Finite Group Databasebeta

← C11×#26367 #14603560

Subgroups — C11×#26367 #14603560

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#479C211yesmaximal, characteristic, complemented
2C2×C11×#428C211yesmaximal, characteristic
3C11×#2442C211yesmaximal, characteristic
4C11×#2362C211yesmaximal, characteristic
5C11×#2097C211yesmaximal, characteristic, complemented
6C11×#2087C211yesmaximal, characteristic, complemented
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2059C211yesmaximal, characteristic, complemented
9C11×#1949C211yesmaximal, characteristic, complemented
10C11×#1919C211yesmaximal, characteristic, complemented
11C11×#1894C211yesmaximal, characteristic
12C11×#1872C211yesmaximal, characteristic
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic
15C11×#1851C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C11×#479—24no—
23C11×#428—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#400—21no—
38C11×#398—21no—
39C11×#391C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#388—21no—
44C11×#388—21no—
45C11×#387—21no—
46C11×#385—21no—
47C11×#382C2211yescharacteristic
48C11×#380—21no—
49C11×#380C2211yescharacteristic
50C4×C11×C4⋊C4—21no—
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#125—22no—
72C11×#125—41no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8Q814yes—
75C4×Q8×C11—22no—
76C4×Q8×C11—41no—
77C11×#117—22no—
78C11×#117—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—41no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11—21no—
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C11×#107—22no—
107C11×#107—22no—
108C11×#107—22no—
109C11×#106—22no—
110C11×#106—41no—
111C11×#106D414yes—
112C11×C4⋊C8—22no—
113C11×C4⋊C8—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—41no—
118C11×C22⋊C8—22no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95D411yescharacteristic
129C11×#95D411yescharacteristic
130#26367C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11C2×D411yescharacteristic
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yes—
138C22×C4×C11—21no—
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—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—81no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×Q812yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C11×M16—28no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D412yes—
173C2×C8×C11#4112yes—
174C11×C4⋊C4—24no—
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—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4—81no—
192C11×C4⋊C4—81no—
193C11×C4⋊C4C2×D412yes—
194C11×C4⋊C4C2×D412yes—
195C11×C4⋊C4C2×Q812yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—42no—
200C11×C22⋊C4—42no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—42no—
206C42×C11—42no—
207C42×C11—42no—
208C2×#479C2×C1111yescharacteristic, complemented
209C2×#428C2×C1111yescharacteristic
210#2442C2×C1111yescharacteristic
211#2362C2×C1111yescharacteristic
212#2097C2×C1111yescharacteristic, complemented
213#2087C2×C1111yescharacteristic, complemented
214#2068C2×C1111yescharacteristic, complemented
215#2059C2×C1111yescharacteristic, complemented
216#1949C2×C1111yescharacteristic, complemented
217#1919C2×C1111yescharacteristic, complemented
218#1894C2×C1111yescharacteristic
219#1872C2×C1111yescharacteristic
220#1865C2×C1111yescharacteristic, complemented
221#1854C2×C1111yescharacteristic
222#1851C2×C1111yescharacteristic
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C22⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—41no—
234Q8×C11—41no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
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—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—84no—
278C2×C4×C11C22⋊Q812yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×Q811yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C8×C11—22no—
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—41no—
289C22×M16C22×C1111yescharacteristic
290C2×#125C22×C1111yescharacteristic
291C2×C22⋊Q8C22×C1111yescharacteristic
292C2×C4×Q8C22×C1111yescharacteristic
293C2×#117C22×C1111yescharacteristic
294C22×C4⋊C4C22×C1111yescharacteristic
295#479—24no—
296#428—24no—
297C2×#107C22×C1111yescharacteristic
298C2×#107C22×C1111yescharacteristic
299C2×#107C22×C1111yescharacteristic
300C2×#106C22×C1111yescharacteristic
301C2×#106C22×C1111yescharacteristic
302C2×#106C22×C1111yescharacteristic
303C2×C4⋊C8C22×C1111yescharacteristic
304C2×C4⋊C8C22×C1111yescharacteristic
305C2×#103C22×C1111yescharacteristic
306C2×#103C22×C1111yescharacteristic
307C2×#103C22×C1111yescharacteristic
308C2×#103C22×C1111yescharacteristic
309C2×C22⋊C8C22×C1111yescharacteristic
310#400—21no—
311#398—21no—
312#391C22×C1111yescharacteristic
313#389C22×C1111yescharacteristic
314#389C22×C1111yescharacteristic
315#389C22×C1111yescharacteristic
316#388—21no—
317#388—21no—
318#387—21no—
319#385—21no—
320#382C22×C1111yescharacteristic
321#380—21no—
322#380C22×C1111yescharacteristic
323C4×C4⋊C4—21no—
324C4×C4⋊C4C22×C1111yescharacteristic
325C4×C22⋊C4C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329#340C22×C1111yescharacteristic
330#340C22×C1111yescharacteristic
331#340C22×C1111yescharacteristic
332#336C22×C1111yescharacteristic
333#336C22×C1111yescharacteristic
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C22⋊Q811yescharacteristic
342C22×C11D4211yescharacteristic
343C22×C11#54711yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57811yescharacteristic
348C4×C11—22no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11#52511yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11D4×Q811yescharacteristic
364C4×C11#55411yescharacteristic
365C22×Q8C23×C1111yescharacteristic
366C23×C4—21no—
367C23×C4C23×C1111yescharacteristic
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C22×C8C23×C1111yescharacteristic
372C22×C8C23×C1111yescharacteristic
373C22×C8C23×C1111yescharacteristic
374C22×C8C23×C1111yescharacteristic
375#125—22no—
376#125—41no—
377C22⋊Q8—22no—
378C22⋊Q8Q8×C1114yes—
379C4×Q8—22no—
380C4×Q8—41no—
381#117—22no—
382#117—41no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C4⋊C4C23×C1111yescharacteristic
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C4⋊C4C23×C1111yescharacteristic
399C2×C4⋊C4C23×C1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4D4×C1111yescharacteristic
404C2×C22⋊C4D4×C1111yescharacteristic
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C23×C1111yescharacteristic
409C2×C42C23×C1111yescharacteristic
410#107—22no—
411#107—22no—
412#107—22no—
413#106—22no—
414#106—41no—
415#106D4×C1114yes—
416C4⋊C8—22no—
417C4⋊C8—22no—
418#103—22no—
419#103—22no—
420#103—22no—
421#103—41no—
422C22⋊C8—22no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95D4×C1111yescharacteristic
433#95D4×C1111yescharacteristic
434C2×C11—42no—
435C2×C11#244911yescharacteristic
436C2×C11#308011yescharacteristic
437C2×C11#308211yescharacteristic
438C2×C11#326911yescharacteristic
439C2×C11#327511yescharacteristic
440C2×C11#334911yescharacteristic
441C2×C11#335111yescharacteristic
442C24C2×D4×C1111yescharacteristic
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×Q8×C1112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×Q8×C1112yes—
470C22×C4C11×#4112yes—
471C22×C4C24×C1111yescharacteristic
472M16—28no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8C2×D4×C1112yes—
484C2×C8C11×#4112yes—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—81no—
503C4⋊C4—81no—
504C4⋊C4C2×D4×C1112yes—
505C4⋊C4C2×D4×C1112yes—
506C4⋊C4C2×Q8×C1112yes—
507C22⋊C4—24no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—42no—
518C42—42no—
519C11#2636711yescharacteristic, direct product factor, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23C11×C22⋊Q812yes—
527C23C22×D4×C1111yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—41no—
531Q8—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
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—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—84no—
575C2×C4C11×C22⋊Q812yes—
576C2×C4C22×D4×C1111yescharacteristic
577C2×C4C22×Q8×C1111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C2×C11×#4111yescharacteristic
580C2×C4C11×H(5,𝔽2)11yescharacteristic
581C2×C4C11×2−1+411yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×C11×C22⋊Q811yescharacteristic
594C22D42×C1111yescharacteristic
595C22C11×#54711yescharacteristic
596C22C11×#57511yescharacteristic
597C22C11×#57511yescharacteristic
598C22C11×#57711yescharacteristic
599C22C11×#57811yescharacteristic
600C4—22no—
601C4—42no—
602C4—41no—
603C4—42no—
604C4—41no—
605C4—42no—
606C4—42no—
607C4—41no—
608C4—41no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C11×#52511yescharacteristic
614C4C11×#53911yescharacteristic
615C4D4×Q8×C1111yescharacteristic
616C4C11×#55411yescharacteristic
617C2—42no—
618C2C11×#244911yescharacteristic
619C2C11×#308011yescharacteristic
620C2C11×#308211yescharacteristic
621C2C11×#326911yescharacteristic
622C2C11×#327511yescharacteristic
623C2C11×#334911yescharacteristic
624C2C11×#335111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×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
1. C2×C11×#479C2semidirect
5. C11×#2097C2semidirect
6. C11×#2087C2semidirect
7. C11×#2068C2semidirect
8. C11×#2059C2semidirect
9. C11×#1949C2semidirect
10. C11×#1919C2semidirect
13. C11×#1865C2semidirect
130. #26367C11direct (N × H)
208. C2×#479C2×C11semidirect
212. #2097C2×C11semidirect
213. #2087C2×C11semidirect
214. #2068C2×C11semidirect
215. #2059C2×C11semidirect
216. #1949C2×C11semidirect
217. #1919C2×C11semidirect
220. #1865C2×C11semidirect
519. C11#26367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4792
C2×C11×#4282
C11×#24422
C11×#23622
C11×#20972
C11×#20872
C11×#20682
C11×#20592
C11×#19492
C11×#19192
C11×#18942
C11×#18722
C11×#18652
C11×#18542
C11×#18512
#2636711