Finite Group Databasebeta

← C11×#23880 #14601073

Subgroups — C11×#23880 #14601073

Order 2816.

1696 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C11×#3489C211yesmaximal, characteristic
3C2×C11×#456C212yesmaximal, complemented
4C11×#3004C211yesmaximal, characteristic, complemented
5C11×#2434C211yesmaximal, characteristic, complemented
6C11×#2007C212yesmaximal, complemented
7C11×#2005C212yesmaximal, complemented
8C11×#1901C211yesmaximal, characteristic, complemented
9C11×#1882C212yesmaximal, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1789C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C2×C11×#137—21no—
16C2×C11×#137—21no—
17C2×C11×#137—28no—
18C2×C11×#137C2212yes—
19C2×C11×#137C2212yes—
20C2×C11×#137C2212yescomplemented
21C22×C11×Q16—21no—
22C22×C11×SD16—21no—
23C22×C11×M16C2211yescharacteristic
24D4×Q8×C11—21no—
25C11×#548—21no—
26C11×#547—21no—
27C11×#547—22no—
28C11×#546—21no—
29C11×#546—22no—
30C11×#537—21no—
31C11×#537C2211yescharacteristic
32C11×#536—21no—
33C11×#536C2211yescharacteristic
34C2×C11×C4⋊Q8C2212yescomplemented
35C11×#525—21no—
36C11×#525C2211yescharacteristic
37C2×C11×C22⋊Q8—21no—
38C2×C11×C22⋊Q8C2211yescharacteristic
39C11×#520C2211yescharacteristic
40C11×#456—28no—
41C11×#451—21no—
42C11×#451—21no—
43C11×#448—21no—
44C11×#448—21no—
45C2×C11×#104C2212yes—
46C2×C11×#104C2212yes—
47C2×C11×#104C2212yescomplemented
48C11×#419C2212yescomplemented
49C2×C11×#101C2212yescomplemented
50C11×#407C2211yescharacteristic
51C11×#395—22no—
52C11×#391C2212yescomplemented
53C11×#385—22no—
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#343C2212yescomplemented
56C11×#339C2212yescomplemented
57C11×2−1+4—24no—
58C11×2−1+4—42no—
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C2×C11×#41—21no—
62C2×C11×#41—22no—
63C2×C11×#41—21no—
64C2×C11×#41—24no—
65C2×C11×#41—42no—
66C2×C11×#41D411yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C2×C11×#41C2311yescharacteristic
70C2×C11×#41C2311yescharacteristic
71C22×Q8×C11—21no—
72C22×Q8×C11—21no—
73C22×Q8×C11—21no—
74C22×Q8×C11—24no—
75C22×Q8×C11—21no—
76C22×Q8×C11—21no—
77C22×Q8×C11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11—42no—
80C22×Q8×C11D411yescharacteristic
81C22×Q8×C11C2312yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11D411yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C11×#137—28no—
89C11×#137—28no—
90C11×#137—24no—
91C11×#137—24no—
92C11×#137—24no—
93C11×#137—24no—
94C11×#137—42no—
95C11×#137D418yescomplemented
96C2×C11×Q16—28no—
97C2×C11×Q16—22no—
98C2×C11×Q16—22no—
99C2×C11×Q16—22no—
100C2×C11×SD16—28no—
101C2×C11×SD16—22no—
102C2×C11×SD16—22no—
103C2×C11×SD16—22no—
104C2×C11×M16—21no—
105C2×C11×M16—24no—
106C2×C11×M16C2312yes—
107C2×C11×M16C2312yes—
108C22×C8×C11—21no—
109C11×C4⋊Q8—22no—
110C11×C4⋊Q8—21no—
111C11×C4⋊Q8—24no—
112C11×C4⋊Q8—42no—
113C11×#124—22no—
114C11×#124—21no—
115C11×#123—22no—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—21no—
119C11×#123—22no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—21no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8—21no—
131C11×C22⋊Q8D411yescharacteristic
132C11×C22⋊Q8D411yescharacteristic
133C11×#121—22no—
134C11×#121—22no—
135C11×#121—22no—
136C11×#121—21no—
137C11×#121—21no—
138C11×#121—22no—
139C11×#121D411yescharacteristic
140C11×#121D411yescharacteristic
141C11×#120—22no—
142C11×#120—21no—
143C4×Q8×C11—21no—
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—21no—
147C4×D4×C11—22no—
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C11×#117—21no—
151C11×#117C2311yescharacteristic
152C2×C11×C4⋊C4—22no—
153C2×C11×C4⋊C4—21no—
154C2×C11×C4⋊C4—24no—
155C2×C11×C4⋊C4D412yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—22no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4D412yes—
160C2×C42×C11C2312yes—
161C11×#104—24no—
162C11×#104—24no—
163C11×#104—42no—
164C11×#103—22no—
165C11×#103—22no—
166C11×#101—24no—
167C11×C22⋊C8—21no—
168C11×C22⋊C8—21no—
169C11×#95—21no—
170C11×#95—24no—
171#23880C1111yesmaximal, characteristic, direct product factor, Sylow
172C24×C11—21no—
173C24×C11C2×D411yescharacteristic
174C11×#41—22no—
175C11×#41—22no—
176C11×#41—22no—
177C11×#41—22no—
178C11×#41—22no—
179C11×#41—22no—
180C11×#41—22no—
181C11×#41—44no—
182C11×#41—41no—
183C11×#41—41no—
184C11×#41—44no—
185C11×#41—44no—
186C11×#41—48no—
187C11×#41—42no—
188C11×#41—42no—
189C11×#41C2×D414yes—
190C2×Q8×C11—22no—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—21no—
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11—24no—
198C2×Q8×C11—24no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11—44no—
205C2×Q8×C11—41no—
206C2×Q8×C11—44no—
207C2×Q8×C11—44no—
208C2×Q8×C11—44no—
209C2×Q8×C11—42no—
210C2×Q8×C11—42no—
211C2×Q8×C11—42no—
212C2×Q8×C11—42no—
213C2×Q8×C11—41no—
214C2×Q8×C11—41no—
215C2×Q8×C11C2×D411yescharacteristic
216C2×Q8×C11C2×D411yescharacteristic
217C2×Q8×C11C2×D414yes—
218C2×Q8×C11C2×D411yescharacteristic
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—22no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—22no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—41no—
231C2×D4×C11—44no—
232C2×D4×C11C2×D411yescharacteristic
233C2×D4×C11C2×D411yescharacteristic
234C2×D4×C11C2×D411yescharacteristic
235C22×C4×C11—21no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—21no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—44no—
249C22×C4×C11—44no—
250C22×C4×C11—41no—
251C22×C4×C11—41no—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2411yescharacteristic
260C11×Q16—28no—
261C11×Q16—28no—
262C11×Q16—44no—
263C11×SD16—28no—
264C11×SD16—28no—
265C11×SD16—44no—
266C11×M16—24no—
267C11×M16—22no—
268C11×M16—22no—
269C11×M16—22no—
270C11×M16C2×D414yes—
271C2×C8×C11—24no—
272C2×C8×C11—22no—
273C2×C8×C11—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—48no—
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C22⋊C4—24no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C42×C11—22no—
301C42×C11—21no—
302C42×C11—22no—
303C42×C11—22no—
304C22×#137C2×C1111yescharacteristic, complemented
305#3489C2×C1111yescharacteristic
306C2×#456C2×C1112yescomplemented
307#3004C2×C1111yescharacteristic, complemented
308#2434C2×C1111yescharacteristic, complemented
309#2007C2×C1112yescomplemented
310#2005C2×C1112yescomplemented
311#1901C2×C1111yescharacteristic, complemented
312#1882C2×C1112yescomplemented
313#1871C2×C1111yescharacteristic, complemented
314#1789C2×C1111yescharacteristic, complemented
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—41no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—81no—
324C23×C11#12011yescharacteristic
325C23×C11#12011yescharacteristic
326C23×C11C22×D411yescharacteristic
327Q8×C11—21no—
328Q8×C11—24no—
329Q8×C11—21no—
330Q8×C11—21no—
331Q8×C11—24no—
332Q8×C11—22no—
333Q8×C11—42no—
334Q8×C11—44no—
335Q8×C11—44no—
336Q8×C11—44no—
337Q8×C11—41no—
338Q8×C11—42no—
339Q8×C11—41no—
340Q8×C11—42no—
341Q8×C11—42no—
342Q8×C11#12012yes—
343D4×C11—24no—
344D4×C11—21no—
345D4×C11—21no—
346D4×C11—21no—
347D4×C11—22no—
348D4×C11—42no—
349D4×C11—42no—
350D4×C11—42no—
351D4×C11—44no—
352D4×C11—42no—
353D4×C11—42no—
354D4×C11—42no—
355D4×C11—81no—
356D4×C11—82no—
357D4×C11#12012yes—
358C2×C4×C11—21no—
359C2×C4×C11—22no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—24no—
368C2×C4×C11—21no—
369C2×C4×C11—22no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—22no—
373C2×C4×C11—21no—
374C2×C4×C11—24no—
375C2×C4×C11—24no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—44no—
380C2×C4×C11—42no—
381C2×C4×C11—44no—
382C2×C4×C11—44no—
383C2×C4×C11—44no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—82no—
392C2×C4×C11#12011yescharacteristic
393C2×C4×C11#12011yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11H(5,𝔽2)12yes—
398C8×C11—24no—
399C8×C11—42no—
400C2×2−1+4C22×C1111yescharacteristic
401C22×#41C22×C1111yescharacteristic
402C23×Q8C22×C1111yescharacteristic
403C2×#137—21no—
404C2×#137—21no—
405C2×#137—28no—
406C2×#137C22×C1112yes—
407C2×#137C22×C1112yes—
408C2×#137C22×C1112yescomplemented
409C22×Q16—21no—
410C22×SD16—21no—
411C22×M16C22×C1111yescharacteristic
412D4×Q8—21no—
413#548—21no—
414#547—21no—
415#547—22no—
416#546—21no—
417#546—22no—
418#537—21no—
419#537C22×C1111yescharacteristic
420#536—21no—
421#536C22×C1111yescharacteristic
422C2×C4⋊Q8C22×C1112yescomplemented
423#525—21no—
424#525C22×C1111yescharacteristic
425C2×C22⋊Q8—21no—
426C2×C22⋊Q8C22×C1111yescharacteristic
427#520C22×C1111yescharacteristic
428#456—28no—
429#451—21no—
430#451—21no—
431#448—21no—
432#448—21no—
433C2×#104C22×C1112yes—
434C2×#104C22×C1112yes—
435C2×#104C22×C1112yescomplemented
436#419C22×C1112yescomplemented
437C2×#101C22×C1112yescomplemented
438#407C22×C1111yescharacteristic
439#395—22no—
440#391C22×C1112yescomplemented
441#385—22no—
442C4×C22⋊C4C22×C1111yescharacteristic
443#343C22×C1112yescomplemented
444#339C22×C1112yescomplemented
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—21no—
450C22×C11—22no—
451C22×C11—21no—
452C22×C11—21no—
453C22×C11—44no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—84no—
463C22×C11#45612yescomplemented
464C22×C11C2×#12011yescharacteristic
465C22×C11D4212yes—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—22no—
469C4×C11—44no—
470C4×C11—42no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11—44no—
474C4×C11—41no—
475C4×C11—42no—
476C4×C11—41no—
477C4×C11C2×#12011yescharacteristic
478C4×C11#53411yescharacteristic
479C4×C11D4212yes—
4802−1+4—24no—
4812−1+4—42no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—22no—
486C2×#41—21no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41D4×C1111yescharacteristic
490C2×#41D4×C1111yescharacteristic
491C2×#41C23×C1111yescharacteristic
492C2×#41C23×C1111yescharacteristic
493C2×#41C23×C1111yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—24no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—42no—
503C22×Q8D4×C1111yescharacteristic
504C22×Q8C23×C1112yes—
505C22×Q8C23×C1111yescharacteristic
506C22×D4—21no—
507C22×D4D4×C1111yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C23×C1111yescharacteristic
511#137—28no—
512#137—28no—
513#137—24no—
514#137—24no—
515#137—24no—
516#137—24no—
517#137—42no—
518#137D4×C1118yescomplemented
519C2×Q16—28no—
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—22no—
523C2×SD16—28no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×M16—21no—
528C2×M16—24no—
529C2×M16C23×C1112yes—
530C2×M16C23×C1112yes—
531C22×C8—21no—
532C4⋊Q8—22no—
533C4⋊Q8—21no—
534C4⋊Q8—24no—
535C4⋊Q8—42no—
536#124—22no—
537#124—21no—
538#123—22no—
539#123—22no—
540#123—22no—
541#123—21no—
542#123—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8D4×C1111yescharacteristic
555C22⋊Q8D4×C1111yescharacteristic
556#121—22no—
557#121—22no—
558#121—22no—
559#121—21no—
560#121—21no—
561#121—22no—
562#121D4×C1111yescharacteristic
563#121D4×C1111yescharacteristic
564#120—22no—
565#120—21no—
566C4×Q8—21no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—21no—
570C4×D4—22no—
571C4×D4—21no—
572C4×D4—21no—
573#117—21no—
574#117C23×C1111yescharacteristic
575C2×C4⋊C4—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4D4×C1112yes—
579C2×C4⋊C4C23×C1111yescharacteristic
580C2×C22⋊C4—22no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4D4×C1112yes—
583C2×C42C23×C1112yes—
584#104—24no—
585#104—24no—
586#104—42no—
587#103—22no—
588#103—22no—
589#101—24no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592#95—21no—
593#95—24no—
594C2×C11—22no—
595C2×C11—22no—
596C2×C11—41no—
597C2×C11—42no—
598C2×C11—81no—
599C2×C11—81no—
600C2×C11#240311yescharacteristic
601C2×C11C2×#45611yescharacteristic
602C2×C11#302211yescharacteristic
603C24—21no—
604C24C2×D4×C1111yescharacteristic
605#41—22no—
606#41—22no—
607#41—22no—
608#41—22no—
609#41—22no—
610#41—22no—
611#41—22no—
612#41—44no—
613#41—41no—
614#41—41no—
615#41—44no—
616#41—44no—
617#41—48no—
618#41—42no—
619#41—42no—
620#41C2×D4×C1114yes—
621C2×Q8—22no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—24no—
629C2×Q8—24no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—44no—
636C2×Q8—41no—
637C2×Q8—44no—
638C2×Q8—44no—
639C2×Q8—44no—
640C2×Q8—42no—
641C2×Q8—42no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—41no—
645C2×Q8—41no—
646C2×Q8C2×D4×C1111yescharacteristic
647C2×Q8C2×D4×C1111yescharacteristic
648C2×Q8C2×D4×C1114yes—
649C2×Q8C2×D4×C1111yescharacteristic
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—41no—
662C2×D4—44no—
663C2×D4C2×D4×C1111yescharacteristic
664C2×D4C2×D4×C1111yescharacteristic
665C2×D4C2×D4×C1111yescharacteristic
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4C2×D4×C1112yes—
684C22×C4C2×D4×C1111yescharacteristic
685C22×C4C2×D4×C1111yescharacteristic
686C22×C4C2×D4×C1111yescharacteristic
687C22×C4C2×D4×C1111yescharacteristic
688C22×C4C2×D4×C1111yescharacteristic
689C22×C4C2×D4×C1112yes—
690C22×C4C24×C1111yescharacteristic
691Q16—28no—
692Q16—28no—
693Q16—44no—
694SD16—28no—
695SD16—28no—
696SD16—44no—
697M16—24no—
698M16—22no—
699M16—22no—
700M16—22no—
701M16C2×D4×C1114yes—
702C2×C8—24no—
703C2×C8—22no—
704C2×C8—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—21no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—48no—
716C4⋊C4C2×D4×C1111yescharacteristic
717C4⋊C4C2×D4×C1111yescharacteristic
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—24no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—21no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C42—22no—
732C42—21no—
733C42—22no—
734C42—22no—
735C11#2388011yescharacteristic, direct product factor, Sylow
736C23—21no—
737C23—22no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—81no—
745C23C11×#12011yescharacteristic
746C23C11×#12011yescharacteristic
747C23C22×D4×C1111yescharacteristic
748Q8—21no—
749Q8—24no—
750Q8—21no—
751Q8—21no—
752Q8—24no—
753Q8—22no—
754Q8—42no—
755Q8—44no—
756Q8—44no—
757Q8—44no—
758Q8—41no—
759Q8—42no—
760Q8—41no—
761Q8—42no—
762Q8—42no—
763Q8C11×#12012yes—
764D4—24no—
765D4—21no—
766D4—21no—
767D4—21no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—44no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—81no—
777D4—82no—
778D4C11×#12012yes—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—82no—
813C2×C4C11×#12011yescharacteristic
814C2×C4C11×#12011yescharacteristic
815C2×C4C22×D4×C1111yescharacteristic
816C2×C4C22×D4×C1112yes—
817C2×C4C22×D4×C1111yescharacteristic
818C2×C4C11×H(5,𝔽2)12yes—
819C8—24no—
820C8—42no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—44no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—84no—
839C22C11×#45612yescomplemented
840C22C2×C11×#12011yescharacteristic
841C22D42×C1112yes—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—44no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—44no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4C2×C11×#12011yescharacteristic
854C4C11×#53411yescharacteristic
855C4D42×C1112yes—
856C2—22no—
857C2—22no—
858C2—41no—
859C2—42no—
860C2—81no—
861C2—81no—
862C2C11×#240311yescharacteristic
863C2C2×C11×#45611yescharacteristic
864C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3489C2
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. C22×C11×#137C2semidirect
3. C2×C11×#456C2semidirect
4. C11×#3004C2semidirect
5. C11×#2434C2semidirect
6. C11×#2007C2semidirect
7. C11×#2005C2semidirect
8. C11×#1901C2semidirect
9. C11×#1882C2semidirect
10. C11×#1871C2semidirect
11. C11×#1789C2semidirect
20. C2×C11×#137C22semidirect
34. C2×C11×C4⋊Q8C22semidirect
47. C2×C11×#104C22semidirect
48. C11×#419C22semidirect
49. C2×C11×#101C22semidirect
52. C11×#391C22semidirect
55. C11×#343C22semidirect
56. C11×#339C22semidirect
95. C11×#137D4semidirect
171. #23880C11direct (N × H)
304. C22×#137C2×C11semidirect
306. C2×#456C2×C11semidirect
307. #3004C2×C11semidirect
308. #2434C2×C11semidirect
309. #2007C2×C11semidirect
310. #2005C2×C11semidirect
311. #1901C2×C11semidirect
312. #1882C2×C11semidirect
313. #1871C2×C11semidirect
314. #1789C2×C11semidirect
408. C2×#137C22×C11semidirect
422. C2×C4⋊Q8C22×C11semidirect
435. C2×#104C22×C11semidirect
436. #419C22×C11semidirect
437. C2×#101C22×C11semidirect
440. #391C22×C11semidirect
443. #343C22×C11semidirect
444. #339C22×C11semidirect
463. C22×C11#456semidirect
518. #137D4×C11semidirect
735. C11#23880direct (N × H)
839. C22C11×#456semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C11×#34892
C2×C11×#4562
C11×#30042
C11×#24342
C11×#20072
C11×#20052
C11×#19012
C11×#18822
C11×#18712
C11×#17892
#2388011