Finite Group Databasebeta

← C11×#24764 #14601957

Subgroups — C11×#24764 #14601957

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#470C211yesmaximal, characteristic
2C2×C11×#467C211yesmaximal, characteristic
3C2×C11×#462C211yesmaximal, characteristic, complemented
4C2×C11×#424C211yesmaximal, characteristic
5C11×#2621C211yesmaximal, characteristic
6C11×#2323C211yesmaximal, characteristic
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2066C211yesmaximal, characteristic, complemented
9C11×#2056C211yesmaximal, characteristic, complemented
10C11×#2056C211yesmaximal, characteristic, complemented
11C11×#1981C211yesmaximal, characteristic, complemented
12C11×#1949C211yesmaximal, characteristic, complemented
13C11×#1894C211yesmaximal, characteristic
14C11×#1892C211yesmaximal, characteristic
15C11×#1805C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#470—24no—
27C11×#467—24no—
28C11×#462—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C11×#424—24no—
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C11×#398—21no—
45C11×#398—21no—
46C11×#397—21no—
47C11×#397—21no—
48C11×#391C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#391C2211yescharacteristic
51C11×#389—21no—
52C11×#389C2211yescharacteristic
53C11×#388—21no—
54C11×#388—21no—
55C11×#387—21no—
56C11×#382C2211yescharacteristic
57C11×#380C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C2×C11×Q16—22no—
68C2×C11×Q16—22no—
69C2×C11×Q16—22no—
70C2×C11×Q16—22no—
71C2×C11×Q16—41no—
72C2×C11×Q16—41no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—41no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8D414yes—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C11×#117—22no—
94C11×#117—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⋊C4D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11—21no—
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×#107—22no—
120C11×#106—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8D414yes—
125C11×#103—22no—
126C11×#103—22no—
127C11×#103—22no—
128C11×#103—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—41no—
132C11×#103—41no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144#24764C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11C2×D411yescharacteristic
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11C2×D412yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11#4112yes—
183C22×C4×C11C2411yescharacteristic
184C11×Q16—44no—
185C11×Q16—44no—
186C11×M16—44no—
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×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—44no—
198C2×C8×C11C2×D412yes—
199C2×C8×C11C2×D412yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
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—21no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4—42no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—81no—
218C11×C4⋊C4C2×D412yes—
219C11×C22⋊C4—24no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—81no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—42no—
228C42×C11—81no—
229C42×C11C2×D412yes—
230C42×C11#4112yes—
231C2×#470C2×C1111yescharacteristic
232C2×#467C2×C1111yescharacteristic
233C2×#462C2×C1111yescharacteristic, complemented
234C2×#424C2×C1111yescharacteristic
235#2621C2×C1111yescharacteristic
236#2323C2×C1111yescharacteristic
237#2068C2×C1111yescharacteristic, complemented
238#2066C2×C1111yescharacteristic, complemented
239#2056C2×C1111yescharacteristic, complemented
240#2056C2×C1111yescharacteristic, complemented
241#1981C2×C1111yescharacteristic, complemented
242#1949C2×C1111yescharacteristic, complemented
243#1894C2×C1111yescharacteristic
244#1892C2×C1111yescharacteristic
245#1805C2×C1111yescharacteristic, complemented
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11#12112yes—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258Q8×C11—41no—
259Q8×C11—41no—
260Q8×C11—41no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—41no—
264Q8×C11—41no—
265Q8×C11—41no—
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—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
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—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—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11#12112yes—
307C2×C4×C11#12112yes—
308C2×C4×C11#12112yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C112−1+411yescharacteristic
315C8×C11—22no—
316C8×C11—22no—
317C8×C11—41no—
318C8×C11—41no—
319C22×Q16C22×C1111yescharacteristic
320C22×Q16C22×C1111yescharacteristic
321C22×M16C22×C1111yescharacteristic
322C23×C8C22×C1111yescharacteristic
323C2×C4⋊Q8C22×C1111yescharacteristic
324C2×C22⋊Q8C22×C1111yescharacteristic
325C2×C22⋊Q8C22×C1111yescharacteristic
326C2×C22⋊Q8C22×C1111yescharacteristic
327C2×C4×Q8C22×C1111yescharacteristic
328C2×#117C22×C1111yescharacteristic
329#470—24no—
330#467—24no—
331#462—24no—
332C2×#107C22×C1111yescharacteristic
333C2×#106C22×C1111yescharacteristic
334#424—24no—
335C2×C4⋊C8C22×C1111yescharacteristic
336C2×C4⋊C8C22×C1111yescharacteristic
337C2×C4⋊C8C22×C1111yescharacteristic
338C2×C4⋊C8C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347#398—21no—
348#398—21no—
349#397—21no—
350#397—21no—
351#391C22×C1111yescharacteristic
352#391C22×C1111yescharacteristic
353#391C22×C1111yescharacteristic
354#389—21no—
355#389C22×C1111yescharacteristic
356#388—21no—
357#388—21no—
358#387—21no—
359#382C22×C1111yescharacteristic
360#380C22×C1111yescharacteristic
361C4×C4⋊C4C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11C2×#12111yescharacteristic
374C22×C11C2×#12111yescharacteristic
375C22×C11#53711yescharacteristic
376C22×C11#57711yescharacteristic
377C22×C11#57811yescharacteristic
378C22×C11#57811yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—42no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11D4211yescharacteristic
394C4×C11#54711yescharacteristic
395C4×C11#54811yescharacteristic
396C4×C11#55311yescharacteristic
397C22×Q8C23×C1111yescharacteristic
398C22×Q8C23×C1111yescharacteristic
399C22×Q8C23×C1111yescharacteristic
400C23×C4C23×C1111yescharacteristic
401C2×Q16—22no—
402C2×Q16—22no—
403C2×Q16—22no—
404C2×Q16—22no—
405C2×Q16—41no—
406C2×Q16—41no—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—41no—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—41no—
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C4⋊Q8—22no—
418C4⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8D4×C1114yes—
425C4×Q8—22no—
426C4×Q8—22no—
427#117—22no—
428#117—22no—
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⋊C4D4×C1111yescharacteristic
437C2×C4⋊C4D4×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×C22⋊C4—21no—
447C2×C22⋊C4D4×C1111yescharacteristic
448C2×C22⋊C4D4×C1111yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C1111yescharacteristic
452C2×C42C23×C1111yescharacteristic
453#107—22no—
454#106—22no—
455C4⋊C8—22no—
456C4⋊C8—22no—
457C4⋊C8—22no—
458C4⋊C8D4×C1114yes—
459#103—22no—
460#103—22no—
461#103—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#103—41no—
466#103—41no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478C2×C11—42no—
479C2×C11#241611yescharacteristic
480C2×C11#304411yescharacteristic
481C2×C11#304611yescharacteristic
482C2×C11#305911yescharacteristic
483C2×C11#306311yescharacteristic
484C2×C11#325811yescharacteristic
485C2×C11#326111yescharacteristic
486C24C2×D4×C1111yescharacteristic
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C2×D4×C1112yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C2×D4×C1111yescharacteristic
520C22×C4C2×D4×C1111yescharacteristic
521C22×C4C2×D4×C1111yescharacteristic
522C22×C4C2×D4×C1112yes—
523C22×C4C11×#4112yes—
524C22×C4C24×C1111yescharacteristic
525Q16—44no—
526Q16—44no—
527M16—44no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—44no—
539C2×C8C2×D4×C1112yes—
540C2×C8C2×D4×C1112yes—
541C4⋊C4—24no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4C2×D4×C1112yes—
560C22⋊C4—24no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C42—21no—
567C42—21no—
568C42—42no—
569C42—81no—
570C42C2×D4×C1112yes—
571C42C11×#4112yes—
572C11#2476411yescharacteristic, direct product factor, Sylow
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23C11×#12112yes—
580C23C22×D4×C1111yescharacteristic
581Q8—22no—
582Q8—22no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
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—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4C11×#12112yes—
634C2×C4C11×#12112yes—
635C2×C4C11×#12112yes—
636C2×C4C22×D4×C1111yescharacteristic
637C2×C4C22×D4×C1111yescharacteristic
638C2×C4C2×C11×#4111yescharacteristic
639C2×C4C2×C11×#4111yescharacteristic
640C2×C4C11×H(5,𝔽2)11yescharacteristic
641C2×C4C11×2−1+411yescharacteristic
642C8—22no—
643C8—22no—
644C8—41no—
645C8—41no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C2×C11×#12111yescharacteristic
654C22C2×C11×#12111yescharacteristic
655C22C11×#53711yescharacteristic
656C22C11×#57711yescharacteristic
657C22C11×#57811yescharacteristic
658C22C11×#57811yescharacteristic
659C22C11×#57811yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4D42×C1111yescharacteristic
674C4C11×#54711yescharacteristic
675C4C11×#54811yescharacteristic
676C4C11×#55311yescharacteristic
677C2—42no—
678C2C11×#241611yescharacteristic
679C2C11×#304411yescharacteristic
680C2C11×#304611yescharacteristic
681C2C11×#305911yescharacteristic
682C2C11×#306311yescharacteristic
683C2C11×#325811yescharacteristic
684C2C11×#326111yescharacteristic
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
3. C2×C11×#462C2semidirect
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
9. C11×#2056C2semidirect
10. C11×#2056C2semidirect
11. C11×#1981C2semidirect
12. C11×#1949C2semidirect
15. C11×#1805C2semidirect
144. #24764C11direct (N × H)
233. C2×#462C2×C11semidirect
237. #2068C2×C11semidirect
238. #2066C2×C11semidirect
239. #2056C2×C11semidirect
240. #2056C2×C11semidirect
241. #1981C2×C11semidirect
242. #1949C2×C11semidirect
245. #1805C2×C11semidirect
572. C11#24764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4702
C2×C11×#4672
C2×C11×#4622
C2×C11×#4242
C11×#26212
C11×#23232
C11×#20682
C11×#20662
C11×#20562
C11×#19812
C11×#19492
C11×#18942
C11×#18922
C11×#18052
#2476411