Finite Group Databasebeta

← C11×#24180 #14601373

Subgroups — C11×#24180 #14601373

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C11×#3036C211yesmaximal, characteristic, complemented
4C11×#2328C211yesmaximal, characteristic, complemented
5C11×#2037C212yesmaximal, complemented
6C11×#2002C212yesmaximal, complemented
7C11×#1995C211yesmaximal, characteristic, complemented
8C11×#1963C211yesmaximal, characteristic, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1860C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2212yes—
13C11×#559—22no—
14C11×#556—21no—
15C11×#555—21no—
16C11×#553—22no—
17C11×#550—21no—
18C11×#547—21no—
19C11×#538—22no—
20C11×#535C2212yes—
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×#127C2211yescharacteristic
24C11×#525—22no—
25C11×#520C2212yes—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C11×#478—22no—
29C11×#476—21no—
30C11×#474—21no—
31C11×#463—22no—
32C11×#461—21no—
33C11×#459—21no—
34C11×#428C2212yes—
35C11×#423C2211yescharacteristic
36C11×#423C2211yescharacteristic
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yes—
39C11×#418C2212yes—
40C11×#417C2212yes—
41C2×C11×#100C2212yes—
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#386—22no—
45C11×#386—22no—
46C11×#382C2211yescharacteristic
47C11×#376C2211yescharacteristic
48C11×#343C2212yes—
49C11×#339C2212yes—
50C11×#339C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41C2312yes—
53C22×D4×C11—22no—
54C22×D4×C11C2311yescharacteristic
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11D412yes—
58C11×AGL(1,ℤ/8)—24no—
59C11×AGL(1,ℤ/8)—42no—
60C2×C11×SD16—22no—
61C2×C11×D8—22no—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C11×C4⋊Q8D411yescharacteristic, complemented
65C11×C4⋊Q8D411yescharacteristic, complemented
66C11×C4⋊Q8D411yescharacteristic, complemented
67C11×#127—22no—
68C11×#127—22no—
69C11×#127—22no—
70C11×#127D411yescharacteristic, complemented
71C11×#126—24no—
72C11×#125D412yescomplemented
73C11×#124—24no—
74C11×#124—22no—
75C11×#124D412yescomplemented
76C11×#123—24no—
77C11×#123—24no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—22no—
82C11×#121—24no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#120—24no—
88C4×Q8×C11—22no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×D4×C11—24no—
92C4×D4×C11—22no—
93C4×D4×C11—24no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C11×#117—22no—
105C11×#117—22no—
106C11×#117C2312yes—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4D412yes—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#107—22no—
118C11×#106—22no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×#104—24no—
124C11×#104—42no—
125C11×#103—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#100—42no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—22no—
133#24180C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11—21no—
135C24×C11C2×D412yes—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—84no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11C2×D412yes—
144C2×D4×C11—22no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—28no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—82no—
162C2×D4×C11—82no—
163C2×D4×C11C2×D412yes—
164C2×D4×C11#4112yescomplemented
165C22×C4×C11—21no—
166C22×C4×C11—24no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11—82no—
175C22×C4×C11—82no—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C11×SD16—44no—
181C11×D8—44no—
182C11×M16—22no—
183C11×M16—22no—
184C11×M16—22no—
185C11×M16—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4C2×D412yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—82no—
212C11×C22⋊C4—82no—
213C42×C11—24no—
214C42×C11—22no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222C42×C11#4112yescomplemented
223#3506C2×C1111yescharacteristic, complemented
224#3077C2×C1111yescharacteristic, complemented
225#3036C2×C1111yescharacteristic, complemented
226#2328C2×C1111yescharacteristic, complemented
227#2037C2×C1112yescomplemented
228#2002C2×C1112yescomplemented
229#1995C2×C1111yescharacteristic, complemented
230#1963C2×C1111yescharacteristic, complemented
231#1883C2×C1112yescomplemented
232#1860C2×C1112yescomplemented
233#1800C2×C1111yescharacteristic, complemented
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11C22×D411yescharacteristic
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—42no—
249Q8×C11—81no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—81no—
264D4×C11—84no—
265D4×C11—88no—
266D4×C11—84no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—44no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—42no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11—82no—
288C2×C4×C11—84no—
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11H(5,𝔽2)11yescharacteristic
298C2×C4×C112−1+411yescharacteristic
299C8×C11—42no—
300C8×C11—42no—
301C2×AGL(1,ℤ/8)C22×C1112yes—
302#559—22no—
303#556—21no—
304#555—21no—
305#553—22no—
306#550—21no—
307#547—21no—
308#538—22no—
309#535C22×C1112yes—
310#533C22×C1111yescharacteristic
311#532C22×C1111yescharacteristic
312C2×#127C22×C1111yescharacteristic
313#525—22no—
314#520C22×C1112yes—
315C2×C4×D4C22×C1111yescharacteristic
316C2×C4×D4C22×C1111yescharacteristic
317#478—22no—
318#476—21no—
319#474—21no—
320#463—22no—
321#461—21no—
322#459—21no—
323#428C22×C1112yes—
324#423C22×C1111yescharacteristic
325#423C22×C1111yescharacteristic
326C2×#104C22×C1112yes—
327C2×#104C22×C1112yes—
328#418C22×C1112yes—
329#417C22×C1112yes—
330C2×#100C22×C1112yes—
331#390C22×C1111yescharacteristic
332#390C22×C1111yescharacteristic
333#386—22no—
334#386—22no—
335#382C22×C1111yescharacteristic
336#376C22×C1111yescharacteristic
337#343C22×C1112yes—
338#339C22×C1112yes—
339#339C22×C1112yes—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—82no—
352C22×C11—82no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11C2×#12011yescharacteristic
356C22×C11#52511yescharacteristic
357C22×C11#53711yescharacteristic
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11#54611yescharacteristic
370C4×C11#54711yescharacteristic
371C4×C11#54811yescharacteristic
372C4×C11#55011yescharacteristic
373C2×#41—22no—
374C2×#41C23×C1112yes—
375C22×D4—22no—
376C22×D4C23×C1111yescharacteristic
377C22×D4C23×C1111yescharacteristic
378C23×C4—21no—
379C23×C4D4×C1112yes—
380AGL(1,ℤ/8)—24no—
381AGL(1,ℤ/8)—42no—
382C2×SD16—22no—
383C2×D8—22no—
384C2×M16C23×C1112yes—
385C2×M16C23×C1112yes—
386C4⋊Q8D4×C1111yescharacteristic, complemented
387C4⋊Q8D4×C1111yescharacteristic, complemented
388C4⋊Q8D4×C1111yescharacteristic, complemented
389#127—22no—
390#127—22no—
391#127—22no—
392#127D4×C1111yescharacteristic, complemented
393#126—24no—
394#125D4×C1112yescomplemented
395#124—24no—
396#124—22no—
397#124D4×C1112yescomplemented
398#123—24no—
399#123—24no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403#121—22no—
404#121—24no—
405#121—21no—
406#121—21no—
407#121—22no—
408#121—22no—
409#120—24no—
410C4×Q8—22no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×D4—24no—
414C4×D4—22no—
415C4×D4—24no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426#117—22no—
427#117—22no—
428#117C23×C1112yes—
429C2×C4⋊C4—22no—
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4D4×C1112yes—
436C2×C42C23×C1111yescharacteristic
437C2×C42C23×C1111yescharacteristic
438C2×C42C23×C1111yescharacteristic
439#107—22no—
440#106—22no—
441C4⋊C8—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445#104—24no—
446#104—42no—
447#103—22no—
448#102—22no—
449#102—22no—
450#102—22no—
451#100—42no—
452#95—21no—
453#95—21no—
454#95—22no—
455C2×C11—21no—
456C2×C11—21no—
457C2×C11—82no—
458C2×C11—82no—
459C2×C11—82no—
460C2×C11#240711yescharacteristic
461C2×C11#301911yescharacteristic
462C2×C11#302111yescharacteristic
463C24—21no—
464C24C2×D4×C1112yes—
465#41—22no—
466#41—22no—
467#41—22no—
468#41—22no—
469#41—84no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8C2×D4×C1112yes—
473C2×D4—22no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—28no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—82no—
491C2×D4—82no—
492C2×D4C2×D4×C1112yes—
493C2×D4C11×#4112yescomplemented
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—82no—
504C22×C4—82no—
505C22×C4C2×D4×C1112yes—
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1111yescharacteristic
508C22×C4C24×C1111yescharacteristic
509SD16—44no—
510D8—44no—
511M16—22no—
512M16—22no—
513M16—22no—
514M16—22no—
515C2×C8—22no—
516C2×C8—22no—
517C4⋊C4—24no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4C2×D4×C1112yes—
529C4⋊C4C2×D4×C1112yes—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—82no—
541C22⋊C4—82no—
542C42—24no—
543C42—22no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42C2×D4×C1111yescharacteristic
548C42C2×D4×C1111yescharacteristic
549C42C2×D4×C1111yescharacteristic
550C42C2×D4×C1111yescharacteristic
551C42C11×#4112yescomplemented
552C11#2418011yescharacteristic, direct product factor, Sylow
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—41no—
563C23—41no—
564C23C22×D4×C1111yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—42no—
568Q8—81no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—81no—
583D4—84no—
584D4—88no—
585D4—84no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—44no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—84no—
608C2×C4C11×#12011yescharacteristic
609C2×C4C11×#12011yescharacteristic
610C2×C4C11×#12011yescharacteristic
611C2×C4C11×#12011yescharacteristic
612C2×C4C22×D4×C1111yescharacteristic
613C2×C4C22×D4×C1111yescharacteristic
614C2×C4C2×C11×#4111yescharacteristic
615C2×C4C2×C11×#4111yescharacteristic
616C2×C4C11×H(5,𝔽2)11yescharacteristic
617C2×C4C11×2−1+411yescharacteristic
618C8—42no—
619C8—42no—
620C22—21no—
621C22—21no—
622C22—44no—
623C22—44no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—82no—
632C22—82no—
633C22—81no—
634C22—81no—
635C22C2×C11×#12011yescharacteristic
636C22C11×#52511yescharacteristic
637C22C11×#53711yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—21no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4C11×#54611yescharacteristic
650C4C11×#54711yescharacteristic
651C4C11×#54811yescharacteristic
652C4C11×#55011yescharacteristic
653C2—21no—
654C2—21no—
655C2—82no—
656C2—82no—
657C2—82no—
658C2C11×#240711yescharacteristic
659C2C11×#301911yescharacteristic
660C2C11×#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×#3506C2semidirect
2. C11×#3077C2semidirect
3. C11×#3036C2semidirect
4. C11×#2328C2semidirect
5. C11×#2037C2semidirect
6. C11×#2002C2semidirect
7. C11×#1995C2semidirect
8. C11×#1963C2semidirect
9. C11×#1883C2semidirect
10. C11×#1860C2semidirect
11. C11×#1800C2semidirect
64. C11×C4⋊Q8D4semidirect
65. C11×C4⋊Q8D4semidirect
66. C11×C4⋊Q8D4semidirect
70. C11×#127D4semidirect
72. C11×#125D4semidirect
75. C11×#124D4semidirect
133. #24180C11direct (N × H)
164. C2×D4×C11#41semidirect
222. C42×C11#41semidirect
223. #3506C2×C11semidirect
224. #3077C2×C11semidirect
225. #3036C2×C11semidirect
226. #2328C2×C11semidirect
227. #2037C2×C11semidirect
228. #2002C2×C11semidirect
229. #1995C2×C11semidirect
230. #1963C2×C11semidirect
231. #1883C2×C11semidirect
232. #1860C2×C11semidirect
233. #1800C2×C11semidirect
386. C4⋊Q8D4×C11semidirect
387. C4⋊Q8D4×C11semidirect
388. C4⋊Q8D4×C11semidirect
392. #127D4×C11semidirect
394. #125D4×C11semidirect
397. #124D4×C11semidirect
493. C2×D4C11×#41semidirect
551. C42C11×#41semidirect
552. C11#24180direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#30772
C11×#30362
C11×#23282
C11×#20372
C11×#20022
C11×#19952
C11×#19632
C11×#18832
C11×#18602
C11×#18002
#2418011