Finite Group Databasebeta

← C11×#23533 #14600726

Subgroups — C11×#23533 #14600726

Order 2816.

1358 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C211yesmaximal, characteristic
2C2×C11×#430C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C2×C11×#417C211yesmaximal, characteristic, complemented
5C2×C11×#413C211yesmaximal, characteristic, complemented
6C11×#2879C211yesmaximal, characteristic, complemented
7C11×#2052C214yesmaximal, complemented
8C11×#2051C214yesmaximal, complemented
9C2×C11×#343C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C11×#575—24no—
13C11×#575—24no—
14C2×C11×#137—21no—
15C2×C11×#137C2212yes—
16C2×C11×AGL(1,ℤ/8)—21no—
17C2×C11×AGL(1,ℤ/8)C2212yes—
18C2×C11×#135—22no—
19C22×C11×M16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C22×C11×M16C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#430—24no—
25C2×C11×#108C2214yescomplemented
26C11×#417—22no—
27C11×#417—22no—
28C11×#417—22no—
29C11×#417C2214yes—
30C2×C11×#103—21no—
31C2×C11×#103C2212yescomplemented
32C2×C11×#102—21no—
33C2×C11×#102C2212yescomplemented
34C11×#413—24no—
35C2×C11×#101C2212yescomplemented
36C2×C11×#100C2212yescomplemented
37C11×#408—22no—
38C11×#408C2214yes—
39C11×#407—22no—
40C11×#343C2214yescomplemented
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41D414yes—
55C2×C11×#41D412yes—
56C2×C11×#41C2312yes—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C11×#137—28no—
68C11×#137—24no—
69C11×#137—24no—
70C11×AGL(1,ℤ/8)—28no—
71C11×AGL(1,ℤ/8)—24no—
72C11×AGL(1,ℤ/8)—24no—
73C11×#135—216no—
74C2×C11×Q16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×D8—22no—
78C2×C11×M16—22no—
79C2×C11×M16—21no—
80C2×C11×M16—22no—
81C2×C11×M16—22no—
82C2×C11×M16—21no—
83C2×C11×M16—21no—
84C2×C11×M16—22no—
85C2×C11×M16—22no—
86C2×C11×M16—22no—
87C2×C11×M16—22no—
88C2×C11×M16D414yes—
89C2×C11×M16D412yes—
90C2×C11×M16D412yes—
91C2×C11×M16C2312yes—
92C2×C11×M16C2312yes—
93C2×C11×M16C2312yes—
94C22×C8×C11—21no—
95C22×C8×C11—21no—
96C22×C8×C11—21no—
97C22×C8×C11C2312yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2312yes—
104C11×#108—28no—
105C11×#103—24no—
106C11×#103—24no—
107C11×#102—24no—
108C11×#102—24no—
109C11×#101—24no—
110C11×#100—24no—
111C11×C22⋊C8—28no—
112#23533C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—21no—
114C24×C11—21no—
115C24×C11#4111yescharacteristic
116C11×#41—24no—
117C11×#41—24no—
118C11×#41—24no—
119C11×#41—24no—
120C11×#41—24no—
121C11×#41—24no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—42no—
127C11×#41—42no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41—42no—
131C11×#41—42no—
132C11×#41—42no—
133C11×#41—42no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×D412yes—
144C2×D4×C11—22no—
145C2×D4×C11—24no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11C2×D412yes—
161C2×D4×C11C2×D412yes—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—82no—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11#4112yes—
183C22×C4×C11#4111yescharacteristic
184C22×C4×C11#4112yes—
185C22×C4×C11C2411yescharacteristic
186C11×Q16—28no—
187C11×SD16—28no—
188C11×SD16—28no—
189C11×D8—28no—
190C11×M16—24no—
191C11×M16—24no—
192C11×M16—24no—
193C11×M16—22no—
194C11×M16—22no—
195C11×M16—22no—
196C11×M16—22no—
197C11×M16—22no—
198C11×M16—42no—
199C11×M16—42no—
200C11×M16C2×D414yes—
201C2×C8×C11—24no—
202C2×C8×C11—22no—
203C2×C8×C11—22no—
204C2×C8×C11—22no—
205C2×C8×C11—22no—
206C2×C8×C11—22no—
207C2×C8×C11—42no—
208C2×C8×C11—42no—
209C2×C8×C11C2×D414yes—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—41no—
213C11×C4⋊C4—41no—
214C2×#575C2×C1111yescharacteristic
215C2×#430C2×C1111yescharacteristic, complemented
216C2×#417C2×C1111yescharacteristic, complemented
217C2×#417C2×C1111yescharacteristic, complemented
218C2×#413C2×C1111yescharacteristic, complemented
219#2879C2×C1111yescharacteristic, complemented
220#2052C2×C1114yescomplemented
221#2051C2×C1114yescomplemented
222C2×#343C2×C1111yescharacteristic, complemented
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—42no—
230C23×C11—81no—
231C23×C11—81no—
232C23×C11—81no—
233C23×C11—81no—
234C23×C11#12111yescharacteristic
235C23×C11#12111yescharacteristic
236C23×C11#12312yes—
237C23×C11#12412yes—
238C23×C11C2×#4111yescharacteristic
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—42no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—44no—
253D4×C11—44no—
254D4×C11—44no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—42no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—82no—
270C2×C4×C11—82no—
271C2×C4×C11—82no—
272C2×C4×C11#12012yes—
273C2×C4×C11#12012yes—
274C2×C4×C11#12112yes—
275C2×C4×C11#12112yes—
276C2×C4×C11#12112yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12111yescharacteristic
279C2×C4×C11#12111yescharacteristic
280C2×C4×C11#12312yes—
281C2×C4×C11#12312yes—
282C2×C4×C11#12312yes—
283C2×C4×C11#12412yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C8×C11—24no—
291C8×C11—24no—
292C8×C11—42no—
293C8×C11—42no—
294C22×#41C22×C1111yescharacteristic
295C22×#41C22×C1111yescharacteristic
296#575—24no—
297#575—24no—
298C2×#137—21no—
299C2×#137C22×C1112yes—
300C2×AGL(1,ℤ/8)—21no—
301C2×AGL(1,ℤ/8)C22×C1112yes—
302C2×#135—22no—
303C22×M16C22×C1111yescharacteristic
304C22×M16C22×C1111yescharacteristic
305C22×M16C22×C1111yescharacteristic
306C22×M16C22×C1111yescharacteristic
307C22×C4⋊C4C22×C1111yescharacteristic
308#430—24no—
309C2×#108C22×C1114yescomplemented
310#417—22no—
311#417—22no—
312#417—22no—
313#417C22×C1114yes—
314C2×#103—21no—
315C2×#103C22×C1112yescomplemented
316C2×#102—21no—
317C2×#102C22×C1112yescomplemented
318#413—24no—
319C2×#101C22×C1112yescomplemented
320C2×#100C22×C1112yescomplemented
321#408—22no—
322#408C22×C1114yes—
323#407—22no—
324#343C22×C1114yescomplemented
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11—84no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11#39412yes—
343C22×C11#39412yes—
344C22×C11C2×#12111yescharacteristic
345C22×C11C2×#12311yescharacteristic
346C22×C11C2×#12411yescharacteristic
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—82no—
350C4×C11#39412yes—
351C4×C11#39412yes—
352C4×C11C2×#12011yescharacteristic
353C4×C11C2×#12111yescharacteristic
354C4×C11C2×#12111yescharacteristic
355C4×C11C2×#12311yescharacteristic
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—22no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41D4×C1112yes—
370C2×#41D4×C1114yes—
371C2×#41C23×C1112yes—
372C22×Q8D4×C1111yescharacteristic
373C22×Q8C23×C1111yescharacteristic
374C22×D4—21no—
375C22×D4—21no—
376C22×D4D4×C1111yescharacteristic
377C22×D4C23×C1111yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—21no—
381C23×C4C23×C1111yescharacteristic
382#137—28no—
383#137—24no—
384#137—24no—
385AGL(1,ℤ/8)—28no—
386AGL(1,ℤ/8)—24no—
387AGL(1,ℤ/8)—24no—
388#135—216no—
389C2×Q16—22no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×D8—22no—
393C2×M16—21no—
394C2×M16—22no—
395C2×M16—22no—
396C2×M16—22no—
397C2×M16—21no—
398C2×M16—21no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16D4×C1114yes—
404C2×M16D4×C1112yes—
405C2×M16D4×C1112yes—
406C2×M16C23×C1112yes—
407C2×M16C23×C1112yes—
408C2×M16C23×C1112yes—
409C22×C8—21no—
410C22×C8—21no—
411C22×C8—21no—
412C22×C8C23×C1112yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4C23×C1112yes—
419#108—28no—
420#103—24no—
421#103—24no—
422#102—24no—
423#102—24no—
424#101—24no—
425#100—24no—
426C22⋊C8—28no—
427C2×C11—21no—
428C2×C11—21no—
429C2×C11—22no—
430C2×C11—22no—
431C2×C11—82no—
432C2×C11—82no—
433C2×C11C2×#39411yescharacteristic
434C2×C11#306811yescharacteristic
435C2×C11#306911yescharacteristic
436C24—21no—
437C24—21no—
438C24C11×#4111yescharacteristic
439#41—24no—
440#41—24no—
441#41—24no—
442#41—24no—
443#41—24no—
444#41—24no—
445#41—22no—
446#41—22no—
447#41—22no—
448#41—22no—
449#41—42no—
450#41—42no—
451#41—42no—
452#41—42no—
453#41—42no—
454#41—42no—
455#41—42no—
456#41—42no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8C2×D4×C1112yes—
466C2×Q8C2×D4×C1112yes—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4C2×D4×C1112yes—
484C2×D4C2×D4×C1112yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—82no—
499C22×C4C2×D4×C1112yes—
500C22×C4C2×D4×C1112yes—
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C11×#4112yes—
506C22×C4C11×#4111yescharacteristic
507C22×C4C11×#4112yes—
508C22×C4C24×C1111yescharacteristic
509Q16—28no—
510SD16—28no—
511SD16—28no—
512D8—28no—
513M16—24no—
514M16—24no—
515M16—24no—
516M16—22no—
517M16—22no—
518M16—22no—
519M16—22no—
520M16—22no—
521M16—42no—
522M16—42no—
523M16C2×D4×C1114yes—
524C2×C8—24no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8C2×D4×C1114yes—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C11#2353311yescharacteristic, direct product factor, Sylow
538C23—22no—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—42no—
545C23—81no—
546C23—81no—
547C23—81no—
548C23—81no—
549C23C11×#12111yescharacteristic
550C23C11×#12111yescharacteristic
551C23C11×#12312yes—
552C23C11×#12412yes—
553C23C2×C11×#4111yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560Q8—42no—
561D4—22no—
562D4—22no—
563D4—22no—
564D4—22no—
565D4—42no—
566D4—42no—
567D4—44no—
568D4—44no—
569D4—44no—
570D4—41no—
571D4—41no—
572D4—42no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—42no—
584C2×C4—82no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4C11×#12012yes—
588C2×C4C11×#12012yes—
589C2×C4C11×#12112yes—
590C2×C4C11×#12112yes—
591C2×C4C11×#12112yes—
592C2×C4C11×#12112yes—
593C2×C4C11×#12111yescharacteristic
594C2×C4C11×#12111yescharacteristic
595C2×C4C11×#12312yes—
596C2×C4C11×#12312yes—
597C2×C4C11×#12312yes—
598C2×C4C11×#12412yes—
599C2×C4C22×D4×C1111yescharacteristic
600C2×C4C22×D4×C1111yescharacteristic
601C2×C4C22×D4×C1111yescharacteristic
602C2×C4C22×D4×C1111yescharacteristic
603C2×C4C2×C11×#4111yescharacteristic
604C2×C4C2×C11×#4111yescharacteristic
605C8—24no—
606C8—24no—
607C8—42no—
608C8—42no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—82no—
622C22—82no—
623C22—84no—
624C22—81no—
625C22—81no—
626C22C11×#39412yes—
627C22C11×#39412yes—
628C22C2×C11×#12111yescharacteristic
629C22C2×C11×#12311yescharacteristic
630C22C2×C11×#12411yescharacteristic
631C4—42no—
632C4—42no—
633C4—82no—
634C4C11×#39412yes—
635C4C11×#39412yes—
636C4C2×C11×#12011yescharacteristic
637C4C2×C11×#12111yescharacteristic
638C4C2×C11×#12111yescharacteristic
639C4C2×C11×#12311yescharacteristic
640C2—21no—
641C2—21no—
642C2—22no—
643C2—22no—
644C2—82no—
645C2—82no—
646C2C2×C11×#39411yescharacteristic
647C2C11×#306811yescharacteristic
648C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#430C2semidirect
3. C2×C11×#417C2semidirect
4. C2×C11×#417C2semidirect
5. C2×C11×#413C2semidirect
6. C11×#2879C2semidirect
7. C11×#2052C2semidirect
8. C11×#2051C2semidirect
9. C2×C11×#343C2semidirect
25. C2×C11×#108C22semidirect
31. C2×C11×#103C22semidirect
33. C2×C11×#102C22semidirect
35. C2×C11×#101C22semidirect
36. C2×C11×#100C22semidirect
40. C11×#343C22semidirect
112. #23533C11direct (N × H)
215. C2×#430C2×C11semidirect
216. C2×#417C2×C11semidirect
217. C2×#417C2×C11semidirect
218. C2×#413C2×C11semidirect
219. #2879C2×C11semidirect
220. #2052C2×C11semidirect
221. #2051C2×C11semidirect
222. C2×#343C2×C11semidirect
309. C2×#108C22×C11semidirect
315. C2×#103C22×C11semidirect
317. C2×#102C22×C11semidirect
319. C2×#101C22×C11semidirect
320. C2×#100C22×C11semidirect
324. #343C22×C11semidirect
537. C11#23533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C2×C11×#4302
C2×C11×#4172
C2×C11×#4132
C11×#28792
C11×#20522
C11×#20512
C2×C11×#3432
#2353311