Finite Group Databasebeta

← C11×#18222 #14595415

Subgroups — C11×#18222 #14595415

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic, complemented
2C11×#3101C211yesmaximal, characteristic, complemented
3C11×#3100C211yesmaximal, characteristic, complemented
4C11×#2535C211yesmaximal, characteristic, complemented
5C11×#1612C214yesmaximal, complemented
6C11×#1600C214yesmaximal, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#1517C211yesmaximal, characteristic, complemented
9C11×#1460C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#556—21no—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#538C2214yes—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#525—22no—
21C2×C11×#121—21no—
22C11×#520—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#483C2212yes—
26C11×#480C2212yes—
27C11×#476—21no—
28C11×#474—21no—
29C11×#461—21no—
30C11×#459—21no—
31C11×#450C2212yes—
32C11×#447C2212yes—
33C4×C11×SD16—22no—
34C4×C11×D8—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C11×#397C2212yes—
38C11×#392C2212yes—
39C11×#386—22no—
40C11×#382C2211yescharacteristic
41C11×#380—21no—
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#323C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D412yes—
52C2×C11×SD16—22no—
53C2×C11×D8—22no—
54C11×C4⋊Q8D411yescharacteristic, complemented
55C11×C4⋊Q8D411yescharacteristic, complemented
56C11×C4⋊Q8D411yescharacteristic, complemented
57C11×#127—22no—
58C11×#127D411yescharacteristic, complemented
59C11×#126—24no—
60C11×#125—21no—
61C11×#124—22no—
62C11×#124—24no—
63C11×#124—21no—
64C11×#123—24no—
65C11×#123—24no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8C2312yes—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—21no—
74C11×#121—44no—
75C11×#121C2312yes—
76C11×#120—24no—
77C4×Q8×C11—22no—
78C4×Q8×C11—21no—
79C4×Q8×C11D412yescomplemented
80C4×D4×C11—22no—
81C4×D4×C11—24no—
82C4×D4×C11—24no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11D412yescomplemented
93C11×#117—22no—
94C11×#117—22no—
95C11×#117—21no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4C2312yes—
104C2×C42×C11C2311yescharacteristic
105C11×#107—22no—
106C11×#106—22no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×#103—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×C22⋊C8C2312yes—
114C11×C22⋊C8C2312yes—
115C4×C8×C11—21no—
116C4×C8×C11—21no—
117C11×#95—22no—
118C11×#95—21no—
119C11×#95C2312yes—
120#18222C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C24×C11C2×D412yes—
123C11×#41—42no—
124C11×#41—42no—
125C11×#41—84no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—42no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—82no—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—82no—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C11×SD16—44no—
161C11×D8—44no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4C2×D412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—82no—
190C42×C11—24no—
191C42×C11—22no—
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196#3506C2×C1111yescharacteristic, complemented
197#3101C2×C1111yescharacteristic, complemented
198#3100C2×C1111yescharacteristic, complemented
199#2535C2×C1111yescharacteristic, complemented
200#1612C2×C1114yescomplemented
201#1600C2×C1114yescomplemented
202#1518C2×C1111yescharacteristic, complemented
203#1517C2×C1111yescharacteristic, complemented
204#1460C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—42no—
220Q8×C11—42no—
221Q8×C11—42no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—42no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—84no—
234D4×C11—84no—
235D4×C11—88no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—82no—
252C2×C4×C11—84no—
253C2×C4×C11—82no—
254C2×C4×C11—82no—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11#13512yes—
260C2×C4×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C8×C11—42no—
264C8×C11—42no—
265#559—22no—
266#556—21no—
267#555—21no—
268#553—22no—
269#550—21no—
270#547—21no—
271#538C22×C1114yes—
272#535—21no—
273#533C22×C1111yescharacteristic
274#532C22×C1111yescharacteristic
275#525—22no—
276C2×#121—21no—
277#520—21no—
278C2×C4×D4C22×C1111yescharacteristic
279C2×C4×D4C22×C1111yescharacteristic
280#483C22×C1112yes—
281#480C22×C1112yes—
282#476—21no—
283#474—21no—
284#461—21no—
285#459—21no—
286#450C22×C1112yes—
287#447C22×C1112yes—
288C4×SD16—22no—
289C4×D8—22no—
290#431C22×C1111yescharacteristic
291#431C22×C1111yescharacteristic
292#397C22×C1112yes—
293#392C22×C1112yes—
294#386—22no—
295#382C22×C1111yescharacteristic
296#380—21no—
297#328C22×C1114yes—
298#327C22×C1114yes—
299#323C22×C1114yes—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—42no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—82no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11C2×#12011yescharacteristic
318C22×C11C2×#13511yescharacteristic
319C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—82no—
329C4×C11—81no—
330C4×C11#44912yes—
331C4×C11#44912yes—
332C2×#41—22no—
333C2×#41—21no—
334C22×D4—22no—
335C22×D4D4×C1111yescharacteristic
336C22×D4C23×C1111yescharacteristic
337C23×C4—21no—
338C23×C4D4×C1112yes—
339C2×SD16—22no—
340C2×D8—22no—
341C4⋊Q8D4×C1111yescharacteristic, complemented
342C4⋊Q8D4×C1111yescharacteristic, complemented
343C4⋊Q8D4×C1111yescharacteristic, complemented
344#127—22no—
345#127D4×C1111yescharacteristic, complemented
346#126—24no—
347#125—21no—
348#124—22no—
349#124—24no—
350#124—21no—
351#123—24no—
352#123—24no—
353C22⋊Q8—22no—
354C22⋊Q8—21no—
355C22⋊Q8C23×C1112yes—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—24no—
360#121—21no—
361#121—44no—
362#121C23×C1112yes—
363#120—24no—
364C4×Q8—22no—
365C4×Q8—21no—
366C4×Q8D4×C1112yescomplemented
367C4×D4—22no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4D4×C1112yescomplemented
380#117—22no—
381#117—22no—
382#117—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C22⋊C4—22no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4C23×C1112yes—
391C2×C42C23×C1111yescharacteristic
392#107—22no—
393#106—22no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396#103—22no—
397#102—22no—
398#102—22no—
399#102—22no—
400C22⋊C8C23×C1112yes—
401C22⋊C8C23×C1112yes—
402C4×C8—21no—
403C4×C8—21no—
404#95—22no—
405#95—21no—
406#95C23×C1112yes—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—82no—
410C2×C11—82no—
411C2×C11—82no—
412C2×C11C2×#44911yescharacteristic
413C2×C11#301911yescharacteristic
414C2×C11#302511yescharacteristic
415C24—21no—
416C24C2×D4×C1112yes—
417#41—42no—
418#41—42no—
419#41—84no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×D4×C1112yes—
423C2×D4—22no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—42no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—82no—
438C2×D4C2×D4×C1112yes—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—82no—
450C22×C4C2×D4×C1112yes—
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C24×C1111yescharacteristic
454SD16—44no—
455D8—44no—
456C2×C8—22no—
457C2×C8—22no—
458C4⋊C4—24no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4C2×D4×C1112yes—
471C4⋊C4C2×D4×C1112yes—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—44no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—82no—
484C42—24no—
485C42—22no—
486C42C2×D4×C1111yescharacteristic
487C42C2×D4×C1111yescharacteristic
488C42C2×D4×C1111yescharacteristic
489C42C2×D4×C1111yescharacteristic
490C11#1822211yescharacteristic, direct product factor, Sylow
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—42no—
497C23—42no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23C22×D4×C1111yescharacteristic
505Q8—42no—
506Q8—42no—
507Q8—42no—
508D4—22no—
509D4—22no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—84no—
520D4—84no—
521D4—88no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—84no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4C11×#12011yescharacteristic
542C2×C4C11×#12011yescharacteristic
543C2×C4C11×#12011yescharacteristic
544C2×C4C11×#12011yescharacteristic
545C2×C4C11×#13512yes—
546C2×C4C11×AGL(1,ℤ/8)12yes—
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C22×D4×C1111yescharacteristic
549C8—42no—
550C8—42no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—82no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×C11×#12011yescharacteristic
569C22C2×C11×#13511yescharacteristic
570C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—82no—
580C4—81no—
581C4C11×#44912yes—
582C4C11×#44912yes—
583C2—21no—
584C2—21no—
585C2—82no—
586C2—82no—
587C2—82no—
588C2C2×C11×#44911yescharacteristic
589C2C11×#301911yescharacteristic
590C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ 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×#3506C2semidirect
2. C11×#3101C2semidirect
3. C11×#3100C2semidirect
4. C11×#2535C2semidirect
5. C11×#1612C2semidirect
6. C11×#1600C2semidirect
7. C11×#1518C2semidirect
8. C11×#1517C2semidirect
9. C11×#1460C2semidirect
54. C11×C4⋊Q8D4semidirect
55. C11×C4⋊Q8D4semidirect
56. C11×C4⋊Q8D4semidirect
58. C11×#127D4semidirect
79. C4×Q8×C11D4semidirect
92. C4×D4×C11D4semidirect
120. #18222C11direct (N × H)
196. #3506C2×C11semidirect
197. #3101C2×C11semidirect
198. #3100C2×C11semidirect
199. #2535C2×C11semidirect
200. #1612C2×C11semidirect
201. #1600C2×C11semidirect
202. #1518C2×C11semidirect
203. #1517C2×C11semidirect
204. #1460C2×C11semidirect
341. C4⋊Q8D4×C11semidirect
342. C4⋊Q8D4×C11semidirect
343. C4⋊Q8D4×C11semidirect
345. #127D4×C11semidirect
366. C4×Q8D4×C11semidirect
379. C4×D4D4×C11semidirect
490. C11#18222direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#31012
C11×#31002
C11×#25352
C11×#16122
C11×#16002
C11×#15182
C11×#15172
C11×#14602
#1822211