Finite Group Databasebeta

← C11×#24337 #14601530

Subgroups — C11×#24337 #14601530

Order 2816.

1070 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2581C211yesmaximal, characteristic, complemented
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2058C211yesmaximal, characteristic, complemented
7C11×#2026C211yesmaximal, characteristic, complemented
8C11×#2024C211yesmaximal, characteristic, complemented
9C11×#1991C211yesmaximal, characteristic, complemented
10C11×#1984C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic
12C11×#1877C211yesmaximal, characteristic
13C11×#1864C211yesmaximal, characteristic
14C11×#1862C211yesmaximal, characteristic
15C11×#1804C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C11×#554—24no—
18C11×#554—24no—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×C11×#125C2211yescharacteristic
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C4⋊C4—21no—
31C11×#479—24no—
32C4×C11×SD16—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C4×C8×C11C2211yescharacteristic
44C11×#400—21no—
45C11×#395—21no—
46C11×#391C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#387—21no—
51C11×#387—21no—
52C11×#382C2211yescharacteristic
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—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16Q814yescomplemented
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—22no—
79C11×#125—22no—
80C11×#125—22no—
81C11×#125—22no—
82C11×#125D414yes—
83C11×C22⋊Q8—28no—
84C11×C22⋊Q8—28no—
85C11×C22⋊Q8—28no—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11D414yes—
96C2×C11×C4⋊C4—28no—
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⋊C4D411yescharacteristic
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C11×#107—22no—
122C11×#106—22no—
123C11×#106—22no—
124C11×C4⋊C8—22no—
125C11×#103—22no—
126C11×#103—22no—
127C11×#103—22no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#102—22no—
131C4×C8×C11—22no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140#24337C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11—21no—
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—81no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×Q812yes—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11C2×D412yes—
158C2×D4×C11C2×Q812yes—
159C2×D4×C11#4112yes—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11—81no—
175C22×C4×C11—81no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C11×SD16—28no—
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×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C2×Q812yes—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
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—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4—42no—
216C11×C4⋊C4C2×D412yes—
217C11×C4⋊C4C2×D412yes—
218C11×C4⋊C4C2×D412yes—
219C11×C22⋊C4—24no—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—24no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—42no—
227C42×C11C2×D412yes—
228C42×C11C2×D412yes—
229C2×#554C2×C1111yescharacteristic
230C2×#479C2×C1111yescharacteristic, complemented
231C2×C4×SD16C2×C1111yescharacteristic
232#2581C2×C1111yescharacteristic, complemented
233#2059C2×C1111yescharacteristic, complemented
234#2058C2×C1111yescharacteristic, complemented
235#2026C2×C1111yescharacteristic, complemented
236#2024C2×C1111yescharacteristic, complemented
237#1991C2×C1111yescharacteristic, complemented
238#1984C2×C1111yescharacteristic, complemented
239#1877C2×C1111yescharacteristic
240#1877C2×C1111yescharacteristic
241#1864C2×C1111yescharacteristic
242#1862C2×C1111yescharacteristic
243#1804C2×C1111yescharacteristic
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—44no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—84no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11C22⋊Q814yes—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—48no—
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—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—84no—
300C2×C4×C11—84no—
301C2×C4×C11#12012yes—
302C2×C4×C11#12012yes—
303C2×C4×C11#13512yes—
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×Q811yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C112−1+411yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C8×C11—22no—
311C8×C11—41no—
312C8×C11—41no—
313C8×C11—41no—
314C22×SD16C22×C1111yescharacteristic
315#554—24no—
316#554—24no—
317C2×C4⋊Q8C22×C1111yescharacteristic
318C2×#125C22×C1111yescharacteristic
319C2×#125C22×C1111yescharacteristic
320C2×C22⋊Q8—21no—
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8—21no—
323C2×C4×Q8C22×C1111yescharacteristic
324C2×C4×Q8C22×C1111yescharacteristic
325C2×C4×D4C22×C1111yescharacteristic
326C2×C4×D4C22×C1111yescharacteristic
327C2×C4×D4C22×C1111yescharacteristic
328C22×C4⋊C4—21no—
329#479—24no—
330C4×SD16—24no—
331C2×#107C22×C1111yescharacteristic
332C2×#106C22×C1111yescharacteristic
333C2×#106C22×C1111yescharacteristic
334C2×C4⋊C8C22×C1111yescharacteristic
335C2×#103C22×C1111yescharacteristic
336C2×#103C22×C1111yescharacteristic
337C2×#103C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#102C22×C1111yescharacteristic
341C2×C4×C8C22×C1111yescharacteristic
342#400—21no—
343#395—21no—
344#391C22×C1111yescharacteristic
345#391C22×C1111yescharacteristic
346#389C22×C1111yescharacteristic
347#389C22×C1111yescharacteristic
348#387—21no—
349#387—21no—
350#382C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#336C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359#336C22×C1111yescharacteristic
360#336C22×C1111yescharacteristic
361C22×C11—24no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11C2×#12011yescharacteristic
369C22×C11#54811yescharacteristic
370C22×C11D4×Q811yescharacteristic
371C22×C11C2×#13511yescharacteristic
372C22×C11#57511yescharacteristic
373C22×C11#57711yescharacteristic
374C22×C11#57711yescharacteristic
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—42no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—42no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11C2×C22⋊Q811yescharacteristic
389C4×C11#53611yescharacteristic
390C4×C11#54811yescharacteristic
391C4×C11D4×Q811yescharacteristic
392C22×Q8—21no—
393C22×Q8D4×C1111yescharacteristic
394C22×Q8C23×C1111yescharacteristic
395C22×D4C23×C1111yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C2×SD16—22no—
400C2×SD16—22no—
401C2×SD16Q8×C1114yescomplemented
402C22×C8C23×C1111yescharacteristic
403C22×C8C23×C1111yescharacteristic
404C22×C8C23×C1111yescharacteristic
405C22×C8C23×C1111yescharacteristic
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408#125—22no—
409#125—22no—
410#125—22no—
411#125D4×C1114yes—
412C22⋊Q8—28no—
413C22⋊Q8—28no—
414C22⋊Q8—28no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4D4×C1114yes—
425C2×C4⋊C4—28no—
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⋊C4D4×C1111yescharacteristic
435C2×C4⋊C4D4×C1111yescharacteristic
436C2×C4⋊C4D4×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—21no—
447C2×C42C23×C1111yescharacteristic
448C2×C42C23×C1111yescharacteristic
449C2×C42C23×C1111yescharacteristic
450#107—22no—
451#106—22no—
452#106—22no—
453C4⋊C8—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460C4×C8—22no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469C2×C11—44no—
470C2×C11#240911yescharacteristic
471C2×C11#300211yescharacteristic
472C2×C11#300911yescharacteristic
473C2×C11#336011yescharacteristic
474C2×C11#337611yescharacteristic
475C2×C11#338111yescharacteristic
476C2×C11#338811yescharacteristic
477C24—21no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—41no—
487C2×Q8—81no—
488C2×Q8—81no—
489C2×Q8C2×Q8×C1112yes—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4C2×D4×C1112yes—
494C2×D4C2×Q8×C1112yes—
495C2×D4C11×#4112yes—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C24×C1111yescharacteristic
519SD16—28no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8C2×Q8×C1112yes—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
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—21no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4C2×D4×C1112yes—
553C4⋊C4C2×D4×C1112yes—
554C4⋊C4C2×D4×C1112yes—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—42no—
563C42C2×D4×C1112yes—
564C42C2×D4×C1112yes—
565C11#2433711yescharacteristic, direct product factor, Sylow
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C22×D4×C1111yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—44no—
577Q8—41no—
578Q8—41no—
579Q8—84no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4C11×C22⋊Q814yes—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—48no—
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—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4C11×#12012yes—
624C2×C4C11×#12012yes—
625C2×C4C11×#13512yes—
626C2×C4C22×D4×C1111yescharacteristic
627C2×C4C22×D4×C1111yescharacteristic
628C2×C4C22×Q8×C1111yescharacteristic
629C2×C4C2×C11×#4111yescharacteristic
630C2×C4C11×2−1+411yescharacteristic
631C2×C4C11×2−1+411yescharacteristic
632C8—22no—
633C8—41no—
634C8—41no—
635C8—41no—
636C22—24no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22C2×C11×#12011yescharacteristic
644C22C11×#54811yescharacteristic
645C22D4×Q8×C1111yescharacteristic
646C22C2×C11×#13511yescharacteristic
647C22C11×#57511yescharacteristic
648C22C11×#57711yescharacteristic
649C22C11×#57711yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4C2×C11×C22⋊Q811yescharacteristic
664C4C11×#53611yescharacteristic
665C4C11×#54811yescharacteristic
666C4D4×Q8×C1111yescharacteristic
667C2—44no—
668C2C11×#240911yescharacteristic
669C2C11×#300211yescharacteristic
670C2C11×#300911yescharacteristic
671C2C11×#336011yescharacteristic
672C2C11×#337611yescharacteristic
673C2C11×#338111yescharacteristic
674C2C11×#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
2. C2×C11×#479C2semidirect
4. C11×#2581C2semidirect
5. C11×#2059C2semidirect
6. C11×#2058C2semidirect
7. C11×#2026C2semidirect
8. C11×#2024C2semidirect
9. C11×#1991C2semidirect
10. C11×#1984C2semidirect
72. C2×C11×SD16Q8semidirect
140. #24337C11direct (N × H)
230. C2×#479C2×C11semidirect
232. #2581C2×C11semidirect
233. #2059C2×C11semidirect
234. #2058C2×C11semidirect
235. #2026C2×C11semidirect
236. #2024C2×C11semidirect
237. #1991C2×C11semidirect
238. #1984C2×C11semidirect
401. C2×SD16Q8×C11semidirect
565. C11#24337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4792
C2×C4×C11×SD162
C11×#25812
C11×#20592
C11×#20582
C11×#20262
C11×#20242
C11×#19912
C11×#19842
C11×#18772
C11×#18642
C11×#18622
C11×#18042
#2433711