Finite Group Databasebeta

← C11×#24487 #14601680

Subgroups — C11×#24487 #14601680

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic, complemented
2C2×C11×#416C211yesmaximal, characteristic
3C11×#2432C211yesmaximal, characteristic
4C11×#2346C211yesmaximal, characteristic, complemented
5C11×#2066C211yesmaximal, characteristic, complemented
6C11×#2065C211yesmaximal, characteristic, complemented
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#2042C211yesmaximal, characteristic, complemented
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1981C211yesmaximal, characteristic, complemented
11C11×#1928C211yesmaximal, characteristic, complemented
12C11×#1925C211yesmaximal, characteristic, complemented
13C11×#1892C211yesmaximal, characteristic, complemented
14C11×#1850C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#485—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#416—24no—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C11×#394—21no—
42C11×#394—21no—
43C11×#391C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#388—21no—
48C11×#388—21no—
49C11×#385—21no—
50C11×#385—21no—
51C11×#382—21no—
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C11×#376—21no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C22×C8×C11—22no—
74C22×C8×C11—41no—
75C22×C8×C11—41no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8—41no—
82C11×#124—22no—
83C11×#124—41no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×#117—22no—
87C11×#117D414yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C11×#107—22no—
113C11×#106—22no—
114C11×C4⋊C8—41no—
115C11×C4⋊C8—41no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—41no—
122C11×#103—41no—
123C11×#103—41no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—41no—
128C11×C22⋊C8—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#24487C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—28no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
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#4112yes—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11#4112yes—
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×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11#4112yes—
187C22×C4×C11C2411yescharacteristic
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—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—44no—
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—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—81no—
213C11×C4⋊C4—81no—
214C11×C4⋊C4C2×D412yes—
215C11×C4⋊C4C2×D412yes—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—81no—
225C42×C11—24no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—42no—
231C42×C11—42no—
232C2×#485C2×C1111yescharacteristic, complemented
233C2×#416C2×C1111yescharacteristic
234#2432C2×C1111yescharacteristic
235#2346C2×C1111yescharacteristic, complemented
236#2066C2×C1111yescharacteristic, complemented
237#2065C2×C1111yescharacteristic, complemented
238#2043C2×C1111yescharacteristic, complemented
239#2042C2×C1111yescharacteristic, complemented
240#1983C2×C1111yescharacteristic, complemented
241#1981C2×C1111yescharacteristic, complemented
242#1928C2×C1111yescharacteristic, complemented
243#1925C2×C1111yescharacteristic, complemented
244#1892C2×C1111yescharacteristic, complemented
245#1850C2×C1111yescharacteristic, complemented
246#1788C2×C1111yescharacteristic
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—22no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11#12112yes—
261C23×C11C22×D411yescharacteristic
262Q8×C11—22no—
263Q8×C11—22no—
264Q8×C11—41no—
265Q8×C11—41no—
266Q8×C11—41no—
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270D4×C11—22no—
271D4×C11—22no—
272D4×C11—48no—
273D4×C11—41no—
274D4×C11—41no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—48no—
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—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11#12112yes—
315C2×C4×C11#13512yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C8×C11—41no—
323C8×C11—41no—
324C8×C11—41no—
325C8×C11—41no—
326C22×#41C22×C1111yescharacteristic
327C23×C8C22×C1111yescharacteristic
328C2×C4⋊Q8C22×C1111yescharacteristic
329C2×#124C22×C1111yescharacteristic
330C2×C22⋊Q8C22×C1111yescharacteristic
331C2×#117C22×C1111yescharacteristic
332#485—24no—
333C2×#107C22×C1111yescharacteristic
334C2×#106C22×C1111yescharacteristic
335C2×C4⋊C8C22×C1111yescharacteristic
336C2×C4⋊C8C22×C1111yescharacteristic
337#416—24no—
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×C22⋊C8C22×C1111yescharacteristic
351#394—21no—
352#394—21no—
353#391C22×C1111yescharacteristic
354#390C22×C1111yescharacteristic
355#389C22×C1111yescharacteristic
356#389C22×C1111yescharacteristic
357#388—21no—
358#388—21no—
359#385—21no—
360#385—21no—
361#382—21no—
362#380C22×C1111yescharacteristic
363C4×C4⋊C4C22×C1111yescharacteristic
364C4×C4⋊C4C22×C1111yescharacteristic
365C4×C22⋊C4C22×C1111yescharacteristic
366#376—21no—
367#340C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#336C22×C1111yescharacteristic
370#336C22×C1111yescharacteristic
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11C2×#12111yescharacteristic
386C22×C11#54611yescharacteristic
387C22×C11#54611yescharacteristic
388C22×C11C2×#13511yescharacteristic
389C22×C11#57511yescharacteristic
390C22×C11#57711yescharacteristic
391C22×C11#57811yescharacteristic
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—42no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11#52511yescharacteristic
405C4×C11#53511yescharacteristic
406C4×C11#55111yescharacteristic
407C4×C11#55111yescharacteristic
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—41no—
413C2×#41—41no—
414C22×Q8C23×C1111yescharacteristic
415C22×Q8C23×C1111yescharacteristic
416C22×D4—21no—
417C22×D4C23×C1111yescharacteristic
418C23×C4—21no—
419C23×C4C23×C1111yescharacteristic
420C22×C8—22no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8C23×C1111yescharacteristic
424C22×C8C23×C1111yescharacteristic
425C22×C8C23×C1111yescharacteristic
426C22×C8C23×C1111yescharacteristic
427C4⋊Q8—22no—
428C4⋊Q8—41no—
429#124—22no—
430#124—41no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433#117—22no—
434#117D4×C1114yes—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4D4×C1111yescharacteristic
453C2×C22⋊C4D4×C1111yescharacteristic
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42C23×C1111yescharacteristic
458C2×C42C23×C1111yescharacteristic
459#107—22no—
460#106—22no—
461C4⋊C8—41no—
462C4⋊C8—41no—
463#103—22no—
464#103—22no—
465#103—22no—
466#103—22no—
467#103—22no—
468#103—41no—
469#103—41no—
470#103—41no—
471#102—22no—
472#102—22no—
473#102—22no—
474#102—41no—
475C22⋊C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95D4×C1111yescharacteristic
484#95D4×C1111yescharacteristic
485C2×C11—42no—
486C2×C11—82no—
487C2×C11#241111yescharacteristic
488C2×C11#303511yescharacteristic
489C2×C11#304611yescharacteristic
490C2×C11#330011yescharacteristic
491C2×C11#330311yescharacteristic
492C2×C11#331511yescharacteristic
493C2×C11#332111yescharacteristic
494C24—21no—
495C24C2×D4×C1111yescharacteristic
496#41—28no—
497#41—44no—
498#41—44no—
499#41—44no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C11×#4112yes—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4C11×#4112yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C2×D4×C1111yescharacteristic
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C2×D4×C1112yes—
540C22×C4C2×D4×C1111yescharacteristic
541C22×C4C11×#4112yes—
542C22×C4C24×C1111yescharacteristic
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—44no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C4⋊C4C2×D4×C1112yes—
570C4⋊C4C2×D4×C1112yes—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—81no—
580C42—24no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—42no—
586C42—42no—
587C11#2448711yescharacteristic, direct product factor, Sylow
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C11×#12112yes—
602C23C22×D4×C1111yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—48no—
614D4—41no—
615D4—41no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—48no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4C11×#12112yes—
656C2×C4C11×#13512yes—
657C2×C4C22×D4×C1111yescharacteristic
658C2×C4C2×C11×#4111yescharacteristic
659C2×C4C2×C11×#4111yescharacteristic
660C2×C4C2×C11×#4111yescharacteristic
661C2×C4C11×H(5,𝔽2)11yescharacteristic
662C2×C4C11×H(5,𝔽2)11yescharacteristic
663C8—41no—
664C8—41no—
665C8—41no—
666C8—41no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C11×#12111yescharacteristic
682C22C11×#54611yescharacteristic
683C22C11×#54611yescharacteristic
684C22C2×C11×#13511yescharacteristic
685C22C11×#57511yescharacteristic
686C22C11×#57711yescharacteristic
687C22C11×#57811yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C11×#52511yescharacteristic
701C4C11×#53511yescharacteristic
702C4C11×#55111yescharacteristic
703C4C11×#55111yescharacteristic
704C2—42no—
705C2—82no—
706C2C11×#241111yescharacteristic
707C2C11×#303511yescharacteristic
708C2C11×#304611yescharacteristic
709C2C11×#330011yescharacteristic
710C2C11×#330311yescharacteristic
711C2C11×#331511yescharacteristic
712C2C11×#332111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#485C2semidirect
4. C11×#2346C2semidirect
5. C11×#2066C2semidirect
6. C11×#2065C2semidirect
7. C11×#2043C2semidirect
8. C11×#2042C2semidirect
9. C11×#1983C2semidirect
10. C11×#1981C2semidirect
11. C11×#1928C2semidirect
12. C11×#1925C2semidirect
13. C11×#1892C2semidirect
14. C11×#1850C2semidirect
138. #24487C11direct (N × H)
232. C2×#485C2×C11semidirect
235. #2346C2×C11semidirect
236. #2066C2×C11semidirect
237. #2065C2×C11semidirect
238. #2043C2×C11semidirect
239. #2042C2×C11semidirect
240. #1983C2×C11semidirect
241. #1981C2×C11semidirect
242. #1928C2×C11semidirect
243. #1925C2×C11semidirect
244. #1892C2×C11semidirect
245. #1850C2×C11semidirect
587. C11#24487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C2×C11×#4162
C11×#24322
C11×#23462
C11×#20662
C11×#20652
C11×#20432
C11×#20422
C11×#19832
C11×#19812
C11×#19282
C11×#19252
C11×#18922
C11×#18502
C11×#17882
#2448711