Finite Group Databasebeta

← C11×#22945 #14600138

Subgroups — C11×#22945 #14600138

Order 2816.

818 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×#483C211yesmaximal, characteristic
2C11×#2362C211yesmaximal, characteristic
3C11×#2345C211yesmaximal, characteristic
4C11×#1944C211yesmaximal, characteristic, complemented
5C11×#1933C211yesmaximal, characteristic, complemented
6C11×#1928C211yesmaximal, characteristic, complemented
7C11×#1920C211yesmaximal, characteristic, complemented
8C11×#1920C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic
10C11×#1865C211yesmaximal, characteristic, complemented
11C11×#1854C211yesmaximal, characteristic
12C4×C11×#106C211yesmaximal, characteristic, complemented
13C11×#1763C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic
15C11×#1736C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C11×#483C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#388—21no—
39C11×#387—21no—
40C11×#387—21no—
41C11×#387—21no—
42C11×#380—21no—
43C11×#380C2211yescharacteristic
44C4×C11×C4⋊C4—21no—
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4—21no—
49C4×C11×C22⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—41no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8C2×C414yes—
72C4×Q8×C11—22no—
73C4×Q8×C11—41no—
74C11×#117—22no—
75C11×#117—41no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2×C414yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C11×#107—41no—
104C11×#106—22no—
105C11×#106C2×C414yes—
106C11×#106C2×C414yes—
107C11×#103—22no—
108C11×#103—41no—
109C11×#103C2×C414yes—
110C11×#103C2×C414yes—
111C11×C22⋊C8C2×C414yes—
112C11×#97—41no—
113C4×C8×C11—22no—
114C11×#95—21no—
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×#95D411yescharacteristic
124C11×#95D411yescharacteristic
125#22945C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—81no—
147C22×C4×C11—81no—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C11×M16—44no—
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—
168C2×C8×C11#4112yes—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
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—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4—81no—
185C11×C4⋊C4C22×C412yes—
186C11×C4⋊C4C22×C412yes—
187C11×C4⋊C4C22×C412yes—
188C11×C4⋊C4#4112yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—42no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—42no—
199C42×C11—42no—
200C42×C11—42no—
201C42×C11—81no—
202C42×C11—81no—
203C2×#483C2×C1111yescharacteristic
204#2362C2×C1111yescharacteristic
205#2345C2×C1111yescharacteristic
206#1944C2×C1111yescharacteristic, complemented
207#1933C2×C1111yescharacteristic, complemented
208#1928C2×C1111yescharacteristic, complemented
209#1920C2×C1111yescharacteristic, complemented
210#1920C2×C1111yescharacteristic, complemented
211#1894C2×C1111yescharacteristic
212#1865C2×C1111yescharacteristic, complemented
213#1854C2×C1111yescharacteristic
214C4×#106C2×C1111yescharacteristic, complemented
215#1763C2×C1111yescharacteristic, complemented
216#1753C2×C1111yescharacteristic
217#1736C2×C1111yescharacteristic
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4×D412yes—
225C23×C11C22×D411yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
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—21no—
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—41no—
270C2×C4×C11—41no—
271C2×C4×C11—84no—
272C2×C4×C11C4×D412yes—
273C2×C4×C11#13712yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C8×C11—22no—
281C8×C11—22no—
282C8×C11—22no—
283C8×C11—41no—
284C22×M16C22×C1111yescharacteristic
285C2×C22⋊Q8C22×C1111yescharacteristic
286C2×C4×Q8C22×C1111yescharacteristic
287C2×#117C22×C1111yescharacteristic
288C22×C4⋊C4C22×C1111yescharacteristic
289#483C4×C1118yescomplemented
290C2×#107C22×C1111yescharacteristic
291C2×#106C22×C1111yescharacteristic
292C2×#106C22×C1111yescharacteristic
293C2×#106C22×C1111yescharacteristic
294C2×#103C22×C1111yescharacteristic
295C2×#103C22×C1111yescharacteristic
296C2×#103C22×C1111yescharacteristic
297C2×#103C22×C1111yescharacteristic
298C2×C22⋊C8C22×C1111yescharacteristic
299C2×#97C22×C1111yescharacteristic
300C2×C4×C8C22×C1111yescharacteristic
301#391C22×C1111yescharacteristic
302#389C22×C1111yescharacteristic
303#389C22×C1111yescharacteristic
304#389C22×C1111yescharacteristic
305#388—21no—
306#388—21no—
307#387—21no—
308#387—21no—
309#387—21no—
310#380—21no—
311#380C22×C1111yescharacteristic
312C4×C4⋊C4—21no—
313C4×C4⋊C4C22×C1111yescharacteristic
314C4×C4⋊C4C22×C1111yescharacteristic
315C4×C4⋊C4C22×C1111yescharacteristic
316C4×C22⋊C4—21no—
317C4×C22⋊C4C22×C1111yescharacteristic
318#340C22×C1111yescharacteristic
319#340C22×C1111yescharacteristic
320#340C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#340C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#336C22×C1111yescharacteristic
327#336C22×C1111yescharacteristic
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C2×C4×D411yescharacteristic
336C22×C11#54611yescharacteristic
337C22×C11#54711yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57511yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57711yescharacteristic
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11C4×#4111yescharacteristic
356C4×C11#52011yescharacteristic
357C4×C11#55111yescharacteristic
358C4×C11#55211yescharacteristic
359C22×Q8C23×C1111yescharacteristic
360C23×C4—21no—
361C23×C4C23×C1111yescharacteristic
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—41no—
365C22×C8C23×C1111yescharacteristic
366C22×C8C23×C1111yescharacteristic
367C22×C8C23×C1111yescharacteristic
368C22×C8C23×C1111yescharacteristic
369C22⋊Q8—22no—
370C22⋊Q8C2×C4×C1114yes—
371C4×Q8—22no—
372C4×Q8—41no—
373#117—22no—
374#117—41no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4C2×C4×C1114yes—
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C4⋊C4C23×C1111yescharacteristic
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4D4×C1111yescharacteristic
394C2×C22⋊C4D4×C1111yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42C23×C1111yescharacteristic
401C2×C42C23×C1111yescharacteristic
402#107—41no—
403#106—22no—
404#106C2×C4×C1114yes—
405#106C2×C4×C1114yes—
406#103—22no—
407#103—41no—
408#103C2×C4×C1114yes—
409#103C2×C4×C1114yes—
410C22⋊C8C2×C4×C1114yes—
411#97—41no—
412C4×C8—22no—
413#95—21no—
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#95D4×C1111yescharacteristic
423#95D4×C1111yescharacteristic
424C2×C11—42no—
425C2×C11#235911yescharacteristic
426C2×C11C4×#13711yescharacteristic
427C2×C11#294911yescharacteristic
428C2×C11#332611yescharacteristic
429C2×C11#333111yescharacteristic
430C2×C11#334411yescharacteristic
431C2×C11#335011yescharacteristic
432C24C2×D4×C1111yescharacteristic
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C22×C4×C1112yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4C22×C4×C1112yes—
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C11×#4112yes—
461C22×C4C24×C1111yescharacteristic
462M16—44no—
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—
474C2×C8C11×#4112yes—
475C4⋊C4—24no—
476C4⋊C4—24no—
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—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4C22×C4×C1112yes—
492C4⋊C4C22×C4×C1112yes—
493C4⋊C4C22×C4×C1112yes—
494C4⋊C4C11×#4112yes—
495C22⋊C4—24no—
496C22⋊C4—22no—
497C22⋊C4—41no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—42no—
506C42—42no—
507C42—81no—
508C42—81no—
509C11#2294511yescharacteristic, direct product factor, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C4×D4×C1112yes—
517C23C22×D4×C1111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
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—41no—
562C2×C4—41no—
563C2×C4—84no—
564C2×C4C4×D4×C1112yes—
565C2×C4C11×#13712yes—
566C2×C4C23×C4×C1111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C2×C11×#4111yescharacteristic
569C2×C4C2×C11×#4111yescharacteristic
570C2×C4C11×H(5,𝔽2)11yescharacteristic
571C2×C4C11×2−1+411yescharacteristic
572C8—22no—
573C8—22no—
574C8—22no—
575C8—41no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×C4×D4×C1111yescharacteristic
584C22C11×#54611yescharacteristic
585C22C11×#54711yescharacteristic
586C22C2×C11×#13711yescharacteristic
587C22C11×#57511yescharacteristic
588C22C11×#57711yescharacteristic
589C22C11×#57711yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C4×C11×#4111yescharacteristic
604C4C11×#52011yescharacteristic
605C4C11×#55111yescharacteristic
606C4C11×#55211yescharacteristic
607C2—42no—
608C2C11×#235911yescharacteristic
609C2C4×C11×#13711yescharacteristic
610C2C11×#294911yescharacteristic
611C2C11×#332611yescharacteristic
612C2C11×#333111yescharacteristic
613C2C11×#334411yescharacteristic
614C2C11×#335011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1944C2semidirect
5. C11×#1933C2semidirect
6. C11×#1928C2semidirect
7. C11×#1920C2semidirect
8. C11×#1920C2semidirect
10. C11×#1865C2semidirect
12. C4×C11×#106C2semidirect
13. C11×#1763C2semidirect
21. C11×#483C4semidirect
125. #22945C11direct (N × H)
206. #1944C2×C11semidirect
207. #1933C2×C11semidirect
208. #1928C2×C11semidirect
209. #1920C2×C11semidirect
210. #1920C2×C11semidirect
212. #1865C2×C11semidirect
214. C4×#106C2×C11semidirect
215. #1763C2×C11semidirect
289. #483C4×C11semidirect
509. C11#22945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C11×#23622
C11×#23452
C11×#19442
C11×#19332
C11×#19282
C11×#19202
C11×#18942
C11×#18652
C11×#18542
C4×C11×#1062
C11×#17632
C11×#17532
C11×#17362
#2294511