Finite Group Databasebeta

← C11×#24084 #14601277

Subgroups — C11×#24084 #14601277

Order 2816.

1060 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3494C211yesmaximal, characteristic
2C11×#3093C211yesmaximal, characteristic, complemented
3C11×#2911C211yesmaximal, characteristic, complemented
4C11×#2500C211yesmaximal, characteristic, complemented
5C11×#2061C211yesmaximal, characteristic, complemented
6C11×#2060C211yesmaximal, characteristic, complemented
7C11×#2037C211yesmaximal, characteristic, complemented
8C11×#2037C211yesmaximal, characteristic, complemented
9C11×#1900C211yesmaximal, characteristic, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1860C211yesmaximal, characteristic, complemented
12C11×#1859C211yesmaximal, characteristic, complemented
13C11×#1856C211yesmaximal, characteristic, complemented
14C11×#1856C211yesmaximal, characteristic, complemented
15C11×#1826C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C11×#555—21no—
18C11×#553—21no—
19C11×#553—21no—
20C11×#551—22no—
21C11×#547—21no—
22C11×#546—22no—
23C11×#544C2211yescharacteristic
24C11×#542—21no—
25C11×#540—21no—
26C11×#535C2211yescharacteristic
27C11×#532—21no—
28C11×#529—21no—
29C11×#525C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C11×#520C2211yescharacteristic
32C11×#518C2211yescharacteristic
33C2×C11×#117C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C11×#485—21no—
36C11×#485—21no—
37C11×#482—21no—
38C11×#482—21no—
39C11×#428—21no—
40C11×#428—21no—
41C11×#428C2211yescharacteristic
42C11×#428C2211yescharacteristic
43C11×#428C2211yescharacteristic
44C11×#428C2211yescharacteristic
45C11×#428C2211yescharacteristic
46C11×#428C2211yescharacteristic
47C11×#427—21no—
48C11×#427—21no—
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C11×#417C2211yescharacteristic
52C11×#417C2211yescharacteristic
53C2×C11×#100C2211yescharacteristic
54C2×C11×#100C2211yescharacteristic
55C11×#407C2211yescharacteristic
56C11×#394—22no—
57C11×#390C2211yescharacteristic
58C11×#390C2211yescharacteristic
59C11×#388—22no—
60C11×#384C2211yescharacteristic
61C11×#382C2211yescharacteristic
62C4×C11×C22⋊C4C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41—22no—
72C2×C11×#41C2311yescharacteristic
73C22×D4×C11D412yes—
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×M16—21no—
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16C2311yescharacteristic
80C2×C11×M16C2311yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C22×C8×C11—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8—21no—
86C11×#127—21no—
87C11×#126—22no—
88C11×#126—22no—
89C11×#125—21no—
90C11×#125—21no—
91C11×#124—22no—
92C11×#124—22no—
93C11×#124—21no—
94C11×#123—22no—
95C11×#123—22no—
96C11×#123—22no—
97C11×#123—22no—
98C11×#123—21no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8D411yescharacteristic
102C11×C22⋊Q8D411yescharacteristic
103C11×#121—22no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121—21no—
111C11×#121—21no—
112C11×#121D411yescharacteristic
113C11×#121D411yescharacteristic
114C11×#120—21no—
115C11×#120—22no—
116C4×Q8×C11—21no—
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—21no—
120C4×D4×C11—22no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11—21no—
126C4×D4×C11—21no—
127C11×#117—22no—
128C11×#117—21no—
129C11×#117—21no—
130C11×#117—21no—
131C11×#117—21no—
132C11×#117—21no—
133C11×#117—21no—
134C11×#117—21no—
135C11×#117D411yescharacteristic
136C11×#117D411yescharacteristic
137C11×#117C2311yescharacteristic
138C11×#117C2311yescharacteristic
139C11×#117C2311yescharacteristic
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4—22no—
142C2×C11×C4⋊C4D411yescharacteristic
143C2×C11×C4⋊C4D411yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4—22no—
149C2×C11×C22⋊C4—21no—
150C2×C11×C22⋊C4—21no—
151C2×C11×C22⋊C4—22no—
152C2×C11×C22⋊C4—22no—
153C2×C11×C22⋊C4D412yes—
154C2×C42×C11—21no—
155C2×C42×C11—21no—
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C11×#107—21no—
159C11×#107—21no—
160C11×#107—21no—
161C11×#107—21no—
162C11×#107—21no—
163C11×#107—21no—
164C11×#106—21no—
165C11×#106—21no—
166C11×#106—21no—
167C11×#106—21no—
168C11×#106—21no—
169C11×#106—21no—
170C11×#104—22no—
171C11×#104—22no—
172C11×#103—21no—
173C11×#103—21no—
174C11×#102—21no—
175C11×#102—21no—
176C11×#100—22no—
177C11×#100—22no—
178C11×C22⋊C8—21no—
179C11×C22⋊C8—21no—
180C11×#95—21no—
181C11×#95—22no—
182#24084C1111yesmaximal, characteristic, direct product factor, Sylow
183C24×C11C2×D412yes—
184C24×C11C2×D411yescharacteristic
185C11×#41—21no—
186C11×#41—21no—
187C11×#41—21no—
188C11×#41—21no—
189C11×#41—84no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2×D411yescharacteristic
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—21no—
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—82no—
206C2×D4×C11C2×D411yescharacteristic
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2411yescharacteristic
228C11×M16—24no—
229C11×M16—21no—
230C11×M16—21no—
231C11×M16—21no—
232C11×M16—21no—
233C11×M16—21no—
234C11×M16—21no—
235C11×M16#4112yescomplemented
236C11×M16#4112yescomplemented
237C2×C8×C11—24no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—22no—
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⋊C4—21no—
256C11×C4⋊C4—82no—
257C11×C4⋊C4C2×D411yescharacteristic
258C11×C4⋊C4C2×D411yescharacteristic
259C11×C4⋊C4C2×D411yescharacteristic
260C11×C4⋊C4C2×D411yescharacteristic
261C11×C4⋊C4C2×D411yescharacteristic
262C11×C4⋊C4C2×D411yescharacteristic
263C11×C22⋊C4—22no—
264C11×C22⋊C4—22no—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—22no—
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—22no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—21no—
278C11×C22⋊C4—21no—
279C11×C22⋊C4—42no—
280C11×C22⋊C4—44no—
281C11×C22⋊C4—41no—
282C11×C22⋊C4—41no—
283C11×C22⋊C4—82no—
284C42×C11—22no—
285C42×C11—21no—
286C42×C11—21no—
287C42×C11—21no—
288C42×C11—21no—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—21no—
292C42×C11—21no—
293C42×C11—21no—
294C42×C11—41no—
295C42×C11—41no—
296#3494C2×C1111yescharacteristic
297#3093C2×C1111yescharacteristic, complemented
298#2911C2×C1111yescharacteristic, complemented
299#2500C2×C1111yescharacteristic, complemented
300#2061C2×C1111yescharacteristic, complemented
301#2060C2×C1111yescharacteristic, complemented
302#2037C2×C1111yescharacteristic, complemented
303#2037C2×C1111yescharacteristic, complemented
304#1900C2×C1111yescharacteristic, complemented
305#1871C2×C1111yescharacteristic, complemented
306#1860C2×C1111yescharacteristic, complemented
307#1859C2×C1111yescharacteristic, complemented
308#1856C2×C1111yescharacteristic, complemented
309#1856C2×C1111yescharacteristic, complemented
310#1826C2×C1111yescharacteristic, complemented
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11#12011yescharacteristic
322C23×C11#12011yescharacteristic
323C23×C11C22×D411yescharacteristic
324Q8×C11—21no—
325Q8×C11—21no—
326Q8×C11—82no—
327D4×C11—21no—
328D4×C11—21no—
329D4×C11—44no—
330D4×C11—42no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—41no—
334D4×C11—41no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—81no—
338D4×C11—82no—
339D4×C11—82no—
340D4×C11—82no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—22no—
360C2×C4×C11—41no—
361C2×C4×C11—42no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—42no—
366C2×C4×C11—41no—
367C2×C4×C11—42no—
368C2×C4×C11—41no—
369C2×C4×C11—42no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—81no—
374C2×C4×C11—82no—
375C2×C4×C11—82no—
376C2×C4×C11—82no—
377C2×C4×C11#12011yescharacteristic
378C2×C4×C11#12011yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C2×#4111yescharacteristic
382C2×C4×C11C2×#4111yescharacteristic
383C2×C4×C112−1+411yescharacteristic
384C2×C4×C112−1+411yescharacteristic
385C8×C11—22no—
386C8×C11—22no—
387C8×C11—41no—
388C8×C11—41no—
389C22×M16C22×C1111yescharacteristic
390#555—21no—
391#553—21no—
392#553—21no—
393#551—22no—
394#547—21no—
395#546—22no—
396#544C22×C1111yescharacteristic
397#542—21no—
398#540—21no—
399#535C22×C1111yescharacteristic
400#532—21no—
401#529—21no—
402#525C22×C1111yescharacteristic
403C2×#121C22×C1111yescharacteristic
404#520C22×C1111yescharacteristic
405#518C22×C1111yescharacteristic
406C2×#117C22×C1111yescharacteristic
407C2×#117C22×C1111yescharacteristic
408#485—21no—
409#485—21no—
410#482—21no—
411#482—21no—
412#428—21no—
413#428—21no—
414#428C22×C1111yescharacteristic
415#428C22×C1111yescharacteristic
416#428C22×C1111yescharacteristic
417#428C22×C1111yescharacteristic
418#428C22×C1111yescharacteristic
419#428C22×C1111yescharacteristic
420#427—21no—
421#427—21no—
422C2×#104C22×C1111yescharacteristic
423C2×#104C22×C1111yescharacteristic
424#417C22×C1111yescharacteristic
425#417C22×C1111yescharacteristic
426C2×#100C22×C1111yescharacteristic
427C2×#100C22×C1111yescharacteristic
428#407C22×C1111yescharacteristic
429#394—22no—
430#390C22×C1111yescharacteristic
431#390C22×C1111yescharacteristic
432#388—22no—
433#384C22×C1111yescharacteristic
434#382C22×C1111yescharacteristic
435C4×C22⋊C4C22×C1111yescharacteristic
436#343C22×C1111yescharacteristic
437#343C22×C1111yescharacteristic
438#339C22×C1111yescharacteristic
439#339C22×C1111yescharacteristic
440#339C22×C1111yescharacteristic
441#339C22×C1111yescharacteristic
442#339C22×C1111yescharacteristic
443#339C22×C1111yescharacteristic
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—21no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—82no—
461C22×C11—82no—
462C22×C11C2×#12011yescharacteristic
463C22×C11#54711yescharacteristic
464C22×C11#54711yescharacteristic
465C4×C11—21no—
466C4×C11—21no—
467C4×C11—42no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11—41no—
474C4×C11—42no—
475C4×C11—41no—
476C4×C11—81no—
477C4×C11—81no—
478C4×C11—81no—
479C4×C11#52511yescharacteristic
480C4×C11#53611yescharacteristic
481C4×C11#54711yescharacteristic
482C4×C11#54711yescharacteristic
483C2×#41—22no—
484C2×#41C23×C1111yescharacteristic
485C22×D4D4×C1112yes—
486C22×D4C23×C1111yescharacteristic
487C23×C4C23×C1111yescharacteristic
488C2×M16—21no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16C23×C1111yescharacteristic
492C2×M16C23×C1111yescharacteristic
493C2×M16C23×C1111yescharacteristic
494C2×M16C23×C1111yescharacteristic
495C22×C8—21no—
496C4⋊Q8—21no—
497C4⋊Q8—21no—
498#127—21no—
499#126—22no—
500#126—22no—
501#125—21no—
502#125—21no—
503#124—22no—
504#124—22no—
505#124—21no—
506#123—22no—
507#123—22no—
508#123—22no—
509#123—22no—
510#123—21no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
513C22⋊Q8D4×C1111yescharacteristic
514C22⋊Q8D4×C1111yescharacteristic
515#121—22no—
516#121—22no—
517#121—22no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121D4×C1111yescharacteristic
525#121D4×C1111yescharacteristic
526#120—21no—
527#120—22no—
528C4×Q8—21no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539#117—22no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117—21no—
544#117—21no—
545#117—21no—
546#117—21no—
547#117D4×C1111yescharacteristic
548#117D4×C1111yescharacteristic
549#117C23×C1111yescharacteristic
550#117C23×C1111yescharacteristic
551#117C23×C1111yescharacteristic
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4D4×C1111yescharacteristic
555C2×C4⋊C4D4×C1111yescharacteristic
556C2×C4⋊C4C23×C1111yescharacteristic
557C2×C4⋊C4C23×C1111yescharacteristic
558C2×C4⋊C4C23×C1111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4D4×C1112yes—
566C2×C42—21no—
567C2×C42—21no—
568C2×C42C23×C1111yescharacteristic
569C2×C42C23×C1111yescharacteristic
570#107—21no—
571#107—21no—
572#107—21no—
573#107—21no—
574#107—21no—
575#107—21no—
576#106—21no—
577#106—21no—
578#106—21no—
579#106—21no—
580#106—21no—
581#106—21no—
582#104—22no—
583#104—22no—
584#103—21no—
585#103—21no—
586#102—21no—
587#102—21no—
588#100—22no—
589#100—22no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592#95—21no—
593#95—22no—
594C2×C11—21no—
595C2×C11—21no—
596C2×C11—41no—
597C2×C11—41no—
598C2×C11—81no—
599C2×C11—82no—
600C2×C11#240611yescharacteristic
601C2×C11#301811yescharacteristic
602C2×C11#301911yescharacteristic
603C24C2×D4×C1112yes—
604C24C2×D4×C1111yescharacteristic
605#41—21no—
606#41—21no—
607#41—21no—
608#41—21no—
609#41—84no—
610C2×Q8—22no—
611C2×Q8C2×D4×C1111yescharacteristic
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—82no—
626C2×D4C2×D4×C1111yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4C2×D4×C1111yescharacteristic
642C22×C4C2×D4×C1111yescharacteristic
643C22×C4C2×D4×C1111yescharacteristic
644C22×C4C2×D4×C1111yescharacteristic
645C22×C4C2×D4×C1111yescharacteristic
646C22×C4C2×D4×C1112yes—
647C22×C4C24×C1111yescharacteristic
648M16—24no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16C11×#4112yescomplemented
656M16C11×#4112yescomplemented
657C2×C8—24no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—82no—
677C4⋊C4C2×D4×C1111yescharacteristic
678C4⋊C4C2×D4×C1111yescharacteristic
679C4⋊C4C2×D4×C1111yescharacteristic
680C4⋊C4C2×D4×C1111yescharacteristic
681C4⋊C4C2×D4×C1111yescharacteristic
682C4⋊C4C2×D4×C1111yescharacteristic
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—42no—
700C22⋊C4—44no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—82no—
704C42—22no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—41no—
715C42—41no—
716C11#2408411yescharacteristic, direct product factor, Sylow
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23C11×#12011yescharacteristic
728C23C11×#12011yescharacteristic
729C23C22×D4×C1111yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—82no—
733D4—21no—
734D4—21no—
735D4—44no—
736D4—42no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—81no—
744D4—82no—
745D4—82no—
746D4—82no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—81no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4C11×#12011yescharacteristic
784C2×C4C11×#12011yescharacteristic
785C2×C4C22×D4×C1111yescharacteristic
786C2×C4C22×D4×C1111yescharacteristic
787C2×C4C2×C11×#4111yescharacteristic
788C2×C4C2×C11×#4111yescharacteristic
789C2×C4C11×2−1+411yescharacteristic
790C2×C4C11×2−1+411yescharacteristic
791C8—22no—
792C8—22no—
793C8—41no—
794C8—41no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—81no—
810C22—81no—
811C22—82no—
812C22—82no—
813C22C2×C11×#12011yescharacteristic
814C22C11×#54711yescharacteristic
815C22C11×#54711yescharacteristic
816C4—21no—
817C4—21no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C11×#52511yescharacteristic
831C4C11×#53611yescharacteristic
832C4C11×#54711yescharacteristic
833C4C11×#54711yescharacteristic
834C2—21no—
835C2—21no—
836C2—41no—
837C2—41no—
838C2—82no—
839C2—81no—
840C2C11×#240611yescharacteristic
841C2C11×#301811yescharacteristic
842C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3093C2semidirect
3. C11×#2911C2semidirect
4. C11×#2500C2semidirect
5. C11×#2061C2semidirect
6. C11×#2060C2semidirect
7. C11×#2037C2semidirect
8. C11×#2037C2semidirect
9. C11×#1900C2semidirect
10. C11×#1871C2semidirect
11. C11×#1860C2semidirect
12. C11×#1859C2semidirect
13. C11×#1856C2semidirect
14. C11×#1856C2semidirect
15. C11×#1826C2semidirect
182. #24084C11direct (N × H)
235. C11×M16#41semidirect
236. C11×M16#41semidirect
297. #3093C2×C11semidirect
298. #2911C2×C11semidirect
299. #2500C2×C11semidirect
300. #2061C2×C11semidirect
301. #2060C2×C11semidirect
302. #2037C2×C11semidirect
303. #2037C2×C11semidirect
304. #1900C2×C11semidirect
305. #1871C2×C11semidirect
306. #1860C2×C11semidirect
307. #1859C2×C11semidirect
308. #1856C2×C11semidirect
309. #1856C2×C11semidirect
310. #1826C2×C11semidirect
655. M16C11×#41semidirect
656. M16C11×#41semidirect
716. C11#24084direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34942
C11×#30932
C11×#29112
C11×#25002
C11×#20612
C11×#20602
C11×#20372
C11×#19002
C11×#18712
C11×#18602
C11×#18592
C11×#18562
C11×#18262
#2408411