Finite Group Databasebeta

← C11×#24378 #14601571

Subgroups — C11×#24378 #14601571

Order 2816.

2002 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic, complemented
2C2×C11×#466C212yesmaximal, complemented
3C2×C11×#447C211yesmaximal, characteristic, complemented
4C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
5C11×#2847C211yesmaximal, characteristic, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#1999C212yesmaximal, complemented
8C11×#1893C212yesmaximal, complemented
9C11×#1874C211yesmaximal, characteristic, complemented
10C11×#1852C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11—21no—
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×D8C2212yescomplemented
16C23×C8×C11C2212yescomplemented
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#121—28no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2212yes—
22C2×C11×#121C2212yes—
23C2×C11×#121C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic, complemented
25C2×C11×#120—21no—
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4—21no—
28C11×#466—28no—
29C11×#447—24no—
30C2×C11×#107C2212yescomplemented
31C2×C11×#102C2212yescomplemented
32C2×C11×#102C2212yescomplemented
33C2×C11×#102C2212yescomplemented
34C2×C11×#102C2212yescomplemented
35C2×C11×C22⋊C8—24no—
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2212yescomplemented
39C11×#386—21no—
40C11×#386—21no—
41C11×#386—21no—
42C11×#380C2211yescharacteristic
43C11×#380C2211yescharacteristic, complemented
44C11×#380C2211yescharacteristic, complemented
45C11×#340C2212yescomplemented
46C11×#340C2212yescomplemented
47C25×C11—21no—
48C25×C11D411yescharacteristic
49C22×D4×C11—28no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—24no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—42no—
60C22×D4×C11—44no—
61C22×D4×C11—44no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2312yes—
64C23×C4×C11—21no—
65C23×C4×C11—24no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—42no—
69C23×C4×C11D411yescharacteristic
70C23×C4×C11D411yescharacteristic
71C23×C4×C11D411yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C2×C11×D8—24no—
76C2×C11×D8—24no—
77C2×C11×D8—42no—
78C22×C8×C11—24no—
79C22×C8×C11—24no—
80C22×C8×C11—42no—
81C22×C8×C11C2312yes—
82C22×C8×C11C2312yes—
83C11×#121—28no—
84C11×#121—28no—
85C11×#121—24no—
86C11×#121—24no—
87C11×#121—24no—
88C11×#121—22no—
89C11×#121—24no—
90C11×#121—22no—
91C11×#121—42no—
92C11×#121D418yescomplemented
93C11×#120—44no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C22⋊C4—28no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
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—
108C2×C11×C22⋊C4—21no—
109C11×#107—24no—
110C11×#102—24no—
111C11×#102—24no—
112C11×#102—24no—
113C11×#102—42no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—24no—
116C11×C22⋊C8D414yescomplemented
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120#24378C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—24no—
126C24×C11—22no—
127C24×C11—21no—
128C24×C11—41no—
129C24×C11—41no—
130C24×C11—42no—
131C24×C11—42no—
132C24×C11—42no—
133C24×C11—42no—
134C24×C11—42no—
135C24×C11—42no—
136C24×C11D814yescomplemented
137C24×C11C2×D411yescharacteristic
138C24×C11C2×D411yescharacteristic
139C24×C11C2×D411yescharacteristic
140C2×D4×C11—24no—
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—48no—
153C2×D4×C11—48no—
154C2×D4×C11—42no—
155C2×D4×C11—432no—
156C2×D4×C11—44no—
157C2×D4×C11—44no—
158C2×D4×C11—44no—
159C2×D4×C11—44no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11C2×D414yes—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—24no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—21no—
185C22×C4×C11—22no—
186C22×C4×C11—21no—
187C22×C4×C11—22no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—41no—
192C22×C4×C11—41no—
193C22×C4×C11—41no—
194C22×C4×C11—48no—
195C22×C4×C11—48no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11#4112yes—
204C22×C4×C11C2411yescharacteristic
205C11×D8—48no—
206C2×C8×C11—22no—
207C2×C8×C11—22no—
208C2×C8×C11—22no—
209C2×C8×C11—22no—
210C2×C8×C11—22no—
211C2×C8×C11—48no—
212C2×C8×C11C2×D414yescomplemented
213C11×C4⋊C4—24no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4C2×D414yes—
220C11×C22⋊C4—28no—
221C11×C22⋊C4—28no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C22×#121C2×C1111yescharacteristic, complemented
229C2×#466C2×C1112yescomplemented
230C2×#447C2×C1111yescharacteristic, complemented
231C22×C22⋊C8C2×C1111yescharacteristic, complemented
232#2847C2×C1111yescharacteristic, complemented
233#2033C2×C1112yescomplemented
234#1999C2×C1112yescomplemented
235#1893C2×C1112yescomplemented
236#1874C2×C1111yescharacteristic, complemented
237#1852C2×C1111yescharacteristic, complemented
238#1786C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—28no—
254C23×C11—28no—
255C23×C11—24no—
256C23×C11—44no—
257C23×C11—44no—
258C23×C11—44no—
259C23×C11—44no—
260C23×C11—44no—
261C23×C11—48no—
262C23×C11—48no—
263C23×C11—48no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—84no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11#12012yes—
282C23×C11#12112yes—
283C23×C11C2×D812yes—
284C23×C11C2×D812yes—
285C23×C11C2×D812yes—
286C23×C11#13512yes—
287C23×C11AGL(1,ℤ/8)12yes—
288C23×C11C22×D411yescharacteristic
289D4×C11—24no—
290D4×C11—24no—
291D4×C11—48no—
292D4×C11—416no—
293D4×C11—416no—
294D4×C11—42no—
295D4×C11—42no—
296D4×C11—42no—
297D4×C11—42no—
298D4×C11—84no—
299D4×C11—84no—
300D4×C11—84no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—21no—
310C2×C4×C11—24no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—44no—
314C2×C4×C11—44no—
315C2×C4×C11—44no—
316C2×C4×C11—48no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11#12012yes—
331C2×C4×C11#12112yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D412yes—
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)12yes—
336C8×C11—24no—
337C8×C11—42no—
338C23×D4—21no—
339C23×D4C22×C1111yescharacteristic
340C24×C4C22×C1111yescharacteristic
341C22×D8C22×C1112yescomplemented
342C23×C8C22×C1112yescomplemented
343C2×#121—21no—
344C2×#121—21no—
345C2×#121—28no—
346C2×#121C22×C1111yescharacteristic
347C2×#121C22×C1112yes—
348C2×#121C22×C1112yes—
349C2×#121C22×C1111yescharacteristic, complemented
350C2×#121C22×C1111yescharacteristic, complemented
351C2×#120—21no—
352C22×C4⋊C4C22×C1111yescharacteristic
353C22×C22⋊C4—21no—
354#466—28no—
355#447—24no—
356C2×#107C22×C1112yescomplemented
357C2×#102C22×C1112yescomplemented
358C2×#102C22×C1112yescomplemented
359C2×#102C22×C1112yescomplemented
360C2×#102C22×C1112yescomplemented
361C2×C22⋊C8—24no—
362C2×C22⋊C8C22×C1111yescharacteristic
363C2×C22⋊C8C22×C1111yescharacteristic
364C2×C22⋊C8C22×C1112yescomplemented
365#386—21no—
366#386—21no—
367#386—21no—
368#380C22×C1111yescharacteristic
369#380C22×C1111yescharacteristic, complemented
370#380C22×C1111yescharacteristic, complemented
371#340C22×C1112yescomplemented
372#340C22×C1112yescomplemented
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—416no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—44no—
394C22×C11—44no—
395C22×C11—44no—
396C22×C11—816no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11—82no—
400C22×C11—82no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11#44714yescomplemented
409C22×C11#46614yescomplemented
410C22×C11C2×#12011yescharacteristic
411C22×C11C2×#12111yescharacteristic
412C22×C11#53411yescharacteristic
413C22×C11C22×D811yescharacteristic
414C22×C11C2×#13511yescharacteristic
415C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C11#57511yescharacteristic
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11—44no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11D4212yes—
425C4×C11#54612yes—
426C25—21no—
427C25D4×C1111yescharacteristic
428C22×D4—28no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—24no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—42no—
439C22×D4—44no—
440C22×D4—44no—
441C22×D4C23×C1111yescharacteristic
442C22×D4C23×C1112yes—
443C23×C4—21no—
444C23×C4—24no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—42no—
448C23×C4D4×C1111yescharacteristic
449C23×C4D4×C1111yescharacteristic
450C23×C4D4×C1111yescharacteristic
451C23×C4C23×C1111yescharacteristic
452C23×C4C23×C1111yescharacteristic
453C23×C4C23×C1111yescharacteristic
454C2×D8—24no—
455C2×D8—24no—
456C2×D8—42no—
457C22×C8—24no—
458C22×C8—24no—
459C22×C8—42no—
460C22×C8C23×C1112yes—
461C22×C8C23×C1112yes—
462#121—28no—
463#121—28no—
464#121—24no—
465#121—24no—
466#121—24no—
467#121—22no—
468#121—24no—
469#121—22no—
470#121—42no—
471#121D4×C1118yescomplemented
472#120—44no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1112yes—
479C2×C22⋊C4—28no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488#107—24no—
489#102—24no—
490#102—24no—
491#102—24no—
492#102—42no—
493C22⋊C8—22no—
494C22⋊C8—24no—
495C22⋊C8D4×C1114yescomplemented
496#95—21no—
497#95—21no—
498#95—21no—
499C2×C11—24no—
500C2×C11—24no—
501C2×C11—42no—
502C2×C11—84no—
503C2×C11—161no—
504C2×C11#241011yescharacteristic
505C2×C11C2×#44711yescharacteristic
506C2×C11#300211yescharacteristic
507C2×C11C2×#46611yescharacteristic
508C2×C11#305511yescharacteristic
509C2×C11#318611yescharacteristic
510C2×C11#318811yescharacteristic
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—24no—
516C24—22no—
517C24—21no—
518C24—41no—
519C24—41no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24C11×D814yescomplemented
527C24C2×D4×C1111yescharacteristic
528C24C2×D4×C1111yescharacteristic
529C24C2×D4×C1111yescharacteristic
530C2×D4—24no—
531C2×D4—28no—
532C2×D4—28no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—42no—
545C2×D4—432no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4C2×D4×C1114yes—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4C2×D4×C1111yescharacteristic
589C22×C4C2×D4×C1111yescharacteristic
590C22×C4C2×D4×C1114yes—
591C22×C4C2×D4×C1111yescharacteristic
592C22×C4C2×D4×C1112yes—
593C22×C4C11×#4112yes—
594C22×C4C24×C1111yescharacteristic
595D8—48no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—48no—
602C2×C8C2×D4×C1114yescomplemented
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4C2×D4×C1114yes—
610C22⋊C4—28no—
611C22⋊C4—28no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C11#2437811yescharacteristic, direct product factor, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—28no—
634C23—28no—
635C23—24no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—48no—
642C23—48no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23C11×#12012yes—
662C23C11×#12112yes—
663C23C2×C11×D812yes—
664C23C2×C11×D812yes—
665C23C2×C11×D812yes—
666C23C11×#13512yes—
667C23C11×AGL(1,ℤ/8)12yes—
668C23C22×D4×C1111yescharacteristic
669D4—24no—
670D4—24no—
671D4—48no—
672D4—416no—
673D4—416no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—84no—
679D4—84no—
680D4—84no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—21no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4C11×#12012yes—
711C2×C4C11×#12112yes—
712C2×C4C22×D4×C1111yescharacteristic
713C2×C4C22×D4×C1112yes—
714C2×C4C2×C11×#4111yescharacteristic
715C2×C4C11×H(5,𝔽2)12yes—
716C8—24no—
717C8—42no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—416no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—816no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22C11×#44714yescomplemented
754C22C11×#46614yescomplemented
755C22C2×C11×#12011yescharacteristic
756C22C2×C11×#12111yescharacteristic
757C22C11×#53411yescharacteristic
758C22C22×C11×D811yescharacteristic
759C22C2×C11×#13511yescharacteristic
760C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
761C22C11×#57511yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—44no—
766C4—81no—
767C4—81no—
768C4—81no—
769C4D42×C1112yes—
770C4C11×#54612yes—
771C2—24no—
772C2—24no—
773C2—42no—
774C2—84no—
775C2—161no—
776C2C11×#241011yescharacteristic
777C2C2×C11×#44711yescharacteristic
778C2C11×#300211yescharacteristic
779C2C2×C11×#46611yescharacteristic
780C2C11×#305511yescharacteristic
781C2C11×#318611yescharacteristic
782C2C11×#318811yescharacteristic
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. C22×C11×#121C2semidirect
2. C2×C11×#466C2semidirect
3. C2×C11×#447C2semidirect
4. C22×C11×C22⋊C8C2semidirect
5. C11×#2847C2semidirect
6. C11×#2033C2semidirect
7. C11×#1999C2semidirect
8. C11×#1893C2semidirect
9. C11×#1874C2semidirect
10. C11×#1852C2semidirect
11. C11×#1786C2semidirect
15. C22×C11×D8C22semidirect
16. C23×C8×C11C22semidirect
23. C2×C11×#121C22semidirect
24. C2×C11×#121C22semidirect
30. C2×C11×#107C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
33. C2×C11×#102C22semidirect
34. C2×C11×#102C22semidirect
38. C2×C11×C22⋊C8C22semidirect
43. C11×#380C22semidirect
44. C11×#380C22semidirect
45. C11×#340C22semidirect
46. C11×#340C22semidirect
92. C11×#121D4semidirect
116. C11×C22⋊C8D4semidirect
120. #24378C11direct (N × H)
136. C24×C11D8semidirect
212. C2×C8×C11C2×D4semidirect
228. C22×#121C2×C11semidirect
229. C2×#466C2×C11semidirect
230. C2×#447C2×C11semidirect
231. C22×C22⋊C8C2×C11semidirect
232. #2847C2×C11semidirect
233. #2033C2×C11semidirect
234. #1999C2×C11semidirect
235. #1893C2×C11semidirect
236. #1874C2×C11semidirect
237. #1852C2×C11semidirect
238. #1786C2×C11semidirect
341. C22×D8C22×C11semidirect
342. C23×C8C22×C11semidirect
349. C2×#121C22×C11semidirect
350. C2×#121C22×C11semidirect
356. C2×#107C22×C11semidirect
357. C2×#102C22×C11semidirect
358. C2×#102C22×C11semidirect
359. C2×#102C22×C11semidirect
360. C2×#102C22×C11semidirect
364. C2×C22⋊C8C22×C11semidirect
369. #380C22×C11semidirect
370. #380C22×C11semidirect
371. #340C22×C11semidirect
372. #340C22×C11semidirect
408. C22×C11#447semidirect
409. C22×C11#466semidirect
471. #121D4×C11semidirect
495. C22⋊C8D4×C11semidirect
526. C24C11×D8semidirect
602. C2×C8C2×D4×C11semidirect
618. C11#24378direct (N × H)
753. C22C11×#447semidirect
754. C22C11×#466semidirect

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×#4662
C2×C11×#4472
C22×C11×C22⋊C82
C11×#28472
C11×#20332
C11×#19992
C11×#18932
C11×#18742
C11×#18522
C11×#17862
#2437811