Finite Group Databasebeta

← C11×#32916 #14610109

Subgroups — C11×#32916 #14610109

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#520C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C2×C11×#452C212yesmaximal
5C11×#2621C211yesmaximal, characteristic, complemented
6C11×#1878C212yesmaximal, complemented
7C11×#1877C212yesmaximal, complemented
8C11×#1872C212yesmaximal, complemented
9C11×#1805C211yesmaximal, characteristic, complemented
10C11×#1804C211yesmaximal, characteristic, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C22⋊Q8C2212yes—
17C11×#520—24no—
18C11×#520—24no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4—21no—
28C22×C11×C4⋊C4C2211yescharacteristic
29C11×#462—24no—
30C11×#461—24no—
31C11×#452—28no—
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×#103C2212yes—
35C2×C11×#103C2212yes—
36C2×C11×#103C2212yes—
37C2×C11×#102C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C11×#398—21no—
40C11×#398—21no—
41C11×#397—21no—
42C11×#397—21no—
43C11×#391C2212yes—
44C11×#382C2211yescharacteristic
45C11×#340C2212yes—
46C11×#340C2212yes—
47C11×#336C2212yes—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41D414yes—
54C22×Q8×C11C2312yes—
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C2×C11×Q16—24no—
64C2×C11×Q16—24no—
65C2×C11×Q16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C22×C8×C11C2312yes—
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11D414yes—
79C4×D4×C11—28no—
80C4×D4×C11—28no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11D414yes—
85C11×#117—28no—
86C11×#117—22no—
87C11×#117—22no—
88C2×C11×C4⋊C4—28no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×C4⋊C8—22no—
112C11×C4⋊C8—22no—
113C11×#103—24no—
114C11×#103—24no—
115C11×#103—24no—
116C11×#102—24no—
117C11×C22⋊C8—24no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—22no—
121C11×#95—22no—
122#32916C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—21no—
124C24×C11C2×D411yescharacteristic
125C11×#41—28no—
126C11×#41—28no—
127C11×#41—28no—
128C11×#41—28no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11C2×D412yes—
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11#4112yes—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11C2×D412yes—
148C2×D4×C11C2×D412yes—
149C2×D4×C11#4112yes—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—82no—
166C22×C4×C11—82no—
167C22×C4×C11—82no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D412yes—
174C22×C4×C11#4112yes—
175C22×C4×C11C2411yescharacteristic
176C11×Q16—48no—
177C11×SD16—48no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4—44no—
196C11×C4⋊C4C2×D412yes—
197C11×C4⋊C4C2×D412yes—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—44no—
203C42×C11—24no—
204C42×C11—24no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11C2×D412yes—
208C42×C11C2×D412yes—
209C2×#520C2×C1111yescharacteristic
210C2×#462C2×C1111yescharacteristic, complemented
211C2×#461C2×C1111yescharacteristic, complemented
212C2×#452C2×C1112yes—
213#2621C2×C1111yescharacteristic, complemented
214#1878C2×C1112yescomplemented
215#1877C2×C1112yescomplemented
216#1872C2×C1112yescomplemented
217#1805C2×C1111yescharacteristic, complemented
218#1804C2×C1111yescharacteristic, complemented
219#1798C2×C1111yescharacteristic, complemented
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11#12112yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—42no—
235Q8×C11—42no—
236Q8×C11—42no—
237Q8×C11—42no—
238Q8×C11#12114yes—
239D4×C11—216no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11#12114yes—
244C2×C4×C11—216no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—84no—
271C2×C4×C11—84no—
272C2×C4×C11—84no—
273C2×C4×C11#12012yes—
274C2×C4×C11#12012yes—
275C2×C4×C11#12112yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C8×C11—42no—
283C8×C11—42no—
284C22×#41C22×C1111yescharacteristic
285C22×Q16C22×C1112yes—
286C22×SD16C22×C1112yes—
287C2×C4⋊Q8C22×C1111yescharacteristic
288C2×C22⋊Q8C22×C1112yes—
289#520—24no—
290#520—24no—
291C2×C4×Q8C22×C1111yescharacteristic
292C2×C4×Q8C22×C1111yescharacteristic
293C2×C4×D4—21no—
294C2×C4×D4—21no—
295C2×C4×D4C22×C1111yescharacteristic
296C2×C4×D4C22×C1111yescharacteristic
297C2×#117—21no—
298C2×#117C22×C1111yescharacteristic
299C22×C4⋊C4—21no—
300C22×C4⋊C4C22×C1111yescharacteristic
301#462—24no—
302#461—24no—
303#452—28no—
304C2×C4⋊C8C22×C1111yescharacteristic
305C2×C4⋊C8C22×C1111yescharacteristic
306C2×#103C22×C1112yes—
307C2×#103C22×C1112yes—
308C2×#103C22×C1112yes—
309C2×#102C22×C1112yes—
310C2×C22⋊C8C22×C1112yes—
311#398—21no—
312#398—21no—
313#397—21no—
314#397—21no—
315#391C22×C1112yes—
316#382C22×C1111yescharacteristic
317#340C22×C1112yes—
318#340C22×C1112yes—
319#336C22×C1112yes—
320C22×C11—22no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—41no—
326C22×C11—42no—
327C22×C11—41no—
328C22×C11—42no—
329C22×C11—44no—
330C22×C11C2×#12011yescharacteristic
331C22×C11C2×#12111yescharacteristic
332C22×C11#52511yescharacteristic
333C22×C11#57712yes—
334C22×C11#57812yes—
335C4×C11—22no—
336C4×C11—24no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—82no—
344C4×C11—82no—
345C4×C11C2×#12111yescharacteristic
346C4×C11C2×#12111yescharacteristic
347C4×C11#52511yescharacteristic
348C4×C11#52511yescharacteristic
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41D4×C1114yes—
355C22×Q8C23×C1112yes—
356C22×Q8C23×C1111yescharacteristic
357C22×D4—21no—
358C22×D4C23×C1111yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C23×C1111yescharacteristic
364C2×Q16—24no—
365C2×Q16—24no—
366C2×Q16—24no—
367C2×SD16—24no—
368C2×SD16—24no—
369C2×SD16—24no—
370C22×C8C23×C1112yes—
371C22×C8C23×C1112yes—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374C22⋊Q8—24no—
375C22⋊Q8—24no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8D4×C1114yes—
380C4×D4—28no—
381C4×D4—28no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4D4×C1114yes—
386#117—28no—
387#117—22no—
388#117—22no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C1111yescharacteristic
399C2×C4⋊C4D4×C1111yescharacteristic
400C2×C4⋊C4C23×C1112yes—
401C2×C4⋊C4C23×C1111yescharacteristic
402C2×C4⋊C4C23×C1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4D4×C1111yescharacteristic
407C2×C22⋊C4D4×C1111yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42C23×C1111yescharacteristic
411C2×C42C23×C1111yescharacteristic
412C4⋊C8—22no—
413C4⋊C8—22no—
414#103—24no—
415#103—24no—
416#103—24no—
417#102—24no—
418C22⋊C8—24no—
419#95—21no—
420#95—21no—
421#95—22no—
422#95—22no—
423C2×C11—42no—
424C2×C11—44no—
425C2×C11#284711yescharacteristic
426C2×C11#300911yescharacteristic
427C2×C11#301111yescharacteristic
428C2×C11#304612yes—
429C2×C11#312012yes—
430C24—21no—
431C24C2×D4×C1111yescharacteristic
432#41—28no—
433#41—28no—
434#41—28no—
435#41—28no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8C2×D4×C1112yes—
446C2×Q8C2×D4×C1112yes—
447C2×Q8C11×#4112yes—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4C2×D4×C1112yes—
455C2×D4C2×D4×C1112yes—
456C2×D4C11×#4112yes—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—82no—
473C22×C4—82no—
474C22×C4—82no—
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1112yes—
481C22×C4C11×#4112yes—
482C22×C4C24×C1111yescharacteristic
483Q16—48no—
484SD16—48no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—22no—
494C4⋊C4—24no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—44no—
503C4⋊C4C2×D4×C1112yes—
504C4⋊C4C2×D4×C1112yes—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—44no—
510C42—24no—
511C42—24no—
512C42—21no—
513C42—21no—
514C42C2×D4×C1112yes—
515C42C2×D4×C1112yes—
516C11#3291611yescharacteristic, direct product factor, Sylow
517C23—21no—
518C23—22no—
519C23—22no—
520C23—21no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—42no—
525C23—42no—
526C23C11×#12112yes—
527C23C22×D4×C1111yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—22no—
531Q8—42no—
532Q8—42no—
533Q8—42no—
534Q8—42no—
535Q8C11×#12114yes—
536D4—216no—
537D4—22no—
538D4—22no—
539D4—22no—
540D4C11×#12114yes—
541C2×C4—216no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—84no—
568C2×C4—84no—
569C2×C4—84no—
570C2×C4C11×#12012yes—
571C2×C4C11×#12012yes—
572C2×C4C11×#12112yes—
573C2×C4C22×D4×C1111yescharacteristic
574C2×C4C22×D4×C1111yescharacteristic
575C2×C4C22×D4×C1111yescharacteristic
576C2×C4C2×C11×#4111yescharacteristic
577C2×C4C2×C11×#4111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C8—42no—
580C8—42no—
581C22—24no—
582C22—22no—
583C22—24no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—44no—
589C22—42no—
590C22—44no—
591C22C2×C11×#12011yescharacteristic
592C22C2×C11×#12111yescharacteristic
593C22C11×#52511yescharacteristic
594C22C11×#57712yes—
595C22C11×#57812yes—
596C4—22no—
597C4—22no—
598C4—22no—
599C4—24no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—41no—
604C4—82no—
605C4—82no—
606C4C2×C11×#12111yescharacteristic
607C4C2×C11×#12111yescharacteristic
608C4C11×#52511yescharacteristic
609C4C11×#52511yescharacteristic
610C2—42no—
611C2—44no—
612C2C11×#284711yescharacteristic
613C2C11×#300911yescharacteristic
614C2C11×#301111yescharacteristic
615C2C11×#304612yes—
616C2C11×#312012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#462C2semidirect
3. C2×C11×#461C2semidirect
5. C11×#2621C2semidirect
6. C11×#1878C2semidirect
7. C11×#1877C2semidirect
8. C11×#1872C2semidirect
9. C11×#1805C2semidirect
10. C11×#1804C2semidirect
11. C11×#1798C2semidirect
122. #32916C11direct (N × H)
210. C2×#462C2×C11semidirect
211. C2×#461C2×C11semidirect
213. #2621C2×C11semidirect
214. #1878C2×C11semidirect
215. #1877C2×C11semidirect
216. #1872C2×C11semidirect
217. #1805C2×C11semidirect
218. #1804C2×C11semidirect
219. #1798C2×C11semidirect
516. C11#32916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5202
C2×C11×#4622
C2×C11×#4612
C2×C11×#4522
C11×#26212
C11×#18782
C11×#18772
C11×#18722
C11×#18052
C11×#18042
C11×#17982
#3291611