Finite Group Databasebeta

← C2×#13078753 #15621884

Subgroups — C2×#13078753 #15621884

Order 2816.

2582 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13078753C2116yesmaximal, direct product factor
4C2×#10622418C211yesmaximal, characteristic, complemented
5C2×#10622387C211yesmaximal, characteristic, complemented
6C2×#10622460C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622670C211yesmaximal, characteristic, complemented
9C2×#10622782C211yesmaximal, characteristic, complemented
10C2×#10622769C211yesmaximal, characteristic
11C2×#10622765C211yesmaximal, characteristic, complemented
12C2×#10622398C211yesmaximal, characteristic, complemented
13C2×#10622430C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×#10622448C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C23×C4×D11—21no—
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic, complemented
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic, complemented
25C22×#4325C2211yescharacteristic
26C2×#66991C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic, complemented
29C22×#4323C2211yescharacteristic
30C2×C4×C22⋊D11—21no—
31#10623211—24no—
32#10623211C2218yescomplemented
33C4×D4×D11—24no—
34C4×D4×D11C2218yescomplemented
35C2×#66946C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66936—21no—
38C2×(C22⋊D11)⋊C4—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C2×C22⋊C4×D11—21no—
41C2×#66932—21no—
42C2×#66930—21no—
43C2×C4×D44C2211yescharacteristic
44C2×C42×D11C2211yescharacteristic
45C2×#66923C2211yescharacteristic, complemented
46C11×#463C2218yescomplemented
47C2×C11×C4⋊C8C2211yescharacteristic, complemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C2×#66899C2211yescharacteristic, complemented
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic, complemented
54#10622782C2218yescomplemented
55#10622777C2218yescomplemented
56#10622769C2218yes—
57#10622765C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×#66879C2211yescharacteristic, complemented
66#10622670C2218yescomplemented
67#10622622C2218yescomplemented
68C2×#66872C2211yescharacteristic, complemented
69C2×#66871C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622460C2218yescomplemented
72#10622448C2218yescomplemented
73#10622430C2218yescomplemented
74#10622418C2218yescomplemented
75#10622398C2218yescomplemented
76#10622387C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C23×Dic11—21no—
86C2×D4×D11—24no—
87C2×D4×D11—24no—
88C2×D4×D11—22no—
89C2×D4×D11C2314yes—
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11—28no—
95C22×C4×D11—48no—
96C22×C4×D11D411yescharacteristic
97C22×C4×D11D411yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C2×C11×SD16—24no—
100C2×C11×SD16C2314yes—
101C2×C11×D8—24no—
102C2×C11×D8C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×#124—22no—
106C11×#124C2314yescomplemented
107C4×D4×C11—22no—
108C4×D4×C11C2314yes—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66999—22no—
118#66999C2314yes—
119Q8×Dic11—22no—
120Q8×Dic11C2314yescomplemented
121C2×#4325—24no—
122C2×#4325C2314yes—
123#66991—22no—
124#66991C2314yes—
125D4×Dic11—22no—
126D4×Dic11—22no—
127D4×Dic11C2314yes—
128D4×Dic11C2314yescomplemented
129C2×#4323—24no—
130C2×#4323C2314yes—
131C4×C22⋊D11—28no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11D411yescharacteristic
145C2×C4×Dic11D411yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149#66946—22no—
150#66946C2314yes—
151C4⋊C4×D11—22no—
152C4⋊C4×D11C2314yes—
153#66936—28no—
154(C22⋊D11)⋊C4—28no—
155(C22⋊D11)⋊C4—28no—
156C22⋊C4×D11—28no—
157#66932—28no—
158#66930—28no—
159C4×D44—22no—
160C4×D44C2314yes—
161C42×D11D414yes—
162C42×D11C2314yes—
163#66923—22no—
164#66923C2314yescomplemented
165C11×C4⋊C8C2314yescomplemented
166C11×#103C2314yescomplemented
167C11×#102C2314yescomplemented
168#66899C2314yescomplemented
169#66896C2314yes—
170#66896C2314yes—
171#66896C2314yescomplemented
172#66885C2314yes—
173#66885C2314yes—
174(C2×D11)⋊C8C2314yes—
175(C2×D11)⋊C8C2314yes—
176#66882C2314yescomplemented
177#66881C2314yescomplemented
178#66879C2314yescomplemented
179#66879C2314yescomplemented
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182C4⋊(C11⋊C8)C2314yescomplemented
183C2×#3114—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11—21no—
186C23×D11—28no—
187C23×D11—21no—
188C23×D11—24no—
189C23×D11—44no—
190C23×D11—44no—
191C23×D11C2×D411yescharacteristic
192C2×Q8×C11—21no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11C2412yes—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11#4114yes—
202C2×D4×C11C2412yes—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—24no—
207C22×C4×C11—44no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—28no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—44no—
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—44no—
221C22×Dic11—44no—
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225D4×D11—216no—
226D4×D11—28no—
227D4×D11—28no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44#4114yes—
231C2×D44C2412yes—
232C2×C4×D11—24no—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—42no—
239C2×C4×D11—44no—
240C2×C4×D11—432no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×C4×D11C2×D412yes—
244C2×C4×D11C2×D414yes—
245C2×C4×D11C2×D414yes—
246C2×C4×D11C2412yes—
247C11×SD16—28no—
248C11×D8—28no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C42×C11C2×D412yes—
259C42×C11C2412yes—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263#4325—28no—
264#4323—28no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11C2412yes—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279C4×Dic11—24no—
280C4×Dic11C2×D412yes—
281C4×Dic11C2×D414yes—
282C4×Dic11C2×D414yes—
283C4×Dic11C2412yes—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288C2×#529—111no—
289C22×C4×D4—111no—
290#3114—1116no—
291C2×#483—111no—
292C2×#480—111no—
293C2×#478—111no—
294C2×#478—111no—
295C2×#463—111no—
296C2×#463D1111yescharacteristic, complemented
297C2×#450—111no—
298C2×#447—111no—
299C2×#442—111no—
300C2×#442—111no—
301C2×#440—111no—
302C2×#440—111no—
303C2×#432—111no—
304C23×C11—24no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—216no—
316C22×D11—24no—
317C22×D11—22no—
318C22×D11—432no—
319C22×D11—48no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—48no—
323C22×D11AGL(1,ℤ/8)14yes—
324C22×D11C22×D412yes—
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—42no—
328D4×C11—24no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—42no—
333D4×C11C2×#4114yes—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—48no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C2×#4112yes—
345C2×C4×C11C2×#4112yes—
346C2×C4×C11C2511yescharacteristic
347C22⋊D11—216no—
348C22⋊D11—48no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—48no—
356C2×Dic11—48no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11C22×D412yes—
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363D44—24no—
364D44—22no—
365D44C2×#4114yes—
366C4×D11—28no—
367C4×D11—24no—
368C4×D11—22no—
369C4×D11—22no—
370C4×D11—44no—
371C4×D11—48no—
372C4×D11—48no—
373C4×D11—48no—
374C8×C11—22no—
375C8×C11—22no—
376C11⋊C8—22no—
377C11⋊C8—22no—
378C23×D4—111no—
379C24×C4—221no—
380C22×SD16—111no—
381C22×SD16C2×D1111yescharacteristic
382C22×D8—111no—
383C22×D8C2×D1111yescharacteristic
384#529—118no—
385#529—224no—
386C2×#126—221no—
387C2×#125—111no—
388C2×#124C2×D1111yescharacteristic, complemented
389C2×#123—221no—
390C2×C22⋊Q8—111no—
391C2×#121—111no—
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4—111no—
395C2×C4×D4—118no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—221no—
399C2×C4×D4—224no—
400C2×C4×D4—221no—
401C2×C4×D4—221no—
402C2×C4×D4C2×D1111yescharacteristic
403C2×#117—221no—
404C22×C4⋊C4—111no—
405C22×C22⋊C4—221no—
406C22×C42—111no—
407#483—118no—
408#480—118no—
409#478—118no—
410#478—118no—
411#463—118no—
412#463C2×D1118yescomplemented
413#450—118no—
414#447—118no—
415#442—118no—
416#442—118no—
417#440—118no—
418#440—118no—
419#432—118no—
420C2×#107—111no—
421C2×#107—111no—
422C2×#106—111no—
423C2×#106—111no—
424C2×C4⋊C8—111no—
425C2×C4⋊C8C2×D1111yescharacteristic, complemented
426C2×#103—111no—
427C2×#103C2×D1111yescharacteristic, complemented
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102C2×D1111yescharacteristic, complemented
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×#97—111no—
437C2×#97—111no—
438C22×C11—24no—
439C22×C11—48no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—84no—
446C22×C11#52512yes—
447C22×C11C2×AGL(1,ℤ/8)12yes—
448C22×C11#57512yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—28no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—24no—
454C2×D11—432no—
455C2×D11—48no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11C2×AGL(1,ℤ/8)14yes—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11#52512yes—
464C4×C11C22×#4111yescharacteristic
465C4×C11C22×#4111yescharacteristic
466Dic11—22no—
467Dic11—22no—
468Dic11—22no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472C25—221no—
473C22×Q8C22×D1111yescharacteristic
474C22×D4—114no—
475C22×D4—111no—
476C22×D4—222no—
477C22×D4—221no—
478C22×D4—224no—
479C22×D4—224no—
480C22×D4—221no—
481C22×D4C22×D1111yescharacteristic
482C22×D4C22×D1111yescharacteristic
483C23×C4—21no—
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—221no—
488C23×C4—228no—
489C23×C4—221no—
490C23×C4—221no—
491C23×C4—221no—
492C23×C4—221no—
493C23×C4—448no—
494C2×SD16—24no—
495C2×SD16—114no—
496C2×SD16—224no—
497C2×SD16C22×D1114yes—
498C2×D8—24no—
499C2×D8—114no—
500C2×D8—224no—
501C2×D8C22×D1114yes—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8C22×D1111yescharacteristic
505C22×C8C22×D1111yescharacteristic
506#126—228no—
507#125—114no—
508#125—222no—
509#124—22no—
510#124C22×D1114yescomplemented
511#123—228no—
512C22⋊Q8—114no—
513C22⋊Q8—222no—
514#121—114no—
515#121—222no—
516C4×Q8—114no—
517C4×Q8—222no—
518C4×D4—22no—
519C4×D4—114no—
520C4×D4—114no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—228no—
524C4×D4—222no—
525C4×D4—228no—
526C4×D4—222no—
527C4×D4—222no—
528C4×D4—228no—
529C4×D4—222no—
530C4×D4C22×D1114yes—
531#117—228no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—222no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—228no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C42—111no—
554C2×C42—111no—
555C2×C42—111no—
556C2×C42—114no—
557C2×C42—114no—
558C2×C42—221no—
559C2×C42C22×D1111yescharacteristic
560#107—114no—
561#107—114no—
562#106—114no—
563#106—114no—
564C4⋊C8—114no—
565C4⋊C8C22×D1114yescomplemented
566#103—114no—
567#103C22×D1114yescomplemented
568#102—114no—
569#102—114no—
570#102—114no—
571#102—114no—
572#102—114no—
573#102C22×D1114yescomplemented
574C22⋊C8—114no—
575C22⋊C8—114no—
576#97—114no—
577#97—114no—
578C2×C11—44no—
579C2×C11—82no—
580C2×C11#311414yescomplemented
581C2×C11C2×#52511yescharacteristic
582C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
583C2×C11C2×#57511yescharacteristic
584D11—24no—
585D11—44no—
586C24—21no—
587C24—21no—
588C24—111no—
589C24—224no—
590C24—228no—
591C24—221no—
592C24—444no—
593C24—444no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8C23×D1112yes—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—114no—
604C2×D4—112no—
605C2×D4—224no—
606C2×D4—228no—
607C2×D4—2216no—
608C2×D4—228no—
609C2×D4—228no—
610C2×D4—224no—
611C2×D4—221no—
612C2×D4—222no—
613C2×D4—444no—
614C2×D4#434114yes—
615C2×D4C23×D1112yes—
616C2×D4C23×D1112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—111no—
622C22×C4—111no—
623C22×C4—111no—
624C22×C4—112no—
625C22×C4—114no—
626C22×C4—112no—
627C22×C4—114no—
628C22×C4—224no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—224no—
632C22×C4—224no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—224no—
639C22×C4—442no—
640C22×C4—444no—
641C22×C4—4432no—
642C22×C4—444no—
643C22×C4—444no—
644C22×C4—444no—
645C22×C4—444no—
646C22×C4D4×D1111yescharacteristic
647C22×C4D4×D1111yescharacteristic
648C22×C4C23×D1111yescharacteristic
649SD16—28no—
650SD16—228no—
651D8—28no—
652D8—228no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—112no—
656C2×C8—112no—
657C2×C8—222no—
658C2×C8—222no—
659C2×C8C23×D1112yes—
660C2×C8C23×D1112yes—
661C4⋊C4—21no—
662C4⋊C4—112no—
663C4⋊C4—112no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—221no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4C23×D1112yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C42—114no—
684C42—112no—
685C42—114no—
686C42—112no—
687C42—224no—
688C42D4×D1112yes—
689C42C23×D1112yes—
690C11C2×#311411yescharacteristic, complemented, Sylow
691C23—24no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—114no—
700C23—112no—
701C23—2216no—
702C23—222no—
703C23—222no—
704C23—224no—
705C23—222no—
706C23—448no—
707C23—448no—
708C23—4432no—
709C23—442no—
710C23—442no—
711C23C2×D4×D1111yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—42no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—114no—
721D4—2216no—
722D4—224no—
723D4—222no—
724D4—448no—
725D4C2×#434114yes—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—48no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—228no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—444no—
747C2×C4—448no—
748C2×C4—448no—
749C2×C4—448no—
750C2×C4—448no—
751C2×C4—448no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4C2×D4×D1112yes—
756C2×C4C2×D4×D1112yes—
757C2×C4C2×D4×D1111yescharacteristic
758C2×C4C2×#434112yes—
759C2×C4#41×D1112yes—
760C2×C4C24×D1111yescharacteristic
761C8—22no—
762C8—22no—
763C8—222no—
764C8—222no—
765C22—24no—
766C22—42no—
767C22—42no—
768C22—48no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—84no—
773C22—114no—
774C22—222no—
775C22—222no—
776C22—228no—
777C22—224no—
778C22—4432no—
779C22—442no—
780C22—442no—
781C22—448no—
782C22#1062313712yes—
783C22#1062329912yes—
784C22D11×AGL(1,ℤ/8)12yes—
785C22C22×D4×D1111yescharacteristic
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—222no—
791C4—222no—
792C4—222no—
793C4—442no—
794C4—442no—
795C4—442no—
796C4#1062313712yes—
797C4C22×#434111yescharacteristic
798C4C2×#41×D1111yescharacteristic
799C2—44no—
800C2—82no—
801C2—224no—
802C2—444no—
803C2#1307875314yesdirect product factor
804C2C2×#1062313711yescharacteristic
805C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
806C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
hypercenterC2×#463D11
hypocenterC11C2×#3114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10623211C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13078753C2direct (N × H)
4. C2×#10622418C2semidirect
5. C2×#10622387C2semidirect
6. C2×#10622460C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622670C2semidirect
9. C2×#10622782C2semidirect
11. C2×#10622765C2semidirect
12. C2×#10622398C2semidirect
13. C2×#10622430C2semidirect
14. C2×#10622777C2semidirect
15. C2×#10622448C2semidirect
16. C2×C11×#463C2semidirect
21. C2×C11×#124C22semidirect
24. C2×Q8×Dic11C22semidirect
28. C2×D4×Dic11C22semidirect
32. #10623211C22semidirect
34. C4×D4×D11C22semidirect
45. C2×#66923C22semidirect
46. C11×#463C22semidirect
47. C2×C11×C4⋊C8C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#102C22semidirect
50. C2×#66899C22semidirect
53. C2×#66896C22semidirect
54. #10622782C22semidirect
55. #10622777C22semidirect
57. #10622765C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66879C22semidirect
65. C2×#66879C22semidirect
66. #10622670C22semidirect
67. #10622622C22semidirect
68. C2×#66872C22semidirect
69. C2×#66871C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622460C22semidirect
72. #10622448C22semidirect
73. #10622430C22semidirect
74. #10622418C22semidirect
75. #10622398C22semidirect
76. #10622387C22semidirect
106. C11×#124C23semidirect
120. Q8×Dic11C23semidirect
128. D4×Dic11C23semidirect
164. #66923C23semidirect
165. C11×C4⋊C8C23semidirect
166. C11×#103C23semidirect
167. C11×#102C23semidirect
168. #66899C23semidirect
171. #66896C23semidirect
176. #66882C23semidirect
177. #66881C23semidirect
178. #66879C23semidirect
179. #66879C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
182. C4⋊(C11⋊C8)C23semidirect
296. C2×#463D11semidirect
388. C2×#124C2×D11semidirect
412. #463C2×D11semidirect
425. C2×C4⋊C8C2×D11semidirect
427. C2×#103C2×D11semidirect
433. C2×#102C2×D11semidirect
510. #124C22×D11semidirect
565. C4⋊C8C22×D11semidirect
567. #103C22×D11semidirect
573. #102C22×D11semidirect
580. C2×C11#3114semidirect
690. C11C2×#3114semidirect
803. C2#13078753direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232112
C2×C4×D4×D112
#130787532
C2×#106224182
C2×#106223872
C2×#106224602
C2×#106226222
C2×#106226702
C2×#106227822
C2×#106227692
C2×#106227652
C2×#106223982
C2×#106224302
C2×#106227772
C2×#106224482
C2×C11×#4632
C2×#311411