Finite Group Databasebeta

← #15634841

Subgroups — #15634841

Order 2816.

1932 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082211C211yesmaximal, characteristic, complemented
2#13081691C214yesmaximal, complemented
3#13081682C214yesmaximal, complemented
4#13081647C212yesmaximal, complemented
5#13081636C212yesmaximal, complemented
6#13081612C212yesmaximal, complemented
7#13081600C212yesmaximal, complemented
8#13079080C212yesmaximal, complemented
9#13079073C211yesmaximal, characteristic, complemented
10#13078106C212yesmaximal, complemented
11#13078099C211yesmaximal, characteristic, complemented
12#13078088C212yesmaximal, complemented
13#13078080C211yesmaximal, characteristic, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#66995C212yesmaximal, complemented
16C4×#66985C211yesmaximal, characteristic, complemented
17C2×C11×#556C211yesmaximal, characteristic, complemented
18C11×#556—21no—
19C11×#556—21no—
20C11×#556—22no—
21C11×#556C2212yes—
22C11×#556C2212yes—
23C11×#556C2214yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#126—22no—
26C2×C11×#124C2212yes—
27C2×C11×C22⋊Q8—21no—
28C2×C4×Q8×C11C2212yes—
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117—21no—
32#10623348—21no—
33C2×#66995C2212yes—
34C2×#66995C2212yes—
35C2×#66995C2212yes—
36C2×#66985C2211yescharacteristic
37C2×#66985C2212yes—
38#10623116C2211yescharacteristic, complemented
39#10623116C2212yescomplemented
40#10623115C2211yescharacteristic, complemented
41#10623115C2212yescomplemented
42#10623111—21no—
43#10623111—22no—
44#10623108C2211yescharacteristic, complemented
45C4×#4343—21no—
46#10623101C2211yescharacteristic, complemented
47#10623045—21no—
48#10623045—22no—
49#10623008C2211yescharacteristic
50#10623008C2212yes—
51C4×#4339C2211yescharacteristic
52C4×#4339C2212yes—
53#10622838C2212yes—
54#10622828C2211yescharacteristic
55#10622705C2212yescomplemented
56#10622703C2212yescomplemented
57#10622703C2212yescomplemented
58#10622699C2214yescomplemented
59#10622698C2212yescomplemented
60#10622696C2212yescomplemented
61#10622696C2212yescomplemented
62#10622673C2214yes—
63#10622672C2214yes—
64#10622672C2214yes—
65#10622671C2214yes—
66#10622670C2214yes—
67#10622670C2214yes—
68#10622667C2214yes—
69#10622667C2214yes—
70#10622644C2214yescomplemented
71#10622643C2214yescomplemented
72C4×#4326C2214yescomplemented
73#10622641C2214yescomplemented
74#10622641C2214yescomplemented
75#10622640C2214yescomplemented
76#10622639C2214yescomplemented
77C4×#4325C2214yescomplemented
78#10622637C2212yescomplemented
79#10622637C2214yescomplemented
80Q8×C11⋊C8C2212yescomplemented
81#10622632C2212yes—
82#10622631C2212yes—
83C4×#4324C2212yes—
84#10622629C2214yes—
85#10622628C2212yes—
86#10622627C2212yes—
87C4×#4323C2212yes—
88#10622579C2212yes—
89#10622579C2211yescharacteristic
90#10622577C2211yescharacteristic
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C4×#4318C2211yescharacteristic
94C4×#4318C2212yes—
95C22×Q8×C11D411yescharacteristic
96C22×Q8×C11C2312yes—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C2×#4343—21no—
100C2×#4339C2311yescharacteristic
101C2×#4339C2312yes—
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8C2312yes—
105C11×C4⋊Q8C2312yes—
106C11×#126—24no—
107C11×#126—24no—
108C11×#126—24no—
109C11×#126—24no—
110C11×#124—22no—
111C11×#124—22no—
112C11×#124C2314yes—
113C11×#124C2314yes—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—24no—
117C4×Q8×C11—22no—
118C4×Q8×C11—22no—
119C4×Q8×C11D411yescharacteristic
120C4×Q8×C11D411yescharacteristic
121C4×Q8×C11D412yes—
122C4×Q8×C11C2314yes—
123C4×Q8×C11C2314yes—
124C4×Q8×C11C2311yescharacteristic
125C4×Q8×C11C2311yescharacteristic
126C4×Q8×C11C2312yes—
127C4×D4×C11—21no—
128C4×D4×C11—21no—
129C4×D4×C11C2312yes—
130C4×D4×C11C2312yes—
131C11×#117—22no—
132C11×#117—22no—
133C11×#117—24no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4D412yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4—22no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—22no—
143C2×C42×C11—22no—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2312yes—
146#67000—21no—
147#67000—22no—
148#66999—21no—
149#66999—22no—
150Q8×Dic11—21no—
151C2×#4326C2314yes—
152C2×#4326C2314yes—
153C2×#4326C2314yes—
154#66995—28no—
155#66995—44no—
156#66995—44no—
157C2×#4325C2314yes—
158C2×#4325C2314yes—
159C2×#4325C2314yes—
160C2×#4324C2312yes—
161C2×#4324C2314yes—
162#66985—24no—
163#66985—44no—
164C2×#4323C2312yes—
165C2×#4323C2314yes—
166#66983—22no—
167#66983—21no—
168#66983—21no—
169#66983—22no—
170C4×C22⋊D11—22no—
171C4×C22⋊D11—21no—
172C4×C22⋊D11—21no—
173C4×C22⋊D11—22no—
174#66979C2311yescharacteristic
175C2×#4318C2312yes—
176C2×#4318C2311yescharacteristic
177C2×#4318C2311yescharacteristic
178#66951—22no—
179#66951—22no—
180#66951—22no—
181#66948—21no—
182#66948—22no—
183#66947—22no—
184#66947—22no—
185#66947—22no—
186#66946—21no—
187#66946—22no—
188#66945—21no—
189#66945—22no—
190#66943—21no—
191#66943—22no—
192#66928C2312yes—
193#66928C2312yes—
194#66928C2312yes—
195#66927C2311yescharacteristic
196#66927C2312yes—
197C4×D44—21no—
198C4×D44—22no—
199C4×D44—21no—
200C4×D44—22no—
201C4×D44C2311yescharacteristic
202C4×D44C2312yes—
203C4×D44C2311yescharacteristic
204C4×D44C2312yes—
205#66925—21no—
206#66925—22no—
207C42×D11—21no—
208C42×D11—22no—
209#66922C2311yescharacteristic
210#66922C2312yes—
211C4×Dic22C2311yescharacteristic
212C4×Dic22C2312yes—
213C4×Dic22C2311yescharacteristic
214C4×Dic22C2312yes—
215#66899C2314yes—
216#66899C2314yes—
217#66896C2312yes—
218#66896C2312yes—
219#66874C2314yes—
220#66874C2312yes—
221#66873C2312yes—
222#66873C2314yes—
223#66872C2312yes—
224#66871C2312yes—
225C4⋊(C11⋊C8)C2312yes—
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2314yes—
228C4⋊(C11⋊C8)C2314yes—
229#66867C2312yes—
230#66867C2314yes—
231C4×C11⋊C8C2312yes—
232C4×C11⋊C8C2314yes—
233#61403—111nomaximal, Sylow
234C24×C11—21no—
235C2×Q8×C11—22no—
236C2×Q8×C11—24no—
237C2×Q8×C11—24no—
238C2×Q8×C11—42no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D412yes—
242C2×Q8×C11C2414yes—
243C2×D4×C11—21no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11C2412yes—
247C22×C4×C11—21no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—44no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2411yescharacteristic
257C2×C22⋊D11—21no—
258C2×C22⋊D11—22no—
259#4343—44no—
260#4339—22no—
261#4339—24no—
262#4339—24no—
263#4339—22no—
264C2×D44—22no—
265C2×D44—21no—
266C2×D44—22no—
267C2×D44—21no—
268C2×D44C2411yescharacteristic
269C2×D44C2412yes—
270C2×C4×D11—21no—
271C2×C4×D11—22no—
272C2×C4×D11—22no—
273C2×C4×D11—21no—
274C2×C4×D11—22no—
275C2×C4×D11—21no—
276C2×Dic22C2411yescharacteristic
277C2×Dic22C2412yes—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4—24no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2412yes—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—24no—
299C42×C11—24no—
300C42×C11—24no—
301C42×C11C2×D411yescharacteristic
302C42×C11C2×D412yes—
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D412yes—
305C42×C11C2411yescharacteristic
306C42×C11C2412yes—
307C42×C11C2412yes—
308C42×C11C2411yescharacteristic
309C22⋊Dic11—21no—
310#4326—28no—
311#4326—44no—
312#4326—44no—
313#4325—28no—
314#4325—44no—
315#4325—44no—
316#4324—24no—
317#4324—44no—
318#4323—24no—
319#4323—44no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—21no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—21no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11—21no—
332C4⋊Dic11—22no—
333C4⋊Dic11—21no—
334C4⋊Dic11C2411yescharacteristic
335C4⋊Dic11C2411yescharacteristic
336Dic11⋊C4—22no—
337Dic11⋊C4—21no—
338Dic11⋊C4—22no—
339Dic11⋊C4—21no—
340C4×Dic11—22no—
341C4×Dic11—21no—
342C4×Dic11—22no—
343C4×Dic11—21no—
344C4×Dic11—21no—
345#4318—24no—
346#4318—22no—
347#4318#4114yescomplemented
348C2×C11⋊C8C2412yes—
349C2×C11⋊C8C2414yes—
350C2×C11⋊C8C2412yes—
351#3480—111no—
352C2×#556D1111yescharacteristic, complemented
353#3402—114no—
354#3401—114no—
355#3398—112no—
356#3397—112no—
357#3394—112no—
358#3393—112no—
359#3153—112no—
360#3152—111no—
361#3040—112no—
362#3039—111no—
363#3037—112no—
364#3036—111no—
365Q8×M16—111no—
366C4×#137—112no—
367C4×AGL(1,ℤ/8)—111no—
368C23×C11—22no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11C22×D411yescharacteristic
373C22×D11—21no—
374C22×D11—22no—
375Q8×C11—22no—
376Q8×C11—22no—
377Q8×C11—24no—
378Q8×C11—24no—
379Q8×C11—42no—
380Q8×C11—44no—
381D4×C11—22no—
382D4×C11—22no—
383D4×C11—42no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—24no—
387C2×C4×C11—42no—
388C2×C4×C11—41no—
389C2×C4×C11—42no—
390C2×C4×C11—44no—
391C2×C4×C11—42no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2×#4112yes—
404C2×C4×C11H(5,𝔽2)12yes—
405C2×C4×C11C2511yescharacteristic
406C22⋊D11—42no—
407C22⋊D11—44no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—22no—
412D44—21no—
413D44—22no—
414D44—22no—
415D44—21no—
416D44—44no—
417D44—42no—
418D44—82no—
419D44—81no—
420C4×D11—44no—
421C4×D11—42no—
422C4×D11—44no—
423C4×D11—42no—
424C4×D11—82no—
425C4×D11—81no—
426Dic22—21no—
427Dic22—22no—
428Dic22—22no—
429Dic22—21no—
430C11⋊C8—24no—
431C11⋊C8—22no—
432C11⋊C8C2×#4114yes—
433C2×#137—112no—
434C2×#137—112no—
435C2×#137—112no—
436C2×AGL(1,ℤ/8)—111no—
437C2×AGL(1,ℤ/8)—112no—
438#559—111no—
439#559—112no—
440#557—111no—
441#556—21no—
442#556—21no—
443#556—22no—
444#556—111no—
445#556—112no—
446#556C2×D1112yes—
447#556C2×D1112yes—
448#556C2×D1114yes—
449#553—221no—
450#553—222no—
451#550—111no—
452#548—221no—
453#532—111no—
454#532—112no—
455C2×C4⋊Q8C2×D1111yescharacteristic
456#529—221no—
457#529—222no—
458C2×#126—22no—
459C2×#124C2×D1112yes—
460C2×C22⋊Q8—21no—
461C4×#41—111no—
462C4×#41—112no—
463C4×#41—221no—
464C2×C4×Q8C2×D1112yes—
465C2×C4×Q8C2×D1111yescharacteristic
466C2×C4×D4C2×D1111yescharacteristic
467C2×#117—21no—
468#497—114no—
469#497—114no—
470#496—114no—
471#495—114no—
472#495—114no—
473#494—112no—
474#492—112no—
475#464—114no—
476#464—114no—
477#464—114no—
478#464—114no—
479#463—114no—
480#463—114no—
481#463—114no—
482#462—112no—
483#462—112no—
484#462—114no—
485#461—112no—
486#461—112no—
487#461—112no—
488#460—114no—
489#459—112no—
490#446—112no—
491#446—114no—
492C8×Q8—112no—
493#442—112no—
494#441—114no—
495#440—114no—
496#440—112no—
497C4×Q16—114no—
498C4×SD16—114no—
499C4×SD16—112no—
500C4×D8—112no—
501#428—111no—
502#423—111no—
503#423—112no—
504#419—112no—
505#418—111no—
506#417—111no—
507#417—112no—
508C4×M16—111no—
509C4×M16—112no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—84no—
516C22×C11#55012yes—
517C22×C11C23×D411yescharacteristic
518C2×D11—41no—
519C2×D11—42no—
520C2×D11—41no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—41no—
524C4×C11—22no—
525C4×C11—21no—
526C4×C11—22no—
527C4×C11—21no—
528C4×C11—21no—
529C4×C11—22no—
530C4×C11—22no—
531C4×C11—44no—
532C4×C11—42no—
533C4×C11#55012yes—
534C4×C11#57512yes—
535C4×C11C22×#4111yescharacteristic
536C4×C11C2×H(5,𝔽2)11yescharacteristic
537Dic11—41no—
538Dic11—41no—
539Dic11—42no—
540Dic11—41no—
541C2×#41—111no—
542C2×#41—112no—
543C2×#41—221no—
544C22×Q8C22⋊D1111yescharacteristic
545C22×Q8C22×D1112yes—
546C22×D4C22×D1111yescharacteristic
547C23×C4—21no—
548#137—228no—
549#137—444no—
550#137—444no—
551AGL(1,ℤ/8)—224no—
552AGL(1,ℤ/8)—444no—
553C2×Q16—114no—
554C2×Q16—114no—
555C2×Q16—114no—
556C2×SD16—114no—
557C2×SD16—112no—
558C2×SD16—114no—
559C2×SD16—114no—
560C2×SD16—114no—
561C2×D8—112no—
562C2×D8—114no—
563C2×M16—111no—
564C2×M16—112no—
565C2×M16—111no—
566C4⋊Q8—21no—
567C4⋊Q8—21no—
568C4⋊Q8—111no—
569C4⋊Q8—112no—
570C4⋊Q8C22×D1112yes—
571C4⋊Q8C22×D1112yes—
572#127—111no—
573#127—112no—
574#126—24no—
575#126—24no—
576#126—24no—
577#126—24no—
578#126—222no—
579#126—222no—
580#126—222no—
581#125—221no—
582#125—222no—
583#124—22no—
584#124—22no—
585#124—112no—
586#124—112no—
587#124—112no—
588#124—221no—
589#124—222no—
590#124C22×D1114yes—
591#124C22×D1114yes—
592#123—222no—
593#123—222no—
594#123—222no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—24no—
598C22⋊Q8—221no—
599C22⋊Q8—222no—
600#121—221no—
601#121—222no—
602#121—222no—
603#121—221no—
604#121—221no—
605#121—222no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—112no—
609C4×Q8—111no—
610C4×Q8—111no—
611C4×Q8—112no—
612C4×Q8—221no—
613C4×Q8C22⋊D1111yescharacteristic
614C4×Q8C22⋊D1111yescharacteristic
615C4×Q8C22⋊D1112yes—
616C4×Q8C22×D1114yes—
617C4×Q8C22×D1114yes—
618C4×Q8C22×D1111yescharacteristic
619C4×Q8C22×D1111yescharacteristic
620C4×Q8C22×D1112yes—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—111no—
624C4×D4—112no—
625C4×D4—112no—
626C4×D4—111no—
627C4×D4—221no—
628C4×D4—222no—
629C4×D4—222no—
630C4×D4—221no—
631C4×D4—221no—
632C4×D4—222no—
633C4×D4—221no—
634C4×D4—222no—
635C4×D4—221no—
636C4×D4—222no—
637C4×D4C22×D1112yes—
638C4×D4C22×D1112yes—
639#117—22no—
640#117—22no—
641#117—24no—
642#117—111no—
643#117—221no—
644#117—222no—
645#117—221no—
646#117—222no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4C22⋊D1111yescharacteristic
651C2×C4⋊C4C22⋊D1112yes—
652C2×C4⋊C4C22×D1111yescharacteristic
653C2×C22⋊C4—22no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—22no—
656C2×C42—22no—
657C2×C42—221no—
658C2×C42—222no—
659C2×C42C22×D1111yescharacteristic
660C2×C42C22×D1112yes—
661#107—112no—
662#106—112no—
663C4⋊C8—112no—
664C4⋊C8—114no—
665C4⋊C8—114no—
666C4⋊C8—112no—
667#103—114no—
668#103—114no—
669#103—112no—
670#103—114no—
671#102—112no—
672#102—112no—
673#102—112no—
674#102—114no—
675#97—114no—
676#97—112no—
677C4×C8—112no—
678C4×C8—114no—
679C2×C11—22no—
680C2×C11—82no—
681C2×C11C2×#55011yescharacteristic
682C2×C11C2×#57511yescharacteristic
683C2×C11#358611yescharacteristic
684D11—81no—
685D11—82no—
686C24—21no—
687#41—222no—
688#41—224no—
689#41—224no—
690#41—222no—
691#41—444no—
692C2×Q8—22no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—42no—
696C2×Q8—111no—
697C2×Q8—112no—
698C2×Q8C2×C22⋊D1111yescharacteristic
699C2×Q8C2×C22⋊D1111yescharacteristic
700C2×Q8C2×C22⋊D1112yes—
701C2×Q8C23×D1114yes—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—21no—
705C2×D4—111no—
706C2×D4—112no—
707C2×D4—221no—
708C2×D4—222no—
709C2×D4—222no—
710C2×D4—221no—
711C2×D4—222no—
712C2×D4—221no—
713C2×D4C23×D1112yes—
714C22×C4—21no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—44no—
719C22×C4—222no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—221no—
725C22×C4C2×C22⋊D1111yescharacteristic
726C22×C4C2×C22⋊D1112yes—
727C22×C4C2×C22⋊D1111yescharacteristic
728C22×C4C2×C22⋊D1112yes—
729C22×C4C23×D1111yescharacteristic
730Q16—228no—
731Q16—444no—
732Q16—444no—
733SD16—224no—
734SD16—228no—
735SD16—444no—
736SD16—444no—
737SD16—444no—
738D8—224no—
739D8—444no—
740M16—114no—
741M16—224no—
742M16—222no—
743C2×C8—112no—
744C2×C8—112no—
745C2×C8—114no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—21no—
753C4⋊C4—111no—
754C4⋊C4—111no—
755C4⋊C4—222no—
756C4⋊C4—221no—
757C4⋊C4—222no—
758C4⋊C4—221no—
759C4⋊C4—222no—
760C4⋊C4—221no—
761C4⋊C4—222no—
762C4⋊C4—221no—
763C4⋊C4C2×C22⋊D1111yescharacteristic
764C4⋊C4C2×C22⋊D1111yescharacteristic
765C4⋊C4C2×C22⋊D1112yes—
766C4⋊C4C2×C22⋊D1112yes—
767C4⋊C4C2×C22⋊D1112yes—
768C4⋊C4C2×C22⋊D1112yes—
769C4⋊C4C2×C22⋊D1112yes—
770C4⋊C4C23×D1112yes—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4—221no—
778C22⋊C4—222no—
779C22⋊C4—221no—
780C22⋊C4—222no—
781C22⋊C4—221no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C42—24no—
789C42—24no—
790C42—221no—
791C42—222no—
792C42—221no—
793C42—222no—
794C42—221no—
795C42C2×C22⋊D1111yescharacteristic
796C42C2×C22⋊D1112yes—
797C42C2×C22⋊D1111yescharacteristic
798C42C2×C22⋊D1112yes—
799C42C23×D1111yescharacteristic
800C42C23×D1112yes—
801C42C23×D1111yescharacteristic
802C42C23×D1112yes—
803C11#6140311yescharacteristic, complemented, Sylow
804C23—22no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—222no—
809C23—221no—
810C23C22×C22⋊D1111yescharacteristic
811Q8—22no—
812Q8—22no—
813Q8—24no—
814Q8—24no—
815Q8—42no—
816Q8—44no—
817Q8—221no—
818Q8—222no—
819Q8—222no—
820Q8—221no—
821D4—22no—
822D4—22no—
823D4—42no—
824D4—221no—
825D4—222no—
826D4—222no—
827D4—221no—
828D4—444no—
829D4—442no—
830D4—444no—
831D4—442no—
832D4—882no—
833D4—881no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—221no—
845C2×C4—221no—
846C2×C4—221no—
847C2×C4—222no—
848C2×C4—444no—
849C2×C4—442no—
850C2×C4—442no—
851C2×C4—444no—
852C2×C4—882no—
853C2×C4—881no—
854C2×C4#41×D1112yes—
855C2×C4#6704212yes—
856C2×C4C22×C22⋊D1112yes—
857C2×C4C22×C22⋊D1112yes—
858C2×C4C22×C22⋊D1111yescharacteristic
859C2×C4C22×C22⋊D1112yes—
860C2×C4C22×C22⋊D1112yes—
861C2×C4C22×C22⋊D1111yescharacteristic
862C2×C4C22×C22⋊D1111yescharacteristic
863C2×C4C22×C22⋊D1111yescharacteristic
864C2×C4C22×C22⋊D1111yescharacteristic
865C2×C4C24×D1111yescharacteristic
866C8—114no—
867C8—224no—
868C8—222no—
869C22—21no—
870C22—21no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—84no—
875C22—442no—
876C22—441no—
877C22—442no—
878C22—441no—
879C22—441no—
880C22—442no—
881C22#1062336512yes—
882C22C23×C22⋊D1111yescharacteristic
883C4—22no—
884C4—21no—
885C4—22no—
886C4—21no—
887C4—21no—
888C4—22no—
889C4—22no—
890C4—42no—
891C4—44no—
892C4—441no—
893C4—441no—
894C4—441no—
895C4—442no—
896C4#1062335312yes—
897C4#1062336512yes—
898C4C2×#41×D1111yescharacteristic
899C4C2×#6704211yescharacteristic
900C2—22no—
901C2—82no—
902C2—882no—
903C2—881no—
904C2C2×#1062336511yescharacteristic
905C2C2×#1062335311yescharacteristic
906C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC22×C11C23×D4
hypercenterC2×#556D11
hypocenterC11#61403
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13082211C2semidirect
2. #13081691C2semidirect
3. #13081682C2semidirect
4. #13081647C2semidirect
5. #13081636C2semidirect
6. #13081612C2semidirect
7. #13081600C2semidirect
8. #13079080C2semidirect
9. #13079073C2semidirect
10. #13078106C2semidirect
11. #13078099C2semidirect
12. #13078088C2semidirect
13. #13078080C2semidirect
14. Q8×#4318C2semidirect
15. C4×#66995C2semidirect
16. C4×#66985C2semidirect
17. C2×C11×#556C2semidirect
38. #10623116C22semidirect
39. #10623116C22semidirect
40. #10623115C22semidirect
41. #10623115C22semidirect
44. #10623108C22semidirect
46. #10623101C22semidirect
55. #10622705C22semidirect
56. #10622703C22semidirect
57. #10622703C22semidirect
58. #10622699C22semidirect
59. #10622698C22semidirect
60. #10622696C22semidirect
61. #10622696C22semidirect
70. #10622644C22semidirect
71. #10622643C22semidirect
72. C4×#4326C22semidirect
73. #10622641C22semidirect
74. #10622641C22semidirect
75. #10622640C22semidirect
76. #10622639C22semidirect
77. C4×#4325C22semidirect
78. #10622637C22semidirect
79. #10622637C22semidirect
80. Q8×C11⋊C8C22semidirect
347. #4318#41semidirect
352. C2×#556D11semidirect
803. C11#61403semidirect

Maximal subgroups

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

subgroupindex
#130822112
#130816912
#130816822
#130816472
#130816362
#130816122
#130816002
#130790802
#130790732
#130781062
#130780992
#130780882
#130780802
Q8×#43182
C4×#669952
C4×#669852
C2×C11×#5562
#6140311