Finite Group Databasebeta

← C11×#24334 #14601527

Subgroups — C11×#24334 #14601527

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 672 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×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2580C211yesmaximal, characteristic
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2058C211yesmaximal, characteristic, complemented
7C11×#2025C211yesmaximal, characteristic
8C11×#2023C211yesmaximal, characteristic
9C11×#1991C211yesmaximal, characteristic, complemented
10C11×#1984C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic
12C11×#1880C211yesmaximal, characteristic
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1863C211yesmaximal, characteristic, complemented
15C11×#1805C211yesmaximal, 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×C4×Q8×C11—21no—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C11×#478—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×#399—21no—
45C11×#393—21no—
46C11×#390C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#385—21no—
51C11×#385—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—
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—
84C4×Q8×C11—28no—
85C4×Q8×C11—22no—
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×C11D414yes—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
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—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×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C11×#107—22no—
126C11×#106—22no—
127C11×#106—22no—
128C11×C4⋊C8—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C4×C8×C11—22no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140#24334C1111yesmaximal, 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—41no—
149C2×Q8×C11—42no—
150C2×Q8×C11—42no—
151C2×Q8×C11C2×D412yes—
152C2×Q8×C11C2×Q812yes—
153C2×Q8×C11#4112yes—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11C2×Q812yes—
160C22×C4×C11—21no—
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—42no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C11×SD16—28no—
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—
189C2×C8×C11C2×Q812yes—
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—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
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—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—81no—
211C11×C4⋊C4—81no—
212C11×C4⋊C4C2×D412yes—
213C11×C4⋊C4C2×D412yes—
214C11×C4⋊C4C2×D412yes—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—81no—
219C11×C22⋊C4—81no—
220C42×C11—24no—
221C42×C11—24no—
222C42×C11—24no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11C2×D412yes—
228C42×C11C2×D412yes—
229C2×#557C2×C1111yescharacteristic, complemented
230C2×#478C2×C1111yescharacteristic
231C2×C4×SD16C2×C1111yescharacteristic
232#2580C2×C1111yescharacteristic
233#2059C2×C1111yescharacteristic, complemented
234#2058C2×C1111yescharacteristic, complemented
235#2025C2×C1111yescharacteristic
236#2023C2×C1111yescharacteristic
237#1991C2×C1111yescharacteristic, complemented
238#1984C2×C1111yescharacteristic, complemented
239#1880C2×C1111yescharacteristic
240#1880C2×C1111yescharacteristic
241#1865C2×C1111yescharacteristic, complemented
242#1863C2×C1111yescharacteristic, complemented
243#1805C2×C1111yescharacteristic, complemented
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—44no—
256Q8×C11—48no—
257Q8×C11C22⋊Q814yes—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—41no—
261D4×C11—41no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
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—84no—
299C2×C4×C11#12012yes—
300C2×C4×C11#12012yes—
301C2×C4×C11#13512yes—
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×Q811yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C112−1+411yescharacteristic
307C2×C4×C112−1+411yescharacteristic
308C8×C11—22no—
309C8×C11—41no—
310C8×C11—41no—
311C8×C11—41no—
312C22×SD16C22×C1111yescharacteristic
313#557—24no—
314#557—24no—
315C2×C4⋊Q8—21no—
316C2×C4⋊Q8C22×C1111yescharacteristic
317C2×#125—21no—
318C2×#125—21no—
319C2×#125C22×C1111yescharacteristic
320C2×#125C22×C1111yescharacteristic
321C2×C4×Q8—21no—
322C2×C4×Q8C22×C1111yescharacteristic
323C2×C4×Q8C22×C1111yescharacteristic
324C2×C4×Q8C22×C1111yescharacteristic
325C2×C4×Q8C22×C1111yescharacteristic
326C2×C4×D4C22×C1111yescharacteristic
327#478—24no—
328C4×SD16—24no—
329C2×#107C22×C1111yescharacteristic
330C2×#106C22×C1111yescharacteristic
331C2×#106C22×C1111yescharacteristic
332C2×C4⋊C8C22×C1111yescharacteristic
333C2×#103C22×C1111yescharacteristic
334C2×#103C22×C1111yescharacteristic
335C2×#103C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×#102C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×C4×C8C22×C1111yescharacteristic
340#399—21no—
341#393—21no—
342#390C22×C1111yescharacteristic
343#390C22×C1111yescharacteristic
344#389C22×C1111yescharacteristic
345#389C22×C1111yescharacteristic
346#385—21no—
347#385—21no—
348#382C22×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
357#336C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11C2×#12011yescharacteristic
367C22×C11#54811yescharacteristic
368C22×C11D4×Q811yescharacteristic
369C22×C11C2×#13511yescharacteristic
370C22×C11#57511yescharacteristic
371C22×C11#57711yescharacteristic
372C22×C11#57711yescharacteristic
373C4×C11—24no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C2×C22⋊Q811yescharacteristic
387C4×C11#53611yescharacteristic
388C4×C11#54811yescharacteristic
389C4×C11D4×Q811yescharacteristic
390C22×Q8—21no—
391C22×Q8D4×C1111yescharacteristic
392C22×Q8C23×C1111yescharacteristic
393C22×D4C23×C1111yescharacteristic
394C23×C4—21no—
395C2×SD16—22no—
396C2×SD16—22no—
397C2×SD16Q8×C1114yescomplemented
398C22×C8C23×C1111yescharacteristic
399C22×C8C23×C1111yescharacteristic
400C22×C8C23×C1111yescharacteristic
401C22×C8C23×C1111yescharacteristic
402C4⋊Q8—28no—
403C4⋊Q8—22no—
404C4⋊Q8—22no—
405#125—28no—
406#125—28no—
407#125—22no—
408#125—22no—
409#125—22no—
410#125D4×C1114yes—
411C4×Q8—28no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8D4×C1114yes—
420C4×D4—22no—
421C4×D4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
433C2×C4⋊C4D4×C1111yescharacteristic
434C2×C4⋊C4D4×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C1111yescharacteristic
450C2×C42C23×C1111yescharacteristic
451C2×C42C23×C1111yescharacteristic
452#107—22no—
453#106—22no—
454#106—22no—
455C4⋊C8—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#102—22no—
460#102—22no—
461#102—22no—
462C4×C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467C2×C11—82no—
468C2×C11#240911yescharacteristic
469C2×C11#300211yescharacteristic
470C2×C11#301011yescharacteristic
471C2×C11#336511yescharacteristic
472C2×C11#337111yescharacteristic
473C2×C11#338111yescharacteristic
474C2×C11#338811yescharacteristic
475C24—21no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—41no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8C2×D4×C1112yes—
486C2×Q8C2×Q8×C1112yes—
487C2×Q8C11×#4112yes—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4C2×Q8×C1112yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1111yescharacteristic
508C22×C4C2×D4×C1111yescharacteristic
509C22×C4C2×D4×C1111yescharacteristic
510C22×C4C24×C1111yescharacteristic
511SD16—28no—
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—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8C2×Q8×C1112yes—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—81no—
545C4⋊C4—81no—
546C4⋊C4C2×D4×C1112yes—
547C4⋊C4C2×D4×C1112yes—
548C4⋊C4C2×D4×C1112yes—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C42—24no—
555C42—24no—
556C42—24no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42C2×D4×C1112yes—
562C42C2×D4×C1112yes—
563C11#2433411yescharacteristic, direct product factor, Sylow
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C22×D4×C1111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—22no—
575Q8—44no—
576Q8—48no—
577Q8C11×C22⋊Q814yes—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
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—21no—
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—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—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—84no—
619C2×C4C11×#12012yes—
620C2×C4C11×#12012yes—
621C2×C4C11×#13512yes—
622C2×C4C22×D4×C1111yescharacteristic
623C2×C4C22×D4×C1111yescharacteristic
624C2×C4C22×Q8×C1111yescharacteristic
625C2×C4C2×C11×#4111yescharacteristic
626C2×C4C11×2−1+411yescharacteristic
627C2×C4C11×2−1+411yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×C11×#12011yescharacteristic
640C22C11×#54811yescharacteristic
641C22D4×Q8×C1111yescharacteristic
642C22C2×C11×#13511yescharacteristic
643C22C11×#57511yescharacteristic
644C22C11×#57711yescharacteristic
645C22C11×#57711yescharacteristic
646C4—24no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C11×C22⋊Q811yescharacteristic
660C4C11×#53611yescharacteristic
661C4C11×#54811yescharacteristic
662C4D4×Q8×C1111yescharacteristic
663C2—82no—
664C2C11×#240911yescharacteristic
665C2C11×#300211yescharacteristic
666C2C11×#301011yescharacteristic
667C2C11×#336511yescharacteristic
668C2C11×#337111yescharacteristic
669C2C11×#338111yescharacteristic
670C2C11×#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×#2058C2semidirect
9. C11×#1991C2semidirect
10. C11×#1984C2semidirect
13. C11×#1865C2semidirect
14. C11×#1863C2semidirect
15. C11×#1805C2semidirect
70. C2×C11×SD16Q8semidirect
140. #24334C11direct (N × H)
229. C2×#557C2×C11semidirect
233. #2059C2×C11semidirect
234. #2058C2×C11semidirect
237. #1991C2×C11semidirect
238. #1984C2×C11semidirect
241. #1865C2×C11semidirect
242. #1863C2×C11semidirect
243. #1805C2×C11semidirect
397. C2×SD16Q8×C11semidirect
563. C11#24334direct (N × H)

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×C4×C11×SD162
C11×#25802
C11×#20592
C11×#20582
C11×#20252
C11×#20232
C11×#19912
C11×#19842
C11×#18802
C11×#18652
C11×#18632
C11×#18052
#2433411