Finite Group Databasebeta

← C11×#27126 #14604319

Subgroups — C11×#27126 #14604319

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2512C211yesmaximal, characteristic
2C11×#2365C211yesmaximal, characteristic, complemented
3C11×#2099C211yesmaximal, characteristic, complemented
4C11×#2067C211yesmaximal, characteristic
5C11×#2057C211yesmaximal, characteristic, complemented
6C11×#2023C211yesmaximal, characteristic
7C11×#1947C211yesmaximal, characteristic, complemented
8C11×#1934C211yesmaximal, characteristic
9C11×#1925C211yesmaximal, characteristic
10C11×#1925C211yesmaximal, characteristic
11C11×#1925C211yesmaximal, characteristic
12C11×#1918C211yesmaximal, characteristic, complemented
13C11×#1918C211yesmaximal, characteristic, complemented
14C11×#1916C211yesmaximal, characteristic, complemented
15C4×C11×#107C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—21no—
18C2×C4×Q8×C11—21no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C11×#397—21no—
30C11×#396—21no—
31C11×#391—21no—
32C11×#390C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#387—21no—
40C11×#387—21no—
41C11×#384C2211yescharacteristic
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×#126—44no—
68C4×Q8×C11—44no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#107—22no—
98C11×#107—22no—
99C11×#107—22no—
100C11×#107—22no—
101C11×C4⋊C8—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—22no—
106C4×C8×C11—22no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#27126C1111yesmaximal, characteristic, direct product factor, Sylow
117C24×C11—21no—
118C2×Q8×C11—24no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11#4112yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4D814yes—
172C11×C4⋊C4#4112yes—
173C11×C4⋊C4#4112yes—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—81no—
180C11×C22⋊C4—81no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188C42×C11—42no—
189C42×C11—42no—
190C42×C11—42no—
191#2512C2×C1111yescharacteristic
192#2365C2×C1111yescharacteristic, complemented
193#2099C2×C1111yescharacteristic, complemented
194#2067C2×C1111yescharacteristic
195#2057C2×C1111yescharacteristic, complemented
196#2023C2×C1111yescharacteristic
197#1947C2×C1111yescharacteristic, complemented
198#1934C2×C1111yescharacteristic
199#1925C2×C1111yescharacteristic
200#1925C2×C1111yescharacteristic
201#1925C2×C1111yescharacteristic
202#1918C2×C1111yescharacteristic, complemented
203#1918C2×C1111yescharacteristic, complemented
204#1916C2×C1111yescharacteristic, complemented
205C4×#107C2×C1111yescharacteristic, complemented
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11C22×D411yescharacteristic
214Q8×C11—48no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
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×C11C2×D812yes—
256C2×C4×C11C2×D812yes—
257C2×C4×C11C2×D812yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C8×C11—22no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C2×C4⋊Q8C22×C1111yescharacteristic
269C2×#126—21no—
270C2×C4×Q8—21no—
271C2×#107C22×C1111yescharacteristic
272C2×#107C22×C1111yescharacteristic
273C2×#107C22×C1111yescharacteristic
274C2×#107C22×C1111yescharacteristic
275C2×C4⋊C8C22×C1111yescharacteristic
276C2×#102C22×C1111yescharacteristic
277C2×#102C22×C1111yescharacteristic
278C2×#102C22×C1111yescharacteristic
279C2×#102C22×C1111yescharacteristic
280C2×C4×C8C22×C1111yescharacteristic
281#397—21no—
282#396—21no—
283#391—21no—
284#390C22×C1111yescharacteristic
285#390C22×C1111yescharacteristic
286#390C22×C1111yescharacteristic
287#389C22×C1111yescharacteristic
288#389C22×C1111yescharacteristic
289#389C22×C1111yescharacteristic
290#388—21no—
291#387—21no—
292#387—21no—
293#384C22×C1111yescharacteristic
294C4×C4⋊C4C22×C1111yescharacteristic
295C4×C4⋊C4C22×C1111yescharacteristic
296C4×C4⋊C4C22×C1111yescharacteristic
297C4×C4⋊C4C22×C1111yescharacteristic
298C4×C4⋊C4C22×C1111yescharacteristic
299#340C22×C1111yescharacteristic
300#340C22×C1111yescharacteristic
301#340C22×C1111yescharacteristic
302#340C22×C1111yescharacteristic
303#340C22×C1111yescharacteristic
304#340C22×C1111yescharacteristic
305#340C22×C1111yescharacteristic
306#340C22×C1111yescharacteristic
307#336C22×C1111yescharacteristic
308#336C22×C1111yescharacteristic
309#336C22×C1111yescharacteristic
310#336C22×C1111yescharacteristic
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11#52511yescharacteristic
319C22×C11#54711yescharacteristic
320C22×C11#54811yescharacteristic
321C22×C11C22×D811yescharacteristic
322C22×C11#57511yescharacteristic
323C22×C11#57711yescharacteristic
324C22×C11#57811yescharacteristic
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#52911yescharacteristic
339C4×C11#54111yescharacteristic
340C4×C11#55611yescharacteristic
341C4×C11#55611yescharacteristic
342C22×Q8—21no—
343C22×D4C23×C1111yescharacteristic
344C22×C8C23×C1111yescharacteristic
345C22×C8C23×C1111yescharacteristic
346C22×C8C23×C1111yescharacteristic
347C22×C8C23×C1111yescharacteristic
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350#126—44no—
351C4×Q8—44no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4D4×C1111yescharacteristic
359C2×C4⋊C4D4×C1111yescharacteristic
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42C23×C1111yescharacteristic
378C2×C42C23×C1111yescharacteristic
379C2×C42C23×C1111yescharacteristic
380#107—22no—
381#107—22no—
382#107—22no—
383#107—22no—
384C4⋊C8—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389C4×C8—22no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95D4×C1111yescharacteristic
398#95D4×C1111yescharacteristic
399C2×C11—161no—
400C2×C11#246911yescharacteristic
401C2×C11#310011yescharacteristic
402C2×C11#312111yescharacteristic
403C2×C11#333411yescharacteristic
404C2×C11#335011yescharacteristic
405C2×C11#335811yescharacteristic
406C2×C11#337711yescharacteristic
407C24—21no—
408C2×Q8—24no—
409C2×Q8—42no—
410C2×Q8—42no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C24×C1111yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8C11×#4112yes—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4C11×D814yes—
462C4⋊C4C11×#4112yes—
463C4⋊C4C11×#4112yes—
464C4⋊C4C11×#4112yes—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—81no—
470C22⋊C4—81no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—42no—
479C42—42no—
480C42—42no—
481C11#2712611yescharacteristic, direct product factor, Sylow
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23C22×D4×C1111yescharacteristic
490Q8—48no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
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×C4C2×C11×D812yes—
532C2×C4C2×C11×D812yes—
533C2×C4C2×C11×D812yes—
534C2×C4C2×C11×#4111yescharacteristic
535C2×C4C2×C11×#4111yescharacteristic
536C2×C4C2×C11×#4111yescharacteristic
537C2×C4C2×C11×#4111yescharacteristic
538C2×C4C11×2−1+411yescharacteristic
539C2×C4C11×2−1+411yescharacteristic
540C8—22no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22C11×#52511yescharacteristic
552C22C11×#54711yescharacteristic
553C22C11×#54811yescharacteristic
554C22C22×C11×D811yescharacteristic
555C22C11×#57511yescharacteristic
556C22C11×#57711yescharacteristic
557C22C11×#57811yescharacteristic
558C4—22no—
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C11×#52911yescharacteristic
572C4C11×#54111yescharacteristic
573C4C11×#55611yescharacteristic
574C4C11×#55611yescharacteristic
575C2—161no—
576C2C11×#246911yescharacteristic
577C2C11×#310011yescharacteristic
578C2C11×#312111yescharacteristic
579C2C11×#333411yescharacteristic
580C2C11×#335011yescharacteristic
581C2C11×#335811yescharacteristic
582C2C11×#337711yescharacteristic
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
2. C11×#2365C2semidirect
3. C11×#2099C2semidirect
5. C11×#2057C2semidirect
7. C11×#1947C2semidirect
12. C11×#1918C2semidirect
13. C11×#1918C2semidirect
14. C11×#1916C2semidirect
15. C4×C11×#107C2semidirect
116. #27126C11direct (N × H)
192. #2365C2×C11semidirect
193. #2099C2×C11semidirect
195. #2057C2×C11semidirect
197. #1947C2×C11semidirect
202. #1918C2×C11semidirect
203. #1918C2×C11semidirect
204. #1916C2×C11semidirect
205. C4×#107C2×C11semidirect
481. C11#27126direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25122
C11×#23652
C11×#20992
C11×#20672
C11×#20572
C11×#20232
C11×#19472
C11×#19342
C11×#19252
C11×#19182
C11×#19162
C4×C11×#1072
#2712611