Finite Group Databasebeta

← C11×#26378 #14603571

Subgroups — C11×#26378 #14603571

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#478C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2453C211yesmaximal, characteristic, complemented
4C11×#2349C211yesmaximal, characteristic
5C11×#2097C211yesmaximal, characteristic, complemented
6C11×#2085C211yesmaximal, characteristic, complemented
7C11×#2066C211yesmaximal, characteristic, complemented
8C11×#2059C211yesmaximal, characteristic, complemented
9C11×#1941C211yesmaximal, characteristic, complemented
10C11×#1916C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic
12C11×#1877C211yesmaximal, characteristic
13C11×#1864C211yesmaximal, characteristic
14C11×#1863C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C11×#478—24no—
23C4×C11×SD16—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C11×#400—21no—
38C11×#398—21no—
39C11×#391C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#389—21no—
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#387—21no—
47C11×#385—21no—
48C11×#385—21no—
49C11×#382C2211yescharacteristic
50C11×#380—21no—
51C4×C11×C4⋊C4C2211yescharacteristic
52C2×C11×#95—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×SD16Q814yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#125—22no—
74C11×#125—41no—
75C4×Q8×C11—22no—
76C4×Q8×C11—41no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C11×#107—22no—
106C11×#107—41no—
107C11×#106—22no—
108C11×#106—22no—
109C11×#106—22no—
110C11×C4⋊C8—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#103—41no—
114C11×#102—22no—
115C11×#102—22no—
116C11×#102D414yes—
117C4×C8×C11—22no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95D411yescharacteristic
129C11×#95D411yescharacteristic
130#26378C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yes—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×Q812yes—
143C2×D4×C11#4112yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11—81no—
159C22×C4×C11—81no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C11×SD16—28no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D412yes—
179C2×C8×C11C2×Q812yes—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—42no—
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⋊C4#4112yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—42no—
203C11×C22⋊C4—42no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—42no—
211C2×#478C2×C1111yescharacteristic
212C2×C4×SD16C2×C1111yescharacteristic
213#2453C2×C1111yescharacteristic, complemented
214#2349C2×C1111yescharacteristic
215#2097C2×C1111yescharacteristic, complemented
216#2085C2×C1111yescharacteristic, complemented
217#2066C2×C1111yescharacteristic, complemented
218#2059C2×C1111yescharacteristic, complemented
219#1941C2×C1111yescharacteristic, complemented
220#1916C2×C1111yescharacteristic, complemented
221#1877C2×C1111yescharacteristic
222#1877C2×C1111yescharacteristic
223#1864C2×C1111yescharacteristic
224#1863C2×C1111yescharacteristic, complemented
225#1862C2×C1111yescharacteristic
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C22×D411yescharacteristic
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11C22⋊Q814yes—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
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—84no—
281C2×C4×C11—84no—
282C2×C4×C11—84no—
283C2×C4×C11#13512yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×Q811yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C8×C11—22no—
291C8×C11—22no—
292C8×C11—41no—
293C8×C11—41no—
294C22×SD16C22×C1111yescharacteristic
295C2×#125C22×C1111yescharacteristic
296C2×C4×Q8C22×C1111yescharacteristic
297C2×C4×D4C22×C1111yescharacteristic
298C2×C4×D4C22×C1111yescharacteristic
299C2×C4×D4C22×C1111yescharacteristic
300#478—24no—
301C4×SD16—24no—
302C2×#107C22×C1111yescharacteristic
303C2×#107C22×C1111yescharacteristic
304C2×#106C22×C1111yescharacteristic
305C2×#106C22×C1111yescharacteristic
306C2×#106C22×C1111yescharacteristic
307C2×C4⋊C8C22×C1111yescharacteristic
308C2×#103C22×C1111yescharacteristic
309C2×#103C22×C1111yescharacteristic
310C2×#103C22×C1111yescharacteristic
311C2×#102C22×C1111yescharacteristic
312C2×#102C22×C1111yescharacteristic
313C2×#102C22×C1111yescharacteristic
314C2×C4×C8C22×C1111yescharacteristic
315#400—21no—
316#398—21no—
317#391C22×C1111yescharacteristic
318#391C22×C1111yescharacteristic
319#389—21no—
320#389C22×C1111yescharacteristic
321#389C22×C1111yescharacteristic
322#389C22×C1111yescharacteristic
323#389C22×C1111yescharacteristic
324#387—21no—
325#385—21no—
326#385—21no—
327#382C22×C1111yescharacteristic
328#380—21no—
329C4×C4⋊C4C22×C1111yescharacteristic
330C2×#95—21no—
331#340C22×C1111yescharacteristic
332#340C22×C1111yescharacteristic
333#340C22×C1111yescharacteristic
334#340C22×C1111yescharacteristic
335#336C22×C1111yescharacteristic
336#336C22×C1111yescharacteristic
337#336C22×C1111yescharacteristic
338#336C22×C1111yescharacteristic
339C22×C11—24no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11#52511yescharacteristic
347C22×C11D4211yescharacteristic
348C22×C11D4×Q811yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57711yescharacteristic
352C22×C11#57711yescharacteristic
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C2×C22⋊Q811yescharacteristic
367C4×C11#53911yescharacteristic
368C4×C11#54711yescharacteristic
369C4×C11#55411yescharacteristic
370C22×Q8C23×C1111yescharacteristic
371C22×D4C23×C1111yescharacteristic
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16Q8×C1114yes—
378C22×C8C23×C1111yescharacteristic
379C22×C8C23×C1111yescharacteristic
380C22×C8C23×C1111yescharacteristic
381C22×C8C23×C1111yescharacteristic
382#125—22no—
383#125—41no—
384C4×Q8—22no—
385C4×Q8—41no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—41no—
391C4×D4—41no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4D4×C1111yescharacteristic
400C2×C4⋊C4D4×C1111yescharacteristic
401C2×C4⋊C4C23×C1111yescharacteristic
402C2×C4⋊C4C23×C1111yescharacteristic
403C2×C4⋊C4C23×C1111yescharacteristic
404C2×C4⋊C4C23×C1111yescharacteristic
405C2×C4⋊C4C23×C1111yescharacteristic
406C2×C4⋊C4C23×C1111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C42—21no—
411C2×C42C23×C1111yescharacteristic
412C2×C42C23×C1111yescharacteristic
413C2×C42C23×C1111yescharacteristic
414#107—22no—
415#107—41no—
416#106—22no—
417#106—22no—
418#106—22no—
419C4⋊C8—22no—
420#103—22no—
421#103—22no—
422#103—41no—
423#102—22no—
424#102—22no—
425#102D4×C1114yes—
426C4×C8—22no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95D4×C1111yescharacteristic
438#95D4×C1111yescharacteristic
439C2×C11—44no—
440C2×C11#244911yescharacteristic
441C2×C11#310211yescharacteristic
442C2×C11#312311yescharacteristic
443C2×C11#326711yescharacteristic
444C2×C11#328211yescharacteristic
445C2×C11#338111yescharacteristic
446C2×C11#338811yescharacteristic
447C24—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8C2×Q8×C1112yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C2×D4×C1112yes—
458C2×D4C2×Q8×C1112yes—
459C2×D4C11×#4112yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1111yescharacteristic
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C24×C1111yescharacteristic
483SD16—28no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8C2×D4×C1112yes—
495C2×C8C2×Q8×C1112yes—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—81no—
514C4⋊C4—81no—
515C4⋊C4C2×D4×C1112yes—
516C4⋊C4C11×#4112yes—
517C22⋊C4—24no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—42no—
527C11#2637811yescharacteristic, direct product factor, Sylow
528C23—22no—
529C23—22no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23C22×D4×C1111yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—41no—
539Q8—41no—
540D4—22no—
541D4—22no—
542D4—22no—
543D4C11×C22⋊Q814yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
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—84no—
583C2×C4—84no—
584C2×C4—84no—
585C2×C4C11×#13512yes—
586C2×C4C22×D4×C1111yescharacteristic
587C2×C4C22×Q8×C1111yescharacteristic
588C2×C4C2×C11×#4111yescharacteristic
589C2×C4C2×C11×#4111yescharacteristic
590C2×C4C11×H(5,𝔽2)11yescharacteristic
591C2×C4C11×2−1+411yescharacteristic
592C8—22no—
593C8—22no—
594C8—41no—
595C8—41no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22C11×#52511yescharacteristic
604C22D42×C1111yescharacteristic
605C22D4×Q8×C1111yescharacteristic
606C22C2×C11×#13511yescharacteristic
607C22C11×#57511yescharacteristic
608C22C11×#57711yescharacteristic
609C22C11×#57711yescharacteristic
610C4—22no—
611C4—42no—
612C4—41no—
613C4—41no—
614C4—42no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—42no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4C2×C11×C22⋊Q811yescharacteristic
624C4C11×#53911yescharacteristic
625C4C11×#54711yescharacteristic
626C4C11×#55411yescharacteristic
627C2—44no—
628C2C11×#244911yescharacteristic
629C2C11×#310211yescharacteristic
630C2C11×#312311yescharacteristic
631C2C11×#326711yescharacteristic
632C2C11×#328211yescharacteristic
633C2C11×#338111yescharacteristic
634C2C11×#338811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2453C2semidirect
5. C11×#2097C2semidirect
6. C11×#2085C2semidirect
7. C11×#2066C2semidirect
8. C11×#2059C2semidirect
9. C11×#1941C2semidirect
10. C11×#1916C2semidirect
14. C11×#1863C2semidirect
130. #26378C11direct (N × H)
213. #2453C2×C11semidirect
215. #2097C2×C11semidirect
216. #2085C2×C11semidirect
217. #2066C2×C11semidirect
218. #2059C2×C11semidirect
219. #1941C2×C11semidirect
220. #1916C2×C11semidirect
224. #1863C2×C11semidirect
527. C11#26378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4782
C2×C4×C11×SD162
C11×#24532
C11×#23492
C11×#20972
C11×#20852
C11×#20662
C11×#20592
C11×#19412
C11×#19162
C11×#18772
C11×#18642
C11×#18632
C11×#18622
#2637811