Finite Group Databasebeta

← C11×#60558 #14637751

Subgroups — C11×#60558 #14637751

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3444C211yesmaximal, characteristic, complemented
2C22×C4×D4×C11C211yesmaximal, characteristic, complemented
3C11×#3114C214yesmaximal, complemented
4C11×#3110C212yesmaximal, complemented
5C11×#3109C212yesmaximal, complemented
6C11×#3105C214yesmaximal, complemented
7C11×#3101C212yesmaximal, complemented
8C11×#3100C212yesmaximal, complemented
9C11×#3092C212yesmaximal, complemented
10C11×#3077C212yesmaximal, complemented
11C11×#3036C212yesmaximal, complemented
12C11×#3003C212yesmaximal, complemented
13C4×C11×AGL(1,ℤ/8)C214yesmaximal, complemented
14C11×#2920C211yesmaximal, characteristic, complemented
15C23×D4×C11C2211yescharacteristic
16C24×C4×C11—21no—
17C2×C11×AGL(1,ℤ/8)C2214yes—
18C11×#533C2211yescharacteristic, complemented
19C11×#533C2211yescharacteristic, complemented
20C11×#533C2211yescharacteristic, complemented
21C11×#532C2211yescharacteristic, complemented
22C11×#532C2211yescharacteristic, complemented
23C11×#532C2211yescharacteristic, complemented
24C11×#529—21no—
25C11×#529—21no—
26C11×#529—21no—
27C11×#529—21no—
28C11×#529C2212yescomplemented
29C11×#529C2212yescomplemented
30C11×#525—21no—
31C11×#525—21no—
32C11×#525C2212yes—
33C4×C11×#41—21no—
34C4×C11×#41—21no—
35C4×C11×#41C2212yescomplemented
36C2×C4×D4×C11—21no—
37C2×C4×D4×C11—21no—
38C2×C4×D4×C11—21no—
39C2×C4×D4×C11—21no—
40C2×C4×D4×C11—21no—
41C2×C4×D4×C11—21no—
42C2×C4×D4×C11C2212yes—
43C2×C4×D4×C11C2212yes—
44C2×C4×D4×C11C2212yes—
45C2×C4×D4×C11C2212yes—
46C2×C4×D4×C11C2212yes—
47C2×C4×D4×C11C2212yes—
48C22×C11×C4⋊C4C2211yescharacteristic
49C22×C11×C22⋊C4—21no—
50C22×C42×C11C2211yescharacteristic
51C11×#484C2214yescomplemented
52C11×#483C2214yescomplemented
53C11×#481C2214yescomplemented
54C11×#480C2214yescomplemented
55C11×#478C2218yescomplemented
56C11×#476C2214yescomplemented
57C11×#474C2214yescomplemented
58C11×#463C2218yescomplemented
59C11×#461C2214yescomplemented
60C11×#459C2214yescomplemented
61C11×#450C2214yes—
62C11×#450C2214yes—
63C11×#447C2214yes—
64C11×#447C2214yes—
65C11×#442C2218yescomplemented
66C11×#440C2218yescomplemented
67C4×C11×SD16C2218yescomplemented
68C4×C11×D8C2218yescomplemented
69C11×#432C2212yescomplemented
70C11×#432C2212yescomplemented
71C11×#431C2212yescomplemented
72C11×#431C2212yescomplemented
73C11×#428C2214yescomplemented
74C11×#423C2212yescomplemented
75C11×#418C2214yes—
76C11×#417C2214yescomplemented
77C11×#407C2212yes—
78C4×C11×M16C2212yescomplemented
79C25×C11—21no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41C2312yes—
83C22×D4×C11—28no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11C2312yes—
88C22×D4×C11C2312yes—
89C22×D4×C11C2312yes—
90C23×C4×C11—21no—
91C23×C4×C11—22no—
92C23×C4×C11—22no—
93C23×C4×C11—22no—
94C23×C4×C11—22no—
95C23×C4×C11—22no—
96C23×C4×C11—22no—
97C23×C4×C11—48no—
98C23×C4×C11D411yescharacteristic
99C23×C4×C11D411yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C11×AGL(1,ℤ/8)—216no—
102C2×C11×SD16C2318yes—
103C2×C11×D8C2318yes—
104C2×C11×M16C2314yes—
105C11×C4⋊Q8C2311yescharacteristic, complemented
106C11×C4⋊Q8C2311yescharacteristic, complemented
107C11×C4⋊Q8C2311yescharacteristic, complemented
108C11×#127C2311yescharacteristic, complemented
109C11×#126—22no—
110C11×#126—22no—
111C11×#125—21no—
112C11×#125—21no—
113C11×#125C2312yescomplemented
114C11×#124—21no—
115C11×#124—21no—
116C11×#124C2312yescomplemented
117C11×#123—22no—
118C11×#123—22no—
119C11×#123—22no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8C2312yes—
125C11×C22⋊Q8C2312yes—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121—21no—
130C11×#121C2312yes—
131C11×#121C2312yes—
132C11×#120—22no—
133C4×Q8×C11—21no—
134C4×Q8×C11—21no—
135C4×Q8×C11—21no—
136C4×Q8×C11—21no—
137C4×Q8×C11C2312yescomplemented
138C4×Q8×C11C2312yescomplemented
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11—22no—
149C4×D4×C11—22no—
150C4×D4×C11—22no—
151C4×D4×C11—22no—
152C4×D4×C11—22no—
153C4×D4×C11—22no—
154C4×D4×C11—22no—
155C4×D4×C11—22no—
156C4×D4×C11—22no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11—21no—
160C4×D4×C11—21no—
161C4×D4×C11C2314yes—
162C4×D4×C11C2314yes—
163C4×D4×C11C2314yes—
164C4×D4×C11C2314yes—
165C4×D4×C11C2312yescomplemented
166C4×D4×C11C2312yescomplemented
167C11×#117—21no—
168C11×#117—21no—
169C11×#117—22no—
170C11×#117—22no—
171C11×#117—22no—
172C11×#117C2312yes—
173C2×C11×C4⋊C4—21no—
174C2×C11×C4⋊C4—21no—
175C2×C11×C4⋊C4—21no—
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C22⋊C4—22no—
180C2×C11×C22⋊C4—22no—
181C2×C11×C22⋊C4—22no—
182C2×C11×C22⋊C4—22no—
183C2×C11×C22⋊C4—22no—
184C2×C11×C22⋊C4—22no—
185C2×C42×C11—22no—
186C2×C42×C11D411yescharacteristic
187C2×C42×C11D411yescharacteristic
188C2×C42×C11D411yescharacteristic
189C2×C42×C11D411yescharacteristic
190C2×C42×C11D411yescharacteristic
191C2×C42×C11D411yescharacteristic
192C2×C42×C11C2311yescharacteristic
193C2×C42×C11C2311yescharacteristic
194C2×C42×C11C2311yescharacteristic
195C2×C42×C11C2311yescharacteristic
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2311yescharacteristic
198C11×#107C2318yescomplemented
199C11×#106C2318yescomplemented
200C11×C4⋊C8C2314yescomplemented
201C11×C4⋊C8C2314yescomplemented
202C11×#103C2318yescomplemented
203C11×#102C2318yes—
204C11×#102C2318yes—
205C11×#102C2318yescomplemented
206C11×C22⋊C8C2314yes—
207C11×C22⋊C8C2314yes—
208C11×#97C2314yescomplemented
209C4×C8×C11C2314yescomplemented
210#60558C1111yesmaximal, characteristic, direct product factor, Sylow
211C24×C11—28no—
212C24×C11—22no—
213C24×C11—22no—
214C24×C11—22no—
215C24×C11—44no—
216C24×C11—44no—
217C24×C11C2×D411yescharacteristic
218C11×#41—28no—
219C11×#41—44no—
220C11×#41—44no—
221C2×Q8×C11—21no—
222C2×Q8×C11—21no—
223C2×Q8×C11C2412yes—
224C2×D4×C11—28no—
225C2×D4×C11—28no—
226C2×D4×C11—28no—
227C2×D4×C11—28no—
228C2×D4×C11—28no—
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—22no—
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—24no—
238C2×D4×C11#4118yescomplemented
239C2×D4×C11C2412yes—
240C2×D4×C11C2414yes—
241C22×C4×C11—24no—
242C22×C4×C11—24no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—24no—
249C22×C4×C11—24no—
250C22×C4×C11—24no—
251C22×C4×C11—22no—
252C22×C4×C11—24no—
253C22×C4×C11—42no—
254C22×C4×C11—48no—
255C22×C4×C11—48no—
256C22×C4×C11—48no—
257C22×C4×C11—48no—
258C22×C4×C11—48no—
259C22×C4×C11—44no—
260C22×C4×C11—48no—
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C11×SD16—216no—
280C11×D8—216no—
281C11×M16—28no—
282C2×C8×C11C2418yes—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4C2412yes—
297C11×C4⋊C4C2412yes—
298C11×C4⋊C4C2414yes—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4—24no—
305C11×C22⋊C4—24no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11—22no—
315C42×C11C2×D411yescharacteristic
316C42×C11C2×D411yescharacteristic
317C42×C11C2×D411yescharacteristic
318C42×C11C2×D411yescharacteristic
319C42×C11C2×D411yescharacteristic
320C42×C11C2×D411yescharacteristic
321C42×C11C2×D411yescharacteristic
322C42×C11C2×D411yescharacteristic
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D411yescharacteristic
326C42×C11C2×D411yescharacteristic
327C42×C11C2411yescharacteristic
328C42×C11C2411yescharacteristic
329C42×C11C2411yescharacteristic
330C42×C11C2411yescharacteristic
331#3444C2×C1111yescharacteristic, complemented
332C22×C4×D4C2×C1111yescharacteristic, complemented
333#3114C2×C1114yescomplemented
334#3110C2×C1112yescomplemented
335#3109C2×C1112yescomplemented
336#3105C2×C1114yescomplemented
337#3101C2×C1112yescomplemented
338#3100C2×C1112yescomplemented
339#3092C2×C1112yescomplemented
340#3077C2×C1112yescomplemented
341#3036C2×C1112yescomplemented
342#3003C2×C1112yescomplemented
343C4×AGL(1,ℤ/8)C2×C1114yescomplemented
344#2920C2×C1111yescharacteristic, complemented
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—28no—
349C23×C11—28no—
350C23×C11—28no—
351C23×C11—24no—
352C23×C11—22no—
353C23×C11—44no—
354C23×C11—44no—
355C23×C11—432no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11C22×D411yescharacteristic
361C23×C11C22×D411yescharacteristic
362C23×C11C22×D411yescharacteristic
363Q8×C11—24no—
364Q8×C11—42no—
365Q8×C11—42no—
366D4×C11—28no—
367D4×C11—28no—
368D4×C11—28no—
369D4×C11—24no—
370D4×C11—24no—
371D4×C11—42no—
372D4×C11—44no—
373D4×C11—44no—
374D4×C11—44no—
375D4×C11—42no—
376D4×C11C2×#4118yes—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—48no—
398C2×C4×C11—48no—
399C2×C4×C11—44no—
400C2×C4×C11—44no—
401C2×C4×C11—44no—
402C2×C4×C11—44no—
403C2×C4×C11—44no—
404C2×C4×C11—48no—
405C2×C4×C11—48no—
406C2×C4×C11—44no—
407C2×C4×C11AGL(1,ℤ/8)14yescomplemented
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C2×#4114yes—
420C2×C4×C11C2511yescharacteristic
421C8×C11—28no—
422C23×D4C22×C1111yescharacteristic
423C24×C4—21no—
424C2×AGL(1,ℤ/8)C22×C1114yes—
425#533C22×C1111yescharacteristic, complemented
426#533C22×C1111yescharacteristic, complemented
427#533C22×C1111yescharacteristic, complemented
428#532C22×C1111yescharacteristic, complemented
429#532C22×C1111yescharacteristic, complemented
430#532C22×C1111yescharacteristic, complemented
431#529—21no—
432#529—21no—
433#529—21no—
434#529—21no—
435#529C22×C1112yescomplemented
436#529C22×C1112yescomplemented
437#525—21no—
438#525—21no—
439#525C22×C1112yes—
440C4×#41—21no—
441C4×#41—21no—
442C4×#41C22×C1112yescomplemented
443C2×C4×D4—21no—
444C2×C4×D4—21no—
445C2×C4×D4—21no—
446C2×C4×D4—21no—
447C2×C4×D4—21no—
448C2×C4×D4—21no—
449C2×C4×D4C22×C1112yes—
450C2×C4×D4C22×C1112yes—
451C2×C4×D4C22×C1112yes—
452C2×C4×D4C22×C1112yes—
453C2×C4×D4C22×C1112yes—
454C2×C4×D4C22×C1112yes—
455C22×C4⋊C4C22×C1111yescharacteristic
456C22×C22⋊C4—21no—
457C22×C42C22×C1111yescharacteristic
458#484C22×C1114yescomplemented
459#483C22×C1114yescomplemented
460#481C22×C1114yescomplemented
461#480C22×C1114yescomplemented
462#478C22×C1118yescomplemented
463#476C22×C1114yescomplemented
464#474C22×C1114yescomplemented
465#463C22×C1118yescomplemented
466#461C22×C1114yescomplemented
467#459C22×C1114yescomplemented
468#450C22×C1114yes—
469#450C22×C1114yes—
470#447C22×C1114yes—
471#447C22×C1114yes—
472#442C22×C1118yescomplemented
473#440C22×C1118yescomplemented
474C4×SD16C22×C1118yescomplemented
475C4×D8C22×C1118yescomplemented
476#432C22×C1112yescomplemented
477#432C22×C1112yescomplemented
478#431C22×C1112yescomplemented
479#431C22×C1112yescomplemented
480#428C22×C1114yescomplemented
481#423C22×C1112yescomplemented
482#418C22×C1114yes—
483#417C22×C1114yescomplemented
484#407C22×C1112yes—
485C4×M16C22×C1112yescomplemented
486C22×C11—28no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—28no—
494C22×C11—416no—
495C22×C11—416no—
496C22×C11—416no—
497C22×C11—44no—
498C22×C11—44no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11#52512yes—
503C22×C11C2×AGL(1,ℤ/8)12yes—
504C22×C11#57512yes—
505C22×C11C23×D411yescharacteristic
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—42no—
515C4×C11—44no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11#52512yes—
519C4×C11C2×AGL(1,ℤ/8)12yes—
520C4×C11C2×AGL(1,ℤ/8)12yes—
521C4×C11C22×#4112yes—
522C25—21no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41C23×C1112yes—
526C22×D4—28no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4C23×C1112yes—
531C22×D4C23×C1112yes—
532C22×D4C23×C1112yes—
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—22no—
539C23×C4—22no—
540C23×C4—48no—
541C23×C4D4×C1111yescharacteristic
542C23×C4D4×C1111yescharacteristic
543C23×C4C23×C1111yescharacteristic
544AGL(1,ℤ/8)—216no—
545C2×SD16C23×C1118yes—
546C2×D8C23×C1118yes—
547C2×M16C23×C1114yes—
548C4⋊Q8C23×C1111yescharacteristic, complemented
549C4⋊Q8C23×C1111yescharacteristic, complemented
550C4⋊Q8C23×C1111yescharacteristic, complemented
551#127C23×C1111yescharacteristic, complemented
552#126—22no—
553#126—22no—
554#125—21no—
555#125—21no—
556#125C23×C1112yescomplemented
557#124—21no—
558#124—21no—
559#124C23×C1112yescomplemented
560#123—22no—
561#123—22no—
562#123—22no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8C23×C1112yes—
568C22⋊Q8C23×C1112yes—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121C23×C1112yes—
574#121C23×C1112yes—
575#120—22no—
576C4×Q8—21no—
577C4×Q8—21no—
578C4×Q8—21no—
579C4×Q8—21no—
580C4×Q8C23×C1112yescomplemented
581C4×Q8C23×C1112yescomplemented
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4C23×C1114yes—
605C4×D4C23×C1114yes—
606C4×D4C23×C1114yes—
607C4×D4C23×C1114yes—
608C4×D4C23×C1112yescomplemented
609C4×D4C23×C1112yescomplemented
610#117—21no—
611#117—21no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117C23×C1112yes—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C1112yes—
620C2×C4⋊C4C23×C1112yes—
621C2×C4⋊C4C23×C1112yes—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C42—22no—
629C2×C42D4×C1111yescharacteristic
630C2×C42D4×C1111yescharacteristic
631C2×C42D4×C1111yescharacteristic
632C2×C42D4×C1111yescharacteristic
633C2×C42D4×C1111yescharacteristic
634C2×C42D4×C1111yescharacteristic
635C2×C42C23×C1111yescharacteristic
636C2×C42C23×C1111yescharacteristic
637C2×C42C23×C1111yescharacteristic
638C2×C42C23×C1111yescharacteristic
639C2×C42C23×C1111yescharacteristic
640C2×C42C23×C1111yescharacteristic
641#107C23×C1118yescomplemented
642#106C23×C1118yescomplemented
643C4⋊C8C23×C1114yescomplemented
644C4⋊C8C23×C1114yescomplemented
645#103C23×C1118yescomplemented
646#102C23×C1118yes—
647#102C23×C1118yes—
648#102C23×C1118yescomplemented
649C22⋊C8C23×C1114yes—
650C22⋊C8C23×C1114yes—
651#97C23×C1114yescomplemented
652C4×C8C23×C1114yescomplemented
653C2×C11—22no—
654C2×C11—22no—
655C2×C11—22no—
656C2×C11—48no—
657C2×C11—82no—
658C2×C11C2×#52511yescharacteristic
659C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
660C2×C11C2×#57511yescharacteristic
661C24—28no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—44no—
666C24—44no—
667C24C2×D4×C1111yescharacteristic
668#41—28no—
669#41—44no—
670#41—44no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8C24×C1112yes—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
688C2×D4C11×#4118yescomplemented
689C2×D4C24×C1112yes—
690C2×D4C24×C1114yes—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—42no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—44no—
710C22×C4—48no—
711C22×C4C2×D4×C1111yescharacteristic
712C22×C4C2×D4×C1111yescharacteristic
713C22×C4C2×D4×C1111yescharacteristic
714C22×C4C2×D4×C1111yescharacteristic
715C22×C4C2×D4×C1111yescharacteristic
716C22×C4C2×D4×C1111yescharacteristic
717C22×C4C2×D4×C1111yescharacteristic
718C22×C4C2×D4×C1111yescharacteristic
719C22×C4C2×D4×C1111yescharacteristic
720C22×C4C2×D4×C1111yescharacteristic
721C22×C4C2×D4×C1111yescharacteristic
722C22×C4C2×D4×C1111yescharacteristic
723C22×C4C2×D4×C1111yescharacteristic
724C22×C4C2×D4×C1111yescharacteristic
725C22×C4C2×D4×C1111yescharacteristic
726C22×C4C24×C1111yescharacteristic
727C22×C4C24×C1111yescharacteristic
728C22×C4C24×C1111yescharacteristic
729SD16—216no—
730D8—216no—
731M16—28no—
732C2×C8C24×C1118yes—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4C24×C1112yes—
747C4⋊C4C24×C1112yes—
748C4⋊C4C24×C1114yes—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—22no—
761C22⋊C4—22no—
762C42—22no—
763C42—22no—
764C42—22no—
765C42C2×D4×C1111yescharacteristic
766C42C2×D4×C1111yescharacteristic
767C42C2×D4×C1111yescharacteristic
768C42C2×D4×C1111yescharacteristic
769C42C2×D4×C1111yescharacteristic
770C42C2×D4×C1111yescharacteristic
771C42C2×D4×C1111yescharacteristic
772C42C2×D4×C1111yescharacteristic
773C42C2×D4×C1111yescharacteristic
774C42C2×D4×C1111yescharacteristic
775C42C2×D4×C1111yescharacteristic
776C42C2×D4×C1111yescharacteristic
777C42C24×C1111yescharacteristic
778C42C24×C1111yescharacteristic
779C42C24×C1111yescharacteristic
780C42C24×C1111yescharacteristic
781C11#6055811yescharacteristic, direct product factor, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—28no—
786C23—28no—
787C23—28no—
788C23—24no—
789C23—22no—
790C23—44no—
791C23—44no—
792C23—432no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23C22×D4×C1111yescharacteristic
798C23C22×D4×C1111yescharacteristic
799C23C22×D4×C1111yescharacteristic
800Q8—24no—
801Q8—42no—
802Q8—42no—
803D4—28no—
804D4—28no—
805D4—28no—
806D4—24no—
807D4—24no—
808D4—42no—
809D4—44no—
810D4—44no—
811D4—44no—
812D4—42no—
813D4C2×C11×#4118yes—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—48no—
835C2×C4—48no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—48no—
842C2×C4—48no—
843C2×C4—44no—
844C2×C4C11×AGL(1,ℤ/8)14yescomplemented
845C2×C4C22×D4×C1111yescharacteristic
846C2×C4C22×D4×C1111yescharacteristic
847C2×C4C22×D4×C1111yescharacteristic
848C2×C4C22×D4×C1111yescharacteristic
849C2×C4C22×D4×C1111yescharacteristic
850C2×C4C22×D4×C1111yescharacteristic
851C2×C4C22×D4×C1111yescharacteristic
852C2×C4C22×D4×C1111yescharacteristic
853C2×C4C22×D4×C1111yescharacteristic
854C2×C4C22×D4×C1111yescharacteristic
855C2×C4C22×D4×C1111yescharacteristic
856C2×C4C2×C11×#4114yes—
857C2×C4C25×C1111yescharacteristic
858C8—28no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—28no—
867C22—416no—
868C22—416no—
869C22—416no—
870C22—44no—
871C22—44no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22C11×#52512yes—
876C22C2×C11×AGL(1,ℤ/8)12yes—
877C22C11×#57512yes—
878C22C23×D4×C1111yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—42no—
888C4—44no—
889C4—42no—
890C4—42no—
891C4C11×#52512yes—
892C4C2×C11×AGL(1,ℤ/8)12yes—
893C4C2×C11×AGL(1,ℤ/8)12yes—
894C4C22×C11×#4112yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—48no—
899C2—82no—
900C2C2×C11×#52511yescharacteristic
901C2C22×C11×AGL(1,ℤ/8)11yescharacteristic
902C2C2×C11×#57511yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3444C2semidirect
2. C22×C4×D4×C11C2semidirect
3. C11×#3114C2semidirect
4. C11×#3110C2semidirect
5. C11×#3109C2semidirect
6. C11×#3105C2semidirect
7. C11×#3101C2semidirect
8. C11×#3100C2semidirect
9. C11×#3092C2semidirect
10. C11×#3077C2semidirect
11. C11×#3036C2semidirect
12. C11×#3003C2semidirect
13. C4×C11×AGL(1,ℤ/8)C2semidirect
14. C11×#2920C2semidirect
18. C11×#533C22semidirect
19. C11×#533C22semidirect
20. C11×#533C22semidirect
21. C11×#532C22semidirect
22. C11×#532C22semidirect
23. C11×#532C22semidirect
28. C11×#529C22semidirect
29. C11×#529C22semidirect
35. C4×C11×#41C22semidirect
51. C11×#484C22semidirect
52. C11×#483C22semidirect
53. C11×#481C22semidirect
54. C11×#480C22semidirect
55. C11×#478C22semidirect
56. C11×#476C22semidirect
57. C11×#474C22semidirect
58. C11×#463C22semidirect
59. C11×#461C22semidirect
60. C11×#459C22semidirect
65. C11×#442C22semidirect
66. C11×#440C22semidirect
67. C4×C11×SD16C22semidirect
68. C4×C11×D8C22semidirect
69. C11×#432C22semidirect
70. C11×#432C22semidirect
71. C11×#431C22semidirect
72. C11×#431C22semidirect
73. C11×#428C22semidirect
74. C11×#423C22semidirect
76. C11×#417C22semidirect
78. C4×C11×M16C22semidirect
105. C11×C4⋊Q8C23semidirect
106. C11×C4⋊Q8C23semidirect
107. C11×C4⋊Q8C23semidirect
108. C11×#127C23semidirect
113. C11×#125C23semidirect
116. C11×#124C23semidirect
137. C4×Q8×C11C23semidirect
138. C4×Q8×C11C23semidirect
165. C4×D4×C11C23semidirect
166. C4×D4×C11C23semidirect
198. C11×#107C23semidirect
199. C11×#106C23semidirect
200. C11×C4⋊C8C23semidirect
201. C11×C4⋊C8C23semidirect
202. C11×#103C23semidirect
205. C11×#102C23semidirect
208. C11×#97C23semidirect
209. C4×C8×C11C23semidirect
210. #60558C11direct (N × H)
238. C2×D4×C11#41semidirect
331. #3444C2×C11semidirect
332. C22×C4×D4C2×C11semidirect
333. #3114C2×C11semidirect
334. #3110C2×C11semidirect
335. #3109C2×C11semidirect
336. #3105C2×C11semidirect
337. #3101C2×C11semidirect
338. #3100C2×C11semidirect
339. #3092C2×C11semidirect
340. #3077C2×C11semidirect
341. #3036C2×C11semidirect
342. #3003C2×C11semidirect
343. C4×AGL(1,ℤ/8)C2×C11semidirect
344. #2920C2×C11semidirect
407. C2×C4×C11AGL(1,ℤ/8)semidirect
425. #533C22×C11semidirect
426. #533C22×C11semidirect
427. #533C22×C11semidirect
428. #532C22×C11semidirect
429. #532C22×C11semidirect
430. #532C22×C11semidirect
435. #529C22×C11semidirect
436. #529C22×C11semidirect
442. C4×#41C22×C11semidirect
458. #484C22×C11semidirect
459. #483C22×C11semidirect
460. #481C22×C11semidirect
461. #480C22×C11semidirect
462. #478C22×C11semidirect
463. #476C22×C11semidirect
464. #474C22×C11semidirect
465. #463C22×C11semidirect
466. #461C22×C11semidirect
467. #459C22×C11semidirect
472. #442C22×C11semidirect
473. #440C22×C11semidirect
474. C4×SD16C22×C11semidirect
475. C4×D8C22×C11semidirect
476. #432C22×C11semidirect
477. #432C22×C11semidirect
478. #431C22×C11semidirect
479. #431C22×C11semidirect
480. #428C22×C11semidirect
481. #423C22×C11semidirect
483. #417C22×C11semidirect
485. C4×M16C22×C11semidirect
548. C4⋊Q8C23×C11semidirect
549. C4⋊Q8C23×C11semidirect
550. C4⋊Q8C23×C11semidirect
551. #127C23×C11semidirect
556. #125C23×C11semidirect
559. #124C23×C11semidirect
580. C4×Q8C23×C11semidirect
581. C4×Q8C23×C11semidirect
608. C4×D4C23×C11semidirect
609. C4×D4C23×C11semidirect
641. #107C23×C11semidirect
642. #106C23×C11semidirect
643. C4⋊C8C23×C11semidirect
644. C4⋊C8C23×C11semidirect
645. #103C23×C11semidirect
648. #102C23×C11semidirect
651. #97C23×C11semidirect
652. C4×C8C23×C11semidirect
688. C2×D4C11×#41semidirect
781. C11#60558direct (N × H)
844. 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
C11×#34442
C22×C4×D4×C112
C11×#31142
C11×#31102
C11×#31092
C11×#31052
C11×#31012
C11×#31002
C11×#30922
C11×#30772
C11×#30362
C11×#30032
C4×C11×AGL(1,ℤ/8)2
C11×#29202
#6055811