Finite Group Databasebeta

← C11×#18201 #14595394

Subgroups — C11×#18201 #14595394

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3492C211yesmaximal, characteristic
2C11×#3091C212yesmaximal, complemented
3C11×#2484C211yesmaximal, characteristic, complemented
4C11×#1617C211yesmaximal, characteristic, complemented
5C11×#1616C211yesmaximal, characteristic, complemented
6C11×#1615C212yesmaximal, complemented
7C11×#1611C211yesmaximal, characteristic, complemented
8C11×#1610C211yesmaximal, characteristic, complemented
9C11×#1609C212yesmaximal, complemented
10C11×#1516C212yesmaximal, complemented
11C2×C11×#324C211yesmaximal, characteristic, complemented
12C11×#554—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#547—22no—
16C11×#544C2211yescharacteristic
17C11×#539—21no—
18C11×#539C2212yes—
19C11×#537C2211yescharacteristic
20C11×#525—21no—
21C11×#525—21no—
22C11×#525C2212yes—
23C11×#520—21no—
24C2×C11×#117C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C11×#485—22no—
27C11×#484C2212yes—
28C11×#483C2212yes—
29C11×#482—22no—
30C11×#481C2212yes—
31C11×#480C2212yes—
32C11×#427—22no—
33C11×#416—22no—
34C2×C11×C22⋊C8C2212yes—
35C11×#400C2211yescharacteristic
36C11×#400C2211yescharacteristic
37C11×#398C2211yescharacteristic
38C11×#398C2211yescharacteristic
39C11×#387—21no—
40C11×#387—21no—
41C11×#385—21no—
42C11×#381—21no—
43C11×#381C2211yescharacteristic
44C11×#328C2212yes—
45C11×#328C2212yes—
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2211yescharacteristic
49C11×#324C2211yescharacteristic
50C11×#324C2212yes—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41D412yes—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C22×C8×C11—22no—
58C11×C4⋊Q8—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125—22no—
62C11×#125—22no—
63C11×#125—22no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8D412yes—
77C11×C22⋊Q8C2312yes—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#121—22no—
82C11×#121—21no—
83C11×#121D412yes—
84C11×#121C2312yes—
85C11×#120—22no—
86C4×Q8×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C11×#117—22no—
95C11×#117—21no—
96C11×#117—21no—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117D412yes—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4D411yescharacteristic
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11—21no—
114C11×#107—22no—
115C11×#107—22no—
116C11×#106—22no—
117C11×#106—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8C2312yes—
124C11×C22⋊C8C2312yes—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18201C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11C2×D411yescharacteristic
136C11×#41—42no—
137C11×#41—44no—
138C11×#41—42no—
139C11×#41—82no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11C2×D412yes—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2411yescharacteristic
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—44no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4C2×D412yes—
194C11×C4⋊C4C2×D412yes—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C42×C11—22no—
208C42×C11—22no—
209C42×C11—22no—
210C42×C11—42no—
211#3492C2×C1111yescharacteristic
212#3091C2×C1112yescomplemented
213#2484C2×C1111yescharacteristic, complemented
214#1617C2×C1111yescharacteristic, complemented
215#1616C2×C1111yescharacteristic, complemented
216#1615C2×C1112yescomplemented
217#1611C2×C1111yescharacteristic, complemented
218#1610C2×C1111yescharacteristic, complemented
219#1609C2×C1112yescomplemented
220#1516C2×C1112yescomplemented
221C2×#324C2×C1111yescharacteristic, complemented
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—41no—
227C23×C11#12011yescharacteristic
228C23×C11#12011yescharacteristic
229C23×C11C22×D411yescharacteristic
230Q8×C11—42no—
231Q8×C11—42no—
232Q8×C11—81no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—44no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—44no—
239D4×C11—81no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—44no—
257C2×C4×C11—42no—
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—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—82no—
272C2×C4×C11—81no—
273C2×C4×C11—82no—
274C2×C4×C11#12012yes—
275C2×C4×C11#13512yes—
276C2×C4×C11C22×D412yes—
277C8×C11—42no—
278C8×C11—42no—
279#554—22no—
280#553—22no—
281#552—22no—
282#547—22no—
283#544C22×C1111yescharacteristic
284#539—21no—
285#539C22×C1112yes—
286#537C22×C1111yescharacteristic
287#525—21no—
288#525—21no—
289#525C22×C1112yes—
290#520—21no—
291C2×#117C22×C1111yescharacteristic
292C22×C4⋊C4C22×C1111yescharacteristic
293#485—22no—
294#484C22×C1112yes—
295#483C22×C1112yes—
296#482—22no—
297#481C22×C1112yes—
298#480C22×C1112yes—
299#427—22no—
300#416—22no—
301C2×C22⋊C8C22×C1112yes—
302#400C22×C1111yescharacteristic
303#400C22×C1111yescharacteristic
304#398C22×C1111yescharacteristic
305#398C22×C1111yescharacteristic
306#387—21no—
307#387—21no—
308#385—21no—
309#381—21no—
310#381C22×C1111yescharacteristic
311#328C22×C1112yes—
312#328C22×C1112yes—
313#327C22×C1112yes—
314#327C22×C1112yes—
315#324C22×C1112yes—
316#324C22×C1111yescharacteristic
317#324C22×C1111yescharacteristic
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11#45812yes—
331C22×C11C2×#12011yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11#57511yescharacteristic
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—42no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11—81no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41D4×C1112yes—
350C23×C4D4×C1111yescharacteristic
351C23×C4D4×C1111yescharacteristic
352C23×C4C23×C1111yescharacteristic
353C22×C8—22no—
354C4⋊Q8—22no—
355#126—22no—
356#126—22no—
357#125—22no—
358#125—22no—
359#125—22no—
360#123—22no—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—22no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8D4×C1112yes—
373C22⋊Q8C23×C1112yes—
374#121—21no—
375#121—21no—
376#121—21no—
377#121—22no—
378#121—21no—
379#121D4×C1112yes—
380#121C23×C1112yes—
381#120—22no—
382C4×Q8—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390#117—22no—
391#117—21no—
392#117—21no—
393#117—22no—
394#117—22no—
395#117D4×C1112yes—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4D4×C1111yescharacteristic
402C2×C4⋊C4D4×C1111yescharacteristic
403C2×C4⋊C4C23×C1111yescharacteristic
404C2×C4⋊C4C23×C1111yescharacteristic
405C2×C4⋊C4C23×C1111yescharacteristic
406C2×C4⋊C4C23×C1111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C42—21no—
410#107—22no—
411#107—22no—
412#106—22no—
413#106—22no—
414#103—22no—
415#103—22no—
416#102—22no—
417#102—22no—
418C22⋊C8—22no—
419C22⋊C8C23×C1112yes—
420C22⋊C8C23×C1112yes—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95C23×C1111yescharacteristic
429#95C23×C1111yescharacteristic
430C2×C11—21no—
431C2×C11—21no—
432C2×C11—22no—
433C2×C11—41no—
434C2×C11—82no—
435C2×C11#300211yescharacteristic
436C2×C11#302011yescharacteristic
437C2×C11C2×#45811yescharacteristic
438C24C2×D4×C1111yescharacteristic
439#41—42no—
440#41—44no—
441#41—42no—
442#41—82no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C1112yes—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4C2×D4×C1112yes—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1112yes—
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1112yes—
474C22×C4C24×C1111yescharacteristic
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—44no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4C2×D4×C1112yes—
497C4⋊C4C2×D4×C1112yes—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—42no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—42no—
514C11#1820111yescharacteristic, direct product factor, Sylow
515C23—21no—
516C23—21no—
517C23—22no—
518C23—22no—
519C23—41no—
520C23C11×#12011yescharacteristic
521C23C11×#12011yescharacteristic
522C23C22×D4×C1111yescharacteristic
523Q8—42no—
524Q8—42no—
525Q8—81no—
526D4—42no—
527D4—42no—
528D4—44no—
529D4—42no—
530D4—42no—
531D4—44no—
532D4—81no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—81no—
566C2×C4—82no—
567C2×C4C11×#12012yes—
568C2×C4C11×#13512yes—
569C2×C4C22×D4×C1112yes—
570C8—42no—
571C8—42no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22C11×#45812yes—
585C22C2×C11×#12011yescharacteristic
586C22C2×C11×#13511yescharacteristic
587C22C11×#57511yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C2—21no—
602C2—21no—
603C2—22no—
604C2—41no—
605C2—82no—
606C2C11×#300211yescharacteristic
607C2C11×#302011yescharacteristic
608C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3492C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3091C2semidirect
3. C11×#2484C2semidirect
4. C11×#1617C2semidirect
5. C11×#1616C2semidirect
6. C11×#1615C2semidirect
7. C11×#1611C2semidirect
8. C11×#1610C2semidirect
9. C11×#1609C2semidirect
10. C11×#1516C2semidirect
11. C2×C11×#324C2semidirect
134. #18201C11direct (N × H)
212. #3091C2×C11semidirect
213. #2484C2×C11semidirect
214. #1617C2×C11semidirect
215. #1616C2×C11semidirect
216. #1615C2×C11semidirect
217. #1611C2×C11semidirect
218. #1610C2×C11semidirect
219. #1609C2×C11semidirect
220. #1516C2×C11semidirect
221. C2×#324C2×C11semidirect
514. C11#18201direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#30912
C11×#24842
C11×#16172
C11×#16162
C11×#16152
C11×#16112
C11×#16102
C11×#16092
C11×#15162
C2×C11×#3242
#1820111