Finite Group Databasebeta

← C11×#23521 #14600714

Subgroups — C11×#23521 #14600714

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C11×#2905C211yesmaximal, characteristic, complemented
3C11×#2896C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic, complemented
5C2×C11×#413C211yesmaximal, characteristic, complemented
6C22×C11×#100C211yesmaximal, characteristic, complemented
7C11×#2046C214yesmaximal, complemented
8C11×#2045C214yesmaximal, complemented
9C11×#1738C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C2×C11×AGL(1,ℤ/8)—24no—
13C2×C11×AGL(1,ℤ/8)—24no—
14C2×C11×AGL(1,ℤ/8)—22no—
15C2×C11×AGL(1,ℤ/8)—22no—
16C22×C11×SD16C2212yes—
17C22×C11×D8C2212yes—
18C22×C11×M16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C11×#424—22no—
24C11×#424C2214yescomplemented
25C11×#423—22no—
26C11×#419C2212yescomplemented
27C11×#418—22no—
28C11×#418C2214yes—
29C11×#418C2212yescomplemented
30C11×#417—22no—
31C11×#416—22no—
32C2×C11×#102—22no—
33C11×#413—24no—
34C2×C11×#101C2212yescomplemented
35C2×C11×#100—24no—
36C2×C11×#100C2214yes—
37C2×C11×#100C2212yescomplemented
38C11×#341C2214yescomplemented
39C25×C11—21no—
40C2×C11×#41—22no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D414yes—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11D414yes—
59C22×D4×C11C2312yes—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C11×AGL(1,ℤ/8)—216no—
64C11×AGL(1,ℤ/8)—216no—
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×D8—24no—
69C2×C11×D8—24no—
70C2×C11×D8—24no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16—22no—
80C2×C11×M16—22no—
81C2×C11×M16—22no—
82C2×C11×M16D412yes—
83C2×C11×M16D412yes—
84C2×C11×M16C2312yes—
85C2×C11×M16C2312yes—
86C2×C11×M16C2312yes—
87C22×C8×C11—21no—
88C22×C8×C11—21no—
89C22×C8×C11—21no—
90C22×C8×C11C2312yes—
91C11×#117—21no—
92C11×#117—21no—
93C11×#117D412yes—
94C11×#117C2312yes—
95C2×C11×C4⋊C4D412yes—
96C2×C11×C22⋊C4—21no—
97C2×C42×C11—21no—
98C11×C4⋊C8—28no—
99C11×#103—24no—
100C11×#102—28no—
101C11×#102—24no—
102C11×#101—24no—
103C11×#100—28no—
104C11×#100—24no—
105#23521C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—24no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—41no—
110C24×C11—41no—
111C24×C11—42no—
112C24×C11—84no—
113C24×C11#4111yescharacteristic
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—24no—
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—42no—
154C2×D4×C11C2×D412yes—
155C2×D4×C11C2×D414yes—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—42no—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11#4112yes—
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C11×SD16—216no—
173C11×D8—216no—
174C11×M16—24no—
175C11×M16—24no—
176C11×M16—22no—
177C11×M16—22no—
178C11×M16—22no—
179C11×M16—22no—
180C11×M16—22no—
181C11×M16—22no—
182C11×M16—42no—
183C11×M16—42no—
184C11×M16—42no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—42no—
191C2×C8×C11—42no—
192C2×C8×C11—42no—
193C2×C8×C11C2×D414yes—
194C11×C4⋊C4—22no—
195C11×C4⋊C4C2×D414yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C42×C11—22no—
199C42×C11—22no—
200C22×AGL(1,ℤ/8)C2×C1111yescharacteristic
201#2905C2×C1111yescharacteristic, complemented
202#2896C2×C1111yescharacteristic, complemented
203C2×#418C2×C1111yescharacteristic, complemented
204C2×#413C2×C1111yescharacteristic, complemented
205C22×#100C2×C1111yescharacteristic, complemented
206#2046C2×C1114yescomplemented
207#2045C2×C1114yescomplemented
208#1738C2×C1111yescharacteristic, complemented
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—82no—
219C23×C11—84no—
220C23×C11—84no—
221C23×C11—84no—
222C23×C11—88no—
223C23×C11—88no—
224C23×C11#12111yescharacteristic
225C23×C11#12111yescharacteristic
226C23×C11#12312yes—
227C23×C11#12312yes—
228C23×C11C2×#4111yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—41no—
233D4×C11—22no—
234D4×C11—24no—
235D4×C11—24no—
236D4×C11—22no—
237D4×C11—44no—
238D4×C11—44no—
239D4×C11—42no—
240D4×C11—41no—
241D4×C11—42no—
242D4×C11—41no—
243D4×C11—44no—
244D4×C11—44no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11—82no—
252C2×C4×C11#12012yes—
253C2×C4×C11#12012yes—
254C2×C4×C11#12112yes—
255C2×C4×C11#12112yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12112yes—
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12312yes—
261C2×C4×C11#12312yes—
262C2×C4×C11#12412yes—
263C2×C4×C11#12412yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C8×C11—24no—
271C8×C11—42no—
272C8×C11—42no—
273C8×C11—42no—
274C22×#41C22×C1111yescharacteristic
275C23×D4C22×C1111yescharacteristic
276C2×AGL(1,ℤ/8)—24no—
277C2×AGL(1,ℤ/8)—24no—
278C2×AGL(1,ℤ/8)—22no—
279C2×AGL(1,ℤ/8)—22no—
280C22×SD16C22×C1112yes—
281C22×D8C22×C1112yes—
282C22×M16C22×C1111yescharacteristic
283C22×M16C22×C1111yescharacteristic
284C22×M16C22×C1111yescharacteristic
285C22×M16C22×C1111yescharacteristic
286C2×#117C22×C1111yescharacteristic
287#424—22no—
288#424C22×C1114yescomplemented
289#423—22no—
290#419C22×C1112yescomplemented
291#418—22no—
292#418C22×C1114yes—
293#418C22×C1112yescomplemented
294#417—22no—
295#416—22no—
296C2×#102—22no—
297#413—24no—
298C2×#101C22×C1112yescomplemented
299C2×#100—24no—
300C2×#100C22×C1114yes—
301C2×#100C22×C1112yescomplemented
302#341C22×C1114yescomplemented
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—82no—
311C22×C11—84no—
312C22×C11—82no—
313C22×C11—88no—
314C22×C11—84no—
315C22×C11—88no—
316C22×C11—82no—
317C22×C11—84no—
318C22×C11#39412yes—
319C22×C11#39412yes—
320C22×C11C2×#12111yescharacteristic
321C22×C11C2×#12311yescharacteristic
322C22×C11C2×#12311yescharacteristic
323C4×C11—42no—
324C4×C11—44no—
325C4×C11#39412yes—
326C4×C11#39412yes—
327C4×C11C2×#12011yescharacteristic
328C4×C11C2×#12111yescharacteristic
329C4×C11C2×#12111yescharacteristic
330C4×C11C2×#12411yescharacteristic
331C25—21no—
332C2×#41—22no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—22no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—22no—
339C2×#41D4×C1114yes—
340C22×Q8C23×C1111yescharacteristic
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—22no—
350C22×D4D4×C1114yes—
351C22×D4C23×C1111yescharacteristic
352C22×D4C23×C1112yes—
353C23×C4—21no—
354C23×C4C23×C1111yescharacteristic
355AGL(1,ℤ/8)—216no—
356AGL(1,ℤ/8)—216no—
357C2×SD16—24no—
358C2×SD16—24no—
359C2×SD16—24no—
360C2×D8—24no—
361C2×D8—24no—
362C2×D8—24no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16D4×C1112yes—
375C2×M16D4×C1112yes—
376C2×M16C23×C1112yes—
377C2×M16C23×C1112yes—
378C2×M16C23×C1112yes—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8C23×C1112yes—
383#117—21no—
384#117—21no—
385#117D4×C1112yes—
386#117C23×C1112yes—
387C2×C4⋊C4D4×C1112yes—
388C2×C22⋊C4—21no—
389C2×C42—21no—
390C4⋊C8—28no—
391#103—24no—
392#102—28no—
393#102—24no—
394#101—24no—
395#100—28no—
396#100—24no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—22no—
400C2×C11—22no—
401C2×C11—82no—
402C2×C11—84no—
403C2×C11C2×#39411yescharacteristic
404C2×C11#306812yes—
405C24—24no—
406C24—21no—
407C24—22no—
408C24—41no—
409C24—41no—
410C24—42no—
411C24—84no—
412C24C11×#4111yescharacteristic
413#41—24no—
414#41—24no—
415#41—24no—
416#41—24no—
417#41—42no—
418#41—42no—
419#41—42no—
420#41—42no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C1112yes—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4C2×D4×C1112yes—
454C2×D4C2×D4×C1114yes—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—42no—
461C22×C4C2×D4×C1112yes—
462C22×C4C2×D4×C1112yes—
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C11×#4111yescharacteristic
468C22×C4C11×#4112yes—
469C22×C4C11×#4112yes—
470C22×C4C24×C1111yescharacteristic
471SD16—216no—
472D8—216no—
473M16—24no—
474M16—24no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—42no—
482M16—42no—
483M16—42no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—42no—
490C2×C8—42no—
491C2×C8—42no—
492C2×C8C2×D4×C1114yes—
493C4⋊C4—22no—
494C4⋊C4C2×D4×C1114yes—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C42—22no—
498C42—22no—
499C11#2352111yescharacteristic, direct product factor, Sylow
500C23—22no—
501C23—24no—
502C23—42no—
503C23—41no—
504C23—42no—
505C23—41no—
506C23—42no—
507C23—44no—
508C23—44no—
509C23—82no—
510C23—84no—
511C23—84no—
512C23—84no—
513C23—88no—
514C23—88no—
515C23C11×#12111yescharacteristic
516C23C11×#12111yescharacteristic
517C23C11×#12312yes—
518C23C11×#12312yes—
519C23C2×C11×#4111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524D4—22no—
525D4—24no—
526D4—24no—
527D4—22no—
528D4—44no—
529D4—44no—
530D4—42no—
531D4—41no—
532D4—42no—
533D4—41no—
534D4—44no—
535D4—44no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—82no—
543C2×C4C11×#12012yes—
544C2×C4C11×#12012yes—
545C2×C4C11×#12112yes—
546C2×C4C11×#12112yes—
547C2×C4C11×#12112yes—
548C2×C4C11×#12112yes—
549C2×C4C11×#12111yescharacteristic
550C2×C4C11×#12111yescharacteristic
551C2×C4C11×#12312yes—
552C2×C4C11×#12312yes—
553C2×C4C11×#12412yes—
554C2×C4C11×#12412yes—
555C2×C4C22×D4×C1111yescharacteristic
556C2×C4C22×D4×C1111yescharacteristic
557C2×C4C22×D4×C1111yescharacteristic
558C2×C4C22×D4×C1111yescharacteristic
559C2×C4C2×C11×#4111yescharacteristic
560C2×C4C2×C11×#4111yescharacteristic
561C8—24no—
562C8—42no—
563C8—42no—
564C8—42no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—44no—
572C22—84no—
573C22—82no—
574C22—84no—
575C22—88no—
576C22—88no—
577C22—82no—
578C22—84no—
579C22—82no—
580C22C11×#39412yes—
581C22C11×#39412yes—
582C22C2×C11×#12111yescharacteristic
583C22C2×C11×#12311yescharacteristic
584C22C2×C11×#12311yescharacteristic
585C4—42no—
586C4—44no—
587C4C11×#39412yes—
588C4C11×#39412yes—
589C4C2×C11×#12011yescharacteristic
590C4C2×C11×#12111yescharacteristic
591C4C2×C11×#12111yescharacteristic
592C4C2×C11×#12411yescharacteristic
593C2—21no—
594C2—21no—
595C2—22no—
596C2—22no—
597C2—84no—
598C2—82no—
599C2C2×C11×#39411yescharacteristic
600C2C11×#306812yes—
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×AGL(1,ℤ/8)C2
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. C11×#2905C2semidirect
3. C11×#2896C2semidirect
4. C2×C11×#418C2semidirect
5. C2×C11×#413C2semidirect
6. C22×C11×#100C2semidirect
7. C11×#2046C2semidirect
8. C11×#2045C2semidirect
9. C11×#1738C2semidirect
24. C11×#424C22semidirect
26. C11×#419C22semidirect
29. C11×#418C22semidirect
34. C2×C11×#101C22semidirect
37. C2×C11×#100C22semidirect
38. C11×#341C22semidirect
105. #23521C11direct (N × H)
201. #2905C2×C11semidirect
202. #2896C2×C11semidirect
203. C2×#418C2×C11semidirect
204. C2×#413C2×C11semidirect
205. C22×#100C2×C11semidirect
206. #2046C2×C11semidirect
207. #2045C2×C11semidirect
208. #1738C2×C11semidirect
288. #424C22×C11semidirect
290. #419C22×C11semidirect
293. #418C22×C11semidirect
298. C2×#101C22×C11semidirect
301. C2×#100C22×C11semidirect
302. #341C22×C11semidirect
499. C11#23521direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C11×#29052
C11×#28962
C2×C11×#4182
C2×C11×#4132
C22×C11×#1002
C11×#20462
C11×#20452
C11×#17382
#2352111