Finite Group Databasebeta

← C11×#18930 #14596123

Subgroups — C11×#18930 #14596123

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3543C211yesmaximal, characteristic, complemented
2C11×#3251C211yesmaximal, characteristic, complemented
3C11×#3212C211yesmaximal, characteristic, complemented
4C11×#3205C211yesmaximal, characteristic, complemented
5C11×#1642C211yesmaximal, characteristic, complemented
6C11×#1641C211yesmaximal, characteristic, complemented
7C11×#1640C211yesmaximal, characteristic, complemented
8C11×#1639C211yesmaximal, characteristic, complemented
9C11×#1621C211yesmaximal, characteristic, complemented
10C11×#1621C211yesmaximal, characteristic, complemented
11C11×#1620C211yesmaximal, characteristic, complemented
12C11×#1619C211yesmaximal, characteristic, complemented
13C11×#1545C211yesmaximal, characteristic, complemented
14C11×#1495C211yesmaximal, characteristic, complemented
15C11×#1482C211yesmaximal, characteristic, complemented
16C11×#560—22no—
17C11×#559C2211yescharacteristic
18C11×#550C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#546—21no—
21C11×#546—21no—
22D42×C11—21no—
23D42×C11—21no—
24D42×C11C2211yescharacteristic
25C11×#540—21no—
26C11×#540—21no—
27C11×#535—21no—
28C11×#535—21no—
29C11×#534—22no—
30C11×#532C2211yescharacteristic, complemented
31C2×C11×#127C2211yescharacteristic
32C11×#529C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C11×#495—21no—
35C11×#493C2211yescharacteristic
36C11×#493C2211yescharacteristic, complemented
37C11×#488—21no—
38C11×#486C2211yescharacteristic
39C11×#486C2211yescharacteristic, complemented
40C11×#478—21no—
41C11×#475C2211yescharacteristic, complemented
42C11×#474C2211yescharacteristic, complemented
43C11×#469—21no—
44C11×#468—21no—
45C11×#463—21no—
46C11×#462C2211yescharacteristic, complemented
47C11×#461C2211yescharacteristic, complemented
48C11×#460C2211yescharacteristic, complemented
49C11×#460C2211yescharacteristic, complemented
50C11×#459—22no—
51C11×#459C2211yescharacteristic, complemented
52C11×#459C2211yescharacteristic, complemented
53C11×#452—21no—
54C11×#449—21no—
55C11×#447—22no—
56C11×#431C2211yescharacteristic, complemented
57C11×#431C2211yescharacteristic, complemented
58C11×#423C2211yescharacteristic, complemented
59C11×#331C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic, complemented
62C11×#331C2211yescharacteristic, complemented
63C11×Q8⋊C8C2211yescharacteristic, complemented
64C11×Q8⋊C8C2211yescharacteristic, complemented
65C11×Q8⋊C8C2211yescharacteristic, complemented
66C11×Q8⋊C8C2211yescharacteristic, complemented
67C11×D4⋊C8C2211yescharacteristic, complemented
68C11×D4⋊C8C2211yescharacteristic, complemented
69C11×D4⋊C8C2211yescharacteristic, complemented
70C11×D4⋊C8C2211yescharacteristic, complemented
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—21no—
74C22×D4×C11—22no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11D412yes—
80C2×C11×Q16—21no—
81C2×C11×SD16—21no—
82C2×C11×SD16—21no—
83C2×C11×SD16—21no—
84C2×C11×D8—22no—
85C2×C11×D8—22no—
86C2×C11×D8—21no—
87C2×C11×D8—21no—
88C2×C11×M16—21no—
89C11×C4⋊Q8C2311yescharacteristic
90C11×#127—21no—
91C11×#127—21no—
92C11×#127—21no—
93C11×#127—21no—
94C11×#127D412yes—
95C11×#127C2311yescharacteristic
96C11×#127C2311yescharacteristic
97C11×#127C2311yescharacteristic
98C11×#126—21no—
99C11×#126—21no—
100C11×#125D411yescharacteristic
101C11×#125D411yescharacteristic
102C11×#124—21no—
103C11×#124—21no—
104C11×#124—21no—
105C11×#124D411yescharacteristic
106C11×#124D411yescharacteristic
107C11×#123—22no—
108C11×#123—22no—
109C11×#123—22no—
110C11×#123—22no—
111C11×#123—21no—
112C11×#123—21no—
113C11×C22⋊Q8D411yescharacteristic
114C11×C22⋊Q8D411yescharacteristic
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121D411yescharacteristic
130C11×#121D411yescharacteristic
131C11×#120—22no—
132C11×#120—22no—
133C11×#120—22no—
134C11×#120—22no—
135C11×#120—22no—
136C11×#120—22no—
137C4×Q8×C11C2311yescharacteristic
138C4×Q8×C11C2311yescharacteristic
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C4×D4×C11—21no—
147C4×D4×C11C2311yescharacteristic
148C4×D4×C11C2311yescharacteristic
149C11×#117—21no—
150C11×#117—21no—
151C2×C11×C22⋊C4—22no—
152C2×C42×C11C2311yescharacteristic
153C11×#107—21no—
154C11×#106—21no—
155C11×C4⋊C8—21no—
156C11×C4⋊C8—21no—
157C11×C4⋊C8C2311yescharacteristic
158C11×C4⋊C8C2311yescharacteristic
159C11×C4⋊C8C2311yescharacteristic
160C11×C4⋊C8C2311yescharacteristic
161C11×#103—21no—
162C11×#103—21no—
163C11×#103—21no—
164C11×#102—22no—
165C11×#102—22no—
166C11×#102—21no—
167C11×#102—21no—
168C11×#102—21no—
169C11×#102—21no—
170C11×#102—21no—
171C11×C22⋊C8—21no—
172C11×C22⋊C8—21no—
173C4×C8×C11—21no—
174C4×C8×C11C2311yescharacteristic
175C4×C8×C11C2311yescharacteristic
176#18930C1111yesmaximal, characteristic, direct product factor, Sylow
177C24×C11—22no—
178C24×C11—22no—
179C11×#41—81no—
180C11×#41—81no—
181C11×#41—81no—
182C11×#41—81no—
183C11×#41—81no—
184C11×#41—81no—
185C2×Q8×C11—21no—
186C2×Q8×C11C2×D411yescharacteristic
187C2×Q8×C11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—41no—
207C2×D4×C11—81no—
208C2×D4×C11—81no—
209C2×D4×C11—81no—
210C2×D4×C11—81no—
211C2×D4×C11—81no—
212C2×D4×C11—81no—
213C2×D4×C11—81no—
214C2×D4×C11—81no—
215C2×D4×C11—82no—
216C2×D4×C11—84no—
217C2×D4×C11C2×D411yescharacteristic
218C2×D4×C11C2×D411yescharacteristic
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2×D412yes—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—41no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C11×Q16—81no—
231C11×SD16—81no—
232C11×SD16—81no—
233C11×SD16—81no—
234C11×D8—81no—
235C11×D8—81no—
236C11×D8—82no—
237C11×D8—82no—
238C11×M16—81no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C2×D411yescharacteristic
256C11×C4⋊C4C2×D411yescharacteristic
257C11×C4⋊C4C2×D411yescharacteristic
258C11×C4⋊C4C2×D411yescharacteristic
259C11×C22⋊C4—22no—
260C11×C22⋊C4—22no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—22no—
264C11×C22⋊C4—22no—
265C11×C22⋊C4—21no—
266C11×C22⋊C4—21no—
267C11×C22⋊C4—21no—
268C11×C22⋊C4—21no—
269C11×C22⋊C4—21no—
270C11×C22⋊C4—21no—
271C11×C22⋊C4—21no—
272C11×C22⋊C4—21no—
273C11×C22⋊C4—21no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—41no—
276C11×C22⋊C4—41no—
277C42×C11—21no—
278C42×C11—21no—
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2411yescharacteristic
283#3543C2×C1111yescharacteristic, complemented
284#3251C2×C1111yescharacteristic, complemented
285#3212C2×C1111yescharacteristic, complemented
286#3205C2×C1111yescharacteristic, complemented
287#1642C2×C1111yescharacteristic, complemented
288#1641C2×C1111yescharacteristic, complemented
289#1640C2×C1111yescharacteristic, complemented
290#1639C2×C1111yescharacteristic, complemented
291#1621C2×C1111yescharacteristic, complemented
292#1621C2×C1111yescharacteristic, complemented
293#1620C2×C1111yescharacteristic, complemented
294#1619C2×C1111yescharacteristic, complemented
295#1545C2×C1111yescharacteristic, complemented
296#1495C2×C1111yescharacteristic, complemented
297#1482C2×C1111yescharacteristic, complemented
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—44no—
303C23×C11—41no—
304C23×C11—82no—
305C23×C11—82no—
306C23×C11—82no—
307C23×C11—82no—
308C23×C11—82no—
309C23×C11#12011yescharacteristic
310Q8×C11—21no—
311Q8×C11—21no—
312Q8×C11—21no—
313Q8×C11—21no—
314Q8×C11—41no—
315Q8×C11—41no—
316D4×C11—21no—
317D4×C11—21no—
318D4×C11—21no—
319D4×C11—21no—
320D4×C11—42no—
321D4×C11—42no—
322D4×C11—42no—
323D4×C11—42no—
324D4×C11—42no—
325D4×C11—41no—
326D4×C11—41no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—41no—
330D4×C11—41no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—41no—
334D4×C11—41no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—82no—
338D4×C11—82no—
339D4×C11—82no—
340D4×C11—82no—
341D4×C11—82no—
342D4×C11—82no—
343D4×C11—82no—
344D4×C11—82no—
345D4×C11—82no—
346D4×C11—82no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—82no—
364C2×C4×C11—82no—
365C2×C4×C11—82no—
366C2×C4×C11—82no—
367C2×C4×C11#12011yescharacteristic
368C2×C4×C11#12011yescharacteristic
369C2×C4×C11#12011yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C8×C11—41no—
374C8×C11—41no—
375C8×C11—41no—
376C8×C11—41no—
377C8×C11—41no—
378C8×C11—41no—
379#560—22no—
380#559C22×C1111yescharacteristic
381#550C22×C1111yescharacteristic
382#550C22×C1111yescharacteristic
383#546—21no—
384#546—21no—
385D42—21no—
386D42—21no—
387D42C22×C1111yescharacteristic
388#540—21no—
389#540—21no—
390#535—21no—
391#535—21no—
392#534—22no—
393#532C22×C1111yescharacteristic, complemented
394C2×#127C22×C1111yescharacteristic
395#529C22×C1111yescharacteristic
396#529C22×C1111yescharacteristic
397#495—21no—
398#493C22×C1111yescharacteristic
399#493C22×C1111yescharacteristic, complemented
400#488—21no—
401#486C22×C1111yescharacteristic
402#486C22×C1111yescharacteristic, complemented
403#478—21no—
404#475C22×C1111yescharacteristic, complemented
405#474C22×C1111yescharacteristic, complemented
406#469—21no—
407#468—21no—
408#463—21no—
409#462C22×C1111yescharacteristic, complemented
410#461C22×C1111yescharacteristic, complemented
411#460C22×C1111yescharacteristic, complemented
412#460C22×C1111yescharacteristic, complemented
413#459—22no—
414#459C22×C1111yescharacteristic, complemented
415#459C22×C1111yescharacteristic, complemented
416#452—21no—
417#449—21no—
418#447—22no—
419#431C22×C1111yescharacteristic, complemented
420#431C22×C1111yescharacteristic, complemented
421#423C22×C1111yescharacteristic, complemented
422#331C22×C1111yescharacteristic
423#331C22×C1111yescharacteristic
424#331C22×C1111yescharacteristic, complemented
425#331C22×C1111yescharacteristic, complemented
426Q8⋊C8C22×C1111yescharacteristic, complemented
427Q8⋊C8C22×C1111yescharacteristic, complemented
428Q8⋊C8C22×C1111yescharacteristic, complemented
429Q8⋊C8C22×C1111yescharacteristic, complemented
430D4⋊C8C22×C1111yescharacteristic, complemented
431D4⋊C8C22×C1111yescharacteristic, complemented
432D4⋊C8C22×C1111yescharacteristic, complemented
433D4⋊C8C22×C1111yescharacteristic, complemented
434C22×C11—21no—
435C22×C11—21no—
436C22×C11—21no—
437C22×C11—41no—
438C22×C11—42no—
439C22×C11—41no—
440C22×C11—42no—
441C22×C11—41no—
442C22×C11—42no—
443C22×C11—41no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—42no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11—81no—
452C22×C11—164no—
453C22×C11—164no—
454C22×C11C2×#12011yescharacteristic
455C4×C11—21no—
456C4×C11—21no—
457C4×C11—21no—
458C4×C11—21no—
459C4×C11—41no—
460C4×C11—41no—
461C4×C11—41no—
462C4×C11—41no—
463C4×C11—41no—
464C4×C11—41no—
465C4×C11—81no—
466C4×C11#57611yescharacteristic
467C4×C11#57611yescharacteristic
468C4×C11#57611yescharacteristic
469C4×C11#57711yescharacteristic
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C22×D4—22no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C1112yes—
479C2×Q16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×M16—21no—
488C4⋊Q8C23×C1111yescharacteristic
489#127—21no—
490#127—21no—
491#127—21no—
492#127—21no—
493#127D4×C1112yes—
494#127C23×C1111yescharacteristic
495#127C23×C1111yescharacteristic
496#127C23×C1111yescharacteristic
497#126—21no—
498#126—21no—
499#125D4×C1111yescharacteristic
500#125D4×C1111yescharacteristic
501#124—21no—
502#124—21no—
503#124—21no—
504#124D4×C1111yescharacteristic
505#124D4×C1111yescharacteristic
506#123—22no—
507#123—22no—
508#123—22no—
509#123—22no—
510#123—21no—
511#123—21no—
512C22⋊Q8D4×C1111yescharacteristic
513C22⋊Q8D4×C1111yescharacteristic
514#121—22no—
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121D4×C1111yescharacteristic
529#121D4×C1111yescharacteristic
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536C4×Q8C23×C1111yescharacteristic
537C4×Q8C23×C1111yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4C23×C1111yescharacteristic
547C4×D4C23×C1111yescharacteristic
548#117—21no—
549#117—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C1111yescharacteristic
552#107—21no—
553#106—21no—
554C4⋊C8—21no—
555C4⋊C8—21no—
556C4⋊C8C23×C1111yescharacteristic
557C4⋊C8C23×C1111yescharacteristic
558C4⋊C8C23×C1111yescharacteristic
559C4⋊C8C23×C1111yescharacteristic
560#103—21no—
561#103—21no—
562#103—21no—
563#102—22no—
564#102—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#102—21no—
570C22⋊C8—21no—
571C22⋊C8—21no—
572C4×C8—21no—
573C4×C8C23×C1111yescharacteristic
574C4×C8C23×C1111yescharacteristic
575C2×C11—41no—
576C2×C11—82no—
577C2×C11—81no—
578C2×C11—81no—
579C2×C11—82no—
580C2×C11—161no—
581C2×C11#300811yescharacteristic
582C2×C11#301211yescharacteristic
583C2×C11#301911yescharacteristic
584C24—22no—
585C24—22no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590#41—81no—
591#41—81no—
592C2×Q8—21no—
593C2×Q8C2×D4×C1111yescharacteristic
594C2×Q8C2×D4×C1111yescharacteristic
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—81no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—82no—
623C2×D4—84no—
624C2×D4C2×D4×C1111yescharacteristic
625C2×D4C2×D4×C1111yescharacteristic
626C2×D4C2×D4×C1112yes—
627C2×D4C2×D4×C1112yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—41no—
634C22×C4C2×D4×C1111yescharacteristic
635C22×C4C2×D4×C1111yescharacteristic
636C22×C4C2×D4×C1111yescharacteristic
637Q16—81no—
638SD16—81no—
639SD16—81no—
640SD16—81no—
641D8—81no—
642D8—81no—
643D8—82no—
644D8—82no—
645M16—81no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4C2×D4×C1111yescharacteristic
663C4⋊C4C2×D4×C1111yescharacteristic
664C4⋊C4C2×D4×C1111yescharacteristic
665C4⋊C4C2×D4×C1111yescharacteristic
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C42—21no—
685C42—21no—
686C42C2×D4×C1111yescharacteristic
687C42C2×D4×C1111yescharacteristic
688C42C2×D4×C1111yescharacteristic
689C42C24×C1111yescharacteristic
690C11#1893011yescharacteristic, direct product factor, Sylow
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—44no—
696C23—41no—
697C23—82no—
698C23—82no—
699C23—82no—
700C23—82no—
701C23—82no—
702C23C11×#12011yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—41no—
708Q8—41no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—82no—
731D4—82no—
732D4—82no—
733D4—82no—
734D4—82no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—82no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4C11×#12011yescharacteristic
761C2×C4C11×#12011yescharacteristic
762C2×C4C11×#12011yescharacteristic
763C2×C4C22×D4×C1111yescharacteristic
764C2×C4C22×D4×C1111yescharacteristic
765C2×C4C22×D4×C1111yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—164no—
791C22—164no—
792C22C2×C11×#12011yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4C11×#57611yescharacteristic
805C4C11×#57611yescharacteristic
806C4C11×#57611yescharacteristic
807C4C11×#57711yescharacteristic
808C2—41no—
809C2—81no—
810C2—81no—
811C2—82no—
812C2—82no—
813C2—161no—
814C2C11×#300811yescharacteristic
815C2C11×#301211yescharacteristic
816C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
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×#3543C2semidirect
2. C11×#3251C2semidirect
3. C11×#3212C2semidirect
4. C11×#3205C2semidirect
5. C11×#1642C2semidirect
6. C11×#1641C2semidirect
7. C11×#1640C2semidirect
8. C11×#1639C2semidirect
9. C11×#1621C2semidirect
10. C11×#1621C2semidirect
11. C11×#1620C2semidirect
12. C11×#1619C2semidirect
13. C11×#1545C2semidirect
14. C11×#1495C2semidirect
15. C11×#1482C2semidirect
30. C11×#532C22semidirect
36. C11×#493C22semidirect
39. C11×#486C22semidirect
41. C11×#475C22semidirect
42. C11×#474C22semidirect
46. C11×#462C22semidirect
47. C11×#461C22semidirect
48. C11×#460C22semidirect
49. C11×#460C22semidirect
51. C11×#459C22semidirect
52. C11×#459C22semidirect
56. C11×#431C22semidirect
57. C11×#431C22semidirect
58. C11×#423C22semidirect
61. C11×#331C22semidirect
62. C11×#331C22semidirect
63. C11×Q8⋊C8C22semidirect
64. C11×Q8⋊C8C22semidirect
65. C11×Q8⋊C8C22semidirect
66. C11×Q8⋊C8C22semidirect
67. C11×D4⋊C8C22semidirect
68. C11×D4⋊C8C22semidirect
69. C11×D4⋊C8C22semidirect
70. C11×D4⋊C8C22semidirect
176. #18930C11direct (N × H)
283. #3543C2×C11semidirect
284. #3251C2×C11semidirect
285. #3212C2×C11semidirect
286. #3205C2×C11semidirect
287. #1642C2×C11semidirect
288. #1641C2×C11semidirect
289. #1640C2×C11semidirect
290. #1639C2×C11semidirect
291. #1621C2×C11semidirect
292. #1621C2×C11semidirect
293. #1620C2×C11semidirect
294. #1619C2×C11semidirect
295. #1545C2×C11semidirect
296. #1495C2×C11semidirect
297. #1482C2×C11semidirect
393. #532C22×C11semidirect
399. #493C22×C11semidirect
402. #486C22×C11semidirect
404. #475C22×C11semidirect
405. #474C22×C11semidirect
409. #462C22×C11semidirect
410. #461C22×C11semidirect
411. #460C22×C11semidirect
412. #460C22×C11semidirect
414. #459C22×C11semidirect
415. #459C22×C11semidirect
419. #431C22×C11semidirect
420. #431C22×C11semidirect
421. #423C22×C11semidirect
424. #331C22×C11semidirect
425. #331C22×C11semidirect
426. Q8⋊C8C22×C11semidirect
427. Q8⋊C8C22×C11semidirect
428. Q8⋊C8C22×C11semidirect
429. Q8⋊C8C22×C11semidirect
430. D4⋊C8C22×C11semidirect
431. D4⋊C8C22×C11semidirect
432. D4⋊C8C22×C11semidirect
433. D4⋊C8C22×C11semidirect
690. C11#18930direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35432
C11×#32512
C11×#32122
C11×#32052
C11×#16422
C11×#16412
C11×#16402
C11×#16392
C11×#16212
C11×#16202
C11×#16192
C11×#15452
C11×#14952
C11×#14822
#1893011