Finite Group Databasebeta

← C11×#32925 #14610118

Subgroups — C11×#32925 #14610118

Order 2816.

1352 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
1C4×C11×2−1+4C211yesmaximal, characteristic, complemented
2C11×#3040C212yesmaximal, complemented
3C2×C11×#456C211yesmaximal, characteristic, complemented
4C2×C11×#454C211yesmaximal, characteristic
5C11×#2545C211yesmaximal, characteristic, complemented
6C11×#1888C211yesmaximal, characteristic, complemented
7C11×#1886C211yesmaximal, characteristic, complemented
8C11×#1883C212yesmaximal, complemented
9C11×#1882C212yesmaximal, complemented
10C11×#1806C212yesmaximal, complemented
11C11×#1801C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C2×C11×#137C2212yes—
14C2×C11×AGL(1,ℤ/8)C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C11×#520—22no—
19C11×#520—22no—
20C11×#520C2212yes—
21C11×#519—22no—
22C11×#519C2211yescharacteristic
23C4×C11×#41—22no—
24C4×C11×#41—22no—
25C4×C11×#41C2212yes—
26C2×C4×Q8×C11—22no—
27C2×C4×Q8×C11C2211yescharacteristic
28C11×#464—22no—
29C11×#464—22no—
30C11×#463—22no—
31C11×#463—22no—
32C11×#456—24no—
33C11×#454—24no—
34C11×#423C2212yes—
35C2×C11×#104C2212yes—
36C2×C11×#104C2212yes—
37C11×#419C2212yes—
38C11×#418C2212yes—
39C2×C11×#101C2211yescharacteristic
40C2×C11×#101C2211yescharacteristic
41C11×#396—22no—
42C11×#391C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#388—22no—
45C4×C11×C4⋊C4C2211yescharacteristic
46C11×#343C2212yes—
47C11×#339C2212yes—
48C11×#339C2212yes—
49C11×2−1+4—24no—
50C11×2−1+4—22no—
51C11×2−1+4D414yes—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41C2312yes—
55C22×Q8×C11—22no—
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C11×#137—24no—
60C11×#137—24no—
61C11×AGL(1,ℤ/8)—24no—
62C11×AGL(1,ℤ/8)—24no—
63C2×C11×Q16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—22no—
66C2×C11×D8—22no—
67C2×C11×M16C2312yes—
68C2×C11×M16C2312yes—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—22no—
71C11×#124—22no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#124—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—24no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11D412yes—
84C4×Q8×C11D412yes—
85C4×D4×C11—22no—
86C4×D4×C11—24no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—24no—
91C4×D4×C11—22no—
92C4×D4×C11D412yes—
93C4×D4×C11D412yes—
94C11×#117—24no—
95C11×#117—24no—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117C2312yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4D412yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11—24no—
111C2×C42×C11—22no—
112C2×C42×C11D412yes—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×C4⋊C8—22no—
117C11×C4⋊C8—22no—
118C11×#104—24no—
119C11×#104—24no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#101—22no—
125C11×#101—22no—
126C11×#95—21no—
127C11×#95—22no—
128#32925C1111yesmaximal, characteristic, direct product factor, Sylow
129C24×C11—21no—
130C11×#41—28no—
131C11×#41—28no—
132C11×#41—28no—
133C11×#41—28no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41C2×D414yes—
137C11×#41#4114yes—
138C2×Q8×C11—22no—
139C2×Q8×C11—28no—
140C2×Q8×C11—28no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11C2×D412yes—
148C2×Q8×C11C2×D412yes—
149C2×Q8×C11#4112yes—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—22no—
156C2×D4×C11C2×D412yes—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C11×Q16—44no—
171C11×SD16—44no—
172C11×SD16—44no—
173C11×D8—44no—
174C11×M16—22no—
175C11×M16—22no—
176C11×M16—22no—
177C11×M16—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—44no—
189C11×C4⋊C4C2×D412yes—
190C11×C4⋊C4C2×D412yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—44no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—42no—
199C11×C22⋊C4—44no—
200C42×C11—24no—
201C42×C11—24no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11C2×D412yes—
212C42×C11C2×D412yes—
213C4×2−1+4C2×C1111yescharacteristic, complemented
214#3040C2×C1112yescomplemented
215C2×#456C2×C1111yescharacteristic, complemented
216C2×#454C2×C1111yescharacteristic
217#2545C2×C1111yescharacteristic, complemented
218#1888C2×C1111yescharacteristic, complemented
219#1886C2×C1111yescharacteristic, complemented
220#1883C2×C1112yescomplemented
221#1882C2×C1112yescomplemented
222#1806C2×C1112yescomplemented
223#1801C2×C1111yescharacteristic, complemented
224C23×C11—22no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11C22×D411yescharacteristic
231Q8×C11—28no—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11—24no—
235Q8×C11—42no—
236Q8×C11—42no—
237Q8×C11#12114yes—
238D4×C11—28no—
239D4×C11—24no—
240D4×C11—24no—
241D4×C11—22no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11#12114yes—
245C2×C4×C11—216no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—44no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—82no—
268C2×C4×C11—84no—
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12012yes—
272C2×C4×C11#12114yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D412yes—
275C2×C4×C11C2×#4112yes—
276C2×C4×C11C2×#4111yescharacteristic
277C8×C11—42no—
278C8×C11—42no—
279C2×2−1+4C22×C1111yescharacteristic
280C2×#137C22×C1112yes—
281C2×AGL(1,ℤ/8)C22×C1112yes—
282C2×C4⋊Q8C22×C1111yescharacteristic
283C2×#124C22×C1111yescharacteristic
284C2×#124C22×C1111yescharacteristic
285#520—22no—
286#520—22no—
287#520C22×C1112yes—
288#519—22no—
289#519C22×C1111yescharacteristic
290C4×#41—22no—
291C4×#41—22no—
292C4×#41C22×C1112yes—
293C2×C4×Q8—22no—
294C2×C4×Q8C22×C1111yescharacteristic
295#464—22no—
296#464—22no—
297#463—22no—
298#463—22no—
299#456—24no—
300#454—24no—
301#423C22×C1112yes—
302C2×#104C22×C1112yes—
303C2×#104C22×C1112yes—
304#419C22×C1112yes—
305#418C22×C1112yes—
306C2×#101C22×C1111yescharacteristic
307C2×#101C22×C1111yescharacteristic
308#396—22no—
309#391C22×C1111yescharacteristic
310#390C22×C1111yescharacteristic
311#388—22no—
312C4×C4⋊C4C22×C1111yescharacteristic
313#343C22×C1112yes—
314#339C22×C1112yes—
315#339C22×C1112yes—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—24no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11C2×#12011yescharacteristic
327C22×C11C2×#12111yescharacteristic
328C22×C11#52511yescharacteristic
329C4×C11—24no—
330C4×C11—24no—
331C4×C11—22no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C2×#12112yes—
341C4×C11#52512yes—
3422−1+4—24no—
3432−1+4—22no—
3442−1+4D4×C1114yes—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41C23×C1112yes—
348C22×Q8—22no—
349C22×Q8C23×C1111yescharacteristic
350C22×Q8C23×C1111yescharacteristic
351C22×D4C23×C1111yescharacteristic
352#137—24no—
353#137—24no—
354AGL(1,ℤ/8)—24no—
355AGL(1,ℤ/8)—24no—
356C2×Q16—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×D8—22no—
360C2×M16C23×C1112yes—
361C2×M16C23×C1112yes—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364#124—22no—
365#124—22no—
366#124—22no—
367#124—22no—
368C4×Q8—22no—
369C4×Q8—24no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8D4×C1112yes—
377C4×Q8D4×C1112yes—
378C4×D4—22no—
379C4×D4—24no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—24no—
384C4×D4—22no—
385C4×D4D4×C1112yes—
386C4×D4D4×C1112yes—
387#117—24no—
388#117—24no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117C23×C1112yes—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4D4×C1112yes—
398C2×C4⋊C4C23×C1111yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—22no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42D4×C1112yes—
406C2×C42C23×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408C2×C42C23×C1111yescharacteristic
409C4⋊C8—22no—
410C4⋊C8—22no—
411#104—24no—
412#104—24no—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417#101—22no—
418#101—22no—
419#95—21no—
420#95—22no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—44no—
424C2×C11—161no—
425C2×C11#284711yescharacteristic
426C2×C11#301811yescharacteristic
427C2×C11#302011yescharacteristic
428C24—21no—
429#41—28no—
430#41—28no—
431#41—28no—
432#41—28no—
433#41—22no—
434#41—22no—
435#41C2×D4×C1114yes—
436#41C11×#4114yes—
437C2×Q8—22no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8C2×D4×C1112yes—
447C2×Q8C2×D4×C1112yes—
448C2×Q8C11×#4112yes—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4C2×D4×C1112yes—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4C2×D4×C1112yes—
465C22×C4C2×D4×C1112yes—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C24×C1111yescharacteristic
469Q16—44no—
470SD16—44no—
471SD16—44no—
472D8—44no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477C2×C8—22no—
478C2×C8—22no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C4⋊C4—44no—
488C4⋊C4C2×D4×C1112yes—
489C4⋊C4C2×D4×C1112yes—
490C22⋊C4—24no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—42no—
498C22⋊C4—44no—
499C42—24no—
500C42—24no—
501C42—22no—
502C42—22no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C2×D4×C1112yes—
511C42C2×D4×C1112yes—
512C11#3292511yescharacteristic, direct product factor, Sylow
513C23—22no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C22×D4×C1111yescharacteristic
520Q8—28no—
521Q8—24no—
522Q8—22no—
523Q8—24no—
524Q8—42no—
525Q8—42no—
526Q8C11×#12114yes—
527D4—28no—
528D4—24no—
529D4—24no—
530D4—22no—
531D4—42no—
532D4—42no—
533D4C11×#12114yes—
534C2×C4—216no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—44no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—84no—
558C2×C4C11×#12011yescharacteristic
559C2×C4C11×#12011yescharacteristic
560C2×C4C11×#12012yes—
561C2×C4C11×#12114yes—
562C2×C4C22×D4×C1111yescharacteristic
563C2×C4C22×D4×C1112yes—
564C2×C4C2×C11×#4112yes—
565C2×C4C2×C11×#4111yescharacteristic
566C8—42no—
567C8—42no—
568C22—21no—
569C22—21no—
570C22—24no—
571C22—42no—
572C22—42no—
573C22—82no—
574C22—82no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22C2×C11×#12011yescharacteristic
579C22C2×C11×#12111yescharacteristic
580C22C11×#52511yescharacteristic
581C4—22no—
582C4—21no—
583C4—21no—
584C4—24no—
585C4—24no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4C2×C11×#12112yes—
593C4C11×#52512yes—
594C2—21no—
595C2—21no—
596C2—44no—
597C2—161no—
598C2C11×#284711yescharacteristic
599C2C11×#301811yescharacteristic
600C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#454C2
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. C4×C11×2−1+4C2semidirect
2. C11×#3040C2semidirect
3. C2×C11×#456C2semidirect
5. C11×#2545C2semidirect
6. C11×#1888C2semidirect
7. C11×#1886C2semidirect
8. C11×#1883C2semidirect
9. C11×#1882C2semidirect
10. C11×#1806C2semidirect
11. C11×#1801C2semidirect
128. #32925C11direct (N × H)
213. C4×2−1+4C2×C11semidirect
214. #3040C2×C11semidirect
215. C2×#456C2×C11semidirect
217. #2545C2×C11semidirect
218. #1888C2×C11semidirect
219. #1886C2×C11semidirect
220. #1883C2×C11semidirect
221. #1882C2×C11semidirect
222. #1806C2×C11semidirect
223. #1801C2×C11semidirect
512. C11#32925direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×2−1+42
C11×#30402
C2×C11×#4562
C2×C11×#4542
C11×#25452
C11×#18882
C11×#18862
C11×#18832
C11×#18822
C11×#18062
C11×#18012
#3292511