Finite Group Databasebeta

← C11×#24871 #14602064

Subgroups — C11×#24871 #14602064

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic, complemented
2C22×C11×#103C211yesmaximal, characteristic, complemented
3C11×#2409C211yesmaximal, characteristic
4C11×#2352C211yesmaximal, characteristic
5C11×#2097C211yesmaximal, characteristic, complemented
6C11×#2074C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#1928C211yesmaximal, characteristic, complemented
10C11×#1927C211yesmaximal, characteristic, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1869C211yesmaximal, characteristic
13C11×#1852C211yesmaximal, characteristic, complemented
14C11×#1807C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#485—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#103—24no—
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C11×#395—21no—
41C11×#393—21no—
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#388—21no—
45C11×#387—21no—
46C11×#386—21no—
47C11×#386—21no—
48C11×#385—21no—
49C11×#382C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11D411yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—41no—
85C11×C22⋊Q8—41no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C11×#117—22no—
89C11×#117—41no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C11×#107—22no—
114C11×#107—41no—
115C11×#106—22no—
116C11×#106—41no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—41no—
123C11×#103—41no—
124C11×#103D414yescomplemented
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—41no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24871C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11C2×D411yescharacteristic
140C24×C11C2×D411yescharacteristic
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—28no—
144C2×Q8×C11—21no—
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—42no—
153C2×Q8×C11—42no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C2×Q8×C11—44no—
157C2×Q8×C11—42no—
158C2×Q8×C11C2×D412yes—
159C2×Q8×C11#4112yes—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
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—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—81no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
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—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—44no—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—42no—
222C11×C4⋊C4C2×D412yes—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—81no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—42no—
234C42×C11—81no—
235C2×#485C2×C1111yescharacteristic, complemented
236C22×#103C2×C1111yescharacteristic, complemented
237#2409C2×C1111yescharacteristic
238#2352C2×C1111yescharacteristic
239#2097C2×C1111yescharacteristic, complemented
240#2074C2×C1111yescharacteristic, complemented
241#2036C2×C1111yescharacteristic, complemented
242#2035C2×C1111yescharacteristic, complemented
243#1928C2×C1111yescharacteristic, complemented
244#1927C2×C1111yescharacteristic, complemented
245#1873C2×C1111yescharacteristic, complemented
246#1869C2×C1111yescharacteristic
247#1852C2×C1111yescharacteristic, complemented
248#1807C2×C1111yescharacteristic, complemented
249#1787C2×C1111yescharacteristic, complemented
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—21no—
261C23×C11#12312yes—
262C23×C11#13512yes—
263C23×C11#13712yes—
264C23×C11C22×D411yescharacteristic
265Q8×C11—22no—
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—22no—
269Q8×C11—48no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274D4×C11—44no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—48no—
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—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—84no—
320C2×C4×C11#12312yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C8×C11—22no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11—41no—
331C23×Q8C22×C1111yescharacteristic
332C23×C8C22×C1111yescharacteristic
333C2×C22⋊Q8C22×C1111yescharacteristic
334C2×C22⋊Q8C22×C1111yescharacteristic
335C2×C4×D4C22×C1111yescharacteristic
336C2×#117C22×C1111yescharacteristic
337C22×C4⋊C4C22×C1111yescharacteristic
338#485—24no—
339C2×#107C22×C1111yescharacteristic
340C2×#107C22×C1111yescharacteristic
341C2×#106C22×C1111yescharacteristic
342C2×#106C22×C1111yescharacteristic
343C2×#103—24no—
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#103C22×C1111yescharacteristic
347C2×#103C22×C1111yescharacteristic
348C2×#103C22×C1111yescharacteristic
349C2×#103C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×C22⋊C8C22×C1111yescharacteristic
353C2×C22⋊C8C22×C1111yescharacteristic
354C2×C22⋊C8C22×C1111yescharacteristic
355#395—21no—
356#393—21no—
357#391C22×C1111yescharacteristic
358#391C22×C1111yescharacteristic
359#388—21no—
360#387—21no—
361#386—21no—
362#386—21no—
363#385—21no—
364#382C22×C1111yescharacteristic
365#380C22×C1111yescharacteristic
366#380C22×C1111yescharacteristic
367#380C22×C1111yescharacteristic
368C4×C4⋊C4C22×C1111yescharacteristic
369C4×C22⋊C4—21no—
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11#48514yescomplemented
390C22×C11C2×#12311yescharacteristic
391C22×C11D4211yescharacteristic
392C22×C11#54611yescharacteristic
393C22×C11C2×#13511yescharacteristic
394C22×C11C2×#13711yescharacteristic
395C22×C11#57711yescharacteristic
396C22×C11#57811yescharacteristic
397C4×C11—22no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11#52511yescharacteristic
410C4×C11#53811yescharacteristic
411C4×C11#54611yescharacteristic
412C4×C11#55111yescharacteristic
413C22×Q8—21no—
414C22×Q8—22no—
415C22×Q8—22no—
416C22×Q8—22no—
417C22×Q8—22no—
418C22×Q8—41no—
419C22×Q8—41no—
420C22×Q8C23×C1111yescharacteristic
421C22×Q8C23×C1111yescharacteristic
422C22×D4D4×C1111yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4C23×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—41no—
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C22×C8C23×C1111yescharacteristic
433C22×C8C23×C1111yescharacteristic
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—41no—
437C22⋊Q8—41no—
438C4×D4—22no—
439C4×D4—22no—
440#117—22no—
441#117—41no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4D4×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⋊C4D4×C1111yescharacteristic
461C2×C22⋊C4D4×C1111yescharacteristic
462C2×C42—21no—
463C2×C42—21no—
464C2×C42C23×C1111yescharacteristic
465#107—22no—
466#107—41no—
467#106—22no—
468#106—41no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103—22no—
474#103—41no—
475#103—41no—
476#103D4×C1114yescomplemented
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—41no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490C2×C11—24no—
491C2×C11—81no—
492C2×C11#241811yescharacteristic
493C2×C11C2×#48511yescharacteristic
494C2×C11#309711yescharacteristic
495C2×C11#327011yescharacteristic
496C2×C11#328211yescharacteristic
497C2×C11#330011yescharacteristic
498C2×C11#332011yescharacteristic
499C24C2×D4×C1111yescharacteristic
500C24C2×D4×C1111yescharacteristic
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—28no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—42no—
518C2×Q8C2×D4×C1112yes—
519C2×Q8C11×#4112yes—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—81no—
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C11×#4112yes—
552C22×C4C11×#4112yes—
553C22×C4C24×C1111yescharacteristic
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—44no—
566C2×C8C2×D4×C1112yes—
567C4⋊C4—22no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4C2×D4×C1112yes—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—81no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—81no—
595C11#2487111yescharacteristic, direct product factor, Sylow
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23C11×#12312yes—
608C23C11×#13512yes—
609C23C11×#13712yes—
610C23C22×D4×C1111yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—48no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—44no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
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×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4C11×#12312yes—
667C2×C4C22×D4×C1111yescharacteristic
668C2×C4C2×C11×#4111yescharacteristic
669C2×C4C2×C11×#4111yescharacteristic
670C2×C4C2×C11×#4111yescharacteristic
671C2×C4C11×H(5,𝔽2)11yescharacteristic
672C2×C4C11×H(5,𝔽2)11yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C11×#48514yescomplemented
691C22C2×C11×#12311yescharacteristic
692C22D42×C1111yescharacteristic
693C22C11×#54611yescharacteristic
694C22C2×C11×#13511yescharacteristic
695C22C2×C11×#13711yescharacteristic
696C22C11×#57711yescharacteristic
697C22C11×#57811yescharacteristic
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C11×#52511yescharacteristic
711C4C11×#53811yescharacteristic
712C4C11×#54611yescharacteristic
713C4C11×#55111yescharacteristic
714C2—24no—
715C2—81no—
716C2C11×#241811yescharacteristic
717C2C2×C11×#48511yescharacteristic
718C2C11×#309711yescharacteristic
719C2C11×#327011yescharacteristic
720C2C11×#328211yescharacteristic
721C2C11×#330011yescharacteristic
722C2C11×#332011yescharacteristic
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
1. C2×C11×#485C2semidirect
2. C22×C11×#103C2semidirect
5. C11×#2097C2semidirect
6. C11×#2074C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1928C2semidirect
10. C11×#1927C2semidirect
11. C11×#1873C2semidirect
13. C11×#1852C2semidirect
14. C11×#1807C2semidirect
15. C11×#1787C2semidirect
124. C11×#103D4semidirect
138. #24871C11direct (N × H)
235. C2×#485C2×C11semidirect
236. C22×#103C2×C11semidirect
239. #2097C2×C11semidirect
240. #2074C2×C11semidirect
241. #2036C2×C11semidirect
242. #2035C2×C11semidirect
243. #1928C2×C11semidirect
244. #1927C2×C11semidirect
245. #1873C2×C11semidirect
247. #1852C2×C11semidirect
248. #1807C2×C11semidirect
249. #1787C2×C11semidirect
389. C22×C11#485semidirect
476. #103D4×C11semidirect
595. C11#24871direct (N × H)
690. C22C11×#485semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C22×C11×#1032
C11×#24092
C11×#23522
C11×#20972
C11×#20742
C11×#20362
C11×#20352
C11×#19282
C11×#19272
C11×#18732
C11×#18692
C11×#18522
C11×#18072
C11×#17872
#2487111