Finite Group Databasebeta

← C11×#24367 #14601560

Subgroups — C11×#24367 #14601560

Order 2816.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#461C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C11×#2432C211yesmaximal, characteristic, complemented
6D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2054C211yesmaximal, characteristic, complemented
9C11×#2013C211yesmaximal, characteristic, complemented
10C11×#2012C211yesmaximal, characteristic, complemented
11C11×#1894C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1877C211yesmaximal, characteristic, complemented
14C11×#1851C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)—24no—
19C2×C11×AGL(1,ℤ/8)—24no—
20C2×C11×AGL(1,ℤ/8)—24no—
21C22×C11×SD16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×D8C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic, complemented
29C2×C11×#124C2211yescharacteristic, complemented
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C22×C11×C22⋊C4—21no—
34C11×#463—24no—
35C11×#461—24no—
36C11×#450—24no—
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×C4⋊C8C2211yescharacteristic, complemented
39C2×C11×#103C2211yescharacteristic, complemented
40C2×C11×#103C2211yescharacteristic, complemented
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×C22⋊C8C2211yescharacteristic
48C11×#394—21no—
49C11×#394—21no—
50C11×#391C2211yescharacteristic, complemented
51C11×#390C2211yescharacteristic
52C11×#390C2211yescharacteristic
53C11×#390C2211yescharacteristic, complemented
54C11×#386—21no—
55C11×#386—21no—
56C11×#385—21no—
57C11×#385—21no—
58C11×#380C2211yescharacteristic
59C11×#379—21no—
60C4×C11×C22⋊C4C2211yescharacteristic
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11C2311yescharacteristic
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11—22no—
75C22×D4×C11—22no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—22no—
79C22×D4×C11—41no—
80C22×D4×C11—41no—
81C22×D4×C11D414yes—
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C11×AGL(1,ℤ/8)—232no—
90C2×C11×SD16—22no—
91C2×C11×SD16—22no—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—41no—
100C2×C11×SD16—41no—
101C2×C11×SD16D414yes—
102C2×C11×D8—22no—
103C2×C11×D8—22no—
104C2×C11×D8—22no—
105C2×C11×D8—22no—
106C2×C11×D8—22no—
107C2×C11×D8D414yes—
108C2×C11×M16—22no—
109C2×C11×M16—22no—
110C2×C11×M16—22no—
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2311yescharacteristic
115C11×C4⋊Q8—22no—
116C11×C4⋊Q8—41no—
117C11×#124—22no—
118C11×#124—41no—
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—41no—
124C4×D4×C11—41no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—44no—
144C2×C11×C22⋊C4D411yescharacteristic
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C11×C4⋊C8—22no—
149C11×C4⋊C8—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—41no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—41no—
158C11×C22⋊C8—22no—
159C11×#95—21no—
160C11×#95—21no—
161C11×#95—21no—
162C11×#95D411yescharacteristic
163C11×#95D411yescharacteristic
164#24367C1111yesmaximal, characteristic, direct product factor, Sylow
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—24no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—81no—
174C24×C11—81no—
175C24×C11C2×D411yescharacteristic
176C11×#41—28no—
177C11×#41—44no—
178C11×#41—44no—
179C11×#41—44no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11C2×D412yes—
192C2×D4×C11—28no—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—44no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11C2×D412yes—
216C2×D4×C11C2×D412yes—
217C2×D4×C11C2×D412yes—
218C2×D4×C11C2×D412yes—
219C2×D4×C11C2×D412yes—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—42no—
230C22×C4×C11—42no—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11—42no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11—81no—
237C22×C4×C11—81no—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11#4112yes—
245C22×C4×C11C2411yescharacteristic
246C11×SD16—28no—
247C11×SD16—28no—
248C11×SD16—44no—
249C11×SD16—44no—
250C11×D8—28no—
251C11×D8—28no—
252C11×M16—28no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11C2×D412yes—
264C2×C8×C11C2×D412yes—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—42no—
272C11×C4⋊C4—42no—
273C11×C4⋊C4—42no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—41no—
276C11×C22⋊C4—42no—
277C11×C22⋊C4—42no—
278C11×C22⋊C4—42no—
279C11×C22⋊C4—42no—
280C11×C22⋊C4—42no—
281C11×C22⋊C4—42no—
282C11×C22⋊C4—42no—
283C11×C22⋊C4—42no—
284C11×C22⋊C4—42no—
285C11×C22⋊C4—42no—
286C11×C22⋊C4—81no—
287C11×C22⋊C4—81no—
288C42×C11—21no—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—21no—
292C22×AGL(1,ℤ/8)C2×C1111yescharacteristic
293C2×#463C2×C1111yescharacteristic, complemented
294C2×#461C2×C1111yescharacteristic, complemented
295C2×#450C2×C1111yescharacteristic, complemented
296#2432C2×C1111yescharacteristic, complemented
297D4×C22⋊C4C2×C1111yescharacteristic, complemented
298#2055C2×C1111yescharacteristic, complemented
299#2054C2×C1111yescharacteristic, complemented
300#2013C2×C1111yescharacteristic, complemented
301#2012C2×C1111yescharacteristic, complemented
302#1894C2×C1111yescharacteristic, complemented
303#1879C2×C1111yescharacteristic, complemented
304#1877C2×C1111yescharacteristic, complemented
305#1851C2×C1111yescharacteristic, complemented
306#1788C2×C1111yescharacteristic, complemented
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—48no—
319C23×C11—48no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—84no—
337C23×C11—84no—
338C23×C11—84no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11#12112yes—
342C23×C11C22×D411yescharacteristic
343Q8×C11—22no—
344Q8×C11—22no—
345Q8×C11—41no—
346Q8×C11—41no—
347Q8×C11—41no—
348Q8×C11—41no—
349Q8×C11—41no—
350Q8×C11—41no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—48no—
359D4×C11—48no—
360D4×C11—41no—
361D4×C11—41no—
362D4×C11—41no—
363D4×C11—41no—
364D4×C11#12014yes—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—48no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—84no—
399C2×C4×C11—84no—
400C2×C4×C11#12112yes—
401C2×C4×C11AGL(1,ℤ/8)12yescomplemented
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C2×#4111yescharacteristic
406C2×C4×C11H(5,𝔽2)11yescharacteristic
407C2×C4×C11H(5,𝔽2)11yescharacteristic
408C8×C11—22no—
409C8×C11—22no—
410C8×C11—41no—
411C8×C11—41no—
412C22×#41C22×C1111yescharacteristic
413C23×D4C22×C1111yescharacteristic
414C2×AGL(1,ℤ/8)—24no—
415C2×AGL(1,ℤ/8)—24no—
416C2×AGL(1,ℤ/8)—24no—
417C22×SD16C22×C1111yescharacteristic
418C22×SD16C22×C1111yescharacteristic
419C22×SD16C22×C1111yescharacteristic
420C22×SD16C22×C1111yescharacteristic
421C22×D8C22×C1111yescharacteristic
422C22×D8C22×C1111yescharacteristic
423C22×M16C22×C1111yescharacteristic
424C2×C4⋊Q8C22×C1111yescharacteristic, complemented
425C2×#124C22×C1111yescharacteristic, complemented
426C2×C22⋊Q8C22×C1111yescharacteristic
427C2×C4×D4C22×C1111yescharacteristic
428C2×C4×D4C22×C1111yescharacteristic
429C22×C22⋊C4—21no—
430#463—24no—
431#461—24no—
432#450—24no—
433C2×C4⋊C8C22×C1111yescharacteristic, complemented
434C2×C4⋊C8C22×C1111yescharacteristic, complemented
435C2×#103C22×C1111yescharacteristic, complemented
436C2×#103C22×C1111yescharacteristic, complemented
437C2×#103C22×C1111yescharacteristic, complemented
438C2×#103C22×C1111yescharacteristic, complemented
439C2×#102C22×C1111yescharacteristic
440C2×#102C22×C1111yescharacteristic
441C2×#102C22×C1111yescharacteristic, complemented
442C2×#102C22×C1111yescharacteristic, complemented
443C2×C22⋊C8C22×C1111yescharacteristic
444#394—21no—
445#394—21no—
446#391C22×C1111yescharacteristic, complemented
447#390C22×C1111yescharacteristic
448#390C22×C1111yescharacteristic
449#390C22×C1111yescharacteristic, complemented
450#386—21no—
451#386—21no—
452#385—21no—
453#385—21no—
454#380C22×C1111yescharacteristic
455#379—21no—
456C4×C22⋊C4C22×C1111yescharacteristic
457#340C22×C1111yescharacteristic, complemented
458#340C22×C1111yescharacteristic, complemented
459#336C22×C1111yescharacteristic, complemented
460#336C22×C1111yescharacteristic, complemented
461C22×C11—22no—
462C22×C11—24no—
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—42no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—41no—
471C22×C11—41no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—816no—
482C22×C11—81no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11C2×#12111yescharacteristic
491C22×C11D4211yescharacteristic
492C22×C11D4211yescharacteristic
493C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
494C22×C11#57511yescharacteristic
495C22×C11#57711yescharacteristic
496C22×C11#57711yescharacteristic
497C4×C11—22no—
498C4×C11—22no—
499C4×C11—42no—
500C4×C11—41no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11—81no—
504C4×C11—81no—
505C4×C11—81no—
506C4×C11—81no—
507C4×C11C2×#12011yescharacteristic
508C4×C11#53411yescharacteristic
509C4×C11#54611yescharacteristic
510C4×C11#54611yescharacteristic
511C25—21no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—41no—
517C2×#41—41no—
518C22×Q8C23×C1111yescharacteristic
519C22×Q8C23×C1111yescharacteristic
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4D4×C1114yes—
528C22×D4C23×C1111yescharacteristic
529C22×D4C23×C1111yescharacteristic
530C22×D4C23×C1111yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C23×C1111yescharacteristic
535AGL(1,ℤ/8)—232no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16D4×C1114yes—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8D4×C1114yes—
554C2×M16—22no—
555C2×M16—22no—
556C2×M16—22no—
557C22×C8C23×C1111yescharacteristic
558C22×C8C23×C1111yescharacteristic
559C22×C8C23×C1111yescharacteristic
560C22×C8C23×C1111yescharacteristic
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563#124—22no—
564#124—41no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—41no—
570C4×D4—41no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4C23×C1111yescharacteristic
575C2×C4⋊C4C23×C1111yescharacteristic
576C2×C4⋊C4C23×C1111yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—44no—
590C2×C22⋊C4D4×C1111yescharacteristic
591C2×C22⋊C4D4×C1111yescharacteristic
592C2×C42C23×C1111yescharacteristic
593C2×C42C23×C1111yescharacteristic
594C4⋊C8—22no—
595C4⋊C8—22no—
596#103—22no—
597#103—22no—
598#103—22no—
599#103—41no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95D4×C1111yescharacteristic
609#95D4×C1111yescharacteristic
610C2×C11—42no—
611C2×C11—44no—
612C2×C11—82no—
613C2×C11—82no—
614C2×C11#241011yescharacteristic
615C2×C11#303611yescharacteristic
616C2×C11#304211yescharacteristic
617C2×C11#326511yescharacteristic
618C2×C11#326711yescharacteristic
619C2×C11#327211yescharacteristic
620C2×C11#327511yescharacteristic
621C24—21no—
622C24—21no—
623C24—21no—
624C24—24no—
625C24—42no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—81no—
630C24—81no—
631C24C2×D4×C1111yescharacteristic
632#41—28no—
633#41—44no—
634#41—44no—
635#41—44no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8C2×D4×C1112yes—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4C2×D4×C1112yes—
672C2×D4C2×D4×C1112yes—
673C2×D4C2×D4×C1112yes—
674C2×D4C2×D4×C1112yes—
675C2×D4C2×D4×C1112yes—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—81no—
693C22×C4—81no—
694C22×C4C2×D4×C1111yescharacteristic
695C22×C4C2×D4×C1111yescharacteristic
696C22×C4C2×D4×C1111yescharacteristic
697C22×C4C2×D4×C1111yescharacteristic
698C22×C4C2×D4×C1112yes—
699C22×C4C2×D4×C1111yescharacteristic
700C22×C4C11×#4112yes—
701C22×C4C24×C1111yescharacteristic
702SD16—28no—
703SD16—28no—
704SD16—44no—
705SD16—44no—
706D8—28no—
707D8—28no—
708M16—28no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8C2×D4×C1112yes—
720C2×C8C2×D4×C1112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—42no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C22⋊C4—22no—
731C22⋊C4—41no—
732C22⋊C4—42no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—21no—
745C42—21no—
746C42—21no—
747C42—21no—
748C11#2436711yescharacteristic, direct product factor, Sylow
749C23—22no—
750C23—22no—
751C23—22no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—22no—
760C23—48no—
761C23—48no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—84no—
779C23—84no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23C11×#12112yes—
784C23C22×D4×C1111yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4C11×#12014yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4C11×#12112yes—
843C2×C4C11×AGL(1,ℤ/8)12yescomplemented
844C2×C4C22×D4×C1111yescharacteristic
845C2×C4C22×D4×C1111yescharacteristic
846C2×C4C22×D4×C1111yescharacteristic
847C2×C4C2×C11×#4111yescharacteristic
848C2×C4C11×H(5,𝔽2)11yescharacteristic
849C2×C4C11×H(5,𝔽2)11yescharacteristic
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C22—22no—
855C22—24no—
856C22—22no—
857C22—22no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—816no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×C11×#12111yescharacteristic
884C22D42×C1111yescharacteristic
885C22D42×C1111yescharacteristic
886C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
887C22C11×#57511yescharacteristic
888C22C11×#57711yescharacteristic
889C22C11×#57711yescharacteristic
890C4—22no—
891C4—22no—
892C4—42no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×C11×#12011yescharacteristic
901C4C11×#53411yescharacteristic
902C4C11×#54611yescharacteristic
903C4C11×#54611yescharacteristic
904C2—42no—
905C2—44no—
906C2—82no—
907C2—82no—
908C2C11×#241011yescharacteristic
909C2C11×#303611yescharacteristic
910C2C11×#304211yescharacteristic
911C2C11×#326511yescharacteristic
912C2C11×#326711yescharacteristic
913C2C11×#327211yescharacteristic
914C2C11×#327511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×AGL(1,ℤ/8)C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#463C2semidirect
3. C2×C11×#461C2semidirect
4. C2×C11×#450C2semidirect
5. C11×#2432C2semidirect
6. D4×C11×C22⋊C4C2semidirect
7. C11×#2055C2semidirect
8. C11×#2054C2semidirect
9. C11×#2013C2semidirect
10. C11×#2012C2semidirect
11. C11×#1894C2semidirect
12. C11×#1879C2semidirect
13. C11×#1877C2semidirect
14. C11×#1851C2semidirect
15. C11×#1788C2semidirect
28. C2×C11×C4⋊Q8C22semidirect
29. C2×C11×#124C22semidirect
37. C2×C11×C4⋊C8C22semidirect
38. C2×C11×C4⋊C8C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#103C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#103C22semidirect
45. C2×C11×#102C22semidirect
46. C2×C11×#102C22semidirect
50. C11×#391C22semidirect
53. C11×#390C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
164. #24367C11direct (N × H)
293. C2×#463C2×C11semidirect
294. C2×#461C2×C11semidirect
295. C2×#450C2×C11semidirect
296. #2432C2×C11semidirect
297. D4×C22⋊C4C2×C11semidirect
298. #2055C2×C11semidirect
299. #2054C2×C11semidirect
300. #2013C2×C11semidirect
301. #2012C2×C11semidirect
302. #1894C2×C11semidirect
303. #1879C2×C11semidirect
304. #1877C2×C11semidirect
305. #1851C2×C11semidirect
306. #1788C2×C11semidirect
401. C2×C4×C11AGL(1,ℤ/8)semidirect
424. C2×C4⋊Q8C22×C11semidirect
425. C2×#124C22×C11semidirect
433. C2×C4⋊C8C22×C11semidirect
434. C2×C4⋊C8C22×C11semidirect
435. C2×#103C22×C11semidirect
436. C2×#103C22×C11semidirect
437. C2×#103C22×C11semidirect
438. C2×#103C22×C11semidirect
441. C2×#102C22×C11semidirect
442. C2×#102C22×C11semidirect
446. #391C22×C11semidirect
449. #390C22×C11semidirect
457. #340C22×C11semidirect
458. #340C22×C11semidirect
459. #336C22×C11semidirect
460. #336C22×C11semidirect
748. C11#24367direct (N × H)
843. C2×C4C11×AGL(1,ℤ/8)semidirect

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×#4632
C2×C11×#4612
C2×C11×#4502
C11×#24322
D4×C11×C22⋊C42
C11×#20552
C11×#20542
C11×#20132
C11×#20122
C11×#18942
C11×#18792
C11×#18772
C11×#18512
C11×#17882
#2436711