Finite Group Databasebeta

← C11×#18884 #14596077

Subgroups — C11×#18884 #14596077

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic, complemented
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3227C211yesmaximal, characteristic, complemented
4C11×#3035C211yesmaximal, characteristic
5C11×#1653C212yesmaximal, complemented
6C11×#1651C212yesmaximal, complemented
7C11×#1627C212yesmaximal, complemented
8C11×#1626C212yesmaximal, complemented
9C2×C11×#332C211yesmaximal, characteristic, complemented
10C11×#1481C211yesmaximal, characteristic, complemented
11C11×#1477C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13Q82×C11—21no—
14C11×#557C2212yes—
15C11×#554—21no—
16C11×#554—22no—
17D4×Q8×C11—22no—
18D4×Q8×C11C2212yes—
19C11×#544—22no—
20C11×#544—21no—
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C2×C11×C4⋊Q8—21no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C11×#520—21no—
27C4×C11×#41C2211yescharacteristic
28C11×#498C2212yes—
29C11×#486C2212yes—
30C11×#481—22no—
31C11×#476—22no—
32C11×#476—21no—
33C11×#475C2212yes—
34C11×#465—22no—
35C11×#464—21no—
36C11×#463—21no—
37C11×#462C2211yescharacteristic
38C11×#461—21no—
39C11×#461C2211yescharacteristic
40C11×#460C2211yescharacteristic
41C11×#460C2212yes—
42C11×#459C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#416—21no—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×Q8⋊C8C2212yes—
51C11×Q8⋊C8C2212yes—
52C11×D4⋊C8C2212yes—
53C2×C11×#41—21no—
54C2×C11×#41D411yescharacteristic
55C22×Q8×C11—22no—
56C22×Q8×C11—21no—
57C11×#135—44no—
58C2×C11×Q16—21no—
59C2×C11×SD16—21no—
60C2×C11×SD16—21no—
61C2×C11×SD16—22no—
62C2×C11×D8—21no—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—24no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8D411yescharacteristic
73C11×C4⋊Q8D412yes—
74C11×C4⋊Q8D411yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2312yes—
77C11×#127C2311yescharacteristic
78C11×#125—22no—
79C11×#125—24no—
80C11×#125—22no—
81C11×#125—21no—
82C11×#124—21no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8—24no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—24no—
89C11×C22⋊Q8D412yes—
90C11×#121—21no—
91C11×#121—21no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—21no—
96C4×Q8×C11D411yescharacteristic
97C4×Q8×C11C2311yescharacteristic
98C4×Q8×C11C2312yes—
99C4×D4×C11—24no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11D411yescharacteristic
106C4×D4×C11C2311yescharacteristic
107C11×#117—22no—
108C11×#117—21no—
109C11×#117—21no—
110C11×#117D411yescharacteristic
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4D412yes—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C11×#106—24no—
118C11×#106—22no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8C2312yes—
123C11×C4⋊C8C2311yescharacteristic
124C11×C4⋊C8C2311yescharacteristic
125C11×#103—22no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—22no—
131C11×#102—24no—
132C11×C22⋊C8—21no—
133C4×C8×C11C2312yes—
134#18884C1111yesmaximal, characteristic, direct product factor, Sylow
135C11×#41—22no—
136C11×#41—42no—
137C11×#41—42no—
138C11×#41SD1614yescomplemented
139C2×Q8×C11—24no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—21no—
144C2×Q8×C11—81no—
145C2×Q8×C11—81no—
146C2×Q8×C11—82no—
147C2×Q8×C11—82no—
148C2×Q8×C11C2×D412yes—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C11×Q16—42no—
166C11×SD16—42no—
167C11×SD16—42no—
168C11×SD16—82no—
169C11×D8—42no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—42no—
175C2×C8×C11—81no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D414yes—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C42×C11—24no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—22no—
208C42×C11C2×D411yescharacteristic
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211C42×C11C2411yescharacteristic
212#3503C2×C1111yescharacteristic, complemented
213#3246C2×C1111yescharacteristic, complemented
214#3227C2×C1111yescharacteristic, complemented
215#3035C2×C1111yescharacteristic
216#1653C2×C1112yescomplemented
217#1651C2×C1112yescomplemented
218#1627C2×C1112yescomplemented
219#1626C2×C1112yescomplemented
220C2×#332C2×C1111yescharacteristic, complemented
221#1481C2×C1111yescharacteristic, complemented
222#1477C2×C1111yescharacteristic, complemented
223C23×C11—21no—
224C23×C11—41no—
225C23×C11#12011yescharacteristic
226Q8×C11—21no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—42no—
230Q8×C11—42no—
231Q8×C11—42no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—82no—
235Q8×C11—84no—
236Q8×C11C2×SD1612yes—
237D4×C11—24no—
238D4×C11—21no—
239D4×C11—42no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—82no—
245D4×C11C2×SD1612yes—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—82no—
261C2×C4×C11—84no—
262C2×C4×C11—82no—
263C2×C4×C11#12011yescharacteristic
264C2×C4×C11#12011yescharacteristic
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11C2×SD1612yes—
267C2×C4×C11#13712yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C8×C11—42no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—42no—
275C2×#135—21no—
276Q82—21no—
277#557C22×C1112yes—
278#554—21no—
279#554—22no—
280D4×Q8—22no—
281D4×Q8C22×C1112yes—
282#544—22no—
283#544—21no—
284#533—21no—
285#533C22×C1111yescharacteristic
286#532C22×C1111yescharacteristic
287C2×C4⋊Q8—21no—
288C2×C4⋊Q8C22×C1111yescharacteristic
289#520—21no—
290C4×#41C22×C1111yescharacteristic
291#498C22×C1112yes—
292#486C22×C1112yes—
293#481—22no—
294#476—22no—
295#476—21no—
296#475C22×C1112yes—
297#465—22no—
298#464—21no—
299#463—21no—
300#462C22×C1111yescharacteristic
301#461—21no—
302#461C22×C1111yescharacteristic
303#460C22×C1111yescharacteristic
304#460C22×C1112yes—
305#459C22×C1111yescharacteristic
306#431C22×C1111yescharacteristic
307C2×C4⋊C8C22×C1111yescharacteristic
308C2×C4⋊C8C22×C1111yescharacteristic
309#416—21no—
310#332C22×C1112yes—
311#332C22×C1112yes—
312Q8⋊C8C22×C1112yes—
313Q8⋊C8C22×C1112yes—
314Q8⋊C8C22×C1112yes—
315D4⋊C8C22×C1112yes—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—22no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11#44812yes—
325C22×C11C2×#12011yescharacteristic
326C4×C11—22no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—42no—
332C4×C11—44no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—81no—
336C4×C11#44812yes—
337C4×C11C22×SD1611yescharacteristic
338C4×C11C2×#13711yescharacteristic
339C4×C11#57611yescharacteristic
340C4×C11#57711yescharacteristic
341C2×#41—21no—
342C2×#41D4×C1111yescharacteristic
343C22×Q8—22no—
344C22×Q8—21no—
345#135—44no—
346C2×Q16—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—22no—
350C2×D8—21no—
351C22×C8—21no—
352C22×C8—21no—
353C4⋊Q8—22no—
354C4⋊Q8—22no—
355C4⋊Q8—24no—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8D4×C1111yescharacteristic
361C4⋊Q8D4×C1112yes—
362C4⋊Q8D4×C1111yescharacteristic
363C4⋊Q8C23×C1111yescharacteristic
364C4⋊Q8C23×C1112yes—
365#127C23×C1111yescharacteristic
366#125—22no—
367#125—24no—
368#125—22no—
369#125—21no—
370#124—21no—
371C22⋊Q8—22no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—24no—
377C22⋊Q8D4×C1112yes—
378#121—21no—
379#121—21no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—21no—
384C4×Q8D4×C1111yescharacteristic
385C4×Q8C23×C1111yescharacteristic
386C4×Q8C23×C1112yes—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4D4×C1111yescharacteristic
394C4×D4C23×C1111yescharacteristic
395#117—22no—
396#117—21no—
397#117—21no—
398#117D4×C1111yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4D4×C1112yes—
403C2×C42—21no—
404C2×C42C23×C1111yescharacteristic
405#106—22no—
406#106—24no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C1112yes—
411C4⋊C8C23×C1111yescharacteristic
412C4⋊C8C23×C1111yescharacteristic
413#103—22no—
414#103—21no—
415#103—21no—
416#102—21no—
417#102—21no—
418#102—22no—
419#102—24no—
420C22⋊C8—21no—
421C4×C8C23×C1112yes—
422C2×C11—22no—
423C2×C11—42no—
424C2×C11—161no—
425C2×C11C2×#44811yescharacteristic
426C2×C11#301211yescharacteristic
427C2×C11#302011yescharacteristic
428#41—22no—
429#41—42no—
430#41—42no—
431#41C11×SD1614yescomplemented
432C2×Q8—24no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—81no—
438C2×Q8—81no—
439C2×Q8—82no—
440C2×Q8—82no—
441C2×Q8C2×D4×C1112yes—
442C2×Q8C2×D4×C1111yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C1111yescharacteristic
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458Q16—42no—
459SD16—42no—
460SD16—42no—
461SD16—82no—
462D8—42no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—42no—
468C2×C8—81no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4C2×D4×C1111yescharacteristic
486C4⋊C4C2×D4×C1111yescharacteristic
487C4⋊C4C2×D4×C1114yes—
488C4⋊C4C2×D4×C1112yes—
489C22⋊C4—24no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—24no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—22no—
501C42C2×D4×C1111yescharacteristic
502C42C2×D4×C1111yescharacteristic
503C42C2×D4×C1111yescharacteristic
504C42C24×C1111yescharacteristic
505C11#1888411yescharacteristic, direct product factor, Sylow
506C23—21no—
507C23—41no—
508C23C11×#12011yescharacteristic
509Q8—21no—
510Q8—22no—
511Q8—22no—
512Q8—42no—
513Q8—42no—
514Q8—42no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—84no—
519Q8C2×C11×SD1612yes—
520D4—24no—
521D4—21no—
522D4—42no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—82no—
528D4C2×C11×SD1612yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—84no—
545C2×C4—82no—
546C2×C4C11×#12011yescharacteristic
547C2×C4C11×#12011yescharacteristic
548C2×C4C11×#12011yescharacteristic
549C2×C4C2×C11×SD1612yes—
550C2×C4C11×#13712yes—
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C22×D4×C1111yescharacteristic
554C8—42no—
555C8—41no—
556C8—41no—
557C8—42no—
558C22—21no—
559C22—21no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C11×#44812yes—
567C22C2×C11×#12011yescharacteristic
568C4—22no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—42no—
574C4—44no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4C11×#44812yes—
579C4C22×C11×SD1611yescharacteristic
580C4C2×C11×#13711yescharacteristic
581C4C11×#57611yescharacteristic
582C4C11×#57711yescharacteristic
583C2—22no—
584C2—42no—
585C2—161no—
586C2C2×C11×#44811yescharacteristic
587C2C11×#301211yescharacteristic
588C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3035C2
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
1. C11×#3503C2semidirect
2. C11×#3246C2semidirect
3. C11×#3227C2semidirect
5. C11×#1653C2semidirect
6. C11×#1651C2semidirect
7. C11×#1627C2semidirect
8. C11×#1626C2semidirect
9. C2×C11×#332C2semidirect
10. C11×#1481C2semidirect
11. C11×#1477C2semidirect
134. #18884C11direct (N × H)
138. C11×#41SD16semidirect
212. #3503C2×C11semidirect
213. #3246C2×C11semidirect
214. #3227C2×C11semidirect
216. #1653C2×C11semidirect
217. #1651C2×C11semidirect
218. #1627C2×C11semidirect
219. #1626C2×C11semidirect
220. C2×#332C2×C11semidirect
221. #1481C2×C11semidirect
222. #1477C2×C11semidirect
431. #41C11×SD16semidirect
505. C11#18884direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#32462
C11×#32272
C11×#30352
C11×#16532
C11×#16512
C11×#16272
C11×#16262
C2×C11×#3322
C11×#14812
C11×#14772
#1888411