Finite Group Databasebeta

← C11×#11129 #14588322

Subgroups — C11×#11129 #14588322

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2911C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C2×C11×#418C211yesmaximal, characteristic
4C11×#2309C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C11×#1740C211yesmaximal, characteristic, complemented
7C11×#1733C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#428—22no—
16C11×#428—22no—
17C11×#427—22no—
18C11×#418—22no—
19C11×#418—22no—
20C11×#418—22no—
21C11×#418C414yescomplemented
22C2×C11×#102—22no—
23C2×C11×#102—22no—
24C11×#390—22no—
25C11×#390—22no—
26C11×#379—22no—
27C11×#344—22no—
28C11×#342—22no—
29C11×#339—22no—
30C25×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C412yes—
43C22×D4×C11D412yes—
44C22×D4×C11Q812yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—21no—
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16C2×C412yes—
56C2×C11×M16D412yes—
57C2×C11×M16D412yes—
58C22×C8×C11—21no—
59C22×C8×C11D412yes—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—21no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117C2×C412yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C11×#107—24no—
90C11×#106—24no—
91C11×#102—28no—
92C11×#102—28no—
93#11129C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—41no—
98C24×C11—41no—
99C24×C11—41no—
100C24×C11—41no—
101C24×C11—84no—
102C24×C11C2×D411yescharacteristic
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11C4⋊C414yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—41no—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×Q811yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C11×M16—22no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—41no—
156C11×M16—41no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—41no—
161C2×C8×C11—41no—
162C2×C8×C11C22⋊C414yescomplemented
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—88no—
180C42×C11—22no—
181C42×C11—41no—
182C42×C11—41no—
183C42×C11—41no—
184C42×C11—41no—
185C42×C11—41no—
186C42×C11—41no—
187C42×C11—41no—
188#2911C2×C1111yescharacteristic, complemented
189C2×#418C2×C1111yescharacteristic
190C2×#418C2×C1111yescharacteristic
191#2309C2×C1111yescharacteristic
192C2×#344C2×C1111yescharacteristic, complemented
193#1740C2×C1111yescharacteristic, complemented
194#1733C2×C1111yescharacteristic, complemented
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—48no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11C4×D411yescharacteristic
211C23×C11#12011yescharacteristic
212C23×C11#12111yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11C22⋊Q811yescharacteristic
215C23×C11#12311yescharacteristic
216C23×C11#12711yescharacteristic
217D4×C11—24no—
218D4×C11—24no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—82no—
232C2×C4×C11—82no—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C2×C4⋊C411yescharacteristic
235C2×C4×C11#11711yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11C22⋊Q811yescharacteristic
248C2×C4×C11C22⋊Q811yescharacteristic
249C2×C4×C11C22⋊Q811yescharacteristic
250C2×C4×C11C22⋊Q811yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11#12311yescharacteristic
253C2×C4×C11#12311yescharacteristic
254C2×C4×C11#12311yescharacteristic
255C2×C4×C11#12311yescharacteristic
256C2×C4×C11#12411yescharacteristic
257C2×C4×C11#12411yescharacteristic
258C2×C4×C11#12411yescharacteristic
259C2×C4×C11#12611yescharacteristic
260C2×C4×C11#12611yescharacteristic
261C8×C11—24no—
262C8×C11—42no—
263C23×D4C22×C1111yescharacteristic
264C22×M16C22×C1111yescharacteristic
265C22×M16C22×C1111yescharacteristic
266C2×#117C22×C1111yescharacteristic
267C2×#117C22×C1111yescharacteristic
268C2×#117C22×C1111yescharacteristic
269C2×#117C22×C1111yescharacteristic
270#428—22no—
271#428—22no—
272#427—22no—
273#418—22no—
274#418—22no—
275#418—22no—
276#418C4×C1114yescomplemented
277C2×#102—22no—
278C2×#102—22no—
279#390—22no—
280#390—22no—
281#379—22no—
282#344—22no—
283#342—22no—
284#339—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—48no—
293C22×C11—44no—
294C22×C11—84no—
295C22×C11—84no—
296C22×C11—84no—
297C22×C11—84no—
298C22×C11—84no—
299C22×C11—84no—
300C22×C11#38511yescharacteristic
301C22×C11#38811yescharacteristic
302C22×C11#39011yescharacteristic
303C22×C11#39211yescharacteristic
304C22×C11#39411yescharacteristic
305C22×C11#39611yescharacteristic
306C22×C11#39911yescharacteristic
307C4×C11—82no—
308C4×C11—82no—
309C4×C11—82no—
310C4×C11—82no—
311C4×C11#38011yescharacteristic
312C4×C11#38511yescharacteristic
313C4×C11#38611yescharacteristic
314C4×C11#38811yescharacteristic
315C4×C11#39311yescharacteristic
316C4×C11#39411yescharacteristic
317C4×C11#39611yescharacteristic
318C4×C11#39711yescharacteristic
319C25—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4C2×C4×C1112yes—
332C22×D4D4×C1112yes—
333C22×D4Q8×C1112yes—
334C23×C4C23×C1111yescharacteristic
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16C2×C4×C1112yes—
345C2×M16D4×C1112yes—
346C2×M16D4×C1112yes—
347C22×C8—21no—
348C22×C8D4×C1112yes—
349#117—21no—
350#117—21no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117C2×C4×C1112yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C1112yes—
368C2×C4⋊C4D4×C1112yes—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4D4×C1112yes—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378#107—24no—
379#106—24no—
380#102—28no—
381#102—28no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—21no—
388C2×C11—84no—
389C2×C11#143911yescharacteristic
390C2×C11#200812yes—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—41no—
398C24—84no—
399C24C2×D4×C1111yescharacteristic
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4C11×C4⋊C414yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—41no—
432C22×C4C22×C4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×Q8×C1111yescharacteristic
440C22×C4C11×#4111yescharacteristic
441C22×C4C11×#4111yescharacteristic
442C22×C4C11×#4111yescharacteristic
443C22×C4C11×#4111yescharacteristic
444C22×C4C11×#4111yescharacteristic
445C22×C4C11×#4111yescharacteristic
446M16—22no—
447M16—22no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—41no—
453M16—41no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8C11×C22⋊C414yescomplemented
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—88no—
477C42—22no—
478C42—41no—
479C42—41no—
480C42—41no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42—41no—
485C11#1112911yescharacteristic, direct product factor, Sylow
486C23—24no—
487C23—42no—
488C23—48no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—84no—
496C23—84no—
497C23—84no—
498C23—84no—
499C23—84no—
500C23—84no—
501C23C4×D4×C1111yescharacteristic
502C23C11×#12011yescharacteristic
503C23C11×#12111yescharacteristic
504C23C11×#12111yescharacteristic
505C23C11×C22⋊Q811yescharacteristic
506C23C11×#12311yescharacteristic
507C23C11×#12711yescharacteristic
508D4—24no—
509D4—24no—
510D4—42no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4C2×C11×C22⋊C411yescharacteristic
525C2×C4C2×C11×C4⋊C411yescharacteristic
526C2×C4C11×#11711yescharacteristic
527C2×C4C4×D4×C1111yescharacteristic
528C2×C4C4×D4×C1111yescharacteristic
529C2×C4C4×D4×C1111yescharacteristic
530C2×C4C11×#12011yescharacteristic
531C2×C4C11×#12011yescharacteristic
532C2×C4C11×#12111yescharacteristic
533C2×C4C11×#12111yescharacteristic
534C2×C4C11×#12111yescharacteristic
535C2×C4C11×#12111yescharacteristic
536C2×C4C11×#12111yescharacteristic
537C2×C4C11×#12111yescharacteristic
538C2×C4C11×C22⋊Q811yescharacteristic
539C2×C4C11×C22⋊Q811yescharacteristic
540C2×C4C11×C22⋊Q811yescharacteristic
541C2×C4C11×C22⋊Q811yescharacteristic
542C2×C4C11×C22⋊Q811yescharacteristic
543C2×C4C11×#12311yescharacteristic
544C2×C4C11×#12311yescharacteristic
545C2×C4C11×#12311yescharacteristic
546C2×C4C11×#12311yescharacteristic
547C2×C4C11×#12411yescharacteristic
548C2×C4C11×#12411yescharacteristic
549C2×C4C11×#12411yescharacteristic
550C2×C4C11×#12611yescharacteristic
551C2×C4C11×#12611yescharacteristic
552C8—24no—
553C8—42no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—48no—
562C22—44no—
563C22—84no—
564C22—84no—
565C22—84no—
566C22—84no—
567C22—84no—
568C22—84no—
569C22C11×#38511yescharacteristic
570C22C11×#38811yescharacteristic
571C22C11×#39011yescharacteristic
572C22C11×#39211yescharacteristic
573C22C11×#39411yescharacteristic
574C22C11×#39611yescharacteristic
575C22C11×#39911yescharacteristic
576C4—82no—
577C4—82no—
578C4—82no—
579C4—82no—
580C4C11×#38011yescharacteristic
581C4C11×#38511yescharacteristic
582C4C11×#38611yescharacteristic
583C4C11×#38811yescharacteristic
584C4C11×#39311yescharacteristic
585C4C11×#39411yescharacteristic
586C4C11×#39611yescharacteristic
587C4C11×#39711yescharacteristic
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—84no—
595C2C11×#143911yescharacteristic
596C2C11×#200812yes—
subgroupG/H
center, socleC22×C11#392
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2911C2semidirect
5. C2×C11×#344C2semidirect
6. C11×#1740C2semidirect
7. C11×#1733C2semidirect
21. C11×#418C4semidirect
93. #11129C11direct (N × H)
162. C2×C8×C11C22⋊C4semidirect
188. #2911C2×C11semidirect
192. C2×#344C2×C11semidirect
193. #1740C2×C11semidirect
194. #1733C2×C11semidirect
276. #418C4×C11semidirect
459. C2×C8C11×C22⋊C4semidirect
485. C11#11129direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29112
C2×C11×#4182
C11×#23092
C2×C11×#3442
C11×#17402
C11×#17332
#1112911