Finite Group Databasebeta

← C2×#13080570 #15630276

Subgroups — C2×#13080570 #15630276

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623142C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic, complemented
3#13080570C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622418C211yesmaximal, characteristic, complemented
7C2×#10622374C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622784C211yesmaximal, characteristic, complemented
10C2×#10622778C211yesmaximal, characteristic, complemented
11C2×#10622769C211yesmaximal, characteristic, complemented
12C2×#10622765C211yesmaximal, characteristic, complemented
13C2×#10622341C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4341—21no—
19C22×D4×D11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C22×C11×D8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic, complemented
23#10623360—24no—
24#10623360C2218yescomplemented
25C2×#67000C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×#66992—21no—
28C2×#66991C2211yescharacteristic
29C2×#66990—21no—
30C2×#66988—21no—
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic, complemented
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66982—21no—
36C2×C4×C22⋊D11C2211yescharacteristic
37C22×(C2×D11)⋊C4—21no—
38C22×C4⋊Dic11C2211yescharacteristic, complemented
39C22×#4318C2211yescharacteristic, complemented
40C22×C8×D11C2211yescharacteristic
41#10623142—24no—
42#10623142C2218yescomplemented
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66941C2211yescharacteristic, complemented
45C2×#66936—21no—
46C2×#66931—21no—
47C11×#449C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51#10622845C2218yescomplemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic, complemented
57#10622784C2218yescomplemented
58#10622778C2218yescomplemented
59#10622769C2218yescomplemented
60#10622765C2218yescomplemented
61C2×#66885C2211yescharacteristic
62C2×#66885C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66881C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×#66879C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622652C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66872C2211yescharacteristic, complemented
71#10622418C2218yescomplemented
72#10622408C2218yescomplemented
73D11×#102C2218yescomplemented
74#10622374C2218yescomplemented
75#10622348C2218yescomplemented
76#10622341C2218yescomplemented
77C24×D11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11D411yescharacteristic
93C23×Dic11—21no—
94C23×Dic11—21no—
95C23×Dic11—21no—
96C2×#4341—28no—
97C2×#4341—48no—
98C2×D4×D11—24no—
99C2×D4×D11—22no—
100C2×D4×D11—42no—
101C2×D4×D11C2314yes—
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×Dic22—21no—
106C2×C11×SD16—42no—
107C2×C11×SD16C2314yescomplemented
108C2×C11×D8—24no—
109C2×C11×D8C2314yes—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#121—22no—
113C11×#121C2314yescomplemented
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11D411yescharacteristic
120#67000—22no—
121#67000C2314yes—
122#66999—22no—
123#66999C2314yes—
124#66992—28no—
125#66991—22no—
126#66991C2314yes—
127#66990—28no—
128#66988—28no—
129D4×Dic11—22no—
130D4×Dic11—22no—
131D4×Dic11C2314yes—
132D4×Dic11C2314yescomplemented
133C2×#4323—42no—
134C2×#4323C2314yes—
135#66983—22no—
136#66983C2314yes—
137#66982—28no—
138C4×C22⋊D11D414yes—
139C4×C22⋊D11C2314yes—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—28no—
145C2×(C2×D11)⋊C4D411yescharacteristic
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11—22no—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2314yescomplemented
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4D411yescharacteristic
156C2×C4×Dic11C2311yescharacteristic
157C2×#4318—42no—
158C2×#4318C2314yescomplemented
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C2×C8×D11—42no—
162C2×C8×D11C2314yes—
163C4⋊C4×D11—22no—
164C4⋊C4×D11C2314yes—
165#66941—22no—
166#66941C2314yescomplemented
167#66936—28no—
168#66931—28no—
169C11×#103C2314yescomplemented
170C11×#102C2314yes—
171C11×C22⋊C8C2314yescomplemented
172#66899C2314yescomplemented
173#66899C2314yescomplemented
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yescomplemented
177#66885C2314yes—
178#66885C2314yes—
179(C2×D11)⋊C8C2314yes—
180#66881C2314yescomplemented
181#66881C2314yescomplemented
182#66879C2314yescomplemented
183Dic11⋊C8C2314yescomplemented
184#66873C2314yes—
185#66872C2314yescomplemented
186C2×#3306—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11—24no—
192C23×D11—44no—
193C23×D11—44no—
194C23×D11—82no—
195C23×D11C2×D411yescharacteristic
196C11×#41—28no—
197C11×#41—44no—
198C11×#41—48no—
199C2×Q8×C11—21no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11C2412yes—
203C2×D4×C11—24no—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11#4114yescomplemented
213C2×D4×C11C2412yes—
214C2×D4×C11C2412yes—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—24no—
220C22×C4×C11—44no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—82no—
232C2×C22⋊D11C2×D414yes—
233C22×Dic11—24no—
234C22×Dic11—24no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—24no—
239C22×Dic11—44no—
240C22×Dic11—44no—
241C22×Dic11—82no—
242C22×Dic11C2×D411yescharacteristic
243C22×Dic11C2×D411yescharacteristic
244C22×Dic11C2×D411yescharacteristic
245#4341—432no—
246D4×D11—28no—
247D4×D11—44no—
248D4×D11—48no—
249C2×D44—21no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44C2412yes—
253C2×C4×D11—24no—
254C2×C4×D11—22no—
255C2×C4×D11—22no—
256C2×C4×D11—44no—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2412yes—
259C2×Dic22—24no—
260C2×Dic22—44no—
261C11×SD16—44no—
262C11×D8—28no—
263C2×C8×C11—22no—
264C2×C8×C11—22no—
265C2×C8×C11C2412yes—
266C2×C8×C11C2412yes—
267C11×C4⋊C4—21no—
268C11×C4⋊C4C2412yes—
269C11×C22⋊C4—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272C22⋊Dic11—24no—
273C22⋊Dic11C2×D414yes—
274#4323—44no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4C2×D414yes—
280C4⋊Dic11—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11C2412yes—
285C4⋊Dic11C2412yes—
286C4⋊Dic11C2412yes—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4C2×D414yes—
291C4×Dic11C2×D412yes—
292C4×Dic11C2412yes—
293#4318—44no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298C8×D11—44no—
299C2×#547—111no—
300C2×#546—111no—
301#3306—1116no—
302C2×#489—111no—
303C2×#481—111no—
304C2×#483—111no—
305C2×#476—111no—
306C2×#469—111no—
307C2×#465—111no—
308C2×#463—111no—
309C2×#449D1111yescharacteristic, complemented
310C2×#447—111no—
311C2×#442—111no—
312C2×#435—111no—
313C2×#417—111no—
314C22×#102—111no—
315C23×C11—24no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11C22×D412yes—
327C23×C11C22×D411yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—48no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—48no—
336C22×D11—84no—
337C22×D11—816no—
338C22×D11AGL(1,ℤ/8)14yes—
339C22×D11C22×D412yes—
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—42no—
343D4×C11—24no—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—22no—
347D4×C11—48no—
348D4×C11—48no—
349D4×C11—42no—
350D4×C11C2×#4114yescomplemented
351C2×C4×C11—22no—
352C2×C4×C11—24no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—48no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C2×#4112yes—
363C2×C4×C11H(5,𝔽2)12yes—
364C2×C4×C11C2511yescharacteristic
365C22⋊D11—28no—
366C22⋊D11—48no—
367C22⋊D11—48no—
368C22⋊D11—84no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—48no—
376C2×Dic11—48no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—84no—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383C2×Dic11C22×D412yes—
384D44—22no—
385D44—22no—
386D44—42no—
387C4×D11—24no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—48no—
391Dic22—48no—
392C8×C11—22no—
393C8×C11—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C22×#41—221no—
397C22×#41C2×D1111yescharacteristic
398C23×D4—111no—
399C22×SD16C2×D1111yescharacteristic, complemented
400C22×D8—111no—
401C22×D8C2×D1111yescharacteristic
402C22×M16—111no—
403C23×C8—111no—
404#547—118no—
405#547—224no—
406#546—118no—
407#546—224no—
408C2×C4⋊Q8—111no—
409C2×#124—111no—
410C2×#123—221no—
411C2×#123—221no—
412C2×#123—221no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—221no—
415C2×#121—111no—
416C2×#121—111no—
417C2×#121—221no—
418C2×#121C2×D1111yescharacteristic, complemented
419C2×#120—221no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C22⋊C4—221no—
426#489—118no—
427#483—118no—
428#481—118no—
429#476—118no—
430#469—118no—
431#465—118no—
432#463—118no—
433#449C2×D1118yescomplemented
434#447—118no—
435#442—118no—
436#435—118no—
437C2×#106—111no—
438C2×#106—111no—
439C2×#106—111no—
440C2×C4⋊C8—111no—
441#417—118no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103C2×D1111yescharacteristic, complemented
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—118no—
452C2×#102C2×D1111yescharacteristic
453C2×C22⋊C8—111no—
454C2×C22⋊C8C2×D1111yescharacteristic, complemented
455C2×#97—111no—
456C22×C11—22no—
457C22×C11—24no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—48no—
461C22×C11—44no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—84no—
468C22×C11#54612yes—
469C22×C11C2×AGL(1,ℤ/8)12yes—
470C22×C11#57712yes—
471C22×C11C23×D411yescharacteristic
472C2×D11—22no—
473C2×D11—28no—
474C2×D11—22no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—84no—
480C2×D11C2×AGL(1,ℤ/8)14yes—
481C4×C11—22no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11#54612yes—
485C4×C11C22×#4111yescharacteristic
486C4×C11C2×H(5,𝔽2)11yescharacteristic
487Dic11—22no—
488Dic11—22no—
489Dic11—22no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493C25—221no—
494C2×#41—22no—
495C2×#41—24no—
496C2×#41—42no—
497C2×#41—228no—
498C2×#41—448no—
499C2×#41C22×D1114yes—
500C22×Q8—221no—
501C22×Q8C22×D1111yescharacteristic
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—111no—
505C22×D4—114no—
506C22×D4—111no—
507C22×D4—222no—
508C22×D4—221no—
509C22×D4—224no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—442no—
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—111no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×SD16—42no—
523C2×SD16C22×D1114yescomplemented
524C2×D8—24no—
525C2×D8—114no—
526C2×D8—442no—
527C2×D8C22×D1114yes—
528C2×M16—114no—
529C2×M16—442no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—114no—
533C22×C8—442no—
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1111yescharacteristic
536C4⋊Q8—114no—
537C4⋊Q8—222no—
538#124—114no—
539#124—222no—
540#123—228no—
541#123—228no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—228no—
545C22⋊Q8—222no—
546#121—22no—
547#121—114no—
548#121—114no—
549#121—228no—
550#121—222no—
551#121—222no—
552#121C22×D1114yescomplemented
553#120—228no—
554C4×D4—114no—
555C4×D4—114no—
556C4×D4—114no—
557C4×D4—114no—
558C4×D4—222no—
559C4×D4—222no—
560C2×C4⋊C4—111no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—111no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—228no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4—221no—
583C2×C22⋊C4—221no—
584C2×C42—111no—
585#106—114no—
586#106—114no—
587#106—114no—
588C4⋊C8—114no—
589#103—114no—
590#103—114no—
591#103C22×D1114yescomplemented
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102—114no—
598#102C22×D1114yes—
599C22⋊C8—114no—
600C22⋊C8C22×D1114yescomplemented
601#97—114no—
602C2×C11—44no—
603C2×C11—42no—
604C2×C11—82no—
605C2×C11#330614yescomplemented
606C2×C11C2×#54611yescharacteristic
607C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
608C2×C11C2×#57711yescharacteristic
609D11—24no—
610D11—82no—
611C24—21no—
612C24—21no—
613C24—111no—
614C24—224no—
615C24—221no—
616C24—444no—
617C24—444no—
618C24—882no—
619C24D4×D1111yescharacteristic
620#41—28no—
621#41—44no—
622#41—48no—
623#41—4432no—
624C2×Q8—21no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—224no—
628C2×Q8—444no—
629C2×Q8C23×D1112yes—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—114no—
640C2×D4—112no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—228no—
644C2×D4—224no—
645C2×D4—224no—
646C2×D4—221no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—444no—
650C2×D4—448no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—882no—
654C2×D4#434114yescomplemented
655C2×D4C23×D1112yes—
656C2×D4C23×D1112yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—44no—
663C22×C4—111no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—224no—
669C22×C4—224no—
670C22×C4—224no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—224no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—882no—
681C22×C4D4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—44no—
686D8—28no—
687D8—444no—
688M16—444no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—112no—
692C2×C8—112no—
693C2×C8—222no—
694C2×C8—222no—
695C2×C8—444no—
696C2×C8C23×D1112yes—
697C2×C8C23×D1112yes—
698C4⋊C4—21no—
699C4⋊C4—114no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—112no—
703C4⋊C4—224no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—224no—
709C4⋊C4—221no—
710C4⋊C4C23×D1112yes—
711C22⋊C4—24no—
712C22⋊C4—114no—
713C22⋊C4—114no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—224no—
721C42—112no—
722C42—112no—
723C11C2×#330611yescharacteristic, complemented, Sylow
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—114no—
736C23—112no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—448no—
741C23—448no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23—884no—
746C23—8816no—
747C23C2×D4×D1112yes—
748C23C2×D4×D1111yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—448no—
753D4—24no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—42no—
760D4—228no—
761D4—222no—
762D4—222no—
763D4—448no—
764D4—448no—
765D4—442no—
766D4—884no—
767D4C2×#434114yescomplemented
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—112no—
778C2×C4—112no—
779C2×C4—112no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—224no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—448no—
790C2×C4—448no—
791C2×C4—448no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4—884no—
796C2×C4C2×D4×D1112yes—
797C2×C4C2×D4×D1111yescharacteristic
798C2×C4C2×#434112yes—
799C2×C4#6703712yes—
800C2×C4C24×D1111yescharacteristic
801C8—22no—
802C8—22no—
803C8—222no—
804C8—222no—
805C22—22no—
806C22—24no—
807C22—22no—
808C22—22no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—48no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—84no—
817C22—114no—
818C22—222no—
819C22—222no—
820C22—228no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22—8816no—
825C22—884no—
826C22#1062312212yes—
827C22#1062330112yes—
828C22D11×AGL(1,ℤ/8)12yes—
829C22C22×D4×D1111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—222no—
834C4—222no—
835C4—222no—
836C4—442no—
837C4—442no—
838C4—442no—
839C4#1062312212yes—
840C4C22×#434111yescharacteristic
841C4C2×#6703711yescharacteristic
842C2—42no—
843C2—44no—
844C2—82no—
845C2—224no—
846C2—882no—
847C2#1308057014yesdirect product factor
848C2C2×#1062312211yescharacteristic
849C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
850C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10623142C2semidirect
2. C2×#10623360C2semidirect
3. #13080570C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622418C2semidirect
7. C2×#10622374C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622784C2semidirect
10. C2×#10622778C2semidirect
11. C2×#10622769C2semidirect
12. C2×#10622765C2semidirect
13. C2×#10622341C2semidirect
14. C2×#10622845C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#449C2semidirect
20. C22×C11×SD16C22semidirect
22. C2×C11×#121C22semidirect
24. #10623360C22semidirect
32. C2×D4×Dic11C22semidirect
38. C22×C4⋊Dic11C22semidirect
39. C22×#4318C22semidirect
42. #10623142C22semidirect
44. C2×#66941C22semidirect
47. C11×#449C22semidirect
48. C2×C11×#103C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. #10622845C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
56. C2×#66896C22semidirect
57. #10622784C22semidirect
58. #10622778C22semidirect
59. #10622769C22semidirect
60. #10622765C22semidirect
64. C2×#66881C22semidirect
65. C2×#66881C22semidirect
66. C2×#66879C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622652C22semidirect
70. C2×#66872C22semidirect
71. #10622418C22semidirect
72. #10622408C22semidirect
73. D11×#102C22semidirect
74. #10622374C22semidirect
75. #10622348C22semidirect
76. #10622341C22semidirect
107. C2×C11×SD16C23semidirect
113. C11×#121C23semidirect
132. D4×Dic11C23semidirect
151. C2×C4⋊Dic11C23semidirect
158. C2×#4318C23semidirect
166. #66941C23semidirect
169. C11×#103C23semidirect
171. C11×C22⋊C8C23semidirect
172. #66899C23semidirect
173. #66899C23semidirect
176. #66896C23semidirect
180. #66881C23semidirect
181. #66881C23semidirect
182. #66879C23semidirect
183. Dic11⋊C8C23semidirect
185. #66872C23semidirect
212. C2×D4×C11#41semidirect
309. C2×#449D11semidirect
350. D4×C11C2×#41semidirect
399. C22×SD16C2×D11semidirect
418. C2×#121C2×D11semidirect
433. #449C2×D11semidirect
444. C2×#103C2×D11semidirect
454. C2×C22⋊C8C2×D11semidirect
523. C2×SD16C22×D11semidirect
552. #121C22×D11semidirect
591. #103C22×D11semidirect
600. C22⋊C8C22×D11semidirect
605. C2×C11#3306semidirect
654. C2×D4#4341semidirect
723. C11C2×#3306semidirect
767. D4C2×#4341semidirect
847. C2#13080570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231422
C2×#106233602
#130805702
C2×#106224082
C2×#106223482
C2×#106224182
C2×#106223742
C2×#106226522
C2×#106227842
C2×#106227782
C2×#106227692
C2×#106227652
C2×#106223412
C2×#106228452
C2×D11×#1022
C2×C11×#4492
C2×#330611