Finite Group Databasebeta

← C11×#24366 #14601559

Subgroups — C11×#24366 #14601559

Order 2816.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 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×#463C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C11×#2431C211yesmaximal, characteristic, complemented
6D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2054C211yesmaximal, characteristic, complemented
9C11×#2012C211yesmaximal, characteristic, complemented
10C11×#2011C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, 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×D8C2211yescharacteristic
24C22×C11×D8C2211yescharacteristic
25C22×C11×D8C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic, complemented
29C2×C11×#124C2211yescharacteristic, complemented
30C2×C11×#121C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C22×C11×C22⋊C4—21no—
34C11×#463—24no—
35C11×#459—24no—
36C11×#447—24no—
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×C4⋊C8C2211yescharacteristic, complemented
39C2×C11×#103C2211yescharacteristic, complemented
40C2×C11×#103C2211yescharacteristic, complemented
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic, complemented
44C2×C11×#102C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×C22⋊C8C2211yescharacteristic
48C11×#392—21no—
49C11×#392—21no—
50C11×#391C2211yescharacteristic, complemented
51C11×#390C2211yescharacteristic
52C11×#390C2211yescharacteristic
53C11×#390C2211yescharacteristic, complemented
54C11×#386—21no—
55C11×#386—21no—
56C11×#386—21no—
57C11×#386—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×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—22no—
81C22×D4×C11—41no—
82C22×D4×C11—41no—
83C22×D4×C11D414yescomplemented
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C11×AGL(1,ℤ/8)—232no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16D414yescomplemented
99C2×C11×D8—22no—
100C2×C11×D8—22no—
101C2×C11×D8—22no—
102C2×C11×D8—22no—
103C2×C11×D8—22no—
104C2×C11×D8—22no—
105C2×C11×D8—22no—
106C2×C11×D8—22no—
107C2×C11×D8—22no—
108C2×C11×D8—41no—
109C2×C11×D8—41no—
110C2×C11×D8D414yescomplemented
111C2×C11×M16—22no—
112C2×C11×M16—22no—
113C2×C11×M16—22no—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C22×C8×C11C2311yescharacteristic
118C11×#127—22no—
119C11×#127—41no—
120C11×#124—22no—
121C11×#124—41no—
122C11×#121—22no—
123C11×#121—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—41no—
127C4×D4×C11—41no—
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—41no—
152C11×#102—22no—
153C11×#102—22no—
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#24366C1111yesmaximal, characteristic, direct product factor, Sylow
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—24no—
169C24×C11—21no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11C2×D411yescharacteristic
177C11×#41—28no—
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11C2×D412yes—
187C2×D4×C11—28no—
188C2×D4×C11—24no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
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—21no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11—44no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—42no—
221C2×D4×C11—81no—
222C2×D4×C11—81no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11C2×D412yes—
226C2×D4×C11C2×D412yes—
227C2×D4×C11C2×D412yes—
228C2×D4×C11C2×D412yes—
229C2×D4×C11C2×D412yes—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—42no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11—81no—
246C22×C4×C11—81no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11#4112yes—
254C22×C4×C11C2411yescharacteristic
255C11×SD16—28no—
256C11×SD16—28no—
257C11×D8—28no—
258C11×D8—28no—
259C11×D8—44no—
260C11×D8—44no—
261C11×M16—28no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11C2×D412yes—
273C2×C8×C11C2×D412yes—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—41no—
282C11×C22⋊C4—42no—
283C11×C22⋊C4—42no—
284C11×C22⋊C4—42no—
285C11×C22⋊C4—42no—
286C11×C22⋊C4—42no—
287C11×C22⋊C4—42no—
288C11×C22⋊C4—42no—
289C11×C22⋊C4—42no—
290C11×C22⋊C4—81no—
291C11×C22⋊C4—81no—
292C11×C22⋊C4—81no—
293C11×C22⋊C4—81no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11—21no—
298C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
299C2×#463C2×C1111yescharacteristic, complemented
300C2×#459C2×C1111yescharacteristic, complemented
301C2×#447C2×C1111yescharacteristic, complemented
302#2431C2×C1111yescharacteristic, complemented
303D4×C22⋊C4C2×C1111yescharacteristic, complemented
304#2055C2×C1111yescharacteristic, complemented
305#2054C2×C1111yescharacteristic, complemented
306#2012C2×C1111yescharacteristic, complemented
307#2011C2×C1111yescharacteristic, complemented
308#1895C2×C1111yescharacteristic, complemented
309#1879C2×C1111yescharacteristic, complemented
310#1877C2×C1111yescharacteristic, complemented
311#1851C2×C1111yescharacteristic, complemented
312#1788C2×C1111yescharacteristic, complemented
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—48no—
325C23×C11—48no—
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—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—84no—
350C23×C11—84no—
351C23×C11—84no—
352C23×C11—84no—
353C23×C11—84no—
354C23×C11#12112yes—
355C23×C11C22×D411yescharacteristic
356Q8×C11—22no—
357Q8×C11—22no—
358Q8×C11—41no—
359Q8×C11—41no—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—48no—
368D4×C11—48no—
369D4×C11—41no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—84no—
378D4×C11—84no—
379D4×C11—84no—
380D4×C11#12014yes—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—22no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—48no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—84no—
412C2×C4×C11—84no—
413C2×C4×C11#12112yes—
414C2×C4×C11AGL(1,ℤ/8)12yescomplemented
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C2×#4111yescharacteristic
419C2×C4×C11H(5,𝔽2)11yescharacteristic
420C2×C4×C11H(5,𝔽2)11yescharacteristic
421C8×C11—22no—
422C8×C11—22no—
423C8×C11—41no—
424C8×C11—41no—
425C22×#41C22×C1111yescharacteristic
426C23×D4C22×C1111yescharacteristic
427C2×AGL(1,ℤ/8)—24no—
428C2×AGL(1,ℤ/8)—24no—
429C2×AGL(1,ℤ/8)—24no—
430C22×SD16C22×C1111yescharacteristic
431C22×SD16C22×C1111yescharacteristic
432C22×D8C22×C1111yescharacteristic
433C22×D8C22×C1111yescharacteristic
434C22×D8C22×C1111yescharacteristic
435C22×D8C22×C1111yescharacteristic
436C22×M16C22×C1111yescharacteristic
437C2×#127C22×C1111yescharacteristic, complemented
438C2×#124C22×C1111yescharacteristic, complemented
439C2×#121C22×C1111yescharacteristic
440C2×C4×D4C22×C1111yescharacteristic
441C2×C4×D4C22×C1111yescharacteristic
442C22×C22⋊C4—21no—
443#463—24no—
444#459—24no—
445#447—24no—
446C2×C4⋊C8C22×C1111yescharacteristic, complemented
447C2×C4⋊C8C22×C1111yescharacteristic, complemented
448C2×#103C22×C1111yescharacteristic, complemented
449C2×#103C22×C1111yescharacteristic, complemented
450C2×#102C22×C1111yescharacteristic
451C2×#102C22×C1111yescharacteristic
452C2×#102C22×C1111yescharacteristic, complemented
453C2×#102C22×C1111yescharacteristic, complemented
454C2×#102C22×C1111yescharacteristic, complemented
455C2×#102C22×C1111yescharacteristic, complemented
456C2×C22⋊C8C22×C1111yescharacteristic
457#392—21no—
458#392—21no—
459#391C22×C1111yescharacteristic, complemented
460#390C22×C1111yescharacteristic
461#390C22×C1111yescharacteristic
462#390C22×C1111yescharacteristic, complemented
463#386—21no—
464#386—21no—
465#386—21no—
466#386—21no—
467#380C22×C1111yescharacteristic
468#379—21no—
469C4×C22⋊C4C22×C1111yescharacteristic
470#340C22×C1111yescharacteristic, complemented
471#340C22×C1111yescharacteristic, complemented
472#336C22×C1111yescharacteristic, complemented
473#336C22×C1111yescharacteristic, complemented
474C22×C11—22no—
475C22×C11—24no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—42no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—42no—
482C22×C11—41no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—41no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—816no—
495C22×C11—81no—
496C22×C11—81no—
497C22×C11—81no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—81no—
502C22×C11—81no—
503C22×C11—81no—
504C22×C11—81no—
505C22×C11—81no—
506C22×C11—81no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11—81no—
510C22×C11C2×#12111yescharacteristic
511C22×C11D4211yescharacteristic
512C22×C11D4211yescharacteristic
513C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
514C22×C11#57511yescharacteristic
515C22×C11#57611yescharacteristic
516C22×C11#57611yescharacteristic
517C4×C11—22no—
518C4×C11—22no—
519C4×C11—42no—
520C4×C11—41no—
521C4×C11—41no—
522C4×C11—41no—
523C4×C11—81no—
524C4×C11—81no—
525C4×C11—81no—
526C4×C11C2×#12011yescharacteristic
527C4×C11#53411yescharacteristic
528C4×C11#54611yescharacteristic
529C4×C11#54611yescharacteristic
530C25—21no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C1111yescharacteristic
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—22no—
546C22×D4—41no—
547C22×D4—41no—
548C22×D4D4×C1114yescomplemented
549C22×D4C23×C1111yescharacteristic
550C22×D4C23×C1111yescharacteristic
551C22×D4C23×C1111yescharacteristic
552C22×D4C23×C1111yescharacteristic
553C23×C4—21no—
554C23×C4—21no—
555C23×C4—21no—
556C23×C4C23×C1111yescharacteristic
557AGL(1,ℤ/8)—232no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16D4×C1114yescomplemented
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—22no—
569C2×D8—22no—
570C2×D8—22no—
571C2×D8—22no—
572C2×D8—22no—
573C2×D8—41no—
574C2×D8—41no—
575C2×D8D4×C1114yescomplemented
576C2×M16—22no—
577C2×M16—22no—
578C2×M16—22no—
579C22×C8C23×C1111yescharacteristic
580C22×C8C23×C1111yescharacteristic
581C22×C8C23×C1111yescharacteristic
582C22×C8C23×C1111yescharacteristic
583#127—22no—
584#127—41no—
585#124—22no—
586#124—41no—
587#121—22no—
588#121—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—41no—
592C4×D4—41no—
593C2×C4⋊C4C23×C1111yescharacteristic
594C2×C4⋊C4C23×C1111yescharacteristic
595C2×C4⋊C4C23×C1111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—44no—
609C2×C22⋊C4D4×C1111yescharacteristic
610C2×C22⋊C4D4×C1111yescharacteristic
611C2×C42C23×C1111yescharacteristic
612C2×C42C23×C1111yescharacteristic
613C4⋊C8—22no—
614C4⋊C8—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—22no—
622#102—41no—
623C22⋊C8—22no—
624#95—21no—
625#95—21no—
626#95—21no—
627#95D4×C1111yescharacteristic
628#95D4×C1111yescharacteristic
629C2×C11—42no—
630C2×C11—44no—
631C2×C11—82no—
632C2×C11—82no—
633C2×C11—161no—
634C2×C11#241011yescharacteristic
635C2×C11#303611yescharacteristic
636C2×C11#304111yescharacteristic
637C2×C11#326411yescharacteristic
638C2×C11#326811yescharacteristic
639C2×C11#327311yescharacteristic
640C2×C11#327411yescharacteristic
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—21no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—81no—
651C24—81no—
652C24C2×D4×C1111yescharacteristic
653#41—28no—
654#41—44no—
655#41—44no—
656#41—44no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C1112yes—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4C2×D4×C1112yes—
702C2×D4C2×D4×C1112yes—
703C2×D4C2×D4×C1112yes—
704C2×D4C2×D4×C1112yes—
705C2×D4C2×D4×C1112yes—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—81no—
722C22×C4—81no—
723C22×C4C2×D4×C1111yescharacteristic
724C22×C4C2×D4×C1111yescharacteristic
725C22×C4C2×D4×C1111yescharacteristic
726C22×C4C2×D4×C1111yescharacteristic
727C22×C4C2×D4×C1112yes—
728C22×C4C2×D4×C1111yescharacteristic
729C22×C4C11×#4112yes—
730C22×C4C24×C1111yescharacteristic
731SD16—28no—
732SD16—28no—
733D8—28no—
734D8—28no—
735D8—44no—
736D8—44no—
737M16—28no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8C2×D4×C1112yes—
749C2×C8C2×D4×C1112yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C22⋊C4—22no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—21no—
774C11#2436611yescharacteristic, direct product factor, Sylow
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23C11×#12112yes—
817C23C22×D4×C1111yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4C11×#12014yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4—84no—
875C2×C4C11×#12112yes—
876C2×C4C11×AGL(1,ℤ/8)12yescomplemented
877C2×C4C22×D4×C1111yescharacteristic
878C2×C4C22×D4×C1111yescharacteristic
879C2×C4C22×D4×C1111yescharacteristic
880C2×C4C2×C11×#4111yescharacteristic
881C2×C4C11×H(5,𝔽2)11yescharacteristic
882C2×C4C11×H(5,𝔽2)11yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—24no—
889C22—22no—
890C22—22no—
891C22—42no—
892C22—41no—
893C22—41no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×C11×#12111yescharacteristic
924C22D42×C1111yescharacteristic
925C22D42×C1111yescharacteristic
926C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
927C22C11×#57511yescharacteristic
928C22C11×#57611yescharacteristic
929C22C11×#57611yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×C11×#12011yescharacteristic
940C4C11×#53411yescharacteristic
941C4C11×#54611yescharacteristic
942C4C11×#54611yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2C11×#241011yescharacteristic
949C2C11×#303611yescharacteristic
950C2C11×#304111yescharacteristic
951C2C11×#326411yescharacteristic
952C2C11×#326811yescharacteristic
953C2C11×#327311yescharacteristic
954C2C11×#327411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C11×#459C2semidirect
4. C2×C11×#447C2semidirect
5. C11×#2431C2semidirect
6. D4×C11×C22⋊C4C2semidirect
7. C11×#2055C2semidirect
8. C11×#2054C2semidirect
9. C11×#2012C2semidirect
10. C11×#2011C2semidirect
11. C11×#1895C2semidirect
12. C11×#1879C2semidirect
13. C11×#1877C2semidirect
14. C11×#1851C2semidirect
15. C11×#1788C2semidirect
28. C2×C11×#127C22semidirect
29. C2×C11×#124C22semidirect
37. C2×C11×C4⋊C8C22semidirect
38. C2×C11×C4⋊C8C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#103C22semidirect
43. C2×C11×#102C22semidirect
44. C2×C11×#102C22semidirect
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
83. C22×D4×C11D4semidirect
98. C2×C11×SD16D4semidirect
110. C2×C11×D8D4semidirect
164. #24366C11direct (N × H)
298. C22×AGL(1,ℤ/8)C2×C11semidirect
299. C2×#463C2×C11semidirect
300. C2×#459C2×C11semidirect
301. C2×#447C2×C11semidirect
302. #2431C2×C11semidirect
303. D4×C22⋊C4C2×C11semidirect
304. #2055C2×C11semidirect
305. #2054C2×C11semidirect
306. #2012C2×C11semidirect
307. #2011C2×C11semidirect
308. #1895C2×C11semidirect
309. #1879C2×C11semidirect
310. #1877C2×C11semidirect
311. #1851C2×C11semidirect
312. #1788C2×C11semidirect
414. C2×C4×C11AGL(1,ℤ/8)semidirect
437. C2×#127C22×C11semidirect
438. C2×#124C22×C11semidirect
446. C2×C4⋊C8C22×C11semidirect
447. C2×C4⋊C8C22×C11semidirect
448. C2×#103C22×C11semidirect
449. C2×#103C22×C11semidirect
452. C2×#102C22×C11semidirect
453. C2×#102C22×C11semidirect
454. C2×#102C22×C11semidirect
455. C2×#102C22×C11semidirect
459. #391C22×C11semidirect
462. #390C22×C11semidirect
470. #340C22×C11semidirect
471. #340C22×C11semidirect
472. #336C22×C11semidirect
473. #336C22×C11semidirect
548. C22×D4D4×C11semidirect
563. C2×SD16D4×C11semidirect
575. C2×D8D4×C11semidirect
774. C11#24366direct (N × H)
876. 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×#4592
C2×C11×#4472
C11×#24312
D4×C11×C22⋊C42
C11×#20552
C11×#20542
C11×#20122
C11×#20112
C11×#18952
C11×#18792
C11×#18772
C11×#18512
C11×#17882
#2436611