Finite Group Databasebeta

← C11×#22114 #14599307

Subgroups — C11×#22114 #14599307

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#478C211yesmaximal, characteristic
2C4×C11×#125C211yesmaximal, characteristic, complemented
3C11×#2293C211yesmaximal, characteristic
4C11×#1989C211yesmaximal, characteristic, complemented
5C11×#1949C211yesmaximal, characteristic, complemented
6C11×#1942C211yesmaximal, characteristic, complemented
7C11×#1941C211yesmaximal, characteristic, complemented
8C11×#1934C211yesmaximal, characteristic
9C11×#1934C211yesmaximal, characteristic
10C11×#1926C211yesmaximal, characteristic
11C11×#1925C211yesmaximal, characteristic
12C11×#1921C211yesmaximal, characteristic, complemented
13C11×#1920C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic
15C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117—21no—
19C11×#478C418yescomplemented
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C2×C4×C8×C11C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#388—21no—
40C11×#387—21no—
41C11×#387—21no—
42C11×#382C2211yescharacteristic
43C4×C11×C4⋊C4—21no—
44C4×C11×C4⋊C4—21no—
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4—21no—
49C43×C11C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125C2×C414yes—
68C4×D4×C11—22no—
69C4×D4×C11C2×C414yes—
70C11×#117—44no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11D411yescharacteristic
93C2×C42×C11D411yescharacteristic
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C11×#107—41no—
100C11×#107C2×C414yes—
101C11×#106—41no—
102C11×#106C2×C414yes—
103C11×C4⋊C8—22no—
104C11×C4⋊C8C2×C414yes—
105C11×#102—41no—
106C11×#102—41no—
107C11×#102C2×C414yes—
108C11×#102C2×C414yes—
109C4×C8×C11—41no—
110C4×C8×C11—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120#22114C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11C22×C412yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C22×C412yes—
156C2×C8×C11C22×C412yes—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C22×C412yes—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4C22×C412yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—41no—
190C42×C11—42no—
191C42×C11—42no—
192C42×C11—42no—
193C42×C11C22×C412yes—
194C42×C11#4112yes—
195C2×#478C2×C1111yescharacteristic
196C4×#125C2×C1111yescharacteristic, complemented
197#2293C2×C1111yescharacteristic
198#1989C2×C1111yescharacteristic, complemented
199#1949C2×C1111yescharacteristic, complemented
200#1942C2×C1111yescharacteristic, complemented
201#1941C2×C1111yescharacteristic, complemented
202#1934C2×C1111yescharacteristic
203#1934C2×C1111yescharacteristic
204#1926C2×C1111yescharacteristic
205#1925C2×C1111yescharacteristic
206#1921C2×C1111yescharacteristic, complemented
207#1920C2×C1111yescharacteristic, complemented
208#1804C2×C1111yescharacteristic
209C4×C4⋊C8C2×C1111yescharacteristic, complemented
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11C22×D411yescharacteristic
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—41no—
221D4×C11—41no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—48no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
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×C11C4×D412yes—
258C2×C4×C11C4×D412yes—
259C2×C4×C11#13512yes—
260C2×C4×C11#13512yes—
261C2×C4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C8×C11—22no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C2×#125C22×C1111yescharacteristic
273C2×C4×D4C22×C1111yescharacteristic
274C2×#117—21no—
275#478C4×C1118yescomplemented
276C2×#107C22×C1111yescharacteristic
277C2×#107C22×C1111yescharacteristic
278C2×#106C22×C1111yescharacteristic
279C2×#106C22×C1111yescharacteristic
280C2×C4⋊C8C22×C1111yescharacteristic
281C2×C4⋊C8C22×C1111yescharacteristic
282C2×#102C22×C1111yescharacteristic
283C2×#102C22×C1111yescharacteristic
284C2×#102C22×C1111yescharacteristic
285C2×#102C22×C1111yescharacteristic
286C2×C4×C8C22×C1111yescharacteristic
287C2×C4×C8C22×C1111yescharacteristic
288#390C22×C1111yescharacteristic
289#390C22×C1111yescharacteristic
290#389C22×C1111yescharacteristic
291#389C22×C1111yescharacteristic
292#389C22×C1111yescharacteristic
293#389C22×C1111yescharacteristic
294#388—21no—
295#388—21no—
296#387—21no—
297#387—21no—
298#382C22×C1111yescharacteristic
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4C22×C1111yescharacteristic
302C4×C4⋊C4C22×C1111yescharacteristic
303C4×C4⋊C4C22×C1111yescharacteristic
304C4×C22⋊C4—21no—
305C43C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#340C22×C1111yescharacteristic
308#340C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#340C22×C1111yescharacteristic
313#340C22×C1111yescharacteristic
314#336C22×C1111yescharacteristic
315#336C22×C1111yescharacteristic
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11C2×C4×D411yescharacteristic
324C22×C11#53611yescharacteristic
325C22×C11#53711yescharacteristic
326C22×C11C2×#13511yescharacteristic
327C22×C11C2×#13511yescharacteristic
328C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C11#57511yescharacteristic
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11#51911yescharacteristic
344C4×C11#52011yescharacteristic
345C4×C11#54111yescharacteristic
346C4×C11#54211yescharacteristic
347C22×D4C23×C1111yescharacteristic
348C23×C4—21no—
349C22×C8C23×C1111yescharacteristic
350C22×C8C23×C1111yescharacteristic
351C22×C8C23×C1111yescharacteristic
352C22×C8C23×C1111yescharacteristic
353#125—22no—
354#125C2×C4×C1114yes—
355C4×D4—22no—
356C4×D4C2×C4×C1114yes—
357#117—44no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1111yescharacteristic
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42D4×C1111yescharacteristic
380C2×C42D4×C1111yescharacteristic
381C2×C42D4×C1111yescharacteristic
382C2×C42D4×C1111yescharacteristic
383C2×C42C23×C1111yescharacteristic
384C2×C42C23×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386#107—41no—
387#107C2×C4×C1114yes—
388#106—41no—
389#106C2×C4×C1114yes—
390C4⋊C8—22no—
391C4⋊C8C2×C4×C1114yes—
392#102—41no—
393#102—41no—
394#102C2×C4×C1114yes—
395#102C2×C4×C1114yes—
396C4×C8—41no—
397C4×C8—41no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407C2×C11—82no—
408C2×C11#232311yescharacteristic
409C2×C11C4×#13511yescharacteristic
410C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
411C2×C11#322811yescharacteristic
412C2×C11#323211yescharacteristic
413C2×C11#324711yescharacteristic
414C2×C11#325011yescharacteristic
415C24—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C22×C4×C1112yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C24×C1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C22×C4×C1112yes—
450C2×C8C22×C4×C1112yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4C22×C4×C1112yes—
469C4⋊C4C22×C4×C1112yes—
470C4⋊C4C22×C4×C1112yes—
471C22⋊C4—24no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—42no—
485C42—42no—
486C42—42no—
487C42C22×C4×C1112yes—
488C42C11×#4112yes—
489C11#2211411yescharacteristic, direct product factor, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C22×D4×C1111yescharacteristic
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—48no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4C4×D4×C1112yes—
538C2×C4C4×D4×C1112yes—
539C2×C4C11×#13512yes—
540C2×C4C11×#13512yes—
541C2×C4C11×AGL(1,ℤ/8)12yes—
542C2×C4C23×C4×C1111yescharacteristic
543C2×C4C2×C11×#4111yescharacteristic
544C2×C4C11×H(5,𝔽2)11yescharacteristic
545C2×C4C11×2−1+411yescharacteristic
546C2×C4C11×2−1+411yescharacteristic
547C2×C4C11×2−1+411yescharacteristic
548C8—22no—
549C8—22no—
550C8—41no—
551C8—41no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×C4×D4×C1111yescharacteristic
560C22C11×#53611yescharacteristic
561C22C11×#53711yescharacteristic
562C22C2×C11×#13511yescharacteristic
563C22C2×C11×#13511yescharacteristic
564C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
565C22C11×#57511yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—42no—
572C4—42no—
573C4—42no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C11×#51911yescharacteristic
580C4C11×#52011yescharacteristic
581C4C11×#54111yescharacteristic
582C4C11×#54211yescharacteristic
583C2—82no—
584C2C11×#232311yescharacteristic
585C2C4×C11×#13511yescharacteristic
586C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
587C2C11×#322811yescharacteristic
588C2C11×#323211yescharacteristic
589C2C11×#324711yescharacteristic
590C2C11×#325011yescharacteristic
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×#1989C2semidirect
5. C11×#1949C2semidirect
6. C11×#1942C2semidirect
7. C11×#1941C2semidirect
12. C11×#1921C2semidirect
13. C11×#1920C2semidirect
15. C4×C11×C4⋊C8C2semidirect
19. C11×#478C4semidirect
120. #22114C11direct (N × H)
196. C4×#125C2×C11semidirect
198. #1989C2×C11semidirect
199. #1949C2×C11semidirect
200. #1942C2×C11semidirect
201. #1941C2×C11semidirect
206. #1921C2×C11semidirect
207. #1920C2×C11semidirect
209. C4×C4⋊C8C2×C11semidirect
275. #478C4×C11semidirect
489. C11#22114direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4782
C4×C11×#1252
C11×#22932
C11×#19892
C11×#19492
C11×#19422
C11×#19412
C11×#19342
C11×#19262
C11×#19252
C11×#19212
C11×#19202
C11×#18042
C4×C11×C4⋊C82
#2211411