Finite Group Databasebeta

← C11×#24300 #14601493

Subgroups — C11×#24300 #14601493

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C11×#474C211yesmaximal, characteristic, complemented
4C4×C11×#121C211yesmaximal, characteristic
5C11×#2059C212yesmaximal, complemented
6C11×#2025C212yesmaximal, complemented
7C11×#1988C211yesmaximal, characteristic, complemented
8C11×#1987C211yesmaximal, characteristic, complemented
9C11×#1875C212yesmaximal
10C11×#1854C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
12C11×#533—24no—
13C11×#533—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2212yes—
25C22×C42×C11C2211yescharacteristic
26C11×#476—24no—
27C11×#474—24no—
28C2×C11×#107C2212yes—
29C2×C11×#106C2212yes—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C11×#390C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#386—21no—
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D414yescomplemented
60C11×C4⋊Q8D414yescomplemented
61C11×#125—24no—
62C11×#125—24no—
63C11×C22⋊Q8—28no—
64C11×C22⋊Q8—28no—
65C11×#121—22no—
66C11×#121Q814yescomplemented
67C4×Q8×C11—28no—
68C4×Q8×C11—28no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—44no—
72C11×#117—24no—
73C11×#117—24no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C42×C11—21no—
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×#107—24no—
99C11×#106—24no—
100C11×C4⋊C8—22no—
101C11×C4⋊C8—22no—
102C11×#102—24no—
103C11×#102—24no—
104C11×C22⋊C8—24no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108#24300C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—21no—
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—24no—
112C2×Q8×C11—24no—
113C2×Q8×C11—42no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×D4×C11—24no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11C2×Q812yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×Q812yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2×D414yes—
172C11×C4⋊C4C2×Q812yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C42×C11—28no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—42no—
185C42×C11C2×D412yes—
186C42×C11C2×D412yes—
187C2×#533C2×C1111yescharacteristic, complemented
188C2×#476C2×C1111yescharacteristic, complemented
189C2×#474C2×C1111yescharacteristic, complemented
190C4×#121C2×C1111yescharacteristic
191#2059C2×C1112yescomplemented
192#2025C2×C1112yescomplemented
193#1988C2×C1111yescharacteristic, complemented
194#1987C2×C1111yescharacteristic, complemented
195#1875C2×C1112yes—
196#1854C2×C1112yescomplemented
197#1797C2×C1111yescharacteristic, complemented
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—22no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11C22⋊Q812yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—48no—
214Q8×C11—48no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—48no—
218D4×C11—41no—
219D4×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—44no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—44no—
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—84no—
252C2×C4×C11#12012yes—
253C2×C4×C11#12012yes—
254C2×C4×C11C22⋊Q812yes—
255C2×C4×C11#13512yes—
256C2×C4×C11AGL(1,ℤ/8)12yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C8×C11—42no—
264C8×C11—42no—
265#533—24no—
266#533—24no—
267C2×C4⋊Q8C22×C1111yescharacteristic
268C2×C4⋊Q8C22×C1111yescharacteristic
269C2×#125C22×C1112yes—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—21no—
272C2×#121C22×C1111yescharacteristic
273C2×C4×Q8—21no—
274C2×C4×Q8—21no—
275C2×C4×D4—21no—
276C2×C4×D4C22×C1111yescharacteristic
277C2×#117C22×C1112yes—
278C22×C42C22×C1111yescharacteristic
279#476—24no—
280#474—24no—
281C2×#107C22×C1112yes—
282C2×#106C22×C1112yes—
283C2×C4⋊C8C22×C1111yescharacteristic
284C2×C4⋊C8C22×C1111yescharacteristic
285C2×#102C22×C1112yes—
286C2×#102C22×C1112yes—
287C2×C22⋊C8C22×C1112yes—
288#390C22×C1111yescharacteristic
289#389C22×C1111yescharacteristic
290#388—21no—
291#386—21no—
292#380C22×C1111yescharacteristic
293C4×C4⋊C4C22×C1111yescharacteristic
294C4×C22⋊C4—21no—
295#340C22×C1112yes—
296#340C22×C1112yes—
297#340C22×C1112yes—
298#340C22×C1112yes—
299#336C22×C1112yes—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11C2×#12011yescharacteristic
315C22×C11C2×C22⋊Q811yescharacteristic
316C22×C11#53611yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C11#57511yescharacteristic
320C22×C11#57511yescharacteristic
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—41no—
325C4×C11—44no—
326C4×C11—41no—
327C4×C11—44no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11#44914yes—
331C4×C11#54811yescharacteristic
332C4×C11#54811yescharacteristic
333C4×C11D4×Q811yescharacteristic
334C4×C11D4×Q811yescharacteristic
335C22×Q8—21no—
336C22×Q8—21no—
337C22×D4—21no—
338C22×D4C23×C1111yescharacteristic
339C23×C4—21no—
340C23×C4D4×C1111yescharacteristic
341C23×C4D4×C1111yescharacteristic
342C23×C4C23×C1111yescharacteristic
343C22×C8C23×C1112yes—
344C22×C8C23×C1112yes—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8D4×C1114yescomplemented
348C4⋊Q8D4×C1114yescomplemented
349#125—24no—
350#125—24no—
351C22⋊Q8—28no—
352C22⋊Q8—28no—
353#121—22no—
354#121Q8×C1114yescomplemented
355C4×Q8—28no—
356C4×Q8—28no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—44no—
360#117—24no—
361#117—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1111yescharacteristic
369C2×C4⋊C4C23×C1112yes—
370C2×C4⋊C4C23×C1112yes—
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—21no—
382C2×C42D4×C1111yescharacteristic
383C2×C42D4×C1111yescharacteristic
384C2×C42C23×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386#107—24no—
387#106—24no—
388C4⋊C8—22no—
389C4⋊C8—22no—
390#102—24no—
391#102—24no—
392C22⋊C8—24no—
393#95—21no—
394#95—21no—
395#95—21no—
396C2×C11—42no—
397C2×C11—82no—
398C2×C11#240911yescharacteristic
399C2×C11C2×#44911yescharacteristic
400C2×C11#300511yescharacteristic
401C2×C11#307611yescharacteristic
402C2×C11#307711yescharacteristic
403C2×C11#323311yescharacteristic
404C2×C11#323511yescharacteristic
405C24—21no—
406C24C2×D4×C1111yescharacteristic
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—42no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—42no—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4C2×Q8×C1112yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×Q8×C1112yes—
446C22×C4C11×#4112yes—
447C22×C4C24×C1111yescharacteristic
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C4⋊C4—28no—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4C2×D4×C1114yes—
467C4⋊C4C2×D4×C1114yes—
468C4⋊C4C2×Q8×C1112yes—
469C22⋊C4—28no—
470C22⋊C4—24no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C42—28no—
476C42—22no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—42no—
481C42C2×D4×C1112yes—
482C42C2×D4×C1112yes—
483C11#2430011yescharacteristic, direct product factor, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C11×C22⋊Q812yes—
498C23C22×D4×C1111yescharacteristic
499Q8—48no—
500Q8—48no—
501D4—22no—
502D4—22no—
503D4—48no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4C11×#12012yes—
539C2×C4C11×#12012yes—
540C2×C4C11×C22⋊Q812yes—
541C2×C4C11×#13512yes—
542C2×C4C11×AGL(1,ℤ/8)12yes—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×Q8×C1111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C11×2−1+411yescharacteristic
548C2×C4C11×2−1+411yescharacteristic
549C8—42no—
550C8—42no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C2×C11×#12011yescharacteristic
566C22C2×C11×C22⋊Q811yescharacteristic
567C22C11×#53611yescharacteristic
568C22C2×C11×#13511yescharacteristic
569C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
570C22C11×#57511yescharacteristic
571C22C11×#57511yescharacteristic
572C4—22no—
573C4—22no—
574C4—41no—
575C4—44no—
576C4—41no—
577C4—44no—
578C4—42no—
579C4—81no—
580C4—81no—
581C4C11×#44914yes—
582C4C11×#54811yescharacteristic
583C4C11×#54811yescharacteristic
584C4D4×Q8×C1111yescharacteristic
585C4D4×Q8×C1111yescharacteristic
586C2—42no—
587C2—82no—
588C2C11×#240911yescharacteristic
589C2C2×C11×#44911yescharacteristic
590C2C11×#300511yescharacteristic
591C2C11×#307611yescharacteristic
592C2C11×#307711yescharacteristic
593C2C11×#323311yescharacteristic
594C2C11×#323511yescharacteristic
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
1. C2×C11×#533C2semidirect
2. C2×C11×#476C2semidirect
3. C2×C11×#474C2semidirect
5. C11×#2059C2semidirect
6. C11×#2025C2semidirect
7. C11×#1988C2semidirect
8. C11×#1987C2semidirect
10. C11×#1854C2semidirect
11. C11×#1797C2semidirect
59. C11×C4⋊Q8D4semidirect
60. C11×C4⋊Q8D4semidirect
66. C11×#121Q8semidirect
108. #24300C11direct (N × H)
187. C2×#533C2×C11semidirect
188. C2×#476C2×C11semidirect
189. C2×#474C2×C11semidirect
191. #2059C2×C11semidirect
192. #2025C2×C11semidirect
193. #1988C2×C11semidirect
194. #1987C2×C11semidirect
196. #1854C2×C11semidirect
197. #1797C2×C11semidirect
347. C4⋊Q8D4×C11semidirect
348. C4⋊Q8D4×C11semidirect
354. #121Q8×C11semidirect
483. C11#24300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4762
C2×C11×#4742
C4×C11×#1212
C11×#20592
C11×#20252
C11×#19882
C11×#19872
C11×#18752
C11×#18542
C11×#17972
#2430011