Finite Group Databasebeta

← C2×#13080577 #15630283

Subgroups — C2×#13080577 #15630283

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×#10623086C211yesmaximal, characteristic, complemented
2#13080577C2116yesmaximal, direct product factor
3C2×#10622668C211yesmaximal, characteristic, complemented
4C2×#10622647C211yesmaximal, characteristic, complemented
5C2×#10622656C211yesmaximal, characteristic, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622661C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic, complemented
11C2×#10622830C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C22×#66896C211yesmaximal, characteristic, complemented
16C2×C11×#546C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×#4341—21no—
20C11×#546—24no—
21C11×#546C2218yescomplemented
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#120—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C22⋊C4—21no—
31C22×#4325C2211yescharacteristic, complemented
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic, complemented
36C22×C4⋊Dic11C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic, complemented
38C22×#4318C2211yescharacteristic, complemented
39C23×C11⋊C8C2211yescharacteristic
40#10623086—24no—
41#10623086C2218yescomplemented
42C2×#66950—21no—
43C2×#66939—21no—
44C2×#66939—21no—
45C2×C4×D44C2211yescharacteristic, complemented
46C2×#66922C2211yescharacteristic, complemented
47#10622851C2218yescomplemented
48#10622845C2218yescomplemented
49C2×#66899C2211yescharacteristic, complemented
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52#10622830C2218yescomplemented
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2218yescomplemented
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
62#10622670C2218yescomplemented
63#10622668C2218yescomplemented
64#10622661C2218yescomplemented
65#10622656C2218yescomplemented
66#10622652C2218yescomplemented
67#10622647C2218yescomplemented
68#10622627C2218yescomplemented
69#10622624C2218yescomplemented
70#10622621C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73C2×#66872C2211yescharacteristic, complemented
74C2×#66872C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—22no—
88C22×D4×C11—42no—
89C22×D4×C11D411yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2314yes—
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C23×Dic11—21no—
100C23×Dic11—21no—
101C2×#4341—28no—
102C2×#4341—48no—
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×Dic22—21no—
106C11×#124—22no—
107C11×#124C2314yes—
108C11×#123—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8C2314yes—
111C11×#121—22no—
112C11×#121—28no—
113C11×#121C2314yes—
114C11×#120—28no—
115C4×D4×C11—22no—
116C4×D4×C11D414yes—
117C4×D4×C11C2314yes—
118C4×D4×C11C2314yes—
119C2×C11×C4⋊C4—21no—
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⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—28no—
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C11×C22⋊C4D411yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C2×#4325—42no—
132C2×#4325C2314yescomplemented
133C2×#4323—24no—
134C2×#4323—42no—
135C2×#4323C2314yes—
136C2×#4323C2314yes—
137#66983—22no—
138#66983—22no—
139#66983C2314yes—
140#66983C2314yescomplemented
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11—22no—
148C2×C4⋊Dic11—22no—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2314yes—
153C2×C4⋊Dic11C2314yescomplemented
154C2×#4318—42no—
155C2×#4318C2314yescomplemented
156C22×C11⋊C8—42no—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2314yes—
162#66950—28no—
163#66939—28no—
164#66939—28no—
165C4×D44—22no—
166C4×D44C2314yescomplemented
167#66922—22no—
168#66922C2314yescomplemented
169#66899C2314yescomplemented
170#66899C2314yescomplemented
171#66899C2314yescomplemented
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177#66896C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179C22⋊(C11⋊C8)C2314yescomplemented
180#66873C2314yescomplemented
181#66872C2314yescomplemented
182#66872C2314yescomplemented
183#66872C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185#66867C2314yescomplemented
186C2×#3306—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—24no—
190C24×C11—44no—
191C24×C11—44no—
192C24×C11—82no—
193C24×C11C2×D411yescharacteristic
194C24×C11C2×D411yescharacteristic
195C23×D11—21no—
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—28no—
205C2×D4×C11—24no—
206C2×D4×C11—24no—
207C2×D4×C11—21no—
208C2×D4×C11—24no—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—22no—
213C2×D4×C11—44no—
214C2×D4×C11—48no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—82no—
218C2×D4×C11C2×D414yes—
219C2×D4×C11#4114yescomplemented
220C2×D4×C11C2412yes—
221C2×D4×C11C2412yes—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—24no—
229C22×C4×C11—24no—
230C22×C4×C11—44no—
231C22×C4×C11—82no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2411yescharacteristic
241C2×C22⋊D11—24no—
242C2×C22⋊D11—24no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C22×Dic11—24no—
246C22×Dic11—24no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—44no—
251C22×Dic11—44no—
252#4341—432no—
253C2×D44—21no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—44no—
259C2×Dic22—24no—
260C2×Dic22—44no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4C2×D414yes—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4C2×D414yes—
271C11×C22⋊C4C2×D414yes—
272C42×C11C2×D412yes—
273C42×C11C2412yes—
274#4325—44no—
275#4323—28no—
276#4323—44no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—24no—
283C4⋊Dic11—21no—
284C4⋊Dic11—24no—
285C4⋊Dic11—24no—
286C4⋊Dic11C2412yes—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289#4318—44no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—44no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298C2×C11⋊C8C2412yes—
299C2×#547—111no—
300C2×#546D1111yescharacteristic, complemented
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×#449—111no—
310C2×#447—111no—
311C2×#442—111no—
312C2×#435—111no—
313C2×#417—111no—
314C22×#102—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—24no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—48no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—48no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—84no—
331C23×C11—816no—
332C23×C11AGL(1,ℤ/8)14yes—
333C23×C11C22×D412yes—
334C23×C11C22×D412yes—
335C23×C11C22×D411yescharacteristic
336C22×D11—22no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—42no—
343D4×C11—28no—
344D4×C11—24no—
345D4×C11—22no—
346D4×C11—22no—
347D4×C11—22no—
348D4×C11—48no—
349D4×C11—48no—
350D4×C11—42no—
351D4×C11—84no—
352D4×C11C2×#4114yescomplemented
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—24no—
358C2×C4×C11—24no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—48no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—84no—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C2×#4112yes—
375C2×C4×C11H(5,𝔽2)12yes—
376C2×C4×C11C2511yescharacteristic
377C22⋊D11—48no—
378C22⋊D11—48no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—48no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—48no—
387D44—22no—
388D44—22no—
389D44—42no—
390C4×D11—48no—
391Dic22—48no—
392C11⋊C8—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C22×#41—221no—
397C22×#41C2×D1111yescharacteristic
398C23×D4C2×D1111yescharacteristic
399C22×SD16—111no—
400C22×D8—111no—
401C22×D8—111no—
402C22×M16—111no—
403C23×C8—111no—
404#547—118no—
405#547—224no—
406#546—24no—
407#546C2×D1118yescomplemented
408C2×C4⋊Q8—111no—
409C2×#124C2×D1111yescharacteristic
410C2×#123—21no—
411C2×#123—221no—
412C2×#123—221no—
413C2×C22⋊Q8—221no—
414C2×C22⋊Q8C2×D1111yescharacteristic
415C2×#121—21no—
416C2×#121—111no—
417C2×#121—111no—
418C2×#121C2×D1111yescharacteristic
419C2×#120—21no—
420C2×C4×D4—111no—
421C2×C4×D4C2×D1111yescharacteristic
422C2×C4×D4C2×D1111yescharacteristic
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C22⋊C4—21no—
426#489—118no—
427#483—118no—
428#481—118no—
429#476—118no—
430#469—118no—
431#465—118no—
432#463—118no—
433#449—118no—
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×#103—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—118no—
451C2×#102—111no—
452C2×#102—111no—
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C2×#97—111no—
456C22×C11—22no—
457C22×C11—28no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—24no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—44no—
464C22×C11—48no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—816no—
471C22×C11—84no—
472C22×C11#54612yes—
473C22×C11C2×AGL(1,ℤ/8)14yes—
474C22×C11C2×AGL(1,ℤ/8)12yes—
475C22×C11#57712yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—84no—
481C4×C11—22no—
482C4×C11—22no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11#54612yes—
488C4×C11C22×#4111yescharacteristic
489C4×C11C2×H(5,𝔽2)11yescharacteristic
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493C25—21no—
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—24no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—42no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4C22⋊D1111yescharacteristic
512C22×D4C22×D1111yescharacteristic
513C22×D4C22×D1114yes—
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—442no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—224no—
527C2×D8—442no—
528C2×M16—114no—
529C2×M16—442no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—111no—
533C22×C8—111no—
534C22×C8—114no—
535C22×C8—442no—
536C4⋊Q8—114no—
537C4⋊Q8—222no—
538#124—22no—
539#124C22×D1114yes—
540#123—28no—
541#123—228no—
542#123—228no—
543C22⋊Q8—22no—
544C22⋊Q8—228no—
545C22⋊Q8C22×D1114yes—
546#121—22no—
547#121—28no—
548#121—114no—
549#121—114no—
550#121—222no—
551#121—222no—
552#121C22×D1114yes—
553#120—28no—
554C4×D4—22no—
555C4×D4—114no—
556C4×D4—222no—
557C4×D4C22⋊D1114yes—
558C4×D4C22×D1114yes—
559C4×D4C22×D1114yes—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—221no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4C22⋊D1111yescharacteristic
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—28no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4C22⋊D1111yescharacteristic
583C2×C22⋊C4C22⋊D1111yescharacteristic
584C2×C42C22×D1111yescharacteristic
585#106—114no—
586#106—114no—
587#106—114no—
588C4⋊C8—114no—
589#103—114no—
590#103—114no—
591#103—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102—114no—
598#102—114no—
599C22⋊C8—114no—
600C22⋊C8—114no—
601#97—114no—
602C2×C11—24no—
603C2×C11—42no—
604C2×C11—44no—
605C2×C11—82no—
606C2×C11#330614yescomplemented
607C2×C11C2×#54611yescharacteristic
608C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
609C2×C11C2×#57711yescharacteristic
610D11—82no—
611C24—21no—
612C24—21no—
613C24—24no—
614C24—44no—
615C24—44no—
616C24—82no—
617C24—221no—
618C24C2×C22⋊D1111yescharacteristic
619C24C2×C22⋊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—28no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—44no—
641C2×D4—48no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—82no—
645C2×D4—112no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—222no—
649C2×D4—222no—
650C2×D4—221no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4#434114yescomplemented
654C2×D4C2×C22⋊D1114yes—
655C2×D4C23×D1112yes—
656C2×D4C23×D1112yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—44no—
666C22×C4—82no—
667C22×C4—224no—
668C22×C4—224no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—224no—
673C22×C4—444no—
674C22×C4—444no—
675C22×C4—444no—
676C22×C4C2×C22⋊D1112yes—
677C22×C4C2×C22⋊D1112yes—
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—444no—
686D8—228no—
687D8—444no—
688M16—444no—
689C2×C8—112no—
690C2×C8—112no—
691C2×C8—112no—
692C2×C8—112no—
693C2×C8—222no—
694C2×C8—222no—
695C2×C8—222no—
696C2×C8—222no—
697C2×C8—444no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—112no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—224no—
707C4⋊C4—224no—
708C4⋊C4—224no—
709C4⋊C4C2×C22⋊D1114yes—
710C4⋊C4C23×D1112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4C2×C22⋊D1114yes—
720C22⋊C4C2×C22⋊D1114yes—
721C42C2×C22⋊D1112yes—
722C42C23×D1112yes—
723C11C2×#330611yescharacteristic, complemented, Sylow
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—48no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—48no—
737C23—42no—
738C23—42no—
739C23—84no—
740C23—816no—
741C23—222no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23#6700214yes—
746C23C22×C22⋊D1112yes—
747C23C22×C22⋊D1112yes—
748C23C22×C22⋊D1111yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—448no—
753D4—28no—
754D4—24no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—48no—
759D4—48no—
760D4—42no—
761D4—84no—
762D4—222no—
763D4—222no—
764D4—448no—
765D4—448no—
766D4—442no—
767D4C2×#434114yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—48no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—84no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—448no—
788C2×C4—448no—
789C2×C4—442no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—448no—
793C2×C4C2×#434112yes—
794C2×C4#6703712yes—
795C2×C4C22×C22⋊D1112yes—
796C2×C4C22×C22⋊D1112yes—
797C2×C4C22×C22⋊D1112yes—
798C2×C4C22×C22⋊D1112yes—
799C2×C4C22×C22⋊D1111yescharacteristic
800C2×C4C24×D1111yescharacteristic
801C8—222no—
802C8—222no—
803C8—222no—
804C8—222no—
805C22—28no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—24no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—48no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—816no—
820C22—84no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22—884no—
825C22#1062333712yes—
826C22C2×#6700214yes—
827C22C2×#6700212yes—
828C22#1062336712yes—
829C22C23×C22⋊D1111yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—442no—
837C4—442no—
838C4—442no—
839C4#1062333712yes—
840C4C22×#434111yescharacteristic
841C4C2×#6703711yescharacteristic
842C2—24no—
843C2—42no—
844C2—44no—
845C2—82no—
846C2—882no—
847C2#1308057714yesdirect product factor
848C2C2×#1062333711yescharacteristic
849C2C22×#6700211yescharacteristic
850C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11C2×#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. #13080577C2direct (N × H)
3. C2×#10622668C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622656C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622661C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622830C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622845C2semidirect
15. C22×#66896C2semidirect
16. C2×C11×#546C2semidirect
21. C11×#546C22semidirect
31. C22×#4325C22semidirect
35. C2×#66983C22semidirect
37. C22×C4⋊Dic11C22semidirect
38. C22×#4318C22semidirect
41. #10623086C22semidirect
45. C2×C4×D44C22semidirect
46. C2×#66922C22semidirect
47. #10622851C22semidirect
48. #10622845C22semidirect
49. C2×#66899C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
52. #10622830C22semidirect
59. C2×#66896C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622670C22semidirect
63. #10622668C22semidirect
64. #10622661C22semidirect
65. #10622656C22semidirect
66. #10622652C22semidirect
67. #10622647C22semidirect
68. #10622627C22semidirect
69. #10622624C22semidirect
70. #10622621C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. C2×#66872C22semidirect
74. C2×#66872C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
132. C2×#4325C23semidirect
140. #66983C23semidirect
153. C2×C4⋊Dic11C23semidirect
155. C2×#4318C23semidirect
166. C4×D44C23semidirect
168. #66922C23semidirect
169. #66899C23semidirect
170. #66899C23semidirect
171. #66899C23semidirect
179. C22⋊(C11⋊C8)C23semidirect
180. #66873C23semidirect
181. #66872C23semidirect
182. #66872C23semidirect
183. #66872C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
185. #66867C23semidirect
219. C2×D4×C11#41semidirect
300. C2×#546D11semidirect
352. D4×C11C2×#41semidirect
407. #546C2×D11semidirect
606. C2×C11#3306semidirect
653. C2×D4#4341semidirect
723. C11C2×#3306semidirect
767. D4C2×#4341semidirect
847. C2#13080577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230862
#130805772
C2×#106226682
C2×#106226472
C2×#106226562
C2×#106226212
C2×#106226522
C2×#106226612
C2×#106226702
C2×#106228512
C2×#106228302
C2×#106226272
C2×#106226242
C2×#106228452
C22×#668962
C2×C11×#5462
C2×#330611