Finite Group Databasebeta

← C11×#23861 #14601054

Subgroups — C11×#23861 #14601054

Order 2816.

2084 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C11×#546C211yesmaximal, characteristic, complemented
3C2×C11×#447C212yesmaximal, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C11×#2408C211yesmaximal, characteristic, complemented
6C11×#2012C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1895C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1788C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic, complemented
14C23×D4×C11C2211yescharacteristic, complemented
15C2×C11×AGL(1,ℤ/8)—24no—
16C2×C11×AGL(1,ℤ/8)—28no—
17C22×C11×SD16C2212yescomplemented
18C22×C11×D8C2212yes—
19C22×C11×D8C2212yes—
20C22×C11×M16C2211yescharacteristic, complemented
21C11×#546—24no—
22C11×#546—24no—
23C2×C11×#124C2211yescharacteristic, complemented
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic, complemented
26C2×C11×#121—21no—
27C2×C11×#121C2212yes—
28C2×C11×#121C2211yescharacteristic
29C2×C11×#120—21no—
30C2×C11×#120—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic, complemented
33C22×C11×C22⋊C4—21no—
34C11×#447—28no—
35C11×#447—24no—
36C2×C11×#103C2212yescomplemented
37C2×C11×#102C2212yescomplemented
38C2×C11×#102C2212yescomplemented
39C2×C11×#102C2212yescomplemented
40C2×C11×C22⋊C8C2212yescomplemented
41C2×C11×C22⋊C8C2211yescharacteristic, complemented
42C11×#394—21no—
43C11×#392—21no—
44C11×#390C2212yescomplemented
45C11×#380C2211yescharacteristic, complemented
46C11×#379—21no—
47C11×#340C2212yescomplemented
48C11×#336C2212yescomplemented
49C25×C11—21no—
50C25×C11—21no—
51C2×C11×#41—22no—
52C2×C11×#41—24no—
53C2×C11×#41—42no—
54C2×C11×#41D414yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11—24no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—24no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—21no—
67C22×D4×C11—42no—
68C22×D4×C11—42no—
69C22×D4×C11D411yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2312yes—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C11×AGL(1,ℤ/8)—232no—
78C2×C11×SD16—24no—
79C2×C11×SD16—24no—
80C2×C11×SD16—24no—
81C2×C11×D8—24no—
82C2×C11×D8—24no—
83C2×C11×D8—24no—
84C2×C11×D8—24no—
85C2×C11×D8—42no—
86C2×C11×D8D418yescomplemented
87C2×C11×M16—22no—
88C2×C11×M16—24no—
89C22×C8×C11C2312yes—
90C22×C8×C11C2312yes—
91C11×#124—22no—
92C11×#124—22no—
93C11×#123—28no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—22no—
96C11×#121—28no—
97C11×#121—22no—
98C11×#121—24no—
99C11×#121—42no—
100C11×#121D414yescomplemented
101C11×#120—28no—
102C11×#120—44no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—28no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C11×#103—42no—
125C11×#102—24no—
126C11×#102—24no—
127C11×#102—24no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—24no—
130C11×#95—21no—
131#23861C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11—24no—
134C24×C11—21no—
135C24×C11—22no—
136C24×C11—44no—
137C24×C11—44no—
138C24×C11—42no—
139C24×C11—42no—
140C24×C11—42no—
141C24×C11—42no—
142C24×C11—42no—
143C24×C11—82no—
144C24×C11—82no—
145C24×C11C2×D411yescharacteristic
146C24×C11C2×D411yescharacteristic
147C11×#41—28no—
148C11×#41—44no—
149C11×#41—48no—
150C2×Q8×C11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11C2×D412yes—
154C2×D4×C11—28no—
155C2×D4×C11—24no—
156C2×D4×C11—22no—
157C2×D4×C11—24no—
158C2×D4×C11—22no—
159C2×D4×C11—24no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—48no—
171C2×D4×C11—41no—
172C2×D4×C11—44no—
173C2×D4×C11—44no—
174C2×D4×C11—44no—
175C2×D4×C11—48no—
176C2×D4×C11—44no—
177C2×D4×C11—44no—
178C2×D4×C11—44no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11—42no—
182C2×D4×C11—82no—
183C2×D4×C11—82no—
184C2×D4×C11C2×D414yes—
185C2×D4×C11C2×D412yes—
186C2×D4×C11C2×D414yes—
187C2×D4×C11C2×D412yes—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—24no—
193C22×C4×C11—24no—
194C22×C4×C11—22no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—44no—
200C22×C4×C11—82no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2411yescharacteristic
208C11×SD16—216no—
209C11×D8—216no—
210C11×D8—48no—
211C11×M16—28no—
212C2×C8×C11—22no—
213C2×C8×C11—22no—
214C2×C8×C11—22no—
215C2×C8×C11—22no—
216C2×C8×C11—22no—
217C2×C8×C11C2×D414yes—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4C2×D412yes—
224C11×C22⋊C4—24no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—44no—
232C11×C22⋊C4—44no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—82no—
235C42×C11—21no—
236C42×C11—21no—
237C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
238C2×#546C2×C1111yescharacteristic, complemented
239C2×#447C2×C1112yescomplemented
240C2×#447C2×C1111yescharacteristic, complemented
241#2408C2×C1111yescharacteristic, complemented
242#2012C2×C1112yescomplemented
243#2000C2×C1112yescomplemented
244#1895C2×C1111yescharacteristic, complemented
245#1879C2×C1112yescomplemented
246#1870C2×C1111yescharacteristic, complemented
247#1788C2×C1111yescharacteristic, complemented
248C23×C11—21no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—24no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—48no—
261C23×C11—48no—
262C23×C11—48no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—88no—
277C23×C11—84no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—88no—
281C23×C11—88no—
282C23×C11—88no—
283C23×C11#12012yes—
284C23×C11AGL(1,ℤ/8)12yescomplemented
285C23×C11C22×D411yescharacteristic
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—42no—
289D4×C11—24no—
290D4×C11—22no—
291D4×C11—24no—
292D4×C11—24no—
293D4×C11—24no—
294D4×C11—48no—
295D4×C11—44no—
296D4×C11—48no—
297D4×C11—48no—
298D4×C11—41no—
299D4×C11—42no—
300D4×C11—41no—
301D4×C11—42no—
302D4×C11—84no—
303D4×C11—88no—
304D4×C11#12014yescomplemented
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—48no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—84no—
328C2×C4×C11#12012yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11H(5,𝔽2)12yes—
333C8×C11—24no—
334C8×C11—42no—
335C22×#41C22×C1111yescharacteristic
336C23×D4C22×C1111yescharacteristic, complemented
337C23×D4C22×C1111yescharacteristic, complemented
338C2×AGL(1,ℤ/8)—24no—
339C2×AGL(1,ℤ/8)—28no—
340C22×SD16C22×C1112yescomplemented
341C22×D8C22×C1112yes—
342C22×D8C22×C1112yes—
343C22×M16C22×C1111yescharacteristic, complemented
344#546—24no—
345#546—24no—
346C2×#124C22×C1111yescharacteristic, complemented
347C2×#123—21no—
348C2×C22⋊Q8C22×C1111yescharacteristic, complemented
349C2×#121—21no—
350C2×#121C22×C1112yes—
351C2×#121C22×C1111yescharacteristic
352C2×#120—21no—
353C2×#120—21no—
354C2×C4×D4C22×C1111yescharacteristic
355C2×C4×D4C22×C1111yescharacteristic, complemented
356C22×C22⋊C4—21no—
357#447—28no—
358#447—24no—
359C2×#103C22×C1112yescomplemented
360C2×#102C22×C1112yescomplemented
361C2×#102C22×C1112yescomplemented
362C2×#102C22×C1112yescomplemented
363C2×C22⋊C8C22×C1112yescomplemented
364C2×C22⋊C8C22×C1111yescharacteristic, complemented
365#394—21no—
366#392—21no—
367#390C22×C1112yescomplemented
368#380C22×C1111yescharacteristic, complemented
369#379—21no—
370#340C22×C1112yescomplemented
371#336C22×C1112yescomplemented
372C22×C11—22no—
373C22×C11—24no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—24no—
378C22×C11—41no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—41no—
382C22×C11—42no—
383C22×C11—44no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—44no—
392C22×C11—44no—
393C22×C11—816no—
394C22×C11—816no—
395C22×C11—82no—
396C22×C11—82no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11—82no—
400C22×C11—82no—
401C22×C11C2×#12011yescharacteristic
402C22×C11D4212yes—
403C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C11#57511yescharacteristic
405C22×C11#57612yes—
406C4×C11—22no—
407C4×C11—41no—
408C4×C11—42no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—42no—
412C4×C11—82no—
413C4×C11C2×#12011yescharacteristic
414C4×C11#53411yescharacteristic
415C4×C11D4212yes—
416C25—21no—
417C25—21no—
418C2×#41—22no—
419C2×#41—24no—
420C2×#41—42no—
421C2×#41D4×C1114yescomplemented
422C22×Q8C23×C1111yescharacteristic
423C22×D4—24no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—24no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—21no—
432C22×D4—22no—
433C22×D4—21no—
434C22×D4—42no—
435C22×D4—42no—
436C22×D4D4×C1111yescharacteristic
437C22×D4C23×C1111yescharacteristic
438C22×D4C23×C1112yes—
439C22×D4C23×C1111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4C23×C1111yescharacteristic
443C23×C4C23×C1111yescharacteristic
444AGL(1,ℤ/8)—232no—
445C2×SD16—24no—
446C2×SD16—24no—
447C2×SD16—24no—
448C2×D8—24no—
449C2×D8—24no—
450C2×D8—24no—
451C2×D8—24no—
452C2×D8—42no—
453C2×D8D4×C1118yescomplemented
454C2×M16—22no—
455C2×M16—24no—
456C22×C8C23×C1112yes—
457C22×C8C23×C1112yes—
458#124—22no—
459#124—22no—
460#123—28no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463#121—28no—
464#121—22no—
465#121—24no—
466#121—42no—
467#121D4×C1114yescomplemented
468#120—28no—
469#120—44no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4D4×C1111yescharacteristic
476C2×C4⋊C4C23×C1112yes—
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C22⋊C4—28no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4D4×C1111yescharacteristic
489C2×C22⋊C4D4×C1111yescharacteristic
490C2×C42C23×C1111yescharacteristic
491#103—42no—
492#102—24no—
493#102—24no—
494#102—24no—
495C22⋊C8—22no—
496C22⋊C8—24no—
497#95—21no—
498C2×C11—42no—
499C2×C11—42no—
500C2×C11—44no—
501C2×C11—82no—
502C2×C11—84no—
503C2×C11#240311yescharacteristic
504C2×C11#300611yescharacteristic
505C2×C11#300811yescharacteristic
506C2×C11#326412yes—
507C2×C11#327312yes—
508C24—21no—
509C24—24no—
510C24—21no—
511C24—22no—
512C24—44no—
513C24—44no—
514C24—42no—
515C24—42no—
516C24—42no—
517C24—42no—
518C24—42no—
519C24—82no—
520C24—82no—
521C24C2×D4×C1111yescharacteristic
522C24C2×D4×C1111yescharacteristic
523#41—28no—
524#41—44no—
525#41—48no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8C2×D4×C1112yes—
530C2×D4—28no—
531C2×D4—24no—
532C2×D4—22no—
533C2×D4—24no—
534C2×D4—22no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—48no—
547C2×D4—41no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—48no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—42no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4C2×D4×C1114yes—
561C2×D4C2×D4×C1112yes—
562C2×D4C2×D4×C1114yes—
563C2×D4C2×D4×C1112yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—44no—
576C22×C4—82no—
577C22×C4C2×D4×C1111yescharacteristic
578C22×C4C2×D4×C1111yescharacteristic
579C22×C4C2×D4×C1111yescharacteristic
580C22×C4C2×D4×C1111yescharacteristic
581C22×C4C2×D4×C1112yes—
582C22×C4C2×D4×C1112yes—
583C22×C4C24×C1111yescharacteristic
584SD16—216no—
585D8—216no—
586D8—48no—
587M16—28no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8C2×D4×C1114yes—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4C2×D4×C1112yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—24no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—42no—
610C22⋊C4—82no—
611C42—21no—
612C42—21no—
613C11#2386111yescharacteristic, direct product factor, Sylow
614C23—21no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—48no—
627C23—48no—
628C23—48no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—88no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—88no—
647C23—88no—
648C23—88no—
649C23C11×#12012yes—
650C23C11×AGL(1,ℤ/8)12yescomplemented
651C23C22×D4×C1111yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—42no—
655D4—24no—
656D4—22no—
657D4—24no—
658D4—24no—
659D4—24no—
660D4—48no—
661D4—44no—
662D4—48no—
663D4—48no—
664D4—41no—
665D4—42no—
666D4—41no—
667D4—42no—
668D4—84no—
669D4—88no—
670D4C11×#12014yescomplemented
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4C11×#12012yes—
695C2×C4C22×D4×C1111yescharacteristic
696C2×C4C22×D4×C1112yes—
697C2×C4C22×D4×C1111yescharacteristic
698C2×C4C11×H(5,𝔽2)12yes—
699C8—24no—
700C8—42no—
701C22—22no—
702C22—24no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—24no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—41no—
711C22—42no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
722C22—816no—
723C22—816no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22C2×C11×#12011yescharacteristic
731C22D42×C1112yes—
732C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
733C22C11×#57511yescharacteristic
734C22C11×#57612yes—
735C4—22no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4C2×C11×#12011yescharacteristic
743C4C11×#53411yescharacteristic
744C4D42×C1112yes—
745C2—42no—
746C2—42no—
747C2—44no—
748C2—82no—
749C2—84no—
750C2C11×#240311yescharacteristic
751C2C11×#300611yescharacteristic
752C2C11×#300811yescharacteristic
753C2C11×#326412yes—
754C2C11×#327312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C2×C11×#546C2semidirect
3. C2×C11×#447C2semidirect
4. C2×C11×#447C2semidirect
5. C11×#2408C2semidirect
6. C11×#2012C2semidirect
7. C11×#2000C2semidirect
8. C11×#1895C2semidirect
9. C11×#1879C2semidirect
10. C11×#1870C2semidirect
11. C11×#1788C2semidirect
13. C23×D4×C11C22semidirect
14. C23×D4×C11C22semidirect
17. C22×C11×SD16C22semidirect
20. C22×C11×M16C22semidirect
23. C2×C11×#124C22semidirect
25. C2×C11×C22⋊Q8C22semidirect
32. C2×C4×D4×C11C22semidirect
36. C2×C11×#103C22semidirect
37. C2×C11×#102C22semidirect
38. C2×C11×#102C22semidirect
39. C2×C11×#102C22semidirect
40. C2×C11×C22⋊C8C22semidirect
41. C2×C11×C22⋊C8C22semidirect
44. C11×#390C22semidirect
45. C11×#380C22semidirect
47. C11×#340C22semidirect
48. C11×#336C22semidirect
54. C2×C11×#41D4semidirect
86. C2×C11×D8D4semidirect
100. C11×#121D4semidirect
131. #23861C11direct (N × H)
237. C22×AGL(1,ℤ/8)C2×C11semidirect
238. C2×#546C2×C11semidirect
239. C2×#447C2×C11semidirect
240. C2×#447C2×C11semidirect
241. #2408C2×C11semidirect
242. #2012C2×C11semidirect
243. #2000C2×C11semidirect
244. #1895C2×C11semidirect
245. #1879C2×C11semidirect
246. #1870C2×C11semidirect
247. #1788C2×C11semidirect
284. C23×C11AGL(1,ℤ/8)semidirect
304. D4×C11#120semidirect
336. C23×D4C22×C11semidirect
337. C23×D4C22×C11semidirect
340. C22×SD16C22×C11semidirect
343. C22×M16C22×C11semidirect
346. C2×#124C22×C11semidirect
348. C2×C22⋊Q8C22×C11semidirect
355. C2×C4×D4C22×C11semidirect
359. C2×#103C22×C11semidirect
360. C2×#102C22×C11semidirect
361. C2×#102C22×C11semidirect
362. C2×#102C22×C11semidirect
363. C2×C22⋊C8C22×C11semidirect
364. C2×C22⋊C8C22×C11semidirect
367. #390C22×C11semidirect
368. #380C22×C11semidirect
370. #340C22×C11semidirect
371. #336C22×C11semidirect
421. C2×#41D4×C11semidirect
453. C2×D8D4×C11semidirect
467. #121D4×C11semidirect
613. C11#23861direct (N × H)
650. C23C11×AGL(1,ℤ/8)semidirect
670. D4C11×#120semidirect

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C2×C11×#5462
C2×C11×#4472
C11×#24082
C11×#20122
C11×#20002
C11×#18952
C11×#18792
C11×#18702
C11×#17882
#2386111