Finite Group Databasebeta

← C11×#60567 #14637760

Subgroups — C11×#60567 #14637760

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#542C211yesmaximal, characteristic, complemented
2C11×#3428C211yesmaximal, characteristic, complemented
3C11×#3125C214yesmaximal, complemented
4C11×#3124C214yesmaximal, complemented
5C11×#3121C214yesmaximal, complemented
6C11×#3118C214yesmaximal, complemented
7C11×#3095C211yesmaximal, characteristic, complemented
8C11×#3094C211yesmaximal, characteristic, complemented
9C11×#3079C212yesmaximal, complemented
10C11×#3040C212yesmaximal, complemented
11C11×#3007C211yesmaximal, characteristic, complemented
12C11×#3006C211yesmaximal, characteristic
13C4×C11×#137C212yesmaximal, complemented
14C4×C11×AGL(1,ℤ/8)C212yesmaximal, complemented
15C11×#2921C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×#137C2212yes—
18C2×C11×AGL(1,ℤ/8)C2212yes—
19C11×#542—22no—
20C11×#542—22no—
21C11×#542C2214yes—
22C11×#542C2214yescomplemented
23C2×C11×C4⋊Q8C2211yescharacteristic, complemented
24C2×C11×#126—21no—
25C2×C11×#124—21no—
26C2×C11×#124C2211yescharacteristic, complemented
27C2×C11×#123—21no—
28C2×C11×C22⋊Q8—21no—
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C11×#520—21no—
32C11×#520—21no—
33C11×#520C2212yescomplemented
34C11×#520C2212yescomplemented
35C11×#519C2212yescomplemented
36C11×#518—21no—
37C11×#518—21no—
38C11×#518C2212yescomplemented
39C4×C11×#41—22no—
40C4×C11×#41C2212yes—
41C4×C11×#41C2212yes—
42C2×C4×Q8×C11C2211yescharacteristic, complemented
43C2×C4×D4×C11C2211yescharacteristic, complemented
44C2×C11×#117—22no—
45C2×C11×#117C2211yescharacteristic
46C2×C11×#117C2211yescharacteristic
47C11×#485C2214yescomplemented
48C11×#484C2212yescomplemented
49C11×#483C2212yescomplemented
50C11×#482C2214yes—
51C11×#481C2212yescomplemented
52C11×#480C2212yescomplemented
53C11×#477C2214yescomplemented
54C11×#476C2214yescomplemented
55C11×#475C2214yescomplemented
56C11×#474C2214yescomplemented
57C11×#464C2214yescomplemented
58C11×#464C2214yescomplemented
59C11×#463C2214yescomplemented
60C11×#463C2214yescomplemented
61C11×#452C2214yescomplemented
62C11×#451C2212yescomplemented
63C11×#450C2212yescomplemented
64C11×#449C2214yes—
65C11×#448C2212yes—
66C11×#447C2212yes—
67C11×#442C2214yescomplemented
68C11×#441C2214yescomplemented
69C11×#440C2214yescomplemented
70C11×#440C2214yescomplemented
71C4×C11×Q16C2214yescomplemented
72C4×C11×SD16C2214yescomplemented
73C4×C11×SD16C2214yescomplemented
74C4×C11×D8C2214yescomplemented
75C11×#433C2214yescomplemented
76C11×#433C2214yescomplemented
77C11×#428C2212yescomplemented
78C11×#428C2212yescomplemented
79C11×#423C2212yescomplemented
80C11×#419C2212yescomplemented
81C11×#418C2212yescomplemented
82C11×#417C2212yes—
83C11×#417C2212yes—
84C11×#407C2211yescharacteristic
85C11×#407C2211yescharacteristic
86C4×C11×M16C2212yescomplemented
87C2×C11×#41—28no—
88C2×C11×#41—21no—
89C2×C11×#41—21no—
90C2×C11×#41C2312yes—
91C2×C11×#41C2312yes—
92C22×Q8×C11—21no—
93C22×Q8×C11C2311yescharacteristic
94C22×Q8×C11C2311yescharacteristic
95C22×D4×C11—21no—
96C22×D4×C11—21no—
97C22×D4×C11C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C23×C4×C11—21no—
101C23×C4×C11C2311yescharacteristic
102C11×#137—28no—
103C11×AGL(1,ℤ/8)—28no—
104C2×C11×Q16C2314yes—
105C2×C11×SD16C2314yes—
106C2×C11×SD16C2314yes—
107C2×C11×D8C2314yes—
108C2×C11×M16C2312yes—
109C2×C11×M16C2312yes—
110C11×C4⋊Q8—22no—
111C11×C4⋊Q8C2314yes—
112C11×#126—24no—
113C11×#126—24no—
114C11×#124—24no—
115C11×#124—24no—
116C11×#124—22no—
117C11×#124C2314yes—
118C11×#123—24no—
119C11×#123—24no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—24no—
123C11×C22⋊Q8—24no—
124C11×C22⋊Q8C2312yes—
125C11×C22⋊Q8C2312yes—
126C11×#121—21no—
127C11×#121—21no—
128C11×#121C2312yes—
129C11×#121C2312yes—
130C4×Q8×C11—22no—
131C4×Q8×C11—22no—
132C4×Q8×C11—22no—
133C4×Q8×C11C2314yes—
134C4×Q8×C11C2312yes—
135C4×Q8×C11C2312yes—
136C4×Q8×C11C2312yes—
137C4×Q8×C11C2312yes—
138C4×D4×C11—22no—
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×C11C2314yes—
150C4×D4×C11C2312yes—
151C4×D4×C11C2312yes—
152C4×D4×C11C2312yes—
153C4×D4×C11C2312yes—
154C11×#117—21no—
155C11×#117—21no—
156C11×#117—22no—
157C11×#117—22no—
158C11×#117—22no—
159C11×#117—22no—
160C11×#117—22no—
161C11×#117—22no—
162C11×#117D412yes—
163C11×#117D412yes—
164C11×#117C2312yes—
165C11×#117C2312yes—
166C11×#117C2312yes—
167C11×#117C2312yes—
168C2×C11×C4⋊C4—21no—
169C2×C11×C4⋊C4—21no—
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4—22no—
172C2×C11×C4⋊C4—22no—
173C2×C11×C4⋊C4D411yescharacteristic
174C2×C11×C4⋊C4D411yescharacteristic
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2311yescharacteristic
178C2×C11×C4⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4—21no—
181C2×C11×C22⋊C4—21no—
182C2×C11×C22⋊C4—21no—
183C2×C11×C22⋊C4—21no—
184C2×C11×C22⋊C4—21no—
185C2×C11×C22⋊C4—22no—
186C2×C11×C22⋊C4—22no—
187C2×C11×C22⋊C4D411yescharacteristic
188C2×C11×C22⋊C4D411yescharacteristic
189C2×C42×C11—21no—
190C2×C42×C11—21no—
191C2×C42×C11—22no—
192C2×C42×C11—22no—
193C2×C42×C11C2311yescharacteristic
194C2×C42×C11C2311yescharacteristic
195C11×#107C2314yes—
196C11×#107C2314yes—
197C11×#106C2314yes—
198C11×#106C2314yes—
199C11×C4⋊C8C2314yes—
200C11×C4⋊C8C2314yes—
201C11×#103C2314yes—
202C11×#103C2314yes—
203C11×#103C2314yes—
204C11×#103C2314yes—
205C11×#102C2314yes—
206C11×#102C2314yes—
207C11×#102C2314yes—
208C11×#102C2314yes—
209C11×C22⋊C8C2312yes—
210C11×C22⋊C8C2312yes—
211C11×C22⋊C8C2312yes—
212C11×C22⋊C8C2312yes—
213C11×#97C2314yes—
214C4×C8×C11C2314yes—
215#60567C1111yesmaximal, characteristic, direct product factor, Sylow
216C24×C11—21no—
217C24×C11—21no—
218C24×C11C2×D411yescharacteristic
219C11×#41—28no—
220C11×#41—28no—
221C11×#41—24no—
222C11×#41—24no—
223C11×#41—24no—
224C11×#41#4118yes—
225C2×Q8×C11—24no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—24no—
229C2×Q8×C11—24no—
230C2×Q8×C11—82no—
231C2×Q8×C11C2412yes—
232C2×Q8×C11C2412yes—
233C2×D4×C11—28no—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—24no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—21no—
240C2×D4×C11—21no—
241C2×D4×C11—24no—
242C2×D4×C11—82no—
243C2×D4×C11C2412yes—
244C2×D4×C11C2412yes—
245C22×C4×C11—28no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—24no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—24no—
260C22×C4×C11—82no—
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×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C11×Q16—28no—
272C11×SD16—28no—
273C11×SD16—28no—
274C11×D8—28no—
275C11×M16—24no—
276C11×M16—24no—
277C2×C8×C11C2414yes—
278C2×C8×C11C2414yes—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—24no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—24no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2×D412yes—
295C11×C4⋊C4C2412yes—
296C11×C4⋊C4C2412yes—
297C11×C4⋊C4C2412yes—
298C11×C4⋊C4C2412yes—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—24no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—24no—
311C11×C22⋊C4—24no—
312C11×C22⋊C4C2×D412yes—
313C11×C22⋊C4C2×D412yes—
314C11×C22⋊C4C2×D412yes—
315C11×C22⋊C4C2×D412yes—
316C42×C11—22no—
317C42×C11—22no—
318C42×C11—22no—
319C42×C11—22no—
320C42×C11—22no—
321C42×C11—22no—
322C42×C11—24no—
323C42×C11C2×D412yes—
324C42×C11C2×D412yes—
325C42×C11C2412yes—
326C42×C11C2412yes—
327C2×#542C2×C1111yescharacteristic, complemented
328#3428C2×C1111yescharacteristic, complemented
329#3125C2×C1114yescomplemented
330#3124C2×C1114yescomplemented
331#3121C2×C1114yescomplemented
332#3118C2×C1114yescomplemented
333#3095C2×C1111yescharacteristic, complemented
334#3094C2×C1111yescharacteristic, complemented
335#3079C2×C1112yescomplemented
336#3040C2×C1112yescomplemented
337#3007C2×C1111yescharacteristic, complemented
338#3006C2×C1111yescharacteristic
339C4×#137C2×C1112yescomplemented
340C4×AGL(1,ℤ/8)C2×C1112yescomplemented
341#2921C2×C1111yescharacteristic, complemented
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—42no—
349C23×C11—42no—
350C23×C11—42no—
351C23×C11—81no—
352C23×C11—81no—
353C23×C11C22×D411yescharacteristic
354C23×C11C22×D411yescharacteristic
355C23×C11C22×D411yescharacteristic
356Q8×C11—24no—
357Q8×C11—22no—
358Q8×C11—24no—
359Q8×C11—42no—
360Q8×C11—84no—
361Q8×C11C2×#4114yes—
362D4×C11—28no—
363D4×C11—24no—
364D4×C11—28no—
365D4×C11—22no—
366D4×C11—24no—
367D4×C11—42no—
368D4×C11—82no—
369D4×C11—82no—
370D4×C11C2×#4114yes—
371C2×C4×C11—24no—
372C2×C4×C11—28no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—28no—
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—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11—82no—
393C2×C4×C11—82no—
394C2×C4×C11—82no—
395C2×C4×C11—82no—
396C2×C4×C11—84no—
397C2×C4×C11—81no—
398C2×C4×C11—81no—
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D412yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C2×#4114yes—
407C2×C4×C11C2511yescharacteristic
408C8×C11—24no—
409C8×C11—24no—
410C22×#41C22×C1111yescharacteristic
411C2×#137C22×C1112yes—
412C2×AGL(1,ℤ/8)C22×C1112yes—
413#542—22no—
414#542—22no—
415#542C22×C1114yes—
416#542C22×C1114yescomplemented
417C2×C4⋊Q8C22×C1111yescharacteristic, complemented
418C2×#126—21no—
419C2×#124—21no—
420C2×#124C22×C1111yescharacteristic, complemented
421C2×#123—21no—
422C2×C22⋊Q8—21no—
423C2×C22⋊Q8C22×C1111yescharacteristic
424C2×#121C22×C1111yescharacteristic
425#520—21no—
426#520—21no—
427#520C22×C1112yescomplemented
428#520C22×C1112yescomplemented
429#519C22×C1112yescomplemented
430#518—21no—
431#518—21no—
432#518C22×C1112yescomplemented
433C4×#41—22no—
434C4×#41C22×C1112yes—
435C4×#41C22×C1112yes—
436C2×C4×Q8C22×C1111yescharacteristic, complemented
437C2×C4×D4C22×C1111yescharacteristic, complemented
438C2×#117—22no—
439C2×#117C22×C1111yescharacteristic
440C2×#117C22×C1111yescharacteristic
441#485C22×C1114yescomplemented
442#484C22×C1112yescomplemented
443#483C22×C1112yescomplemented
444#482C22×C1114yes—
445#481C22×C1112yescomplemented
446#480C22×C1112yescomplemented
447#477C22×C1114yescomplemented
448#476C22×C1114yescomplemented
449#475C22×C1114yescomplemented
450#474C22×C1114yescomplemented
451#464C22×C1114yescomplemented
452#464C22×C1114yescomplemented
453#463C22×C1114yescomplemented
454#463C22×C1114yescomplemented
455#452C22×C1114yescomplemented
456#451C22×C1112yescomplemented
457#450C22×C1112yescomplemented
458#449C22×C1114yes—
459#448C22×C1112yes—
460#447C22×C1112yes—
461#442C22×C1114yescomplemented
462#441C22×C1114yescomplemented
463#440C22×C1114yescomplemented
464#440C22×C1114yescomplemented
465C4×Q16C22×C1114yescomplemented
466C4×SD16C22×C1114yescomplemented
467C4×SD16C22×C1114yescomplemented
468C4×D8C22×C1114yescomplemented
469#433C22×C1114yescomplemented
470#433C22×C1114yescomplemented
471#428C22×C1112yescomplemented
472#428C22×C1112yescomplemented
473#423C22×C1112yescomplemented
474#419C22×C1112yescomplemented
475#418C22×C1112yescomplemented
476#417C22×C1112yes—
477#417C22×C1112yes—
478#407C22×C1111yescharacteristic
479#407C22×C1111yescharacteristic
480C4×M16C22×C1112yescomplemented
481C22×C11—21no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—24no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—82no—
496C22×C11—84no—
497C22×C11—84no—
498C22×C11#52512yes—
499C22×C11C23×D411yescharacteristic
500C4×C11—22no—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—21no—
505C4×C11—24no—
506C4×C11—21no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11#52512yes—
513C4×C11C22×#4112yes—
514C2×#41—28no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41C23×C1112yes—
518C2×#41C23×C1112yes—
519C22×Q8—21no—
520C22×Q8C23×C1111yescharacteristic
521C22×Q8C23×C1111yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4C23×C1111yescharacteristic
525C22×D4C23×C1111yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C23×C1111yescharacteristic
529#137—28no—
530AGL(1,ℤ/8)—28no—
531C2×Q16C23×C1114yes—
532C2×SD16C23×C1114yes—
533C2×SD16C23×C1114yes—
534C2×D8C23×C1114yes—
535C2×M16C23×C1112yes—
536C2×M16C23×C1112yes—
537C4⋊Q8—22no—
538C4⋊Q8C23×C1114yes—
539#126—24no—
540#126—24no—
541#124—24no—
542#124—24no—
543#124—22no—
544#124C23×C1114yes—
545#123—24no—
546#123—24no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—24no—
550C22⋊Q8—24no—
551C22⋊Q8C23×C1112yes—
552C22⋊Q8C23×C1112yes—
553#121—21no—
554#121—21no—
555#121C23×C1112yes—
556#121C23×C1112yes—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8C23×C1114yes—
561C4×Q8C23×C1112yes—
562C4×Q8C23×C1112yes—
563C4×Q8C23×C1112yes—
564C4×Q8C23×C1112yes—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4C23×C1114yes—
577C4×D4C23×C1112yes—
578C4×D4C23×C1112yes—
579C4×D4C23×C1112yes—
580C4×D4C23×C1112yes—
581#117—21no—
582#117—21no—
583#117—22no—
584#117—22no—
585#117—22no—
586#117—22no—
587#117—22no—
588#117—22no—
589#117D4×C1112yes—
590#117D4×C1112yes—
591#117C23×C1112yes—
592#117C23×C1112yes—
593#117C23×C1112yes—
594#117C23×C1112yes—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4D4×C1111yescharacteristic
601C2×C4⋊C4D4×C1111yescharacteristic
602C2×C4⋊C4C23×C1111yescharacteristic
603C2×C4⋊C4C23×C1111yescharacteristic
604C2×C4⋊C4C23×C1111yescharacteristic
605C2×C4⋊C4C23×C1111yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4D4×C1111yescharacteristic
615C2×C22⋊C4D4×C1111yescharacteristic
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42C23×C1111yescharacteristic
621C2×C42C23×C1111yescharacteristic
622#107C23×C1114yes—
623#107C23×C1114yes—
624#106C23×C1114yes—
625#106C23×C1114yes—
626C4⋊C8C23×C1114yes—
627C4⋊C8C23×C1114yes—
628#103C23×C1114yes—
629#103C23×C1114yes—
630#103C23×C1114yes—
631#103C23×C1114yes—
632#102C23×C1114yes—
633#102C23×C1114yes—
634#102C23×C1114yes—
635#102C23×C1114yes—
636C22⋊C8C23×C1112yes—
637C22⋊C8C23×C1112yes—
638C22⋊C8C23×C1112yes—
639C22⋊C8C23×C1112yes—
640#97C23×C1114yes—
641C4×C8C23×C1114yes—
642C2×C11—22no—
643C2×C11—41no—
644C2×C11—41no—
645C2×C11—44no—
646C2×C11—82no—
647C2×C11C2×#52511yescharacteristic
648C2×C11#358511yescharacteristic
649C2×C11#358611yescharacteristic
650C24—21no—
651C24—21no—
652C24C2×D4×C1111yescharacteristic
653#41—28no—
654#41—28no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41C11×#4118yes—
659C2×Q8—24no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—82no—
665C2×Q8C24×C1112yes—
666C2×Q8C24×C1112yes—
667C2×D4—28no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—24no—
676C2×D4—82no—
677C2×D4C24×C1112yes—
678C2×D4C24×C1112yes—
679C22×C4—28no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—24no—
694C22×C4—82no—
695C22×C4C2×D4×C1111yescharacteristic
696C22×C4C2×D4×C1111yescharacteristic
697C22×C4C2×D4×C1111yescharacteristic
698C22×C4C2×D4×C1111yescharacteristic
699C22×C4C2×D4×C1111yescharacteristic
700C22×C4C2×D4×C1111yescharacteristic
701C22×C4C2×D4×C1111yescharacteristic
702C22×C4C24×C1111yescharacteristic
703C22×C4C24×C1111yescharacteristic
704C22×C4C24×C1111yescharacteristic
705Q16—28no—
706SD16—28no—
707SD16—28no—
708D8—28no—
709M16—24no—
710M16—24no—
711C2×C8C24×C1114yes—
712C2×C8C24×C1114yes—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—24no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—24no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4C2×D4×C1112yes—
726C4⋊C4C2×D4×C1112yes—
727C4⋊C4C2×D4×C1112yes—
728C4⋊C4C2×D4×C1112yes—
729C4⋊C4C24×C1112yes—
730C4⋊C4C24×C1112yes—
731C4⋊C4C24×C1112yes—
732C4⋊C4C24×C1112yes—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—24no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4C2×D4×C1112yes—
747C22⋊C4C2×D4×C1112yes—
748C22⋊C4C2×D4×C1112yes—
749C22⋊C4C2×D4×C1112yes—
750C42—22no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—24no—
757C42C2×D4×C1112yes—
758C42C2×D4×C1112yes—
759C42C24×C1112yes—
760C42C24×C1112yes—
761C11#6056711yescharacteristic, direct product factor, Sylow
762C23—24no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—81no—
772C23—81no—
773C23C22×D4×C1111yescharacteristic
774C23C22×D4×C1111yescharacteristic
775C23C22×D4×C1111yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—24no—
779Q8—42no—
780Q8—84no—
781Q8C2×C11×#4114yes—
782D4—28no—
783D4—24no—
784D4—28no—
785D4—22no—
786D4—24no—
787D4—42no—
788D4—82no—
789D4—82no—
790D4C2×C11×#4114yes—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—84no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4C22×D4×C1112yes—
820C2×C4C22×D4×C1111yescharacteristic
821C2×C4C22×D4×C1112yes—
822C2×C4C22×D4×C1112yes—
823C2×C4C22×D4×C1112yes—
824C2×C4C22×D4×C1111yescharacteristic
825C2×C4C22×D4×C1111yescharacteristic
826C2×C4C2×C11×#4114yes—
827C2×C4C25×C1111yescharacteristic
828C8—24no—
829C8—24no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—24no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—82no—
845C22—84no—
846C22—84no—
847C22C11×#52512yes—
848C22C23×D4×C1111yescharacteristic
849C4—21no—
850C4—24no—
851C4—21no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4C11×#52512yes—
862C4C22×C11×#4112yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—44no—
867C2—82no—
868C2C2×C11×#52511yescharacteristic
869C2C11×#358511yescharacteristic
870C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3006C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#542C2semidirect
2. C11×#3428C2semidirect
3. C11×#3125C2semidirect
4. C11×#3124C2semidirect
5. C11×#3121C2semidirect
6. C11×#3118C2semidirect
7. C11×#3095C2semidirect
8. C11×#3094C2semidirect
9. C11×#3079C2semidirect
10. C11×#3040C2semidirect
11. C11×#3007C2semidirect
13. C4×C11×#137C2semidirect
14. C4×C11×AGL(1,ℤ/8)C2semidirect
15. C11×#2921C2semidirect
22. C11×#542C22semidirect
23. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×#124C22semidirect
33. C11×#520C22semidirect
34. C11×#520C22semidirect
35. C11×#519C22semidirect
38. C11×#518C22semidirect
42. C2×C4×Q8×C11C22semidirect
43. C2×C4×D4×C11C22semidirect
47. C11×#485C22semidirect
48. C11×#484C22semidirect
49. C11×#483C22semidirect
51. C11×#481C22semidirect
52. C11×#480C22semidirect
53. C11×#477C22semidirect
54. C11×#476C22semidirect
55. C11×#475C22semidirect
56. C11×#474C22semidirect
57. C11×#464C22semidirect
58. C11×#464C22semidirect
59. C11×#463C22semidirect
60. C11×#463C22semidirect
61. C11×#452C22semidirect
62. C11×#451C22semidirect
63. C11×#450C22semidirect
67. C11×#442C22semidirect
68. C11×#441C22semidirect
69. C11×#440C22semidirect
70. C11×#440C22semidirect
71. C4×C11×Q16C22semidirect
72. C4×C11×SD16C22semidirect
73. C4×C11×SD16C22semidirect
74. C4×C11×D8C22semidirect
75. C11×#433C22semidirect
76. C11×#433C22semidirect
77. C11×#428C22semidirect
78. C11×#428C22semidirect
79. C11×#423C22semidirect
80. C11×#419C22semidirect
81. C11×#418C22semidirect
86. C4×C11×M16C22semidirect
215. #60567C11direct (N × H)
327. C2×#542C2×C11semidirect
328. #3428C2×C11semidirect
329. #3125C2×C11semidirect
330. #3124C2×C11semidirect
331. #3121C2×C11semidirect
332. #3118C2×C11semidirect
333. #3095C2×C11semidirect
334. #3094C2×C11semidirect
335. #3079C2×C11semidirect
336. #3040C2×C11semidirect
337. #3007C2×C11semidirect
339. C4×#137C2×C11semidirect
340. C4×AGL(1,ℤ/8)C2×C11semidirect
341. #2921C2×C11semidirect
416. #542C22×C11semidirect
417. C2×C4⋊Q8C22×C11semidirect
420. C2×#124C22×C11semidirect
427. #520C22×C11semidirect
428. #520C22×C11semidirect
429. #519C22×C11semidirect
432. #518C22×C11semidirect
436. C2×C4×Q8C22×C11semidirect
437. C2×C4×D4C22×C11semidirect
441. #485C22×C11semidirect
442. #484C22×C11semidirect
443. #483C22×C11semidirect
445. #481C22×C11semidirect
446. #480C22×C11semidirect
447. #477C22×C11semidirect
448. #476C22×C11semidirect
449. #475C22×C11semidirect
450. #474C22×C11semidirect
451. #464C22×C11semidirect
452. #464C22×C11semidirect
453. #463C22×C11semidirect
454. #463C22×C11semidirect
455. #452C22×C11semidirect
456. #451C22×C11semidirect
457. #450C22×C11semidirect
461. #442C22×C11semidirect
462. #441C22×C11semidirect
463. #440C22×C11semidirect
464. #440C22×C11semidirect
465. C4×Q16C22×C11semidirect
466. C4×SD16C22×C11semidirect
467. C4×SD16C22×C11semidirect
468. C4×D8C22×C11semidirect
469. #433C22×C11semidirect
470. #433C22×C11semidirect
471. #428C22×C11semidirect
472. #428C22×C11semidirect
473. #423C22×C11semidirect
474. #419C22×C11semidirect
475. #418C22×C11semidirect
480. C4×M16C22×C11semidirect
761. C11#60567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5422
C11×#34282
C11×#31252
C11×#31242
C11×#31212
C11×#31182
C11×#30952
C11×#30942
C11×#30792
C11×#30402
C11×#30072
C11×#30062
C4×C11×#1372
C4×C11×AGL(1,ℤ/8)2
C11×#29212
#6056711