Finite Group Databasebeta

← C11×#27058 #14604251

Subgroups — C11×#27058 #14604251

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2496C211yesmaximal, characteristic
2C11×#2362C211yesmaximal, characteristic
3C11×#2072C211yesmaximal, characteristic, complemented
4C11×#2066C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic
6C11×#2036C211yesmaximal, characteristic
7C11×#1947C211yesmaximal, characteristic, complemented
8C11×#1943C211yesmaximal, characteristic, complemented
9C11×#1924C211yesmaximal, characteristic
10C11×#1921C211yesmaximal, characteristic, complemented
11C11×#1918C211yesmaximal, characteristic, complemented
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic
14C11×#1825C211yesmaximal, characteristic
15C11×#1763C211yesmaximal, characteristic, complemented
16C2×C11×#126—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C11×#400—21no—
33C11×#397—21no—
34C11×#391C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#388—21no—
40C11×#387—21no—
41C11×#387—21no—
42C11×#384C2211yescharacteristic
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×#126—44no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C11×#117—22no—
71C11×#117—41no—
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⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
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×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×#107—22no—
99C11×#107—22no—
100C11×#107—22no—
101C11×#106—41no—
102C11×C4⋊C8—22no—
103C11×#103—22no—
104C11×#103—22no—
105C11×#103—22no—
106C11×#103—41no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—41no—
109C11×#97—41no—
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×#95—21no—
119C11×#95D411yescharacteristic
120C11×#95D411yescharacteristic
121#27058C1111yesmaximal, characteristic, direct product factor, Sylow
122C24×C11C2×D411yescharacteristic
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11#4112yes—
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—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
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—21no—
160C2×C8×C11#4112yes—
161C11×C4⋊C4—24no—
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—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4#4112yes—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—42no—
193C42×C11—42no—
194C42×C11—42no—
195C42×C11—42no—
196#2496C2×C1111yescharacteristic
197#2362C2×C1111yescharacteristic
198#2072C2×C1111yescharacteristic, complemented
199#2066C2×C1111yescharacteristic, complemented
200#2036C2×C1111yescharacteristic
201#2036C2×C1111yescharacteristic
202#1947C2×C1111yescharacteristic, complemented
203#1943C2×C1111yescharacteristic, complemented
204#1924C2×C1111yescharacteristic
205#1921C2×C1111yescharacteristic, complemented
206#1918C2×C1111yescharacteristic, complemented
207#1863C2×C1111yescharacteristic, complemented
208#1854C2×C1111yescharacteristic
209#1825C2×C1111yescharacteristic
210#1763C2×C1111yescharacteristic, complemented
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
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—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×C11AGL(1,ℤ/8)12yes—
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C8×C11—22no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C2×#126—21no—
277C2×C22⋊Q8C22×C1111yescharacteristic
278C2×C4×Q8C22×C1111yescharacteristic
279C2×#117C22×C1111yescharacteristic
280C2×#107C22×C1111yescharacteristic
281C2×#107C22×C1111yescharacteristic
282C2×#107C22×C1111yescharacteristic
283C2×#106C22×C1111yescharacteristic
284C2×C4⋊C8C22×C1111yescharacteristic
285C2×#103C22×C1111yescharacteristic
286C2×#103C22×C1111yescharacteristic
287C2×#103C22×C1111yescharacteristic
288C2×#103C22×C1111yescharacteristic
289C2×C22⋊C8C22×C1111yescharacteristic
290C2×C22⋊C8C22×C1111yescharacteristic
291C2×#97C22×C1111yescharacteristic
292#400—21no—
293#397—21no—
294#391C22×C1111yescharacteristic
295#389C22×C1111yescharacteristic
296#389C22×C1111yescharacteristic
297#389C22×C1111yescharacteristic
298#388—21no—
299#388—21no—
300#387—21no—
301#387—21no—
302#384C22×C1111yescharacteristic
303#380C22×C1111yescharacteristic
304#380C22×C1111yescharacteristic
305C4×C4⋊C4—21no—
306C4×C4⋊C4C22×C1111yescharacteristic
307C4×C4⋊C4C22×C1111yescharacteristic
308C4×C22⋊C4C22×C1111yescharacteristic
309#340C22×C1111yescharacteristic
310#340C22×C1111yescharacteristic
311#340C22×C1111yescharacteristic
312#340C22×C1111yescharacteristic
313#340C22×C1111yescharacteristic
314#340C22×C1111yescharacteristic
315#340C22×C1111yescharacteristic
316#340C22×C1111yescharacteristic
317#336C22×C1111yescharacteristic
318#336C22×C1111yescharacteristic
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11#52511yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#54711yescharacteristic
329C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57811yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11#52911yescharacteristic
347C4×C11#53911yescharacteristic
348C4×C11#55311yescharacteristic
349C4×C11#55611yescharacteristic
350C22×Q8C23×C1111yescharacteristic
351C23×C4C23×C1111yescharacteristic
352C22×C8C23×C1111yescharacteristic
353C22×C8C23×C1111yescharacteristic
354C22×C8C23×C1111yescharacteristic
355C22×C8C23×C1111yescharacteristic
356#126—44no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C4×Q8—22no—
360C4×Q8—41no—
361#117—22no—
362#117—41no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C4⋊C4C23×C1111yescharacteristic
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C4⋊C4C23×C1111yescharacteristic
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4D4×C1111yescharacteristic
382C2×C22⋊C4D4×C1111yescharacteristic
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C23×C1111yescharacteristic
388C2×C42C23×C1111yescharacteristic
389#107—22no—
390#107—22no—
391#107—22no—
392#106—41no—
393C4⋊C8—22no—
394#103—22no—
395#103—22no—
396#103—22no—
397#103—41no—
398C22⋊C8—22no—
399C22⋊C8—41no—
400#97—41no—
401#95—21no—
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#95D4×C1111yescharacteristic
411#95D4×C1111yescharacteristic
412C2×C11—81no—
413C2×C11#246611yescharacteristic
414C2×C11#311511yescharacteristic
415C2×C11#312711yescharacteristic
416C2×C11#331311yescharacteristic
417C2×C11#333011yescharacteristic
418C2×C11#334311yescharacteristic
419C2×C11#334911yescharacteristic
420C24C2×D4×C1111yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C11×#4112yes—
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×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C24×C1111yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C11×#4112yes—
459C4⋊C4—24no—
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—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4C11×#4112yes—
479C4⋊C4C11×#4112yes—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—41no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—42no—
492C42—42no—
493C42—42no—
494C11#2705811yescharacteristic, direct product factor, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C22×D4×C1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4C11×AGL(1,ℤ/8)12yes—
550C2×C4C2×C11×#4111yescharacteristic
551C2×C4C2×C11×#4111yescharacteristic
552C2×C4C2×C11×#4111yescharacteristic
553C2×C4C2×C11×#4111yescharacteristic
554C2×C4C11×H(5,𝔽2)11yescharacteristic
555C2×C4C11×2−1+411yescharacteristic
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C11×#52511yescharacteristic
568C22C11×#54611yescharacteristic
569C22C11×#54711yescharacteristic
570C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
571C22C11×#57511yescharacteristic
572C22C11×#57811yescharacteristic
573C22C11×#57811yescharacteristic
574C4—22no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C11×#52911yescharacteristic
588C4C11×#53911yescharacteristic
589C4C11×#55311yescharacteristic
590C4C11×#55611yescharacteristic
591C2—81no—
592C2C11×#246611yescharacteristic
593C2C11×#311511yescharacteristic
594C2C11×#312711yescharacteristic
595C2C11×#331311yescharacteristic
596C2C11×#333011yescharacteristic
597C2C11×#334311yescharacteristic
598C2C11×#334911yescharacteristic
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×#2072C2semidirect
4. C11×#2066C2semidirect
7. C11×#1947C2semidirect
8. C11×#1943C2semidirect
10. C11×#1921C2semidirect
11. C11×#1918C2semidirect
12. C11×#1863C2semidirect
15. C11×#1763C2semidirect
121. #27058C11direct (N × H)
198. #2072C2×C11semidirect
199. #2066C2×C11semidirect
202. #1947C2×C11semidirect
203. #1943C2×C11semidirect
205. #1921C2×C11semidirect
206. #1918C2×C11semidirect
207. #1863C2×C11semidirect
210. #1763C2×C11semidirect
494. C11#27058direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24962
C11×#23622
C11×#20722
C11×#20662
C11×#20362
C11×#19472
C11×#19432
C11×#19242
C11×#19212
C11×#19182
C11×#18632
C11×#18542
C11×#18252
C11×#17632
#2705811