Finite Group Databasebeta

← C11×#24067 #14601260

Subgroups — C11×#24067 #14601260

Order 2816.

1176 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic, complemented
3C2×C11×#481C211yesmaximal, characteristic
4C2×C11×#389C211yesmaximal, characteristic, complemented
5C11×#2059C212yesmaximal, complemented
6C11×#2042C212yesmaximal, complemented
7C11×#1874C211yesmaximal, characteristic
8C11×#1872C211yesmaximal, characteristic, complemented
9C11×#1865C212yesmaximal, complemented
10C11×#1862C212yesmaximal, complemented
11C11×#1817C211yesmaximal, characteristic, complemented
12C11×#529—24no—
13C11×#529—24no—
14C2×C11×#126—21no—
15C2×C11×#125C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C22×C11×C4⋊C4—21no—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C11×#484—24no—
29C11×#481—24no—
30C2×C11×#107C2212yes—
31C2×C11×#106C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#389—21no—
39C11×#389—21no—
40C11×#389C2212yes—
41C11×#389C2212yes—
42C2×C11×#95—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#336C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×#126—28no—
59C11×#125—22no—
60C11×#125—22no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#123—28no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8D414yes—
66C11×#121—22no—
67C11×#121D414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×D4×C11—28no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C11×#117—28no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—44no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—22no—
96C2×C42×C11—22no—
97C2×C42×C11—21no—
98C2×C42×C11D411yescharacteristic
99C2×C42×C11D411yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C11×#107—24no—
103C11×#106—24no—
104C11×#103—24no—
105C11×#103—24no—
106C11×#102—24no—
107C11×#102—24no—
108C11×C22⋊C8—22no—
109C11×C22⋊C8—22no—
110C11×#95—22no—
111C11×#95—22no—
112#24067C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—21no—
114C24×C11C2×D411yescharacteristic
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11C2×D412yes—
119C2×D4×C11—24no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—41no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—44no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—44no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4#4114yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C42×C11—24no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C2×#529C2×C1111yescharacteristic
191C2×#484C2×C1111yescharacteristic, complemented
192C2×#481C2×C1111yescharacteristic
193C2×#389C2×C1111yescharacteristic, complemented
194#2059C2×C1112yescomplemented
195#2042C2×C1112yescomplemented
196#1874C2×C1111yescharacteristic
197#1872C2×C1111yescharacteristic, complemented
198#1865C2×C1112yescomplemented
199#1862C2×C1112yescomplemented
200#1817C2×C1111yescharacteristic, complemented
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11#12012yes—
213C23×C11#13512yes—
214C23×C11#13712yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—24no—
217Q8×C11—42no—
218D4×C11—24no—
219D4×C11—48no—
220D4×C11—42no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
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—44no—
241C2×C4×C11—48no—
242C2×C4×C11—48no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—44no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—84no—
256C2×C4×C11#12012yes—
257C2×C4×C11AGL(1,ℤ/8)12yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4112yes—
261C2×C4×C112−1+412yes—
262C8×C11—42no—
263C8×C11—42no—
264#529—24no—
265#529—24no—
266C2×#126—21no—
267C2×#125C22×C1111yescharacteristic
268C2×#124C22×C1111yescharacteristic
269C2×#123—21no—
270C2×C22⋊Q8C22×C1111yescharacteristic
271C2×#121C22×C1111yescharacteristic
272C2×C4×Q8C22×C1111yescharacteristic
273C2×C4×D4—21no—
274C2×C4×D4C22×C1111yescharacteristic
275C2×#117—21no—
276C22×C4⋊C4—21no—
277C22×C4⋊C4C22×C1111yescharacteristic
278C22×C4⋊C4C22×C1111yescharacteristic
279C22×C42C22×C1111yescharacteristic
280#484—24no—
281#481—24no—
282C2×#107C22×C1112yes—
283C2×#106C22×C1112yes—
284C2×#103C22×C1112yes—
285C2×#103C22×C1112yes—
286C2×#102C22×C1112yes—
287C2×#102C22×C1112yes—
288C2×C22⋊C8C22×C1111yescharacteristic
289C2×C22⋊C8C22×C1111yescharacteristic
290#389—21no—
291#389—21no—
292#389C22×C1112yes—
293#389C22×C1112yes—
294C2×#95—21no—
295#340C22×C1112yes—
296#340C22×C1112yes—
297#336C22×C1112yes—
298#336C22×C1112yes—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11#45214yes—
313C22×C11C2×#12011yescharacteristic
314C22×C11#52511yescharacteristic
315C22×C11#53611yescharacteristic
316C22×C11C2×#13511yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11C2×#13711yescharacteristic
319C22×C11#57511yescharacteristic
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—82no—
330C4×C11#54712yes—
331C4×C11#54712yes—
332C22×Q8C23×C1111yescharacteristic
333C22×D4—21no—
334C22×D4C23×C1111yescharacteristic
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4D4×C1111yescharacteristic
339C23×C4D4×C1111yescharacteristic
340C23×C4C23×C1111yescharacteristic
341C22×C8C23×C1112yes—
342C22×C8C23×C1112yes—
343#126—28no—
344#125—22no—
345#125—22no—
346#124—22no—
347#124—22no—
348#123—28no—
349C22⋊Q8—22no—
350C22⋊Q8D4×C1114yes—
351#121—22no—
352#121D4×C1114yes—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—28no—
356C4×D4—22no—
357C4×D4—22no—
358#117—28no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4C23×C1112yes—
372C2×C4⋊C4C23×C1111yescharacteristic
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C4⋊C4C23×C1112yes—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42—21no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42D4×C1111yescharacteristic
384C2×C42D4×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386C2×C42C23×C1111yescharacteristic
387#107—24no—
388#106—24no—
389#103—24no—
390#103—24no—
391#102—24no—
392#102—24no—
393C22⋊C8—22no—
394C22⋊C8—22no—
395#95—22no—
396#95—22no—
397C2×C11—24no—
398C2×C11—82no—
399C2×C11#240611yescharacteristic
400C2×C11C2×#45211yescharacteristic
401C2×C11#300611yescharacteristic
402C2×C11#310511yescharacteristic
403C2×C11#311711yescharacteristic
404C2×C11#323211yescharacteristic
405C2×C11#323911yescharacteristic
406C24—21no—
407C24C2×D4×C1111yescharacteristic
408C2×Q8—21no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8C2×D4×C1112yes—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4C2×D4×C1112yes—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1112yes—
446C22×C4C2×D4×C1112yes—
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C24×C1111yescharacteristic
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—44no—
466C4⋊C4—42no—
467C4⋊C4—44no—
468C4⋊C4C2×D4×C1112yes—
469C4⋊C4C2×D4×C1112yes—
470C4⋊C4C11×#4114yes—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C42—24no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C11#2406711yescharacteristic, direct product factor, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C11×#12012yes—
496C23C11×#13512yes—
497C23C11×#13712yes—
498C23C22×D4×C1111yescharacteristic
499Q8—24no—
500Q8—42no—
501D4—24no—
502D4—48no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—48no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—84no—
539C2×C4C11×#12012yes—
540C2×C4C11×AGL(1,ℤ/8)12yes—
541C2×C4C22×D4×C1111yescharacteristic
542C2×C4C22×D4×C1111yescharacteristic
543C2×C4C2×C11×#4112yes—
544C2×C4C11×2−1+412yes—
545C8—42no—
546C8—42no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C11×#45214yes—
561C22C2×C11×#12011yescharacteristic
562C22C11×#52511yescharacteristic
563C22C11×#53611yescharacteristic
564C22C2×C11×#13511yescharacteristic
565C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
566C22C2×C11×#13711yescharacteristic
567C22C11×#57511yescharacteristic
568C4—22no—
569C4—22no—
570C4—42no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—44no—
577C4—82no—
578C4C11×#54712yes—
579C4C11×#54712yes—
580C2—24no—
581C2—82no—
582C2C11×#240611yescharacteristic
583C2C2×C11×#45211yescharacteristic
584C2C11×#300611yescharacteristic
585C2C11×#310511yescharacteristic
586C2C11×#311711yescharacteristic
587C2C11×#323211yescharacteristic
588C2C11×#323911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#484C2semidirect
4. C2×C11×#389C2semidirect
5. C11×#2059C2semidirect
6. C11×#2042C2semidirect
8. C11×#1872C2semidirect
9. C11×#1865C2semidirect
10. C11×#1862C2semidirect
11. C11×#1817C2semidirect
112. #24067C11direct (N × H)
191. C2×#484C2×C11semidirect
193. C2×#389C2×C11semidirect
194. #2059C2×C11semidirect
195. #2042C2×C11semidirect
197. #1872C2×C11semidirect
198. #1865C2×C11semidirect
199. #1862C2×C11semidirect
200. #1817C2×C11semidirect
483. C11#24067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4842
C2×C11×#4812
C2×C11×#3892
C11×#20592
C11×#20422
C11×#18742
C11×#18722
C11×#18652
C11×#18622
C11×#18172
#2406711