Finite Group Databasebeta

← C11×#27100 #14604293

Subgroups — C11×#27100 #14604293

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2497C211yesmaximal, characteristic
2C11×#2360C211yesmaximal, characteristic
3C11×#2087C211yesmaximal, characteristic, complemented
4C11×#2083C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic
6C11×#2036C211yesmaximal, characteristic
7C11×#1933C211yesmaximal, characteristic, complemented
8C11×#1928C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic
10C11×#1921C211yesmaximal, characteristic, complemented
11C11×#1863C211yesmaximal, characteristic, complemented
12C11×#1852C211yesmaximal, characteristic
13C11×#1824C211yesmaximal, characteristic
14C11×#1803C211yesmaximal, characteristic, complemented
15C4×C11×#107C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
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×#400—21no—
32C11×#396—21no—
33C11×#391C2211yescharacteristic
34C11×#389—21no—
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#387—21no—
40C11×#387—21no—
41C11×#385—21no—
42C11×#384C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4—21no—
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×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#107—22no—
98C11×#107—22no—
99C11×#107—22no—
100C11×#107—41no—
101C11×C4⋊C8—41no—
102C11×#103—22no—
103C11×#103—22no—
104C11×#103—22no—
105C11×#103—41no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—41no—
108C4×C8×C11—22no—
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#27100C1111yesmaximal, 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×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—81no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
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—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11#4112yes—
163C11×C4⋊C4—24no—
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—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4—81no—
183C11×C4⋊C4#4112yes—
184C11×C4⋊C4#4112yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—81no—
188C11×C22⋊C4—81no—
189C11×C22⋊C4Q1614yes—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—42no—
195C42×C11—81no—
196C42×C11—81no—
197#2497C2×C1111yescharacteristic
198#2360C2×C1111yescharacteristic
199#2087C2×C1111yescharacteristic, complemented
200#2083C2×C1111yescharacteristic, complemented
201#2036C2×C1111yescharacteristic
202#2036C2×C1111yescharacteristic
203#1933C2×C1111yescharacteristic, complemented
204#1928C2×C1111yescharacteristic, complemented
205#1923C2×C1111yescharacteristic
206#1921C2×C1111yescharacteristic, complemented
207#1863C2×C1111yescharacteristic, complemented
208#1852C2×C1111yescharacteristic
209#1824C2×C1111yescharacteristic
210#1803C2×C1111yescharacteristic, complemented
211C4×#107C2×C1111yescharacteristic, complemented
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C2×Q1612yes—
219C23×C11C22×D411yescharacteristic
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—41no—
223Q8×C11—41no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—84no—
266C2×C4×C11C2×Q1612yes—
267C2×C4×C11C2×Q1612yes—
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C8×C11—22no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C2×C22⋊Q8C22×C1111yescharacteristic
279C2×C4×Q8C22×C1111yescharacteristic
280C22×C4⋊C4C22×C1111yescharacteristic
281C2×#107C22×C1111yescharacteristic
282C2×#107C22×C1111yescharacteristic
283C2×#107C22×C1111yescharacteristic
284C2×#107C22×C1111yescharacteristic
285C2×C4⋊C8C22×C1111yescharacteristic
286C2×#103C22×C1111yescharacteristic
287C2×#103C22×C1111yescharacteristic
288C2×#103C22×C1111yescharacteristic
289C2×#103C22×C1111yescharacteristic
290C2×C22⋊C8C22×C1111yescharacteristic
291C2×C22⋊C8C22×C1111yescharacteristic
292C2×C4×C8C22×C1111yescharacteristic
293#400—21no—
294#396—21no—
295#391C22×C1111yescharacteristic
296#389—21no—
297#389C22×C1111yescharacteristic
298#389C22×C1111yescharacteristic
299#389C22×C1111yescharacteristic
300#388—21no—
301#387—21no—
302#387—21no—
303#385—21no—
304#384C22×C1111yescharacteristic
305#380C22×C1111yescharacteristic
306#380C22×C1111yescharacteristic
307C4×C4⋊C4C22×C1111yescharacteristic
308C4×C4⋊C4C22×C1111yescharacteristic
309C4×C22⋊C4—21no—
310C4×C22⋊C4C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#340C22×C1111yescharacteristic
313#340C22×C1111yescharacteristic
314#340C22×C1111yescharacteristic
315#340C22×C1111yescharacteristic
316#340C22×C1111yescharacteristic
317#340C22×C1111yescharacteristic
318#340C22×C1111yescharacteristic
319#336C22×C1111yescharacteristic
320#336C22×C1111yescharacteristic
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11#52511yescharacteristic
329C22×C11#54611yescharacteristic
330C22×C11#54711yescharacteristic
331C22×C11C22×Q1611yescharacteristic
332C22×C11#57511yescharacteristic
333C22×C11#57611yescharacteristic
334C22×C11#57711yescharacteristic
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—42no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11#52911yescharacteristic
349C4×C11#54211yescharacteristic
350C4×C11#55211yescharacteristic
351C4×C11#55311yescharacteristic
352C22×Q8C23×C1111yescharacteristic
353C23×C4—21no—
354C23×C4C23×C1111yescharacteristic
355C22×C8C23×C1111yescharacteristic
356C22×C8C23×C1111yescharacteristic
357C22×C8C23×C1111yescharacteristic
358C22×C8C23×C1111yescharacteristic
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C4×Q8—22no—
362C4×Q8—41no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C4⋊C4C23×C1111yescharacteristic
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4D4×C1111yescharacteristic
384C2×C22⋊C4D4×C1111yescharacteristic
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42C23×C1111yescharacteristic
389C2×C42C23×C1111yescharacteristic
390#107—22no—
391#107—22no—
392#107—22no—
393#107—41no—
394C4⋊C8—41no—
395#103—22no—
396#103—22no—
397#103—22no—
398#103—41no—
399C22⋊C8—22no—
400C22⋊C8—41no—
401C4×C8—22no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95D4×C1111yescharacteristic
412#95D4×C1111yescharacteristic
413C2×C11—42no—
414C2×C11#246811yescharacteristic
415C2×C11#310411yescharacteristic
416C2×C11#311911yescharacteristic
417C2×C11#329911yescharacteristic
418C2×C11#332211yescharacteristic
419C2×C11#333811yescharacteristic
420C2×C11#334811yescharacteristic
421C24C2×D4×C1111yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C11×#4112yes—
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×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—81no—
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C24×C1111yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8C11×#4112yes—
463C4⋊C4—24no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4C11×#4112yes—
484C4⋊C4C11×#4112yes—
485C22⋊C4—24no—
486C22⋊C4—41no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4C11×Q1614yes—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—42no—
495C42—81no—
496C42—81no—
497C11#2710011yescharacteristic, direct product factor, Sylow
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×C11×Q1612yes—
505C23C22×D4×C1111yescharacteristic
506Q8—22no—
507Q8—22no—
508Q8—41no—
509Q8—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
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×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—84no—
552C2×C4C2×C11×Q1612yes—
553C2×C4C2×C11×Q1612yes—
554C2×C4C2×C11×#4111yescharacteristic
555C2×C4C2×C11×#4111yescharacteristic
556C2×C4C2×C11×#4111yescharacteristic
557C2×C4C2×C11×#4111yescharacteristic
558C2×C4C11×H(5,𝔽2)11yescharacteristic
559C2×C4C11×2−1+411yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22C11×#52511yescharacteristic
572C22C11×#54611yescharacteristic
573C22C11×#54711yescharacteristic
574C22C22×C11×Q1611yescharacteristic
575C22C11×#57511yescharacteristic
576C22C11×#57611yescharacteristic
577C22C11×#57711yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C11×#52911yescharacteristic
592C4C11×#54211yescharacteristic
593C4C11×#55211yescharacteristic
594C4C11×#55311yescharacteristic
595C2—42no—
596C2C11×#246811yescharacteristic
597C2C11×#310411yescharacteristic
598C2C11×#311911yescharacteristic
599C2C11×#329911yescharacteristic
600C2C11×#332211yescharacteristic
601C2C11×#333811yescharacteristic
602C2C11×#334811yescharacteristic
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×#2087C2semidirect
4. C11×#2083C2semidirect
7. C11×#1933C2semidirect
8. C11×#1928C2semidirect
10. C11×#1921C2semidirect
11. C11×#1863C2semidirect
14. C11×#1803C2semidirect
15. C4×C11×#107C2semidirect
120. #27100C11direct (N × H)
199. #2087C2×C11semidirect
200. #2083C2×C11semidirect
203. #1933C2×C11semidirect
204. #1928C2×C11semidirect
206. #1921C2×C11semidirect
207. #1863C2×C11semidirect
210. #1803C2×C11semidirect
211. C4×#107C2×C11semidirect
497. C11#27100direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24972
C11×#23602
C11×#20872
C11×#20832
C11×#20362
C11×#19332
C11×#19282
C11×#19232
C11×#19212
C11×#18632
C11×#18522
C11×#18242
C11×#18032
C4×C11×#1072
#2710011