Finite Group Databasebeta

← C11×#24808 #14602001

Subgroups — C11×#24808 #14602001

Order 2816.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3069C211yesmaximal, characteristic, complemented
2C11×#3068C211yesmaximal, characteristic
3C2×C11×#471C211yesmaximal, characteristic, complemented
4C2×C11×#471C211yesmaximal, characteristic, complemented
5C11×#2955C211yesmaximal, characteristic, complemented
6C11×#2916C211yesmaximal, characteristic, complemented
7C11×#2070C211yesmaximal, characteristic, complemented
8C11×#2069C211yesmaximal, characteristic, complemented
9C11×#2049C211yesmaximal, characteristic, complemented
10C11×#2048C211yesmaximal, characteristic, complemented
11C11×#1977C211yesmaximal, characteristic, complemented
12C11×#1953C211yesmaximal, characteristic, complemented
13C11×#1903C211yesmaximal, characteristic, complemented
14C11×#1902C211yesmaximal, characteristic, complemented
15C11×#1813C211yesmaximal, characteristic, complemented
16C11×#575C2211yescharacteristic
17C2×C11×#137C2211yescharacteristic
18C2×C11×#137C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C11×#568C2211yescharacteristic
23C11×#568C2211yescharacteristic
24C2×C11×#131C2211yescharacteristic
25C2×C11×#131C2211yescharacteristic
26C11×#473—22no—
27C11×#472—22no—
28C11×#471—22no—
29C11×#471—22no—
30C11×#471—22no—
31C11×#471—22no—
32C11×#471—22no—
33C11×#471—22no—
34C11×#444—22no—
35C11×#443—22no—
36C11×#430—22no—
37C11×#430C2211yescharacteristic
38C11×#430C2211yescharacteristic
39C11×#430C2211yescharacteristic
40C11×#430C2211yescharacteristic
41C11×#430C2211yescharacteristic
42C2×C11×#108—22no—
43C2×C11×#108C2211yescharacteristic
44C2×C11×#108C2211yescharacteristic
45C2×C11×#108C2211yescharacteristic
46C11×#421C2211yescharacteristic
47C11×#421C2211yescharacteristic
48C11×#419C2211yescharacteristic
49C11×#418C2211yescharacteristic
50C11×#413C2211yescharacteristic
51C11×#413C2211yescharacteristic
52C2×C11×#101C2211yescharacteristic
53C2×C11×#101C2211yescharacteristic
54C2×C11×#101C2211yescharacteristic
55C2×C11×#100C2211yescharacteristic
56C2×C11×#100C2211yescharacteristic
57C2×C11×#100C2211yescharacteristic
58C11×#405C2211yescharacteristic
59C11×#344C2211yescharacteristic
60C11×#344C2211yescharacteristic
61C11×#338C2211yescharacteristic
62C11×#338C2211yescharacteristic
63C2×C11×#41C2311yescharacteristic
64C2×C11×#41C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C11×#137—21no—
68C11×#137—22no—
69C11×#137—22no—
70C11×#137—22no—
71C11×#137—41no—
72C11×#137D412yes—
73C11×AGL(1,ℤ/8)—21no—
74C11×AGL(1,ℤ/8)—22no—
75C11×AGL(1,ℤ/8)—22no—
76C11×AGL(1,ℤ/8)—22no—
77C11×AGL(1,ℤ/8)—41no—
78C11×AGL(1,ℤ/8)D412yes—
79C11×#135—22no—
80C2×C11×Q16—21no—
81C2×C11×Q16—21no—
82C2×C11×SD16—21no—
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×SD16—21no—
86C2×C11×SD16—21no—
87C2×C11×SD16—21no—
88C2×C11×SD16—21no—
89C2×C11×SD16—21no—
90C2×C11×SD16—21no—
91C2×C11×SD16—21no—
92C2×C11×D8—21no—
93C2×C11×D8—21no—
94C11×#131—21no—
95C11×#131—21no—
96C11×#131—22no—
97C11×#131—22no—
98C11×#131—21no—
99C11×#131—21no—
100C11×#131—21no—
101C11×#131—21no—
102C11×#131—41no—
103C11×#131—41no—
104C11×#131D412yes—
105C11×#131D412yes—
106C2×C11×M16—21no—
107C2×C11×M16—21no—
108C2×C11×M16—22no—
109C2×C11×M16—22no—
110C2×C11×M16C2311yescharacteristic
111C2×C11×M16C2311yescharacteristic
112C2×C11×M16C2311yescharacteristic
113C2×C11×M16C2311yescharacteristic
114C2×C11×M16C2311yescharacteristic
115C2×C11×M16C2311yescharacteristic
116C2×C11×M16C2311yescharacteristic
117C2×C11×M16C2311yescharacteristic
118C2×C11×M16C2311yescharacteristic
119C22×C8×C11—21no—
120C22×C8×C11—21no—
121C22×C8×C11C2311yescharacteristic
122C11×#117C2311yescharacteristic
123C11×#108—22no—
124C11×#108—22no—
125C11×#108—22no—
126C11×#108—22no—
127C11×#108—22no—
128C11×#108—21no—
129C11×#108—21no—
130C11×#108—21no—
131C11×#108—21no—
132C11×#108D412yes—
133C11×#108D412yes—
134C11×#104—22no—
135C11×#104—22no—
136C11×#103—41no—
137C11×#102—41no—
138C11×#101—21no—
139C11×#101—21no—
140C11×#101—22no—
141C11×#101—22no—
142C11×#101—22no—
143C11×#100—21no—
144C11×#100—21no—
145C11×#100—22no—
146C11×#100—22no—
147C11×#100—22no—
148C11×#97—21no—
149C4×C8×C11—21no—
150#24808C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—21no—
155C11×#41—21no—
156C11×#41—21no—
157C11×#41—21no—
158C11×#41C2×D412yes—
159C11×#41C2×D412yes—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11C2×D411yescharacteristic
167C2×Q8×C11#4111yescharacteristic
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11C2×D411yescharacteristic
177C2×D4×C11#4111yescharacteristic
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11C2411yescharacteristic
182C11×Q16—22no—
183C11×Q16—42no—
184C11×Q16—42no—
185C11×SD16—22no—
186C11×SD16—22no—
187C11×SD16—42no—
188C11×SD16—42no—
189C11×SD16—41no—
190C11×SD16—41no—
191C11×SD16—41no—
192C11×SD16—41no—
193C11×SD16—42no—
194C11×SD16—42no—
195C11×D8—22no—
196C11×D8—42no—
197C11×D8—42no—
198C11×M16—22no—
199C11×M16—22no—
200C11×M16—21no—
201C11×M16—21no—
202C11×M16—21no—
203C11×M16—21no—
204C11×M16—21no—
205C11×M16—21no—
206C11×M16—21no—
207C11×M16—21no—
208C11×M16—21no—
209C11×M16—21no—
210C11×M16—21no—
211C11×M16—21no—
212C11×M16—21no—
213C11×M16—21no—
214C11×M16—42no—
215C11×M16—42no—
216C11×M16—41no—
217C11×M16—41no—
218C11×M16C2×D412yes—
219C11×M16C2×D412yes—
220C11×M16C2×D412yes—
221C11×M16C2×D412yes—
222C2×C8×C11—22no—
223C2×C8×C11—22no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—42no—
234C2×C8×C11—42no—
235C2×C8×C11—41no—
236C2×C8×C11—41no—
237C2×C8×C11C2×D411yescharacteristic
238C2×C8×C11C2×D411yescharacteristic
239C2×C8×C11C2×D411yescharacteristic
240C2×C8×C11C2×D411yescharacteristic
241C2×C8×C11#4111yescharacteristic
242C2×C8×C11#4111yescharacteristic
243C11×C4⋊C4—21no—
244C11×C22⋊C4—21no—
245C42×C11—21no—
246#3069C2×C1111yescharacteristic, complemented
247#3068C2×C1111yescharacteristic
248C2×#471C2×C1111yescharacteristic, complemented
249C2×#471C2×C1111yescharacteristic, complemented
250#2955C2×C1111yescharacteristic, complemented
251#2916C2×C1111yescharacteristic, complemented
252#2070C2×C1111yescharacteristic, complemented
253#2069C2×C1111yescharacteristic, complemented
254#2049C2×C1111yescharacteristic, complemented
255#2048C2×C1111yescharacteristic, complemented
256#1977C2×C1111yescharacteristic, complemented
257#1953C2×C1111yescharacteristic, complemented
258#1903C2×C1111yescharacteristic, complemented
259#1902C2×C1111yescharacteristic, complemented
260#1813C2×C1111yescharacteristic, complemented
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—161no—
267C23×C112−1+411yescharacteristic
268Q8×C11—21no—
269Q8×C11—21no—
270Q8×C11—21no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275Q8×C11#12112yes—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—21no—
279D4×C11—21no—
280D4×C11—21no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—41no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11#12112yes—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C8×C11—22no—
305C8×C11—22no—
306C8×C11—22no—
307C8×C11—22no—
308C8×C11—41no—
309C8×C11—41no—
310C8×C11—41no—
311C8×C11—41no—
312C8×C11—41no—
313C8×C11#12111yescharacteristic
314C8×C11#12111yescharacteristic
315C8×C11#12111yescharacteristic
316C8×C11#12111yescharacteristic
317#575C22×C1111yescharacteristic
318C2×#137C22×C1111yescharacteristic
319C2×#137C22×C1111yescharacteristic
320C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
321C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
322C22×SD16C22×C1111yescharacteristic
323#568C22×C1111yescharacteristic
324#568C22×C1111yescharacteristic
325C2×#131C22×C1111yescharacteristic
326C2×#131C22×C1111yescharacteristic
327#473—22no—
328#472—22no—
329#471—22no—
330#471—22no—
331#471—22no—
332#471—22no—
333#471—22no—
334#471—22no—
335#444—22no—
336#443—22no—
337#430—22no—
338#430C22×C1111yescharacteristic
339#430C22×C1111yescharacteristic
340#430C22×C1111yescharacteristic
341#430C22×C1111yescharacteristic
342#430C22×C1111yescharacteristic
343C2×#108—22no—
344C2×#108C22×C1111yescharacteristic
345C2×#108C22×C1111yescharacteristic
346C2×#108C22×C1111yescharacteristic
347#421C22×C1111yescharacteristic
348#421C22×C1111yescharacteristic
349#419C22×C1111yescharacteristic
350#418C22×C1111yescharacteristic
351#413C22×C1111yescharacteristic
352#413C22×C1111yescharacteristic
353C2×#101C22×C1111yescharacteristic
354C2×#101C22×C1111yescharacteristic
355C2×#101C22×C1111yescharacteristic
356C2×#100C22×C1111yescharacteristic
357C2×#100C22×C1111yescharacteristic
358C2×#100C22×C1111yescharacteristic
359#405C22×C1111yescharacteristic
360#344C22×C1111yescharacteristic
361#344C22×C1111yescharacteristic
362#338C22×C1111yescharacteristic
363#338C22×C1111yescharacteristic
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—161no—
371C22×C11—161no—
372C22×C11—161no—
373C22×C11#53711yescharacteristic
374C22×C11#54711yescharacteristic
375C22×C11#54811yescharacteristic
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11C2×#12111yescharacteristic
381C4×C11C2×#12111yescharacteristic
382C4×C11D4211yescharacteristic
383C4×C11#55311yescharacteristic
384C2×#41C23×C1111yescharacteristic
385C2×#41C23×C1111yescharacteristic
386C22×Q8C23×C1111yescharacteristic
387C22×D4C23×C1111yescharacteristic
388#137—21no—
389#137—22no—
390#137—22no—
391#137—22no—
392#137—41no—
393#137D4×C1112yes—
394AGL(1,ℤ/8)—21no—
395AGL(1,ℤ/8)—22no—
396AGL(1,ℤ/8)—22no—
397AGL(1,ℤ/8)—22no—
398AGL(1,ℤ/8)—41no—
399AGL(1,ℤ/8)D4×C1112yes—
400#135—22no—
401C2×Q16—21no—
402C2×Q16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—21no—
406C2×SD16—21no—
407C2×SD16—21no—
408C2×SD16—21no—
409C2×SD16—21no—
410C2×SD16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×D8—21no—
414C2×D8—21no—
415#131—21no—
416#131—21no—
417#131—22no—
418#131—22no—
419#131—21no—
420#131—21no—
421#131—21no—
422#131—21no—
423#131—41no—
424#131—41no—
425#131D4×C1112yes—
426#131D4×C1112yes—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—22no—
430C2×M16—22no—
431C2×M16C23×C1111yescharacteristic
432C2×M16C23×C1111yescharacteristic
433C2×M16C23×C1111yescharacteristic
434C2×M16C23×C1111yescharacteristic
435C2×M16C23×C1111yescharacteristic
436C2×M16C23×C1111yescharacteristic
437C2×M16C23×C1111yescharacteristic
438C2×M16C23×C1111yescharacteristic
439C2×M16C23×C1111yescharacteristic
440C22×C8—21no—
441C22×C8—21no—
442C22×C8C23×C1111yescharacteristic
443#117C23×C1111yescharacteristic
444#108—22no—
445#108—22no—
446#108—22no—
447#108—22no—
448#108—22no—
449#108—21no—
450#108—21no—
451#108—21no—
452#108—21no—
453#108D4×C1112yes—
454#108D4×C1112yes—
455#104—22no—
456#104—22no—
457#103—41no—
458#102—41no—
459#101—21no—
460#101—21no—
461#101—22no—
462#101—22no—
463#101—22no—
464#100—21no—
465#100—21no—
466#100—22no—
467#100—22no—
468#100—22no—
469#97—21no—
470C4×C8—21no—
471C2×C11—21no—
472C2×C11—21no—
473C2×C11—21no—
474C2×C11—42no—
475C2×C11—81no—
476C2×C11—161no—
477C2×C11#241611yescharacteristic
478C24—21no—
479#41—21no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41C2×D4×C1112yes—
486#41C2×D4×C1112yes—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8C2×D4×C1111yescharacteristic
494C2×Q8C11×#4111yescharacteristic
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4C2×D4×C1111yescharacteristic
504C2×D4C11×#4111yescharacteristic
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4C24×C1111yescharacteristic
509Q16—22no—
510Q16—42no—
511Q16—42no—
512SD16—22no—
513SD16—22no—
514SD16—42no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518SD16—41no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522D8—22no—
523D8—42no—
524D8—42no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—22no—
530M16—22no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—42no—
542M16—42no—
543M16—41no—
544M16—41no—
545M16C2×D4×C1112yes—
546M16C2×D4×C1112yes—
547M16C2×D4×C1112yes—
548M16C2×D4×C1112yes—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—42no—
561C2×C8—42no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8C2×D4×C1111yescharacteristic
565C2×C8C2×D4×C1111yescharacteristic
566C2×C8C2×D4×C1111yescharacteristic
567C2×C8C2×D4×C1111yescharacteristic
568C2×C8C11×#4111yescharacteristic
569C2×C8C11×#4111yescharacteristic
570C4⋊C4—21no—
571C22⋊C4—21no—
572C42—21no—
573C11#2480811yescharacteristic, direct product factor, Sylow
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C23C11×2−1+411yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8C11×#12112yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4C11×#12112yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C22×D4×C1111yescharacteristic
612C2×C4C22×D4×C1111yescharacteristic
613C2×C4C22×D4×C1111yescharacteristic
614C2×C4C2×C11×#4111yescharacteristic
615C2×C4C2×C11×#4111yescharacteristic
616C2×C4C11×H(5,𝔽2)11yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8C11×#12111yescharacteristic
627C8C11×#12111yescharacteristic
628C8C11×#12111yescharacteristic
629C8C11×#12111yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22C11×#53711yescharacteristic
640C22C11×#54711yescharacteristic
641C22C11×#54811yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×C11×#12111yescharacteristic
647C4C2×C11×#12111yescharacteristic
648C4D42×C1111yescharacteristic
649C4C11×#55311yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2C11×#241611yescharacteristic
subgroupG/H
center, socleC2×C11#2416
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3068C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3069C2semidirect
3. C2×C11×#471C2semidirect
4. C2×C11×#471C2semidirect
5. C11×#2955C2semidirect
6. C11×#2916C2semidirect
7. C11×#2070C2semidirect
8. C11×#2069C2semidirect
9. C11×#2049C2semidirect
10. C11×#2048C2semidirect
11. C11×#1977C2semidirect
12. C11×#1953C2semidirect
13. C11×#1903C2semidirect
14. C11×#1902C2semidirect
15. C11×#1813C2semidirect
150. #24808C11direct (N × H)
246. #3069C2×C11semidirect
248. C2×#471C2×C11semidirect
249. C2×#471C2×C11semidirect
250. #2955C2×C11semidirect
251. #2916C2×C11semidirect
252. #2070C2×C11semidirect
253. #2069C2×C11semidirect
254. #2049C2×C11semidirect
255. #2048C2×C11semidirect
256. #1977C2×C11semidirect
257. #1953C2×C11semidirect
258. #1903C2×C11semidirect
259. #1902C2×C11semidirect
260. #1813C2×C11semidirect
573. C11#24808direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30692
C11×#30682
C2×C11×#4712
C11×#29552
C11×#29162
C11×#20702
C11×#20692
C11×#20492
C11×#20482
C11×#19772
C11×#19532
C11×#19032
C11×#19022
C11×#18132
#2480811