Finite Group Databasebeta

← C11×#24324 #14601517

Subgroups — C11×#24324 #14601517

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3504C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C11×#2566C211yesmaximal, characteristic, complemented
5C11×#2061C211yesmaximal, characteristic, complemented
6C11×#2060C211yesmaximal, characteristic, complemented
7C11×#2027C211yesmaximal, characteristic, complemented
8C11×#2027C211yesmaximal, characteristic, complemented
9C11×#1998C211yesmaximal, characteristic, complemented
10C11×#1986C211yesmaximal, characteristic, complemented
11C11×#1883C211yesmaximal, characteristic
12C11×#1883C211yesmaximal, characteristic
13C11×#1860C211yesmaximal, characteristic, complemented
14C11×#1859C211yesmaximal, characteristic, complemented
15C11×#1806C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C11×#557—21no—
18C11×#557—21no—
19C11×#554—21no—
20C11×#554—21no—
21C11×#554—22no—
22C11×#554—22no—
23C11×#544—21no—
24C11×#544—21no—
25C11×#544C2211yescharacteristic
26C11×#544C2211yescharacteristic
27C11×#533—21no—
28C11×#533C2211yescharacteristic
29C2×C11×#125—21no—
30C2×C11×#125C2211yescharacteristic
31C11×#520C2211yescharacteristic
32C11×#520C2211yescharacteristic
33C4×C11×#41C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C11×#478—21no—
36C11×#478—21no—
37C11×#476—21no—
38C11×#474—21no—
39C11×#442—21no—
40C11×#440—21no—
41C4×C11×SD16—21no—
42C4×C11×D8—21no—
43C11×#428C2211yescharacteristic
44C11×#428C2211yescharacteristic
45C11×#428C2211yescharacteristic
46C11×#423C2211yescharacteristic
47C2×C11×#104C2211yescharacteristic
48C2×C11×#104C2211yescharacteristic
49C11×#418C2211yescharacteristic
50C11×#418C2211yescharacteristic
51C11×#418C2211yescharacteristic
52C11×#417C2211yescharacteristic
53C4×C11×M16C2211yescharacteristic
54C11×#396—22no—
55C11×#390C2211yescharacteristic
56C11×#390C2211yescharacteristic
57C11×#385—22no—
58C11×#384C2211yescharacteristic
59C11×#382C2211yescharacteristic
60C4×C11×C4⋊C4C2211yescharacteristic
61C11×#343C2211yescharacteristic
62C11×#343C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C11×AGL(1,ℤ/8)—22no—
75C11×AGL(1,ℤ/8)Q814yescomplemented
76C2×C11×SD16—21no—
77C2×C11×D8—21no—
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C2×C11×M16C2311yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8—21no—
86C11×C4⋊Q8—21no—
87C11×C4⋊Q8—21no—
88C11×C4⋊Q8D411yescharacteristic
89C11×C4⋊Q8D411yescharacteristic
90C11×#125—22no—
91C11×#125—22no—
92C11×#125—22no—
93C11×#125—22no—
94C11×#125—21no—
95C11×#125—21no—
96C11×#125—21no—
97C11×#125—21no—
98C11×#125—21no—
99C11×#125—21no—
100C11×#125—21no—
101C11×#125—21no—
102C11×#125D411yescharacteristic
103C11×#125D411yescharacteristic
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C4×Q8×C11—22no—
115C4×Q8×C11—22no—
116C4×Q8×C11—21no—
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11—21no—
120C4×Q8×C11D411yescharacteristic
121C4×Q8×C11D411yescharacteristic
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11—21no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11—21no—
132C4×D4×C11D411yescharacteristic
133C4×D4×C11D411yescharacteristic
134C11×#117—21no—
135C11×#117—21no—
136C11×#117—21no—
137C11×#117C2311yescharacteristic
138C11×#117C2311yescharacteristic
139C11×#117C2311yescharacteristic
140C2×C11×C4⋊C4—22no—
141C2×C11×C4⋊C4—22no—
142C2×C11×C4⋊C4—21no—
143C2×C11×C4⋊C4—21no—
144C2×C11×C4⋊C4—21no—
145C2×C11×C4⋊C4—22no—
146C2×C11×C4⋊C4D412yes—
147C2×C11×C4⋊C4D412yes—
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4—21no—
152C2×C11×C22⋊C4—22no—
153C2×C11×C22⋊C4—22no—
154C2×C42×C11—21no—
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C11×#107—21no—
159C11×#107—21no—
160C11×#107—21no—
161C11×#106—21no—
162C11×#106—21no—
163C11×#106—21no—
164C11×C4⋊C8—21no—
165C11×C4⋊C8—21no—
166C11×#104—22no—
167C11×#104—22no—
168C11×#103—21no—
169C11×#102—21no—
170C11×#102—21no—
171C11×#102—21no—
172C11×#102—21no—
173C11×#102—21no—
174C11×#102—21no—
175C11×#102—21no—
176C11×#97—21no—
177C4×C8×C11—21no—
178C11×#95—21no—
179C11×#95—22no—
180#24324C1111yesmaximal, characteristic, direct product factor, Sylow
181C24×C11—21no—
182C11×#41—21no—
183C11×#41—21no—
184C11×#41C2×Q812yes—
185C11×#41#4112yes—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11C2×D411yescharacteristic
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11C2×D411yescharacteristic
198C2×D4×C11C2×Q812yes—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—41no—
208C22×C4×C11—41no—
209C22×C4×C11—82no—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C11×SD16—24no—
216C11×D8—24no—
217C11×M16—21no—
218C11×M16—21no—
219C11×M16—21no—
220C11×M16—21no—
221C11×M16—21no—
222C11×M16—21no—
223C11×M16—21no—
224C11×M16C2×Q812yes—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—22no—
233C11×C4⋊C4—22no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—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⋊C4—42no—
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—21no—
266C11×C22⋊C4—21no—
267C11×C22⋊C4—21no—
268C11×C22⋊C4—21no—
269C11×C22⋊C4—21no—
270C11×C22⋊C4—44no—
271C11×C22⋊C4—41no—
272C11×C22⋊C4—41no—
273C11×C22⋊C4—82no—
274C42×C11—22no—
275C42×C11—22no—
276C42×C11—21no—
277C42×C11—21no—
278C42×C11—21no—
279C42×C11—21no—
280C42×C11—21no—
281C42×C11—21no—
282C42×C11—21no—
283C42×C11—21no—
284C42×C11—21no—
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289#3504C2×C1111yescharacteristic, complemented
290#3077C2×C1111yescharacteristic, complemented
291C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
292#2566C2×C1111yescharacteristic, complemented
293#2061C2×C1111yescharacteristic, complemented
294#2060C2×C1111yescharacteristic, complemented
295#2027C2×C1111yescharacteristic, complemented
296#2027C2×C1111yescharacteristic, complemented
297#1998C2×C1111yescharacteristic, complemented
298#1986C2×C1111yescharacteristic, complemented
299#1883C2×C1111yescharacteristic
300#1883C2×C1111yescharacteristic
301#1860C2×C1111yescharacteristic, complemented
302#1859C2×C1111yescharacteristic, complemented
303#1806C2×C1111yescharacteristic, complemented
304C23×C11—21no—
305C23×C11—22no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C22×D411yescharacteristic
311Q8×C11—21no—
312Q8×C11—81no—
313Q8×C11—81no—
314Q8×C11—82no—
315Q8×C11—82no—
316Q8×C11C22⋊Q812yes—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—21no—
321D4×C11—22no—
322D4×C11—41no—
323D4×C11—41no—
324D4×C11C22⋊Q812yes—
325C2×C4×C11—21no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—42no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—81no—
349C2×C4×C11—81no—
350C2×C4×C11—82no—
351C2×C4×C11—82no—
352C2×C4×C11—82no—
353C2×C4×C11—82no—
354C2×C4×C11#12011yescharacteristic
355C2×C4×C11#12011yescharacteristic
356C2×C4×C11#12011yescharacteristic
357C2×C4×C11#12011yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C22×Q811yescharacteristic
361C2×C4×C11C2×#4111yescharacteristic
362C2×C4×C112−1+411yescharacteristic
363C2×C4×C112−1+411yescharacteristic
364C8×C11—22no—
365C8×C11—41no—
366C8×C11—41no—
367C8×C11—41no—
368C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
369#557—21no—
370#557—21no—
371#554—21no—
372#554—21no—
373#554—22no—
374#554—22no—
375#544—21no—
376#544—21no—
377#544C22×C1111yescharacteristic
378#544C22×C1111yescharacteristic
379#533—21no—
380#533C22×C1111yescharacteristic
381C2×#125—21no—
382C2×#125C22×C1111yescharacteristic
383#520C22×C1111yescharacteristic
384#520C22×C1111yescharacteristic
385C4×#41C22×C1111yescharacteristic
386C2×C4×D4C22×C1111yescharacteristic
387#478—21no—
388#478—21no—
389#476—21no—
390#474—21no—
391#442—21no—
392#440—21no—
393C4×SD16—21no—
394C4×D8—21no—
395#428C22×C1111yescharacteristic
396#428C22×C1111yescharacteristic
397#428C22×C1111yescharacteristic
398#423C22×C1111yescharacteristic
399C2×#104C22×C1111yescharacteristic
400C2×#104C22×C1111yescharacteristic
401#418C22×C1111yescharacteristic
402#418C22×C1111yescharacteristic
403#418C22×C1111yescharacteristic
404#417C22×C1111yescharacteristic
405C4×M16C22×C1111yescharacteristic
406#396—22no—
407#390C22×C1111yescharacteristic
408#390C22×C1111yescharacteristic
409#385—22no—
410#384C22×C1111yescharacteristic
411#382C22×C1111yescharacteristic
412C4×C4⋊C4C22×C1111yescharacteristic
413#343C22×C1111yescharacteristic
414#343C22×C1111yescharacteristic
415#343C22×C1111yescharacteristic
416#343C22×C1111yescharacteristic
417#339C22×C1111yescharacteristic
418#339C22×C1111yescharacteristic
419#339C22×C1111yescharacteristic
420#339C22×C1111yescharacteristic
421#339C22×C1111yescharacteristic
422#339C22×C1111yescharacteristic
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—22no—
426C22×C11—44no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—42no—
430C22×C11—82no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11C2×#12011yescharacteristic
434C22×C11#54811yescharacteristic
435C22×C11D4×Q811yescharacteristic
436C4×C11—22no—
437C4×C11—21no—
438C4×C11—21no—
439C4×C11—21no—
440C4×C11—21no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—42no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11—41no—
450C4×C11—81no—
451C4×C11—81no—
452C4×C11C2×C22⋊Q811yescharacteristic
453C4×C11#53611yescharacteristic
454C4×C11#54811yescharacteristic
455C4×C11D4×Q811yescharacteristic
456C2×#41C23×C1111yescharacteristic
457C22×D4C23×C1111yescharacteristic
458C23×C4—21no—
459AGL(1,ℤ/8)—22no—
460AGL(1,ℤ/8)Q8×C1114yescomplemented
461C2×SD16—21no—
462C2×D8—21no—
463C2×M16C23×C1111yescharacteristic
464C2×M16C23×C1111yescharacteristic
465C2×M16C23×C1111yescharacteristic
466C2×M16C23×C1111yescharacteristic
467C4⋊Q8—22no—
468C4⋊Q8—22no—
469C4⋊Q8—21no—
470C4⋊Q8—21no—
471C4⋊Q8—21no—
472C4⋊Q8—21no—
473C4⋊Q8D4×C1111yescharacteristic
474C4⋊Q8D4×C1111yescharacteristic
475#125—22no—
476#125—22no—
477#125—22no—
478#125—22no—
479#125—21no—
480#125—21no—
481#125—21no—
482#125—21no—
483#125—21no—
484#125—21no—
485#125—21no—
486#125—21no—
487#125D4×C1111yescharacteristic
488#125D4×C1111yescharacteristic
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8—21no—
505C4×Q8D4×C1111yescharacteristic
506C4×Q8D4×C1111yescharacteristic
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4D4×C1111yescharacteristic
518C4×D4D4×C1111yescharacteristic
519#117—21no—
520#117—21no—
521#117—21no—
522#117C23×C1111yescharacteristic
523#117C23×C1111yescharacteristic
524#117C23×C1111yescharacteristic
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4D4×C1112yes—
532C2×C4⋊C4D4×C1112yes—
533C2×C4⋊C4C23×C1111yescharacteristic
534C2×C4⋊C4C23×C1111yescharacteristic
535C2×C4⋊C4C23×C1111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C42—21no—
540C2×C42C23×C1111yescharacteristic
541C2×C42C23×C1111yescharacteristic
542C2×C42C23×C1111yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551#104—22no—
552#104—22no—
553#103—21no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#97—21no—
562C4×C8—21no—
563#95—21no—
564#95—22no—
565C2×C11—21no—
566C2×C11—21no—
567C2×C11—42no—
568C2×C11—82no—
569C2×C11#240911yescharacteristic
570C2×C11#301811yescharacteristic
571C2×C11#302111yescharacteristic
572C24—21no—
573#41—21no—
574#41—21no—
575#41C2×Q8×C1112yes—
576#41C11×#4112yes—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C1111yescharacteristic
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4C2×D4×C1111yescharacteristic
589C2×D4C2×Q8×C1112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—82no—
601C22×C4C2×D4×C1112yes—
602C22×C4C2×D4×C1112yes—
603C22×C4C2×D4×C1111yescharacteristic
604C22×C4C2×D4×C1111yescharacteristic
605C22×C4C24×C1111yescharacteristic
606SD16—24no—
607D8—24no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16C2×Q8×C1112yes—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—42no—
647C4⋊C4—82no—
648C4⋊C4C2×D4×C1111yescharacteristic
649C4⋊C4C2×D4×C1111yescharacteristic
650C4⋊C4C2×D4×C1111yescharacteristic
651C4⋊C4C2×D4×C1111yescharacteristic
652C4⋊C4C2×D4×C1111yescharacteristic
653C4⋊C4C2×D4×C1111yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—44no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—82no—
665C42—22no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42C2×D4×C1111yescharacteristic
677C42C2×D4×C1111yescharacteristic
678C42C2×D4×C1111yescharacteristic
679C42C2×D4×C1111yescharacteristic
680C11#2432411yescharacteristic, direct product factor, Sylow
681C23—21no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23C22×D4×C1111yescharacteristic
688Q8—21no—
689Q8—81no—
690Q8—81no—
691Q8—82no—
692Q8—82no—
693Q8C11×C22⋊Q812yes—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—21no—
698D4—22no—
699D4—41no—
700D4—41no—
701D4C11×C22⋊Q812yes—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4C11×#12011yescharacteristic
732C2×C4C11×#12011yescharacteristic
733C2×C4C11×#12011yescharacteristic
734C2×C4C11×#12011yescharacteristic
735C2×C4C22×D4×C1111yescharacteristic
736C2×C4C22×D4×C1111yescharacteristic
737C2×C4C22×Q8×C1111yescharacteristic
738C2×C4C2×C11×#4111yescharacteristic
739C2×C4C11×2−1+411yescharacteristic
740C2×C4C11×2−1+411yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—22no—
748C22—44no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—82no—
753C22—81no—
754C22—81no—
755C22C2×C11×#12011yescharacteristic
756C22C11×#54811yescharacteristic
757C22D4×Q8×C1111yescharacteristic
758C4—22no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—42no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4—81no—
774C4C2×C11×C22⋊Q811yescharacteristic
775C4C11×#53611yescharacteristic
776C4C11×#54811yescharacteristic
777C4D4×Q8×C1111yescharacteristic
778C2—21no—
779C2—21no—
780C2—42no—
781C2—82no—
782C2C11×#240911yescharacteristic
783C2C11×#301811yescharacteristic
784C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3504C2semidirect
2. C11×#3077C2semidirect
4. C11×#2566C2semidirect
5. C11×#2061C2semidirect
6. C11×#2060C2semidirect
7. C11×#2027C2semidirect
8. C11×#2027C2semidirect
9. C11×#1998C2semidirect
10. C11×#1986C2semidirect
13. C11×#1860C2semidirect
14. C11×#1859C2semidirect
15. C11×#1806C2semidirect
75. C11×AGL(1,ℤ/8)Q8semidirect
180. #24324C11direct (N × H)
289. #3504C2×C11semidirect
290. #3077C2×C11semidirect
292. #2566C2×C11semidirect
293. #2061C2×C11semidirect
294. #2060C2×C11semidirect
295. #2027C2×C11semidirect
296. #2027C2×C11semidirect
297. #1998C2×C11semidirect
298. #1986C2×C11semidirect
301. #1860C2×C11semidirect
302. #1859C2×C11semidirect
303. #1806C2×C11semidirect
460. AGL(1,ℤ/8)Q8×C11semidirect
680. C11#24324direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35042
C11×#30772
C4×C11×AGL(1,ℤ/8)2
C11×#25662
C11×#20612
C11×#20602
C11×#20272
C11×#19982
C11×#19862
C11×#18832
C11×#18602
C11×#18592
C11×#18062
#2432411