Finite Group Databasebeta

← C11×#22406 #14599599

Subgroups — C11×#22406 #14599599

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#410C212yesmaximal, complemented
3C11×#2344C212yesmaximal, complemented
4C11×#1964C212yesmaximal, complemented
5C11×#1899C214yesmaximal, complemented
6C11×#1799C211yesmaximal, characteristic, complemented
7C11×#1782C212yesmaximal, complemented
8C4×C11×#99C211yesmaximal, characteristic, complemented
9C22×C11×#41C2212yes—
10C11×#547—22no—
11C11×#547—24no—
12C11×#547—22no—
13C2×C11×C4⋊Q8C411yescharacteristic, complemented
14C2×C11×#123C412yescomplemented
15C2×C11×#123C2212yes—
16C2×C11×C22⋊Q8C412yescomplemented
17C2×C11×#121C411yescharacteristic, complemented
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C411yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2214yes—
22C22×C11×C4⋊C4C411yescharacteristic, complemented
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#410—28no—
25C2×C11×#99C2214yes—
26C2×C11×#99C2211yescharacteristic
27C2×C11×#99C2212yes—
28C2×C11×#99C2214yes—
29C2×C11×#99C2211yescharacteristic
30C11×#389—22no—
31C11×#387—24no—
32C11×#381C2214yes—
33C11×#380C2212yes—
34C4×C11×C4⋊C4—22no—
35C4×C11×C22⋊C4C2212yes—
36C11×#342C2212yes—
37C11×#342C2212yes—
38C2×C11×#41—24no—
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—24no—
42C2×C11×#41—44no—
43C22×Q8×C11C2×C412yes—
44C22×D4×C11C2×C412yes—
45C22×D4×C11C2×C411yescharacteristic
46C22×D4×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2×C412yes—
49C23×C4×C11C2×C412yes—
50C23×C4×C11C2×C411yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×#123—24no—
56C11×#123—24no—
57C11×#123—24no—
58C11×#123—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—24no—
61C11×#121—22no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C11×#117—28no—
71C11×#117—44no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C412yes—
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C4⋊C4C2×C412yes—
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C4⋊C4C2×C411yescharacteristic
83C2×C11×C4⋊C4C2×C412yes—
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4D414yes—
86C2×C11×C4⋊C4D412yes—
87C2×C11×C22⋊C4C2×C412yes—
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C412yes—
90C2×C11×C22⋊C4C2×C412yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C11×C22⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4C2312yes—
95C2×C42×C11—24no—
96C2×C42×C11—22no—
97C2×C42×C11C2×C411yescharacteristic
98C11×#99—24no—
99C11×#99—22no—
100C11×#99—28no—
101C11×#99—44no—
102C11×#99D414yescomplemented
103C11×#95—22no—
104C11×#95—24no—
105C11×#95—22no—
106C11×#95—24no—
107#22406C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11C22×C412yes—
109C24×C11C22×C411yescharacteristic
110C24×C11C2411yescharacteristic
111C11×#41—48no—
112C11×#41—48no—
113C11×#41—48no—
114C11×#41—48no—
115C2×Q8×C11—24no—
116C2×Q8×C11—24no—
117C2×Q8×C11—42no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—24no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11C2×D412yes—
131C2×D4×C11#4112yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—48no—
169C11×C4⋊C4—44no—
170C11×C4⋊C4C22⋊C412yes—
171C11×C4⋊C4C22⋊C411yescharacteristic
172C11×C4⋊C4C22⋊C411yescharacteristic
173C11×C4⋊C4C22⋊C412yes—
174C11×C4⋊C4C22⋊C412yes—
175C11×C4⋊C4C22⋊C414yes—
176C11×C4⋊C4C22⋊C414yes—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4C2×D414yes—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—48no—
192C42×C11—44no—
193C2×#547C2×C1111yescharacteristic
194C2×#410C2×C1112yescomplemented
195#2344C2×C1112yescomplemented
196#1964C2×C1112yescomplemented
197#1899C2×C1114yescomplemented
198#1799C2×C1111yescharacteristic, complemented
199#1782C2×C1112yescomplemented
200C4×#99C2×C1111yescharacteristic, complemented
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C4×D412yes—
213C23×C11C23×C411yescharacteristic
214C23×C11C22×D412yes—
215C23×C11C22×D411yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11H(5,𝔽2)12yes—
218Q8×C11—48no—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—48no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—42no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—44no—
258C2×C4×C11—42no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11—42no—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C412yes—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C2×C22⋊C414yes—
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C4×D412yes—
269C22×#41C22×C1112yes—
270#547—22no—
271#547—24no—
272#547—22no—
273C2×C4⋊Q8C4×C1111yescharacteristic, complemented
274C2×#123C4×C1112yescomplemented
275C2×#123C22×C1112yes—
276C2×C22⋊Q8C4×C1112yescomplemented
277C2×#121C4×C1111yescharacteristic, complemented
278C2×#121C22×C1111yescharacteristic
279C2×C4×D4C4×C1111yescharacteristic, complemented
280C2×C4×D4C22×C1111yescharacteristic
281C2×#117C22×C1114yes—
282C22×C4⋊C4C4×C1111yescharacteristic, complemented
283C22×C4⋊C4C22×C1111yescharacteristic
284#410—28no—
285C2×#99C22×C1112yes—
286C2×#99C22×C1114yes—
287C2×#99C22×C1111yescharacteristic
288C2×#99C22×C1114yes—
289C2×#99C22×C1111yescharacteristic
290#389—22no—
291#387—24no—
292#381C22×C1114yes—
293#380C22×C1112yes—
294C4×C4⋊C4—22no—
295C4×C22⋊C4C22×C1112yes—
296#342C22×C1112yes—
297#342C22×C1112yes—
298C22×C11—22no—
299C22×C11—21no—
300C22×C11—22no—
301C22×C11—21no—
302C22×C11—22no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11#51811yescharacteristic
318C22×C11D4212yes—
319C22×C11#54612yes—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—24no—
323C4×C11—22no—
324C4×C11—21no—
325C4×C11—22no—
326C4×C11—44no—
327C4×C11—42no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—84no—
331C4×C11—82no—
332C4×C11#41012yescomplemented
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—44no—
338C22×Q8C2×C4×C1112yes—
339C22×D4C2×C4×C1112yes—
340C22×D4C2×C4×C1111yescharacteristic
341C22×D4C23×C1112yes—
342C22×D4C23×C1111yescharacteristic
343C23×C4C2×C4×C1112yes—
344C23×C4C2×C4×C1112yes—
345C23×C4C2×C4×C1111yescharacteristic
346C23×C4C23×C1112yes—
347C23×C4C23×C1111yescharacteristic
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350#123—24no—
351#123—24no—
352#123—24no—
353#123—24no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—21no—
365#117—28no—
366#117—44no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4C2×C4×C1111yescharacteristic
373C2×C4⋊C4C2×C4×C1112yes—
374C2×C4⋊C4C2×C4×C1111yescharacteristic
375C2×C4⋊C4C2×C4×C1112yes—
376C2×C4⋊C4C2×C4×C1111yescharacteristic
377C2×C4⋊C4C2×C4×C1111yescharacteristic
378C2×C4⋊C4C2×C4×C1112yes—
379C2×C4⋊C4D4×C1112yes—
380C2×C4⋊C4D4×C1114yes—
381C2×C4⋊C4D4×C1112yes—
382C2×C22⋊C4C2×C4×C1112yes—
383C2×C22⋊C4C2×C4×C1111yescharacteristic
384C2×C22⋊C4C2×C4×C1112yes—
385C2×C22⋊C4C2×C4×C1112yes—
386C2×C22⋊C4C23×C1114yes—
387C2×C22⋊C4C23×C1112yes—
388C2×C22⋊C4C23×C1111yescharacteristic
389C2×C22⋊C4C23×C1112yes—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42C2×C4×C1111yescharacteristic
393#99—24no—
394#99—22no—
395#99—28no—
396#99—44no—
397#99D4×C1114yescomplemented
398#95—22no—
399#95—24no—
400#95—22no—
401#95—24no—
402C2×C11—22no—
403C2×C11—22no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—42no—
407C2×C11—82no—
408C2×C11D4×C22⋊C411yescharacteristic
409C2×C11C2×#41011yescharacteristic
410C2×C11#288411yescharacteristic
411C24C22×C4×C1112yes—
412C24C22×C4×C1111yescharacteristic
413C24C24×C1111yescharacteristic
414#41—48no—
415#41—48no—
416#41—48no—
417#41—48no—
418C2×Q8—24no—
419C2×Q8—24no—
420C2×Q8—42no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—24no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—24no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4C2×D4×C1112yes—
434C2×D4C11×#4112yes—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4C22×C4×C1112yes—
454C22×C4C22×C4×C1111yescharacteristic
455C22×C4C22×C4×C1112yes—
456C22×C4C22×C4×C1112yes—
457C22×C4C22×C4×C1111yescharacteristic
458C22×C4C22×C4×C1111yescharacteristic
459C22×C4C22×C4×C1111yescharacteristic
460C22×C4C22×C4×C1111yescharacteristic
461C22×C4C2×D4×C1114yes—
462C22×C4C2×D4×C1114yes—
463C22×C4C2×D4×C1112yes—
464C22×C4C2×D4×C1112yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—24no—
471C4⋊C4—48no—
472C4⋊C4—44no—
473C4⋊C4C11×C22⋊C412yes—
474C4⋊C4C11×C22⋊C411yescharacteristic
475C4⋊C4C11×C22⋊C411yescharacteristic
476C4⋊C4C11×C22⋊C412yes—
477C4⋊C4C11×C22⋊C412yes—
478C4⋊C4C11×C22⋊C414yes—
479C4⋊C4C11×C22⋊C414yes—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—24no—
491C22⋊C4C2×D4×C1114yes—
492C42—21no—
493C42—21no—
494C42—48no—
495C42—44no—
496C11#2240611yescharacteristic, direct product factor, Sylow
497C23—21no—
498C23—21no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—42no—
507C23—42no—
508C23C4×D4×C1112yes—
509C23C23×C4×C1111yescharacteristic
510C23C22×D4×C1112yes—
511C23C22×D4×C1111yescharacteristic
512C23C2×C11×#4111yescharacteristic
513C23C11×H(5,𝔽2)12yes—
514Q8—48no—
515D4—24no—
516D4—24no—
517D4—48no—
518D4—42no—
519D4—44no—
520D4—44no—
521D4—42no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4C2×C11×C22⋊C411yescharacteristic
559C2×C4C2×C11×C22⋊C412yes—
560C2×C4C2×C11×C22⋊C412yes—
561C2×C4C2×C11×C22⋊C412yes—
562C2×C4C2×C11×C22⋊C414yes—
563C2×C4C2×C11×C22⋊C411yescharacteristic
564C2×C4C4×D4×C1112yes—
565C22—22no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—82no—
581C22—82no—
582C22C22×C11×C22⋊C411yescharacteristic
583C22C2×C4×D4×C1111yescharacteristic
584C22C11×#51811yescharacteristic
585C22D42×C1112yes—
586C22C11×#54612yes—
587C4—22no—
588C4—22no—
589C4—24no—
590C4—22no—
591C4—21no—
592C4—22no—
593C4—44no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—84no—
598C4—82no—
599C4C11×#41012yescomplemented
600C2—22no—
601C2—22no—
602C2—21no—
603C2—21no—
604C2—42no—
605C2—82no—
606C2D4×C11×C22⋊C411yescharacteristic
607C2C2×C11×#41011yescharacteristic
608C2C11×#288411yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#547C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#410C2semidirect
3. C11×#2344C2semidirect
4. C11×#1964C2semidirect
5. C11×#1899C2semidirect
6. C11×#1799C2semidirect
7. C11×#1782C2semidirect
8. C4×C11×#99C2semidirect
13. C2×C11×C4⋊Q8C4semidirect
14. C2×C11×#123C4semidirect
16. C2×C11×C22⋊Q8C4semidirect
17. C2×C11×#121C4semidirect
19. C2×C4×D4×C11C4semidirect
22. C22×C11×C4⋊C4C4semidirect
102. C11×#99D4semidirect
107. #22406C11direct (N × H)
194. C2×#410C2×C11semidirect
195. #2344C2×C11semidirect
196. #1964C2×C11semidirect
197. #1899C2×C11semidirect
198. #1799C2×C11semidirect
199. #1782C2×C11semidirect
200. C4×#99C2×C11semidirect
273. C2×C4⋊Q8C4×C11semidirect
274. C2×#123C4×C11semidirect
276. C2×C22⋊Q8C4×C11semidirect
277. C2×#121C4×C11semidirect
279. C2×C4×D4C4×C11semidirect
282. C22×C4⋊C4C4×C11semidirect
332. C4×C11#410semidirect
397. #99D4×C11semidirect
496. C11#22406direct (N × H)
599. C4C11×#410semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4102
C11×#23442
C11×#19642
C11×#18992
C11×#17992
C11×#17822
C4×C11×#992
#2240611