Finite Group Databasebeta

← #15620940

Subgroups — #15620940

Order 2816.

2918 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×#10623353C211yesmaximal, characteristic, complemented
2C23×#4318C211yesmaximal, characteristic, complemented
3C2×#10623322C211yesmaximal, characteristic, complemented
4#13078248C214yesmaximal, complemented
5#13078242C214yesmaximal, complemented
6#13078237C214yesmaximal, complemented
7#13078231C214yesmaximal, complemented
8#13078222C214yesmaximal, complemented
9#13078194C214yesmaximal, complemented
10#13077205C211yesmaximal, characteristic, complemented
11#13077135C211yesmaximal, characteristic, complemented
12#13077133C211yesmaximal, characteristic, complemented
13C2×C11×#525C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C11×#525—21no—
18C11×#525—21no—
19C11×#525—22no—
20C11×#525C2214yes—
21C11×#525C2212yescomplemented
22C11×#525C2212yescomplemented
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2212yescomplemented
25C2×C11×#121C2212yescomplemented
26C2×C11×#120—21no—
27C2×C4×D4×C11—22no—
28C2×C11×#117C2211yescharacteristic
29C2×#67006—21no—
30C2×#67004C2212yescomplemented
31#10623353—28no—
32C2×#67003C2214yescomplemented
33C2×#67002C2212yescomplemented
34C2×#66995C2212yescomplemented
35C2×#66985C2212yescomplemented
36#10623322—21no—
37#10623322—21no—
38#10623322—22no—
39#10623322C2214yes—
40#10623322C2212yescomplemented
41#10623322C2212yescomplemented
42C2×#66983C2212yescomplemented
43C2×#66982—21no—
44C2×C4×C22⋊D11—22no—
45C2×#66979C2211yescharacteristic
46C2×#66977C2212yescomplemented
47C22×#4318—28no—
48C22×#4318C2211yescharacteristic
49C22×#4318C2211yescharacteristic
50C22×#4318C2212yescomplemented
51C22×#4318C2214yescomplemented
52C22×#4318C2214yescomplemented
53C23×C11⋊C8C2212yescomplemented
54#10622846C2214yescomplemented
55#10622845C2214yescomplemented
56#10622838C2212yescomplemented
57#10622828C2212yescomplemented
58#10622665C2218yescomplemented
59#10622664C2218yescomplemented
60#10622662C2218yescomplemented
61#10622661C2218yescomplemented
62#10622655C2218yescomplemented
63#10622654C2218yescomplemented
64#10622652C2218yescomplemented
65#10622651C2218yescomplemented
66#10622617C2212yescomplemented
67#10622615C2214yescomplemented
68#10622614C2212yescomplemented
69#10622611C2214yescomplemented
70#10622608C2214yescomplemented
71#10622579C2214yescomplemented
72#10622577C2214yescomplemented
73C25×C11D411yescharacteristic
74C2×C11×#41—21no—
75C2×C11×#41—21no—
76C2×C11×#41—24no—
77C2×C11×#41—24no—
78C2×C11×#41C2312yes—
79C2×C11×#41C2312yes—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—22no—
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—24no—
85C23×C4×C11—24no—
86C23×C4×C11—21no—
87C23×C4×C11D412yes—
88C23×C4×C11D411yescharacteristic
89C23×C4×C11D412yes—
90C23×C4×C11D411yescharacteristic
91C23×C4×C11D411yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2312yes—
94C23×C4×C11C2312yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—22no—
98C22×C22⋊D11—21no—
99C2×#4339—21no—
100C2×#4339—21no—
101C2×#4339—24no—
102C2×#4339—24no—
103C2×#4339C2312yes—
104C2×#4339C2312yes—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×Dic22C2311yescharacteristic
108C11×#123—24no—
109C11×#123—22no—
110C11×#123—22no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8C2314yes—
114C11×C22⋊Q8C2314yes—
115C11×#121—22no—
116C11×#121—22no—
117C11×#121C2314yes—
118C11×#121C2314yes—
119C11×#120—24no—
120C11×#120—22no—
121C11×#120—22no—
122C4×D4×C11—24no—
123C4×D4×C11—24no—
124C4×D4×C11—24no—
125C4×D4×C11—24no—
126C11×#117—21no—
127C11×#117—21no—
128C11×#117C2312yes—
129C11×#117C2312yes—
130C2×C11×C4⋊C4—22no—
131C2×C11×C4⋊C4C2312yes—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—22no—
135C2×C42×C11—21no—
136#67006—24no—
137#67006—22no—
138#67006—22no—
139C2×C22⋊Dic11—22no—
140C2×C22⋊Dic11—21no—
141#67004—28no—
142#67003—216no—
143#67002—28no—
144C2×#4326C2314yescomplemented
145#66995—28no—
146C2×#4325C2314yescomplemented
147C2×#4324C2314yescomplemented
148#66985—28no—
149C2×#4323C2314yescomplemented
150#66983—22no—
151#66983—22no—
152#66983C2314yes—
153#66983C2314yes—
154#66982—24no—
155#66982—22no—
156#66982—22no—
157C4×C22⋊D11—24no—
158C4×C22⋊D11—24no—
159C4×C22⋊D11—24no—
160C4×C22⋊D11—24no—
161C2×(C2×D11)⋊C4—22no—
162#66979—21no—
163#66979—21no—
164#66979C2312yes—
165#66979C2312yes—
166C2×C4⋊Dic11C2312yes—
167#66977—22no—
168#66977—22no—
169#66977C2314yes—
170#66977C2314yes—
171C2×Dic11⋊C4—22no—
172C2×C4×Dic11—21no—
173C2×#4318—24no—
174C2×#4318—216no—
175C2×#4318—216no—
176C2×#4318—28no—
177C2×#4318D418yescomplemented
178C2×#4318C2312yes—
179C2×#4318C2312yes—
180C2×#4318C2318yes—
181C2×#4318C2312yes—
182C2×#4318C2312yes—
183C22×C11⋊C8—28no—
184C22×C11⋊C8C2312yes—
185C22×C11⋊C8C2318yes—
186C22×C11⋊C8C2312yes—
187#66899C2318yescomplemented
188#66896C2318yescomplemented
189#66874C2318yescomplemented
190#66873C2318yescomplemented
191#66872C2318yescomplemented
192#66871C2318yescomplemented
193#60444—111nomaximal, Sylow
194C24×C11—24no—
195C24×C11—21no—
196C24×C11—44no—
197C24×C11C2×D411yescharacteristic
198C24×C11C2×D412yes—
199C24×C11C2×D412yes—
200C24×C11C2×D411yescharacteristic
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C11×#41—24no—
204C11×#41—24no—
205C11×#41—24no—
206C11×#41—24no—
207C11×#41—44no—
208C11×#41—44no—
209C2×Q8×C11—21no—
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11C2412yes—
213C2×D4×C11—24no—
214C2×D4×C11—24no—
215C2×D4×C11—22no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—21no—
219C2×D4×C11—22no—
220C2×D4×C11—48no—
221C2×D4×C11—44no—
222C2×D4×C11C2412yes—
223C22×C4×C11—24no—
224C22×C4×C11—28no—
225C22×C4×C11—28no—
226C22×C4×C11—24no—
227C22×C4×C11—24no—
228C22×C4×C11—22no—
229C22×C4×C11—24no—
230C22×C4×C11—24no—
231C22×C4×C11—22no—
232C22×C4×C11—24no—
233C22×C4×C11—24no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—21no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—44no—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D414yes—
255C22×C4×C11#4114yes—
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C2×C22⋊D11—24no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—48no—
266C2×C22⋊D11—44no—
267C22×Dic11—22no—
268C22×Dic11—21no—
269#4339—24no—
270#4339—24no—
271#4339—24no—
272#4339—24no—
273#4339—44no—
274#4339—44no—
275C2×D44—21no—
276C2×D44—22no—
277C2×D44—22no—
278C2×D44C2412yes—
279C2×C4×D11—22no—
280C2×C4×D11—22no—
281C2×C4×D11—44no—
282C2×Dic22—22no—
283C2×Dic22—21no—
284C2×Dic22—22no—
285C2×Dic22C2412yes—
286C11×C4⋊C4—24no—
287C11×C4⋊C4—24no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4C2414yes—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C11×C22⋊C4—24no—
296C42×C11—22no—
297C42×C11—22no—
298C22⋊Dic11—24no—
299C22⋊Dic11—24no—
300C22⋊Dic11—22no—
301C22⋊Dic11—22no—
302#4326—28no—
303#4325—28no—
304#4324—28no—
305#4323—28no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308C4⋊Dic11—22no—
309C4⋊Dic11C2414yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312C4×Dic11—22no—
313C4×Dic11—22no—
314#4318—216no—
315#4318—24no—
316#4318—24no—
317#4318C2×D418yescomplemented
318#4318C2×D418yescomplemented
319C2×C11⋊C8—216no—
320C2×C11⋊C8—24no—
321C2×C11⋊C8C2×D418yescomplemented
322C2×C11⋊C8C2414yes—
323C2×C11⋊C8C2414yes—
324C2×#575—111no—
325C23×M16—111no—
326C2×#525—111no—
327C2×#525D1111yescharacteristic, complemented
328#3056—114no—
329#3056—114no—
330#3055—114no—
331#3055—114no—
332#3054—114no—
333#3050—114no—
334#2911—111no—
335#2896—111no—
336#2896—111no—
337C23×C11—22no—
338C23×C11—24no—
339C23×C11—24no—
340C23×C11—24no—
341C23×C11—22no—
342C23×C11—24no—
343C23×C11—24no—
344C23×C11—22no—
345C23×C11—42no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11—416no—
350C23×C11—44no—
351C23×C11—42no—
352C23×C11#12114yes—
353C23×C11C22×D412yes—
354C23×C11C22×D411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C22×D411yescharacteristic
357C23×C11C22×D412yes—
358C22×D11—22no—
359C22×D11—44no—
360C22×D11—42no—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—42no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—48no—
367D4×C11—44no—
368D4×C11—44no—
369D4×C11—48no—
370D4×C11—42no—
371C2×C4×C11—24no—
372C2×C4×C11—24no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—24no—
377C2×C4×C11—24no—
378C2×C4×C11—24no—
379C2×C4×C11—24no—
380C2×C4×C11—24no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—44no—
388C2×C4×C11—42no—
389C2×C4×C11—44no—
390C2×C4×C11—44no—
391C2×C4×C11#12114yes—
392C2×C4×C11#12114yes—
393C2×C4×C11#12114yes—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D412yes—
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D412yes—
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C2×#4112yes—
403C2×C4×C11C2×#4112yes—
404C2×C4×C11C2×#4112yes—
405C2×C4×C11C2511yescharacteristic
406C22⋊D11—48no—
407C22⋊D11—44no—
408C22⋊D11—44no—
409C22⋊D11—48no—
410C2×Dic11—24no—
411C2×Dic11—22no—
412C2×Dic11—44no—
413C2×Dic11—42no—
414D44—22no—
415D44—22no—
416D44—42no—
417C4×D11—44no—
418C4×D11—44no—
419Dic22—22no—
420Dic22—22no—
421Dic22—42no—
422C11⋊C8—24no—
423C11⋊C8C22×D418yes—
424C22×#41—111no—
425C22×#41C2×D1111yescharacteristic
426C24×C4C2×D1111yescharacteristic
427#575—228no—
428C2×#137—112no—
429C2×#137—112no—
430C2×AGL(1,ℤ/8)—112no—
431C2×AGL(1,ℤ/8)—112no—
432C2×#135—114no—
433C22×M16—111no—
434C22×M16—111no—
435C22×M16—112no—
436C22×M16—114no—
437C22×M16—114no—
438C22×M16—228no—
439C23×C8—112no—
440#525—21no—
441#525—21no—
442#525—22no—
443#525—114no—
444#525—112no—
445#525—112no—
446#525—222no—
447#525—221no—
448#525—221no—
449#525C2×D1114yes—
450#525C2×D1112yescomplemented
451#525C2×D1112yescomplemented
452C2×#123—21no—
453C2×#123—221no—
454C2×C22⋊Q8—112no—
455C2×C22⋊Q8C2×D1112yescomplemented
456C2×#121—112no—
457C2×#121C2×D1112yescomplemented
458C2×#120—21no—
459C2×#120—221no—
460C2×C4×D4—22no—
461C2×C4×D4—222no—
462C2×#117—111no—
463C2×#117C2×D1111yescharacteristic
464#470—118no—
465#469—118no—
466#468—118no—
467#468—118no—
468#467—118no—
469#466—118no—
470#465—118no—
471#465—118no—
472#428—114no—
473#428—114no—
474#427—114no—
475#419—112no—
476#419—112no—
477#418—112no—
478#418—112no—
479#417—114no—
480#417—114no—
481#416—114no—
482#416—114no—
483C22×C11—28no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—22no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—44no—
493C22×C11—48no—
494C22×C11—48no—
495C22×C11—44no—
496C22×C11—42no—
497C22×C11—44no—
498C22×C11—84no—
499C22×C11C2×#12112yes—
500C22×C11C2×#12112yes—
501C22×C11C2×#12112yes—
502C22×C11#57514yescomplemented
503C22×C11C23×D411yescharacteristic
504C2×D11—42no—
505C2×D11—44no—
506C2×D11—84no—
507C4×C11—22no—
508C4×C11—22no—
509C4×C11—42no—
510C4×C11—44no—
511C4×C11C2×#12112yes—
512C4×C11C2×#12112yes—
513C4×C11C2×#12112yes—
514C4×C11C23×D411yescharacteristic
515C4×C11C22×#4111yescharacteristic
516Dic11—42no—
517Dic11—44no—
518C25C22⋊D1111yescharacteristic
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—24no—
522C2×#41—24no—
523C2×#41—112no—
524C2×#41—112no—
525C2×#41—221no—
526C2×#41—221no—
527C2×#41—224no—
528C2×#41—224no—
529C2×#41C22×D1112yes—
530C2×#41C22×D1112yes—
531C22×Q8—111no—
532C22×Q8C22×D1111yescharacteristic
533C22×D4—22no—
534C22×D4—21no—
535C22×D4—111no—
536C22×D4—222no—
537C22×D4—221no—
538C22×D4C22×D1111yescharacteristic
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—21no—
542C23×C4—221no—
543C23×C4C22⋊D1112yes—
544C23×C4C22⋊D1112yes—
545C23×C4C22⋊D1111yescharacteristic
546C23×C4C22⋊D1111yescharacteristic
547C23×C4C22⋊D1111yescharacteristic
548C23×C4C22×D1112yes—
549C23×C4C22×D1112yes—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553#137—228no—
554#137—228no—
555AGL(1,ℤ/8)—228no—
556AGL(1,ℤ/8)—228no—
557#135—2216no—
558C2×Q16—114no—
559C2×SD16—114no—
560C2×SD16—114no—
561C2×D8—114no—
562C2×M16—118no—
563C2×M16—112no—
564C2×M16—112no—
565C2×M16—112no—
566C2×M16—112no—
567C2×M16—118no—
568C2×M16—228no—
569C2×M16—2216no—
570C2×M16—2216no—
571C2×M16—224no—
572C22×C8—112no—
573C22×C8—112no—
574C22×C8—118no—
575C22×C8—228no—
576#123—24no—
577#123—22no—
578#123—22no—
579#123—224no—
580#123—222no—
581#123—222no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—114no—
585C22⋊Q8—114no—
586C22⋊Q8—222no—
587C22⋊Q8—222no—
588C22⋊Q8C22×D1114yes—
589C22⋊Q8C22×D1114yes—
590#121—22no—
591#121—22no—
592#121—114no—
593#121—114no—
594#121—222no—
595#121—222no—
596#121C22×D1114yes—
597#121C22×D1114yes—
598#120—24no—
599#120—22no—
600#120—22no—
601#120—222no—
602#120—224no—
603#120—222no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—224no—
609C4×D4—224no—
610C4×D4—224no—
611C4×D4—224no—
612#117—21no—
613#117—21no—
614#117—112no—
615#117—112no—
616#117—221no—
617#117—221no—
618#117C22×D1112yes—
619#117C22×D1112yes—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4C22×D1112yes—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C42—21no—
631C2×C42—221no—
632#107—118no—
633#106—118no—
634#103—118no—
635#103—118no—
636#102—118no—
637#102—118no—
638C2×C11—22no—
639C2×C11—22no—
640C2×C11—24no—
641C2×C11—22no—
642C2×C11—42no—
643C2×C11—82no—
644C2×C11C22×#12111yescharacteristic
645C2×C11C2×#57512yes—
646D11—82no—
647C24—24no—
648C24—21no—
649C24—44no—
650C24—221no—
651C24C2×C22⋊D1111yescharacteristic
652C24C2×C22⋊D1112yes—
653C24C2×C22⋊D1112yes—
654C24C2×C22⋊D1111yescharacteristic
655C24C2×C22⋊D1111yescharacteristic
656#41—24no—
657#41—24no—
658#41—24no—
659#41—24no—
660#41—44no—
661#41—44no—
662#41—224no—
663#41—224no—
664#41—224no—
665#41—224no—
666#41—444no—
667#41—444no—
668C2×Q8—21no—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—112no—
672C2×Q8—221no—
673C2×Q8—222no—
674C2×Q8—222no—
675C2×Q8C23×D1112yes—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—21no—
683C2×D4—48no—
684C2×D4—44no—
685C2×D4—112no—
686C2×D4—224no—
687C2×D4—224no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—222no—
692C2×D4—221no—
693C2×D4—448no—
694C2×D4—444no—
695C2×D4C23×D1112yes—
696C22×C4—24no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—22no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—44no—
714C22×C4—222no—
715C22×C4—221no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—444no—
719C22×C4D4×D1114yes—
720C22×C4#434114yes—
721C22×C4C2×C22⋊D1112yes—
722C22×C4C2×C22⋊D1112yes—
723C22×C4C2×C22⋊D1112yes—
724C22×C4C2×C22⋊D1112yes—
725C22×C4C2×C22⋊D1112yes—
726C22×C4C2×C22⋊D1112yes—
727C22×C4C2×C22⋊D1111yescharacteristic
728C22×C4C2×C22⋊D1111yescharacteristic
729C22×C4C2×C22⋊D1112yes—
730C22×C4C2×C22⋊D1112yes—
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1111yescharacteristic
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C23×D1112yes—
735C22×C4C23×D1112yes—
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738C22×C4C23×D1111yescharacteristic
739Q16—228no—
740SD16—228no—
741SD16—228no—
742D8—228no—
743M16—118no—
744M16—118no—
745M16—2216no—
746M16—224no—
747M16—224no—
748C2×C8—118no—
749C2×C8—114no—
750C2×C8—114no—
751C2×C8—2216no—
752C2×C8—224no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—114no—
757C4⋊C4—222no—
758C4⋊C4—224no—
759C4⋊C4—224no—
760C4⋊C4C23×D1114yes—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—222no—
768C22⋊C4—222no—
769C22⋊C4—224no—
770C22⋊C4—224no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C42—22no—
774C42—22no—
775C42—222no—
776C42—222no—
777C11#6044411yescharacteristic, complemented, Sylow
778C23—22no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—22no—
783C23—24no—
784C23—24no—
785C23—22no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—416no—
791C23—44no—
792C23—42no—
793C23—222no—
794C23—444no—
795C23—442no—
796C23#6699214yes—
797C23C22×C22⋊D1112yes—
798C23C22×C22⋊D1111yescharacteristic
799C23C22×C22⋊D1111yescharacteristic
800C23C22×C22⋊D1111yescharacteristic
801C23C22×C22⋊D1112yes—
802Q8—22no—
803Q8—22no—
804Q8—42no—
805Q8—222no—
806Q8—222no—
807Q8—442no—
808D4—22no—
809D4—22no—
810D4—48no—
811D4—44no—
812D4—44no—
813D4—48no—
814D4—42no—
815D4—222no—
816D4—222no—
817D4—448no—
818D4—444no—
819D4—444no—
820D4—448no—
821D4—442no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—224no—
843C2×C4—222no—
844C2×C4—444no—
845C2×C4—442no—
846C2×C4—444no—
847C2×C4—444no—
848C2×C4#6699214yes—
849C2×C4#6699214yes—
850C2×C4#6699214yes—
851C2×C4C2×D4×D1112yes—
852C2×C4C2×D4×D1112yes—
853C2×C4C2×D4×D1112yes—
854C2×C4C2×#434112yes—
855C2×C4C2×#434112yes—
856C2×C4C2×#434112yes—
857C2×C4C22×C22⋊D1112yes—
858C2×C4C22×C22⋊D1112yes—
859C2×C4C22×C22⋊D1111yescharacteristic
860C2×C4C22×C22⋊D1111yescharacteristic
861C2×C4C22×C22⋊D1111yescharacteristic
862C2×C4C24×D1111yescharacteristic
863C8—118no—
864C8—224no—
865C22—28no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—44no—
875C22—48no—
876C22—48no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—84no—
881C22—444no—
882C22—442no—
883C22—884no—
884C22C2×#6699212yes—
885C22C2×#6699212yes—
886C22C2×#6699212yes—
887C22#1062335314yescomplemented
888C22C23×C22⋊D1111yescharacteristic
889C4—22no—
890C4—22no—
891C4—44no—
892C4—42no—
893C4—444no—
894C4—442no—
895C4C2×#6699212yes—
896C4C2×#6699212yes—
897C4C2×#6699212yes—
898C4C22×D4×D1111yescharacteristic
899C4C22×#434111yescharacteristic
900C2—22no—
901C2—24no—
902C2—22no—
903C2—22no—
904C2—42no—
905C2—82no—
906C2—882no—
907C2C22×#6699211yescharacteristic
908C2C2×#1062335312yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC22×C11C23×D4
hypercenterC2×#525D11
hypocenterC11#60444
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C23×#4318C2semidirect
3. C2×#10623322C2semidirect
4. #13078248C2semidirect
5. #13078242C2semidirect
6. #13078237C2semidirect
7. #13078231C2semidirect
8. #13078222C2semidirect
9. #13078194C2semidirect
10. #13077205C2semidirect
11. #13077135C2semidirect
12. #13077133C2semidirect
13. C2×C11×#525C2semidirect
21. C11×#525C22semidirect
22. C11×#525C22semidirect
24. C2×C11×C22⋊Q8C22semidirect
25. C2×C11×#121C22semidirect
30. C2×#67004C22semidirect
32. C2×#67003C22semidirect
33. C2×#67002C22semidirect
34. C2×#66995C22semidirect
35. C2×#66985C22semidirect
40. #10623322C22semidirect
41. #10623322C22semidirect
42. C2×#66983C22semidirect
46. C2×#66977C22semidirect
50. C22×#4318C22semidirect
51. C22×#4318C22semidirect
52. C22×#4318C22semidirect
53. C23×C11⋊C8C22semidirect
54. #10622846C22semidirect
55. #10622845C22semidirect
56. #10622838C22semidirect
57. #10622828C22semidirect
58. #10622665C22semidirect
59. #10622664C22semidirect
60. #10622662C22semidirect
61. #10622661C22semidirect
62. #10622655C22semidirect
63. #10622654C22semidirect
64. #10622652C22semidirect
65. #10622651C22semidirect
66. #10622617C22semidirect
67. #10622615C22semidirect
68. #10622614C22semidirect
69. #10622611C22semidirect
70. #10622608C22semidirect
71. #10622579C22semidirect
72. #10622577C22semidirect
144. C2×#4326C23semidirect
146. C2×#4325C23semidirect
147. C2×#4324C23semidirect
149. C2×#4323C23semidirect
177. C2×#4318D4semidirect
187. #66899C23semidirect
188. #66896C23semidirect
189. #66874C23semidirect
190. #66873C23semidirect
191. #66872C23semidirect
192. #66871C23semidirect
317. #4318C2×D4semidirect
318. #4318C2×D4semidirect
321. C2×C11⋊C8C2×D4semidirect
327. C2×#525D11semidirect
450. #525C2×D11semidirect
451. #525C2×D11semidirect
455. C2×C22⋊Q8C2×D11semidirect
457. C2×#121C2×D11semidirect
502. C22×C11#575semidirect
777. C11#60444semidirect
887. C22#10623353semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C23×#43182
C2×#106233222
#130782482
#130782422
#130782372
#130782312
#130782222
#130781942
#130772052
#130771352
#130771332
C2×C11×#5252
#6044411