Finite Group Databasebeta

← C11×#24310 #14601503

Subgroups — C11×#24310 #14601503

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C11×#475C211yesmaximal, characteristic, complemented
4C11×#2323C211yesmaximal, characteristic
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2058C211yesmaximal, characteristic, complemented
7C11×#2026C211yesmaximal, characteristic, complemented
8C11×#2024C211yesmaximal, characteristic, complemented
9C11×#1989C211yesmaximal, characteristic, complemented
10C11×#1987C211yesmaximal, characteristic, complemented
11C11×#1873C211yesmaximal, characteristic
12C11×#1872C211yesmaximal, characteristic
13C11×#1854C211yesmaximal, characteristic
14C11×#1853C211yesmaximal, characteristic
15C11×#1798C211yesmaximal, characteristic
16C11×#544—24no—
17C11×#544—24no—
18C2×C11×C4⋊Q8—21no—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×#125C2211yescharacteristic
23C2×C11×#125C2211yescharacteristic
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#479—24no—
32C11×#475—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C11×#391C2211yescharacteristic
46C11×#389—21no—
47C11×#389C2211yescharacteristic
48C11×#388—21no—
49C11×#388—21no—
50C11×#387—21no—
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11—21no—
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C4⋊Q8—28no—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8D414yes—
77C11×#125—28no—
78C11×#125—22no—
79C11×#125—22no—
80C11×#125—22no—
81C11×#125D414yes—
82C11×C22⋊Q8—28no—
83C11×C22⋊Q8—28no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8Q814yescomplemented
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C11×#117—22no—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4D411yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C11×#107—22no—
124C11×#106—22no—
125C11×#106—22no—
126C11×#106—22no—
127C11×C4⋊C8—22no—
128C11×C4⋊C8—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—22no—
132C11×#103—22no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8—22no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140#24310C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—81no—
150C2×Q8×C11—81no—
151C2×Q8×C11—81no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×Q812yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×Q812yes—
175C22×C4×C11#4112yes—
176C22×C4×C11C2411yescharacteristic
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—81no—
210C11×C4⋊C4C2×D412yes—
211C11×C4⋊C4C2×D412yes—
212C11×C4⋊C4C2×D412yes—
213C11×C4⋊C4C2×D412yes—
214C11×C4⋊C4C2×Q812yes—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—81no—
220C42×C11—24no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—42no—
224C42×C11—81no—
225C42×C11C2×D412yes—
226C42×C11C2×D412yes—
227C2×#544C2×C1111yescharacteristic
228C2×#479C2×C1111yescharacteristic, complemented
229C2×#475C2×C1111yescharacteristic, complemented
230#2323C2×C1111yescharacteristic
231#2059C2×C1111yescharacteristic, complemented
232#2058C2×C1111yescharacteristic, complemented
233#2026C2×C1111yescharacteristic, complemented
234#2024C2×C1111yescharacteristic, complemented
235#1989C2×C1111yescharacteristic, complemented
236#1987C2×C1111yescharacteristic, complemented
237#1873C2×C1111yescharacteristic
238#1872C2×C1111yescharacteristic
239#1854C2×C1111yescharacteristic
240#1853C2×C1111yescharacteristic
241#1798C2×C1111yescharacteristic
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11C22⋊Q812yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—84no—
255Q8×C11—84no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—84no—
297C2×C4×C11#12012yes—
298C2×C4×C11#12012yes—
299C2×C4×C11C22⋊Q812yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C22×Q811yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C112−1+411yescharacteristic
305C2×C4×C112−1+411yescharacteristic
306C8×C11—41no—
307C8×C11—41no—
308C8×C11—41no—
309C8×C11—41no—
310#544—24no—
311#544—24no—
312C2×C4⋊Q8—21no—
313C2×C4⋊Q8C22×C1111yescharacteristic
314C2×C4⋊Q8C22×C1111yescharacteristic
315C2×#125—21no—
316C2×#125C22×C1111yescharacteristic
317C2×#125C22×C1111yescharacteristic
318C2×C22⋊Q8—21no—
319C2×C22⋊Q8—21no—
320C2×C22⋊Q8C22×C1111yescharacteristic
321C2×C4×Q8C22×C1111yescharacteristic
322C2×#117C22×C1111yescharacteristic
323C2×#117C22×C1111yescharacteristic
324C22×C4⋊C4C22×C1111yescharacteristic
325#479—24no—
326#475—24no—
327C2×#107C22×C1111yescharacteristic
328C2×#106C22×C1111yescharacteristic
329C2×#106C22×C1111yescharacteristic
330C2×#106C22×C1111yescharacteristic
331C2×C4⋊C8C22×C1111yescharacteristic
332C2×C4⋊C8C22×C1111yescharacteristic
333C2×#103C22×C1111yescharacteristic
334C2×#103C22×C1111yescharacteristic
335C2×#103C22×C1111yescharacteristic
336C2×#103C22×C1111yescharacteristic
337C2×C22⋊C8C22×C1111yescharacteristic
338C2×C22⋊C8C22×C1111yescharacteristic
339#391C22×C1111yescharacteristic
340#389—21no—
341#389C22×C1111yescharacteristic
342#388—21no—
343#388—21no—
344#387—21no—
345#380C22×C1111yescharacteristic
346C4×C4⋊C4C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#336C22×C1111yescharacteristic
356#336C22×C1111yescharacteristic
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12011yescharacteristic
365C22×C11C2×C22⋊Q811yescharacteristic
366C22×C11#53611yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—42no—
375C4×C11—42no—
376C4×C11—41no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11#54811yescharacteristic
385C4×C11#54811yescharacteristic
386C4×C11D4×Q811yescharacteristic
387C4×C11D4×Q811yescharacteristic
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8C23×C1111yescharacteristic
391C23×C4—21no—
392C23×C4C23×C1111yescharacteristic
393C22×C8C23×C1111yescharacteristic
394C22×C8C23×C1111yescharacteristic
395C22×C8C23×C1111yescharacteristic
396C22×C8C23×C1111yescharacteristic
397C4⋊Q8—28no—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8—22no—
401C4⋊Q8D4×C1114yes—
402#125—28no—
403#125—22no—
404#125—22no—
405#125—22no—
406#125D4×C1114yes—
407C22⋊Q8—28no—
408C22⋊Q8—28no—
409C22⋊Q8—22no—
410C22⋊Q8Q8×C1114yescomplemented
411C4×Q8—22no—
412C4×Q8—22no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4D4×C1111yescharacteristic
430C2×C4⋊C4D4×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4D4×C1111yescharacteristic
442C2×C22⋊C4D4×C1111yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42C23×C1111yescharacteristic
447C2×C42C23×C1111yescharacteristic
448#107—22no—
449#106—22no—
450#106—22no—
451#106—22no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#103—22no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465C2×C11—42no—
466C2×C11#240911yescharacteristic
467C2×C11#300911yescharacteristic
468C2×C11#301311yescharacteristic
469C2×C11#308211yescharacteristic
470C2×C11#308411yescharacteristic
471C2×C11#324211yescharacteristic
472C2×C11#324411yescharacteristic
473C24C2×D4×C1111yescharacteristic
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—81no—
482C2×Q8—81no—
483C2×Q8—81no—
484C2×Q8—81no—
485C2×Q8C2×Q8×C1112yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×Q8×C1112yes—
507C22×C4C11×#4112yes—
508C22×C4C24×C1111yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—81no—
542C4⋊C4C2×D4×C1112yes—
543C4⋊C4C2×D4×C1112yes—
544C4⋊C4C2×D4×C1112yes—
545C4⋊C4C2×D4×C1112yes—
546C4⋊C4C2×Q8×C1112yes—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—81no—
552C42—24no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—81no—
557C42C2×D4×C1112yes—
558C42C2×D4×C1112yes—
559C11#2431011yescharacteristic, direct product factor, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C11×C22⋊Q812yes—
567C23C22×D4×C1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573Q8—84no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—84no—
615C2×C4C11×#12012yes—
616C2×C4C11×#12012yes—
617C2×C4C11×C22⋊Q812yes—
618C2×C4C22×D4×C1111yescharacteristic
619C2×C4C22×D4×C1111yescharacteristic
620C2×C4C22×Q8×C1111yescharacteristic
621C2×C4C2×C11×#4111yescharacteristic
622C2×C4C11×2−1+411yescharacteristic
623C2×C4C11×2−1+411yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×C11×#12011yescharacteristic
636C22C2×C11×C22⋊Q811yescharacteristic
637C22C11×#53611yescharacteristic
638C22C11×#57711yescharacteristic
639C22C11×#57711yescharacteristic
640C22C11×#57711yescharacteristic
641C22C11×#57811yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—42no—
646C4—41no—
647C4—42no—
648C4—42no—
649C4—42no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4C11×#54811yescharacteristic
656C4C11×#54811yescharacteristic
657C4D4×Q8×C1111yescharacteristic
658C4D4×Q8×C1111yescharacteristic
659C2—42no—
660C2C11×#240911yescharacteristic
661C2C11×#300911yescharacteristic
662C2C11×#301311yescharacteristic
663C2C11×#308211yescharacteristic
664C2C11×#308411yescharacteristic
665C2C11×#324211yescharacteristic
666C2C11×#324411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
3. C2×C11×#475C2semidirect
5. C11×#2059C2semidirect
6. C11×#2058C2semidirect
7. C11×#2026C2semidirect
8. C11×#2024C2semidirect
9. C11×#1989C2semidirect
10. C11×#1987C2semidirect
85. C11×C22⋊Q8Q8semidirect
140. #24310C11direct (N × H)
228. C2×#479C2×C11semidirect
229. C2×#475C2×C11semidirect
231. #2059C2×C11semidirect
232. #2058C2×C11semidirect
233. #2026C2×C11semidirect
234. #2024C2×C11semidirect
235. #1989C2×C11semidirect
236. #1987C2×C11semidirect
410. C22⋊Q8Q8×C11semidirect
559. C11#24310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#4792
C2×C11×#4752
C11×#23232
C11×#20592
C11×#20582
C11×#20262
C11×#20242
C11×#19892
C11×#19872
C11×#18732
C11×#18722
C11×#18542
C11×#18532
C11×#17982
#2431011