Finite Group Databasebeta

← C11×#24106 #14601299

Subgroups — C11×#24106 #14601299

Order 2816.

1046 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C2×C11×#485C211yesmaximal, characteristic, complemented
3C2×C11×#428C211yesmaximal, characteristic, complemented
4C11×#2485C211yesmaximal, characteristic
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2059C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic
11C11×#1865C211yesmaximal, characteristic, complemented
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1824C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C11×#552—24no—
18C11×#552—24no—
19C2×C11×#126—21no—
20C2×C11×#125—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117—21no—
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#485—24no—
32C11×#428—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#107C2211yescharacteristic
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×#106C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C11×#397—21no—
47C11×#394—21no—
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#388—21no—
51C11×#387—21no—
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C11×#380C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#126—28no—
76C11×#125—28no—
77C11×#125—22no—
78C11×#125—22no—
79C11×#123—28no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8D414yes—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C11×#117—28no—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—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⋊C4D414yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11—21no—
121C2×C42×C11—21no—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124C11×#107—22no—
125C11×#107—22no—
126C11×#107—22no—
127C11×#106—22no—
128C11×#106—22no—
129C11×#106—22no—
130C11×#103—22no—
131C11×#103—22no—
132C11×#103—22no—
133C11×#103—22no—
134C11×C22⋊C8—22no—
135C11×C22⋊C8—22no—
136C11×C22⋊C8—22no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142#24106C1111yesmaximal, characteristic, direct product factor, Sylow
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D412yes—
151C2×D4×C11—22no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—21no—
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—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2411yescharacteristic
182C11×M16—28no—
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×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11#4112yes—
194C2×C8×C11#4112yes—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
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—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—81no—
215C11×C4⋊C4C2×D412yes—
216C11×C4⋊C4C2×D412yes—
217C11×C4⋊C4C2×D412yes—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—24no—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C42×C11—24no—
228C42×C11—24no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—42no—
232C2×#552C2×C1111yescharacteristic
233C2×#485C2×C1111yescharacteristic, complemented
234C2×#428C2×C1111yescharacteristic, complemented
235#2485C2×C1111yescharacteristic
236#2059C2×C1111yescharacteristic, complemented
237#2059C2×C1111yescharacteristic, complemented
238#2036C2×C1111yescharacteristic, complemented
239#2035C2×C1111yescharacteristic, complemented
240#1894C2×C1111yescharacteristic, complemented
241#1870C2×C1111yescharacteristic
242#1865C2×C1111yescharacteristic, complemented
243#1863C2×C1111yescharacteristic, complemented
244#1854C2×C1111yescharacteristic, complemented
245#1854C2×C1111yescharacteristic, complemented
246#1824C2×C1111yescharacteristic, complemented
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11#12012yes—
261C23×C11C22×D411yescharacteristic
262Q8×C11—22no—
263Q8×C11—22no—
264Q8×C11—41no—
265Q8×C11—41no—
266D4×C11—44no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
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—48no—
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—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11#12012yes—
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C112−1+411yescharacteristic
317C2×C4×C112−1+411yescharacteristic
318C8×C11—22no—
319C8×C11—22no—
320C8×C11—41no—
321C8×C11—41no—
322C22×M16C22×C1111yescharacteristic
323#552—24no—
324#552—24no—
325C2×#126—21no—
326C2×#125—21no—
327C2×#125C22×C1111yescharacteristic
328C2×#123—21no—
329C2×C22⋊Q8C22×C1111yescharacteristic
330C2×C22⋊Q8C22×C1111yescharacteristic
331C2×C4×Q8C22×C1111yescharacteristic
332C2×C4×D4C22×C1111yescharacteristic
333C2×#117—21no—
334C2×#117C22×C1111yescharacteristic
335C2×#117C22×C1111yescharacteristic
336C22×C4⋊C4C22×C1111yescharacteristic
337#485—24no—
338#428—24no—
339C2×#107C22×C1111yescharacteristic
340C2×#107C22×C1111yescharacteristic
341C2×#107C22×C1111yescharacteristic
342C2×#106C22×C1111yescharacteristic
343C2×#106C22×C1111yescharacteristic
344C2×#106C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#103C22×C1111yescharacteristic
348C2×#103C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×C22⋊C8C22×C1111yescharacteristic
351C2×C22⋊C8C22×C1111yescharacteristic
352#397—21no—
353#394—21no—
354#389C22×C1111yescharacteristic
355#389C22×C1111yescharacteristic
356#388—21no—
357#387—21no—
358#380C22×C1111yescharacteristic
359#380C22×C1111yescharacteristic
360#380C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369C22×C11—22no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11C2×#12011yescharacteristic
384C22×C11#54711yescharacteristic
385C22×C11#54711yescharacteristic
386C22×C11#57511yescharacteristic
387C22×C11#57511yescharacteristic
388C22×C11#57711yescharacteristic
389C22×C11#57811yescharacteristic
390C4×C11—22no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—42no—
395C4×C11—42no—
396C4×C11—41no—
397C4×C11—42no—
398C4×C11—81no—
399C4×C11—81no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11#52511yescharacteristic
403C4×C11#53611yescharacteristic
404C4×C11#54711yescharacteristic
405C4×C11#54711yescharacteristic
406C22×Q8C23×C1111yescharacteristic
407C22×D4D4×C1111yescharacteristic
408C23×C4—21no—
409C23×C4C23×C1111yescharacteristic
410C23×C4C23×C1111yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—22no—
414C22×C8C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418#126—28no—
419#125—28no—
420#125—22no—
421#125—22no—
422#123—28no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8D4×C1114yes—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×D4—22no—
430C4×D4—22no—
431#117—28no—
432#117—22no—
433#117—22no—
434#117—22no—
435#117—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4D4×C1111yescharacteristic
446C2×C4⋊C4D4×C1114yes—
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C4⋊C4C23×C1111yescharacteristic
449C2×C4⋊C4C23×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C4⋊C4C23×C1111yescharacteristic
453C2×C4⋊C4C23×C1111yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C1111yescharacteristic
462C2×C22⋊C4D4×C1111yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C23×C1111yescharacteristic
467#107—22no—
468#107—22no—
469#107—22no—
470#106—22no—
471#106—22no—
472#106—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485C2×C11—42no—
486C2×C11—81no—
487C2×C11#240611yescharacteristic
488C2×C11#300511yescharacteristic
489C2×C11#301311yescharacteristic
490C2×C11#334811yescharacteristic
491C2×C11#334911yescharacteristic
492C2×C11#335111yescharacteristic
493C2×C11#335211yescharacteristic
494C24C2×D4×C1111yescharacteristic
495C24C2×D4×C1111yescharacteristic
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C2×D4×C1112yes—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—41no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1112yes—
531C22×C4C2×D4×C1112yes—
532C22×C4C24×C1111yescharacteristic
533M16—28no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C11×#4112yes—
545C2×C8C11×#4112yes—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
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—81no—
566C4⋊C4C2×D4×C1112yes—
567C4⋊C4C2×D4×C1112yes—
568C4⋊C4C2×D4×C1112yes—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—24no—
579C42—24no—
580C42—21no—
581C42—21no—
582C42—42no—
583C11#2410611yescharacteristic, direct product factor, Sylow
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23C11×#12012yes—
598C23C22×D4×C1111yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—44no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—48no—
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×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
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×C4C11×#12012yes—
649C2×C4C22×D4×C1111yescharacteristic
650C2×C4C22×D4×C1111yescharacteristic
651C2×C4C2×C11×#4111yescharacteristic
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C11×2−1+411yescharacteristic
654C2×C4C11×2−1+411yescharacteristic
655C8—22no—
656C8—22no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22C2×C11×#12011yescharacteristic
674C22C11×#54711yescharacteristic
675C22C11×#54711yescharacteristic
676C22C11×#57511yescharacteristic
677C22C11×#57511yescharacteristic
678C22C11×#57711yescharacteristic
679C22C11×#57811yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—41no—
684C4—42no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4C11×#52511yescharacteristic
693C4C11×#53611yescharacteristic
694C4C11×#54711yescharacteristic
695C4C11×#54711yescharacteristic
696C2—42no—
697C2—81no—
698C2C11×#240611yescharacteristic
699C2C11×#300511yescharacteristic
700C2C11×#301311yescharacteristic
701C2C11×#334811yescharacteristic
702C2C11×#334911yescharacteristic
703C2C11×#335111yescharacteristic
704C2C11×#335211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#485C2semidirect
3. C2×C11×#428C2semidirect
5. C11×#2059C2semidirect
6. C11×#2059C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1894C2semidirect
11. C11×#1865C2semidirect
12. C11×#1863C2semidirect
13. C11×#1854C2semidirect
14. C11×#1854C2semidirect
15. C11×#1824C2semidirect
142. #24106C11direct (N × H)
233. C2×#485C2×C11semidirect
234. C2×#428C2×C11semidirect
236. #2059C2×C11semidirect
237. #2059C2×C11semidirect
238. #2036C2×C11semidirect
239. #2035C2×C11semidirect
240. #1894C2×C11semidirect
242. #1865C2×C11semidirect
243. #1863C2×C11semidirect
244. #1854C2×C11semidirect
245. #1854C2×C11semidirect
246. #1824C2×C11semidirect
583. C11#24106direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4852
C2×C11×#4282
C11×#24852
C11×#20592
C11×#20362
C11×#20352
C11×#18942
C11×#18702
C11×#18652
C11×#18632
C11×#18542
C11×#18242
#2410611