Finite Group Databasebeta

← C11×#22939 #14600132

Subgroups — C11×#22939 #14600132

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic
2C11×#2362C211yesmaximal, characteristic
3C11×#2346C211yesmaximal, characteristic
4C11×#1944C211yesmaximal, characteristic, complemented
5C11×#1935C211yesmaximal, characteristic, complemented
6C11×#1928C211yesmaximal, characteristic, complemented
7C11×#1921C211yesmaximal, characteristic, complemented
8C11×#1919C211yesmaximal, characteristic, complemented
9C11×#1892C211yesmaximal, characteristic
10C11×#1865C211yesmaximal, characteristic, complemented
11C11×#1854C211yesmaximal, characteristic
12C11×#1776C211yesmaximal, characteristic, complemented
13C11×#1763C211yesmaximal, characteristic, complemented
14C11×#1752C211yesmaximal, characteristic
15C11×#1735C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C11×#485C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#388—21no—
39C11×#388—21no—
40C11×#388—21no—
41C11×#387—21no—
42C11×#382—21no—
43C11×#380C2211yescharacteristic
44C4×C11×C4⋊C4—21no—
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C11×#376—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8C2×C414yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—41no—
73C11×#117—22no—
74C11×#117—22no—
75C11×#117—41no—
76C11×#117C2×C414yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C11×#107—41no—
104C11×#107C2×C414yes—
105C11×#106—22no—
106C11×#106C2×C414yes—
107C11×#103—22no—
108C11×#103—41no—
109C11×#103C2×C414yes—
110C11×#103C2×C414yes—
111C11×C22⋊C8C2×C414yes—
112C11×#97—22no—
113C11×#97—41no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95D411yescharacteristic
124C11×#95D411yescharacteristic
125#22939C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—44no—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C2×C8×C11#4112yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4C22×C412yes—
182C11×C4⋊C4C22×C412yes—
183C11×C4⋊C4C22×C412yes—
184C11×C4⋊C4#4112yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—81no—
191C42×C11—24no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—42no—
197C42×C11—42no—
198C42×C11—42no—
199C42×C11—42no—
200C42×C11—42no—
201C2×#485C2×C1111yescharacteristic
202#2362C2×C1111yescharacteristic
203#2346C2×C1111yescharacteristic
204#1944C2×C1111yescharacteristic, complemented
205#1935C2×C1111yescharacteristic, complemented
206#1928C2×C1111yescharacteristic, complemented
207#1921C2×C1111yescharacteristic, complemented
208#1919C2×C1111yescharacteristic, complemented
209#1892C2×C1111yescharacteristic
210#1865C2×C1111yescharacteristic, complemented
211#1854C2×C1111yescharacteristic
212#1776C2×C1111yescharacteristic, complemented
213#1763C2×C1111yescharacteristic, complemented
214#1752C2×C1111yescharacteristic
215#1735C2×C1111yescharacteristic
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11C4×D412yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—41no—
227Q8×C11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
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×C11C4×D412yes—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C8×C11—22no—
278C8×C11—22no—
279C8×C11—22no—
280C8×C11—41no—
281C23×C8C22×C1111yescharacteristic
282C2×C22⋊Q8C22×C1111yescharacteristic
283C2×C4×Q8C22×C1111yescharacteristic
284C2×#117C22×C1111yescharacteristic
285C2×#117C22×C1111yescharacteristic
286#485C4×C1118yescomplemented
287C2×#107C22×C1111yescharacteristic
288C2×#107C22×C1111yescharacteristic
289C2×#106C22×C1111yescharacteristic
290C2×#106C22×C1111yescharacteristic
291C2×#103C22×C1111yescharacteristic
292C2×#103C22×C1111yescharacteristic
293C2×#103C22×C1111yescharacteristic
294C2×#103C22×C1111yescharacteristic
295C2×C22⋊C8C22×C1111yescharacteristic
296C2×#97C22×C1111yescharacteristic
297C2×#97C22×C1111yescharacteristic
298#391C22×C1111yescharacteristic
299#389C22×C1111yescharacteristic
300#389C22×C1111yescharacteristic
301#389C22×C1111yescharacteristic
302#388—21no—
303#388—21no—
304#388—21no—
305#388—21no—
306#387—21no—
307#382—21no—
308#380C22×C1111yescharacteristic
309C4×C4⋊C4—21no—
310C4×C4⋊C4C22×C1111yescharacteristic
311C4×C4⋊C4C22×C1111yescharacteristic
312C4×C4⋊C4C22×C1111yescharacteristic
313C4×C22⋊C4C22×C1111yescharacteristic
314#376—21no—
315#340C22×C1111yescharacteristic
316#340C22×C1111yescharacteristic
317#340C22×C1111yescharacteristic
318#340C22×C1111yescharacteristic
319#340C22×C1111yescharacteristic
320#340C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#336C22×C1111yescharacteristic
324#336C22×C1111yescharacteristic
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#54611yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C4×#4111yescharacteristic
353C4×C11#52011yescharacteristic
354C4×C11#55111yescharacteristic
355C4×C11#55211yescharacteristic
356C22×Q8C23×C1111yescharacteristic
357C23×C4C23×C1111yescharacteristic
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—41no—
361C22×C8C23×C1111yescharacteristic
362C22×C8C23×C1111yescharacteristic
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365C22⋊Q8—22no—
366C22⋊Q8C2×C4×C1114yes—
367C4×Q8—22no—
368C4×Q8—41no—
369#117—22no—
370#117—22no—
371#117—41no—
372#117C2×C4×C1114yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1111yescharacteristic
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4D4×C1111yescharacteristic
390C2×C22⋊C4D4×C1111yescharacteristic
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C1111yescharacteristic
398C2×C42C23×C1111yescharacteristic
399#107—41no—
400#107C2×C4×C1114yes—
401#106—22no—
402#106C2×C4×C1114yes—
403#103—22no—
404#103—41no—
405#103C2×C4×C1114yes—
406#103C2×C4×C1114yes—
407C22⋊C8C2×C4×C1114yes—
408#97—22no—
409#97—41no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95D4×C1111yescharacteristic
420#95D4×C1111yescharacteristic
421C2×C11—42no—
422C2×C11#235911yescharacteristic
423C2×C11#294311yescharacteristic
424C2×C11#294711yescharacteristic
425C2×C11#331511yescharacteristic
426C2×C11#332111yescharacteristic
427C2×C11#334811yescharacteristic
428C2×C11#334911yescharacteristic
429C24C2×D4×C1111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C22×C4×C1112yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4C22×C4×C1112yes—
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C11×#4112yes—
455C22×C4C24×C1111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—44no—
466C2×C8C22×C4×C1112yes—
467C2×C8C22×C4×C1112yes—
468C2×C8C11×#4112yes—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4C22×C4×C1112yes—
485C4⋊C4C22×C4×C1112yes—
486C4⋊C4C22×C4×C1112yes—
487C4⋊C4C11×#4112yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—42no—
493C22⋊C4—81no—
494C42—24no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C42—42no—
501C42—42no—
502C42—42no—
503C42—42no—
504C11#2293911yescharacteristic, direct product factor, Sylow
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23C4×D4×C1112yes—
512C23C22×D4×C1111yescharacteristic
513Q8—22no—
514Q8—22no—
515Q8—41no—
516Q8—41no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4C4×D4×C1112yes—
560C2×C4C23×C4×C1111yescharacteristic
561C2×C4C2×C11×#4111yescharacteristic
562C2×C4C2×C11×#4111yescharacteristic
563C2×C4C2×C11×#4111yescharacteristic
564C2×C4C11×H(5,𝔽2)11yescharacteristic
565C2×C4C11×2−1+411yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8—41no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×C4×D4×C1111yescharacteristic
578C22C11×#54611yescharacteristic
579C22C11×#54711yescharacteristic
580C22C11×#57511yescharacteristic
581C22C11×#57511yescharacteristic
582C22C11×#57711yescharacteristic
583C22C11×#57811yescharacteristic
584C4—22no—
585C4—42no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C4×C11×#4111yescharacteristic
598C4C11×#52011yescharacteristic
599C4C11×#55111yescharacteristic
600C4C11×#55211yescharacteristic
601C2—42no—
602C2C11×#235911yescharacteristic
603C2C11×#294311yescharacteristic
604C2C11×#294711yescharacteristic
605C2C11×#331511yescharacteristic
606C2C11×#332111yescharacteristic
607C2C11×#334811yescharacteristic
608C2C11×#334911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1944C2semidirect
5. C11×#1935C2semidirect
6. C11×#1928C2semidirect
7. C11×#1921C2semidirect
8. C11×#1919C2semidirect
10. C11×#1865C2semidirect
12. C11×#1776C2semidirect
13. C11×#1763C2semidirect
21. C11×#485C4semidirect
125. #22939C11direct (N × H)
204. #1944C2×C11semidirect
205. #1935C2×C11semidirect
206. #1928C2×C11semidirect
207. #1921C2×C11semidirect
208. #1919C2×C11semidirect
210. #1865C2×C11semidirect
212. #1776C2×C11semidirect
213. #1763C2×C11semidirect
286. #485C4×C11semidirect
504. C11#22939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C11×#23622
C11×#23462
C11×#19442
C11×#19352
C11×#19282
C11×#19212
C11×#19192
C11×#18922
C11×#18652
C11×#18542
C11×#17762
C11×#17632
C11×#17522
C11×#17352
#2293911