Finite Group Databasebeta

← C11×#11060 #14588253

Subgroups — C11×#11060 #14588253

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#104C211yesmaximal, characteristic
2C11×#2896C211yesmaximal, characteristic
3C2×C11×#410C211yesmaximal, characteristic
4C11×#2296C211yesmaximal, characteristic, complemented
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C11×#1733C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×C11×#104—22no—
16C2×C11×#104—22no—
17C2×C11×#104—22no—
18C11×#419C412yescomplemented
19C11×#418C412yescomplemented
20C11×#417—22no—
21C11×#416—22no—
22C11×#410—22no—
23C11×#410—22no—
24C2×C11×#99—22no—
25C11×#389—22no—
26C11×#385—22no—
27C4×C11×C4⋊C4—22no—
28C11×#344—22no—
29C11×#339—22no—
30C11×#339—22no—
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41D412yes—
42C2×C11×#41Q812yes—
43C22×Q8×C11C2×C411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
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×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16C2×C412yes—
60C2×C11×M16D412yes—
61C22×C8×C11—21no—
62C22×C8×C11—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×#117C2×C412yes—
73C11×#117D412yes—
74C11×#117D412yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D412yes—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11D412yes—
91C11×#104—28no—
92C11×#103—24no—
93C11×#102—24no—
94C11×#99—28no—
95C11×#95—24no—
96#11060C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C4⋊C412yescomplemented
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11C4⋊C412yescomplemented
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—44no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×Q811yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—48no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4C22⋊C414yes—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—41no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—41no—
194C42×C11—41no—
195C42×C11—41no—
196C42×C11—41no—
197C42×C11—41no—
198C22×#104C2×C1111yescharacteristic
199#2896C2×C1111yescharacteristic
200C2×#410C2×C1111yescharacteristic
201#2296C2×C1111yescharacteristic, complemented
202C2×#344C2×C1111yescharacteristic, complemented
203#1733C2×C1111yescharacteristic, complemented
204C2×#339C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—82no—
210C23×C11C4×D411yescharacteristic
211C23×C11#12011yescharacteristic
212C23×C11#12011yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11#12111yescharacteristic
215C23×C11C22⋊Q811yescharacteristic
216C23×C11#12411yescharacteristic
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—41no—
220Q8×C11—41no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—82no—
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C4⋊C411yescharacteristic
249C2×C4×C11#11711yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11C22⋊Q811yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11C22⋊Q811yescharacteristic
264C2×C4×C11C22⋊Q811yescharacteristic
265C2×C4×C11#12311yescharacteristic
266C2×C4×C11#12311yescharacteristic
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12311yescharacteristic
269C2×C4×C11#12311yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12411yescharacteristic
272C2×C4×C11#12611yescharacteristic
273C2×C4×C11#12611yescharacteristic
274C2×C4×C11#12711yescharacteristic
275C8×C11—42no—
276C8×C11—42no—
277C22×#41C22×C1111yescharacteristic
278C22×M16C22×C1111yescharacteristic
279C22×M16C22×C1111yescharacteristic
280C2×#117C22×C1111yescharacteristic
281C2×#117C22×C1111yescharacteristic
282C2×#117C22×C1111yescharacteristic
283C22×C42C22×C1111yescharacteristic
284C2×#104—22no—
285C2×#104—22no—
286C2×#104—22no—
287#419C4×C1112yescomplemented
288#418C4×C1112yescomplemented
289#417—22no—
290#416—22no—
291#410—22no—
292#410—22no—
293C2×#99—22no—
294#389—22no—
295#385—22no—
296C4×C4⋊C4—22no—
297#344—22no—
298#339—22no—
299#339—22no—
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—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11#38511yescharacteristic
312C22×C11#38611yescharacteristic
313C22×C11#38811yescharacteristic
314C22×C11#39211yescharacteristic
315C22×C11#39311yescharacteristic
316C22×C11#39411yescharacteristic
317C22×C11#39611yescharacteristic
318C4×C11—44no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11—82no—
322C4×C11—82no—
323C4×C11#38011yescharacteristic
324C4×C11#38511yescharacteristic
325C4×C11#38811yescharacteristic
326C4×C11#39011yescharacteristic
327C4×C11#39411yescharacteristic
328C4×C11#39611yescharacteristic
329C4×C11#39711yescharacteristic
330C4×C11#39911yescharacteristic
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41D4×C1112yes—
342C2×#41Q8×C1112yes—
343C22×Q8C2×C4×C1111yescharacteristic
344C22×D4—21no—
345C22×D4C2×C4×C1111yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4C23×C1111yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16C2×C4×C1112yes—
360C2×M16D4×C1112yes—
361C22×C8—21no—
362C22×C8—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117C2×C4×C1112yes—
373#117D4×C1112yes—
374#117D4×C1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4D4×C1112yes—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4D4×C1112yes—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42D4×C1112yes—
391#104—28no—
392#103—24no—
393#102—24no—
394#99—28no—
395#95—24no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—82no—
403C2×C11#143911yescharacteristic
404C2×C11#190612yes—
405C24—21no—
406C24C2×D4×C1111yescharacteristic
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C11×C4⋊C412yescomplemented
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C11×C4⋊C412yescomplemented
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—44no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4C22×C4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×Q8×C1111yescharacteristic
463C22×C4C11×#4111yescharacteristic
464C22×C4C11×#4111yescharacteristic
465C22×C4C11×#4111yescharacteristic
466C22×C4C11×#4111yescharacteristic
467C22×C4C11×#4111yescharacteristic
468C22×C4C11×#4111yescharacteristic
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—41no—
474M16—41no—
475M16—41no—
476M16—41no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—48no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C11×C22⋊C414yes—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—22no—
500C42—22no—
501C42—41no—
502C42—41no—
503C42—41no—
504C42—41no—
505C42—41no—
506C11#1106011yescharacteristic, direct product factor, Sylow
507C23—22no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—82no—
512C23C4×D4×C1111yescharacteristic
513C23C11×#12011yescharacteristic
514C23C11×#12011yescharacteristic
515C23C11×#12111yescharacteristic
516C23C11×#12111yescharacteristic
517C23C11×C22⋊Q811yescharacteristic
518C23C11×#12411yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523D4—22no—
524D4—22no—
525D4—42no—
526D4—42no—
527D4—42no—
528D4—42no—
529D4—41no—
530D4—41no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—82no—
549C2×C4C2×C11×C22⋊C411yescharacteristic
550C2×C4C2×C11×C4⋊C411yescharacteristic
551C2×C4C11×#11711yescharacteristic
552C2×C4C4×D4×C1111yescharacteristic
553C2×C4C4×D4×C1111yescharacteristic
554C2×C4C4×D4×C1111yescharacteristic
555C2×C4C11×#12011yescharacteristic
556C2×C4C11×#12111yescharacteristic
557C2×C4C11×#12111yescharacteristic
558C2×C4C11×#12111yescharacteristic
559C2×C4C11×#12111yescharacteristic
560C2×C4C11×#12111yescharacteristic
561C2×C4C11×#12111yescharacteristic
562C2×C4C11×C22⋊Q811yescharacteristic
563C2×C4C11×C22⋊Q811yescharacteristic
564C2×C4C11×C22⋊Q811yescharacteristic
565C2×C4C11×C22⋊Q811yescharacteristic
566C2×C4C11×C22⋊Q811yescharacteristic
567C2×C4C11×#12311yescharacteristic
568C2×C4C11×#12311yescharacteristic
569C2×C4C11×#12311yescharacteristic
570C2×C4C11×#12311yescharacteristic
571C2×C4C11×#12311yescharacteristic
572C2×C4C11×#12411yescharacteristic
573C2×C4C11×#12411yescharacteristic
574C2×C4C11×#12611yescharacteristic
575C2×C4C11×#12611yescharacteristic
576C2×C4C11×#12711yescharacteristic
577C8—42no—
578C8—42no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22C11×#38511yescharacteristic
591C22C11×#38611yescharacteristic
592C22C11×#38811yescharacteristic
593C22C11×#39211yescharacteristic
594C22C11×#39311yescharacteristic
595C22C11×#39411yescharacteristic
596C22C11×#39611yescharacteristic
597C4—44no—
598C4—44no—
599C4—42no—
600C4—82no—
601C4—82no—
602C4C11×#38011yescharacteristic
603C4C11×#38511yescharacteristic
604C4C11×#38811yescharacteristic
605C4C11×#39011yescharacteristic
606C4C11×#39411yescharacteristic
607C4C11×#39611yescharacteristic
608C4C11×#39711yescharacteristic
609C4C11×#39911yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—82no—
617C2C11×#143911yescharacteristic
618C2C11×#190612yes—
subgroupG/H
centerC2×C4×C11#121
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#386
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2296C2semidirect
5. C2×C11×#344C2semidirect
6. C11×#1733C2semidirect
7. C2×C11×#339C2semidirect
18. C11×#419C4semidirect
19. C11×#418C4semidirect
96. #11060C11direct (N × H)
120. C2×Q8×C11C4⋊C4semidirect
132. C2×D4×C11C4⋊C4semidirect
201. #2296C2×C11semidirect
202. C2×#344C2×C11semidirect
203. #1733C2×C11semidirect
204. C2×#339C2×C11semidirect
287. #419C4×C11semidirect
288. #418C4×C11semidirect
428. C2×Q8C11×C4⋊C4semidirect
440. C2×D4C11×C4⋊C4semidirect
506. C11#11060direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1042
C11×#28962
C2×C11×#4102
C11×#22962
C2×C11×#3442
C11×#17332
C2×C11×#3392
#1106011