Finite Group Databasebeta

← C2×#13080757 #15630331

Subgroups — C2×#13080757 #15630331

Order 2816.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic, complemented
2#13080757C2116yesmaximal, direct product factor
3C2×#10622684C211yesmaximal, characteristic, complemented
4C2×#10622647C211yesmaximal, characteristic, complemented
5C2×#10622648C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622651C211yesmaximal, characteristic, complemented
9C2×#10622685C211yesmaximal, characteristic, complemented
10C2×#10622830C211yesmaximal, characteristic, complemented
11C2×#10622830C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622828C211yesmaximal, characteristic, complemented
15C22×#66896C211yesmaximal, characteristic, complemented
16C2×D42×C11C211yesmaximal, characteristic, complemented
17C23×D4×C11—21no—
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20D42×C11—24no—
21D42×C11C2218yescomplemented
22C2×C11×#127C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#120—21no—
27C2×C11×#120—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×#66992—21no—
31C22×#4323C2211yescharacteristic
32C22×#4323C2211yescharacteristic, complemented
33C22×#4323C2211yescharacteristic, complemented
34C2×#66983C2211yescharacteristic, complemented
35C2×#66983C2211yescharacteristic, complemented
36C2×#66979C2211yescharacteristic, complemented
37C22×C4⋊Dic11C2211yescharacteristic, complemented
38C22×#4318C2211yescharacteristic, complemented
39C23×C11⋊C8C2211yescharacteristic, complemented
40#10623096—24no—
41#10623096C2218yescomplemented
42C2×#66951—21no—
43C2×#66936—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×C4×D44C2211yescharacteristic, complemented
46C2×#66923C2211yescharacteristic, complemented
47#10622830C2218yescomplemented
48#10622830C2218yescomplemented
49#10622828C2218yescomplemented
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2218yescomplemented
54C2×#66896C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic, complemented
57C2×#66896C2211yescharacteristic, complemented
58C2×#66896C2211yescharacteristic, complemented
59C2×#66896C2211yescharacteristic, complemented
60C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
61C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
62#10622685C2218yescomplemented
63#10622684C2218yescomplemented
64#10622652C2218yescomplemented
65#10622651C2218yescomplemented
66#10622648C2218yescomplemented
67#10622647C2218yescomplemented
68#10622627C2218yescomplemented
69#10622624C2218yescomplemented
70#10622622C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73C2×#66872C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C25×C11—21no—
78C25×C11—21no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—28no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—22no—
88C22×D4×C11—22no—
89C22×D4×C11—21no—
90C22×D4×C11—42no—
91C22×D4×C11—42no—
92C22×D4×C11—48no—
93C22×D4×C11D411yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C22×D4×C11C2314yes—
97C22×D4×C11C2314yes—
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C22×C22⋊D11—21no—
103C22×C22⋊D11—21no—
104C23×Dic11—21no—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C11×#127—22no—
108C11×#127C2314yes—
109C11×#121—22no—
110C11×#121—22no—
111C11×#121—28no—
112C11×#121C2314yes—
113C11×#121C2314yes—
114C11×#120—28no—
115C11×#120—28no—
116C4×D4×C11—22no—
117C4×D4×C11D414yes—
118C4×D4×C11C2314yes—
119C4×D4×C11C2314yes—
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C11×C22⋊C4D411yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×C22⋊Dic11—21no—
129#66992—28no—
130C2×#4323—24no—
131C2×#4323—42no—
132C2×#4323—42no—
133C2×#4323C2314yes—
134C2×#4323C2314yescomplemented
135C2×#4323C2314yescomplemented
136#66983—22no—
137#66983—22no—
138#66983C2314yescomplemented
139#66983C2314yescomplemented
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143#66979—22no—
144#66979C2314yescomplemented
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11—22no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2314yescomplemented
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×#4318—42no—
155C2×#4318C2314yescomplemented
156C22×C11⋊C8—42no—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2314yescomplemented
162#66951—28no—
163#66936—28no—
164(C22⋊D11)⋊C4—28no—
165C4×D44—22no—
166C4×D44C2314yescomplemented
167#66923—22no—
168#66923C2314yescomplemented
169#66896C2314yes—
170#66896C2314yes—
171#66896C2314yes—
172#66896C2314yescomplemented
173#66896C2314yescomplemented
174#66896C2314yescomplemented
175#66896C2314yescomplemented
176#66896C2314yescomplemented
177#66896C2314yescomplemented
178C22⋊(C11⋊C8)C2314yescomplemented
179C22⋊(C11⋊C8)C2314yescomplemented
180#66873C2314yescomplemented
181#66872C2314yescomplemented
182#66872C2314yescomplemented
183#66871C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185#66867C2314yescomplemented
186C2×#3318—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—24no—
191C24×C11—24no—
192C24×C11—44no—
193C24×C11—44no—
194C24×C11—44no—
195C24×C11—44no—
196C24×C11—82no—
197C24×C11—82no—
198C24×C11C2×D411yescharacteristic
199C24×C11C2×D411yescharacteristic
200C23×D11—21no—
201C2×D4×C11—24no—
202C2×D4×C11—28no—
203C2×D4×C11—28no—
204C2×D4×C11—24no—
205C2×D4×C11—24no—
206C2×D4×C11—21no—
207C2×D4×C11—24no—
208C2×D4×C11—24no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—48no—
221C2×D4×C11—48no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
224C2×D4×C11—44no—
225C2×D4×C11—432no—
226C2×D4×C11—44no—
227C2×D4×C11—44no—
228C2×D4×C11—82no—
229C2×D4×C11C2×D414yes—
230C2×D4×C11#4114yes—
231C2×D4×C11C2412yes—
232C2×D4×C11C2412yes—
233C2×D4×C11C2412yes—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—21no—
239C22×C4×C11—24no—
240C22×C4×C11—44no—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—24no—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—82no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—24no—
258C22×Dic11—82no—
259C2×D44—21no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44C2412yes—
263C2×C4×D11—24no—
264C2×C4×D11—82no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4C2×D414yes—
267C11×C4⋊C4C2412yes—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4C2×D414yes—
272C11×C22⋊C4C2×D414yes—
273C42×C11C2×D412yes—
274C42×C11C2412yes—
275C22⋊Dic11—24no—
276#4323—28no—
277#4323—44no—
278#4323—44no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11—24no—
286C4⋊Dic11C2412yes—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291C4×Dic11—24no—
292#4318—44no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—44no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301C2×C11⋊C8C2412yes—
302C2×#553—111no—
303C2×D42D1111yescharacteristic, complemented
304#3318—1116no—
305C2×#490—111no—
306C2×#481—111no—
307C2×#482—111no—
308C2×#478—111no—
309C2×#469—111no—
310C2×#466—111no—
311C2×#459—111no—
312C2×#447—111no—
313C2×#447—111no—
314C2×#442—111no—
315C2×#435—111no—
316C2×#418—111no—
317C22×#102—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—24no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—48no—
328C23×C11—48no—
329C23×C11—48no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—48no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—816no—
342C23×C11—816no—
343C23×C11AGL(1,ℤ/8)14yes—
344C23×C11C22×D412yes—
345C23×C11C22×D412yes—
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351D4×C11—28no—
352D4×C11—24no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—48no—
359D4×C11—48no—
360D4×C11—48no—
361D4×C11—48no—
362D4×C11—48no—
363D4×C11—42no—
364D4×C11—42no—
365D4×C11—84no—
366D4×C11C2×#4114yes—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—24no—
372C2×C4×C11—24no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—48no—
379C2×C4×C11—42no—
380C2×C4×C11C22×D412yes—
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D412yes—
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C2×#4112yes—
386C2×C4×C11H(5,𝔽2)12yes—
387C2×C4×C11C2511yescharacteristic
388C22⋊D11—48no—
389C22⋊D11—84no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—42no—
396C2×Dic11—84no—
397D44—22no—
398D44—22no—
399D44—42no—
400C4×D11—84no—
401C11⋊C8—22no—
402C11⋊C8—22no—
403C11⋊C8—22no—
404C11⋊C8—22no—
405C23×D4—21no—
406C23×D4C2×D1111yescharacteristic
407C23×D4C2×D1111yescharacteristic
408C22×D8—111no—
409C22×D8—111no—
410C22×D8—111no—
411C22×M16—111no—
412C23×C8—111no—
413#553—118no—
414#553—224no—
415D42—24no—
416D42C2×D1118yescomplemented
417C2×#127C2×D1111yescharacteristic
418C2×#126—221no—
419C2×#125—111no—
420C2×#123—221no—
421C2×#121—21no—
422C2×#121—111no—
423C2×#121—111no—
424C2×#121—221no—
425C2×#121C2×D1111yescharacteristic
426C2×#121C2×D1111yescharacteristic
427C2×#120—21no—
428C2×#120—21no—
429C2×C4×D4—111no—
430C2×C4×D4—221no—
431C2×C4×D4C2×D1111yescharacteristic
432C2×C4×D4C2×D1111yescharacteristic
433C2×#117—111no—
434C22×C4⋊C4—111no—
435#490—118no—
436#482—118no—
437#481—118no—
438#478—118no—
439#469—118no—
440#466—118no—
441#459—118no—
442#447—118no—
443#447—118no—
444#442—118no—
445#435—118no—
446C2×#107—111no—
447C2×#106—111no—
448C2×#106—111no—
449C2×C4⋊C8—111no—
450#418—118no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
459C2×#102—111no—
460C2×#102—118no—
461C2×#102—111no—
462C2×C22⋊C8—111no—
463C2×C22⋊C8—111no—
464C2×#97—111no—
465C22×C11—22no—
466C22×C11—28no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—24no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—44no—
473C22×C11—48no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—816no—
483C22×C11—816no—
484C22×C11—84no—
485C22×C11—84no—
486C22×C11#54612yes—
487C22×C11C2×AGL(1,ℤ/8)14yes—
488C22×C11C2×AGL(1,ℤ/8)12yes—
489C22×C11#57612yes—
490C22×C11C23×D411yescharacteristic
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—84no—
495C4×C11—22no—
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—22no—
499C4×C11—42no—
500C4×C11#54612yes—
501C4×C11C22×#4111yescharacteristic
502C4×C11C2×H(5,𝔽2)11yescharacteristic
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506C25—21no—
507C25—21no—
508C22×D4—24no—
509C22×D4—24no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—28no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—42no—
520C22×D4—42no—
521C22×D4—48no—
522C22×D4—111no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4C22⋊D1111yescharacteristic
526C22×D4C22×D1111yescharacteristic
527C22×D4C22×D1111yescharacteristic
528C22×D4C22×D1114yes—
529C22×D4C22×D1114yes—
530C22×D4C22×D1111yescharacteristic
531C23×C4—21no—
532C23×C4—221no—
533C23×C4—221no—
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536C2×D8—114no—
537C2×D8—114no—
538C2×D8—114no—
539C2×D8—224no—
540C2×D8—442no—
541C2×D8—442no—
542C2×M16—114no—
543C2×M16—442no—
544C22×C8—111no—
545C22×C8—111no—
546C22×C8—111no—
547C22×C8—111no—
548C22×C8—114no—
549C22×C8—442no—
550#127—22no—
551#127C22×D1114yes—
552#126—228no—
553#125—114no—
554#125—222no—
555#123—228no—
556#121—22no—
557#121—22no—
558#121—28no—
559#121—114no—
560#121—114no—
561#121—228no—
562#121—222no—
563#121—222no—
564#121C22×D1114yes—
565#121C22×D1114yes—
566#120—28no—
567#120—28no—
568C4×D4—22no—
569C4×D4—114no—
570C4×D4—228no—
571C4×D4—222no—
572C4×D4C22⋊D1114yes—
573C4×D4C22×D1114yes—
574C4×D4C22×D1114yes—
575#117—114no—
576#117—222no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—221no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4C22⋊D1111yescharacteristic
586C2×C4⋊C4C22×D1111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C22⋊C4C22⋊D1111yescharacteristic
595C2×C22⋊C4C22⋊D1111yescharacteristic
596C2×C42—221no—
597C2×C42C22×D1111yescharacteristic
598#107—114no—
599#106—114no—
600#106—114no—
601C4⋊C8—114no—
602#102—114no—
603#102—114no—
604#102—114no—
605#102—114no—
606#102—114no—
607#102—114no—
608#102—114no—
609#102—114no—
610#102—114no—
611#102—114no—
612C22⋊C8—114no—
613C22⋊C8—114no—
614#97—114no—
615C2×C11—24no—
616C2×C11—42no—
617C2×C11—44no—
618C2×C11—82no—
619C2×C11—82no—
620C2×C11#331814yescomplemented
621C2×C11C2×#54611yescharacteristic
622C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
623C2×C11C2×#57611yescharacteristic
624D11—82no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—24no—
629C24—24no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24—44no—
634C24—82no—
635C24—82no—
636C24—221no—
637C24C2×C22⋊D1111yescharacteristic
638C24C2×C22⋊D1111yescharacteristic
639C2×D4—24no—
640C2×D4—28no—
641C2×D4—28no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—44no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—432no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—112no—
668C2×D4—224no—
669C2×D4—224no—
670C2×D4—222no—
671C2×D4—222no—
672C2×D4—221no—
673C2×D4—444no—
674C2×D4—882no—
675C2×D4#434114yes—
676C2×D4C2×C22⋊D1114yes—
677C2×D4C23×D1112yes—
678C2×D4C23×D1112yes—
679C2×D4C23×D1112yes—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—44no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—224no—
691C22×C4—224no—
692C22×C4—882no—
693C22×C4—882no—
694C22×C4C2×C22⋊D1112yes—
695C22×C4C2×C22⋊D1112yes—
696C22×C4C2×C22⋊D1111yescharacteristic
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1111yescharacteristic
699C22×C4C2×C22⋊D1111yescharacteristic
700C22×C4C23×D1112yes—
701C22×C4C23×D1112yes—
702C22×C4C23×D1111yescharacteristic
703D8—228no—
704D8—444no—
705D8—444no—
706M16—444no—
707C2×C8—112no—
708C2×C8—112no—
709C2×C8—112no—
710C2×C8—112no—
711C2×C8—222no—
712C2×C8—222no—
713C2×C8—222no—
714C2×C8—222no—
715C2×C8—444no—
716C4⋊C4—21no—
717C4⋊C4—112no—
718C4⋊C4—112no—
719C4⋊C4—112no—
720C4⋊C4—221no—
721C4⋊C4—221no—
722C4⋊C4—224no—
723C4⋊C4—221no—
724C4⋊C4—224no—
725C4⋊C4—224no—
726C4⋊C4C2×C22⋊D1114yes—
727C4⋊C4C23×D1112yes—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C22⋊C4C2×C22⋊D1114yes—
736C22⋊C4C2×C22⋊D1114yes—
737C42—224no—
738C42C2×C22⋊D1112yes—
739C42C23×D1112yes—
740C11C2×#331811yescharacteristic, complemented, Sylow
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—24no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—48no—
751C23—48no—
752C23—48no—
753C23—42no—
754C23—42no—
755C23—48no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—84no—
763C23—84no—
764C23—816no—
765C23—816no—
766C23—222no—
767C23—442no—
768C23—442no—
769C23—442no—
770C23#6698514yes—
771C23C22×C22⋊D1112yes—
772C23C22×C22⋊D1112yes—
773C23C22×C22⋊D1111yescharacteristic
774D4—28no—
775D4—24no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—48no—
783D4—48no—
784D4—48no—
785D4—48no—
786D4—42no—
787D4—42no—
788D4—84no—
789D4—222no—
790D4—222no—
791D4—448no—
792D4—442no—
793D4—884no—
794D4C2×#434114yes—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—48no—
807C2×C4—42no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—442no—
812C2×C4—442no—
813C2×C4—442no—
814C2×C4—884no—
815C2×C4—884no—
816C2×C4C2×#434112yes—
817C2×C4#6703712yes—
818C2×C4C22×C22⋊D1112yes—
819C2×C4C22×C22⋊D1112yes—
820C2×C4C22×C22⋊D1112yes—
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1111yescharacteristic
823C2×C4C24×D1111yescharacteristic
824C8—222no—
825C8—222no—
826C8—222no—
827C8—222no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—44no—
836C22—48no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—816no—
846C22—816no—
847C22—84no—
848C22—84no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—884no—
853C22C2×#6698514yes—
854C22C2×#6698512yes—
855C22#1062333712yes—
856C22#1062336612yes—
857C22C23×C22⋊D1111yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4#1062333712yes—
867C4C22×#434111yescharacteristic
868C4C2×#6703711yescharacteristic
869C2—24no—
870C2—42no—
871C2—44no—
872C2—82no—
873C2—82no—
874C2—882no—
875C2#1308075714yesdirect product factor
876C2C2×#1062333711yescharacteristic
877C2C22×#6698511yescharacteristic
878C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D42×C11C2
socleC23×C11C22×D4
hypercenterC2×D42D11
hypocenterC11C2×#3318
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#10623096C2semidirect
2. #13080757C2direct (N × H)
3. C2×#10622684C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622651C2semidirect
9. C2×#10622685C2semidirect
10. C2×#10622830C2semidirect
11. C2×#10622830C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622828C2semidirect
15. C22×#66896C2semidirect
16. C2×D42×C11C2semidirect
21. D42×C11C22semidirect
32. C22×#4323C22semidirect
33. C22×#4323C22semidirect
34. C2×#66983C22semidirect
35. C2×#66983C22semidirect
36. C2×#66979C22semidirect
37. C22×C4⋊Dic11C22semidirect
38. C22×#4318C22semidirect
39. C23×C11⋊C8C22semidirect
41. #10623096C22semidirect
45. C2×C4×D44C22semidirect
46. C2×#66923C22semidirect
47. #10622830C22semidirect
48. #10622830C22semidirect
49. #10622828C22semidirect
53. C2×#66896C22semidirect
54. C2×#66896C22semidirect
55. C2×#66896C22semidirect
56. C2×#66896C22semidirect
57. C2×#66896C22semidirect
58. C2×#66896C22semidirect
59. C2×#66896C22semidirect
60. C2×C22⋊(C11⋊C8)C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622685C22semidirect
63. #10622684C22semidirect
64. #10622652C22semidirect
65. #10622651C22semidirect
66. #10622648C22semidirect
67. #10622647C22semidirect
68. #10622627C22semidirect
69. #10622624C22semidirect
70. #10622622C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. C2×#66872C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
134. C2×#4323C23semidirect
135. C2×#4323C23semidirect
138. #66983C23semidirect
139. #66983C23semidirect
144. #66979C23semidirect
150. C2×C4⋊Dic11C23semidirect
155. C2×#4318C23semidirect
161. C22×C11⋊C8C23semidirect
166. C4×D44C23semidirect
168. #66923C23semidirect
172. #66896C23semidirect
173. #66896C23semidirect
174. #66896C23semidirect
175. #66896C23semidirect
176. #66896C23semidirect
177. #66896C23semidirect
178. C22⋊(C11⋊C8)C23semidirect
179. C22⋊(C11⋊C8)C23semidirect
180. #66873C23semidirect
181. #66872C23semidirect
182. #66872C23semidirect
183. #66871C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
185. #66867C23semidirect
303. C2×D42D11semidirect
416. D42C2×D11semidirect
620. C2×C11#3318semidirect
740. C11C2×#3318semidirect
875. C2#13080757direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
#130807572
C2×#106226842
C2×#106226472
C2×#106226482
C2×#106226222
C2×#106226522
C2×#106226512
C2×#106226852
C2×#106228302
C2×#106226272
C2×#106226242
C2×#106228282
C22×#668962
C2×D42×C112
C2×#331811