacteristic, complemented
221#1652C2×C1111yescharacteristic, complemented
222#1641C2×C1111yescharacteristic
223#1626C2×C1111yescharacteristic, complemented
224#1584C2×C1111yescharacteristic, complemented
225SD16⋊C8C2×C1111yescharacteristic, complemented
226C23×C11—21no—
227C23×C11—41no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11#13512yes—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—81no—
247D4×C11—82no—
248D4×C11—161no—
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—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—82no—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274#557C22×C1111yescharacteristic
275#557C22×C1111yescharacteristic
276#556C22×C1111yescharacteristic
277#550C22×C1111yescharacteristic
278#498C22×C1111yescharacteristic
279#494—21no—
280#494C22×C1111yescharacteristic
281#490—21no—
282#488—21no—
283#487C22×C1111yescharacteristic
284#486C22×C1111yescharacteristic
285#486C22×C1111yescharacteristic
286#486C22×C1111yescharacteristic
287#482—21no—
288#479—21no—
289#478—21no—
290#475C22×C1111yescharacteristic
291#474C22×C1111yescharacteristic
292#474C22×C1111yescharacteristic
293#465—21no—
294#464—21no—
295#462—21no—
296#462—21no—
297#462C22×C1111yescharacteristic
298#462C22×C1111yescharacteristic
299#462C22×C1111yescharacteristic
300#460—21no—
301#460C22×C1111yescharacteristic
302#460C22×C1111yescharacteristic
303#452—21no—
304#446C22×C1111yescharacteristic
305C8×Q8C22×C1111yescharacteristic
306C8×Q8C22×C1111yescharacteristic
307#440—21no—
308C4×Q16—21no—
309C4×Q16—21no—
310C4×Q16C22×C1111yescharacteristic
311C4×SD16C22×C1111yescharacteristic
312C8×D4C22×C1111yescharacteristic
313#416—21no—
314#335C22×C1111yescharacteristic
315#335C22×C1111yescharacteristic
316#332C22×C1111yescharacteristic
317#332C22×C1111yescharacteristic
318#332C22×C1111yescharacteristic
319#331C22×C1111yescharacteristic
320Q8⋊C8C22×C1111yescharacteristic
321Q8⋊C8C22×C1111yescharacteristic
322Q8⋊C8C22×C1111yescharacteristic
323D4⋊C8C22×C1111yescharacteristic
324#322C22×C1111yescharacteristic
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11D4211yescharacteristic
332C4×C11—22no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11C2×#13511yescharacteristic
344C4×C11#57511yescharacteristic
345C4×C11#57611yescharacteristic
346C4×C11#57811yescharacteristic
347C2×#41—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×Q16—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16D4×C1111yescharacteristic
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16D4×C1111yescharacteristic
357C22×C8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8C23×C1111yescharacteristic
361C4⋊Q8C23×C1111yescharacteristic
362C4⋊Q8C23×C1111yescharacteristic
363#127—21no—
364#127C23×C1111yescharacteristic
365#126—41no—
366#125—21no—
367#125—21no—
368#125—41no—
369#125—41no—
370#124—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C23×C1111yescharacteristic
380C4×Q8C23×C1111yescharacteristic
381C4×Q8C23×C1111yescharacteristic
382C4×D4—21no—
383C4×D4C23×C1111yescharacteristic
384#117—21no—
385#107—21no—
386#107—21no—
387#107D4×C1111yescharacteristic
388#106—21no—
389#106—41no—
390#106D4×C1111yescharacteristic
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C1111yescharacteristic
395C4⋊C8C23×C1111yescharacteristic
396C4⋊C8C23×C1111yescharacteristic
397C4⋊C8C23×C1111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103D4×C1111yescharacteristic
405#103D4×C1111yescharacteristic
406#103D4×C1111yescharacteristic
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—41no—
416#102D4×C1111yescharacteristic
417C22⋊C8—21no—
418#97—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8C23×C1111yescharacteristic
422C4×C8C23×C1111yescharacteristic
423C4×C8C23×C1111yescharacteristic
424C2×C11—81no—
425C2×C11—161no—
426C2×C11#326811yescharacteristic
427C2×C11#328511yescharacteristic
428C2×C11#328911yescharacteristic
429#41—42no—
430#41—81no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C1111yescharacteristic
435C2×Q8C2×D4×C1111yescharacteristic
436C2×Q8C2×D4×C1111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C2×D4×C1111yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445Q16—41no—
446Q16—42no—
447Q16—42no—
448Q16—81no—
449Q16—81no—
450Q16—81no—
451SD16—22no—
452SD16—42no—
453SD16—81no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8C2×D4×C1111yescharacteristic
461C2×C8C2×D4×C1111yescharacteristic
462C2×C8C2×D4×C1111yescharacteristic
463C2×C8C2×D4×C1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C1111yescharacteristic
481C4⋊C4C2×D4×C1111yescharacteristic
482C4⋊C4C2×D4×C1111yescharacteristic
483C4⋊C4C2×D4×C1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—41no—
492C42—41no—
493C42—41no—
494C42C24×C1111yescharacteristic
495C11#1984711yescharacteristic, direct product factor, Sylow
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8C11×#13512yes—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C22×D4×C1111yescharacteristic
534C2×C4C11×H(5,𝔽2)11yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D42×C1111yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×C11×#13511yescharacteristic
563C4C11×#57511yescharacteristic
564C4C11×#57611yescharacteristic
565C4C11×#57811yescharacteristic
566C2—81no—
567C2—161no—
568C2C11×#326811yescharacteristic
569C2C11×#328511yescharacteristic
570C2C11×#328911yescharacteristic
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×#3395C2semidirect
3. C11×#3364C2semidirect
5. C11×#1720C2semidirect
6. C11×#1700C2semidirect
7. C11×#1682C2semidirect
8. C11×#1682C2semidirect
9. C11×#1669C2semidirect
10. C11×#1653C2semidirect
11. C11×#1652C2semidirect
13. C11×#1626C2semidirect
14. C11×#1584C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19847C11direct (N × H)
211. #3395C2×C11semidirect
213. #3364C2×C11semidirect
215. #1720C2×C11semidirect
216. #1700C2×C11semidirect
217. #1682C2×C11semidirect
218. #1682C2×C11semidirect
219. #1669C2×C11semidirect
220. #1653C2×C11semidirect
221. #1652C2×C11semidirect
223. #1626C2×C11semidirect
224. #1584C2×C11semidirect
225. SD16⋊C8C2×C11semidirect
495. C11#19847direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33952
C11×#33682
C11×#33642
C11×#33042
C11×#17202
C11×#17002
C11×#16822
C11×#16692
C11×#16532
C11×#16522
C11×#16412
C11×#16262
C11×#15842
C11×SD16⋊C82
#1984711