Finite Group Databasebeta

← C11×#60561 #14637754

Subgroups — C11×#60561 #14637754

Order 2816.

2428 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic, complemented
2C2×C4×C11×#41C211yesmaximal, characteristic, complemented
3C11×#3115C214yesmaximal, complemented
4C11×#3112C212yesmaximal, complemented
5C11×#3109C212yesmaximal, complemented
6C11×#3106C214yesmaximal, complemented
7C11×#3103C212yesmaximal, complemented
8C11×#3100C212yesmaximal, complemented
9C11×#3094C212yesmaximal, complemented
10C11×#3079C212yesmaximal, complemented
11C11×#3038C212yesmaximal, complemented
12C11×#3006C212yesmaximal, complemented
13C4×C11×AGL(1,ℤ/8)C214yesmaximal, complemented
14C11×#2920C211yesmaximal, characteristic, complemented
15C22×C11×#41—21no—
16C22×C11×#41C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2214yes—
18C11×#532—21no—
19C11×#532—21no—
20C11×#532—21no—
21C11×#532—21no—
22C11×#532C2212yes—
23C11×#532C2212yes—
24C11×#532C2212yescomplemented
25C11×#532C2212yescomplemented
26C2×C11×C4⋊Q8C2211yescharacteristic, complemented
27C2×C11×#127C2211yescharacteristic, complemented
28C2×C11×#124—21no—
29C2×C11×#121—21no—
30C2×C11×#121C2212yes—
31C4×C11×#41—21no—
32C4×C11×#41—21no—
33C4×C11×#41—21no—
34C4×C11×#41—21no—
35C4×C11×#41C2212yes—
36C4×C11×#41C2212yes—
37C4×C11×#41C2212yescomplemented
38C4×C11×#41C2212yescomplemented
39C2×C4×Q8×C11C2211yescharacteristic, complemented
40C2×C4×Q8×C11C2211yescharacteristic, complemented
41C2×C4×D4×C11—21no—
42C2×C4×D4×C11—21no—
43C2×C4×D4×C11—21no—
44C2×C4×D4×C11C2211yescharacteristic, complemented
45C2×C4×D4×C11C2211yescharacteristic, complemented
46C2×C4×D4×C11C2212yescomplemented
47C2×C11×#117—21no—
48C2×C11×#117C2211yescharacteristic
49C22×C42×C11—21no—
50C22×C42×C11C2211yescharacteristic
51C11×#482C2218yescomplemented
52C11×#481C2214yescomplemented
53C11×#480C2214yescomplemented
54C11×#477C2214yescomplemented
55C11×#476C2214yescomplemented
56C11×#475C2214yescomplemented
57C11×#474C2214yescomplemented
58C11×#460C2214yescomplemented
59C11×#460C2214yescomplemented
60C11×#459C2214yescomplemented
61C11×#459C2214yescomplemented
62C11×#449C2218yescomplemented
63C11×#448C2214yescomplemented
64C11×#447C2214yescomplemented
65C11×#442C2218yescomplemented
66C11×#440C2218yescomplemented
67C4×C11×SD16C2218yescomplemented
68C4×C11×D8C2218yescomplemented
69C11×#432C2212yescomplemented
70C11×#432C2212yescomplemented
71C11×#431C2212yescomplemented
72C11×#431C2212yescomplemented
73C11×#428C2214yescomplemented
74C11×#423C2212yescomplemented
75C11×#418C2214yescomplemented
76C11×#417C2214yes—
77C11×#407C2212yes—
78C4×C11×M16C2212yescomplemented
79C2×C11×#41—28no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—22no—
83C2×C11×#41—22no—
84C2×C11×#41—22no—
85C2×C11×#41—22no—
86C2×C11×#41—48no—
87C2×C11×#41C2312yes—
88C2×C11×#41C2312yes—
89C22×Q8×C11—21no—
90C22×Q8×C11C2311yescharacteristic
91C22×D4×C11—21no—
92C22×D4×C11—22no—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11C2311yescharacteristic
96C22×D4×C11C2312yes—
97C23×C4×C11—21no—
98C23×C4×C11—21no—
99C23×C4×C11—21no—
100C23×C4×C11—22no—
101C23×C4×C11D411yescharacteristic
102C23×C4×C11D411yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C11×AGL(1,ℤ/8)—216no—
105C2×C11×SD16C2318yes—
106C2×C11×D8C2318yes—
107C2×C11×M16C2314yes—
108C11×C4⋊Q8—21no—
109C11×C4⋊Q8—21no—
110C11×C4⋊Q8C2312yes—
111C11×C4⋊Q8C2312yes—
112C11×#127—21no—
113C11×#127—21no—
114C11×#127C2312yes—
115C11×#127C2312yes—
116C11×#124—22no—
117C11×#124—22no—
118C11×#124—22no—
119C11×#124—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—22no—
125C11×#121—22no—
126C11×#121C2314yes—
127C11×#121C2314yes—
128C4×Q8×C11—21no—
129C4×Q8×C11—21no—
130C4×Q8×C11—21no—
131C4×Q8×C11—21no—
132C4×Q8×C11C2312yes—
133C4×Q8×C11C2312yes—
134C4×Q8×C11C2312yes—
135C4×Q8×C11C2312yes—
136C4×D4×C11—22no—
137C4×D4×C11—22no—
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—21no—
149C4×D4×C11—21no—
150C4×D4×C11—21no—
151C4×D4×C11—21no—
152C4×D4×C11—22no—
153C4×D4×C11—22no—
154C4×D4×C11C2312yes—
155C4×D4×C11C2312yes—
156C4×D4×C11C2312yes—
157C4×D4×C11C2312yes—
158C4×D4×C11C2314yes—
159C4×D4×C11C2314yes—
160C11×#117—21no—
161C11×#117—21no—
162C11×#117—22no—
163C11×#117—22no—
164C11×#117—22no—
165C11×#117—22no—
166C11×#117C2312yes—
167C11×#117C2312yes—
168C2×C11×C4⋊C4—21no—
169C2×C11×C4⋊C4—21no—
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C22⋊C4—21no—
175C2×C11×C22⋊C4—21no—
176C2×C11×C22⋊C4—21no—
177C2×C11×C22⋊C4—22no—
178C2×C11×C22⋊C4—22no—
179C2×C42×C11—21no—
180C2×C42×C11—21no—
181C2×C42×C11—21no—
182C2×C42×C11—22no—
183C2×C42×C11—22no—
184C2×C42×C11—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×#107C2318yes—
199C11×#106C2318yes—
200C11×C4⋊C8C2314yes—
201C11×C4⋊C8C2314yes—
202C11×#103C2318yes—
203C11×#102C2318yes—
204C11×#102C2318yes—
205C11×#102C2318yes—
206C11×C22⋊C8C2314yes—
207C11×C22⋊C8C2314yes—
208C11×#97C2314yes—
209C4×C8×C11C2314yes—
210#60561C1111yesmaximal, characteristic, direct product factor, Sylow
211C24×C11—21no—
212C24×C11—22no—
213C24×C11C2×D411yescharacteristic
214C11×#41—28no—
215C11×#41—28no—
216C11×#41—24no—
217C11×#41—24no—
218C11×#41—24no—
219C11×#41—48no—
220C11×#41—48no—
221C11×#41—48no—
222C11×#41—48no—
223C11×#41#4118yescomplemented
224C2×Q8×C11—24no—
225C2×Q8×C11—21no—
226C2×Q8×C11—22no—
227C2×Q8×C11—22no—
228C2×Q8×C11—44no—
229C2×Q8×C11C2412yes—
230C2×D4×C11—28no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—24no—
234C2×D4×C11—24no—
235C2×D4×C11—24no—
236C2×D4×C11—21no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—28no—
243C2×D4×C11—44no—
244C2×D4×C11—44no—
245C2×D4×C11—48no—
246C2×D4×C11C2414yes—
247C2×D4×C11C2412yes—
248C22×C4×C11—28no—
249C22×C4×C11—21no—
250C22×C4×C11—24no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—24no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—24no—
261C22×C4×C11—22no—
262C22×C4×C11—24no—
263C22×C4×C11—42no—
264C22×C4×C11—44no—
265C22×C4×C11—48no—
266C22×C4×C11—44no—
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×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C11×SD16—216no—
286C11×D8—216no—
287C11×M16—28no—
288C2×C8×C11C2418yes—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4C2412yes—
299C11×C4⋊C4C2412yes—
300C11×C4⋊C4C2414yes—
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—24no—
309C11×C22⋊C4—24no—
310C11×C22⋊C4—24no—
311C42×C11—22no—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11—22no—
315C42×C11—22no—
316C42×C11—22no—
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×C11C2×D411yescharacteristic
328C42×C11C2×D411yescharacteristic
329C42×C11C2411yescharacteristic
330C42×C11C2411yescharacteristic
331C42×C11C2411yescharacteristic
332C42×C11C2411yescharacteristic
333C2×#532C2×C1111yescharacteristic, complemented
334C2×C4×#41C2×C1111yescharacteristic, complemented
335#3115C2×C1114yescomplemented
336#3112C2×C1112yescomplemented
337#3109C2×C1112yescomplemented
338#3106C2×C1114yescomplemented
339#3103C2×C1112yescomplemented
340#3100C2×C1112yescomplemented
341#3094C2×C1112yescomplemented
342#3079C2×C1112yescomplemented
343#3038C2×C1112yescomplemented
344#3006C2×C1112yescomplemented
345C4×AGL(1,ℤ/8)C2×C1114yescomplemented
346#2920C2×C1111yescharacteristic, complemented
347C23×C11—24no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—24no—
352C23×C11—41no—
353C23×C11—42no—
354C23×C11—44no—
355C23×C11—44no—
356C23×C11—42no—
357C23×C11—44no—
358C23×C11C22×D411yescharacteristic
359C23×C11C22×D411yescharacteristic
360C23×C11C22×D411yescharacteristic
361Q8×C11—24no—
362Q8×C11—22no—
363Q8×C11—44no—
364Q8×C11—44no—
365Q8×C11C2×#4114yescomplemented
366D4×C11—28no—
367D4×C11—24no—
368D4×C11—28no—
369D4×C11—22no—
370D4×C11—28no—
371D4×C11—44no—
372D4×C11—44no—
373D4×C11—48no—
374D4×C11—48no—
375D4×C11—44no—
376D4×C11—44no—
377D4×C11—44no—
378D4×C11C2×#4114yescomplemented
379C2×C4×C11—24no—
380C2×C4×C11—28no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—28no—
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—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—24no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—44no—
403C2×C4×C11—48no—
404C2×C4×C11—42no—
405C2×C4×C11—44no—
406C2×C4×C11—42no—
407C2×C4×C11—44no—
408C2×C4×C11—44no—
409C2×C4×C11—48no—
410C2×C4×C11—44no—
411C2×C4×C11AGL(1,ℤ/8)14yescomplemented
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×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C2×#4114yes—
424C2×C4×C11C2511yescharacteristic
425C8×C11—28no—
426C22×#41—21no—
427C22×#41C22×C1111yescharacteristic
428C2×AGL(1,ℤ/8)C22×C1114yes—
429#532—21no—
430#532—21no—
431#532—21no—
432#532—21no—
433#532C22×C1112yes—
434#532C22×C1112yes—
435#532C22×C1112yescomplemented
436#532C22×C1112yescomplemented
437C2×C4⋊Q8C22×C1111yescharacteristic, complemented
438C2×#127C22×C1111yescharacteristic, complemented
439C2×#124—21no—
440C2×#121—21no—
441C2×#121C22×C1112yes—
442C4×#41—21no—
443C4×#41—21no—
444C4×#41—21no—
445C4×#41—21no—
446C4×#41C22×C1112yes—
447C4×#41C22×C1112yes—
448C4×#41C22×C1112yescomplemented
449C4×#41C22×C1112yescomplemented
450C2×C4×Q8C22×C1111yescharacteristic, complemented
451C2×C4×Q8C22×C1111yescharacteristic, complemented
452C2×C4×D4—21no—
453C2×C4×D4—21no—
454C2×C4×D4—21no—
455C2×C4×D4C22×C1111yescharacteristic, complemented
456C2×C4×D4C22×C1111yescharacteristic, complemented
457C2×C4×D4C22×C1112yescomplemented
458C2×#117—21no—
459C2×#117C22×C1111yescharacteristic
460C22×C42—21no—
461C22×C42C22×C1111yescharacteristic
462#482C22×C1118yescomplemented
463#481C22×C1114yescomplemented
464#480C22×C1114yescomplemented
465#477C22×C1114yescomplemented
466#476C22×C1114yescomplemented
467#475C22×C1114yescomplemented
468#474C22×C1114yescomplemented
469#460C22×C1114yescomplemented
470#460C22×C1114yescomplemented
471#459C22×C1114yescomplemented
472#459C22×C1114yescomplemented
473#449C22×C1118yescomplemented
474#448C22×C1114yescomplemented
475#447C22×C1114yescomplemented
476#442C22×C1118yescomplemented
477#440C22×C1118yescomplemented
478C4×SD16C22×C1118yescomplemented
479C4×D8C22×C1118yescomplemented
480#432C22×C1112yescomplemented
481#432C22×C1112yescomplemented
482#431C22×C1112yescomplemented
483#431C22×C1112yescomplemented
484#428C22×C1114yescomplemented
485#423C22×C1112yescomplemented
486#418C22×C1114yescomplemented
487#417C22×C1114yes—
488#407C22×C1112yes—
489C4×M16C22×C1112yescomplemented
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—21no—
495C22×C11—24no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—44no—
499C22×C11—48no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—44no—
503C22×C11—44no—
504C22×C11—44no—
505C22×C11—88no—
506C22×C11#52512yes—
507C22×C11C2×AGL(1,ℤ/8)12yes—
508C22×C11C23×D411yescharacteristic
509C4×C11—21no—
510C4×C11—24no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—21no—
515C4×C11—21no—
516C4×C11—21no—
517C4×C11—42no—
518C4×C11—44no—
519C4×C11—42no—
520C4×C11#52512yes—
521C4×C11C2×AGL(1,ℤ/8)12yes—
522C4×C11C2×AGL(1,ℤ/8)12yes—
523C4×C11#57512yes—
524C4×C11C22×#4112yes—
525C2×#41—28no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—48no—
533C2×#41C23×C1112yes—
534C2×#41C23×C1112yes—
535C22×Q8—21no—
536C22×Q8C23×C1111yescharacteristic
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4C23×C1111yescharacteristic
542C22×D4C23×C1112yes—
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4D4×C1111yescharacteristic
548C23×C4D4×C1111yescharacteristic
549C23×C4C23×C1111yescharacteristic
550AGL(1,ℤ/8)—216no—
551C2×SD16C23×C1118yes—
552C2×D8C23×C1118yes—
553C2×M16C23×C1114yes—
554C4⋊Q8—21no—
555C4⋊Q8—21no—
556C4⋊Q8C23×C1112yes—
557C4⋊Q8C23×C1112yes—
558#127—21no—
559#127—21no—
560#127C23×C1112yes—
561#127C23×C1112yes—
562#124—22no—
563#124—22no—
564#124—22no—
565#124—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121C23×C1114yes—
573#121C23×C1114yes—
574C4×Q8—21no—
575C4×Q8—21no—
576C4×Q8—21no—
577C4×Q8—21no—
578C4×Q8C23×C1112yes—
579C4×Q8C23×C1112yes—
580C4×Q8C23×C1112yes—
581C4×Q8C23×C1112yes—
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—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4C23×C1112yes—
601C4×D4C23×C1112yes—
602C4×D4C23×C1112yes—
603C4×D4C23×C1112yes—
604C4×D4C23×C1114yes—
605C4×D4C23×C1114yes—
606#117—21no—
607#117—21no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117C23×C1112yes—
613#117C23×C1112yes—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4C23×C1111yescharacteristic
618C2×C4⋊C4C23×C1111yescharacteristic
619C2×C4⋊C4C23×C1112yes—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42D4×C1111yescharacteristic
633C2×C42D4×C1111yescharacteristic
634C2×C42D4×C1111yescharacteristic
635C2×C42D4×C1111yescharacteristic
636C2×C42D4×C1111yescharacteristic
637C2×C42D4×C1111yescharacteristic
638C2×C42C23×C1111yescharacteristic
639C2×C42C23×C1111yescharacteristic
640C2×C42C23×C1111yescharacteristic
641C2×C42C23×C1111yescharacteristic
642C2×C42C23×C1111yescharacteristic
643C2×C42C23×C1111yescharacteristic
644#107C23×C1118yes—
645#106C23×C1118yes—
646C4⋊C8C23×C1114yes—
647C4⋊C8C23×C1114yes—
648#103C23×C1118yes—
649#102C23×C1118yes—
650#102C23×C1118yes—
651#102C23×C1118yes—
652C22⋊C8C23×C1114yes—
653C22⋊C8C23×C1114yes—
654#97C23×C1114yes—
655C4×C8C23×C1114yes—
656C2×C11—22no—
657C2×C11—22no—
658C2×C11—41no—
659C2×C11—44no—
660C2×C11—84no—
661C2×C11C2×#52511yescharacteristic
662C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
663C2×C11C2×#57511yescharacteristic
664C24—21no—
665C24—22no—
666C24C2×D4×C1111yescharacteristic
667#41—28no—
668#41—28no—
669#41—24no—
670#41—24no—
671#41—24no—
672#41—48no—
673#41—48no—
674#41—48no—
675#41—48no—
676#41C11×#4118yescomplemented
677C2×Q8—24no—
678C2×Q8—21no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—44no—
682C2×Q8C24×C1112yes—
683C2×D4—28no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—28no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4C24×C1114yes—
700C2×D4C24×C1112yes—
701C22×C4—28no—
702C22×C4—21no—
703C22×C4—24no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—42no—
717C22×C4—48no—
718C22×C4—44no—
719C22×C4—44no—
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×C4C2×D4×C1111yescharacteristic
727C22×C4C2×D4×C1111yescharacteristic
728C22×C4C2×D4×C1111yescharacteristic
729C22×C4C2×D4×C1111yescharacteristic
730C22×C4C2×D4×C1111yescharacteristic
731C22×C4C2×D4×C1111yescharacteristic
732C22×C4C2×D4×C1111yescharacteristic
733C22×C4C2×D4×C1111yescharacteristic
734C22×C4C2×D4×C1111yescharacteristic
735C22×C4C24×C1111yescharacteristic
736C22×C4C24×C1111yescharacteristic
737C22×C4C24×C1111yescharacteristic
738SD16—216no—
739D8—216no—
740M16—28no—
741C2×C8C24×C1118yes—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—22no—
751C4⋊C4C24×C1112yes—
752C4⋊C4C24×C1112yes—
753C4⋊C4C24×C1114yes—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C42—22no—
765C42—22no—
766C42—22no—
767C42—22no—
768C42—22no—
769C42—22no—
770C42C2×D4×C1111yescharacteristic
771C42C2×D4×C1111yescharacteristic
772C42C2×D4×C1111yescharacteristic
773C42C2×D4×C1111yescharacteristic
774C42C2×D4×C1111yescharacteristic
775C42C2×D4×C1111yescharacteristic
776C42C2×D4×C1111yescharacteristic
777C42C2×D4×C1111yescharacteristic
778C42C2×D4×C1111yescharacteristic
779C42C2×D4×C1111yescharacteristic
780C42C2×D4×C1111yescharacteristic
781C42C2×D4×C1111yescharacteristic
782C42C24×C1111yescharacteristic
783C42C24×C1111yescharacteristic
784C42C24×C1111yescharacteristic
785C42C24×C1111yescharacteristic
786C11#6056111yescharacteristic, direct product factor, Sylow
787C23—24no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—41no—
793C23—42no—
794C23—44no—
795C23—44no—
796C23—42no—
797C23—44no—
798C23C22×D4×C1111yescharacteristic
799C23C22×D4×C1111yescharacteristic
800C23C22×D4×C1111yescharacteristic
801Q8—24no—
802Q8—22no—
803Q8—44no—
804Q8—44no—
805Q8C2×C11×#4114yescomplemented
806D4—28no—
807D4—24no—
808D4—28no—
809D4—22no—
810D4—28no—
811D4—44no—
812D4—44no—
813D4—48no—
814D4—48no—
815D4—44no—
816D4—44no—
817D4—44no—
818D4C2×C11×#4114yescomplemented
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—44no—
843C2×C4—48no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—48no—
850C2×C4—44no—
851C2×C4C11×AGL(1,ℤ/8)14yescomplemented
852C2×C4C22×D4×C1111yescharacteristic
853C2×C4C22×D4×C1111yescharacteristic
854C2×C4C22×D4×C1111yescharacteristic
855C2×C4C22×D4×C1111yescharacteristic
856C2×C4C22×D4×C1111yescharacteristic
857C2×C4C22×D4×C1111yescharacteristic
858C2×C4C22×D4×C1111yescharacteristic
859C2×C4C22×D4×C1111yescharacteristic
860C2×C4C22×D4×C1111yescharacteristic
861C2×C4C22×D4×C1111yescharacteristic
862C2×C4C22×D4×C1111yescharacteristic
863C2×C4C2×C11×#4114yes—
864C2×C4C25×C1111yescharacteristic
865C8—28no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—24no—
872C22—21no—
873C22—21no—
874C22—44no—
875C22—48no—
876C22—42no—
877C22—42no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—88no—
882C22C11×#52512yes—
883C22C2×C11×AGL(1,ℤ/8)12yes—
884C22C23×D4×C1111yescharacteristic
885C4—21no—
886C4—24no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—21no—
893C4—44no—
894C4—42no—
895C4—42no—
896C4C11×#52512yes—
897C4C2×C11×AGL(1,ℤ/8)12yes—
898C4C2×C11×AGL(1,ℤ/8)12yes—
899C4C11×#57512yes—
900C4C22×C11×#4112yes—
901C2—22no—
902C2—22no—
903C2—41no—
904C2—44no—
905C2—84no—
906C2C2×C11×#52511yescharacteristic
907C2C22×C11×AGL(1,ℤ/8)11yescharacteristic
908C2C2×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. C2×C11×#532C2semidirect
2. C2×C4×C11×#41C2semidirect
3. C11×#3115C2semidirect
4. C11×#3112C2semidirect
5. C11×#3109C2semidirect
6. C11×#3106C2semidirect
7. C11×#3103C2semidirect
8. C11×#3100C2semidirect
9. C11×#3094C2semidirect
10. C11×#3079C2semidirect
11. C11×#3038C2semidirect
12. C11×#3006C2semidirect
13. C4×C11×AGL(1,ℤ/8)C2semidirect
14. C11×#2920C2semidirect
24. C11×#532C22semidirect
25. C11×#532C22semidirect
26. C2×C11×C4⋊Q8C22semidirect
27. C2×C11×#127C22semidirect
37. C4×C11×#41C22semidirect
38. C4×C11×#41C22semidirect
39. C2×C4×Q8×C11C22semidirect
40. C2×C4×Q8×C11C22semidirect
44. C2×C4×D4×C11C22semidirect
45. C2×C4×D4×C11C22semidirect
46. C2×C4×D4×C11C22semidirect
51. C11×#482C22semidirect
52. C11×#481C22semidirect
53. C11×#480C22semidirect
54. C11×#477C22semidirect
55. C11×#476C22semidirect
56. C11×#475C22semidirect
57. C11×#474C22semidirect
58. C11×#460C22semidirect
59. C11×#460C22semidirect
60. C11×#459C22semidirect
61. C11×#459C22semidirect
62. C11×#449C22semidirect
63. C11×#448C22semidirect
64. C11×#447C22semidirect
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
75. C11×#418C22semidirect
78. C4×C11×M16C22semidirect
210. #60561C11direct (N × H)
223. C11×#41#41semidirect
333. C2×#532C2×C11semidirect
334. C2×C4×#41C2×C11semidirect
335. #3115C2×C11semidirect
336. #3112C2×C11semidirect
337. #3109C2×C11semidirect
338. #3106C2×C11semidirect
339. #3103C2×C11semidirect
340. #3100C2×C11semidirect
341. #3094C2×C11semidirect
342. #3079C2×C11semidirect
343. #3038C2×C11semidirect
344. #3006C2×C11semidirect
345. C4×AGL(1,ℤ/8)C2×C11semidirect
346. #2920C2×C11semidirect
365. Q8×C11C2×#41semidirect
378. D4×C11C2×#41semidirect
411. C2×C4×C11AGL(1,ℤ/8)semidirect
435. #532C22×C11semidirect
436. #532C22×C11semidirect
437. C2×C4⋊Q8C22×C11semidirect
438. C2×#127C22×C11semidirect
448. C4×#41C22×C11semidirect
449. C4×#41C22×C11semidirect
450. C2×C4×Q8C22×C11semidirect
451. C2×C4×Q8C22×C11semidirect
455. C2×C4×D4C22×C11semidirect
456. C2×C4×D4C22×C11semidirect
457. C2×C4×D4C22×C11semidirect
462. #482C22×C11semidirect
463. #481C22×C11semidirect
464. #480C22×C11semidirect
465. #477C22×C11semidirect
466. #476C22×C11semidirect
467. #475C22×C11semidirect
468. #474C22×C11semidirect
469. #460C22×C11semidirect
470. #460C22×C11semidirect
471. #459C22×C11semidirect
472. #459C22×C11semidirect
473. #449C22×C11semidirect
474. #448C22×C11semidirect
475. #447C22×C11semidirect
476. #442C22×C11semidirect
477. #440C22×C11semidirect
478. C4×SD16C22×C11semidirect
479. C4×D8C22×C11semidirect
480. #432C22×C11semidirect
481. #432C22×C11semidirect
482. #431C22×C11semidirect
483. #431C22×C11semidirect
484. #428C22×C11semidirect
485. #423C22×C11semidirect
486. #418C22×C11semidirect
489. C4×M16C22×C11semidirect
676. #41C11×#41semidirect
786. C11#60561direct (N × H)
805. Q8C2×C11×#41semidirect
818. D4C2×C11×#41semidirect
851. 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
C2×C11×#5322
C2×C4×C11×#412
C11×#31152
C11×#31122
C11×#31092
C11×#31062
C11×#31032
C11×#31002
C11×#30942
C11×#30792
C11×#30382
C11×#30062
C4×C11×AGL(1,ℤ/8)2
C11×#29202
#6056111