Finite Group Databasebeta

← C11×#24381 #14601574

Subgroups — C11×#24381 #14601574

Order 2816.

1658 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C11×#465C212yesmaximal, complemented
3C2×C11×#448C211yesmaximal, characteristic, complemented
4C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
5C11×#2847C211yesmaximal, characteristic
6C11×#2035C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1892C212yesmaximal, complemented
9C11×#1874C211yesmaximal, characteristic, complemented
10C11×#1853C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C22×C11×SD16C2212yescomplemented
15C23×C8×C11C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#120—21no—
25C22×C11×C4⋊C4—21no—
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4—21no—
28C11×#465—28no—
29C11×#448—24no—
30C2×C11×#106C2212yescomplemented
31C2×C11×#103C2212yescomplemented
32C2×C11×#103C2212yescomplemented
33C2×C11×#103C2212yescomplemented
34C2×C11×#102C2212yescomplemented
35C2×C11×C22⋊C8—24no—
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2211yescharacteristic
39C11×#386—21no—
40C11×#386—21no—
41C11×#386—21no—
42C11×#380C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#340C2212yescomplemented
46C11×#340C2212yescomplemented
47C25×C11D411yescharacteristic
48C22×Q8×C11—24no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2312yes—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11—24no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—42no—
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C2×C11×SD16—24no—
71C2×C11×SD16—24no—
72C2×C11×SD16—42no—
73C22×C8×C11—24no—
74C22×C8×C11—24no—
75C22×C8×C11—42no—
76C22×C8×C11C2312yes—
77C22×C8×C11C2312yes—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—28no—
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8D418yescomplemented
84C11×#121—22no—
85C11×#121—24no—
86C11×#121—22no—
87C11×#121—42no—
88C11×#120—44no—
89C2×C11×C4⋊C4—28no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C22⋊C4—28no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—21no—
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—
107C11×#106—24no—
108C11×#103—24no—
109C11×#103—24no—
110C11×#103—42no—
111C11×#102—24no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—24no—
114C11×C22⋊C8D414yescomplemented
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118#24381C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—21no—
124C24×C11—41no—
125C24×C11—41no—
126C24×C11SD1614yescomplemented
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C24×C11C2×D411yescharacteristic
130C2×Q8×C11—24no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—48no—
137C2×Q8×C11—48no—
138C2×Q8×C11—42no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D414yes—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—42no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11—48no—
180C22×C4×C11—48no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11C2411yescharacteristic
192C11×SD16—48no—
193C2×C8×C11—22no—
194C2×C8×C11—22no—
195C2×C8×C11—22no—
196C2×C8×C11—22no—
197C2×C8×C11—22no—
198C2×C8×C11—48no—
199C2×C8×C11C2×D414yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—28no—
202C11×C4⋊C4—28no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4C2×D414yes—
209C11×C22⋊C4—28no—
210C11×C22⋊C4—28no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C22×C22⋊Q8C2×C1111yescharacteristic, complemented
218C2×#465C2×C1112yescomplemented
219C2×#448C2×C1111yescharacteristic, complemented
220C22×C22⋊C8C2×C1111yescharacteristic, complemented
221#2847C2×C1111yescharacteristic
222#2035C2×C1112yescomplemented
223#2000C2×C1112yescomplemented
224#1892C2×C1112yescomplemented
225#1874C2×C1111yescharacteristic, complemented
226#1853C2×C1111yescharacteristic, complemented
227#1787C2×C1111yescharacteristic, complemented
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
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—28no—
243C23×C11—28no—
244C23×C11—44no—
245C23×C11—44no—
246C23×C11—44no—
247C23×C11—44no—
248C23×C11—44no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11#12012yes—
257C23×C11#12112yes—
258C23×C11C2×SD1612yes—
259C23×C11C2×SD1612yes—
260C23×C11C2×SD1612yes—
261C23×C11#13512yes—
262C23×C11#13712yes—
263C23×C11C22×D411yescharacteristic
264Q8×C11—24no—
265Q8×C11—24no—
266Q8×C11—48no—
267Q8×C11—42no—
268Q8×C11—42no—
269D4×C11—42no—
270D4×C11—42no—
271D4×C11—84no—
272D4×C11—84no—
273D4×C11—84no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—44no—
288C2×C4×C11—44no—
289C2×C4×C11—44no—
290C2×C4×C11—48no—
291C2×C4×C11—48no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
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#12012yes—
308C2×C4×C11#12112yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D412yes—
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11H(5,𝔽2)12yes—
313C8×C11—24no—
314C8×C11—42no—
315C23×Q8C22×C1111yescharacteristic
316C24×C4C22×C1111yescharacteristic
317C22×SD16C22×C1112yescomplemented
318C23×C8C22×C1112yes—
319C2×C22⋊Q8—21no—
320C2×C22⋊Q8—21no—
321C2×C22⋊Q8—28no—
322C2×C22⋊Q8C22×C1112yes—
323C2×C22⋊Q8C22×C1112yes—
324C2×#121C22×C1111yescharacteristic
325C2×#121C22×C1111yescharacteristic
326C2×#121C22×C1111yescharacteristic
327C2×#120—21no—
328C22×C4⋊C4—21no—
329C22×C4⋊C4C22×C1111yescharacteristic
330C22×C22⋊C4—21no—
331#465—28no—
332#448—24no—
333C2×#106C22×C1112yescomplemented
334C2×#103C22×C1112yescomplemented
335C2×#103C22×C1112yescomplemented
336C2×#103C22×C1112yescomplemented
337C2×#102C22×C1112yescomplemented
338C2×C22⋊C8—24no—
339C2×C22⋊C8C22×C1111yescharacteristic
340C2×C22⋊C8C22×C1112yes—
341C2×C22⋊C8C22×C1111yescharacteristic
342#386—21no—
343#386—21no—
344#386—21no—
345#380C22×C1111yescharacteristic
346#380C22×C1111yescharacteristic
347#380C22×C1111yescharacteristic
348#340C22×C1112yescomplemented
349#340C22×C1112yescomplemented
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—416no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11#44814yescomplemented
378C22×C11#46514yescomplemented
379C22×C11C2×#12011yescharacteristic
380C22×C11C2×#12111yescharacteristic
381C22×C11#53411yescharacteristic
382C22×C11C22×SD1611yescharacteristic
383C22×C11C2×#13511yescharacteristic
384C22×C11C2×#13711yescharacteristic
385C22×C11#57511yescharacteristic
386C4×C11—22no—
387C4×C11—22no—
388C4×C11—41no—
389C4×C11—44no—
390C4×C11—44no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11D4212yes—
395C4×C11#54612yes—
396C25D4×C1111yescharacteristic
397C22×Q8—24no—
398C22×Q8—21no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—42no—
402C22×Q8C23×C1112yes—
403C22×D4—21no—
404C22×D4—21no—
405C22×D4—21no—
406C22×D4C23×C1111yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—42no—
413C23×C4D4×C1111yescharacteristic
414C23×C4D4×C1111yescharacteristic
415C23×C4D4×C1111yescharacteristic
416C23×C4C23×C1111yescharacteristic
417C23×C4C23×C1111yescharacteristic
418C23×C4C23×C1111yescharacteristic
419C2×SD16—24no—
420C2×SD16—24no—
421C2×SD16—42no—
422C22×C8—24no—
423C22×C8—24no—
424C22×C8—42no—
425C22×C8C23×C1112yes—
426C22×C8C23×C1112yes—
427C22⋊Q8—28no—
428C22⋊Q8—28no—
429C22⋊Q8—24no—
430C22⋊Q8—24no—
431C22⋊Q8—24no—
432C22⋊Q8D4×C1118yescomplemented
433#121—22no—
434#121—24no—
435#121—22no—
436#121—42no—
437#120—44no—
438C2×C4⋊C4—28no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C4⋊C4C23×C1111yescharacteristic
446C2×C4⋊C4C23×C1112yes—
447C2×C22⋊C4—28no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456#106—24no—
457#103—24no—
458#103—24no—
459#103—42no—
460#102—24no—
461C22⋊C8—22no—
462C22⋊C8—24no—
463C22⋊C8D4×C1114yescomplemented
464#95—21no—
465#95—21no—
466#95—21no—
467C2×C11—24no—
468C2×C11—24no—
469C2×C11—42no—
470C2×C11—161no—
471C2×C11#241011yescharacteristic
472C2×C11C2×#44811yescharacteristic
473C2×C11#300211yescharacteristic
474C2×C11C2×#46511yescharacteristic
475C2×C11#305611yescharacteristic
476C2×C11#318711yescharacteristic
477C2×C11#319011yescharacteristic
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—21no—
483C24—41no—
484C24—41no—
485C24C11×SD1614yescomplemented
486C24C2×D4×C1111yescharacteristic
487C24C2×D4×C1111yescharacteristic
488C24C2×D4×C1111yescharacteristic
489C2×Q8—24no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—48no—
496C2×Q8—48no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8C2×D4×C1114yes—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1114yes—
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1112yes—
549C22×C4C11×#4112yes—
550C22×C4C24×C1111yescharacteristic
551SD16—48no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—48no—
558C2×C8C2×D4×C1114yes—
559C4⋊C4—24no—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—22no—
563C4⋊C4—21no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—22no—
567C4⋊C4C2×D4×C1114yes—
568C22⋊C4—28no—
569C22⋊C4—28no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C11#2438111yescharacteristic, direct product factor, Sylow
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—28no—
592C23—28no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C11×#12012yes—
606C23C11×#12112yes—
607C23C2×C11×SD1612yes—
608C23C2×C11×SD1612yes—
609C23C2×C11×SD1612yes—
610C23C11×#13512yes—
611C23C11×#13712yes—
612C23C22×D4×C1111yescharacteristic
613Q8—24no—
614Q8—24no—
615Q8—48no—
616Q8—42no—
617Q8—42no—
618D4—42no—
619D4—42no—
620D4—84no—
621D4—84no—
622D4—84no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—48no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
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×C4C11×#12012yes—
657C2×C4C11×#12112yes—
658C2×C4C22×D4×C1111yescharacteristic
659C2×C4C22×D4×C1112yes—
660C2×C4C2×C11×#4111yescharacteristic
661C2×C4C11×H(5,𝔽2)12yes—
662C8—24no—
663C8—42no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—416no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C11×#44814yescomplemented
692C22C11×#46514yescomplemented
693C22C2×C11×#12011yescharacteristic
694C22C2×C11×#12111yescharacteristic
695C22C11×#53411yescharacteristic
696C22C22×C11×SD1611yescharacteristic
697C22C2×C11×#13511yescharacteristic
698C22C2×C11×#13711yescharacteristic
699C22C11×#57511yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—44no—
704C4—44no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4D42×C1112yes—
709C4C11×#54612yes—
710C2—24no—
711C2—24no—
712C2—42no—
713C2—161no—
714C2C11×#241011yescharacteristic
715C2C2×C11×#44811yescharacteristic
716C2C11×#300211yescharacteristic
717C2C2×C11×#46511yescharacteristic
718C2C11×#305611yescharacteristic
719C2C11×#318711yescharacteristic
720C2C11×#319011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2847C2
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. C22×C11×C22⋊Q8C2semidirect
2. C2×C11×#465C2semidirect
3. C2×C11×#448C2semidirect
4. C22×C11×C22⋊C8C2semidirect
6. C11×#2035C2semidirect
7. C11×#2000C2semidirect
8. C11×#1892C2semidirect
9. C11×#1874C2semidirect
10. C11×#1853C2semidirect
11. C11×#1787C2semidirect
14. C22×C11×SD16C22semidirect
30. C2×C11×#106C22semidirect
31. C2×C11×#103C22semidirect
32. C2×C11×#103C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#102C22semidirect
45. C11×#340C22semidirect
46. C11×#340C22semidirect
83. C11×C22⋊Q8D4semidirect
114. C11×C22⋊C8D4semidirect
118. #24381C11direct (N × H)
126. C24×C11SD16semidirect
217. C22×C22⋊Q8C2×C11semidirect
218. C2×#465C2×C11semidirect
219. C2×#448C2×C11semidirect
220. C22×C22⋊C8C2×C11semidirect
222. #2035C2×C11semidirect
223. #2000C2×C11semidirect
224. #1892C2×C11semidirect
225. #1874C2×C11semidirect
226. #1853C2×C11semidirect
227. #1787C2×C11semidirect
317. C22×SD16C22×C11semidirect
333. C2×#106C22×C11semidirect
334. C2×#103C22×C11semidirect
335. C2×#103C22×C11semidirect
336. C2×#103C22×C11semidirect
337. C2×#102C22×C11semidirect
348. #340C22×C11semidirect
349. #340C22×C11semidirect
377. C22×C11#448semidirect
378. C22×C11#465semidirect
432. C22⋊Q8D4×C11semidirect
463. C22⋊C8D4×C11semidirect
485. C24C11×SD16semidirect
576. C11#24381direct (N × H)
691. C22C11×#448semidirect
692. C22C11×#465semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C2×C11×#4652
C2×C11×#4482
C22×C11×C22⋊C82
C11×#28472
C11×#20352
C11×#20002
C11×#18922
C11×#18742
C11×#18532
C11×#17872
#2438111