Finite Group Databasebeta

← C11×#23414 #14600607

Subgroups — C11×#23414 #14600607

Order 2816.

1980 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#575C211yesmaximal, characteristic, complemented
2C11×#3449C212yesmaximal, complemented
3C2×C11×#421C212yesmaximal, complemented
4C11×#2879C211yesmaximal, characteristic, complemented
5C11×#2010C218yesmaximal, complemented
6C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
7C22×C11×#41C2212yes—
8C22×C11×#41C2211yescharacteristic
9C11×#575—24no—
10C11×#575—22no—
11C11×#575C2214yes—
12C2×C11×#137—22no—
13C2×C11×AGL(1,ℤ/8)—22no—
14C2×C11×#135—22no—
15C22×C11×M16C2211yescharacteristic
16C22×C11×M16C2211yescharacteristic
17C11×#537—24no—
18C11×#536—22no—
19C11×#536—22no—
20C11×#535—22no—
21C11×#535—22no—
22C11×#534—24no—
23C11×#532—24no—
24C11×#525—24no—
25C11×#525C2218yescomplemented
26C2×C11×#117C2212yes—
27C11×#421—24no—
28C11×#421C2218yescomplemented
29C2×C11×#104—24no—
30C11×#408—22no—
31C11×#408—22no—
32C11×#407C2214yescomplemented
33C11×H(3,ℤ/4)C2214yescomplemented
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41D414yescomplemented
53C2×C11×#41C2314yes—
54C22×Q8×C11D411yescharacteristic
55C22×Q8×C11D412yescomplemented
56C22×D4×C11—22no—
57C22×D4×C11D412yes—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11D412yescomplemented
60C23×C4×C11—22no—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C11×#137—28no—
64C11×#137—28no—
65C11×AGL(1,ℤ/8)—28no—
66C11×AGL(1,ℤ/8)—28no—
67C11×#135—28no—
68C11×#135—28no—
69C2×C11×Q16—22no—
70C2×C11×SD16—24no—
71C2×C11×D8—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—21no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16D412yescomplemented
78C2×C11×M16C2312yes—
79C2×C11×M16C2312yes—
80C22×C8×C11—21no—
81C22×C8×C11D412yescomplemented
82C11×C4⋊Q8—24no—
83C11×#127—24no—
84C11×#124—24no—
85C11×#124—24no—
86C11×#123—28no—
87C11×#123—28no—
88C11×C22⋊Q8—28no—
89C11×C22⋊Q8—28no—
90C11×#121—28no—
91C11×#121—216no—
92C11×#121—28no—
93C11×#120—28no—
94C11×#120—28no—
95C4×D4×C11—216no—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117D414yescomplemented
99C11×#117C2314yes—
100C2×C11×C4⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C42×C11D414yescomplemented
103C11×#104—216no—
104C11×C22⋊C8—28no—
105#23414C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—22no—
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—42no—
123C11×#41—42no—
124C11×#41—42no—
125C11×#41—42no—
126C11×#41—42no—
127C11×#41—42no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41—42no—
131C11×#41—41no—
132C11×#41—41no—
133C11×#41—42no—
134C11×#41—42no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11C2×D414yes—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—24no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—24no—
151C2×D4×C11—216no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11C2×D414yes—
166C22×C4×C11—22no—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—24no—
173C22×C4×C11—22no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11#4111yescharacteristic
187C22×C4×C11#4111yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C11×Q16—28no—
190C11×SD16—216no—
191C11×D8—28no—
192C11×M16—24no—
193C11×M16—24no—
194C11×M16—24no—
195C11×M16—41no—
196C11×M16—41no—
197C2×C8×C11—22no—
198C2×C8×C11—22no—
199C2×C8×C11—22no—
200C2×C8×C11—42no—
201C2×C8×C11C2×D414yes—
202C11×C4⋊C4—216no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—24no—
205C11×C22⋊C4—216no—
206C11×C22⋊C4—216no—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C42×C11—24no—
210C42×C11C2×D418yes—
211C2×#575C2×C1111yescharacteristic, complemented
212#3449C2×C1112yescomplemented
213C2×#421C2×C1112yescomplemented
214#2879C2×C1111yescharacteristic, complemented
215#2010C2×C1118yescomplemented
216C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—81no—
223C23×C11—82no—
224C23×C11—84no—
225C23×C11#12012yes—
226C23×C11#12012yes—
227C23×C11#12111yescharacteristic
228C23×C11#12111yescharacteristic
229C23×C11C22×D411yescharacteristic
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—41no—
233Q8×C11—42no—
234Q8×C11—41no—
235Q8×C11—42no—
236Q8×C11—42no—
237D4×C11—24no—
238D4×C11—24no—
239D4×C11—44no—
240D4×C11—44no—
241D4×C11—42no—
242D4×C11—44no—
243D4×C11—42no—
244D4×C11—44no—
245D4×C11—44no—
246D4×C11—41no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—41no—
251D4×C11—816no—
252C2×C4×C11—28no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11—42no—
262C2×C4×C11—44no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—84no—
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12012yes—
269C2×C4×C11#12012yes—
270C2×C4×C11#12012yes—
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#12112yes—
274C2×C4×C11#12112yes—
275C2×C4×C11#12111yescharacteristic
276C2×C4×C11#12111yescharacteristic
277C2×C4×C11#12712yes—
278C2×C4×C11#12711yescharacteristic
279C2×C4×C11#12711yescharacteristic
280C2×C4×C11C22×D412yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D412yes—
283C2×C4×C11C2×#4111yescharacteristic
284C8×C11—24no—
285C8×C11—42no—
286C22×#41C22×C1112yes—
287C22×#41C22×C1111yescharacteristic
288#575—24no—
289#575—22no—
290#575C22×C1114yes—
291C2×#137—22no—
292C2×AGL(1,ℤ/8)—22no—
293C2×#135—22no—
294C22×M16C22×C1111yescharacteristic
295C22×M16C22×C1111yescharacteristic
296#537—24no—
297#536—22no—
298#536—22no—
299#535—22no—
300#535—22no—
301#534—24no—
302#532—24no—
303#525—24no—
304#525C22×C1118yescomplemented
305C2×#117C22×C1112yes—
306#421—24no—
307#421C22×C1118yescomplemented
308C2×#104—24no—
309#408—22no—
310#408—22no—
311#407C22×C1114yescomplemented
312H(3,ℤ/4)C22×C1114yescomplemented
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—48no—
319C22×C11—48no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—42no—
323C22×C11—84no—
324C22×C11—84no—
325C22×C11#39211yescharacteristic
326C22×C11#39212yes—
327C22×C11#39211yescharacteristic
328C22×C11C2×#12012yes—
329C22×C11C2×#12111yescharacteristic
330C4×C11—48no—
331C4×C11—42no—
332C4×C11—44no—
333C4×C11#39211yescharacteristic
334C4×C11#39212yes—
335C4×C11#39211yescharacteristic
336C4×C11C2×#12011yescharacteristic
337C4×C11C2×#12112yes—
338C4×C11C2×#12711yescharacteristic
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41D4×C1114yescomplemented
358C2×#41C23×C1114yes—
359C22×Q8D4×C1111yescharacteristic
360C22×Q8D4×C1112yescomplemented
361C22×D4—22no—
362C22×D4D4×C1112yes—
363C22×D4D4×C1111yescharacteristic
364C22×D4D4×C1112yescomplemented
365C23×C4—22no—
366C23×C4C23×C1112yes—
367C23×C4C23×C1111yescharacteristic
368#137—28no—
369#137—28no—
370AGL(1,ℤ/8)—28no—
371AGL(1,ℤ/8)—28no—
372#135—28no—
373#135—28no—
374C2×Q16—22no—
375C2×SD16—24no—
376C2×D8—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—21no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16D4×C1112yescomplemented
383C2×M16C23×C1112yes—
384C2×M16C23×C1112yes—
385C22×C8—21no—
386C22×C8D4×C1112yescomplemented
387C4⋊Q8—24no—
388#127—24no—
389#124—24no—
390#124—24no—
391#123—28no—
392#123—28no—
393C22⋊Q8—28no—
394C22⋊Q8—28no—
395#121—28no—
396#121—216no—
397#121—28no—
398#120—28no—
399#120—28no—
400C4×D4—216no—
401#117—22no—
402#117—22no—
403#117D4×C1114yescomplemented
404#117C23×C1114yes—
405C2×C4⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C42D4×C1114yescomplemented
408#104—216no—
409C22⋊C8—28no—
410C2×C11—22no—
411C2×C11—21no—
412C2×C11—21no—
413C2×C11—22no—
414C2×C11—21no—
415C2×C11—82no—
416C2×C11—84no—
417C2×C11C2×#39211yescharacteristic
418C24—22no—
419C24C2×D4×C1112yes—
420C24C2×D4×C1111yescharacteristic
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—24no—
427#41—24no—
428#41—24no—
429#41—41no—
430#41—41no—
431#41—42no—
432#41—42no—
433#41—42no—
434#41—42no—
435#41—42no—
436#41—42no—
437#41—42no—
438#41—42no—
439#41—42no—
440#41—42no—
441#41—42no—
442#41—42no—
443#41—41no—
444#41—41no—
445#41—42no—
446#41—42no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8C2×D4×C1114yes—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—216no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4C2×D4×C1114yes—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4C2×D4×C1112yes—
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1112yes—
493C22×C4C2×D4×C1112yes—
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C2×D4×C1112yes—
497C22×C4C2×D4×C1112yes—
498C22×C4C11×#4111yescharacteristic
499C22×C4C11×#4111yescharacteristic
500C22×C4C24×C1111yescharacteristic
501Q16—28no—
502SD16—216no—
503D8—28no—
504M16—24no—
505M16—24no—
506M16—24no—
507M16—41no—
508M16—41no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—42no—
513C2×C8C2×D4×C1114yes—
514C4⋊C4—216no—
515C4⋊C4—24no—
516C4⋊C4—24no—
517C22⋊C4—216no—
518C22⋊C4—216no—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C42—24no—
522C42C2×D4×C1118yes—
523C11#2341411yescharacteristic, direct product factor, Sylow
524C23—24no—
525C23—24no—
526C23—22no—
527C23—42no—
528C23—42no—
529C23—81no—
530C23—82no—
531C23—84no—
532C23C11×#12012yes—
533C23C11×#12012yes—
534C23C11×#12111yescharacteristic
535C23C11×#12111yescharacteristic
536C23C22×D4×C1111yescharacteristic
537Q8—24no—
538Q8—24no—
539Q8—41no—
540Q8—42no—
541Q8—41no—
542Q8—42no—
543Q8—42no—
544D4—24no—
545D4—24no—
546D4—44no—
547D4—44no—
548D4—42no—
549D4—44no—
550D4—42no—
551D4—44no—
552D4—44no—
553D4—41no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—41no—
558D4—816no—
559C2×C4—28no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—84no—
573C2×C4C11×#12011yescharacteristic
574C2×C4C11×#12011yescharacteristic
575C2×C4C11×#12012yes—
576C2×C4C11×#12012yes—
577C2×C4C11×#12012yes—
578C2×C4C11×#12112yes—
579C2×C4C11×#12112yes—
580C2×C4C11×#12112yes—
581C2×C4C11×#12112yes—
582C2×C4C11×#12111yescharacteristic
583C2×C4C11×#12111yescharacteristic
584C2×C4C11×#12712yes—
585C2×C4C11×#12711yescharacteristic
586C2×C4C11×#12711yescharacteristic
587C2×C4C22×D4×C1112yes—
588C2×C4C22×D4×C1111yescharacteristic
589C2×C4C22×D4×C1112yes—
590C2×C4C2×C11×#4111yescharacteristic
591C8—24no—
592C8—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—48no—
599C22—48no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—84no—
604C22—84no—
605C22C11×#39211yescharacteristic
606C22C11×#39212yes—
607C22C11×#39211yescharacteristic
608C22C2×C11×#12012yes—
609C22C2×C11×#12111yescharacteristic
610C4—48no—
611C4—42no—
612C4—44no—
613C4C11×#39211yescharacteristic
614C4C11×#39212yes—
615C4C11×#39211yescharacteristic
616C4C2×C11×#12011yescharacteristic
617C4C2×C11×#12112yes—
618C4C2×C11×#12711yescharacteristic
619C2—22no—
620C2—21no—
621C2—21no—
622C2—22no—
623C2—21no—
624C2—82no—
625C2—84no—
626C2C2×C11×#39211yescharacteristic
subgroupG/H
centerC4×C11C2×#127
commutator, Frattini, cosocleC22×C4C24×C11
socleC2×C11C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#575C2semidirect
2. C11×#3449C2semidirect
3. C2×C11×#421C2semidirect
4. C11×#2879C2semidirect
5. C11×#2010C2semidirect
6. C2×C11×H(3,ℤ/4)C2semidirect
25. C11×#525C22semidirect
28. C11×#421C22semidirect
32. C11×#407C22semidirect
33. C11×H(3,ℤ/4)C22semidirect
52. C2×C11×#41D4semidirect
55. C22×Q8×C11D4semidirect
59. C22×D4×C11D4semidirect
77. C2×C11×M16D4semidirect
81. C22×C8×C11D4semidirect
98. C11×#117D4semidirect
102. C2×C42×C11D4semidirect
105. #23414C11direct (N × H)
211. C2×#575C2×C11semidirect
212. #3449C2×C11semidirect
213. C2×#421C2×C11semidirect
214. #2879C2×C11semidirect
215. #2010C2×C11semidirect
216. C2×H(3,ℤ/4)C2×C11semidirect
304. #525C22×C11semidirect
307. #421C22×C11semidirect
311. #407C22×C11semidirect
312. H(3,ℤ/4)C22×C11semidirect
357. C2×#41D4×C11semidirect
360. C22×Q8D4×C11semidirect
364. C22×D4D4×C11semidirect
382. C2×M16D4×C11semidirect
386. C22×C8D4×C11semidirect
403. #117D4×C11semidirect
407. C2×C42D4×C11semidirect
523. C11#23414direct (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
C11×#34492
C2×C11×#4212
C11×#28792
C11×#20102
C2×C11×H(3,ℤ/4)2
#2341411