Finite Group Databasebeta

← C11×#23920 #14601113

Subgroups — C11×#23920 #14601113

Order 2816.

2272 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic, complemented
2C22×C11×#121C211yesmaximal, characteristic, complemented
3C2×C11×#449C212yesmaximal, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#447C211yesmaximal, characteristic, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1999C212yesmaximal, complemented
8C11×#1875C212yesmaximal, complemented
9C11×#1874C211yesmaximal, characteristic, complemented
10C11×#1872C211yesmaximal, characteristic, complemented
11C11×#1779C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic, complemented
13C23×D4×C11—21no—
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C22×C11×SD16C2212yescomplemented
17C22×C11×D8C2212yescomplemented
18C11×#525—24no—
19C11×#525—24no—
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic, complemented
23C2×C11×#121—21no—
24C2×C11×#121—21no—
25C2×C11×#121—28no—
26C2×C11×#121C2212yes—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2212yes—
29C2×C11×#121C2211yescharacteristic, complemented
30C2×C11×#120—21no—
31C2×C4×D4×C11—21no—
32C2×C4×D4×C11—21no—
33C2×C11×#117C2211yescharacteristic, complemented
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4—21no—
36C11×#450—24no—
37C11×#449—28no—
38C11×#447—24no—
39C2×C11×#103C2212yescomplemented
40C2×C11×#102C2212yescomplemented
41C2×C11×#102C2212yescomplemented
42C2×C11×#102C2212yescomplemented
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2212yescomplemented
46C2×C11×C22⋊C8C2212yescomplemented
47C11×#340C2212yescomplemented
48C11×#340C2212yescomplemented
49C25×C11—21no—
50C25×C11D411yescharacteristic
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—24no—
54C2×C11×#41—42no—
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11—28no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—24no—
63C22×D4×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—42no—
67C22×D4×C11—44no—
68C22×D4×C11—44no—
69C22×D4×C11C2312yes—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11—24no—
74C23×C4×C11—22no—
75C23×C4×C11—22no—
76C23×C4×C11—42no—
77C23×C4×C11D411yescharacteristic
78C23×C4×C11D411yescharacteristic
79C23×C4×C11D411yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C2×C11×SD16—24no—
84C2×C11×SD16—24no—
85C2×C11×SD16—42no—
86C2×C11×D8—24no—
87C2×C11×D8—24no—
88C2×C11×D8—42no—
89C22×C8×C11C2312yes—
90C22×C8×C11C2312yes—
91C11×#123—28no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8D414yescomplemented
96C11×#121—28no—
97C11×#121—28no—
98C11×#121—24no—
99C11×#121—22no—
100C11×#121—24no—
101C11×#121—22no—
102C11×#121—24no—
103C11×#121—22no—
104C11×#121D418yescomplemented
105C11×#121D414yescomplemented
106C11×#120—28no—
107C4×D4×C11—28no—
108C4×D4×C11—28no—
109C11×#117—22no—
110C11×#117—22no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—28no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C42×C11—21no—
127C11×#103—24no—
128C11×#102—24no—
129C11×#102—24no—
130C11×#102—24no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8—22no—
133C11×C22⋊C8—24no—
134C11×C22⋊C8—42no—
135#23920C1111yesmaximal, characteristic, direct product factor, Sylow
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—24no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—21no—
143C24×C11—22no—
144C24×C11—41no—
145C24×C11—41no—
146C24×C11—42no—
147C24×C11—42no—
148C24×C11—42no—
149C24×C11—42no—
150C24×C11—42no—
151C24×C11—42no—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C24×C11C2×D411yescharacteristic
155C11×#41—48no—
156C11×#41—48no—
157C2×Q8×C11—21no—
158C2×Q8×C11—22no—
159C2×Q8×C11—22no—
160C2×Q8×C11C2×D412yescomplemented
161C2×D4×C11—24no—
162C2×D4×C11—24no—
163C2×D4×C11—24no—
164C2×D4×C11—28no—
165C2×D4×C11—24no—
166C2×D4×C11—28no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—21no—
172C2×D4×C11—22no—
173C2×D4×C11—22no—
174C2×D4×C11—22no—
175C2×D4×C11—48no—
176C2×D4×C11—48no—
177C2×D4×C11—42no—
178C2×D4×C11—42no—
179C2×D4×C11—432no—
180C2×D4×C11—44no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—42no—
188C2×D4×C11—44no—
189C2×D4×C11—42no—
190C2×D4×C11C2×D414yes—
191C2×D4×C11C2×D412yescomplemented
192C22×C4×C11—22no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—22no—
213C22×C4×C11—41no—
214C22×C4×C11—41no—
215C22×C4×C11—41no—
216C22×C4×C11—48no—
217C22×C4×C11—48no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D414yes—
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2411yescharacteristic
229C11×SD16—48no—
230C11×D8—48no—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2×D414yes—
244C11×C4⋊C4C2×D412yescomplemented
245C11×C4⋊C4C2×D412yescomplemented
246C11×C22⋊C4—28no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—28no—
252C11×C22⋊C4—24no—
253C42×C11—24no—
254C2×#525C2×C1111yescharacteristic, complemented
255C22×#121C2×C1111yescharacteristic, complemented
256C2×#449C2×C1112yescomplemented
257C2×#450C2×C1111yescharacteristic, complemented
258C2×#447C2×C1111yescharacteristic, complemented
259#2000C2×C1112yescomplemented
260#1999C2×C1112yescomplemented
261#1875C2×C1112yescomplemented
262#1874C2×C1111yescharacteristic, complemented
263#1872C2×C1111yescharacteristic, complemented
264#1779C2×C1111yescharacteristic, complemented
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—28no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—22no—
283C23×C11—24no—
284C23×C11—44no—
285C23×C11—44no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—48no—
290C23×C11—48no—
291C23×C11—48no—
292C23×C11—44no—
293C23×C11—41no—
294C23×C11—42no—
295C23×C11—41no—
296C23×C11—42no—
297C23×C11—41no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—42no—
305C23×C11—84no—
306C23×C11—84no—
307C23×C11—84no—
308C23×C11—84no—
309C23×C11#12012yes—
310C23×C11#12012yes—
311C23×C11#13512yes—
312C23×C11AGL(1,ℤ/8)12yes—
313C23×C11AGL(1,ℤ/8)12yes—
314C23×C11C22×D411yescharacteristic
315Q8×C11—24no—
316Q8×C11—42no—
317D4×C11—24no—
318D4×C11—24no—
319D4×C11—24no—
320D4×C11—48no—
321D4×C11—48no—
322D4×C11—416no—
323D4×C11—416no—
324D4×C11—48no—
325D4×C11—48no—
326D4×C11—42no—
327D4×C11—42no—
328D4×C11—42no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—24no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—21no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—48no—
348C2×C4×C11—48no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11#12012yes—
360C2×C4×C11#12012yes—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11H(5,𝔽2)12yes—
365C8×C11—42no—
366C8×C11—42no—
367C22×#41C22×C1111yescharacteristic, complemented
368C23×D4—21no—
369C23×D4C22×C1111yescharacteristic
370C24×C4C22×C1111yescharacteristic
371C22×SD16C22×C1112yescomplemented
372C22×D8C22×C1112yescomplemented
373#525—24no—
374#525—24no—
375C2×#123—21no—
376C2×C22⋊Q8C22×C1111yescharacteristic
377C2×C22⋊Q8C22×C1111yescharacteristic, complemented
378C2×#121—21no—
379C2×#121—21no—
380C2×#121—28no—
381C2×#121C22×C1112yes—
382C2×#121C22×C1111yescharacteristic
383C2×#121C22×C1112yes—
384C2×#121C22×C1111yescharacteristic, complemented
385C2×#120—21no—
386C2×C4×D4—21no—
387C2×C4×D4—21no—
388C2×#117C22×C1111yescharacteristic, complemented
389C22×C4⋊C4C22×C1111yescharacteristic
390C22×C22⋊C4—21no—
391#450—24no—
392#449—28no—
393#447—24no—
394C2×#103C22×C1112yescomplemented
395C2×#102C22×C1112yescomplemented
396C2×#102C22×C1112yescomplemented
397C2×#102C22×C1112yescomplemented
398C2×C22⋊C8C22×C1111yescharacteristic
399C2×C22⋊C8C22×C1111yescharacteristic
400C2×C22⋊C8C22×C1112yescomplemented
401C2×C22⋊C8C22×C1112yescomplemented
402#340C22×C1112yescomplemented
403#340C22×C1112yescomplemented
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—416no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—42no—
426C22×C11—44no—
427C22×C11—42no—
428C22×C11—44no—
429C22×C11—44no—
430C22×C11—42no—
431C22×C11—816no—
432C22×C11—81no—
433C22×C11—82no—
434C22×C11—81no—
435C22×C11—82no—
436C22×C11—82no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11—82no—
440C22×C11#44914yescomplemented
441C22×C11C2×#12011yescharacteristic
442C22×C11C2×#12011yescharacteristic
443C22×C11#53411yescharacteristic
444C22×C11C2×#13511yescharacteristic
445C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
447C22×C11#57511yescharacteristic
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—41no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—44no—
454C4×C11—42no—
455C4×C11D4212yes—
456C4×C11D4212yes—
457C25—21no—
458C25D4×C1111yescharacteristic
459C2×#41—22no—
460C2×#41—22no—
461C2×#41—24no—
462C2×#41—42no—
463C22×Q8C23×C1111yescharacteristic
464C22×D4—28no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—24no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—42no—
475C22×D4—44no—
476C22×D4—44no—
477C22×D4C23×C1112yes—
478C22×D4C23×C1111yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—24no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—42no—
485C23×C4D4×C1111yescharacteristic
486C23×C4D4×C1111yescharacteristic
487C23×C4D4×C1111yescharacteristic
488C23×C4C23×C1111yescharacteristic
489C23×C4C23×C1111yescharacteristic
490C23×C4C23×C1111yescharacteristic
491C2×SD16—24no—
492C2×SD16—24no—
493C2×SD16—42no—
494C2×D8—24no—
495C2×D8—24no—
496C2×D8—42no—
497C22×C8C23×C1112yes—
498C22×C8C23×C1112yes—
499#123—28no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8D4×C1114yescomplemented
504#121—28no—
505#121—28no—
506#121—24no—
507#121—22no—
508#121—24no—
509#121—22no—
510#121—24no—
511#121—22no—
512#121D4×C1118yescomplemented
513#121D4×C1114yescomplemented
514#120—28no—
515C4×D4—28no—
516C4×D4—28no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4C23×C1112yes—
524C2×C4⋊C4C23×C1111yescharacteristic
525C2×C4⋊C4C23×C1111yescharacteristic
526C2×C22⋊C4—28no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C42—21no—
535#103—24no—
536#102—24no—
537#102—24no—
538#102—24no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—24no—
542C22⋊C8—42no—
543C2×C11—24no—
544C2×C11—42no—
545C2×C11—42no—
546C2×C11—82no—
547C2×C11—84no—
548C2×C11#240311yescharacteristic
549C2×C11C2×#44911yescharacteristic
550C2×C11#300211yescharacteristic
551C2×C11#300311yescharacteristic
552C2×C11#300611yescharacteristic
553C2×C11#318811yescharacteristic
554C2×C11#319411yescharacteristic
555C24—22no—
556C24—22no—
557C24—22no—
558C24—24no—
559C24—22no—
560C24—22no—
561C24—21no—
562C24—22no—
563C24—41no—
564C24—41no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24C2×D4×C1111yescharacteristic
572C24C2×D4×C1111yescharacteristic
573C24C2×D4×C1111yescharacteristic
574#41—48no—
575#41—48no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8C2×D4×C1112yescomplemented
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—28no—
584C2×D4—24no—
585C2×D4—28no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—48no—
595C2×D4—48no—
596C2×D4—42no—
597C2×D4—432no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—44no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4C2×D4×C1114yes—
610C2×D4C2×D4×C1112yescomplemented
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4C2×D4×C1111yescharacteristic
642C22×C4C2×D4×C1111yescharacteristic
643C22×C4C2×D4×C1111yescharacteristic
644C22×C4C2×D4×C1114yes—
645C22×C4C2×D4×C1112yes—
646C22×C4C2×D4×C1112yes—
647C22×C4C24×C1111yescharacteristic
648SD16—48no—
649D8—48no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4C2×D4×C1114yes—
663C4⋊C4C2×D4×C1112yescomplemented
664C4⋊C4C2×D4×C1112yescomplemented
665C22⋊C4—28no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—28no—
671C22⋊C4—24no—
672C42—24no—
673C11#2392011yescharacteristic, direct product factor, Sylow
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—28no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—24no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—48no—
699C23—48no—
700C23—48no—
701C23—44no—
702C23—41no—
703C23—42no—
704C23—41no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—84no—
715C23—84no—
716C23—84no—
717C23—84no—
718C23C11×#12012yes—
719C23C11×#12012yes—
720C23C11×#13512yes—
721C23C11×AGL(1,ℤ/8)12yes—
722C23C11×AGL(1,ℤ/8)12yes—
723C23C22×D4×C1111yescharacteristic
724Q8—24no—
725Q8—42no—
726D4—24no—
727D4—24no—
728D4—24no—
729D4—48no—
730D4—48no—
731D4—416no—
732D4—416no—
733D4—48no—
734D4—48no—
735D4—42no—
736D4—42no—
737D4—42no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—21no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4C11×#12012yes—
769C2×C4C11×#12012yes—
770C2×C4C22×D4×C1112yes—
771C2×C4C22×D4×C1111yescharacteristic
772C2×C4C22×D4×C1111yescharacteristic
773C2×C4C11×H(5,𝔽2)12yes—
774C8—42no—
775C8—42no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—416no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—816no—
804C22—82no—
805C22—81no—
806C22—82no—
807C22—81no—
808C22—82no—
809C22—81no—
810C22—81no—
811C22—82no—
812C22C11×#44914yescomplemented
813C22C2×C11×#12011yescharacteristic
814C22C2×C11×#12011yescharacteristic
815C22C11×#53411yescharacteristic
816C22C2×C11×#13511yescharacteristic
817C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
818C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
819C22C11×#57511yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4D42×C1112yes—
828C4D42×C1112yes—
829C2—24no—
830C2—42no—
831C2—42no—
832C2—84no—
833C2—82no—
834C2C11×#240311yescharacteristic
835C2C2×C11×#44911yescharacteristic
836C2C11×#300211yescharacteristic
837C2C11×#300311yescharacteristic
838C2C11×#300611yescharacteristic
839C2C11×#318811yescharacteristic
840C2C11×#319411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#525C2semidirect
2. C22×C11×#121C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#447C2semidirect
6. C11×#2000C2semidirect
7. C11×#1999C2semidirect
8. C11×#1875C2semidirect
9. C11×#1874C2semidirect
10. C11×#1872C2semidirect
11. C11×#1779C2semidirect
12. C22×C11×#41C22semidirect
16. C22×C11×SD16C22semidirect
17. C22×C11×D8C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
29. C2×C11×#121C22semidirect
33. C2×C11×#117C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#102C22semidirect
41. C2×C11×#102C22semidirect
42. C2×C11×#102C22semidirect
45. C2×C11×C22⋊C8C22semidirect
46. C2×C11×C22⋊C8C22semidirect
47. C11×#340C22semidirect
48. C11×#340C22semidirect
95. C11×C22⋊Q8D4semidirect
104. C11×#121D4semidirect
105. C11×#121D4semidirect
135. #23920C11direct (N × H)
160. C2×Q8×C11C2×D4semidirect
191. C2×D4×C11C2×D4semidirect
244. C11×C4⋊C4C2×D4semidirect
245. C11×C4⋊C4C2×D4semidirect
254. C2×#525C2×C11semidirect
255. C22×#121C2×C11semidirect
256. C2×#449C2×C11semidirect
257. C2×#450C2×C11semidirect
258. C2×#447C2×C11semidirect
259. #2000C2×C11semidirect
260. #1999C2×C11semidirect
261. #1875C2×C11semidirect
262. #1874C2×C11semidirect
263. #1872C2×C11semidirect
264. #1779C2×C11semidirect
367. C22×#41C22×C11semidirect
371. C22×SD16C22×C11semidirect
372. C22×D8C22×C11semidirect
377. C2×C22⋊Q8C22×C11semidirect
384. C2×#121C22×C11semidirect
388. C2×#117C22×C11semidirect
394. C2×#103C22×C11semidirect
395. C2×#102C22×C11semidirect
396. C2×#102C22×C11semidirect
397. C2×#102C22×C11semidirect
400. C2×C22⋊C8C22×C11semidirect
401. C2×C22⋊C8C22×C11semidirect
402. #340C22×C11semidirect
403. #340C22×C11semidirect
440. C22×C11#449semidirect
503. C22⋊Q8D4×C11semidirect
512. #121D4×C11semidirect
513. #121D4×C11semidirect
579. C2×Q8C2×D4×C11semidirect
610. C2×D4C2×D4×C11semidirect
663. C4⋊C4C2×D4×C11semidirect
664. C4⋊C4C2×D4×C11semidirect
673. C11#23920direct (N × H)
812. C22C11×#449semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C22×C11×#1212
C2×C11×#4492
C2×C11×#4502
C2×C11×#4472
C11×#20002
C11×#19992
C11×#18752
C11×#18742
C11×#18722
C11×#17792
#2392011