Finite Group Databasebeta

← C11×#22222 #14599415

Subgroups — C11×#22222 #14599415

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#488C211yesmaximal, characteristic
2C4×C11×#125C211yesmaximal, characteristic, complemented
3C4×C11×#124C211yesmaximal, characteristic
4C11×#1991C211yesmaximal, characteristic, complemented
5C11×#1958C211yesmaximal, characteristic
6C11×#1928C211yesmaximal, characteristic, complemented
7C11×#1927C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic
9C11×#1925C211yesmaximal, characteristic
10C11×#1865C211yesmaximal, characteristic, complemented
11C11×#1864C211yesmaximal, characteristic
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1862C211yesmaximal, characteristic
14C11×#1846C211yesmaximal, characteristic, complemented
15C11×#1744C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C11×#488C418yescomplemented
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#391C2211yescharacteristic
36C11×#390C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#388—21no—
40C11×#388—21no—
41C11×#387—21no—
42C11×#387—21no—
43C11×#382C2211yescharacteristic
44C11×#382C2211yescharacteristic
45C4×C11×C4⋊C4—21no—
46C4×C11×C4⋊C4—21no—
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4—21no—
50C4×C11×C22⋊C4—21no—
51C43×C11C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#125—22no—
68C11×#125C2×C414yescomplemented
69C11×#124—22no—
70C11×#124C2×C414yes—
71C4×Q8×C11—41no—
72C4×Q8×C11—41no—
73C4×D4×C11—41no—
74C4×D4×C11—41no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#107—41no—
102C11×#107—41no—
103C11×#106—41no—
104C11×#106—41no—
105C11×#103—41no—
106C11×#103—41no—
107C11×#103C2×C414yescomplemented
108C11×#103C2×C414yescomplemented
109C11×#102—41no—
110C11×#102—41no—
111C11×#102C2×C414yes—
112C11×#102C2×C414yes—
113C4×C8×C11—22no—
114C4×C8×C11C2×C414yescomplemented
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125#22222C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C22×C412yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C22×C412yes—
167C2×C8×C11C22×C412yes—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4C22×C412yes—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—41no—
197C42×C11—41no—
198C42×C11—42no—
199C42×C11—42no—
200C42×C11—42no—
201C42×C11C22×C412yes—
202C42×C11#4112yes—
203C2×#488C2×C1111yescharacteristic
204C4×#125C2×C1111yescharacteristic, complemented
205C4×#124C2×C1111yescharacteristic
206#1991C2×C1111yescharacteristic, complemented
207#1958C2×C1111yescharacteristic
208#1928C2×C1111yescharacteristic, complemented
209#1927C2×C1111yescharacteristic, complemented
210#1926C2×C1111yescharacteristic
211#1925C2×C1111yescharacteristic
212#1865C2×C1111yescharacteristic, complemented
213#1864C2×C1111yescharacteristic
214#1863C2×C1111yescharacteristic, complemented
215#1862C2×C1111yescharacteristic
216#1846C2×C1111yescharacteristic, complemented
217#1744C2×C1111yescharacteristic, complemented
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11C22×D411yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—41no—
233D4×C11—41no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
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—41no—
268C2×C4×C11—41no—
269C2×C4×C11—84no—
270C2×C4×C11C4×D412yes—
271C2×C4×C11C4×D412yes—
272C2×C4×C11#13512yes—
273C2×C4×C11#13512yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C8×C11—22no—
281C8×C11—22no—
282C8×C11—41no—
283C8×C11—41no—
284C2×#125C22×C1111yescharacteristic
285C2×#124C22×C1111yescharacteristic
286C2×C4×Q8C22×C1111yescharacteristic
287C2×C4×D4C22×C1111yescharacteristic
288#488C4×C1118yescomplemented
289C2×#107C22×C1111yescharacteristic
290C2×#107C22×C1111yescharacteristic
291C2×#106C22×C1111yescharacteristic
292C2×#106C22×C1111yescharacteristic
293C2×#103C22×C1111yescharacteristic
294C2×#103C22×C1111yescharacteristic
295C2×#103C22×C1111yescharacteristic
296C2×#103C22×C1111yescharacteristic
297C2×#102C22×C1111yescharacteristic
298C2×#102C22×C1111yescharacteristic
299C2×#102C22×C1111yescharacteristic
300C2×#102C22×C1111yescharacteristic
301C2×C4×C8C22×C1111yescharacteristic
302C2×C4×C8C22×C1111yescharacteristic
303#391C22×C1111yescharacteristic
304#390C22×C1111yescharacteristic
305#389C22×C1111yescharacteristic
306#389C22×C1111yescharacteristic
307#388—21no—
308#388—21no—
309#387—21no—
310#387—21no—
311#382C22×C1111yescharacteristic
312#382C22×C1111yescharacteristic
313C4×C4⋊C4—21no—
314C4×C4⋊C4—21no—
315C4×C4⋊C4C22×C1111yescharacteristic
316C4×C4⋊C4C22×C1111yescharacteristic
317C4×C22⋊C4—21no—
318C4×C22⋊C4—21no—
319C43C22×C1111yescharacteristic
320#340C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#340C22×C1111yescharacteristic
324#336C22×C1111yescharacteristic
325#336C22×C1111yescharacteristic
326#336C22×C1111yescharacteristic
327#336C22×C1111yescharacteristic
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11C2×C4×D411yescharacteristic
336C22×C11#53511yescharacteristic
337C22×C11#53611yescharacteristic
338C22×C11C2×#13511yescharacteristic
339C22×C11C2×#13511yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57511yescharacteristic
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11#52011yescharacteristic
356C4×C11#52011yescharacteristic
357C4×C11#54211yescharacteristic
358C4×C11#54211yescharacteristic
359C22×Q8C23×C1111yescharacteristic
360C22×D4C23×C1111yescharacteristic
361C23×C4—21no—
362C22×C8C23×C1111yescharacteristic
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365C22×C8C23×C1111yescharacteristic
366#125—22no—
367#125C2×C4×C1114yescomplemented
368#124—22no—
369#124C2×C4×C1114yes—
370C4×Q8—41no—
371C4×Q8—41no—
372C4×D4—41no—
373C4×D4—41no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1111yescharacteristic
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42D4×C1111yescharacteristic
394C2×C42D4×C1111yescharacteristic
395C2×C42D4×C1111yescharacteristic
396C2×C42D4×C1111yescharacteristic
397C2×C42C23×C1111yescharacteristic
398C2×C42C23×C1111yescharacteristic
399C2×C42C23×C1111yescharacteristic
400#107—41no—
401#107—41no—
402#106—41no—
403#106—41no—
404#103—41no—
405#103—41no—
406#103C2×C4×C1114yescomplemented
407#103C2×C4×C1114yescomplemented
408#102—41no—
409#102—41no—
410#102C2×C4×C1114yes—
411#102C2×C4×C1114yes—
412C4×C8—22no—
413C4×C8C2×C4×C1114yescomplemented
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424C2×C11—82no—
425C2×C11#232611yescharacteristic
426C2×C11C4×#13511yescharacteristic
427C2×C11#294311yescharacteristic
428C2×C11#321111yescharacteristic
429C2×C11#321211yescharacteristic
430C2×C11#323211yescharacteristic
431C2×C11#323311yescharacteristic
432C24—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C22×C4×C1112yes—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C22×C4×C1112yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C24×C1111yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8C22×C4×C1112yes—
473C2×C8C22×C4×C1112yes—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4C22×C4×C1112yes—
490C4⋊C4C22×C4×C1112yes—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C42—22no—
497C42—22no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42—41no—
504C42—42no—
505C42—42no—
506C42—42no—
507C42C22×C4×C1112yes—
508C42C11×#4112yes—
509C11#2222211yescharacteristic, direct product factor, Sylow
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×D4×C1111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—84no—
562C2×C4C4×D4×C1112yes—
563C2×C4C4×D4×C1112yes—
564C2×C4C11×#13512yes—
565C2×C4C11×#13512yes—
566C2×C4C23×C4×C1111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C11×H(5,𝔽2)11yescharacteristic
569C2×C4C11×H(5,𝔽2)11yescharacteristic
570C2×C4C11×2−1+411yescharacteristic
571C2×C4C11×2−1+411yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×C4×D4×C1111yescharacteristic
584C22C11×#53511yescharacteristic
585C22C11×#53611yescharacteristic
586C22C2×C11×#13511yescharacteristic
587C22C2×C11×#13511yescharacteristic
588C22C11×#57511yescharacteristic
589C22C11×#57511yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C11×#52011yescharacteristic
604C4C11×#52011yescharacteristic
605C4C11×#54211yescharacteristic
606C4C11×#54211yescharacteristic
607C2—82no—
608C2C11×#232611yescharacteristic
609C2C4×C11×#13511yescharacteristic
610C2C11×#294311yescharacteristic
611C2C11×#321111yescharacteristic
612C2C11×#321211yescharacteristic
613C2C11×#323211yescharacteristic
614C2C11×#323311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#125C2semidirect
4. C11×#1991C2semidirect
6. C11×#1928C2semidirect
7. C11×#1927C2semidirect
10. C11×#1865C2semidirect
12. C11×#1863C2semidirect
14. C11×#1846C2semidirect
15. C11×#1744C2semidirect
20. C11×#488C4semidirect
68. C11×#125C2×C4semidirect
107. C11×#103C2×C4semidirect
108. C11×#103C2×C4semidirect
114. C4×C8×C11C2×C4semidirect
125. #22222C11direct (N × H)
204. C4×#125C2×C11semidirect
206. #1991C2×C11semidirect
208. #1928C2×C11semidirect
209. #1927C2×C11semidirect
212. #1865C2×C11semidirect
214. #1863C2×C11semidirect
216. #1846C2×C11semidirect
217. #1744C2×C11semidirect
288. #488C4×C11semidirect
367. #125C2×C4×C11semidirect
406. #103C2×C4×C11semidirect
407. #103C2×C4×C11semidirect
413. C4×C8C2×C4×C11semidirect
509. C11#22222direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4882
C4×C11×#1252
C4×C11×#1242
C11×#19912
C11×#19582
C11×#19282
C11×#19272
C11×#19262
C11×#19252
C11×#18652
C11×#18642
C11×#18632
C11×#18622
C11×#18462
C11×#17442
#2222211