Finite Group Databasebeta

← C11×#62005 #14639198

Subgroups — C11×#62005 #14639198

Order 2816.

1836 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic
2Q8×C11×#41C211yesmaximal, characteristic, complemented
3C11×#3395C211yesmaximal, characteristic, complemented
4C11×#3392C211yesmaximal, characteristic, complemented
5C11×#3363C211yesmaximal, characteristic, complemented
6C11×#3362C211yesmaximal, characteristic, complemented
7C11×#3333C213yesmaximal, complemented
8C11×#3331C213yesmaximal, complemented
9C11×#3278C213yesmaximal, complemented
10C11×#3276C213yesmaximal, complemented
11C11×#3252C213yesmaximal, complemented
12C11×#3210C213yesmaximal, complemented
13C11×#3108C213yesmaximal, complemented
14C11×#3037C213yesmaximal, complemented
15C11×#2991C211yesmaximal, characteristic, complemented
16C2×C11×#137C2216yes—
17Q82×C11C2211yescharacteristic
18C11×#557—21no—
19C11×#557C2211yescharacteristic
20C11×#557C2211yescharacteristic
21C11×#554—23no—
22C11×#554C2213yes—
23C11×#553—23no—
24C11×#550—21no—
25C11×#550C2213yes—
26C11×#550C2211yescharacteristic
27D4×Q8×C11C2213yes—
28C11×#547C2213yes—
29C11×#540—23no—
30C11×#533—23no—
31C11×#533C2213yes—
32C11×#532C2213yes—
33C11×#529C2213yes—
34C11×#520—21no—
35C4×C11×#41—21no—
36C4×C11×#41C2211yescharacteristic
37C2×C4×Q8×C11C2213yes—
38C11×#494C2213yes—
39C11×#492C2213yes—
40C11×#487C2213yes—
41C11×#486C2213yes—
42C11×#483C2213yes—
43C11×#480C2213yes—
44C11×#479C2213yes—
45C11×#479C2211yescharacteristic
46C11×#477C2213yes—
47C11×#476C2213yes—
48C11×#470C2216yes—
49C11×#468C2216yes—
50C11×#464C2213yes—
51C11×#464C2216yes—
52C11×#464C2213yes—
53C11×#462C2213yes—
54C11×#462C2213yes—
55C11×#462C2213yes—
56C11×#461C2213yes—
57C11×#460C2213yes—
58C11×#460C2213yes—
59C11×#452C2216yes—
60C11×#452C2216yes—
61C11×#451C2213yes—
62C11×#448C2213yes—
63C8×Q8×C11C2211yescharacteristic
64C8×Q8×C11C2211yescharacteristic
65C4×C11×Q16C2213yes—
66C4×C11×Q16C2213yes—
67C4×C11×SD16C2213yes—
68C4×C11×SD16C2213yes—
69C11×#436C2213yes—
70C11×#436C2213yes—
71C11×#431C2213yes—
72C11×#423C2213yes—
73C11×#417C2216yes—
74C2×C11×#41—21no—
75C2×C11×#41D411yescharacteristic
76C2×C11×#41C2316yes—
77C22×Q8×C11C2313yes—
78C11×#137—412no—
79C2×C11×Q16C2313yes—
80C2×C11×Q16C2313yes—
81C2×C11×Q16C2316yes—
82C2×C11×SD16C2313yes—
83C2×C11×SD16C2313yes—
84C2×C11×SD16C2316yes—
85C2×C11×M16C2316yes—
86C11×C4⋊Q8—23no—
87C11×C4⋊Q8—23no—
88C11×C4⋊Q8C2313yes—
89C11×C4⋊Q8C2313yes—
90C11×C4⋊Q8C2313yes—
91C11×#127—23no—
92C11×#127C2313yes—
93C11×#126—23no—
94C11×#125—23no—
95C11×#125—23no—
96C11×#125—23no—
97C11×#125—23no—
98C11×#125C2311yescharacteristic
99C11×#124C2313yes—
100C11×#123—23no—
101C11×#123—26no—
102C11×C22⋊Q8—23no—
103C11×C22⋊Q8—26no—
104C11×C22⋊Q8—26no—
105C11×C22⋊Q8C2313yes—
106C11×C22⋊Q8C2316yes—
107C11×#121—23no—
108C11×#121—23no—
109C11×#121—23no—
110C11×#121—23no—
111C11×#121—26no—
112C11×#121C2313yes—
113C4×Q8×C11—21no—
114C4×Q8×C11—21no—
115C4×Q8×C11—21no—
116C4×Q8×C11—23no—
117C4×Q8×C11—23no—
118C4×Q8×C11—23no—
119C4×Q8×C11D411yescharacteristic
120C4×Q8×C11C2311yescharacteristic
121C4×Q8×C11C2313yes—
122C4×Q8×C11C2313yes—
123C4×Q8×C11C2313yes—
124C4×Q8×C11C2313yes—
125C4×Q8×C11C2311yescharacteristic
126C4×D4×C11—23no—
127C4×D4×C11—23no—
128C4×D4×C11—23no—
129C4×D4×C11—23no—
130C4×D4×C11—23no—
131C4×D4×C11—23no—
132C4×D4×C11D413yes—
133C4×D4×C11C2313yes—
134C4×D4×C11C2313yes—
135C11×#117—23no—
136C11×#117—23no—
137C11×#117D413yes—
138C2×C11×C4⋊C4—23no—
139C2×C11×C4⋊C4—23no—
140C2×C11×C4⋊C4C2313yes—
141C2×C42×C11—23no—
142C2×C42×C11C2313yes—
143C11×#107C2311yescharacteristic
144C11×#107C2313yes—
145C11×#106C2311yescharacteristic
146C11×#106C2313yes—
147C11×C4⋊C8C2313yes—
148C11×C4⋊C8C2313yes—
149C11×C4⋊C8C2313yes—
150C11×C4⋊C8C2311yescharacteristic
151C11×#103C2313yes—
152C11×#103C2316yes—
153C11×#103C2311yescharacteristic
154C11×#103C2313yes—
155C11×#103C2311yescharacteristic
156C11×#103C2313yes—
157C11×#103C2313yes—
158C11×#102C2313yes—
159C11×#102C2316yes—
160C11×#102C2313yes—
161C11×C22⋊C8C2313yes—
162C11×C22⋊C8C2313yes—
163C4×C8×C11C2313yes—
164C4×C8×C11C2313yes—
165#62005C1111yesmaximal, characteristic, direct product factor, Sylow
166C11×#41—24no—
167C11×#41—46no—
168C11×#41—46no—
169C11×#41—44no—
170C2×Q8×C11—23no—
171C2×Q8×C11—23no—
172C2×Q8×C11—26no—
173C2×Q8×C11—43no—
174C2×Q8×C11C2×D411yescharacteristic
175C2×Q8×C11C2413yes—
176C2×Q8×C11C2413yes—
177C2×Q8×C11C2411yescharacteristic
178C2×D4×C11—23no—
179C2×D4×C11—26no—
180C2×D4×C11—23no—
181C2×D4×C11—23no—
182C2×D4×C11C2×D413yes—
183C2×D4×C11C2413yes—
184C22×C4×C11—23no—
185C22×C4×C11—23no—
186C22×C4×C11—23no—
187C22×C4×C11—26no—
188C22×C4×C11C2×D413yes—
189C22×C4×C11C2×D413yes—
190C22×C4×C11C2413yes—
191C11×Q16—26no—
192C11×Q16—43no—
193C11×Q16—46no—
194C11×SD16—26no—
195C11×SD16—43no—
196C11×SD16—46no—
197C11×M16—46no—
198C2×C8×C11C2411yescharacteristic
199C2×C8×C11C2411yescharacteristic
200C2×C8×C11C2413yes—
201C2×C8×C11C2413yes—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—23no—
204C11×C4⋊C4—23no—
205C11×C4⋊C4—23no—
206C11×C4⋊C4—23no—
207C11×C4⋊C4—23no—
208C11×C4⋊C4—23no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—23no—
211C11×C4⋊C4—23no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—23no—
214C11×C4⋊C4—23no—
215C11×C4⋊C4—26no—
216C11×C4⋊C4—23no—
217C11×C4⋊C4C2×D413yes—
218C11×C4⋊C4C2×D413yes—
219C11×C4⋊C4C2411yescharacteristic
220C11×C4⋊C4C2413yes—
221C11×C4⋊C4C2411yescharacteristic
222C11×C4⋊C4C2411yescharacteristic
223C11×C22⋊C4—26no—
224C11×C22⋊C4—23no—
225C11×C22⋊C4—23no—
226C11×C22⋊C4—23no—
227C11×C22⋊C4—23no—
228C11×C22⋊C4—23no—
229C11×C22⋊C4C2×D416yes—
230C42×C11—21no—
231C42×C11—23no—
232C42×C11—23no—
233C42×C11—23no—
234C42×C11—23no—
235C42×C11C2×D413yes—
236C42×C11C2×D413yes—
237C42×C11C2413yes—
238C42×C11C2411yescharacteristic
239#3517C2×C1111yescharacteristic
240Q8×#41C2×C1111yescharacteristic, complemented
241#3395C2×C1111yescharacteristic, complemented
242#3392C2×C1111yescharacteristic, complemented
243#3363C2×C1111yescharacteristic, complemented
244#3362C2×C1111yescharacteristic, complemented
245#3333C2×C1113yescomplemented
246#3331C2×C1113yescomplemented
247#3278C2×C1113yescomplemented
248#3276C2×C1113yescomplemented
249#3252C2×C1113yescomplemented
250#3210C2×C1113yescomplemented
251#3108C2×C1113yescomplemented
252#3037C2×C1113yescomplemented
253#2991C2×C1111yescharacteristic, complemented
254C23×C11—23no—
255C23×C11C22×D413yes—
256Q8×C11—21no—
257Q8×C11—23no—
258Q8×C11—23no—
259Q8×C11—23no—
260Q8×C11—23no—
261Q8×C11—46no—
262Q8×C11—83no—
263Q8×C11#13714yescomplemented
264Q8×C11H(5,𝔽2)12yes—
265D4×C11—26no—
266D4×C11—23no—
267D4×C11—23no—
268D4×C11—46no—
269D4×C11—83no—
270D4×C11—83no—
271D4×C11—86no—
272C2×C4×C11—21no—
273C2×C4×C11—26no—
274C2×C4×C11—23no—
275C2×C4×C11—23no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—23no—
279C2×C4×C11—23no—
280C2×C4×C11—23no—
281C2×C4×C11—21no—
282C2×C4×C11—43no—
283C2×C4×C11—46no—
284C2×C4×C11—46no—
285C2×C4×C11—86no—
286C2×C4×C11—83no—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D413yes—
290C2×C4×C11C22×D413yes—
291C2×C4×C11C22×D413yes—
292C2×C4×C11C2511yescharacteristic
293C8×C11—23no—
294C8×C11—23no—
295C8×C11—21no—
296C8×C11—21no—
297C2×#137C22×C1116yes—
298Q82C22×C1111yescharacteristic
299#557—21no—
300#557C22×C1111yescharacteristic
301#557C22×C1111yescharacteristic
302#554—23no—
303#554C22×C1113yes—
304#553—23no—
305#550—21no—
306#550C22×C1113yes—
307#550C22×C1111yescharacteristic
308D4×Q8C22×C1113yes—
309#547C22×C1113yes—
310#540—23no—
311#533—23no—
312#533C22×C1113yes—
313#532C22×C1113yes—
314#529C22×C1113yes—
315#520—21no—
316C4×#41—21no—
317C4×#41C22×C1111yescharacteristic
318C2×C4×Q8C22×C1113yes—
319#494C22×C1113yes—
320#492C22×C1113yes—
321#487C22×C1113yes—
322#486C22×C1113yes—
323#483C22×C1113yes—
324#480C22×C1113yes—
325#479C22×C1111yescharacteristic
326#479C22×C1113yes—
327#477C22×C1113yes—
328#476C22×C1113yes—
329#470C22×C1116yes—
330#468C22×C1116yes—
331#464C22×C1113yes—
332#464C22×C1113yes—
333#464C22×C1116yes—
334#462C22×C1113yes—
335#462C22×C1113yes—
336#462C22×C1113yes—
337#461C22×C1113yes—
338#460C22×C1113yes—
339#460C22×C1113yes—
340#452C22×C1116yes—
341#452C22×C1116yes—
342#451C22×C1113yes—
343#448C22×C1113yes—
344C8×Q8C22×C1111yescharacteristic
345C8×Q8C22×C1111yescharacteristic
346C4×Q16C22×C1113yes—
347C4×Q16C22×C1113yes—
348C4×SD16C22×C1113yes—
349C4×SD16C22×C1113yes—
350#436C22×C1113yes—
351#436C22×C1113yes—
352#431C22×C1113yes—
353#423C22×C1113yes—
354#417C22×C1116yes—
355C22×C11—23no—
356C22×C11—23no—
357C22×C11—23no—
358C22×C11—43no—
359C22×C11—43no—
360C22×C11—43no—
361C22×C11C23×D411yescharacteristic
362C4×C11—21no—
363C4×C11—23no—
364C4×C11—23no—
365C4×C11—22no—
366C4×C11—21no—
367C4×C11—41no—
368C4×C11—43no—
369C4×C11—41no—
370C4×C11—43no—
371C4×C11—43no—
372C4×C11—41no—
373C4×C11C2×#13716yes—
374C4×C11C2×H(5,𝔽2)11yescharacteristic
375C4×C11#58511yescharacteristic
376C2×#41—21no—
377C2×#41D4×C1111yescharacteristic
378C2×#41C23×C1116yes—
379C22×Q8C23×C1113yes—
380#137—412no—
381C2×Q16C23×C1113yes—
382C2×Q16C23×C1116yes—
383C2×Q16C23×C1113yes—
384C2×SD16C23×C1113yes—
385C2×SD16C23×C1116yes—
386C2×SD16C23×C1113yes—
387C2×M16C23×C1116yes—
388C4⋊Q8—23no—
389C4⋊Q8—23no—
390C4⋊Q8C23×C1113yes—
391C4⋊Q8C23×C1113yes—
392C4⋊Q8C23×C1113yes—
393#127—23no—
394#127C23×C1113yes—
395#126—23no—
396#125—23no—
397#125—23no—
398#125—23no—
399#125—23no—
400#125C23×C1111yescharacteristic
401#124C23×C1113yes—
402#123—23no—
403#123—26no—
404C22⋊Q8—23no—
405C22⋊Q8—26no—
406C22⋊Q8—26no—
407C22⋊Q8C23×C1113yes—
408C22⋊Q8C23×C1116yes—
409#121—23no—
410#121—23no—
411#121—23no—
412#121—23no—
413#121—26no—
414#121C23×C1113yes—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—23no—
419C4×Q8—23no—
420C4×Q8—23no—
421C4×Q8D4×C1111yescharacteristic
422C4×Q8C23×C1111yescharacteristic
423C4×Q8C23×C1113yes—
424C4×Q8C23×C1113yes—
425C4×Q8C23×C1113yes—
426C4×Q8C23×C1113yes—
427C4×Q8C23×C1111yescharacteristic
428C4×D4—23no—
429C4×D4—23no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4D4×C1113yes—
435C4×D4C23×C1113yes—
436C4×D4C23×C1113yes—
437#117—23no—
438#117—23no—
439#117D4×C1113yes—
440C2×C4⋊C4—23no—
441C2×C4⋊C4—23no—
442C2×C4⋊C4C23×C1113yes—
443C2×C42—23no—
444C2×C42C23×C1113yes—
445#107C23×C1111yescharacteristic
446#107C23×C1113yes—
447#106C23×C1111yescharacteristic
448#106C23×C1113yes—
449C4⋊C8C23×C1113yes—
450C4⋊C8C23×C1113yes—
451C4⋊C8C23×C1113yes—
452C4⋊C8C23×C1111yescharacteristic
453#103C23×C1113yes—
454#103C23×C1116yes—
455#103C23×C1111yescharacteristic
456#103C23×C1113yes—
457#103C23×C1111yescharacteristic
458#103C23×C1113yes—
459#103C23×C1113yes—
460#102C23×C1113yes—
461#102C23×C1116yes—
462#102C23×C1113yes—
463C22⋊C8C23×C1113yes—
464C22⋊C8C23×C1113yes—
465C4×C8C23×C1113yes—
466C4×C8C23×C1113yes—
467C2×C11—43no—
468C2×C11—83no—
469C2×C11#348811yescharacteristic
470C2×C11C22×#13711yescharacteristic
471C2×C11#358411yescharacteristic
472#41—24no—
473#41—46no—
474#41—46no—
475#41—44no—
476C2×Q8—23no—
477C2×Q8—23no—
478C2×Q8—26no—
479C2×Q8—43no—
480C2×Q8C2×D4×C1111yescharacteristic
481C2×Q8C24×C1113yes—
482C2×Q8C24×C1113yes—
483C2×Q8C24×C1111yescharacteristic
484C2×D4—23no—
485C2×D4—26no—
486C2×D4—23no—
487C2×D4—23no—
488C2×D4C2×D4×C1113yes—
489C2×D4C24×C1113yes—
490C22×C4—23no—
491C22×C4—23no—
492C22×C4—23no—
493C22×C4—26no—
494C22×C4C2×D4×C1113yes—
495C22×C4C2×D4×C1113yes—
496C22×C4C24×C1113yes—
497Q16—26no—
498Q16—46no—
499Q16—43no—
500SD16—26no—
501SD16—46no—
502SD16—43no—
503M16—46no—
504C2×C8C24×C1111yescharacteristic
505C2×C8C24×C1111yescharacteristic
506C2×C8C24×C1113yes—
507C2×C8C24×C1113yes—
508C4⋊C4—21no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—21no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—21no—
519C4⋊C4—23no—
520C4⋊C4—23no—
521C4⋊C4—26no—
522C4⋊C4—23no—
523C4⋊C4C2×D4×C1113yes—
524C4⋊C4C2×D4×C1113yes—
525C4⋊C4C24×C1111yescharacteristic
526C4⋊C4C24×C1113yes—
527C4⋊C4C24×C1111yescharacteristic
528C4⋊C4C24×C1111yescharacteristic
529C22⋊C4—26no—
530C22⋊C4—23no—
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—23no—
534C22⋊C4—23no—
535C22⋊C4C2×D4×C1116yes—
536C42—21no—
537C42—23no—
538C42—23no—
539C42—23no—
540C42—23no—
541C42C2×D4×C1113yes—
542C42C2×D4×C1113yes—
543C42C24×C1113yes—
544C42C24×C1111yescharacteristic
545C11#6200511yescharacteristic, direct product factor, Sylow
546C23—23no—
547C23C22×D4×C1113yes—
548Q8—21no—
549Q8—23no—
550Q8—23no—
551Q8—23no—
552Q8—23no—
553Q8—46no—
554Q8—83no—
555Q8C11×#13714yescomplemented
556Q8C11×H(5,𝔽2)12yes—
557D4—26no—
558D4—23no—
559D4—23no—
560D4—46no—
561D4—83no—
562D4—83no—
563D4—86no—
564C2×C4—21no—
565C2×C4—26no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—43no—
575C2×C4—46no—
576C2×C4—46no—
577C2×C4—86no—
578C2×C4—83no—
579C2×C4C22×D4×C1111yescharacteristic
580C2×C4C22×D4×C1111yescharacteristic
581C2×C4C22×D4×C1113yes—
582C2×C4C22×D4×C1113yes—
583C2×C4C22×D4×C1113yes—
584C2×C4C25×C1111yescharacteristic
585C8—23no—
586C8—23no—
587C8—21no—
588C8—21no—
589C22—23no—
590C22—23no—
591C22—23no—
592C22—43no—
593C22—43no—
594C22—43no—
595C22C23×D4×C1111yescharacteristic
596C4—23no—
597C4—22no—
598C4—21no—
599C4—21no—
600C4—23no—
601C4—43no—
602C4—43no—
603C4—41no—
604C4—41no—
605C4—43no—
606C4—41no—
607C4C2×C11×#13716yes—
608C4C2×C11×H(5,𝔽2)11yescharacteristic
609C4C11×#58511yescharacteristic
610C2—43no—
611C2—83no—
612C2C11×#348811yescharacteristic
613C2C22×C11×#13711yescharacteristic
614C2C11×#358411yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3517C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C11×#41C2semidirect
3. C11×#3395C2semidirect
4. C11×#3392C2semidirect
5. C11×#3363C2semidirect
6. C11×#3362C2semidirect
7. C11×#3333C2semidirect
8. C11×#3331C2semidirect
9. C11×#3278C2semidirect
10. C11×#3276C2semidirect
11. C11×#3252C2semidirect
12. C11×#3210C2semidirect
13. C11×#3108C2semidirect
14. C11×#3037C2semidirect
15. C11×#2991C2semidirect
165. #62005C11direct (N × H)
240. Q8×#41C2×C11semidirect
241. #3395C2×C11semidirect
242. #3392C2×C11semidirect
243. #3363C2×C11semidirect
244. #3362C2×C11semidirect
245. #3333C2×C11semidirect
246. #3331C2×C11semidirect
247. #3278C2×C11semidirect
248. #3276C2×C11semidirect
249. #3252C2×C11semidirect
250. #3210C2×C11semidirect
251. #3108C2×C11semidirect
252. #3037C2×C11semidirect
253. #2991C2×C11semidirect
263. Q8×C11#137semidirect
545. C11#62005direct (N × H)
555. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#35172
Q8×C11×#412
C11×#33952
C11×#33922
C11×#33632
C11×#33622
C11×#33332
C11×#33312
C11×#32782
C11×#32762
C11×#32522
C11×#32102
C11×#31082
C11×#30372
C11×#29912
#6200511