Finite Group Databasebeta

← C11×#24346 #14601539

Subgroups — C11×#24346 #14601539

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2057C211yesmaximal, characteristic, complemented
7C11×#2025C211yesmaximal, characteristic
8C11×#2023C211yesmaximal, characteristic
9C11×#1992C211yesmaximal, characteristic, complemented
10C11×#1985C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic
12C11×#1880C211yesmaximal, characteristic
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1863C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C11×#557—24no—
18C11×#557—24no—
19C2×C11×C4⋊Q8—21no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×#125—21no—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#125C2211yescharacteristic
25C2×C11×C22⋊Q8—21no—
26C2×C4×Q8×C11—21no—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C11×#478—24no—
33C11×#440—24no—
34C2×C11×#107C2211yescharacteristic
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#97C2211yescharacteristic
45C11×#396—21no—
46C11×#396—21no—
47C11×#390C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#384C2211yescharacteristic
52C11×#380—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11D411yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16Q814yescomplemented
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C4⋊Q8—28no—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8—22no—
78C11×#125—28no—
79C11×#125—28no—
80C11×#125—22no—
81C11×#125—22no—
82C11×#125—22no—
83C11×#125D414yes—
84C11×C22⋊Q8—44no—
85C4×Q8×C11—28no—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11D414yes—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C42×C11—21no—
123C2×C42×C11—21no—
124C2×C42×C11—21no—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#107—22no—
130C11×#106—22no—
131C11×C4⋊C8—22no—
132C11×#103—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#102—22no—
136C11×#102—22no—
137C11×#102—22no—
138C11×#97—22no—
139C11×#95—21no—
140C11×#95—21no—
141#24346C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11—21no—
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—42no—
151C2×Q8×C11—42no—
152C2×Q8×C11C2×D412yes—
153C2×Q8×C11C2×Q812yes—
154C2×Q8×C11#4112yes—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C2×Q812yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C11×SD16—28no—
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—
189C2×C8×C11—21no—
190C2×C8×C11C2×Q812yes—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
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—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—81no—
215C11×C4⋊C4C2×D412yes—
216C11×C4⋊C4C2×D412yes—
217C11×C4⋊C4C2×D412yes—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—81no—
222C11×C22⋊C4—81no—
223C42×C11—24no—
224C42×C11—24no—
225C42×C11—24no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11C2×D412yes—
231C42×C11C2×D412yes—
232C2×#557C2×C1111yescharacteristic, complemented
233C2×#478C2×C1111yescharacteristic
234C2×#440C2×C1111yescharacteristic
235#2538C2×C1111yescharacteristic
236#2059C2×C1111yescharacteristic, complemented
237#2057C2×C1111yescharacteristic, complemented
238#2025C2×C1111yescharacteristic
239#2023C2×C1111yescharacteristic
240#1992C2×C1111yescharacteristic, complemented
241#1985C2×C1111yescharacteristic, complemented
242#1880C2×C1111yescharacteristic
243#1880C2×C1111yescharacteristic
244#1865C2×C1111yescharacteristic, complemented
245#1863C2×C1111yescharacteristic, complemented
246#1803C2×C1111yescharacteristic, complemented
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11C22×D411yescharacteristic
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—44no—
259Q8×C11—48no—
260Q8×C11C22⋊Q814yescomplemented
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—41no—
264D4×C11—41no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
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—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—84no—
302C2×C4×C11#12012yes—
303C2×C4×C11#12012yes—
304C2×C4×C11AGL(1,ℤ/8)12yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×Q811yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C8×C11—22no—
312C8×C11—41no—
313C8×C11—41no—
314C8×C11—41no—
315C22×SD16C22×C1111yescharacteristic
316#557—24no—
317#557—24no—
318C2×C4⋊Q8—21no—
319C2×C4⋊Q8C22×C1111yescharacteristic
320C2×#125—21no—
321C2×#125—21no—
322C2×#125C22×C1111yescharacteristic
323C2×#125C22×C1111yescharacteristic
324C2×C22⋊Q8—21no—
325C2×C4×Q8—21no—
326C2×C4×Q8C22×C1111yescharacteristic
327C2×C4×Q8C22×C1111yescharacteristic
328C2×C4×Q8C22×C1111yescharacteristic
329C2×C4×Q8C22×C1111yescharacteristic
330C2×C4×D4C22×C1111yescharacteristic
331#478—24no—
332#440—24no—
333C2×#107C22×C1111yescharacteristic
334C2×#107C22×C1111yescharacteristic
335C2×#106C22×C1111yescharacteristic
336C2×C4⋊C8C22×C1111yescharacteristic
337C2×#103C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#102C22×C1111yescharacteristic
341C2×#102C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#97C22×C1111yescharacteristic
344#396—21no—
345#396—21no—
346#390C22×C1111yescharacteristic
347#390C22×C1111yescharacteristic
348#389C22×C1111yescharacteristic
349#389C22×C1111yescharacteristic
350#384C22×C1111yescharacteristic
351#380—21no—
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359#336C22×C1111yescharacteristic
360#336C22×C1111yescharacteristic
361#336C22×C1111yescharacteristic
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11C2×#12011yescharacteristic
370C22×C11#54811yescharacteristic
371C22×C11D4×Q811yescharacteristic
372C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57711yescharacteristic
375C22×C11#57811yescharacteristic
376C4×C11—24no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11C2×C22⋊Q811yescharacteristic
390C4×C11#53611yescharacteristic
391C4×C11#54811yescharacteristic
392C4×C11D4×Q811yescharacteristic
393C22×Q8—21no—
394C22×Q8D4×C1111yescharacteristic
395C22×Q8C23×C1111yescharacteristic
396C22×D4C23×C1111yescharacteristic
397C23×C4—21no—
398C2×SD16—22no—
399C2×SD16—22no—
400C2×SD16Q8×C1114yescomplemented
401C22×C8C23×C1111yescharacteristic
402C22×C8C23×C1111yescharacteristic
403C22×C8C23×C1111yescharacteristic
404C22×C8C23×C1111yescharacteristic
405C4⋊Q8—28no—
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408#125—28no—
409#125—28no—
410#125—22no—
411#125—22no—
412#125—22no—
413#125D4×C1114yes—
414C22⋊Q8—44no—
415C4×Q8—28no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8D4×C1114yes—
424C4×D4—22no—
425C4×D4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4D4×C1111yescharacteristic
439C2×C4⋊C4D4×C1111yescharacteristic
440C2×C4⋊C4D4×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C4⋊C4C23×C1111yescharacteristic
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42C23×C1111yescharacteristic
456C2×C42C23×C1111yescharacteristic
457C2×C42C23×C1111yescharacteristic
458#107—22no—
459#107—22no—
460#106—22no—
461C4⋊C8—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#102—22no—
466#102—22no—
467#102—22no—
468#97—22no—
469#95—21no—
470#95—21no—
471C2×C11—82no—
472C2×C11#240911yescharacteristic
473C2×C11#300611yescharacteristic
474C2×C11#301311yescharacteristic
475C2×C11#336811yescharacteristic
476C2×C11#337711yescharacteristic
477C2×C11#338611yescharacteristic
478C2×C11#338811yescharacteristic
479C24—21no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—41no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8C2×D4×C1112yes—
490C2×Q8C2×Q8×C1112yes—
491C2×Q8C11×#4112yes—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4C2×Q8×C1112yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4C2×D4×C1111yescharacteristic
509C22×C4C2×D4×C1111yescharacteristic
510C22×C4C2×D4×C1111yescharacteristic
511C22×C4C2×D4×C1111yescharacteristic
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C24×C1111yescharacteristic
515SD16—28no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C2×Q8×C1112yes—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—81no—
552C4⋊C4C2×D4×C1112yes—
553C4⋊C4C2×D4×C1112yes—
554C4⋊C4C2×D4×C1112yes—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C42—24no—
561C42—24no—
562C42—24no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42C2×D4×C1112yes—
568C42C2×D4×C1112yes—
569C11#2434611yescharacteristic, direct product factor, Sylow
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C22×D4×C1111yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—22no—
581Q8—44no—
582Q8—48no—
583Q8C11×C22⋊Q814yescomplemented
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4C11×#12012yes—
626C2×C4C11×#12012yes—
627C2×C4C11×AGL(1,ℤ/8)12yes—
628C2×C4C22×D4×C1111yescharacteristic
629C2×C4C22×D4×C1111yescharacteristic
630C2×C4C22×Q8×C1111yescharacteristic
631C2×C4C2×C11×#4111yescharacteristic
632C2×C4C11×2−1+411yescharacteristic
633C2×C4C11×2−1+411yescharacteristic
634C8—22no—
635C8—41no—
636C8—41no—
637C8—41no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22C2×C11×#12011yescharacteristic
646C22C11×#54811yescharacteristic
647C22D4×Q8×C1111yescharacteristic
648C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
649C22C11×#57511yescharacteristic
650C22C11×#57711yescharacteristic
651C22C11×#57811yescharacteristic
652C4—24no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—41no—
657C4—42no—
658C4—42no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4C2×C11×C22⋊Q811yescharacteristic
666C4C11×#53611yescharacteristic
667C4C11×#54811yescharacteristic
668C4D4×Q8×C1111yescharacteristic
669C2—82no—
670C2C11×#240911yescharacteristic
671C2C11×#300611yescharacteristic
672C2C11×#301311yescharacteristic
673C2C11×#336811yescharacteristic
674C2C11×#337711yescharacteristic
675C2C11×#338611yescharacteristic
676C2C11×#338811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#557C2semidirect
5. C11×#2059C2semidirect
6. C11×#2057C2semidirect
9. C11×#1992C2semidirect
10. C11×#1985C2semidirect
13. C11×#1865C2semidirect
14. C11×#1863C2semidirect
15. C11×#1803C2semidirect
70. C2×C11×SD16Q8semidirect
141. #24346C11direct (N × H)
232. C2×#557C2×C11semidirect
236. #2059C2×C11semidirect
237. #2057C2×C11semidirect
240. #1992C2×C11semidirect
241. #1985C2×C11semidirect
244. #1865C2×C11semidirect
245. #1863C2×C11semidirect
246. #1803C2×C11semidirect
260. Q8×C11C22⋊Q8semidirect
400. C2×SD16Q8×C11semidirect
569. C11#24346direct (N × H)
583. Q8C11×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4782
C2×C11×#4402
C11×#25382
C11×#20592
C11×#20572
C11×#20252
C11×#20232
C11×#19922
C11×#19852
C11×#18802
C11×#18652
C11×#18632
C11×#18032
#2434611