Finite Group Databasebeta

← C11×#19047 #14596240

Subgroups — C11×#19047 #14596240

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3563C211yesmaximal, characteristic
2C11×#3236C211yesmaximal, characteristic, complemented
3C11×#3181C211yesmaximal, characteristic
4C11×#3162C211yesmaximal, characteristic, complemented
5C11×#1664C212yesmaximal, complemented
6C11×#1663C212yesmaximal, complemented
7C11×#1663C212yesmaximal, complemented
8C11×#1660C212yesmaximal, complemented
9C11×#1532C211yesmaximal, characteristic
10C11×#1531C211yesmaximal, characteristic, complemented
11C2×C11×#330C211yesmaximal, characteristic, complemented
12C11×#564C2212yes—
13C11×#563C2212yes—
14C11×#557—21no—
15C11×#554—21no—
16C11×#552—21no—
17C11×#552—22no—
18C11×#552—21no—
19C11×#544—21no—
20C11×#544—21no—
21C11×#541—21no—
22C11×#541—22no—
23C11×#539—21no—
24C11×#533C2211yescharacteristic
25C11×#533C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic
28C11×#501—21no—
29C11×#501—21no—
30C11×#501C2212yes—
31C11×#501C2212yes—
32C11×#501C2211yescharacteristic
33C11×#501C2212yes—
34C11×#497C2211yescharacteristic
35C11×#491C2211yescharacteristic
36C11×#491C2212yes—
37C11×#489C2211yescharacteristic
38C11×#484—21no—
39C11×#483—21no—
40C11×#479—22no—
41C11×#467—21no—
42C11×#465—21no—
43C11×#441—21no—
44C11×#440—21no—
45C11×#432C2211yescharacteristic
46C11×#427—22no—
47C2×C11×#97C2211yescharacteristic
48C2×C11×#97C2211yescharacteristic
49C11×#330C2212yes—
50C11×#330C2212yes—
51C11×#330C2212yes—
52C11×#330C2212yes—
53C11×#330C2212yes—
54C11×#329C2212yes—
55C2×C11×Q16—21no—
56C2×C11×SD16—21no—
57C22×C8×C11—21no—
58C22×C8×C11—21no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—22no—
69C11×#126—22no—
70C11×#126—21no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#125—21no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#125—22no—
77C11×#125—22no—
78C11×#125—22no—
79C11×#125—22no—
80C11×#125—21no—
81C11×#125—21no—
82C11×#125—21no—
83C11×#125D412yes—
84C11×#125C2312yes—
85C11×#125C2311yescharacteristic
86C11×#125C2312yes—
87C11×#124C2311yescharacteristic
88C11×#123—22no—
89C11×#123—22no—
90C11×#123—21no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—21no—
100C11×C22⋊Q8—21no—
101C11×C22⋊Q8D411yescharacteristic
102C11×#121D411yescharacteristic
103C4×Q8×C11—21no—
104C4×Q8×C11—22no—
105C4×Q8×C11—21no—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11D411yescharacteristic
111C4×D4×C11—22no—
112C4×D4×C11—21no—
113C4×D4×C11D411yescharacteristic
114C11×#117—22no—
115C11×#117—21no—
116C11×#117—22no—
117C11×#117—21no—
118C11×#117—21no—
119C11×#117D412yes—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4D411yescharacteristic
124C2×C11×C4⋊C4D411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C11×#107—22no—
127C11×#107—22no—
128C11×#107—21no—
129C11×#107—22no—
130C11×#106—22no—
131C11×#106—22no—
132C11×#106—21no—
133C11×#106—22no—
134C11×C4⋊C8—21no—
135C11×#103—21no—
136C11×#103—21no—
137C11×#103—21no—
138C11×#103—22no—
139C11×#103—22no—
140C11×#102—21no—
141C11×C22⋊C8—21no—
142C11×#97—21no—
143C11×#97—21no—
144C11×#97C2311yescharacteristic
145C11×#97C2312yes—
146C11×#97C2312yes—
147C11×#97C2311yescharacteristic
148#19047C1111yesmaximal, characteristic, direct product factor, Sylow
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C11×Q16—42no—
165C11×SD16—42no—
166C2×C8×C11—24no—
167C2×C8×C11—22no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—22no—
171C2×C8×C11—42no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4C2×D412yes—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D412yes—
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D412yes—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—41no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11—21no—
221C42×C11—41no—
222C42×C11C2×D411yescharacteristic
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2411yescharacteristic
226#3563C2×C1111yescharacteristic
227#3236C2×C1111yescharacteristic, complemented
228#3181C2×C1111yescharacteristic
229#3162C2×C1111yescharacteristic, complemented
230#1664C2×C1112yescomplemented
231#1663C2×C1112yescomplemented
232#1663C2×C1112yescomplemented
233#1660C2×C1112yescomplemented
234#1532C2×C1111yescharacteristic
235#1531C2×C1111yescharacteristic, complemented
236C2×#330C2×C1111yescharacteristic, complemented
237C23×C11—21no—
238C23×C11#12011yescharacteristic
239Q8×C11—41no—
240Q8×C11—42no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—42no—
244Q8×C11—81no—
245Q8×C11—82no—
246D4×C11—41no—
247D4×C11—42no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—81no—
263C2×C4×C11—82no—
264C2×C4×C11#12011yescharacteristic
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C8×C11—24no—
271C8×C11—22no—
272C8×C11—42no—
273C8×C11—41no—
274#564C22×C1112yes—
275#563C22×C1112yes—
276#557—21no—
277#554—21no—
278#552—21no—
279#552—22no—
280#552—21no—
281#544—21no—
282#544—21no—
283#541—21no—
284#541—22no—
285#539—21no—
286#533C22×C1111yescharacteristic
287#533C22×C1111yescharacteristic
288#529C22×C1111yescharacteristic
289C2×#125C22×C1111yescharacteristic
290#501—21no—
291#501—21no—
292#501C22×C1112yes—
293#501C22×C1112yes—
294#501C22×C1111yescharacteristic
295#501C22×C1112yes—
296#497C22×C1111yescharacteristic
297#491C22×C1111yescharacteristic
298#491C22×C1112yes—
299#489C22×C1111yescharacteristic
300#484—21no—
301#483—21no—
302#479—22no—
303#467—21no—
304#465—21no—
305#441—21no—
306#440—21no—
307#432C22×C1111yescharacteristic
308#427—22no—
309C2×#97C22×C1111yescharacteristic
310C2×#97C22×C1111yescharacteristic
311#330C22×C1112yes—
312#330C22×C1112yes—
313#330C22×C1112yes—
314#330C22×C1112yes—
315#330C22×C1112yes—
316#329C22×C1112yes—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11#45612yes—
323C22×C11C2×#12011yescharacteristic
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—81no—
338C4×C11—81no—
339C2×Q16—21no—
340C2×SD16—21no—
341C22×C8—21no—
342C22×C8—21no—
343C4⋊Q8—22no—
344C4⋊Q8—21no—
345C4⋊Q8—22no—
346C4⋊Q8D4×C1111yescharacteristic
347C4⋊Q8D4×C1111yescharacteristic
348C4⋊Q8C23×C1111yescharacteristic
349C4⋊Q8C23×C1111yescharacteristic
350#126—22no—
351#126—22no—
352#126—22no—
353#126—22no—
354#126—21no—
355#125—22no—
356#125—22no—
357#125—21no—
358#125—22no—
359#125—22no—
360#125—22no—
361#125—22no—
362#125—22no—
363#125—22no—
364#125—21no—
365#125—21no—
366#125—21no—
367#125D4×C1112yes—
368#125C23×C1112yes—
369#125C23×C1111yescharacteristic
370#125C23×C1112yes—
371#124C23×C1111yescharacteristic
372#123—22no—
373#123—22no—
374#123—21no—
375C22⋊Q8—22no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8D4×C1111yescharacteristic
386#121D4×C1111yescharacteristic
387C4×Q8—21no—
388C4×Q8—22no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8D4×C1111yescharacteristic
395C4×D4—22no—
396C4×D4—21no—
397C4×D4D4×C1111yescharacteristic
398#117—22no—
399#117—21no—
400#117—22no—
401#117—21no—
402#117—21no—
403#117D4×C1112yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4D4×C1111yescharacteristic
408C2×C4⋊C4D4×C1111yescharacteristic
409C2×C42C23×C1111yescharacteristic
410#107—22no—
411#107—22no—
412#107—21no—
413#107—22no—
414#106—22no—
415#106—22no—
416#106—21no—
417#106—22no—
418C4⋊C8—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—22no—
423#103—22no—
424#102—21no—
425C22⋊C8—21no—
426#97—21no—
427#97—21no—
428#97C23×C1112yes—
429#97C23×C1112yes—
430#97C23×C1111yescharacteristic
431#97C23×C1111yescharacteristic
432C2×C11—22no—
433C2×C11—81no—
434C2×C11C2×#45611yescharacteristic
435C2×C11#301811yescharacteristic
436C2×C11#302011yescharacteristic
437C2×Q8—22no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C1111yescharacteristic
443C2×D4—21no—
444C2×D4C2×D4×C1111yescharacteristic
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452Q16—42no—
453SD16—42no—
454C2×C8—24no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—22no—
459C2×C8—42no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C1112yes—
489C4⋊C4C2×D4×C1111yescharacteristic
490C4⋊C4C2×D4×C1112yes—
491C4⋊C4C2×D4×C1111yescharacteristic
492C4⋊C4C2×D4×C1112yes—
493C4⋊C4C2×D4×C1112yes—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—41no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—21no—
509C42—41no—
510C42C2×D4×C1111yescharacteristic
511C42C2×D4×C1111yescharacteristic
512C42C2×D4×C1111yescharacteristic
513C42C24×C1111yescharacteristic
514C11#1904711yescharacteristic, direct product factor, Sylow
515C23—21no—
516C23C11×#12011yescharacteristic
517Q8—41no—
518Q8—42no—
519Q8—41no—
520Q8—41no—
521Q8—42no—
522Q8—81no—
523Q8—82no—
524D4—41no—
525D4—42no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—81no—
541C2×C4—82no—
542C2×C4C11×#12011yescharacteristic
543C2×C4C11×#12011yescharacteristic
544C2×C4C11×#12011yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C22×D4×C1111yescharacteristic
547C2×C4C22×D4×C1111yescharacteristic
548C8—24no—
549C8—22no—
550C8—41no—
551C8—42no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C11×#45612yes—
558C22C2×C11×#12011yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—81no—
573C4—81no—
574C2—22no—
575C2—81no—
576C2C2×C11×#45611yescharacteristic
577C2C11×#301811yescharacteristic
578C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3236C2semidirect
4. C11×#3162C2semidirect
5. C11×#1664C2semidirect
6. C11×#1663C2semidirect
7. C11×#1663C2semidirect
8. C11×#1660C2semidirect
10. C11×#1531C2semidirect
11. C2×C11×#330C2semidirect
148. #19047C11direct (N × H)
227. #3236C2×C11semidirect
229. #3162C2×C11semidirect
230. #1664C2×C11semidirect
231. #1663C2×C11semidirect
232. #1663C2×C11semidirect
233. #1660C2×C11semidirect
235. #1531C2×C11semidirect
236. C2×#330C2×C11semidirect
514. C11#19047direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35632
C11×#32362
C11×#31812
C11×#31622
C11×#16642
C11×#16632
C11×#16602
C11×#15322
C11×#15312
C2×C11×#3302
#1904711