Finite Group Databasebeta

← C11×#19790 #14596983

Subgroups — C11×#19790 #14596983

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3381C211yesmaximal, characteristic, complemented
2C11×#3372C211yesmaximal, characteristic, complemented
3C11×#3295C211yesmaximal, characteristic
4C11×#3295C211yesmaximal, characteristic
5C11×#1720C211yesmaximal, characteristic, complemented
6C11×#1698C211yesmaximal, characteristic, complemented
7C11×#1683C211yesmaximal, characteristic, complemented
8C11×#1678C211yesmaximal, characteristic, complemented
9C11×#1671C211yesmaximal, characteristic, complemented
10C11×#1639C211yesmaximal, characteristic
11C11×#1632C211yesmaximal, characteristic, complemented
12C11×#1632C211yesmaximal, characteristic, complemented
13C11×#1626C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic, complemented
17C11×#554C2211yescharacteristic
18C11×#554C2211yescharacteristic
19D42×C11C2211yescharacteristic
20C11×#499—21no—
21C11×#498C2211yescharacteristic, complemented
22C11×#494C2211yescharacteristic, complemented
23C11×#491—21no—
24C11×#487C2211yescharacteristic, complemented
25C11×#486C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#481—21no—
29C11×#481—21no—
30C11×#479—21no—
31C11×#479—21no—
32C11×#478—21no—
33C11×#477C2211yescharacteristic, complemented
34C11×#477C2211yescharacteristic, complemented
35C11×#476C2211yescharacteristic
36C11×#476C2211yescharacteristic
37C11×#474C2211yescharacteristic
38C11×#465—21no—
39C11×#465—21no—
40C11×#461—21no—
41C11×#461C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#460C2211yescharacteristic
44C11×#450—21no—
45C11×#450—21no—
46C11×#446C2211yescharacteristic, complemented
47C8×Q8×C11C2211yescharacteristic, complemented
48C11×#440—21no—
49C4×C11×SD16—21no—
50C4×C11×SD16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C2×C11×#102—21no—
55C2×C11×#102—21no—
56C11×#335C2211yescharacteristic, complemented
57C11×#334C2211yescharacteristic, complemented
58C11×#333C2211yescharacteristic, complemented
59C11×#333C2211yescharacteristic, complemented
60C11×#332C2211yescharacteristic, complemented
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic, complemented
63C11×Q8⋊C8C2211yescharacteristic, complemented
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C2×C11×Q16—41no—
70C2×C11×SD16—21no—
71C2×C11×SD16—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×#127C2311yescharacteristic
82C11×#125—21no—
83C11×#125—21no—
84C11×#125—21no—
85C11×#125—41no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—41no—
89C11×C22⋊Q8—41no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#120—41no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11C2311yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11C2311yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106D411yescharacteristic
111C11×#106D411yescharacteristic
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×#103D411yescharacteristic
124C11×#103D411yescharacteristic
125C11×#102—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—41no—
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#19790C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—81no—
159C2×D4×C11—81no—
160C2×D4×C11C2×D411yescharacteristic
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C11×Q16—82no—
167C11×SD16—22no—
168C11×SD16—22no—
169C11×SD16—42no—
170C11×SD16—81no—
171C11×SD16—81no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—81no—
178C2×C8×C11—81no—
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
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—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C22⋊C4—21no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—41no—
210C42×C11C2411yescharacteristic
211#3381C2×C1111yescharacteristic, complemented
212#3372C2×C1111yescharacteristic, complemented
213#3295C2×C1111yescharacteristic
214#3295C2×C1111yescharacteristic
215#1720C2×C1111yescharacteristic, complemented
216#1698C2×C1111yescharacteristic, complemented
217#1683C2×C1111yescharacteristic, complemented
218#1678C2×C1111yescharacteristic, complemented
219#1671C2×C1111yescharacteristic, complemented
220#1639C2×C1111yescharacteristic
221#1632C2×C1111yescharacteristic, complemented
222#1632C2×C1111yescharacteristic, complemented
223#1626C2×C1111yescharacteristic, complemented
224#1582C2×C1111yescharacteristic, complemented
225SD16⋊C8C2×C1111yescharacteristic, complemented
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—41no—
229C23×C11—82no—
230C23×C11—82no—
231C23×C11—161no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—81no—
239Q8×C11—81no—
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—82no—
249D4×C11#13512yes—
250D4×C11#13712yes—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—161no—
265C2×C4×C11—161no—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278#557C22×C1111yescharacteristic, complemented
279#554C22×C1111yescharacteristic
280#554C22×C1111yescharacteristic
281D42C22×C1111yescharacteristic
282#499—21no—
283#498C22×C1111yescharacteristic, complemented
284#494C22×C1111yescharacteristic, complemented
285#491—21no—
286#487C22×C1111yescharacteristic, complemented
287#486C22×C1111yescharacteristic
288#486C22×C1111yescharacteristic
289#486C22×C1111yescharacteristic
290#481—21no—
291#481—21no—
292#479—21no—
293#479—21no—
294#478—21no—
295#477C22×C1111yescharacteristic, complemented
296#477C22×C1111yescharacteristic, complemented
297#476C22×C1111yescharacteristic
298#476C22×C1111yescharacteristic
299#474C22×C1111yescharacteristic
300#465—21no—
301#465—21no—
302#461—21no—
303#461C22×C1111yescharacteristic
304#460C22×C1111yescharacteristic
305#460C22×C1111yescharacteristic
306#450—21no—
307#450—21no—
308#446C22×C1111yescharacteristic, complemented
309C8×Q8C22×C1111yescharacteristic, complemented
310#440—21no—
311C4×SD16—21no—
312C4×SD16C22×C1111yescharacteristic
313C4×SD16C22×C1111yescharacteristic
314C8×D4C22×C1111yescharacteristic
315C8×D4C22×C1111yescharacteristic
316C2×#102—21no—
317C2×#102—21no—
318#335C22×C1111yescharacteristic, complemented
319#334C22×C1111yescharacteristic, complemented
320#333C22×C1111yescharacteristic, complemented
321#333C22×C1111yescharacteristic, complemented
322#332C22×C1111yescharacteristic, complemented
323#331C22×C1111yescharacteristic
324Q8⋊C8C22×C1111yescharacteristic, complemented
325Q8⋊C8C22×C1111yescharacteristic, complemented
326D4⋊C8C22×C1111yescharacteristic
327D4⋊C8C22×C1111yescharacteristic
328#322C22×C1111yescharacteristic, complemented
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—164no—
339C22×C11D4211yescharacteristic
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C2×#13511yescharacteristic
351C4×C11C2×#13711yescharacteristic
352C4×C11#57711yescharacteristic
353C4×C11#57711yescharacteristic
354C22×D4—21no—
355C22×D4—21no—
356C2×Q16—41no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16D4×C1111yescharacteristic
361C2×SD16D4×C1111yescharacteristic
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C23×C1111yescharacteristic
366C4⋊Q8C23×C1111yescharacteristic
367C4⋊Q8C23×C1111yescharacteristic
368#127C23×C1111yescharacteristic
369#125—21no—
370#125—21no—
371#125—21no—
372#125—41no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—41no—
376C22⋊Q8—41no—
377#121—21no—
378#121—21no—
379#120—41no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8C23×C1111yescharacteristic
383C4×Q8C23×C1111yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C23×C1111yescharacteristic
387C4×D4C23×C1111yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106D4×C1111yescharacteristic
398#106D4×C1111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C1111yescharacteristic
402C4⋊C8C23×C1111yescharacteristic
403C4⋊C8C23×C1111yescharacteristic
404C4⋊C8C23×C1111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103D4×C1111yescharacteristic
411#103D4×C1111yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—41no—
422#102D4×C1111yescharacteristic
423#102D4×C1111yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427C4×C8—21no—
428C4×C8C23×C1111yescharacteristic
429C4×C8C23×C1111yescharacteristic
430C4×C8C23×C1111yescharacteristic
431C2×C11—42no—
432C2×C11—42no—
433C2×C11—161no—
434C2×C11#326611yescharacteristic
435C2×C11#328211yescharacteristic
436C2×C11#328811yescharacteristic
437C24—41no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×D4×C1111yescharacteristic
442C2×Q8C2×D4×C1111yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C1111yescharacteristic
453C2×D4C2×D4×C1111yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—82no—
459SD16—22no—
460SD16—22no—
461SD16—42no—
462SD16—81no—
463SD16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8—81no—
471C2×C8C2×D4×C1111yescharacteristic
472C2×C8C2×D4×C1111yescharacteristic
473C2×C8C2×D4×C1111yescharacteristic
474C2×C8C2×D4×C1111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C1111yescharacteristic
491C4⋊C4C2×D4×C1111yescharacteristic
492C4⋊C4C2×D4×C1111yescharacteristic
493C4⋊C4C2×D4×C1111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C24×C1111yescharacteristic
503C11#1979011yescharacteristic, direct product factor, Sylow
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4C11×#13512yes—
528D4C11×#13712yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—161no—
543C2×C4—161no—
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C11×H(5,𝔽2)11yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D42×C1111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×C11×#13511yescharacteristic
578C4C2×C11×#13711yescharacteristic
579C4C11×#57711yescharacteristic
580C4C11×#57711yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2C11×#326611yescharacteristic
585C2C11×#328211yescharacteristic
586C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalD42×C11C22
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×#3372C2semidirect
5. C11×#1720C2semidirect
6. C11×#1698C2semidirect
7. C11×#1683C2semidirect
8. C11×#1678C2semidirect
9. C11×#1671C2semidirect
11. C11×#1632C2semidirect
12. C11×#1632C2semidirect
13. C11×#1626C2semidirect
14. C11×#1582C2semidirect
15. C11×SD16⋊C8C2semidirect
16. C11×#557C22semidirect
21. C11×#498C22semidirect
22. C11×#494C22semidirect
24. C11×#487C22semidirect
33. C11×#477C22semidirect
34. C11×#477C22semidirect
46. C11×#446C22semidirect
47. C8×Q8×C11C22semidirect
56. C11×#335C22semidirect
57. C11×#334C22semidirect
58. C11×#333C22semidirect
59. C11×#333C22semidirect
60. C11×#332C22semidirect
62. C11×Q8⋊C8C22semidirect
63. C11×Q8⋊C8C22semidirect
66. C11×#322C22semidirect
144. #19790C11direct (N × H)
211. #3381C2×C11semidirect
212. #3372C2×C11semidirect
215. #1720C2×C11semidirect
216. #1698C2×C11semidirect
217. #1683C2×C11semidirect
218. #1678C2×C11semidirect
219. #1671C2×C11semidirect
221. #1632C2×C11semidirect
222. #1632C2×C11semidirect
223. #1626C2×C11semidirect
224. #1582C2×C11semidirect
225. SD16⋊C8C2×C11semidirect
278. #557C22×C11semidirect
283. #498C22×C11semidirect
284. #494C22×C11semidirect
286. #487C22×C11semidirect
295. #477C22×C11semidirect
296. #477C22×C11semidirect
308. #446C22×C11semidirect
309. C8×Q8C22×C11semidirect
318. #335C22×C11semidirect
319. #334C22×C11semidirect
320. #333C22×C11semidirect
321. #333C22×C11semidirect
322. #332C22×C11semidirect
324. Q8⋊C8C22×C11semidirect
325. Q8⋊C8C22×C11semidirect
328. #322C22×C11semidirect
503. C11#19790direct (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×#33722
C11×#32952
C11×#17202
C11×#16982
C11×#16832
C11×#16782
C11×#16712
C11×#16392
C11×#16322
C11×#16262
C11×#15822
C11×SD16⋊C82
#1979011