Finite Group Databasebeta

← C11×#27044 #14604237

Subgroups — C11×#27044 #14604237

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2494C211yesmaximal, characteristic
2C11×#2362C211yesmaximal, characteristic
3C11×#2074C211yesmaximal, characteristic, complemented
4C11×#2068C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic
6C11×#2035C211yesmaximal, characteristic
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1942C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic
10C11×#1919C211yesmaximal, characteristic, complemented
11C11×#1919C211yesmaximal, characteristic, complemented
12C11×#1865C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic
14C11×#1825C211yesmaximal, characteristic
15C4×C11×#103C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#401—21no—
32C11×#397—21no—
33C11×#391C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#388—21no—
39C11×#388—21no—
40C11×#387—21no—
41C11×#387—21no—
42C11×#382C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C4×C11×C4⋊C4—21no—
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C11×#107—22no—
96C11×#107—41no—
97C11×#106—22no—
98C11×#106—22no—
99C11×C4⋊C8—22no—
100C11×#103—22no—
101C11×#103—22no—
102C11×#103—22no—
103C11×#103—41no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8—41no—
106C4×C8×C11—41no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120#27044C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11C2×D411yescharacteristic
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
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#4112yes—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
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—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4#4112yes—
178C11×C4⋊C4#4112yes—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—81no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11—42no—
191C42×C11—42no—
192C42×C11—81no—
193#2494C2×C1111yescharacteristic
194#2362C2×C1111yescharacteristic
195#2074C2×C1111yescharacteristic, complemented
196#2068C2×C1111yescharacteristic, complemented
197#2036C2×C1111yescharacteristic
198#2035C2×C1111yescharacteristic
199#1949C2×C1111yescharacteristic, complemented
200#1942C2×C1111yescharacteristic, complemented
201#1923C2×C1111yescharacteristic
202#1919C2×C1111yescharacteristic, complemented
203#1919C2×C1111yescharacteristic, complemented
204#1865C2×C1111yescharacteristic, complemented
205#1854C2×C1111yescharacteristic
206#1825C2×C1111yescharacteristic
207C4×#103C2×C1111yescharacteristic, complemented
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
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#13512yes—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C2×C22⋊Q8C22×C1111yescharacteristic
274C2×C4×Q8C22×C1111yescharacteristic
275C2×#117C22×C1111yescharacteristic
276C2×#107C22×C1111yescharacteristic
277C2×#107C22×C1111yescharacteristic
278C2×#106C22×C1111yescharacteristic
279C2×#106C22×C1111yescharacteristic
280C2×C4⋊C8C22×C1111yescharacteristic
281C2×#103C22×C1111yescharacteristic
282C2×#103C22×C1111yescharacteristic
283C2×#103C22×C1111yescharacteristic
284C2×#103C22×C1111yescharacteristic
285C2×C22⋊C8C22×C1111yescharacteristic
286C2×C22⋊C8C22×C1111yescharacteristic
287C2×C4×C8C22×C1111yescharacteristic
288#401—21no—
289#397—21no—
290#391C22×C1111yescharacteristic
291#389C22×C1111yescharacteristic
292#389C22×C1111yescharacteristic
293#389C22×C1111yescharacteristic
294#388—21no—
295#388—21no—
296#388—21no—
297#387—21no—
298#387—21no—
299#382C22×C1111yescharacteristic
300#380C22×C1111yescharacteristic
301#380C22×C1111yescharacteristic
302C4×C4⋊C4—21no—
303C4×C4⋊C4C22×C1111yescharacteristic
304C4×C4⋊C4C22×C1111yescharacteristic
305C4×C22⋊C4C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#340C22×C1111yescharacteristic
308#340C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#340C22×C1111yescharacteristic
313#340C22×C1111yescharacteristic
314#336C22×C1111yescharacteristic
315#336C22×C1111yescharacteristic
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11#52511yescharacteristic
324C22×C11#54611yescharacteristic
325C22×C11#54711yescharacteristic
326C22×C11C2×#13511yescharacteristic
327C22×C11#57511yescharacteristic
328C22×C11#57711yescharacteristic
329C22×C11#57811yescharacteristic
330C4×C11—22no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11#52911yescharacteristic
344C4×C11#53911yescharacteristic
345C4×C11#55311yescharacteristic
346C4×C11#55611yescharacteristic
347C22×Q8C23×C1111yescharacteristic
348C23×C4C23×C1111yescharacteristic
349C22×C8C23×C1111yescharacteristic
350C22×C8C23×C1111yescharacteristic
351C22×C8C23×C1111yescharacteristic
352C22×C8C23×C1111yescharacteristic
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C4×Q8—22no—
356C4×Q8—41no—
357#117—22no—
358#117—41no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1111yescharacteristic
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4D4×C1111yescharacteristic
376C2×C22⋊C4D4×C1111yescharacteristic
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42C23×C1111yescharacteristic
382C2×C42C23×C1111yescharacteristic
383#107—22no—
384#107—41no—
385#106—22no—
386#106—22no—
387C4⋊C8—22no—
388#103—22no—
389#103—22no—
390#103—22no—
391#103—41no—
392C22⋊C8—22no—
393C22⋊C8—41no—
394C4×C8—41no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95D4×C1111yescharacteristic
407#95D4×C1111yescharacteristic
408C2×C11—81no—
409C2×C11#246611yescharacteristic
410C2×C11#310211yescharacteristic
411C2×C11#312111yescharacteristic
412C2×C11#330111yescharacteristic
413C2×C11#331511yescharacteristic
414C2×C11#334211yescharacteristic
415C2×C11#335111yescharacteristic
416C24C2×D4×C1111yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C11×#4112yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C24×C1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8C11×#4112yes—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—81no—
472C4⋊C4C11×#4112yes—
473C4⋊C4C11×#4112yes—
474C22⋊C4—24no—
475C22⋊C4—22no—
476C22⋊C4—41no—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C22⋊C4—81no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—42no—
486C42—42no—
487C42—81no—
488C11#2704411yescharacteristic, direct product factor, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×D4×C1111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4C11×#13512yes—
544C2×C4C2×C11×#4111yescharacteristic
545C2×C4C2×C11×#4111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C2×C11×#4111yescharacteristic
548C2×C4C11×H(5,𝔽2)11yescharacteristic
549C2×C4C11×2−1+411yescharacteristic
550C8—22no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22C11×#52511yescharacteristic
562C22C11×#54611yescharacteristic
563C22C11×#54711yescharacteristic
564C22C2×C11×#13511yescharacteristic
565C22C11×#57511yescharacteristic
566C22C11×#57711yescharacteristic
567C22C11×#57811yescharacteristic
568C4—22no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C11×#52911yescharacteristic
582C4C11×#53911yescharacteristic
583C4C11×#55311yescharacteristic
584C4C11×#55611yescharacteristic
585C2—81no—
586C2C11×#246611yescharacteristic
587C2C11×#310211yescharacteristic
588C2C11×#312111yescharacteristic
589C2C11×#330111yescharacteristic
590C2C11×#331511yescharacteristic
591C2C11×#334211yescharacteristic
592C2C11×#335111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×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
3. C11×#2074C2semidirect
4. C11×#2068C2semidirect
7. C11×#1949C2semidirect
8. C11×#1942C2semidirect
10. C11×#1919C2semidirect
11. C11×#1919C2semidirect
12. C11×#1865C2semidirect
15. C4×C11×#103C2semidirect
120. #27044C11direct (N × H)
195. #2074C2×C11semidirect
196. #2068C2×C11semidirect
199. #1949C2×C11semidirect
200. #1942C2×C11semidirect
202. #1919C2×C11semidirect
203. #1919C2×C11semidirect
204. #1865C2×C11semidirect
207. C4×#103C2×C11semidirect
488. C11#27044direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24942
C11×#23622
C11×#20742
C11×#20682
C11×#20362
C11×#20352
C11×#19492
C11×#19422
C11×#19232
C11×#19192
C11×#18652
C11×#18542
C11×#18252
C4×C11×#1032
#2704411