Finite Group Databasebeta

← #15626849

Subgroups — #15626849

Order 2816.

1932 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082032C211yesmaximal, characteristic, complemented
2#13080051C214yesmaximal, complemented
3#13080021C214yesmaximal, complemented
4#13079994C212yesmaximal, complemented
5#13079972C212yesmaximal, complemented
6#13079936C212yesmaximal, complemented
7#13079923C212yesmaximal, complemented
8#13078447C212yesmaximal, complemented
9#13078409C211yesmaximal, characteristic, complemented
10#13078398C211yesmaximal, characteristic, complemented
11#13078292C212yesmaximal, complemented
12#13078261C212yesmaximal, complemented
13#13078119C212yesmaximal, complemented
14#13078092C211yesmaximal, characteristic, complemented
15C2×#10622685C211yesmaximal, characteristic, complemented
16#13077184C211yesmaximal, characteristic, complemented
17C11×#3508C211yesmaximal, characteristic, complemented
18C11×#559—21no—
19C11×#559—21no—
20C11×#550—21no—
21C11×#550—21no—
22C11×#546—22no—
23C11×#546—22no—
24C11×#540C2214yescomplemented
25C11×#535C2212yes—
26C11×#533C2211yescharacteristic
27C11×#532C2212yescomplemented
28C11×#532C2212yescomplemented
29C2×C11×#127C2211yescharacteristic
30C11×#518C2212yes—
31C4×C11×#41C2211yescharacteristic
32#10623364C2211yescharacteristic
33#10623361C2211yescharacteristic
34C2×#67001C2212yes—
35C2×#66985C2212yes—
36C22×#4323C2212yes—
37#10623113—21no—
38#10623111—21no—
39#10623093—21no—
40#10623091—22no—
41#10623079—21no—
42#10623078—22no—
43#10623066C2212yescomplemented
44#10623065C2212yescomplemented
45#10623056C2211yescharacteristic
46#10623050C2211yescharacteristic
47#10623010C2212yescomplemented
48#10623008C2212yescomplemented
49C4×#4339C2211yescharacteristic
50C2×C4×D44C2211yescharacteristic
51#10622828C2212yes—
52C2×#66896C2212yes—
53#10622707C2211yescharacteristic, complemented
54#10622704C2211yescharacteristic, complemented
55#10622700C2211yescharacteristic, complemented
56#10622700C2212yescomplemented
57#10622697C2211yescharacteristic, complemented
58#10622697C2212yescomplemented
59#10622688C2212yescomplemented
60#10622688C2212yescomplemented
61#10622685C2212yes—
62#10622685C2212yes—
63#10622685C2214yes—
64#10622685C2212yescomplemented
65#10622685C2212yescomplemented
66#10622679C2212yescomplemented
67#10622679C2214yescomplemented
68#10622676C2212yescomplemented
69#10622655C2214yescomplemented
70#10622654C2214yescomplemented
71#10622652C2214yescomplemented
72#10622652C2214yescomplemented
73#10622652C2214yescomplemented
74#10622651C2214yescomplemented
75#10622651C2214yescomplemented
76#10622651C2214yescomplemented
77#10622629C2214yescomplemented
78#10622629C2214yescomplemented
79#10622628C2214yescomplemented
80#10622628C2214yescomplemented
81#10622622C2214yescomplemented
82#10622622C2214yescomplemented
83#10622621C2214yescomplemented
84#10622620C2214yescomplemented
85#10622615C2212yes—
86#10622614C2212yes—
87#10622612C2212yes—
88#10622612C2214yescomplemented
89#10622611C2212yes—
90#10622608C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yescomplemented
93C2×C4⋊(C11⋊C8)C2211yescharacteristic
94C2×C4⋊(C11⋊C8)C2212yescomplemented
95C2×C11×#41—22no—
96C2×C11×#41—22no—
97C2×C11×#41C2311yescharacteristic
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11C2312yes—
101C2×#4339—22no—
102C2×#4339C2311yescharacteristic
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C11×C4⋊Q8C2311yescharacteristic
106C11×C4⋊Q8C2311yescharacteristic
107C11×#127—22no—
108C11×#127—21no—
109C11×#127—21no—
110C11×#127C2312yes—
111C11×#127C2312yes—
112C11×#125C2312yes—
113C11×#124—22no—
114C11×#124—22no—
115C11×#124—22no—
116C11×#123—24no—
117C11×#123—24no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—21no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—24no—
123C11×#121—24no—
124C11×#121C2314yes—
125C11×#121C2314yes—
126C11×#120—24no—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11D411yescharacteristic
130C4×Q8×C11D411yescharacteristic
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11—22no—
135C4×D4×C11D412yes—
136C4×D4×C11D411yescharacteristic
137C4×D4×C11D412yes—
138C4×D4×C11D411yescharacteristic
139C4×D4×C11C2314yes—
140C4×D4×C11C2314yes—
141C11×#117C2312yes—
142C11×#117C2311yescharacteristic
143C11×#117C2312yes—
144C2×C11×C22⋊C4—24no—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2312yes—
147#67001—44no—
148#67000—21no—
149#66999—21no—
150#66993—21no—
151#66992—22no—
152#66991—21no—
153#66990—22no—
154C2×#4324C2314yes—
155#66985—44no—
156C2×#4323—44no—
157C2×#4323C2314yes—
158C2×#4323C2314yes—
159C2×#4323C2314yes—
160#66983—22no—
161#66983C2312yes—
162#66983C2312yes—
163#66983C2312yes—
164#66982—22no—
165C4×C22⋊D11—21no—
166C4×C22⋊D11—21no—
167C4×C22⋊D11—22no—
168C2×(C2×D11)⋊C4—21no—
169#66979C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171#66977C2312yes—
172C2×#4318C2312yes—
173C2×#4318C2314yes—
174C22×C11⋊C8C2312yes—
175C22×C11⋊C8C2314yes—
176#66951—22no—
177#66949—22no—
178#66948—21no—
179#66948—21no—
180#66947—22no—
181#66947—22no—
182#66943—21no—
183#66941—21no—
184#66938—22no—
185#66937—22no—
186#66937—22no—
187#66936—22no—
188#66935—22no—
189#66931—22no—
190#66929—22no—
191#66928—22no—
192#66928C2312yes—
193#66927C2312yes—
194C4×D44—21no—
195C4×D44—21no—
196C4×D44—22no—
197C4×D44C2312yes—
198C4×D44C2312yes—
199C4×D44C2311yescharacteristic
200C4×D44C2311yescharacteristic
201#66925—21no—
202#66925—22no—
203C42×D11—21no—
204#66923C2312yes—
205#66922C2312yes—
206C4×Dic22C2311yescharacteristic
207C4×Dic22C2311yescharacteristic
208#66896C2314yes—
209#66896C2314yes—
210#66896C2314yes—
211#66896C2314yes—
212#66874C2312yes—
213#66874C2312yes—
214#66873C2314yes—
215#66873C2314yes—
216#66873C2312yes—
217#66873C2312yes—
218#66872C2314yes—
219#66872C2312yes—
220#66872C2312yes—
221#66871C2314yes—
222#66871C2312yes—
223#66871C2312yes—
224C4⋊(C11⋊C8)C2311yescharacteristic
225C4⋊(C11⋊C8)C2311yescharacteristic
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2314yes—
231#60922—111nomaximal, Sylow
232C24×C11—22no—
233C23×D11—21no—
234C11×#41—22no—
235C11×#41—22no—
236C11×#41—84no—
237C11×#41—84no—
238C2×Q8×C11—21no—
239C2×Q8×C11—21no—
240C2×Q8×C11C2×D411yescharacteristic
241C2×D4×C11—24no—
242C2×D4×C11—24no—
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—82no—
251C2×D4×C11—82no—
252C2×D4×C11C2×D412yes—
253C2×D4×C11C2×D411yescharacteristic
254C2×D4×C11C2414yes—
255C22×C4×C11—24no—
256C22×C4×C11—24no—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—21no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—22no—
267C22×Dic11—21no—
268#4339—22no—
269#4339—22no—
270#4339—84no—
271C2×D44—21no—
272C2×D44—22no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44C2411yescharacteristic
277C2×D44C2412yes—
278C2×C4×D11—21no—
279C2×C4×D11—21no—
280C2×C4×D11—22no—
281C2×C4×D11—21no—
282C2×C4×D11—22no—
283C2×C4×D11—82no—
284C2×Dic22—22no—
285C2×Dic22C2411yescharacteristic
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2412yes—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—24no—
300C11×C22⋊C4—24no—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C42×C11—22no—
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D412yes—
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D412yes—
309C42×C11C2411yescharacteristic
310C42×C11C2411yescharacteristic
311C42×C11C2412yes—
312C22⋊Dic11—21no—
313C22⋊Dic11—22no—
314#4324—44no—
315#4323—44no—
316#4323—44no—
317#4323—44no—
318(C2×D11)⋊C4—21no—
319(C2×D11)⋊C4—21no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—21no—
329C4⋊Dic11C2411yescharacteristic
330C4⋊Dic11C2411yescharacteristic
331C4⋊Dic11C2412yes—
332Dic11⋊C4—21no—
333Dic11⋊C4—21no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337C4×Dic11—21no—
338C4×Dic11—21no—
339C4×Dic11—21no—
340#4318—24no—
341#4318—44no—
342C2×C11⋊C8—24no—
343C2×C11⋊C8—44no—
344C2×C11⋊C8C2412yes—
345C2×C11⋊C8C2414yes—
346C2×C11⋊C8C2412yes—
347#3508D1111yescharacteristic, complemented
348#3460—111no—
349#3259—114no—
350#3257—114no—
351#3253—112no—
352#3251—112no—
353#3247—112no—
354#3245—112no—
355#3081—112no—
356#3077—111no—
357#3076—111no—
358#3062—112no—
359#3058—112no—
360#3041—112no—
361#3038—111no—
362C2×#459—111no—
363#2906—111no—
364C23×C11—24no—
365C23×C11—44no—
366C23×C11—82no—
367C23×C11—82no—
368C23×C11C22×D412yes—
369C23×C11C22×D411yescharacteristic
370C22×D11—22no—
371C22×D11—21no—
372C22×D11—42no—
373C22×D11—81no—
374C22×D11—81no—
375Q8×C11—22no—
376Q8×C11—42no—
377Q8×C11—42no—
378D4×C11—24no—
379D4×C11—22no—
380D4×C11—24no—
381D4×C11—24no—
382D4×C11—44no—
383D4×C11—44no—
384D4×C11—44no—
385D4×C11—82no—
386D4×C11—82no—
387D4×C11—84no—
388D4×C11—84no—
389C2×C4×C11—22no—
390C2×C4×C11—24no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—41no—
396C2×C4×C11—42no—
397C2×C4×C11—84no—
398C2×C4×C11—84no—
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D412yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11H(5,𝔽2)12yes—
408C2×C4×C112−1+412yes—
409C2×C4×C11C2511yescharacteristic
410C22⋊D11—42no—
411C22⋊D11—82no—
412C22⋊D11—82no—
413C22⋊D11—82no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—22no—
418C2×Dic11—81no—
419D44—22no—
420D44—21no—
421D44—22no—
422D44—21no—
423D44—42no—
424D44—82no—
425D44—82no—
426C4×D11—42no—
427C4×D11—44no—
428C4×D11—42no—
429C4×D11—81no—
430C4×D11—82no—
431Dic22—21no—
432Dic22—21no—
433Dic22—82no—
434C11⋊C8—22no—
435C11⋊C8—22no—
436C11⋊C8—24no—
437C2×AGL(1,ℤ/8)—112no—
438C22×D8—112no—
439C2×#131—112no—
440#559—21no—
441#559—21no—
442#550—21no—
443#550—21no—
444#546—22no—
445#546—22no—
446#544—111no—
447#542—112no—
448#542—221no—
449#540—112no—
450#540—221no—
451#540C2×D1114yescomplemented
452#538—222no—
453#537—111no—
454#535—111no—
455#535—111no—
456#535C2×D1112yes—
457#533C2×D1111yescharacteristic
458#532—112no—
459#532—221no—
460#532C2×D1112yescomplemented
461#532C2×D1112yescomplemented
462C2×#127C2×D1111yescharacteristic
463#529—112no—
464#529—221no—
465#525—222no—
466#518C2×D1112yes—
467C4×#41—111no—
468C4×#41C2×D1111yescharacteristic
469C2×C4×D4—111no—
470#479—112no—
471#478—112no—
472#478—114no—
473#478—114no—
474#478—114no—
475#477—111no—
476#476—111no—
477#476—112no—
478#476—114no—
479#475—111no—
480#474—111no—
481#474—112no—
482#474—114no—
483#469—114no—
484#469—114no—
485#469—114no—
486#468—114no—
487#466—114no—
488#466—114no—
489#466—114no—
490#465—114no—
491#463—114no—
492#463—114no—
493#460—112no—
494#460—112no—
495#459—112no—
496#459—112no—
497#459—112no—
498#459—114no—
499#459—112no—
500#459—114no—
501#459—114no—
502#428—112no—
503#427—112no—
504#424—112no—
505#424—114no—
506#423—111no—
507#423—112no—
508C2×C4⋊C8—111no—
509C2×C4⋊C8—112no—
510#418—112no—
511#418—112no—
512#416—112no—
513C2×#102—112no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—22no—
519C22×C11—44no—
520C22×C11—44no—
521C22×C11—44no—
522C22×C11—164no—
523C22×C11#53712yes—
524C22×C11C23×D411yescharacteristic
525C2×D11—42no—
526C2×D11—41no—
527C2×D11—42no—
528C2×D11—41no—
529C2×D11—42no—
530C2×D11—41no—
531C2×D11—84no—
532C4×C11—21no—
533C4×C11—22no—
534C4×C11—21no—
535C4×C11—22no—
536C4×C11—22no—
537C4×C11—21no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11#53712yes—
541C4×C11#57612yes—
542C4×C11C2×H(5,𝔽2)11yescharacteristic
543C4×C11C2×2−1+411yescharacteristic
544Dic11—41no—
545Dic11—41no—
546Dic11—41no—
547Dic11—42no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—111no—
551C2×#41—222no—
552C2×#41C22×D1111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—111no—
556C22×D4C22×D1112yes—
557C23×C4—221no—
558AGL(1,ℤ/8)—444no—
559C2×SD16—114no—
560C2×D8—114no—
561C2×D8—114no—
562C2×D8—114no—
563C2×D8—444no—
564#131—444no—
565C2×M16—112no—
566C2×M16—114no—
567C22×C8—112no—
568C22×C8—114no—
569C4⋊Q8—112no—
570C4⋊Q8—221no—
571C4⋊Q8C22×D1111yescharacteristic
572C4⋊Q8C22×D1111yescharacteristic
573#127—22no—
574#127—21no—
575#127—21no—
576#127—112no—
577#127—221no—
578#127C22×D1112yes—
579#127C22×D1112yes—
580#126—222no—
581#126—222no—
582#125—112no—
583#125—221no—
584#125C22×D1112yes—
585#124—22no—
586#124—22no—
587#124—22no—
588#124—112no—
589#124—221no—
590#124—222no—
591#124—222no—
592#123—24no—
593#123—24no—
594#123—222no—
595#123—222no—
596#123—222no—
597#123—222no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—112no—
601C22⋊Q8—221no—
602C22⋊Q8—222no—
603C22⋊Q8—222no—
604#121—22no—
605#121—22no—
606#121—24no—
607#121—24no—
608#121—112no—
609#121—112no—
610#121—112no—
611#121—222no—
612#121—221no—
613#121—222no—
614#121—221no—
615#121—221no—
616#121—222no—
617#121—222no—
618#121C22×D1114yes—
619#121C22×D1114yes—
620#120—24no—
621#120—222no—
622#120—222no—
623C4×Q8—21no—
624C4×Q8—21no—
625C4×Q8—111no—
626C4×Q8—111no—
627C4×Q8C22⋊D1111yescharacteristic
628C4×Q8C22⋊D1111yescharacteristic
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—112no—
634C4×D4—112no—
635C4×D4—111no—
636C4×D4—111no—
637C4×D4—221no—
638C4×D4—221no—
639C4×D4—222no—
640C4×D4—221no—
641C4×D4—221no—
642C4×D4—222no—
643C4×D4C22⋊D1112yes—
644C4×D4C22⋊D1111yescharacteristic
645C4×D4C22⋊D1112yes—
646C4×D4C22⋊D1111yescharacteristic
647C4×D4C22×D1114yes—
648C4×D4C22×D1114yes—
649#117—111no—
650#117—221no—
651#117—222no—
652#117C22×D1112yes—
653#117C22×D1111yescharacteristic
654#117C22×D1112yes—
655C2×C4⋊C4—111no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—221no—
658C2×C42—221no—
659C2×C42C22×D1111yescharacteristic
660C2×C42C22×D1112yes—
661#107—112no—
662#107—112no—
663#107—114no—
664#106—112no—
665#106—112no—
666#106—114no—
667C4⋊C8—111no—
668C4⋊C8—111no—
669C4⋊C8—112no—
670C4⋊C8—112no—
671C4⋊C8—114no—
672C4⋊C8—112no—
673C4⋊C8—114no—
674#103—112no—
675#103—112no—
676#102—114no—
677#102—114no—
678#102—114no—
679#102—114no—
680#102—112no—
681#102—112no—
682#102—114no—
683#102—114no—
684C2×C11—22no—
685C2×C11—42no—
686C2×C11—84no—
687C2×C11C2×#53711yescharacteristic
688C2×C11C2×#57611yescharacteristic
689C2×C11#358511yescharacteristic
690D11—81no—
691D11—82no—
692C24—22no—
693C24—221no—
694#41—22no—
695#41—22no—
696#41—84no—
697#41—84no—
698#41—222no—
699#41—222no—
700#41—884no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—111no—
704C2×Q8—222no—
705C2×Q8C2×C22⋊D1111yescharacteristic
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—82no—
716C2×D4—82no—
717C2×D4—112no—
718C2×D4—111no—
719C2×D4—221no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—222no—
725C2×D4—221no—
726C2×D4—222no—
727C2×D4—222no—
728C2×D4C2×C22⋊D1112yes—
729C2×D4C2×C22⋊D1111yescharacteristic
730C2×D4C23×D1114yes—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—222no—
737C22×C4—221no—
738C22×C4—222no—
739C22×C4—882no—
740C22×C4C2×C22⋊D1112yes—
741C22×C4C2×C22⋊D1111yescharacteristic
742C22×C4C2×C22⋊D1111yescharacteristic
743C22×C4C2×C22⋊D1112yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1111yescharacteristic
746SD16—444no—
747D8—444no—
748D8—444no—
749D8—444no—
750M16—224no—
751M16—444no—
752C2×C8—114no—
753C2×C8—112no—
754C2×C8—112no—
755C2×C8—224no—
756C2×C8—444no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—112no—
762C4⋊C4—111no—
763C4⋊C4—111no—
764C4⋊C4—221no—
765C4⋊C4—221no—
766C4⋊C4—221no—
767C4⋊C4—222no—
768C4⋊C4—222no—
769C4⋊C4—222no—
770C4⋊C4—222no—
771C4⋊C4C2×C22⋊D1111yescharacteristic
772C4⋊C4C2×C22⋊D1111yescharacteristic
773C4⋊C4C2×C22⋊D1112yes—
774C4⋊C4C2×C22⋊D1112yes—
775C4⋊C4C23×D1112yes—
776C4⋊C4C23×D1112yes—
777C22⋊C4—22no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—221no—
783C22⋊C4—222no—
784C22⋊C4—222no—
785C22⋊C4—222no—
786C22⋊C4—221no—
787C22⋊C4—221no—
788C22⋊C4—222no—
789C22⋊C4—222no—
790C22⋊C4—222no—
791C22⋊C4—222no—
792C22⋊C4—222no—
793C22⋊C4C2×C22⋊D1112yes—
794C22⋊C4C2×C22⋊D1112yes—
795C22⋊C4C2×C22⋊D1112yes—
796C42—22no—
797C42—221no—
798C42—221no—
799C42—221no—
800C42C2×C22⋊D1111yescharacteristic
801C42C2×C22⋊D1112yes—
802C42C2×C22⋊D1111yescharacteristic
803C42C2×C22⋊D1112yes—
804C42C23×D1111yescharacteristic
805C42C23×D1111yescharacteristic
806C42C23×D1112yes—
807C11#6092211yescharacteristic, complemented, Sylow
808C23—24no—
809C23—44no—
810C23—82no—
811C23—82no—
812C23—222no—
813C23—221no—
814C23—442no—
815C23—881no—
816C23—881no—
817C23C22×C22⋊D1112yes—
818C23C22×C22⋊D1111yescharacteristic
819Q8—22no—
820Q8—42no—
821Q8—42no—
822Q8—221no—
823Q8—221no—
824Q8—882no—
825D4—24no—
826D4—22no—
827D4—24no—
828D4—24no—
829D4—44no—
830D4—44no—
831D4—44no—
832D4—82no—
833D4—82no—
834D4—84no—
835D4—84no—
836D4—222no—
837D4—221no—
838D4—222no—
839D4—221no—
840D4—442no—
841D4—442no—
842D4—882no—
843D4—882no—
844D4—882no—
845D4—882no—
846D4—882no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—84no—
856C2×C4—84no—
857C2×C4—221no—
858C2×C4—221no—
859C2×C4—221no—
860C2×C4—222no—
861C2×C4—442no—
862C2×C4—444no—
863C2×C4—442no—
864C2×C4—882no—
865C2×C4—881no—
866C2×C4—881no—
867C2×C4#6704212yes—
868C2×C4#6704312yes—
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C22×C22⋊D1112yes—
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1112yes—
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C22×C22⋊D1111yescharacteristic
876C2×C4C22×C22⋊D1111yescharacteristic
877C2×C4C24×D1111yescharacteristic
878C8—222no—
879C8—222no—
880C8—224no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—164no—
890C22—441no—
891C22—442no—
892C22—441no—
893C22—442no—
894C22—442no—
895C22—441no—
896C22—884no—
897C22#1062336412yes—
898C22C23×C22⋊D1111yescharacteristic
899C4—21no—
900C4—22no—
901C4—21no—
902C4—22no—
903C4—22no—
904C4—21no—
905C4—42no—
906C4—42no—
907C4—441no—
908C4—441no—
909C4—442no—
910C4—441no—
911C4#1062336412yes—
912C4#1062336612yes—
913C4C2×#6704211yescharacteristic
914C4C2×#6704311yescharacteristic
915C2—22no—
916C2—42no—
917C2—84no—
918C2—882no—
919C2—881no—
920C2C2×#1062336411yescharacteristic
921C2C2×#1062336611yescharacteristic
922C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3508C2
socleC22×C11C23×D4
hypercenter#3508D11
hypocenterC11#60922
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13082032C2semidirect
2. #13080051C2semidirect
3. #13080021C2semidirect
4. #13079994C2semidirect
5. #13079972C2semidirect
6. #13079936C2semidirect
7. #13079923C2semidirect
8. #13078447C2semidirect
9. #13078409C2semidirect
10. #13078398C2semidirect
11. #13078292C2semidirect
12. #13078261C2semidirect
13. #13078119C2semidirect
14. #13078092C2semidirect
15. C2×#10622685C2semidirect
16. #13077184C2semidirect
17. C11×#3508C2semidirect
24. C11×#540C22semidirect
27. C11×#532C22semidirect
28. C11×#532C22semidirect
43. #10623066C22semidirect
44. #10623065C22semidirect
47. #10623010C22semidirect
48. #10623008C22semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622700C22semidirect
56. #10622700C22semidirect
57. #10622697C22semidirect
58. #10622697C22semidirect
59. #10622688C22semidirect
60. #10622688C22semidirect
64. #10622685C22semidirect
65. #10622685C22semidirect
66. #10622679C22semidirect
67. #10622679C22semidirect
68. #10622676C22semidirect
69. #10622655C22semidirect
70. #10622654C22semidirect
71. #10622652C22semidirect
72. #10622652C22semidirect
73. #10622652C22semidirect
74. #10622651C22semidirect
75. #10622651C22semidirect
76. #10622651C22semidirect
77. #10622629C22semidirect
78. #10622629C22semidirect
79. #10622628C22semidirect
80. #10622628C22semidirect
81. #10622622C22semidirect
82. #10622622C22semidirect
83. #10622621C22semidirect
84. #10622620C22semidirect
88. #10622612C22semidirect
92. #10622537C22semidirect
94. C2×C4⋊(C11⋊C8)C22semidirect
347. #3508D11semidirect
451. #540C2×D11semidirect
460. #532C2×D11semidirect
461. #532C2×D11semidirect
807. C11#60922semidirect

Maximal subgroups

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

subgroupindex
#130820322
#130800512
#130800212
#130799942
#130799722
#130799362
#130799232
#130784472
#130784092
#130783982
#130782922
#130782612
#130781192
#130780922
C2×#106226852
#130771842
C11×#35082
#6092211