Finite Group Databasebeta

← C11×#24174 #14601367

Subgroups — C11×#24174 #14601367

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3512C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C11×#2566C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#2039C211yesmaximal, characteristic, complemented
7C11×#2006C211yesmaximal, characteristic, complemented
8C11×#2006C211yesmaximal, characteristic, complemented
9C11×#1998C211yesmaximal, characteristic, complemented
10C11×#1980C211yesmaximal, characteristic, complemented
11C11×#1883C211yesmaximal, characteristic, complemented
12C11×#1883C211yesmaximal, characteristic, complemented
13C11×#1860C211yesmaximal, characteristic, complemented
14C11×#1859C211yesmaximal, characteristic, complemented
15C11×#1806C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C11×#553—21no—
20C11×#553—21no—
21C11×#553—22no—
22C11×#553—22no—
23C11×#552—21no—
24C11×#552—21no—
25C11×#541—21no—
26C11×#540—21no—
27C11×#537C2211yescharacteristic
28C11×#537C2211yescharacteristic
29C11×#532C2211yescharacteristic
30C11×#529—21no—
31C11×#529—21no—
32C2×C11×#125C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C11×#520C2211yescharacteristic
35C4×C11×#41C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C11×#463—21no—
38C11×#463—21no—
39C11×#461—21no—
40C11×#459—21no—
41C11×#442—21no—
42C11×#440—21no—
43C4×C11×SD16—21no—
44C4×C11×D8—21no—
45C11×#428C2211yescharacteristic
46C11×#423C2211yescharacteristic
47C2×C11×#104C2211yescharacteristic
48C2×C11×#104C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C2×C11×#104C2211yescharacteristic
52C2×C11×#104C2211yescharacteristic
53C11×#418C2211yescharacteristic
54C11×#417C2211yescharacteristic
55C11×#417C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C4×C11×M16C2211yescharacteristic
58C11×#396—22no—
59C11×#390C2211yescharacteristic
60C11×#390C2211yescharacteristic
61C11×#385—22no—
62C11×#384C2211yescharacteristic
63C11×#382C2211yescharacteristic
64C4×C11×C4⋊C4C2211yescharacteristic
65C11×#343C2211yescharacteristic
66C11×#343C2211yescharacteristic
67C11×#343C2211yescharacteristic
68C11×#343C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C2×C11×#41C2311yescharacteristic
73C2×C11×#41C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C11×AGL(1,ℤ/8)—22no—
77C11×AGL(1,ℤ/8)—22no—
78C11×AGL(1,ℤ/8)—22no—
79C11×AGL(1,ℤ/8)—22no—
80C11×AGL(1,ℤ/8)—41no—
81C11×AGL(1,ℤ/8)—41no—
82C2×C11×SD16—21no—
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×D8—21no—
86C2×C11×D8—21no—
87C2×C11×D8—21no—
88C2×C11×M16C2311yescharacteristic
89C2×C11×M16C2311yescharacteristic
90C2×C11×M16C2311yescharacteristic
91C2×C11×M16C2311yescharacteristic
92C11×C4⋊Q8D411yescharacteristic
93C11×#127D411yescharacteristic
94C11×#126—22no—
95C11×#126—22no—
96C11×#126—22no—
97C11×#126—22no—
98C11×#125—22no—
99C11×#125—22no—
100C11×#125—21no—
101C11×#125—21no—
102C11×#125—21no—
103C11×#125—21no—
104C11×#124D411yescharacteristic
105C11×#124D411yescharacteristic
106C11×#123—22no—
107C11×#123—22no—
108C11×#123—22no—
109C11×#123—22no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—21no—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121—22no—
123C11×#121—22no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11D411yescharacteristic
127C4×Q8×C11D411yescharacteristic
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—21no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11—22no—
135C4×D4×C11—22no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11D411yescharacteristic
143C4×D4×C11D411yescharacteristic
144C11×#117—22no—
145C11×#117—22no—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117—21no—
149C11×#117C2311yescharacteristic
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4—21no—
153C2×C11×C4⋊C4—22no—
154C2×C11×C4⋊C4D412yes—
155C2×C11×C4⋊C4D412yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—22no—
161C2×C11×C22⋊C4—22no—
162C2×C42×C11—21no—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C11×#107—21no—
167C11×#106—21no—
168C11×C4⋊C8—21no—
169C11×C4⋊C8—21no—
170C11×#104—22no—
171C11×#104—22no—
172C11×#104—41no—
173C11×#104—41no—
174C11×#104—41no—
175C11×#104—41no—
176C11×#103—21no—
177C11×#103—21no—
178C11×#103—21no—
179C11×#102—21no—
180C11×#102—21no—
181C11×#102—21no—
182C11×#102—21no—
183C11×#102—21no—
184C11×#97—21no—
185C4×C8×C11—21no—
186C11×#95—21no—
187C11×#95—22no—
188#24174C1111yesmaximal, characteristic, direct product factor, Sylow
189C24×C11—21no—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41—21no—
194C11×#41—21no—
195C11×#41—21no—
196C11×#41—21no—
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—21no—
202C2×Q8×C11C2×D411yescharacteristic
203C2×Q8×C11C2×D411yescharacteristic
204C2×Q8×C11C2×D411yescharacteristic
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11C2×D411yescharacteristic
218C2×D4×C11C2×D411yescharacteristic
219C2×D4×C11C2×D411yescharacteristic
220C2×D4×C11#4112yes—
221C22×C4×C11—21no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—41no—
232C22×C4×C11—41no—
233C22×C4×C11—82no—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2411yescharacteristic
239C11×SD16—24no—
240C11×SD16—42no—
241C11×SD16—42no—
242C11×D8—24no—
243C11×D8—42no—
244C11×D8—42no—
245C11×M16—21no—
246C11×M16—21no—
247C11×M16—21no—
248C11×M16—21no—
249C11×M16—21no—
250C11×M16—21no—
251C11×M16—21no—
252C11×M16#4112yes—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C11×C4⋊C4—22no—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—22no—
261C11×C4⋊C4—22no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4—22no—
264C11×C4⋊C4—22no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—42no—
276C11×C4⋊C4—82no—
277C11×C4⋊C4C2×D411yescharacteristic
278C11×C4⋊C4C2×D411yescharacteristic
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—44no—
293C11×C22⋊C4—41no—
294C11×C22⋊C4—41no—
295C11×C22⋊C4—82no—
296C42×C11—22no—
297C42×C11—22no—
298C42×C11—21no—
299C42×C11—21no—
300C42×C11—21no—
301C42×C11—21no—
302C42×C11—21no—
303C42×C11—21no—
304C42×C11—21no—
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309#3512C2×C1111yescharacteristic, complemented
310#3036C2×C1111yescharacteristic, complemented
311C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
312#2566C2×C1111yescharacteristic, complemented
313#2040C2×C1111yescharacteristic, complemented
314#2039C2×C1111yescharacteristic, complemented
315#2006C2×C1111yescharacteristic, complemented
316#2006C2×C1111yescharacteristic, complemented
317#1998C2×C1111yescharacteristic, complemented
318#1980C2×C1111yescharacteristic, complemented
319#1883C2×C1111yescharacteristic, complemented
320#1883C2×C1111yescharacteristic, complemented
321#1860C2×C1111yescharacteristic, complemented
322#1859C2×C1111yescharacteristic, complemented
323#1806C2×C1111yescharacteristic, complemented
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—22no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11C22×D411yescharacteristic
333Q8×C11—21no—
334Q8×C11—21no—
335Q8×C11—21no—
336Q8×C11—21no—
337Q8×C11—21no—
338Q8×C11—21no—
339D4×C11—21no—
340D4×C11—22no—
341D4×C11—21no—
342D4×C11—22no—
343D4×C11—21no—
344D4×C11—21no—
345D4×C11—21no—
346D4×C11—21no—
347D4×C11—41no—
348D4×C11—41no—
349D4×C11—41no—
350D4×C11—41no—
351D4×C11—41no—
352D4×C11—41no—
353D4×C11—41no—
354D4×C11—41no—
355D4×C11—81no—
356D4×C11—81no—
357D4×C11—82no—
358D4×C11—82no—
359C2×C4×C11—22no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—42no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—81no—
385C2×C4×C11—81no—
386C2×C4×C11—82no—
387C2×C4×C11—82no—
388C2×C4×C11—82no—
389C2×C4×C11—82no—
390C2×C4×C11#12011yescharacteristic
391C2×C4×C11#12011yescharacteristic
392C2×C4×C11#12011yescharacteristic
393C2×C4×C11#12011yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C2×#4111yescharacteristic
397C2×C4×C11C2×#4111yescharacteristic
398C2×C4×C11H(5,𝔽2)11yescharacteristic
399C2×C4×C112−1+411yescharacteristic
400C8×C11—22no—
401C8×C11—41no—
402C8×C11—41no—
403C8×C11—41no—
404C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
405C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
406C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
407#553—21no—
408#553—21no—
409#553—22no—
410#553—22no—
411#552—21no—
412#552—21no—
413#541—21no—
414#540—21no—
415#537C22×C1111yescharacteristic
416#537C22×C1111yescharacteristic
417#532C22×C1111yescharacteristic
418#529—21no—
419#529—21no—
420C2×#125C22×C1111yescharacteristic
421#520C22×C1111yescharacteristic
422#520C22×C1111yescharacteristic
423C4×#41C22×C1111yescharacteristic
424C2×C4×D4C22×C1111yescharacteristic
425#463—21no—
426#463—21no—
427#461—21no—
428#459—21no—
429#442—21no—
430#440—21no—
431C4×SD16—21no—
432C4×D8—21no—
433#428C22×C1111yescharacteristic
434#423C22×C1111yescharacteristic
435C2×#104C22×C1111yescharacteristic
436C2×#104C22×C1111yescharacteristic
437C2×#104C22×C1111yescharacteristic
438C2×#104C22×C1111yescharacteristic
439C2×#104C22×C1111yescharacteristic
440C2×#104C22×C1111yescharacteristic
441#418C22×C1111yescharacteristic
442#417C22×C1111yescharacteristic
443#417C22×C1111yescharacteristic
444#417C22×C1111yescharacteristic
445C4×M16C22×C1111yescharacteristic
446#396—22no—
447#390C22×C1111yescharacteristic
448#390C22×C1111yescharacteristic
449#385—22no—
450#384C22×C1111yescharacteristic
451#382C22×C1111yescharacteristic
452C4×C4⋊C4C22×C1111yescharacteristic
453#343C22×C1111yescharacteristic
454#343C22×C1111yescharacteristic
455#343C22×C1111yescharacteristic
456#343C22×C1111yescharacteristic
457#339C22×C1111yescharacteristic
458#339C22×C1111yescharacteristic
459C22×C11—21no—
460C22×C11—21no—
461C22×C11—44no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—42no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11—41no—
470C22×C11—41no—
471C22×C11—41no—
472C22×C11—82no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11C2×#12011yescharacteristic
476C22×C11#54811yescharacteristic
477C22×C11#55011yescharacteristic
478C4×C11—21no—
479C4×C11—21no—
480C4×C11—21no—
481C4×C11—21no—
482C4×C11—42no—
483C4×C11—41no—
484C4×C11—41no—
485C4×C11—41no—
486C4×C11—42no—
487C4×C11—41no—
488C4×C11—42no—
489C4×C11—41no—
490C4×C11—81no—
491C4×C11—81no—
492C4×C11#52511yescharacteristic
493C4×C11#53711yescharacteristic
494C4×C11#54611yescharacteristic
495C4×C11#54711yescharacteristic
496C2×#41C23×C1111yescharacteristic
497C2×#41C23×C1111yescharacteristic
498C2×#41C23×C1111yescharacteristic
499C22×D4C23×C1111yescharacteristic
500C23×C4—21no—
501AGL(1,ℤ/8)—22no—
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—41no—
506AGL(1,ℤ/8)—41no—
507C2×SD16—21no—
508C2×SD16—21no—
509C2×SD16—21no—
510C2×D8—21no—
511C2×D8—21no—
512C2×D8—21no—
513C2×M16C23×C1111yescharacteristic
514C2×M16C23×C1111yescharacteristic
515C2×M16C23×C1111yescharacteristic
516C2×M16C23×C1111yescharacteristic
517C4⋊Q8D4×C1111yescharacteristic
518#127D4×C1111yescharacteristic
519#126—22no—
520#126—22no—
521#126—22no—
522#126—22no—
523#125—22no—
524#125—22no—
525#125—21no—
526#125—21no—
527#125—21no—
528#125—21no—
529#124D4×C1111yescharacteristic
530#124D4×C1111yescharacteristic
531#123—22no—
532#123—22no—
533#123—22no—
534#123—22no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539#121—22no—
540#121—22no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#121—22no—
548#121—22no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8D4×C1111yescharacteristic
552C4×Q8D4×C1111yescharacteristic
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4D4×C1111yescharacteristic
568C4×D4D4×C1111yescharacteristic
569#117—22no—
570#117—22no—
571#117—21no—
572#117—21no—
573#117—21no—
574#117C23×C1111yescharacteristic
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4D4×C1112yes—
580C2×C4⋊C4D4×C1112yes—
581C2×C4⋊C4C23×C1111yescharacteristic
582C2×C4⋊C4C23×C1111yescharacteristic
583C2×C4⋊C4C23×C1111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C42—21no—
588C2×C42C23×C1111yescharacteristic
589C2×C42C23×C1111yescharacteristic
590C2×C42C23×C1111yescharacteristic
591#107—21no—
592#106—21no—
593C4⋊C8—21no—
594C4⋊C8—21no—
595#104—22no—
596#104—22no—
597#104—41no—
598#104—41no—
599#104—41no—
600#104—41no—
601#103—21no—
602#103—21no—
603#103—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607#102—21no—
608#102—21no—
609#97—21no—
610C4×C8—21no—
611#95—21no—
612#95—22no—
613C2×C11—21no—
614C2×C11—21no—
615C2×C11—81no—
616C2×C11—81no—
617C2×C11—81no—
618C2×C11—82no—
619C2×C11#240711yescharacteristic
620C2×C11#301811yescharacteristic
621C2×C11#302111yescharacteristic
622C24—21no—
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635C2×Q8C2×D4×C1111yescharacteristic
636C2×Q8C2×D4×C1111yescharacteristic
637C2×Q8C2×D4×C1111yescharacteristic
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4C2×D4×C1111yescharacteristic
651C2×D4C2×D4×C1111yescharacteristic
652C2×D4C2×D4×C1111yescharacteristic
653C2×D4C11×#4112yes—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—82no—
667C22×C4C2×D4×C1112yes—
668C22×C4C2×D4×C1112yes—
669C22×C4C2×D4×C1111yescharacteristic
670C22×C4C2×D4×C1111yescharacteristic
671C22×C4C24×C1111yescharacteristic
672SD16—24no—
673SD16—42no—
674SD16—42no—
675D8—24no—
676D8—42no—
677D8—42no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16C11×#4112yes—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—42no—
709C4⋊C4—82no—
710C4⋊C4C2×D4×C1111yescharacteristic
711C4⋊C4C2×D4×C1111yescharacteristic
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—44no—
726C22⋊C4—41no—
727C22⋊C4—41no—
728C22⋊C4—82no—
729C42—22no—
730C42—22no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42C2×D4×C1111yescharacteristic
739C42C2×D4×C1111yescharacteristic
740C42C2×D4×C1111yescharacteristic
741C42C2×D4×C1111yescharacteristic
742C11#2417411yescharacteristic, direct product factor, Sylow
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—42no—
748C23—42no—
749C23—41no—
750C23—41no—
751C23C22×D4×C1111yescharacteristic
752Q8—21no—
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758D4—21no—
759D4—22no—
760D4—21no—
761D4—22no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—21no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—81no—
775D4—81no—
776D4—82no—
777D4—82no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4C11×#12011yescharacteristic
810C2×C4C11×#12011yescharacteristic
811C2×C4C11×#12011yescharacteristic
812C2×C4C11×#12011yescharacteristic
813C2×C4C22×D4×C1111yescharacteristic
814C2×C4C22×D4×C1111yescharacteristic
815C2×C4C2×C11×#4111yescharacteristic
816C2×C4C2×C11×#4111yescharacteristic
817C2×C4C11×H(5,𝔽2)11yescharacteristic
818C2×C4C11×2−1+411yescharacteristic
819C8—22no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—44no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—81no—
839C22C2×C11×#12011yescharacteristic
840C22C11×#54811yescharacteristic
841C22C11×#55011yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4C11×#52511yescharacteristic
857C4C11×#53711yescharacteristic
858C4C11×#54611yescharacteristic
859C4C11×#54711yescharacteristic
860C2—21no—
861C2—21no—
862C2—82no—
863C2—81no—
864C2—81no—
865C2—81no—
866C2C11×#240711yescharacteristic
867C2C11×#301811yescharacteristic
868C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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×#3512C2semidirect
2. C11×#3036C2semidirect
3. C4×C11×AGL(1,ℤ/8)C2semidirect
4. C11×#2566C2semidirect
5. C11×#2040C2semidirect
6. C11×#2039C2semidirect
7. C11×#2006C2semidirect
8. C11×#2006C2semidirect
9. C11×#1998C2semidirect
10. C11×#1980C2semidirect
11. C11×#1883C2semidirect
12. C11×#1883C2semidirect
13. C11×#1860C2semidirect
14. C11×#1859C2semidirect
15. C11×#1806C2semidirect
188. #24174C11direct (N × H)
309. #3512C2×C11semidirect
310. #3036C2×C11semidirect
311. C4×AGL(1,ℤ/8)C2×C11semidirect
312. #2566C2×C11semidirect
313. #2040C2×C11semidirect
314. #2039C2×C11semidirect
315. #2006C2×C11semidirect
316. #2006C2×C11semidirect
317. #1998C2×C11semidirect
318. #1980C2×C11semidirect
319. #1883C2×C11semidirect
320. #1883C2×C11semidirect
321. #1860C2×C11semidirect
322. #1859C2×C11semidirect
323. #1806C2×C11semidirect
742. C11#24174direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35122
C11×#30362
C4×C11×AGL(1,ℤ/8)2
C11×#25662
C11×#20402
C11×#20392
C11×#20062
C11×#19982
C11×#19802
C11×#18832
C11×#18602
C11×#18592
C11×#18062
#2417411