Finite Group Databasebeta

← C11×#24724 #14601917

Subgroups — C11×#24724 #14601917

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3080C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C11×#2925C211yesmaximal, characteristic, complemented
5C11×#2079C211yesmaximal, characteristic, complemented
6C11×#2078C211yesmaximal, characteristic, complemented
7C11×#2051C211yesmaximal, characteristic
8C11×#2051C211yesmaximal, characteristic
9C11×#1998C211yesmaximal, characteristic, complemented
10C11×#1952C211yesmaximal, characteristic, complemented
11C11×#1951C211yesmaximal, characteristic, complemented
12C11×#1950C211yesmaximal, characteristic, complemented
13C11×#1931C211yesmaximal, characteristic, complemented
14C11×#1931C211yesmaximal, characteristic, complemented
15C11×#1800C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C11×#479—21no—
21C11×#479—21no—
22C11×#478—21no—
23C11×#478—21no—
24C11×#478—21no—
25C11×#478—21no—
26C11×#478—21no—
27C11×#478—21no—
28C11×#442—21no—
29C11×#440—21no—
30C4×C11×SD16—21no—
31C4×C11×D8—21no—
32C11×#433—21no—
33C11×#433—21no—
34C11×#432—21no—
35C11×#431—21no—
36C2×C11×#108C2211yescharacteristic
37C2×C11×#108C2211yescharacteristic
38C11×#428C2211yescharacteristic
39C11×#428C2211yescharacteristic
40C11×#428C2211yescharacteristic
41C2×C11×#107C2211yescharacteristic
42C2×C11×#106C2211yescharacteristic
43C11×#423C2211yescharacteristic
44C11×#423C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#418C2211yescharacteristic
47C11×#417C2211yescharacteristic
48C11×#417C2211yescharacteristic
49C11×#417C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#100C2211yescharacteristic
53C2×C11×#100C2211yescharacteristic
54C11×#408C2211yescharacteristic
55C11×#408C2211yescharacteristic
56C11×#405C2211yescharacteristic
57C11×#405C2211yescharacteristic
58C4×C11×M16C2211yescharacteristic
59C11×#343C2211yescharacteristic
60C11×#343C2211yescharacteristic
61C11×#343C2211yescharacteristic
62C11×#343C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#341C2211yescharacteristic
66C11×#341C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C11×AGL(1,ℤ/8)—22no—
71C11×AGL(1,ℤ/8)—22no—
72C2×C11×SD16—21no—
73C2×C11×D8—21no—
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#125—21no—
83C11×#125—21no—
84C11×#125—21no—
85C11×#125—21no—
86C4×Q8×C11D411yescharacteristic
87C4×Q8×C11D411yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11D411yescharacteristic
95C4×D4×C11D411yescharacteristic
96C11×#117—21no—
97C11×#117C2311yescharacteristic
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C11×#108—22no—
107C11×#108—22no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#107—21no—
112C11×#107—21no—
113C11×#106—21no—
114C11×#106—21no—
115C11×#106—21no—
116C11×#106—21no—
117C11×#106—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8D411yescharacteristic
123C11×C4⋊C8D411yescharacteristic
124C11×C4⋊C8D411yescharacteristic
125C11×C4⋊C8D411yescharacteristic
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#102—21no—
137C11×#102—21no—
138C11×#100—22no—
139C11×#100—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97—21no—
145C11×#97—21no—
146C11×#97—21no—
147C4×C8×C11—21no—
148C4×C8×C11—21no—
149C4×C8×C11—21no—
150#24724C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—21no—
155C11×#41—21no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11#4112yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—82no—
174C22×C4×C11#4111yescharacteristic
175C22×C4×C11#4111yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C11×SD16—24no—
178C11×D8—24no—
179C11×M16—21no—
180C11×M16—21no—
181C11×M16—21no—
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16—21no—
187C11×M16—21no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16#4112yes—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11C2×D411yescharacteristic
202C2×C8×C11C2×D411yescharacteristic
203C2×C8×C11C2×D411yescharacteristic
204C2×C8×C11C2×D411yescharacteristic
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—41no—
214C11×C4⋊C4—41no—
215C11×C4⋊C4—41no—
216C11×C4⋊C4—41no—
217C11×C4⋊C4C2×D411yescharacteristic
218C11×C4⋊C4C2×D411yescharacteristic
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231#3080C2×C1111yescharacteristic, complemented
232C2×#478C2×C1111yescharacteristic, complemented
233C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
234#2925C2×C1111yescharacteristic, complemented
235#2079C2×C1111yescharacteristic, complemented
236#2078C2×C1111yescharacteristic, complemented
237#2051C2×C1111yescharacteristic
238#2051C2×C1111yescharacteristic
239#1998C2×C1111yescharacteristic, complemented
240#1952C2×C1111yescharacteristic, complemented
241#1951C2×C1111yescharacteristic, complemented
242#1950C2×C1111yescharacteristic, complemented
243#1931C2×C1111yescharacteristic, complemented
244#1931C2×C1111yescharacteristic, complemented
245#1800C2×C1111yescharacteristic, complemented
246C23×C11—21no—
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—81no—
251C23×C11—81no—
252C23×C11C2×#4111yescharacteristic
253Q8×C11—21no—
254Q8×C11—21no—
255D4×C11—21no—
256D4×C11—22no—
257D4×C11—21no—
258D4×C11—22no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—81no—
275C2×C4×C11—82no—
276C2×C4×C11—82no—
277C2×C4×C11—81no—
278C2×C4×C11—81no—
279C2×C4×C11—81no—
280C2×C4×C11#12111yescharacteristic
281C2×C4×C11#12111yescharacteristic
282C2×C4×C11#12111yescharacteristic
283C2×C4×C11#12111yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C8×C11—22no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—21no—
295C8×C11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C8×C11—41no—
300C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
301C2×#125C22×C1111yescharacteristic
302C4×#41C22×C1111yescharacteristic
303C2×C4×D4C22×C1111yescharacteristic
304#479—21no—
305#479—21no—
306#478—21no—
307#478—21no—
308#478—21no—
309#478—21no—
310#478—21no—
311#478—21no—
312#442—21no—
313#440—21no—
314C4×SD16—21no—
315C4×D8—21no—
316#433—21no—
317#433—21no—
318#432—21no—
319#431—21no—
320C2×#108C22×C1111yescharacteristic
321C2×#108C22×C1111yescharacteristic
322#428C22×C1111yescharacteristic
323#428C22×C1111yescharacteristic
324#428C22×C1111yescharacteristic
325C2×#107C22×C1111yescharacteristic
326C2×#106C22×C1111yescharacteristic
327#423C22×C1111yescharacteristic
328#423C22×C1111yescharacteristic
329C2×C4⋊C8C22×C1111yescharacteristic
330#418C22×C1111yescharacteristic
331#417C22×C1111yescharacteristic
332#417C22×C1111yescharacteristic
333#417C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#100C22×C1111yescharacteristic
337C2×#100C22×C1111yescharacteristic
338#408C22×C1111yescharacteristic
339#408C22×C1111yescharacteristic
340#405C22×C1111yescharacteristic
341#405C22×C1111yescharacteristic
342C4×M16C22×C1111yescharacteristic
343#343C22×C1111yescharacteristic
344#343C22×C1111yescharacteristic
345#343C22×C1111yescharacteristic
346#343C22×C1111yescharacteristic
347#343C22×C1111yescharacteristic
348#343C22×C1111yescharacteristic
349#341C22×C1111yescharacteristic
350#341C22×C1111yescharacteristic
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—41no—
354C22×C11—42no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—82no—
358C22×C11—82no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11C2×#12111yescharacteristic
362C22×C11#55211yescharacteristic
363C22×C11#55611yescharacteristic
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52511yescharacteristic
375C4×C11#53611yescharacteristic
376C4×C11#54711yescharacteristic
377C4×C11#54811yescharacteristic
378C2×#41C23×C1111yescharacteristic
379C22×D4C23×C1111yescharacteristic
380C23×C4—21no—
381AGL(1,ℤ/8)—22no—
382AGL(1,ℤ/8)—22no—
383C2×SD16—21no—
384C2×D8—21no—
385C2×M16C23×C1111yescharacteristic
386C2×M16C23×C1111yescharacteristic
387C2×M16C23×C1111yescharacteristic
388C2×M16C23×C1111yescharacteristic
389C2×M16C23×C1111yescharacteristic
390C2×M16C23×C1111yescharacteristic
391C22×C8C23×C1111yescharacteristic
392C22×C8C23×C1111yescharacteristic
393#125—21no—
394#125—21no—
395#125—21no—
396#125—21no—
397C4×Q8D4×C1111yescharacteristic
398C4×Q8D4×C1111yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4D4×C1111yescharacteristic
406C4×D4D4×C1111yescharacteristic
407#117—21no—
408#117C23×C1111yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4C23×C1111yescharacteristic
412C2×C4⋊C4C23×C1111yescharacteristic
413C2×C4⋊C4C23×C1111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C42—21no—
416C2×C42C23×C1111yescharacteristic
417#108—22no—
418#108—22no—
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#106—21no—
425#106—21no—
426#106—21no—
427#106—21no—
428#106—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433C4⋊C8D4×C1111yescharacteristic
434C4⋊C8D4×C1111yescharacteristic
435C4⋊C8D4×C1111yescharacteristic
436C4⋊C8D4×C1111yescharacteristic
437#103—21no—
438#103—21no—
439#103—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#100—22no—
450#100—22no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455#97—21no—
456#97—21no—
457#97—21no—
458C4×C8—21no—
459C4×C8—21no—
460C4×C8—21no—
461C2×C11—21no—
462C2×C11—21no—
463C2×C11—81no—
464C2×C11—82no—
465C2×C11#241511yescharacteristic
466C2×C11#306711yescharacteristic
467C2×C11#306811yescharacteristic
468C24—21no—
469#41—21no—
470#41—21no—
471#41—21no—
472#41—21no—
473C2×Q8C2×D4×C1111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4C2×D4×C1111yescharacteristic
481C2×D4C11×#4112yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—82no—
491C22×C4C11×#4111yescharacteristic
492C22×C4C11×#4111yescharacteristic
493C22×C4C24×C1111yescharacteristic
494SD16—24no—
495D8—24no—
496M16—21no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16—21no—
503M16—21no—
504M16—21no—
505M16—21no—
506M16—21no—
507M16C11×#4112yes—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8C2×D4×C1111yescharacteristic
519C2×C8C2×D4×C1111yescharacteristic
520C2×C8C2×D4×C1111yescharacteristic
521C2×C8C2×D4×C1111yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4C2×D4×C1111yescharacteristic
535C4⋊C4C2×D4×C1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42C2×D4×C1111yescharacteristic
545C42C2×D4×C1111yescharacteristic
546C42C2×D4×C1111yescharacteristic
547C42C2×D4×C1111yescharacteristic
548C11#2472411yescharacteristic, direct product factor, Sylow
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—81no—
554C23—81no—
555C23C2×C11×#4111yescharacteristic
556Q8—21no—
557Q8—21no—
558D4—21no—
559D4—22no—
560D4—21no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—81no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4C11×#12111yescharacteristic
584C2×C4C11×#12111yescharacteristic
585C2×C4C11×#12111yescharacteristic
586C2×C4C11×#12111yescharacteristic
587C2×C4C22×D4×C1111yescharacteristic
588C2×C4C22×D4×C1111yescharacteristic
589C2×C4C2×C11×#4111yescharacteristic
590C2×C4C2×C11×#4111yescharacteristic
591C2×C4C11×2−1+411yescharacteristic
592C2×C4C11×2−1+411yescharacteristic
593C8—22no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—41no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—41no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22C2×C11×#12111yescharacteristic
614C22C11×#55211yescharacteristic
615C22C11×#55611yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4C11×#52511yescharacteristic
627C4C11×#53611yescharacteristic
628C4C11×#54711yescharacteristic
629C4C11×#54811yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—82no—
634C2C11×#241511yescharacteristic
635C2C11×#306711yescharacteristic
636C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
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×#3080C2semidirect
2. C2×C11×#478C2semidirect
4. C11×#2925C2semidirect
5. C11×#2079C2semidirect
6. C11×#2078C2semidirect
9. C11×#1998C2semidirect
10. C11×#1952C2semidirect
11. C11×#1951C2semidirect
12. C11×#1950C2semidirect
13. C11×#1931C2semidirect
14. C11×#1931C2semidirect
15. C11×#1800C2semidirect
150. #24724C11direct (N × H)
231. #3080C2×C11semidirect
232. C2×#478C2×C11semidirect
234. #2925C2×C11semidirect
235. #2079C2×C11semidirect
236. #2078C2×C11semidirect
239. #1998C2×C11semidirect
240. #1952C2×C11semidirect
241. #1951C2×C11semidirect
242. #1950C2×C11semidirect
243. #1931C2×C11semidirect
244. #1931C2×C11semidirect
245. #1800C2×C11semidirect
548. C11#24724direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30802
C2×C11×#4782
C4×C11×AGL(1,ℤ/8)2
C11×#29252
C11×#20792
C11×#20782
C11×#20512
C11×#19982
C11×#19522
C11×#19512
C11×#19502
C11×#19312
C11×#18002
#2472411