Finite Group Databasebeta

← C11×#16282 #14593475

Subgroups — C11×#16282 #14593475

Order 2816.

2206 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#394C212yesmaximal, complemented
2C2×C11×#394C212yesmaximal, complemented
3C2×C11×#392C211yesmaximal, characteristic
4C2×C11×#386C212yesmaximal, complemented
5C2×C11×#385C211yesmaximal, characteristic, complemented
6C11×#1441C212yesmaximal, complemented
7C11×#1439C212yesmaximal, complemented
8C11×#1439C212yesmaximal, complemented
9C11×#1439C211yesmaximal, characteristic, complemented
10C23×D4×C11C2212yes—
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C11×#394—28no—
25C11×#394—28no—
26C11×#392—24no—
27C11×#386—28no—
28C11×#385—24no—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2211yescharacteristic
36C25×C11C2312yes—
37C25×C11C2311yescharacteristic
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11—24no—
41C22×D4×C11—24no—
42C22×D4×C11—24no—
43C22×D4×C11—22no—
44C22×D4×C11—24no—
45C22×D4×C11—42no—
46C22×D4×C11—41no—
47C22×D4×C11—41no—
48C22×D4×C11—42no—
49C22×D4×C11—42no—
50C23×C4×C11—22no—
51C23×C4×C11—24no—
52C23×C4×C11—41no—
53C23×C4×C11—41no—
54C23×C4×C11—42no—
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—42no—
67C2×C11×C4⋊C4—42no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4—42no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
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—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4—42no—
86C2×C11×C22⋊C4—42no—
87C2×C11×C22⋊C4—42no—
88C2×C11×C22⋊C4—42no—
89C2×C11×C22⋊C4—42no—
90C2×C11×C22⋊C4—42no—
91C2×C11×C22⋊C4D414yes—
92C2×C11×C22⋊C4D414yescomplemented
93C2×C11×C22⋊C4D418yescomplemented
94C11×#95—24no—
95C11×#95—24no—
96C11×#95—24no—
97C11×#95—22no—
98C11×#95—24no—
99C11×#95—24no—
100C11×#95—41no—
101#16282C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11C2×D414yes—
125C24×C11C2×D412yes—
126C24×C11C2×D412yes—
127C24×C11#4112yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—216no—
130C2×D4×C11—48no—
131C2×D4×C11—48no—
132C2×D4×C11—48no—
133C2×D4×C11—44no—
134C2×D4×C11—48no—
135C2×D4×C11—48no—
136C2×D4×C11—44no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—44no—
140C2×D4×C11—48no—
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—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
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—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—44no—
181C22×C4×C11—48no—
182C22×C4×C11—48no—
183C22×C4×C11—44no—
184C22×C4×C11—44no—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D414yes—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4114yes—
191C11×C4⋊C4—48no—
192C11×C4⋊C4—48no—
193C11×C4⋊C4—44no—
194C11×C22⋊C4—28no—
195C11×C22⋊C4—44no—
196C11×C22⋊C4—48no—
197C11×C22⋊C4—48no—
198C11×C22⋊C4—48no—
199C11×C22⋊C4—48no—
200C11×C22⋊C4—48no—
201C11×C22⋊C4—48no—
202C2×#394C2×C1112yescomplemented
203C2×#394C2×C1112yescomplemented
204C2×#392C2×C1111yescharacteristic
205C2×#386C2×C1112yescomplemented
206C2×#385C2×C1111yescharacteristic, complemented
207#1441C2×C1112yescomplemented
208#1439C2×C1112yescomplemented
209#1439C2×C1112yescomplemented
210#1439C2×C1111yescharacteristic, complemented
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—41no—
235C23×C11—42no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11#12114yes—
269C23×C11C22×D411yescharacteristic
270C23×C11C22×D411yescharacteristic
271C23×C11C22×D412yes—
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4112yes—
274C23×C11H(5,𝔽2)11yescharacteristic
275C23×C11H(5,𝔽2)11yescharacteristic
276C23×C11H(5,𝔽2)12yes—
277C23×C11H(5,𝔽2)12yes—
278C23×C112−1+411yescharacteristic
279C23×C112−1+411yescharacteristic
280D4×C11—432no—
281D4×C11—416no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—416no—
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—41no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11—41no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C23×D4C22×C1112yes—
329C23×D4C22×C1111yescharacteristic
330C24×C4C22×C1111yescharacteristic
331C22×C4⋊C4C22×C1112yes—
332C22×C4⋊C4C22×C1112yes—
333C22×C4⋊C4C22×C1111yescharacteristic
334C22×C22⋊C4C22×C1112yes—
335C22×C22⋊C4C22×C1112yes—
336C22×C22⋊C4C22×C1112yes—
337C22×C22⋊C4C22×C1112yes—
338C22×C22⋊C4C22×C1112yes—
339C22×C22⋊C4C22×C1111yescharacteristic
340C22×C22⋊C4C22×C1111yescharacteristic
341C22×C22⋊C4C22×C1112yes—
342#394—28no—
343#394—28no—
344#392—24no—
345#386—28no—
346#385—24no—
347C2×#95C22×C1111yescharacteristic
348C2×#95C22×C1112yes—
349C2×#95C22×C1112yes—
350C2×#95C22×C1112yes—
351C2×#95C22×C1112yes—
352C2×#95C22×C1112yes—
353C2×#95C22×C1111yescharacteristic
354C22×C11—24no—
355C22×C11—28no—
356C22×C11—42no—
357C22×C11—44no—
358C22×C11—44no—
359C22×C11—44no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11—44no—
371C22×C11—44no—
372C22×C11—82no—
373C22×C11—82no—
374C22×C11—82no—
375C22×C11—82no—
376C22×C11—82no—
377C22×C11—82no—
378C22×C11—82no—
379C22×C11—82no—
380C22×C11C2×#12111yescharacteristic
381C22×C11#52512yes—
382C22×C11#53411yescharacteristic
383C22×C11#53412yes—
384C22×C11#53611yescharacteristic
385C22×C11#53711yescharacteristic
386C22×C11#53711yescharacteristic
387C22×C11#53712yes—
388C22×C11#53812yes—
389C22×C11#53911yescharacteristic
390C22×C11#53911yescharacteristic
391C22×C11#54012yes—
392C22×C11#54212yes—
393C22×C11D4212yes—
394C22×C11D4212yes—
395C22×C11D4211yescharacteristic
396C22×C11#54612yes—
397C22×C11#54612yes—
398C22×C11#54712yes—
399C22×C11#55911yescharacteristic
400C22×C11#56011yescharacteristic
401C22×C11H(3,𝔽4)11yescharacteristic
402C22×C11#56212yes—
403C4×C11—44no—
404C4×C11—44no—
405C4×C11—42no—
406C4×C11—44no—
407C4×C11—44no—
408C4×C11—42no—
409C4×C11—82no—
410C25C23×C1112yes—
411C25C23×C1111yescharacteristic
412C22×D4—24no—
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—24no—
417C22×D4—22no—
418C22×D4—24no—
419C22×D4—42no—
420C22×D4—41no—
421C22×D4—41no—
422C22×D4—42no—
423C22×D4—42no—
424C23×C4—22no—
425C23×C4—24no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—42no—
429C23×C4C23×C1112yes—
430C23×C4C23×C1112yes—
431C23×C4C23×C1112yes—
432C23×C4C23×C1111yescharacteristic
433C23×C4C23×C1112yes—
434C23×C4C23×C1111yescharacteristic
435C23×C4C23×C1112yes—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—42no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—41no—
457C2×C22⋊C4—41no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4D4×C1114yes—
466C2×C22⋊C4D4×C1114yescomplemented
467C2×C22⋊C4D4×C1118yescomplemented
468#95—24no—
469#95—24no—
470#95—24no—
471#95—22no—
472#95—24no—
473#95—24no—
474#95—41no—
475C2×C11—44no—
476C2×C11—84no—
477C2×C11#242412yes—
478C2×C11#245511yescharacteristic
479C2×C11#261811yescharacteristic
480C2×C11#263012yes—
481C2×C11#267112yes—
482C2×C11#267212yes—
483C2×C11#267511yescharacteristic
484C2×C11#267911yescharacteristic
485C2×C11#270911yescharacteristic
486C2×C11#271211yescharacteristic
487C2×C11#282411yescharacteristic
488C24—22no—
489C24—22no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C2×D4×C1114yes—
511C24C2×D4×C1112yes—
512C24C2×D4×C1112yes—
513C24C11×#4112yes—
514C24C24×C1111yescharacteristic
515C2×D4—216no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—44no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—44no—
523C2×D4—48no—
524C2×D4—48no—
525C2×D4—44no—
526C2×D4—48no—
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—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4C2×D4×C1112yes—
572C22×C4C2×D4×C1114yes—
573C22×C4C2×D4×C1114yes—
574C22×C4C2×D4×C1114yes—
575C22×C4C2×D4×C1112yes—
576C22×C4C11×#4114yes—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—44no—
580C22⋊C4—28no—
581C22⋊C4—44no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C11#1628211yescharacteristic, direct product factor, Sylow
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—41no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23C11×#12114yes—
647C23C22×D4×C1111yescharacteristic
648C23C22×D4×C1111yescharacteristic
649C23C22×D4×C1112yes—
650C23C2×C11×#4111yescharacteristic
651C23C2×C11×#4112yes—
652C23C11×H(5,𝔽2)11yescharacteristic
653C23C11×H(5,𝔽2)11yescharacteristic
654C23C11×H(5,𝔽2)12yes—
655C23C11×H(5,𝔽2)12yes—
656C23C11×2−1+411yescharacteristic
657C23C11×2−1+411yescharacteristic
658D4—432no—
659D4—416no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—416no—
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×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C22—28no—
707C22—24no—
708C22—44no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22C2×C11×#12111yescharacteristic
733C22C11×#52512yes—
734C22C11×#53412yes—
735C22C11×#53411yescharacteristic
736C22C11×#53611yescharacteristic
737C22C11×#53711yescharacteristic
738C22C11×#53712yes—
739C22C11×#53711yescharacteristic
740C22C11×#53812yes—
741C22C11×#53911yescharacteristic
742C22C11×#53911yescharacteristic
743C22C11×#54012yes—
744C22C11×#54212yes—
745C22D42×C1112yes—
746C22D42×C1112yes—
747C22D42×C1111yescharacteristic
748C22C11×#54612yes—
749C22C11×#54612yes—
750C22C11×#54712yes—
751C22C11×#55911yescharacteristic
752C22C11×#56011yescharacteristic
753C22C11×H(3,𝔽4)11yescharacteristic
754C22C11×#56212yes—
755C4—44no—
756C4—44no—
757C4—42no—
758C4—44no—
759C4—44no—
760C4—42no—
761C4—82no—
762C2—44no—
763C2—84no—
764C2C11×#242412yes—
765C2C11×#245511yescharacteristic
766C2C11×#261811yescharacteristic
767C2C11×#263012yes—
768C2C11×#267112yes—
769C2C11×#267212yes—
770C2C11×#267511yescharacteristic
771C2C11×#267911yescharacteristic
772C2C11×#270911yescharacteristic
773C2C11×#271211yescharacteristic
774C2C11×#282411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC2×C11×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#394C2semidirect
2. C2×C11×#394C2semidirect
4. C2×C11×#386C2semidirect
5. C2×C11×#385C2semidirect
6. C11×#1441C2semidirect
7. C11×#1439C2semidirect
8. C11×#1439C2semidirect
9. C11×#1439C2semidirect
92. C2×C11×C22⋊C4D4semidirect
93. C2×C11×C22⋊C4D4semidirect
101. #16282C11direct (N × H)
202. C2×#394C2×C11semidirect
203. C2×#394C2×C11semidirect
205. C2×#386C2×C11semidirect
206. C2×#385C2×C11semidirect
207. #1441C2×C11semidirect
208. #1439C2×C11semidirect
209. #1439C2×C11semidirect
210. #1439C2×C11semidirect
466. C2×C22⋊C4D4×C11semidirect
467. C2×C22⋊C4D4×C11semidirect
588. C11#16282direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3942
C2×C11×#3922
C2×C11×#3862
C2×C11×#3852
C11×#14412
C11×#14392
#1628211