Finite Group Databasebeta

← C11×#23458 #14600651

Subgroups — C11×#23458 #14600651

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C2×C11×#417C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C11×#2311C211yesmaximal, characteristic
5C11×#2026C212yesmaximal, complemented
6C11×#2025C212yesmaximal, complemented
7C11×#2024C212yesmaximal, complemented
8C11×#2023C212yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C2×C11×#340C211yesmaximal, characteristic, complemented
11C11×#1729C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C11×#544—24no—
16C11×#544—24no—
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×#125—21no—
20C2×C11×#125C2212yes—
21C2×C11×C22⋊Q8—22no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C11×#417—24no—
27C11×#416—24no—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2212yes—
34C11×#391C2212yes—
35C11×#390C2212yes—
36C11×#386—22no—
37C11×#380—21no—
38C11×#380—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41Q814yescomplemented
51C22×Q8×C11—22no—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C2×C11×M16—22no—
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8—24no—
70C11×C4⋊Q8—24no—
71C11×#125—28no—
72C11×#125—24no—
73C11×#125—24no—
74C11×C22⋊Q8—216no—
75C11×#117—22no—
76C11×#117—22no—
77C11×#117—22no—
78C11×#117D414yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4D414yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—21no—
99C2×C42×C11C2312yes—
100C11×#103—22no—
101C11×#103—22no—
102C11×#103—24no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—24no—
106C11×#95—22no—
107C11×#95—22no—
108#23458C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—21no—
110C24×C11C2×D411yescharacteristic
111C11×#41—28no—
112C11×#41—28no—
113C11×#41—44no—
114C11×#41—44no—
115C2×Q8×C11—28no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—82no—
122C2×Q8×C11—82no—
123C2×Q8×C11C2×Q812yes—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11C2×Q812yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—81no—
144C22×C4×C11—81no—
145C22×C4×C11—81no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×Q812yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C11×M16—44no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—22no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—44no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C2×D414yes—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—82no—
186C11×C22⋊C4—82no—
187C42×C11—24no—
188C42×C11—22no—
189C42×C11—22no—
190C2×#544C2×C1111yescharacteristic, complemented
191C2×#417C2×C1111yescharacteristic
192C2×#416C2×C1111yescharacteristic
193#2311C2×C1111yescharacteristic
194#2026C2×C1112yescomplemented
195#2025C2×C1112yescomplemented
196#2024C2×C1112yescomplemented
197#2023C2×C1112yescomplemented
198#1736C2×C1111yescharacteristic, complemented
199C2×#340C2×C1111yescharacteristic, complemented
200#1729C2×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×C11C22⋊Q812yes—
214C23×C11#12412yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—88no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—48no—
224D4×C11—41no—
225D4×C11—41no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—48no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—84no—
249C2×C4×C11—84no—
250C2×C4×C11#12012yes—
251C2×C4×C11C22⋊Q814yes—
252C2×C4×C11C22⋊Q814yes—
253C2×C4×C11C22⋊Q812yes—
254C2×C4×C11#12414yes—
255C2×C4×C11#12414yes—
256C2×C4×C11#12412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—42no—
266C22×#41C22×C1111yescharacteristic
267C22×M16C22×C1111yescharacteristic
268C23×C8C22×C1111yescharacteristic
269#544—24no—
270#544—24no—
271C2×C4⋊Q8—21no—
272C2×C4⋊Q8C22×C1112yes—
273C2×#125—21no—
274C2×#125C22×C1112yes—
275C2×C22⋊Q8—22no—
276C2×#117C22×C1111yescharacteristic
277C2×#117C22×C1111yescharacteristic
278C22×C4⋊C4C22×C1111yescharacteristic
279C22×C4⋊C4C22×C1111yescharacteristic
280#417—24no—
281#416—24no—
282C2×#103C22×C1111yescharacteristic
283C2×#103C22×C1111yescharacteristic
284C2×#103C22×C1112yes—
285C2×#102C22×C1111yescharacteristic
286C2×#102C22×C1111yescharacteristic
287C2×#102C22×C1112yes—
288#391C22×C1112yes—
289#390C22×C1112yes—
290#386—22no—
291#380—21no—
292#380—21no—
293#340C22×C1112yes—
294#340C22×C1112yes—
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#39314yes—
313C22×C11C2×#12011yescharacteristic
314C22×C11C2×C22⋊Q811yescharacteristic
315C22×C11C2×#12411yescharacteristic
316C22×C11#57611yescharacteristic
317C22×C11#57711yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57811yescharacteristic
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—82no—
327C4×C11#39314yes—
328C4×C11C2×C22⋊Q811yescharacteristic
329C4×C11C2×C22⋊Q811yescharacteristic
330C4×C11C2×#12411yescharacteristic
331C4×C11C2×#12411yescharacteristic
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41Q8×C1114yescomplemented
338C22×Q8—22no—
339C22×Q8C23×C1111yescharacteristic
340C22×D4—21no—
341C22×D4C23×C1111yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4C23×C1111yescharacteristic
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8C23×C1111yescharacteristic
353C22×C8C23×C1111yescharacteristic
354C22×C8C23×C1112yes—
355C4⋊Q8—28no—
356C4⋊Q8—24no—
357C4⋊Q8—24no—
358#125—28no—
359#125—24no—
360#125—24no—
361C22⋊Q8—216no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117D4×C1114yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C1111yescharacteristic
375C2×C4⋊C4D4×C1111yescharacteristic
376C2×C4⋊C4D4×C1114yes—
377C2×C4⋊C4C23×C1112yes—
378C2×C4⋊C4C23×C1112yes—
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4D4×C1112yes—
385C2×C42—21no—
386C2×C42C23×C1112yes—
387#103—22no—
388#103—22no—
389#103—24no—
390#102—22no—
391#102—22no—
392#102—24no—
393#95—22no—
394#95—22no—
395C2×C11—24no—
396C2×C11—82no—
397C2×C11C2×#39311yescharacteristic
398C2×C11#301211yescharacteristic
399C2×C11#301311yescharacteristic
400C2×C11#308311yescharacteristic
401C2×C11#308411yescharacteristic
402C2×C11#313611yescharacteristic
403C2×C11#313711yescharacteristic
404C24—21no—
405C24C2×D4×C1111yescharacteristic
406#41—28no—
407#41—28no—
408#41—44no—
409#41—44no—
410C2×Q8—28no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—82no—
417C2×Q8—82no—
418C2×Q8C2×Q8×C1112yes—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×Q8×C1112yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—81no—
439C22×C4—81no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4C2×D4×C1112yes—
443C22×C4C2×D4×C1112yes—
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1112yes—
446C22×C4C2×D4×C1112yes—
447C22×C4C2×Q8×C1112yes—
448C22×C4C11×#4112yes—
449C22×C4C11×#4112yes—
450C22×C4C11×#4112yes—
451C22×C4C24×C1111yescharacteristic
452M16—44no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—44no—
463C4⋊C4—28no—
464C4⋊C4—28no—
465C4⋊C4—28no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—42no—
475C4⋊C4C2×D4×C1114yes—
476C4⋊C4C2×D4×C1112yes—
477C4⋊C4C2×D4×C1112yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—82no—
481C22⋊C4—82no—
482C42—24no—
483C42—22no—
484C42—22no—
485C11#2345811yescharacteristic, direct product factor, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C11×#12012yes—
498C23C11×C22⋊Q812yes—
499C23C11×#12412yes—
500C23C22×D4×C1111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505Q8—88no—
506D4—22no—
507D4—22no—
508D4—48no—
509D4—41no—
510D4—41no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4—84no—
535C2×C4C11×#12012yes—
536C2×C4C11×C22⋊Q814yes—
537C2×C4C11×C22⋊Q814yes—
538C2×C4C11×C22⋊Q812yes—
539C2×C4C11×#12414yes—
540C2×C4C11×#12414yes—
541C2×C4C11×#12412yes—
542C2×C4C22×D4×C1111yescharacteristic
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×Q8×C1111yescharacteristic
545C2×C4C2×C11×#4111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C2×C11×#4111yescharacteristic
548C8—41no—
549C8—41no—
550C8—42no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C11×#39314yes—
565C22C2×C11×#12011yescharacteristic
566C22C2×C11×C22⋊Q811yescharacteristic
567C22C2×C11×#12411yescharacteristic
568C22C11×#57611yescharacteristic
569C22C11×#57711yescharacteristic
570C22C11×#57711yescharacteristic
571C22C11×#57811yescharacteristic
572C4—42no—
573C4—42no—
574C4—44no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4C11×#39314yes—
580C4C2×C11×C22⋊Q811yescharacteristic
581C4C2×C11×C22⋊Q811yescharacteristic
582C4C2×C11×#12411yescharacteristic
583C4C2×C11×#12411yescharacteristic
584C2—24no—
585C2—82no—
586C2C2×C11×#39311yescharacteristic
587C2C11×#301211yescharacteristic
588C2C11×#301311yescharacteristic
589C2C11×#308311yescharacteristic
590C2C11×#308411yescharacteristic
591C2C11×#313611yescharacteristic
592C2C11×#313711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#544C2semidirect
5. C11×#2026C2semidirect
6. C11×#2025C2semidirect
7. C11×#2024C2semidirect
8. C11×#2023C2semidirect
9. C11×#1736C2semidirect
10. C2×C11×#340C2semidirect
11. C11×#1729C2semidirect
50. C2×C11×#41Q8semidirect
108. #23458C11direct (N × H)
190. C2×#544C2×C11semidirect
194. #2026C2×C11semidirect
195. #2025C2×C11semidirect
196. #2024C2×C11semidirect
197. #2023C2×C11semidirect
198. #1736C2×C11semidirect
199. C2×#340C2×C11semidirect
200. #1729C2×C11semidirect
337. C2×#41Q8×C11semidirect
485. C11#23458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#4172
C2×C11×#4162
C11×#23112
C11×#20262
C11×#20252
C11×#20242
C11×#20232
C11×#17362
C2×C11×#3402
C11×#17292
#2345811