Finite Group Databasebeta

← C11×#18379 #14595572

Subgroups — C11×#18379 #14595572

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3492C211yesmaximal, characteristic
2C11×#3190C212yesmaximal, complemented
3C11×#2583C211yesmaximal, characteristic, complemented
4C11×#1611C211yesmaximal, characteristic, complemented
5C11×#1610C211yesmaximal, characteristic, complemented
6C11×#1609C212yesmaximal, complemented
7C11×#1605C211yesmaximal, characteristic, complemented
8C11×#1604C211yesmaximal, characteristic, complemented
9C11×#1603C212yesmaximal, complemented
10C11×#1501C212yesmaximal, complemented
11C2×C11×#324C211yesmaximal, characteristic, complemented
12C11×#554—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#547—22no—
16C11×#544C2211yescharacteristic
17C11×#539—21no—
18C11×#539C2212yes—
19C11×#537C2211yescharacteristic
20C11×#525—21no—
21C11×#525—21no—
22C11×#525C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C11×#520—21no—
25C22×C11×C4⋊C4C2211yescharacteristic
26C11×#485—22no—
27C11×#483C2212yes—
28C11×#480C2212yes—
29C11×#467—22no—
30C11×#465—22no—
31C11×#452—22no—
32C11×#451C2212yes—
33C11×#448C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C11×#398C2211yescharacteristic
36C11×#398C2211yescharacteristic
37C11×#395C2211yescharacteristic
38C11×#395C2211yescharacteristic
39C11×#389—21no—
40C11×#389—21no—
41C11×#385—21no—
42C11×#385—21no—
43C4×C11×C22⋊C4C2211yescharacteristic
44C11×#328C2212yes—
45C11×#328C2212yes—
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2211yescharacteristic
49C11×#324C2211yescharacteristic
50C11×#324C2212yes—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41D412yes—
54C22×Q8×C11C2311yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×Q16—22no—
59C2×C11×SD16—22no—
60C22×C8×C11—22no—
61C11×C4⋊Q8—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125—22no—
65C11×#125—22no—
66C11×#125—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8D412yes—
82C11×C22⋊Q8C2312yes—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—22no—
87C11×#121—21no—
88C11×#121D412yes—
89C11×#121C2312yes—
90C11×#120—22no—
91C4×Q8×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C11×#117—22no—
100C11×#117—21no—
101C11×#117—21no—
102C11×#117D412yes—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C11×#107—22no—
120C11×#106—22no—
121C11×#103—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#102—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8C2312yes—
127C11×C22⋊C8C2312yes—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18379C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11C2×D411yescharacteristic
136C11×#41—42no—
137C11×#41—42no—
138C11×#41—82no—
139C11×#41—82no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—22no—
143C2×Q8×C11—81no—
144C2×Q8×C11C2×D412yes—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—41no—
164C22×C4×C11—81no—
165C22×C4×C11—81no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2411yescharacteristic
174C11×Q16—82no—
175C11×SD16—82no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—82no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—81no—
198C11×C4⋊C4—81no—
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4C2×D412yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C42×C11—22no—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—81no—
217#3492C2×C1111yescharacteristic
218#3190C2×C1112yescomplemented
219#2583C2×C1111yescharacteristic, complemented
220#1611C2×C1111yescharacteristic, complemented
221#1610C2×C1111yescharacteristic, complemented
222#1609C2×C1112yescomplemented
223#1605C2×C1111yescharacteristic, complemented
224#1604C2×C1111yescharacteristic, complemented
225#1603C2×C1112yescomplemented
226#1501C2×C1112yescomplemented
227C2×#324C2×C1111yescharacteristic, complemented
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11#12011yescharacteristic
234C23×C11#12011yescharacteristic
235C23×C11C22×D411yescharacteristic
236Q8×C11—42no—
237Q8×C11—42no—
238Q8×C11—42no—
239Q8×C11—42no—
240Q8×C11—81no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—44no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—44no—
247D4×C11—81no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—44no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—82no—
281C2×C4×C11—81no—
282C2×C4×C11—82no—
283C2×C4×C11#12012yes—
284C2×C4×C11#13512yes—
285C2×C4×C11C22×D412yes—
286C8×C11—42no—
287C8×C11—42no—
288#554—22no—
289#553—22no—
290#552—22no—
291#547—22no—
292#544C22×C1111yescharacteristic
293#539—21no—
294#539C22×C1112yes—
295#537C22×C1111yescharacteristic
296#525—21no—
297#525—21no—
298#525C22×C1112yes—
299C2×C22⋊Q8C22×C1111yescharacteristic
300#520—21no—
301C22×C4⋊C4C22×C1111yescharacteristic
302#485—22no—
303#483C22×C1112yes—
304#480C22×C1112yes—
305#467—22no—
306#465—22no—
307#452—22no—
308#451C22×C1112yes—
309#448C22×C1112yes—
310C2×C22⋊C8C22×C1112yes—
311#398C22×C1111yescharacteristic
312#398C22×C1111yescharacteristic
313#395C22×C1111yescharacteristic
314#395C22×C1111yescharacteristic
315#389—21no—
316#389—21no—
317#385—21no—
318#385—21no—
319C4×C22⋊C4C22×C1111yescharacteristic
320#328C22×C1112yes—
321#328C22×C1112yes—
322#327C22×C1112yes—
323#327C22×C1112yes—
324#324C22×C1112yes—
325#324C22×C1111yescharacteristic
326#324C22×C1111yescharacteristic
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11#45612yes—
340C22×C11C2×#12011yescharacteristic
341C22×C11C2×#13511yescharacteristic
342C22×C11#57511yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11—81no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41D4×C1112yes—
359C22×Q8C23×C1111yescharacteristic
360C23×C4D4×C1111yescharacteristic
361C23×C4D4×C1111yescharacteristic
362C23×C4C23×C1111yescharacteristic
363C2×Q16—22no—
364C2×SD16—22no—
365C22×C8—22no—
366C4⋊Q8—22no—
367#126—22no—
368#126—22no—
369#125—22no—
370#125—22no—
371#125—22no—
372#123—22no—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—22no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8D4×C1112yes—
387C22⋊Q8C23×C1112yes—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—22no—
392#121—21no—
393#121D4×C1112yes—
394#121C23×C1112yes—
395#120—22no—
396C4×Q8—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404#117—22no—
405#117—21no—
406#117—21no—
407#117D4×C1112yes—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4D4×C1111yescharacteristic
417C2×C4⋊C4D4×C1111yescharacteristic
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—21no—
424#107—22no—
425#106—22no—
426#103—22no—
427#103—22no—
428#103—22no—
429#102—22no—
430C22⋊C8—22no—
431C22⋊C8C23×C1112yes—
432C22⋊C8C23×C1112yes—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95C23×C1111yescharacteristic
438#95C23×C1111yescharacteristic
439C2×C11—21no—
440C2×C11—21no—
441C2×C11—22no—
442C2×C11—41no—
443C2×C11—82no—
444C2×C11#300211yescharacteristic
445C2×C11C2×#45611yescharacteristic
446C2×C11#302611yescharacteristic
447C24C2×D4×C1111yescharacteristic
448#41—42no—
449#41—42no—
450#41—82no—
451#41—82no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—81no—
456C2×Q8C2×D4×C1112yes—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—21no—
462C2×D4C2×D4×C1112yes—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1111yescharacteristic
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1112yes—
484C22×C4C2×D4×C1112yes—
485C22×C4C24×C1111yescharacteristic
486Q16—82no—
487SD16—82no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—82no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—81no—
510C4⋊C4—81no—
511C4⋊C4C2×D4×C1112yes—
512C4⋊C4C2×D4×C1112yes—
513C22⋊C4—24no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—81no—
529C11#1837911yescharacteristic, direct product factor, Sylow
530C23—21no—
531C23—21no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23C11×#12011yescharacteristic
536C23C11×#12011yescharacteristic
537C23C22×D4×C1111yescharacteristic
538Q8—42no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543D4—42no—
544D4—42no—
545D4—44no—
546D4—42no—
547D4—42no—
548D4—44no—
549D4—81no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—81no—
584C2×C4—82no—
585C2×C4C11×#12012yes—
586C2×C4C11×#13512yes—
587C2×C4C22×D4×C1112yes—
588C8—42no—
589C8—42no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22C11×#45612yes—
603C22C2×C11×#12011yescharacteristic
604C22C2×C11×#13511yescharacteristic
605C22C11×#57511yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—42no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C2—21no—
620C2—21no—
621C2—22no—
622C2—41no—
623C2—82no—
624C2C11×#300211yescharacteristic
625C2C2×C11×#45611yescharacteristic
626C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3492C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3190C2semidirect
3. C11×#2583C2semidirect
4. C11×#1611C2semidirect
5. C11×#1610C2semidirect
6. C11×#1609C2semidirect
7. C11×#1605C2semidirect
8. C11×#1604C2semidirect
9. C11×#1603C2semidirect
10. C11×#1501C2semidirect
11. C2×C11×#324C2semidirect
134. #18379C11direct (N × H)
218. #3190C2×C11semidirect
219. #2583C2×C11semidirect
220. #1611C2×C11semidirect
221. #1610C2×C11semidirect
222. #1609C2×C11semidirect
223. #1605C2×C11semidirect
224. #1604C2×C11semidirect
225. #1603C2×C11semidirect
226. #1501C2×C11semidirect
227. C2×#324C2×C11semidirect
529. C11#18379direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#31902
C11×#25832
C11×#16112
C11×#16102
C11×#16092
C11×#16052
C11×#16042
C11×#16032
C11×#15012
C2×C11×#3242
#1837911