Finite Group Databasebeta

← #15634869

Subgroups — #15634869

Order 2816.

1996 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082211C211yesmaximal, characteristic, complemented
2#13081700C214yesmaximal, complemented
3#13081676C214yesmaximal, complemented
4#13081669C212yesmaximal, complemented
5#13081654C212yesmaximal, complemented
6#13081624C212yesmaximal, complemented
7#13081608C212yesmaximal, complemented
8#13079080C212yesmaximal, complemented
9#13079066C211yesmaximal, characteristic, complemented
10#13078106C212yesmaximal, complemented
11#13078092C211yesmaximal, characteristic, complemented
12#13078088C211yesmaximal, characteristic, complemented
13#13078080C212yesmaximal, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#66995C211yesmaximal, characteristic, complemented
16C4×#66985C212yesmaximal, complemented
17C2×C11×#559C211yesmaximal, characteristic, complemented
18C11×#559—21no—
19C11×#559—21no—
20C11×#559—22no—
21C11×#559C2212yes—
22C11×#559C2212yes—
23C11×#559C2214yes—
24C2×C11×#127C2211yescharacteristic
25C2×C11×#124—21no—
26C2×C11×#124C2212yes—
27C2×C11×#123—22no—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2212yes—
32#10623348—21no—
33C2×#66995C2211yescharacteristic
34C2×#66995C2212yes—
35C2×#66985C2212yes—
36C2×#66985C2212yes—
37C2×#66985C2212yes—
38#10623116C2211yescharacteristic, complemented
39#10623116C2212yescomplemented
40#10623115C2211yescharacteristic, complemented
41#10623115C2212yescomplemented
42#10623111—22no—
43#10623111—21no—
44#10623108C2211yescharacteristic, complemented
45C4×#4343—21no—
46#10623101C2211yescharacteristic, complemented
47#10623045—21no—
48#10623045—22no—
49#10623008C2211yescharacteristic
50#10623008C2212yes—
51C4×#4339C2211yescharacteristic
52C4×#4339C2212yes—
53#10622838C2211yescharacteristic
54#10622828C2212yes—
55#10622689C2212yes—
56#10622688C2212yes—
57#10622688C2212yes—
58#10622687C2214yes—
59#10622686C2212yes—
60#10622685C2212yes—
61#10622685C2212yes—
62#10622673C2214yescomplemented
63#10622672C2214yescomplemented
64#10622672C2214yescomplemented
65#10622671C2214yescomplemented
66#10622670C2214yescomplemented
67#10622670C2214yescomplemented
68#10622667C2214yescomplemented
69#10622667C2214yescomplemented
70#10622644C2212yescomplemented
71#10622643C2212yescomplemented
72C4×#4326C2212yescomplemented
73#10622641C2214yescomplemented
74#10622640C2212yescomplemented
75#10622639C2212yescomplemented
76C4×#4325C2212yescomplemented
77#10622637C2212yescomplemented
78#10622637C2214yescomplemented
79Q8×C11⋊C8C2212yescomplemented
80#10622632C2214yescomplemented
81#10622631C2214yescomplemented
82C4×#4324C2214yescomplemented
83#10622629C2214yescomplemented
84#10622629C2214yescomplemented
85#10622628C2214yescomplemented
86#10622627C2214yescomplemented
87C4×#4323C2214yescomplemented
88#10622579C2211yescharacteristic
89#10622579C2212yes—
90#10622577C2211yescharacteristic
91#10622537C2212yes—
92#10622537C2211yescharacteristic
93C4×#4318C2211yescharacteristic
94C4×#4318C2212yes—
95C22×Q8×C11D411yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11C2312yes—
100C23×C4×C11—22no—
101C2×#4343—21no—
102C2×#4339C2312yes—
103C2×#4339C2311yescharacteristic
104C11×#127—21no—
105C11×#127—21no—
106C11×#127C2312yes—
107C11×#127C2312yes—
108C11×#124—22no—
109C11×#124—22no—
110C11×#124—24no—
111C11×#124—22no—
112C11×#124—22no—
113C11×#124C2314yes—
114C11×#124C2314yes—
115C11×#123—24no—
116C11×#123—24no—
117C11×#123—24no—
118C11×#123—24no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11D411yescharacteristic
122C4×Q8×C11D412yes—
123C4×Q8×C11D411yescharacteristic
124C4×Q8×C11C2312yes—
125C4×Q8×C11C2312yes—
126C4×Q8×C11C2311yescharacteristic
127C4×Q8×C11C2311yescharacteristic
128C4×Q8×C11C2312yes—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—24no—
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11C2314yes—
135C4×D4×C11C2314yes—
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—22no—
142C2×C11×C22⋊C4—22no—
143C2×C42×C11—21no—
144C2×C42×C11C2312yes—
145C2×C42×C11C2311yescharacteristic
146#67000—21no—
147#67000—22no—
148#66999—21no—
149#66999—22no—
150Q8×Dic11—21no—
151C2×#4326C2312yes—
152C2×#4326C2314yes—
153#66995—24no—
154#66995—44no—
155C2×#4325C2312yes—
156C2×#4325C2314yes—
157C2×#4324C2314yes—
158C2×#4324C2314yes—
159C2×#4324C2314yes—
160#66985—28no—
161#66985—44no—
162#66985—44no—
163C2×#4323C2314yes—
164C2×#4323C2314yes—
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×#4318C2311yescharacteristic
176C2×#4318C2312yes—
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#66927C2312yes—
196#66927C2311yescharacteristic
197C4×D44—22no—
198C4×D44—21no—
199C4×D44—22no—
200C4×D44—21no—
201C4×D44C2312yes—
202C4×D44C2311yescharacteristic
203C4×D44C2312yes—
204C4×D44C2311yescharacteristic
205#66925—22no—
206#66925—21no—
207C42×D11—22no—
208C42×D11—21no—
209#66922C2312yes—
210#66922C2311yescharacteristic
211C4×Dic22C2312yes—
212C4×Dic22C2311yescharacteristic
213C4×Dic22C2312yes—
214C4×Dic22C2311yescharacteristic
215#66899C2312yes—
216#66899C2312yes—
217#66896C2314yes—
218#66896C2314yes—
219#66874C2312yes—
220#66874C2314yes—
221#66873C2314yes—
222#66873C2312yes—
223#66872C2312yes—
224#66871C2312yes—
225C4⋊(C11⋊C8)C2314yes—
226C4⋊(C11⋊C8)C2314yes—
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2312yes—
229#66867C2314yes—
230#66867C2312yes—
231C4×C11⋊C8C2314yes—
232C4×C11⋊C8C2312yes—
233#61405—111nomaximal, Sylow
234C24×C11—22no—
235C2×Q8×C11—21no—
236C2×Q8×C11—22no—
237C2×Q8×C11—22no—
238C2×Q8×C11—42no—
239C2×Q8×C11C2×D411yescharacteristic
240C2×Q8×C11C2×D411yescharacteristic
241C2×Q8×C11C2×D412yes—
242C2×Q8×C11C2412yes—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—22no—
248C2×D4×C11—24no—
249C2×D4×C11—24no—
250C2×D4×C11—44no—
251C2×D4×C11—82no—
252C2×D4×C11C2414yes—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—24no—
256C22×C4×C11—24no—
257C22×C4×C11—84no—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—22no—
264C2×C22⋊D11—21no—
265#4343—44no—
266#4339—24no—
267#4339—22no—
268#4339—22no—
269#4339—24no—
270C2×D44—22no—
271C2×D44—21no—
272C2×D44—22no—
273C2×D44—21no—
274C2×D44C2412yes—
275C2×D44C2411yescharacteristic
276C2×C4×D11—22no—
277C2×C4×D11—21no—
278C2×C4×D11—22no—
279C2×C4×D11—21no—
280C2×C4×D11—22no—
281C2×C4×D11—21no—
282C2×Dic22C2412yes—
283C2×Dic22C2411yescharacteristic
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2412yes—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—24no—
300C11×C22⋊C4—24no—
301C42×C11—22no—
302C42×C11—22no—
303C42×C11C2×D412yes—
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D412yes—
306C42×C11C2×D411yescharacteristic
307C42×C11C2411yescharacteristic
308C42×C11C2412yes—
309C42×C11C2412yes—
310C42×C11C2411yescharacteristic
311C22⋊Dic11—21no—
312#4326—24no—
313#4326—44no—
314#4325—24no—
315#4325—44no—
316#4324—28no—
317#4324—44no—
318#4324—44no—
319#4323—28no—
320#4323—44no—
321#4323—44no—
322(C2×D11)⋊C4—21no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—21no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332C4⋊Dic11—22no—
333C4⋊Dic11—21no—
334C4⋊Dic11—22no—
335C4⋊Dic11—21no—
336C4⋊Dic11C2411yescharacteristic
337C4⋊Dic11C2411yescharacteristic
338Dic11⋊C4—22no—
339Dic11⋊C4—21no—
340Dic11⋊C4—21no—
341Dic11⋊C4—22no—
342C4×Dic11—22no—
343C4×Dic11—21no—
344C4×Dic11—22no—
345C4×Dic11—21no—
346C4×Dic11—21no—
347#4318—22no—
348#4318—24no—
349#4318#4114yescomplemented
350C2×C11⋊C8C2414yes—
351C2×C11⋊C8C2412yes—
352C2×C11⋊C8C2412yes—
353#3480—111no—
354C2×#559D1111yescharacteristic, complemented
355#3403—114no—
356#3401—114no—
357#3400—112no—
358#3399—112no—
359#3396—112no—
360#3394—112no—
361#3153—112no—
362#3151—111no—
363#3040—112no—
364#3038—111no—
365#3037—111no—
366#3036—112no—
367Q8×M16—111no—
368C4×#137—111no—
369C4×AGL(1,ℤ/8)—112no—
370C23×C11—24no—
371C23×C11—44no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11C22×D411yescharacteristic
375C22×D11—22no—
376C22×D11—21no—
377Q8×C11—22no—
378Q8×C11—22no—
379Q8×C11—22no—
380Q8×C11—22no—
381Q8×C11—42no—
382Q8×C11—42no—
383D4×C11—24no—
384D4×C11—24no—
385D4×C11—44no—
386D4×C11—44no—
387D4×C11—44no—
388D4×C11—82no—
389D4×C11—82no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—42no—
394C2×C4×C11—41no—
395C2×C4×C11—42no—
396C2×C4×C11—42no—
397C2×C4×C11—42no—
398C2×C4×C11—84no—
399C2×C4×C11—84no—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D412yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C2×#4112yes—
410C2×C4×C11H(5,𝔽2)12yes—
411C2×C4×C11C2511yescharacteristic
412C22⋊D11—44no—
413C22⋊D11—42no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—22no—
417C2×Dic11—21no—
418D44—22no—
419D44—21no—
420D44—21no—
421D44—22no—
422D44—44no—
423D44—42no—
424D44—82no—
425D44—81no—
426C4×D11—44no—
427C4×D11—44no—
428C4×D11—42no—
429C4×D11—42no—
430C4×D11—82no—
431C4×D11—81no—
432Dic22—22no—
433Dic22—21no—
434Dic22—21no—
435Dic22—22no—
436C11⋊C8—22no—
437C11⋊C8—24no—
438C11⋊C8C2×#4114yes—
439C2×#137—111no—
440C2×#137—112no—
441C2×AGL(1,ℤ/8)—112no—
442C2×AGL(1,ℤ/8)—112no—
443C2×AGL(1,ℤ/8)—112no—
444#559—21no—
445#559—21no—
446#559—22no—
447#559—111no—
448#559—112no—
449#559C2×D1112yes—
450#559C2×D1112yes—
451#559C2×D1114yes—
452#557—111no—
453#556—111no—
454#556—112no—
455#553—221no—
456#553—222no—
457#550—111no—
458#548—221no—
459#532—111no—
460#532—112no—
461C2×#127C2×D1111yescharacteristic
462#529—222no—
463#529—221no—
464C2×#124—21no—
465C2×#124C2×D1112yes—
466C2×#123—22no—
467C4×#41—112no—
468C4×#41—111no—
469C4×#41—221no—
470C2×C4×Q8C2×D1111yescharacteristic
471C2×C4×Q8C2×D1111yescharacteristic
472C2×C4×D4—21no—
473C2×C4×D4C2×D1112yes—
474#497—114no—
475#496—114no—
476#496—114no—
477#495—114no—
478#495—114no—
479#493—112no—
480#492—112no—
481#464—114no—
482#464—114no—
483#464—114no—
484#463—114no—
485#463—114no—
486#463—114no—
487#463—114no—
488#462—112no—
489#461—114no—
490#460—112no—
491#460—112no—
492#460—112no—
493#459—112no—
494#459—112no—
495#459—114no—
496#446—112no—
497#446—114no—
498C8×Q8—112no—
499#442—114no—
500#441—112no—
501#440—112no—
502#440—114no—
503C4×Q16—112no—
504C4×SD16—112no—
505C4×SD16—114no—
506C4×D8—114no—
507#428—111no—
508#423—112no—
509#423—111no—
510#419—111no—
511#418—112no—
512#417—112no—
513#417—111no—
514C4×M16—111no—
515C4×M16—112no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—44no—
519C22×C11—44no—
520C22×C11—44no—
521C22×C11—88no—
522C22×C11#55012yes—
523C22×C11C23×D411yescharacteristic
524C2×D11—42no—
525C2×D11—41no—
526C2×D11—42no—
527C2×D11—41no—
528C2×D11—42no—
529C2×D11—41no—
530C4×C11—22no—
531C4×C11—22no—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—22no—
536C4×C11—22no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11#55012yes—
540C4×C11#57512yes—
541C4×C11C22×#4111yescharacteristic
542C4×C11C2×H(5,𝔽2)11yescharacteristic
543Dic11—41no—
544Dic11—42no—
545Dic11—41no—
546Dic11—41no—
547C2×#41—112no—
548C2×#41—111no—
549C2×#41—221no—
550C22×Q8C22⋊D1111yescharacteristic
551C22×Q8C22×D1111yescharacteristic
552C22×D4—21no—
553C22×D4—21no—
554C22×D4C22×D1112yes—
555C23×C4—22no—
556#137—224no—
557#137—444no—
558AGL(1,ℤ/8)—228no—
559AGL(1,ℤ/8)—444no—
560AGL(1,ℤ/8)—444no—
561C2×Q16—112no—
562C2×Q16—114no—
563C2×SD16—112no—
564C2×SD16—114no—
565C2×SD16—114no—
566C2×SD16—114no—
567C2×SD16—114no—
568C2×D8—114no—
569C2×D8—114no—
570C2×D8—114no—
571C2×M16—111no—
572C2×M16—111no—
573C2×M16—112no—
574C4⋊Q8—112no—
575C4⋊Q8—111no—
576#127—21no—
577#127—21no—
578#127—112no—
579#127—111no—
580#127C22×D1112yes—
581#127C22×D1112yes—
582#126—222no—
583#126—222no—
584#126—222no—
585#125—221no—
586#125—222no—
587#124—22no—
588#124—22no—
589#124—24no—
590#124—22no—
591#124—22no—
592#124—112no—
593#124—112no—
594#124—112no—
595#124—221no—
596#124—222no—
597#124C22×D1114yes—
598#124C22×D1114yes—
599#123—24no—
600#123—24no—
601#123—24no—
602#123—24no—
603#123—222no—
604#123—222no—
605#123—222no—
606C22⋊Q8—221no—
607C22⋊Q8—222no—
608#121—221no—
609#121—222no—
610#121—222no—
611#121—221no—
612#121—221no—
613#121—222no—
614C4×Q8—21no—
615C4×Q8—21no—
616C4×Q8—112no—
617C4×Q8—111no—
618C4×Q8—111no—
619C4×Q8—112no—
620C4×Q8—221no—
621C4×Q8C22⋊D1111yescharacteristic
622C4×Q8C22⋊D1112yes—
623C4×Q8C22⋊D1111yescharacteristic
624C4×Q8C22×D1112yes—
625C4×Q8C22×D1112yes—
626C4×Q8C22×D1111yescharacteristic
627C4×Q8C22×D1111yescharacteristic
628C4×Q8C22×D1112yes—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—24no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—111no—
635C4×D4—112no—
636C4×D4—112no—
637C4×D4—111no—
638C4×D4—221no—
639C4×D4—222no—
640C4×D4—222no—
641C4×D4—221no—
642C4×D4—221no—
643C4×D4—222no—
644C4×D4—222no—
645C4×D4—221no—
646C4×D4—222no—
647C4×D4—221no—
648C4×D4C22×D1114yes—
649C4×D4C22×D1114yes—
650#117—111no—
651#117—221no—
652#117—222no—
653#117—222no—
654#117—221no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4C22⋊D1111yescharacteristic
657C2×C4⋊C4C22⋊D1112yes—
658C2×C4⋊C4C22×D1111yescharacteristic
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C42—21no—
663C2×C42—222no—
664C2×C42—221no—
665C2×C42C22×D1112yes—
666C2×C42C22×D1111yescharacteristic
667#107—112no—
668#106—112no—
669C4⋊C8—112no—
670C4⋊C8—114no—
671C4⋊C8—112no—
672C4⋊C8—114no—
673#103—112no—
674#103—112no—
675#103—114no—
676#103—112no—
677#102—114no—
678#102—114no—
679#102—114no—
680#102—112no—
681#97—112no—
682#97—114no—
683C4×C8—114no—
684C4×C8—112no—
685C2×C11—22no—
686C2×C11—84no—
687C2×C11C2×#55011yescharacteristic
688C2×C11C2×#57511yescharacteristic
689C2×C11#358511yescharacteristic
690D11—82no—
691D11—81no—
692C24—22no—
693#41—224no—
694#41—222no—
695#41—222no—
696#41—224no—
697#41—444no—
698C2×Q8—21no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—42no—
702C2×Q8—112no—
703C2×Q8—111no—
704C2×Q8C2×C22⋊D1111yescharacteristic
705C2×Q8C2×C22⋊D1111yescharacteristic
706C2×Q8C2×C22⋊D1112yes—
707C2×Q8C23×D1112yes—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—44no—
716C2×D4—82no—
717C2×D4—112no—
718C2×D4—111no—
719C2×D4—222no—
720C2×D4—221no—
721C2×D4—222no—
722C2×D4—221no—
723C2×D4—222no—
724C2×D4—221no—
725C2×D4C23×D1114yes—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—84no—
731C22×C4—222no—
732C22×C4—221no—
733C22×C4—222no—
734C22×C4—221no—
735C22×C4—222no—
736C22×C4—221no—
737C22×C4C2×C22⋊D1111yescharacteristic
738C22×C4C2×C22⋊D1112yes—
739C22×C4C2×C22⋊D1112yes—
740C22×C4C2×C22⋊D1111yescharacteristic
741C22×C4C23×D1111yescharacteristic
742Q16—224no—
743Q16—444no—
744SD16—228no—
745SD16—224no—
746SD16—444no—
747SD16—444no—
748SD16—444no—
749D8—228no—
750D8—444no—
751D8—444no—
752M16—114no—
753M16—222no—
754M16—224no—
755C2×C8—112no—
756C2×C8—114no—
757C2×C8—112no—
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—111no—
762C4⋊C4—111no—
763C4⋊C4—221no—
764C4⋊C4—222no—
765C4⋊C4—222no—
766C4⋊C4—221no—
767C4⋊C4—222no—
768C4⋊C4—221no—
769C4⋊C4—222no—
770C4⋊C4—221no—
771C4⋊C4C2×C22⋊D1111yescharacteristic
772C4⋊C4C2×C22⋊D1112yes—
773C4⋊C4C2×C22⋊D1111yescharacteristic
774C4⋊C4C2×C22⋊D1112yes—
775C4⋊C4C2×C22⋊D1112yes—
776C4⋊C4C2×C22⋊D1112yes—
777C4⋊C4C2×C22⋊D1112yes—
778C4⋊C4C23×D1112yes—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—221no—
786C22⋊C4—222no—
787C22⋊C4—221no—
788C22⋊C4—221no—
789C22⋊C4—222no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4—222no—
793C22⋊C4—222no—
794C22⋊C4—222no—
795C22⋊C4—222no—
796C42—22no—
797C42—22no—
798C42—221no—
799C42—222no—
800C42—221no—
801C42—222no—
802C42—221no—
803C42C2×C22⋊D1112yes—
804C42C2×C22⋊D1111yescharacteristic
805C42C2×C22⋊D1112yes—
806C42C2×C22⋊D1111yescharacteristic
807C42C23×D1112yes—
808C42C23×D1111yescharacteristic
809C42C23×D1112yes—
810C42C23×D1111yescharacteristic
811C11#6140511yescharacteristic, complemented, Sylow
812C23—24no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—222no—
817C23—221no—
818C23C22×C22⋊D1111yescharacteristic
819Q8—22no—
820Q8—22no—
821Q8—22no—
822Q8—22no—
823Q8—42no—
824Q8—42no—
825Q8—222no—
826Q8—221no—
827Q8—221no—
828Q8—222no—
829D4—24no—
830D4—24no—
831D4—44no—
832D4—44no—
833D4—44no—
834D4—82no—
835D4—82no—
836D4—222no—
837D4—221no—
838D4—221no—
839D4—222no—
840D4—444no—
841D4—444no—
842D4—442no—
843D4—442no—
844D4—882no—
845D4—881no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—84no—
855C2×C4—84no—
856C2×C4—221no—
857C2×C4—221no—
858C2×C4—222no—
859C2×C4—221no—
860C2×C4—444no—
861C2×C4—442no—
862C2×C4—444no—
863C2×C4—442no—
864C2×C4—882no—
865C2×C4—881no—
866C2×C4#41×D1112yes—
867C2×C4#6704212yes—
868C2×C4C22×C22⋊D1111yescharacteristic
869C2×C4C22×C22⋊D1112yes—
870C2×C4C22×C22⋊D1112yes—
871C2×C4C22×C22⋊D1111yescharacteristic
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1112yes—
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C22×C22⋊D1111yescharacteristic
876C2×C4C22×C22⋊D1111yescharacteristic
877C2×C4C24×D1111yescharacteristic
878C8—114no—
879C8—222no—
880C8—224no—
881C22—21no—
882C22—21no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—88no—
887C22—442no—
888C22—441no—
889C22—442no—
890C22—441no—
891C22—442no—
892C22—441no—
893C22#1062336512yes—
894C22C23×C22⋊D1111yescharacteristic
895C4—22no—
896C4—22no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—22no—
901C4—22no—
902C4—42no—
903C4—42no—
904C4—441no—
905C4—441no—
906C4—442no—
907C4—441no—
908C4#1062335312yes—
909C4#1062336512yes—
910C4C2×#41×D1111yescharacteristic
911C4C2×#6704211yescharacteristic
912C2—22no—
913C2—84no—
914C2—882no—
915C2—881no—
916C2C2×#1062336511yescharacteristic
917C2C2×#1062335311yescharacteristic
918C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC22×C11C23×D4
hypercenterC2×#559D11
hypocenterC11#61405
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #13082211C2semidirect
2. #13081700C2semidirect
3. #13081676C2semidirect
4. #13081669C2semidirect
5. #13081654C2semidirect
6. #13081624C2semidirect
7. #13081608C2semidirect
8. #13079080C2semidirect
9. #13079066C2semidirect
10. #13078106C2semidirect
11. #13078092C2semidirect
12. #13078088C2semidirect
13. #13078080C2semidirect
14. Q8×#4318C2semidirect
15. C4×#66995C2semidirect
16. C4×#66985C2semidirect
17. C2×C11×#559C2semidirect
38. #10623116C22semidirect
39. #10623116C22semidirect
40. #10623115C22semidirect
41. #10623115C22semidirect
44. #10623108C22semidirect
46. #10623101C22semidirect
62. #10622673C22semidirect
63. #10622672C22semidirect
64. #10622672C22semidirect
65. #10622671C22semidirect
66. #10622670C22semidirect
67. #10622670C22semidirect
68. #10622667C22semidirect
69. #10622667C22semidirect
70. #10622644C22semidirect
71. #10622643C22semidirect
72. C4×#4326C22semidirect
73. #10622641C22semidirect
74. #10622640C22semidirect
75. #10622639C22semidirect
76. C4×#4325C22semidirect
77. #10622637C22semidirect
78. #10622637C22semidirect
79. Q8×C11⋊C8C22semidirect
80. #10622632C22semidirect
81. #10622631C22semidirect
82. C4×#4324C22semidirect
83. #10622629C22semidirect
84. #10622629C22semidirect
85. #10622628C22semidirect
86. #10622627C22semidirect
87. C4×#4323C22semidirect
349. #4318#41semidirect
354. C2×#559D11semidirect
811. C11#61405semidirect

Maximal subgroups

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

subgroupindex
#130822112
#130817002
#130816762
#130816692
#130816542
#130816242
#130816082
#130790802
#130790662
#130781062
#130780922
#130780882
#130780802
Q8×#43182
C4×#669952
C4×#669852
C2×C11×#5592
#6140511