Finite Group Databasebeta

← C11×#32963 #14610156

Subgroups — C11×#32963 #14610156

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#520C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C2×C11×#474C211yesmaximal, characteristic, complemented
4C11×#2628C211yesmaximal, characteristic, complemented
5C11×#1863C212yesmaximal, complemented
6C11×#1862C212yesmaximal, complemented
7C11×#1852C212yesmaximal, complemented
8C11×#1805C211yesmaximal, characteristic, complemented
9C11×#1804C211yesmaximal, characteristic, complemented
10C11×#1798C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal
12C22×C11×#41C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C11×#520—24no—
15C11×#520—24no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4—21no—
25C22×C11×C4⋊C4C2211yescharacteristic
26C11×#477—24no—
27C11×#474—24no—
28C2×C11×#107C2212yes—
29C2×C11×#107C2212yes—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×C22⋊C8C2212yes—
37C11×#400—21no—
38C11×#399—21no—
39C11×#395—21no—
40C11×#393—21no—
41C11×#389C2212yes—
42C11×#382C2211yescharacteristic
43C11×#380C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41Q814yescomplemented
53C22×Q8×C11—21no—
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11D414yes—
70C4×D4×C11—28no—
71C4×D4×C11—28no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11D414yes—
76C11×#117—28no—
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C11×#107—24no—
103C11×#107—24no—
104C11×C4⋊C8—22no—
105C11×C4⋊C8—22no—
106C11×#103—24no—
107C11×#103—24no—
108C11×#102—24no—
109C11×#102—24no—
110C11×C22⋊C8—24no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—22no—
115#32963C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C24×C11C2×D411yescharacteristic
118C11×#41—28no—
119C11×#41—28no—
120C11×#41—28no—
121C11×#41—28no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—42no—
126C2×Q8×C11—82no—
127C2×Q8×C11C2×D412yes—
128C2×Q8×C11C2×Q812yes—
129C2×Q8×C11#4112yes—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11C2×D412yes—
137C2×D4×C11C2×Q812yes—
138C2×D4×C11#4112yes—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—82no—
155C22×C4×C11—82no—
156C22×C4×C11—82no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×Q812yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—82no—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—82no—
191C42×C11—24no—
192C42×C11—24no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C2×D412yes—
196C42×C11C2×D412yes—
197C2×#520C2×C1111yescharacteristic
198C2×#477C2×C1111yescharacteristic, complemented
199C2×#474C2×C1111yescharacteristic, complemented
200#2628C2×C1111yescharacteristic, complemented
201#1863C2×C1112yescomplemented
202#1862C2×C1112yescomplemented
203#1852C2×C1112yescomplemented
204#1805C2×C1111yescharacteristic, complemented
205#1804C2×C1111yescharacteristic, complemented
206#1798C2×C1111yescharacteristic, complemented
207#1788C2×C1112yes—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C22⋊Q812yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—84no—
223Q8×C11C22⋊Q814yes—
224D4×C11—216no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—22no—
228D4×C11C22⋊Q814yes—
229C2×C4×C11—216no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—84no—
256C2×C4×C11—84no—
257C2×C4×C11—84no—
258C2×C4×C11#12012yes—
259C2×C4×C11#12012yes—
260C2×C4×C11C22⋊Q812yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C8×C11—42no—
268C8×C11—42no—
269C22×#41C22×C1111yescharacteristic
270C2×C4⋊Q8C22×C1111yescharacteristic
271#520—24no—
272#520—24no—
273C2×C4×Q8C22×C1111yescharacteristic
274C2×C4×Q8C22×C1111yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4—21no—
277C2×C4×D4C22×C1111yescharacteristic
278C2×C4×D4C22×C1111yescharacteristic
279C2×#117—21no—
280C2×#117C22×C1111yescharacteristic
281C22×C4⋊C4—21no—
282C22×C4⋊C4C22×C1111yescharacteristic
283#477—24no—
284#474—24no—
285C2×#107C22×C1112yes—
286C2×#107C22×C1112yes—
287C2×C4⋊C8C22×C1111yescharacteristic
288C2×C4⋊C8C22×C1111yescharacteristic
289C2×#103C22×C1112yes—
290C2×#103C22×C1112yes—
291C2×#102C22×C1112yes—
292C2×#102C22×C1112yes—
293C2×C22⋊C8C22×C1112yes—
294#400—21no—
295#399—21no—
296#395—21no—
297#393—21no—
298#389C22×C1112yes—
299#382C22×C1111yescharacteristic
300#380C22×C1112yes—
301#340C22×C1112yes—
302#340C22×C1112yes—
303#336C22×C1112yes—
304C22×C11—24no—
305C22×C11—22no—
306C22×C11—24no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—41no—
311C22×C11—42no—
312C22×C11—41no—
313C22×C11—42no—
314C22×C11C2×#12011yescharacteristic
315C22×C11C2×C22⋊Q811yescharacteristic
316C22×C11#52511yescharacteristic
317C22×C11#57612yes—
318C22×C11#57812yes—
319C4×C11—22no—
320C4×C11—24no—
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—41no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—41no—
327C4×C11—82no—
328C4×C11—82no—
329C4×C11C2×C22⋊Q811yescharacteristic
330C4×C11C2×C22⋊Q811yescharacteristic
331C4×C11#52511yescharacteristic
332C4×C11#52511yescharacteristic
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41Q8×C1114yescomplemented
339C22×Q8—21no—
340C22×Q8C23×C1111yescharacteristic
341C22×D4—21no—
342C22×D4C23×C1111yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4C23×C1111yescharacteristic
348C22×C8C23×C1112yes—
349C22×C8C23×C1112yes—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8D4×C1114yes—
356C4×D4—28no—
357C4×D4—28no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4D4×C1114yes—
362#117—28no—
363#117—22no—
364#117—22no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4D4×C1111yescharacteristic
374C2×C4⋊C4D4×C1111yescharacteristic
375C2×C4⋊C4C23×C1112yes—
376C2×C4⋊C4C23×C1112yes—
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4D4×C1111yescharacteristic
383C2×C22⋊C4D4×C1111yescharacteristic
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C23×C1111yescharacteristic
387C2×C42C23×C1111yescharacteristic
388#107—24no—
389#107—24no—
390C4⋊C8—22no—
391C4⋊C8—22no—
392#103—24no—
393#103—24no—
394#102—24no—
395#102—24no—
396C22⋊C8—24no—
397#95—22no—
398#95—21no—
399#95—21no—
400#95—22no—
401C2×C11—42no—
402C2×C11—44no—
403C2×C11#284811yescharacteristic
404C2×C11#300811yescharacteristic
405C2×C11#301111yescharacteristic
406C2×C11#308312yes—
407C2×C11#312412yes—
408C24—21no—
409C24C2×D4×C1111yescharacteristic
410#41—28no—
411#41—28no—
412#41—28no—
413#41—28no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—42no—
418C2×Q8—82no—
419C2×Q8C2×D4×C1112yes—
420C2×Q8C2×Q8×C1112yes—
421C2×Q8C11×#4112yes—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4C2×D4×C1112yes—
429C2×D4C2×Q8×C1112yes—
430C2×D4C11×#4112yes—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—82no—
447C22×C4—82no—
448C22×C4—82no—
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×Q8×C1112yes—
455C22×C4C11×#4112yes—
456C22×C4C24×C1111yescharacteristic
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—42no—
475C4⋊C4—82no—
476C4⋊C4C2×D4×C1112yes—
477C4⋊C4C2×D4×C1112yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—82no—
483C42—24no—
484C42—24no—
485C42—21no—
486C42—21no—
487C42C2×D4×C1112yes—
488C42C2×D4×C1112yes—
489C11#3296311yescharacteristic, direct product factor, Sylow
490C23—21no—
491C23—22no—
492C23—22no—
493C23—21no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23C11×C22⋊Q812yes—
500C23C22×D4×C1111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—22no—
504Q8—84no—
505Q8C11×C22⋊Q814yes—
506D4—216no—
507D4—22no—
508D4—22no—
509D4—22no—
510D4C11×C22⋊Q814yes—
511C2×C4—216no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4—84no—
540C2×C4C11×#12012yes—
541C2×C4C11×#12012yes—
542C2×C4C11×C22⋊Q812yes—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×Q8×C1111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C2×C11×#4111yescharacteristic
548C2×C4C2×C11×#4111yescharacteristic
549C8—42no—
550C8—42no—
551C22—24no—
552C22—22no—
553C22—24no—
554C22—41no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—44no—
561C22C2×C11×#12011yescharacteristic
562C22C2×C11×C22⋊Q811yescharacteristic
563C22C11×#52511yescharacteristic
564C22C11×#57612yes—
565C22C11×#57812yes—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—24no—
570C4—41no—
571C4—42no—
572C4—42no—
573C4—41no—
574C4—82no—
575C4—82no—
576C4C2×C11×C22⋊Q811yescharacteristic
577C4C2×C11×C22⋊Q811yescharacteristic
578C4C11×#52511yescharacteristic
579C4C11×#52511yescharacteristic
580C2—42no—
581C2—44no—
582C2C11×#284811yescharacteristic
583C2C11×#300811yescharacteristic
584C2C11×#301111yescharacteristic
585C2C11×#308312yes—
586C2C11×#312412yes—
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
2. C2×C11×#477C2semidirect
3. C2×C11×#474C2semidirect
4. C11×#2628C2semidirect
5. C11×#1863C2semidirect
6. C11×#1862C2semidirect
7. C11×#1852C2semidirect
8. C11×#1805C2semidirect
9. C11×#1804C2semidirect
10. C11×#1798C2semidirect
52. C2×C11×#41Q8semidirect
115. #32963C11direct (N × H)
198. C2×#477C2×C11semidirect
199. C2×#474C2×C11semidirect
200. #2628C2×C11semidirect
201. #1863C2×C11semidirect
202. #1862C2×C11semidirect
203. #1852C2×C11semidirect
204. #1805C2×C11semidirect
205. #1804C2×C11semidirect
206. #1798C2×C11semidirect
338. C2×#41Q8×C11semidirect
489. C11#32963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5202
C2×C11×#4772
C2×C11×#4742
C11×#26282
C11×#18632
C11×#18622
C11×#18522
C11×#18052
C11×#18042
C11×#17982
C11×#17882
#3296311