Finite Group Databasebeta

← C11×#23957 #14601150

Subgroups — C11×#23957 #14601150

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3495C211yesmaximal, characteristic, complemented
2C11×#3003C211yesmaximal, characteristic
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C11×#2435C211yesmaximal, characteristic, complemented
5C11×#2027C212yesmaximal, complemented
6C11×#2003C212yesmaximal, complemented
7C11×#1901C211yesmaximal, characteristic, complemented
8C11×#1888C212yesmaximal, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1826C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C22×C11×M16C2211yescharacteristic
15C11×#556—21no—
16C11×#554—21no—
17C11×#552—21no—
18C11×#552—22no—
19C11×#552—21no—
20C11×#551—22no—
21C11×#544C2211yescharacteristic, complemented
22C11×#542—21no—
23C11×#541—21no—
24C11×#536C2211yescharacteristic, complemented
25C11×#533—21no—
26C11×#529—21no—
27C2×C11×#124C2212yes—
28C11×#525C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C11×#520C2211yescharacteristic, complemented
31C11×#519C2211yescharacteristic, complemented
32C2×C11×#117C2211yescharacteristic
33C11×#450—21no—
34C11×#450—21no—
35C11×#447—21no—
36C11×#447—21no—
37C2×C11×#104C2212yescomplemented
38C11×#418—21no—
39C11×#418—21no—
40C11×#418C2212yes—
41C11×#418C2212yes—
42C11×#418C2212yes—
43C2×C11×#102—21no—
44C2×C11×#102—21no—
45C2×C11×#101C2212yescomplemented
46C11×#407C2211yescharacteristic
47C11×#394—22no—
48C11×#390C2212yes—
49C11×#379—22no—
50C4×C11×C22⋊C4C2211yescharacteristic
51C11×#343C2212yescomplemented
52C11×#339C2212yescomplemented
53C11×#339C2212yescomplemented
54C11×#339C2212yescomplemented
55C25×C11—21no—
56C2×C11×#41C2311yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—24no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11—42no—
65C22×D4×C11C2312yes—
66C23×C4×C11C2311yescharacteristic
67C11×AGL(1,ℤ/8)—24no—
68C11×AGL(1,ℤ/8)—42no—
69C2×C11×SD16—22no—
70C2×C11×D8—22no—
71C2×C11×M16—21no—
72C2×C11×M16—42no—
73C2×C11×M16C2312yes—
74C2×C11×M16C2312yes—
75C22×C8×C11—21no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—21no—
79C11×#126—22no—
80C11×#126—22no—
81C11×#126—22no—
82C11×#126—22no—
83C11×#125—22no—
84C11×#125—22no—
85C11×#125—22no—
86C11×#125—21no—
87C11×#125—21no—
88C11×#124—22no—
89C11×#124—21no—
90C11×#124—24no—
91C11×#124—42no—
92C11×#123—22no—
93C11×#123—22no—
94C11×#123—21no—
95C11×#123—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8—21no—
100C11×C22⋊Q8—21no—
101C11×C22⋊Q8—21no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8—21no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8D411yescharacteristic
106C11×C22⋊Q8D411yescharacteristic
107C11×#121D411yescharacteristic
108C11×#121D411yescharacteristic
109C11×#120—21no—
110C4×Q8×C11—22no—
111C4×Q8×C11—21no—
112C4×Q8×C11—21no—
113C4×Q8×C11—21no—
114C4×Q8×C11—21no—
115C4×Q8×C11—21no—
116C4×D4×C11—22no—
117C4×D4×C11—21no—
118C4×D4×C11—22no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C11×#117—22no—
122C11×#117—22no—
123C11×#117—21no—
124C11×#117—21no—
125C11×#117—22no—
126C11×#117—21no—
127C11×#117D411yescharacteristic
128C11×#117D411yescharacteristic
129C11×#117C2311yescharacteristic
130C11×#117C2311yescharacteristic
131C11×#117C2311yescharacteristic
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4D412yes—
134C2×C11×C4⋊C4D411yescharacteristic
135C2×C11×C4⋊C4D411yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4D412yes—
142C2×C42×C11—21no—
143C2×C42×C11C2312yes—
144C11×#104—42no—
145C11×#102—22no—
146C11×#102—22no—
147C11×#102—22no—
148C11×#102—22no—
149C11×#102—22no—
150C11×#102—22no—
151C11×#101—42no—
152C11×C22⋊C8—21no—
153C11×C22⋊C8—21no—
154C11×#95—21no—
155#23957C1111yesmaximal, characteristic, direct product factor, Sylow
156C24×C11—22no—
157C24×C11—44no—
158C24×C11—44no—
159C24×C11—41no—
160C24×C11—41no—
161C24×C11—82no—
162C24×C11C2×D411yescharacteristic
163C11×#41—22no—
164C11×#41—22no—
165C2×Q8×C11—22no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C2×Q8×C11C2×D411yescharacteristic
171C2×D4×C11—24no—
172C2×D4×C11—24no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—41no—
187C2×D4×C11—41no—
188C2×D4×C11C2×D411yescharacteristic
189C2×D4×C11#4114yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—22no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—22no—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2411yescharacteristic
205C11×SD16—44no—
206C11×D8—44no—
207C11×M16—22no—
208C11×M16—22no—
209C11×M16—22no—
210C11×M16—22no—
211C11×M16—42no—
212C2×C8×C11—22no—
213C2×C8×C11—22no—
214C2×C8×C11—42no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—22no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4C2×D411yescharacteristic
232C11×C4⋊C4C2×D411yescharacteristic
233C11×C4⋊C4C2×D411yescharacteristic
234C11×C4⋊C4C2×D411yescharacteristic
235C11×C4⋊C4C2×D411yescharacteristic
236C11×C4⋊C4C2×D411yescharacteristic
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—21no—
241C11×C22⋊C4—21no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—21no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—21no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—48no—
252C11×C22⋊C4—42no—
253C11×C22⋊C4—84no—
254C42×C11—22no—
255C42×C11—22no—
256C42×C11—22no—
257C42×C11—21no—
258C42×C11—21no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—22no—
263C42×C11—22no—
264#3495C2×C1111yescharacteristic, complemented
265#3003C2×C1111yescharacteristic
266C2×#418C2×C1111yescharacteristic, complemented
267#2435C2×C1111yescharacteristic, complemented
268#2027C2×C1112yescomplemented
269#2003C2×C1112yescomplemented
270#1901C2×C1111yescharacteristic, complemented
271#1888C2×C1112yescomplemented
272#1883C2×C1112yescomplemented
273#1871C2×C1111yescharacteristic, complemented
274#1826C2×C1111yescharacteristic, complemented
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—21no—
278C23×C11—24no—
279C23×C11—41no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11—42no—
285C23×C11—42no—
286C23×C11—82no—
287C23×C11—82no—
288C23×C11—82no—
289C23×C11—816no—
290C23×C11—82no—
291C23×C11#12011yescharacteristic
292C23×C11#12011yescharacteristic
293C23×C11C22×D411yescharacteristic
294Q8×C11—22no—
295Q8×C11—41no—
296Q8×C11—41no—
297Q8×C11—42no—
298Q8×C11—82no—
299D4×C11—24no—
300D4×C11—22no—
301D4×C11—24no—
302D4×C11—44no—
303D4×C11—44no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—42no—
308D4×C11—81no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—42no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—81no—
334C2×C4×C11—82no—
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12011yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4112yes—
340C2×C4×C11H(5,𝔽2)12yes—
341C8×C11—42no—
342C8×C11—42no—
343C23×D4C22×C1111yescharacteristic
344C2×AGL(1,ℤ/8)C22×C1112yes—
345C22×M16C22×C1111yescharacteristic
346#556—21no—
347#554—21no—
348#552—21no—
349#552—22no—
350#552—21no—
351#551—22no—
352#544C22×C1111yescharacteristic, complemented
353#542—21no—
354#541—21no—
355#536C22×C1111yescharacteristic, complemented
356#533—21no—
357#529—21no—
358C2×#124C22×C1112yes—
359#525C22×C1111yescharacteristic
360C2×C22⋊Q8C22×C1111yescharacteristic
361#520C22×C1111yescharacteristic, complemented
362#519C22×C1111yescharacteristic, complemented
363C2×#117C22×C1111yescharacteristic
364#450—21no—
365#450—21no—
366#447—21no—
367#447—21no—
368C2×#104C22×C1112yescomplemented
369#418—21no—
370#418—21no—
371#418C22×C1112yes—
372#418C22×C1112yes—
373#418C22×C1112yes—
374C2×#102—21no—
375C2×#102—21no—
376C2×#101C22×C1112yescomplemented
377#407C22×C1111yescharacteristic
378#394—22no—
379#390C22×C1112yes—
380#379—22no—
381C4×C22⋊C4C22×C1111yescharacteristic
382#343C22×C1112yescomplemented
383#339C22×C1112yescomplemented
384#339C22×C1112yescomplemented
385#339C22×C1112yescomplemented
386C22×C11—21no—
387C22×C11—21no—
388C22×C11—21no—
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—44no—
394C22×C11—48no—
395C22×C11—41no—
396C22×C11—44no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—84no—
400C22×C11—88no—
401C22×C11—88no—
402C22×C11—82no—
403C22×C11—82no—
404C22×C11#45412yes—
405C22×C11C2×#12011yescharacteristic
406C22×C11#54612yes—
407C4×C11—21no—
408C4×C11—21no—
409C4×C11—42no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—82no—
419C4×C11#52511yescharacteristic
420C4×C11#53511yescharacteristic
421C4×C11#54612yes—
422C25—21no—
423C2×#41C23×C1111yescharacteristic
424C22×Q8C23×C1111yescharacteristic
425C22×D4—24no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—42no—
432C22×D4C23×C1112yes—
433C23×C4C23×C1111yescharacteristic
434AGL(1,ℤ/8)—24no—
435AGL(1,ℤ/8)—42no—
436C2×SD16—22no—
437C2×D8—22no—
438C2×M16—21no—
439C2×M16—42no—
440C2×M16C23×C1112yes—
441C2×M16C23×C1112yes—
442C22×C8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446#126—22no—
447#126—22no—
448#126—22no—
449#126—22no—
450#125—22no—
451#125—22no—
452#125—22no—
453#125—21no—
454#125—21no—
455#124—22no—
456#124—21no—
457#124—24no—
458#124—42no—
459#123—22no—
460#123—22no—
461#123—21no—
462#123—22no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8D4×C1111yescharacteristic
473C22⋊Q8D4×C1111yescharacteristic
474#121D4×C1111yescharacteristic
475#121D4×C1111yescharacteristic
476#120—21no—
477C4×Q8—22no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×D4—22no—
484C4×D4—21no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4—21no—
488#117—22no—
489#117—22no—
490#117—21no—
491#117—21no—
492#117—22no—
493#117—21no—
494#117D4×C1111yescharacteristic
495#117D4×C1111yescharacteristic
496#117C23×C1111yescharacteristic
497#117C23×C1111yescharacteristic
498#117C23×C1111yescharacteristic
499C2×C4⋊C4—21no—
500C2×C4⋊C4D4×C1112yes—
501C2×C4⋊C4D4×C1111yescharacteristic
502C2×C4⋊C4D4×C1111yescharacteristic
503C2×C4⋊C4C23×C1111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4D4×C1112yes—
509C2×C42—21no—
510C2×C42C23×C1112yes—
511#104—42no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—22no—
518#101—42no—
519C22⋊C8—21no—
520C22⋊C8—21no—
521#95—21no—
522C2×C11—22no—
523C2×C11—22no—
524C2×C11—41no—
525C2×C11—81no—
526C2×C11—84no—
527C2×C11#240411yescharacteristic
528C2×C11C2×#45411yescharacteristic
529C2×C11#302111yescharacteristic
530C24—22no—
531C24—44no—
532C24—44no—
533C24—41no—
534C24—41no—
535C24—82no—
536C24C2×D4×C1111yescharacteristic
537#41—22no—
538#41—22no—
539C2×Q8—22no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8C2×D4×C1111yescharacteristic
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4C2×D4×C1111yescharacteristic
563C2×D4C11×#4114yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4C2×D4×C1112yes—
572C22×C4C2×D4×C1111yescharacteristic
573C22×C4C2×D4×C1111yescharacteristic
574C22×C4C2×D4×C1111yescharacteristic
575C22×C4C2×D4×C1111yescharacteristic
576C22×C4C2×D4×C1111yescharacteristic
577C22×C4C2×D4×C1112yes—
578C22×C4C24×C1111yescharacteristic
579SD16—44no—
580D8—44no—
581M16—22no—
582M16—22no—
583M16—22no—
584M16—22no—
585M16—42no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—42no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4C2×D4×C1111yescharacteristic
606C4⋊C4C2×D4×C1111yescharacteristic
607C4⋊C4C2×D4×C1111yescharacteristic
608C4⋊C4C2×D4×C1111yescharacteristic
609C4⋊C4C2×D4×C1111yescharacteristic
610C4⋊C4C2×D4×C1111yescharacteristic
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—48no—
626C22⋊C4—42no—
627C22⋊C4—84no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—22no—
638C11#2395711yescharacteristic, direct product factor, Sylow
639C23—22no—
640C23—22no—
641C23—21no—
642C23—24no—
643C23—41no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23—82no—
651C23—82no—
652C23—82no—
653C23—816no—
654C23—82no—
655C23C11×#12011yescharacteristic
656C23C11×#12011yescharacteristic
657C23C22×D4×C1111yescharacteristic
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—42no—
662Q8—82no—
663D4—24no—
664D4—22no—
665D4—24no—
666D4—44no—
667D4—44no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—81no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4C11×#12011yescharacteristic
700C2×C4C11×#12011yescharacteristic
701C2×C4C22×D4×C1111yescharacteristic
702C2×C4C22×D4×C1111yescharacteristic
703C2×C4C2×C11×#4112yes—
704C2×C4C11×H(5,𝔽2)12yes—
705C8—42no—
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—44no—
715C22—48no—
716C22—41no—
717C22—44no—
718C22—41no—
719C22—41no—
720C22—84no—
721C22—88no—
722C22—88no—
723C22—82no—
724C22—82no—
725C22C11×#45412yes—
726C22C2×C11×#12011yescharacteristic
727C22C11×#54612yes—
728C4—21no—
729C4—21no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—82no—
740C4C11×#52511yescharacteristic
741C4C11×#53511yescharacteristic
742C4C11×#54612yes—
743C2—22no—
744C2—22no—
745C2—41no—
746C2—84no—
747C2—81no—
748C2C11×#240411yescharacteristic
749C2C2×C11×#45411yescharacteristic
750C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3003C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3495C2semidirect
3. C2×C11×#418C2semidirect
4. C11×#2435C2semidirect
5. C11×#2027C2semidirect
6. C11×#2003C2semidirect
7. C11×#1901C2semidirect
8. C11×#1888C2semidirect
9. C11×#1883C2semidirect
10. C11×#1871C2semidirect
11. C11×#1826C2semidirect
21. C11×#544C22semidirect
24. C11×#536C22semidirect
30. C11×#520C22semidirect
31. C11×#519C22semidirect
37. C2×C11×#104C22semidirect
45. C2×C11×#101C22semidirect
51. C11×#343C22semidirect
52. C11×#339C22semidirect
53. C11×#339C22semidirect
54. C11×#339C22semidirect
155. #23957C11direct (N × H)
264. #3495C2×C11semidirect
266. C2×#418C2×C11semidirect
267. #2435C2×C11semidirect
268. #2027C2×C11semidirect
269. #2003C2×C11semidirect
270. #1901C2×C11semidirect
271. #1888C2×C11semidirect
272. #1883C2×C11semidirect
273. #1871C2×C11semidirect
274. #1826C2×C11semidirect
352. #544C22×C11semidirect
355. #536C22×C11semidirect
361. #520C22×C11semidirect
362. #519C22×C11semidirect
368. C2×#104C22×C11semidirect
376. C2×#101C22×C11semidirect
382. #343C22×C11semidirect
383. #339C22×C11semidirect
384. #339C22×C11semidirect
385. #339C22×C11semidirect
638. C11#23957direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34952
C11×#30032
C2×C11×#4182
C11×#24352
C11×#20272
C11×#20032
C11×#19012
C11×#18882
C11×#18832
C11×#18712
C11×#18262
#2395711