Finite Group Databasebeta

← C11×#24379 #14601572

Subgroups — C11×#24379 #14601572

Order 2816.

1924 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C2×C11×#465C212yesmaximal, complemented
3C2×C11×#450C211yesmaximal, characteristic, complemented
4C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
5C11×#2848C211yesmaximal, characteristic, complemented
6C11×#2034C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1893C212yesmaximal, complemented
9C11×#1872C211yesmaximal, characteristic, complemented
10C11×#1853C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11—21no—
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×SD16C2212yescomplemented
16C23×C8×C11C2212yescomplemented
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic, complemented
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C2×C11×#121—21no—
21C2×C11×#121—21no—
22C2×C11×#121—28no—
23C2×C11×#121C2212yes—
24C2×C11×#121C2212yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4—21no—
27C11×#465—28no—
28C11×#450—24no—
29C2×C11×#106C2212yescomplemented
30C2×C11×#103C2212yescomplemented
31C2×C11×#102C2212yescomplemented
32C2×C11×#102C2212yescomplemented
33C2×C11×#102C2212yescomplemented
34C2×C11×C22⋊C8—24no—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yescomplemented
38C11×#385—21no—
39C11×#385—21no—
40C11×#385—21no—
41C11×#380C2211yescharacteristic
42C11×#380C2211yescharacteristic, complemented
43C11×#380C2211yescharacteristic, complemented
44C11×#379—21no—
45C11×#340C2212yescomplemented
46C11×#340C2212yescomplemented
47C25×C11—21no—
48C25×C11D411yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—28no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—24no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—42no—
58C22×D4×C11—44no—
59C22×D4×C11—44no—
60C22×D4×C11C2312yes—
61C23×C4×C11—21no—
62C23×C4×C11—24no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—42no—
66C23×C4×C11D411yescharacteristic
67C23×C4×C11D411yescharacteristic
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C2×C11×SD16—24no—
73C2×C11×SD16—24no—
74C2×C11×SD16—42no—
75C22×C8×C11—24no—
76C22×C8×C11—24no—
77C22×C8×C11—42no—
78C22×C8×C11C2312yes—
79C22×C8×C11C2312yes—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—42no—
84C11×#121—28no—
85C11×#121—28no—
86C11×#121—24no—
87C11×#121—24no—
88C11×#121—24no—
89C11×#121D418yes—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C22⋊C4—28no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
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—
108C11×#106—24no—
109C11×#103—24no—
110C11×#102—24no—
111C11×#102—24no—
112C11×#102—42no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—24no—
115C11×C22⋊C8D414yescomplemented
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119#24379C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—24no—
125C24×C11—22no—
126C24×C11—41no—
127C24×C11—41no—
128C24×C11—42no—
129C24×C11—42no—
130C24×C11—42no—
131C24×C11—42no—
132C24×C11—42no—
133C24×C11—42no—
134C24×C11SD1614yescomplemented
135C24×C11C2×D411yescharacteristic
136C24×C11C2×D411yescharacteristic
137C24×C11C2×D411yescharacteristic
138C2×Q8×C11—22no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—48no—
151C2×D4×C11—48no—
152C2×D4×C11—42no—
153C2×D4×C11—432no—
154C2×D4×C11—44no—
155C2×D4×C11—44no—
156C2×D4×C11—44no—
157C2×D4×C11—44no—
158C2×D4×C11—42no—
159C2×D4×C11C2×D414yes—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11—41no—
184C22×C4×C11—48no—
185C22×C4×C11—48no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11#4112yes—
194C22×C4×C11C2411yescharacteristic
195C11×SD16—48no—
196C2×C8×C11—22no—
197C2×C8×C11—22no—
198C2×C8×C11—22no—
199C2×C8×C11—22no—
200C2×C8×C11—22no—
201C2×C8×C11—48no—
202C2×C8×C11C2×D414yescomplemented
203C11×C4⋊C4—24no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4C2×D414yes—
213C11×C22⋊C4—28no—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C22×#121C2×C1111yescharacteristic
222C2×#465C2×C1112yescomplemented
223C2×#450C2×C1111yescharacteristic, complemented
224C22×C22⋊C8C2×C1111yescharacteristic, complemented
225#2848C2×C1111yescharacteristic, complemented
226#2034C2×C1112yescomplemented
227#2000C2×C1112yescomplemented
228#1893C2×C1112yescomplemented
229#1872C2×C1111yescharacteristic, complemented
230#1853C2×C1111yescharacteristic, complemented
231#1786C2×C1111yescharacteristic, complemented
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—28no—
247C23×C11—28no—
248C23×C11—24no—
249C23×C11—44no—
250C23×C11—44no—
251C23×C11—44no—
252C23×C11—44no—
253C23×C11—44no—
254C23×C11—48no—
255C23×C11—48no—
256C23×C11—48no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—84no—
264C23×C11—84no—
265C23×C11—84no—
266C23×C11—84no—
267C23×C11#12012yes—
268C23×C11#12112yes—
269C23×C11C2×SD1612yes—
270C23×C11C2×SD1612yes—
271C23×C11C2×SD1612yes—
272C23×C11#13512yes—
273C23×C11AGL(1,ℤ/8)12yes—
274C23×C11C22×D411yescharacteristic
275Q8×C11—42no—
276Q8×C11—42no—
277D4×C11—24no—
278D4×C11—24no—
279D4×C11—48no—
280D4×C11—416no—
281D4×C11—416no—
282D4×C11—42no—
283D4×C11—42no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—21no—
293C2×C4×C11—24no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11—48no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
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#12012yes—
317C2×C4×C11#12112yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D412yes—
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)12yes—
322C8×C11—24no—
323C8×C11—42no—
324C23×D4—21no—
325C23×D4C22×C1111yescharacteristic
326C24×C4C22×C1111yescharacteristic
327C22×SD16C22×C1112yescomplemented
328C23×C8C22×C1112yescomplemented
329C2×C22⋊Q8C22×C1111yescharacteristic
330C2×C22⋊Q8C22×C1111yescharacteristic, complemented
331C2×C22⋊Q8C22×C1111yescharacteristic, complemented
332C2×#121—21no—
333C2×#121—21no—
334C2×#121—28no—
335C2×#121C22×C1112yes—
336C2×#121C22×C1112yes—
337C22×C4⋊C4C22×C1111yescharacteristic
338C22×C22⋊C4—21no—
339#465—28no—
340#450—24no—
341C2×#106C22×C1112yescomplemented
342C2×#103C22×C1112yescomplemented
343C2×#102C22×C1112yescomplemented
344C2×#102C22×C1112yescomplemented
345C2×#102C22×C1112yescomplemented
346C2×C22⋊C8—24no—
347C2×C22⋊C8C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1112yescomplemented
350#385—21no—
351#385—21no—
352#385—21no—
353#380C22×C1111yescharacteristic
354#380C22×C1111yescharacteristic, complemented
355#380C22×C1111yescharacteristic, complemented
356#379—21no—
357#340C22×C1112yescomplemented
358#340C22×C1112yescomplemented
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—416no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—44no—
380C22×C11—44no—
381C22×C11—44no—
382C22×C11—816no—
383C22×C11—82no—
384C22×C11—82no—
385C22×C11—82no—
386C22×C11—82no—
387C22×C11#45014yescomplemented
388C22×C11#46514yescomplemented
389C22×C11C2×#12011yescharacteristic
390C22×C11C2×#12111yescharacteristic
391C22×C11#53411yescharacteristic
392C22×C11C22×SD1611yescharacteristic
393C22×C11C2×#13511yescharacteristic
394C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C11#57511yescharacteristic
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—41no—
399C4×C11—44no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11D4212yes—
405C4×C11#54612yes—
406C25—21no—
407C25D4×C1111yescharacteristic
408C22×Q8C23×C1111yescharacteristic
409C22×D4—28no—
410C22×D4—22no—
411C22×D4—22no—
412C22×D4—24no—
413C22×D4—21no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—42no—
417C22×D4—44no—
418C22×D4—44no—
419C22×D4C23×C1112yes—
420C23×C4—21no—
421C23×C4—24no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—42no—
425C23×C4D4×C1111yescharacteristic
426C23×C4D4×C1111yescharacteristic
427C23×C4D4×C1111yescharacteristic
428C23×C4C23×C1111yescharacteristic
429C23×C4C23×C1111yescharacteristic
430C23×C4C23×C1111yescharacteristic
431C2×SD16—24no—
432C2×SD16—24no—
433C2×SD16—42no—
434C22×C8—24no—
435C22×C8—24no—
436C22×C8—42no—
437C22×C8C23×C1112yes—
438C22×C8C23×C1112yes—
439C22⋊Q8—22no—
440C22⋊Q8—24no—
441C22⋊Q8—22no—
442C22⋊Q8—42no—
443#121—28no—
444#121—28no—
445#121—24no—
446#121—24no—
447#121—24no—
448#121D4×C1118yes—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1112yes—
458C2×C22⋊C4—28no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467#106—24no—
468#103—24no—
469#102—24no—
470#102—24no—
471#102—42no—
472C22⋊C8—22no—
473C22⋊C8—24no—
474C22⋊C8D4×C1114yescomplemented
475#95—21no—
476#95—21no—
477#95—21no—
478C2×C11—24no—
479C2×C11—24no—
480C2×C11—42no—
481C2×C11—84no—
482C2×C11#241011yescharacteristic
483C2×C11C2×#45011yescharacteristic
484C2×C11#300211yescharacteristic
485C2×C11C2×#46511yescharacteristic
486C2×C11#305511yescharacteristic
487C2×C11#318711yescharacteristic
488C2×C11#318811yescharacteristic
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—24no—
494C24—22no—
495C24—41no—
496C24—41no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24C11×SD1614yescomplemented
504C24C2×D4×C1111yescharacteristic
505C24C2×D4×C1111yescharacteristic
506C24C2×D4×C1111yescharacteristic
507C2×Q8—22no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—22no—
511C2×D4—24no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—42no—
522C2×D4—432no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4C2×D4×C1114yes—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4C2×D4×C1111yescharacteristic
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1114yes—
560C22×C4C2×D4×C1111yescharacteristic
561C22×C4C2×D4×C1112yes—
562C22×C4C11×#4112yes—
563C22×C4C24×C1111yescharacteristic
564SD16—48no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—48no—
571C2×C8C2×D4×C1114yescomplemented
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—22no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4C2×D4×C1114yes—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C11#2437911yescharacteristic, direct product factor, Sylow
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—28no—
606C23—28no—
607C23—24no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—48no—
614C23—48no—
615C23—48no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—84no—
623C23—84no—
624C23—84no—
625C23—84no—
626C23C11×#12012yes—
627C23C11×#12112yes—
628C23C2×C11×SD1612yes—
629C23C2×C11×SD1612yes—
630C23C2×C11×SD1612yes—
631C23C11×#13512yes—
632C23C11×AGL(1,ℤ/8)12yes—
633C23C22×D4×C1111yescharacteristic
634Q8—42no—
635Q8—42no—
636D4—24no—
637D4—24no—
638D4—48no—
639D4—416no—
640D4—416no—
641D4—42no—
642D4—42no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—21no—
652C2×C4—24no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4C11×#12012yes—
676C2×C4C11×#12112yes—
677C2×C4C22×D4×C1111yescharacteristic
678C2×C4C22×D4×C1112yes—
679C2×C4C2×C11×#4111yescharacteristic
680C2×C4C11×H(5,𝔽2)12yes—
681C8—24no—
682C8—42no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—416no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—816no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22C11×#45014yescomplemented
712C22C11×#46514yescomplemented
713C22C2×C11×#12011yescharacteristic
714C22C2×C11×#12111yescharacteristic
715C22C11×#53411yescharacteristic
716C22C22×C11×SD1611yescharacteristic
717C22C2×C11×#13511yescharacteristic
718C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
719C22C11×#57511yescharacteristic
720C4—22no—
721C4—22no—
722C4—41no—
723C4—44no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4D42×C1112yes—
729C4C11×#54612yes—
730C2—24no—
731C2—24no—
732C2—42no—
733C2—84no—
734C2C11×#241011yescharacteristic
735C2C2×C11×#45011yescharacteristic
736C2C11×#300211yescharacteristic
737C2C2×C11×#46511yescharacteristic
738C2C11×#305511yescharacteristic
739C2C11×#318711yescharacteristic
740C2C11×#318811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#121C2
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
2. C2×C11×#465C2semidirect
3. C2×C11×#450C2semidirect
4. C22×C11×C22⋊C8C2semidirect
5. C11×#2848C2semidirect
6. C11×#2034C2semidirect
7. C11×#2000C2semidirect
8. C11×#1893C2semidirect
9. C11×#1872C2semidirect
10. C11×#1853C2semidirect
11. C11×#1786C2semidirect
15. C22×C11×SD16C22semidirect
16. C23×C8×C11C22semidirect
18. C2×C11×C22⋊Q8C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
29. C2×C11×#106C22semidirect
30. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
33. C2×C11×#102C22semidirect
37. C2×C11×C22⋊C8C22semidirect
42. C11×#380C22semidirect
43. C11×#380C22semidirect
45. C11×#340C22semidirect
46. C11×#340C22semidirect
115. C11×C22⋊C8D4semidirect
119. #24379C11direct (N × H)
134. C24×C11SD16semidirect
202. C2×C8×C11C2×D4semidirect
222. C2×#465C2×C11semidirect
223. C2×#450C2×C11semidirect
224. C22×C22⋊C8C2×C11semidirect
225. #2848C2×C11semidirect
226. #2034C2×C11semidirect
227. #2000C2×C11semidirect
228. #1893C2×C11semidirect
229. #1872C2×C11semidirect
230. #1853C2×C11semidirect
231. #1786C2×C11semidirect
327. C22×SD16C22×C11semidirect
328. C23×C8C22×C11semidirect
330. C2×C22⋊Q8C22×C11semidirect
331. C2×C22⋊Q8C22×C11semidirect
341. C2×#106C22×C11semidirect
342. C2×#103C22×C11semidirect
343. C2×#102C22×C11semidirect
344. C2×#102C22×C11semidirect
345. C2×#102C22×C11semidirect
349. C2×C22⋊C8C22×C11semidirect
354. #380C22×C11semidirect
355. #380C22×C11semidirect
357. #340C22×C11semidirect
358. #340C22×C11semidirect
387. C22×C11#450semidirect
388. C22×C11#465semidirect
474. C22⋊C8D4×C11semidirect
503. C24C11×SD16semidirect
571. C2×C8C2×D4×C11semidirect
590. C11#24379direct (N × H)
711. C22C11×#450semidirect
712. C22C11×#465semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C2×C11×#4652
C2×C11×#4502
C22×C11×C22⋊C82
C11×#28482
C11×#20342
C11×#20002
C11×#18932
C11×#18722
C11×#18532
C11×#17862
#2437911