Finite Group Databasebeta

← C11×#14505 #14591698

Subgroups — C11×#14505 #14591698

Order 2816.

2070 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
1C22×C11×#123C211yesmaximal, characteristic
2C2×C11×#390C211yesmaximal, characteristic
3C2×C11×#386C211yesmaximal, characteristic
4C11×#1441C212yesmaximal, complemented
5C11×#1440C212yesmaximal, complemented
6C11×#1440C212yesmaximal, complemented
7C11×#1436C212yesmaximal, complemented
8C11×C22⋊#95C212yesmaximal, complemented
9C11×C22⋊#95C212yesmaximal, complemented
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C2×C11×#123—24no—
14C2×C11×#123—24no—
15C2×C11×#123C418yescomplemented
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#390—24no—
26C11×#386—24no—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C25×C11C2311yescharacteristic
37C25×C11C2311yescharacteristic
38C22×D4×C11—41no—
39C22×D4×C11—41no—
40C22×D4×C11—41no—
41C22×D4×C11—41no—
42C22×D4×C11C2×C414yes—
43C22×D4×C11D414yes—
44C22×D4×C11D414yes—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11—41no—
50C23×C4×C11—41no—
51C23×C4×C11—41no—
52C23×C4×C11—41no—
53C23×C4×C11—41no—
54C23×C4×C11—41no—
55C23×C4×C11—42no—
56C23×C4×C11C2×C414yescomplemented
57C23×C4×C11C2312yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C11×#123—232no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4—41no—
70C2×C11×C4⋊C4C2×C418yescomplemented
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—42no—
83C2×C11×C22⋊C4—42no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4C2×C418yes—
88C2×C11×C22⋊C4C2×C414yescomplemented
89C2×C42×C11—22no—
90C2×C42×C11—41no—
91C2×C42×C11—41no—
92C11×#95—24no—
93C11×#95—24no—
94C11×#95—24no—
95C11×#95—42no—
96C11×#95—42no—
97C11×#95—42no—
98C11×#95—42no—
99C11×#95—42no—
100C11×#95—42no—
101#14505C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11C22×C412yes—
119C24×C11C22×C412yes—
120C24×C11C2×D412yes—
121C24×C11C2×D412yes—
122C24×C11C2×D412yes—
123C24×C11C2×D412yes—
124C24×C11C2411yescharacteristic
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11C22⋊C4116yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—28no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
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—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—44no—
176C22×C4×C11—44no—
177C22×C4×C11—44no—
178C22×C4×C11—48no—
179C22×C4×C11—48no—
180C22×C4×C11—44no—
181C22×C4×C11—44no—
182C22×C4×C11—44no—
183C22×C4×C11—44no—
184C22×C4×C11—44no—
185C22×C4×C11—44no—
186C22×C4×C11C22×C414yes—
187C22×C4×C11C22×C414yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11#4114yes—
192C22×C4×C11#4114yes—
193C11×C4⋊C4—216no—
194C11×C4⋊C4—44no—
195C11×C22⋊C4—216no—
196C11×C22⋊C4—28no—
197C11×C22⋊C4—48no—
198C11×C22⋊C4—48no—
199C11×C22⋊C4—48no—
200C11×C22⋊C4—44no—
201C42×C11—44no—
202C22×#123C2×C1111yescharacteristic
203C2×#390C2×C1111yescharacteristic
204C2×#386C2×C1111yescharacteristic
205#1441C2×C1112yescomplemented
206#1440C2×C1112yescomplemented
207#1440C2×C1112yescomplemented
208#1436C2×C1112yescomplemented
209C22⋊#95C2×C1112yescomplemented
210C22⋊#95C2×C1112yescomplemented
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11C2×C22⋊C414yes—
256C23×C11C2×C22⋊C414yes—
257C23×C11C23×C411yescharacteristic
258C23×C11C22×D411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C2×#4112yes—
261C23×C11C2×#4112yes—
262C23×C11H(5,𝔽2)11yescharacteristic
263C23×C11H(5,𝔽2)11yescharacteristic
264C23×C11H(5,𝔽2)11yescharacteristic
265C23×C11H(5,𝔽2)11yescharacteristic
266C23×C11H(5,𝔽2)12yes—
267C23×C112−1+412yes—
268D4×C11—416no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
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—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—416no—
288C2×C4×C11—416no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
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—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11C2×C22⋊C414yes—
320C23×D4C22×C1111yescharacteristic
321C24×C4C22×C1111yescharacteristic
322C24×C4C22×C1111yescharacteristic
323C2×#123—24no—
324C2×#123—24no—
325C2×#123C4×C1118yescomplemented
326C22×C4⋊C4C22×C1112yes—
327C22×C4⋊C4C22×C1111yescharacteristic
328C22×C22⋊C4C22×C1112yes—
329C22×C22⋊C4C22×C1112yes—
330C22×C22⋊C4C22×C1112yes—
331C22×C22⋊C4C22×C1112yes—
332C22×C22⋊C4C22×C1111yescharacteristic
333C22×C22⋊C4C22×C1111yescharacteristic
334C22×C42C22×C1111yescharacteristic
335#390—24no—
336#386—24no—
337C2×#95C22×C1112yes—
338C2×#95C22×C1112yes—
339C2×#95C22×C1112yes—
340C2×#95C22×C1112yes—
341C2×#95C22×C1112yes—
342C2×#95C22×C1112yes—
343C2×#95C22×C1112yes—
344C2×#95C22×C1112yes—
345C2×#95C22×C1112yes—
346C22×C11—24no—
347C22×C11—24no—
348C22×C11—28no—
349C22×C11—28no—
350C22×C11—44no—
351C22×C11—44no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—44no—
359C22×C11—44no—
360C22×C11—44no—
361C22×C11—44no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11C22×C22⋊C411yescharacteristic
369C22×C11C4×#4112yes—
370C22×C11#51811yescharacteristic
371C22×C11#51811yescharacteristic
372C22×C11#52012yes—
373C22×C11#53411yescharacteristic
374C22×C11#53411yescharacteristic
375C22×C11#53411yescharacteristic
376C22×C11#53411yescharacteristic
377C22×C11#53812yes—
378C22×C11#53912yes—
379C22×C11#54012yes—
380C22×C11#54212yes—
381C22×C11#54612yes—
382C22×C11#54612yes—
383C22×C11#54712yes—
384C22×C11#54712yes—
385C22×C11#55111yescharacteristic
386C22×C11#55312yes—
387C22×C11#55911yescharacteristic
388C22×C11#56011yescharacteristic
389C22×C11#56212yes—
390C22×C11#56311yescharacteristic
391C4×C11—24no—
392C4×C11—44no—
393C4×C11—44no—
394C4×C11—44no—
395C4×C11—44no—
396C4×C11—82no—
397C4×C11—82no—
398C25C23×C1111yescharacteristic
399C25C23×C1111yescharacteristic
400C22×D4—41no—
401C22×D4—41no—
402C22×D4—41no—
403C22×D4—41no—
404C22×D4C2×C4×C1114yes—
405C22×D4D4×C1114yes—
406C22×D4D4×C1114yes—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—24no—
411C23×C4—41no—
412C23×C4—41no—
413C23×C4—41no—
414C23×C4—41no—
415C23×C4—41no—
416C23×C4—41no—
417C23×C4—42no—
418C23×C4C2×C4×C1114yescomplemented
419C23×C4C23×C1112yes—
420C23×C4C23×C1112yes—
421C23×C4C23×C1112yes—
422C23×C4C23×C1112yes—
423C23×C4C23×C1112yes—
424C23×C4C23×C1112yes—
425C23×C4C23×C1111yescharacteristic
426#123—232no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4C2×C4×C1118yescomplemented
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—41no—
448C2×C22⋊C4—41no—
449C2×C22⋊C4C2×C4×C1118yes—
450C2×C22⋊C4C2×C4×C1114yescomplemented
451C2×C42—22no—
452C2×C42—41no—
453C2×C42—41no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463C2×C11—44no—
464C2×C11—44no—
465C2×C11#230811yescharacteristic
466C2×C11#233512yes—
467C2×C11#233912yes—
468C2×C11#237411yescharacteristic
469C2×C11#237611yescharacteristic
470C2×C11#269711yescharacteristic
471C2×C11#270112yes—
472C2×C11#270812yes—
473C2×C11#270911yescharacteristic
474C2×C11#271711yescharacteristic
475C2×C11#272411yescharacteristic
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24C22×C4×C1112yes—
493C24C22×C4×C1112yes—
494C24C2×D4×C1112yes—
495C24C2×D4×C1112yes—
496C24C2×D4×C1112yes—
497C24C2×D4×C1112yes—
498C24C24×C1111yescharacteristic
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4C11×C22⋊C4116yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—28no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
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—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4C22×C4×C1114yes—
561C22×C4C22×C4×C1114yes—
562C22×C4C22×C4×C1112yes—
563C22×C4C2×D4×C1112yes—
564C22×C4C2×D4×C1112yes—
565C22×C4C11×#4114yes—
566C22×C4C11×#4114yes—
567C4⋊C4—216no—
568C4⋊C4—44no—
569C22⋊C4—216no—
570C22⋊C4—28no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—44no—
575C42—44no—
576C11#1450511yescharacteristic, direct product factor, Sylow
577C23—24no—
578C23—24no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23C2×C11×C22⋊C414yes—
622C23C2×C11×C22⋊C414yes—
623C23C23×C4×C1111yescharacteristic
624C23C22×D4×C1111yescharacteristic
625C23C22×D4×C1111yescharacteristic
626C23C2×C11×#4112yes—
627C23C2×C11×#4112yes—
628C23C11×H(5,𝔽2)11yescharacteristic
629C23C11×H(5,𝔽2)11yescharacteristic
630C23C11×H(5,𝔽2)11yescharacteristic
631C23C11×H(5,𝔽2)11yescharacteristic
632C23C11×H(5,𝔽2)12yes—
633C23C11×2−1+412yes—
634D4—416no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—416no—
654C2×C4—416no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4C2×C11×C22⋊C414yes—
686C22—24no—
687C22—24no—
688C22—28no—
689C22—28no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—44no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22C22×C11×C22⋊C411yescharacteristic
709C22C4×C11×#4112yes—
710C22C11×#51811yescharacteristic
711C22C11×#51811yescharacteristic
712C22C11×#52012yes—
713C22C11×#53411yescharacteristic
714C22C11×#53411yescharacteristic
715C22C11×#53411yescharacteristic
716C22C11×#53411yescharacteristic
717C22C11×#53812yes—
718C22C11×#53912yes—
719C22C11×#54012yes—
720C22C11×#54212yes—
721C22C11×#54612yes—
722C22C11×#54612yes—
723C22C11×#54712yes—
724C22C11×#54712yes—
725C22C11×#55111yescharacteristic
726C22C11×#55312yes—
727C22C11×#55911yescharacteristic
728C22C11×#56011yescharacteristic
729C22C11×#56212yes—
730C22C11×#56311yescharacteristic
731C4—24no—
732C4—44no—
733C4—44no—
734C4—44no—
735C4—44no—
736C4—82no—
737C4—82no—
738C2—44no—
739C2—44no—
740C2C11×#230811yescharacteristic
741C2C11×#233512yes—
742C2C11×#233912yes—
743C2C11×#237411yescharacteristic
744C2C11×#237611yescharacteristic
745C2C11×#269711yescharacteristic
746C2C11×#270112yes—
747C2C11×#270812yes—
748C2C11×#270911yescharacteristic
749C2C11×#271711yescharacteristic
750C2C11×#272411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1441C2semidirect
5. C11×#1440C2semidirect
6. C11×#1440C2semidirect
7. C11×#1436C2semidirect
8. C11×C22⋊#95C2semidirect
9. C11×C22⋊#95C2semidirect
15. C2×C11×#123C4semidirect
56. C23×C4×C11C2×C4semidirect
70. C2×C11×C4⋊C4C2×C4semidirect
88. C2×C11×C22⋊C4C2×C4semidirect
101. #14505C11direct (N × H)
205. #1441C2×C11semidirect
206. #1440C2×C11semidirect
207. #1440C2×C11semidirect
208. #1436C2×C11semidirect
209. C22⋊#95C2×C11semidirect
210. C22⋊#95C2×C11semidirect
325. C2×#123C4×C11semidirect
418. C23×C4C2×C4×C11semidirect
432. C2×C4⋊C4C2×C4×C11semidirect
450. C2×C22⋊C4C2×C4×C11semidirect
576. C11#14505direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C2×C11×#3902
C2×C11×#3862
C11×#14412
C11×#14402
C11×#14362
C11×C22⋊#952
#1450511