Finite Group Databasebeta

← #15638713

Subgroups — #15638713

Order 2816.

2114 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic, complemented
2#13080796C214yesmaximal, complemented
3#13080676C214yesmaximal, complemented
4#13080197C214yesmaximal, complemented
5#13080167C214yesmaximal, complemented
6#13079615C211yesmaximal, characteristic, complemented
7#13079599C211yesmaximal, characteristic, complemented
8#13079426C212yesmaximal, complemented
9#13079393C212yesmaximal, complemented
10#13078742C211yesmaximal, characteristic, complemented
11#13078734C211yesmaximal, characteristic, complemented
12#13077849C212yesmaximal, complemented
13#13077832C212yesmaximal, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C11×#3506C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C11×#559—22no—
19C11×#556C2212yescomplemented
20C11×#555C2212yescomplemented
21C11×#553—22no—
22C11×#550C2212yescomplemented
23C11×#547C2212yescomplemented
24C11×#538—21no—
25C11×#538—21no—
26C11×#535—21no—
27C11×#533C2211yescharacteristic
28C11×#532C2211yescharacteristic
29C11×#525C2212yes—
30C11×#525C2212yes—
31C11×#520—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67004C2214yescomplemented
34C2×#67003C2214yescomplemented
35C2×#66992—21no—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38#10623083—22no—
39#10623083—22no—
40#10623083C2214yes—
41#10623083C2214yes—
42C2×#66949—21no—
43C2×#66938—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47#10622852C2214yescomplemented
48#10622851C2214yescomplemented
49#10622820C2212yes—
50C2×C22⋊(C11⋊C8)C2212yes—
51#10622707C2212yescomplemented
52#10622704C2212yescomplemented
53#10622703C2212yescomplemented
54#10622702C2212yescomplemented
55#10622702C2212yescomplemented
56#10622699C2212yescomplemented
57#10622688C2212yescomplemented
58#10622687C2212yescomplemented
59#10622664C2214yescomplemented
60#10622663C2212yes—
61#10622663C2212yes—
62#10622663C2214yescomplemented
63#10622662C2214yescomplemented
64#10622660C2214yescomplemented
65#10622659C2212yes—
66#10622656C2212yes—
67#10622654C2214yescomplemented
68#10622653C2212yes—
69#10622653C2212yes—
70#10622653C2214yescomplemented
71#10622652C2214yescomplemented
72#10622650C2214yescomplemented
73#10622649C2212yes—
74#10622646C2212yes—
75#10622643C2214yescomplemented
76#10622641C2214yescomplemented
77#10622631C2214yescomplemented
78#10622629C2214yescomplemented
79#10622624C2214yescomplemented
80#10622624C2214yescomplemented
81#10622617C2214yescomplemented
82#10622616C2214yescomplemented
83#10622615C2214yescomplemented
84#10622609C2214yescomplemented
85#10622539C2211yescharacteristic
86#10622539C2211yescharacteristic
87C2×C11×#41—21no—
88C2×C11×#41C2312yes—
89C2×C11×#41C2312yes—
90C22×D4×C11D411yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C23×Dic11—21no—
96C2×#4339—22no—
97C2×#4339—44no—
98C2×#4339C2314yes—
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×Dic22—21no—
102C22×Dic22—22no—
103C22×Dic22—44no—
104C22×Dic22C2311yescharacteristic
105C22×Dic22C2314yes—
106C22×Dic22C2311yescharacteristic
107C11×C4⋊Q8C2311yescharacteristic
108C11×C4⋊Q8C2311yescharacteristic
109C11×C4⋊Q8C2311yescharacteristic
110C11×#127—22no—
111C11×#127C2311yescharacteristic
112C11×#126—22no—
113C11×#126—22no—
114C11×#125—21no—
115C11×#124—22no—
116C11×#124—22no—
117C11×#124—22no—
118C11×#124—21no—
119C11×#123—22no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8C2312yes—
125C11×C22⋊Q8C2312yes—
126C11×C22⋊Q8C2312yes—
127C11×#121—22no—
128C11×#121—22no—
129C11×#121—21no—
130C11×#121—22no—
131C11×#121—22no—
132C11×#121C2312yes—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C11×#120—22no—
136C11×#120—22no—
137C4×Q8×C11—22no—
138C4×Q8×C11—21no—
139C4×Q8×C11C2312yes—
140C4×D4×C11—22no—
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—21no—
146C4×D4×C11D412yes—
147C4×D4×C11D412yes—
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2312yes—
151C11×#117—21no—
152C11×#117—22no—
153C11×#117C2312yes—
154C11×#117C2312yes—
155C2×C11×C4⋊C4—22no—
156C2×C11×C4⋊C4D411yescharacteristic
157C2×C11×C22⋊C4D411yescharacteristic
158C2×C11×C22⋊C4D411yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C22⋊Dic11—21no—
161#67004—48no—
162#67003—48no—
163C2×#4326C2314yes—
164C2×#4326C2314yes—
165C2×#4325C2314yes—
166#66992—24no—
167#66992—24no—
168C2×#4324C2314yes—
169C2×#4324C2314yes—
170C2×#4323C2314yes—
171#66983—22no—
172#66983C2314yes—
173C2×(C2×D11)⋊C4—21no—
174C2×(C2×D11)⋊C4—21no—
175C2×(C2×D11)⋊C4—21no—
176C2×C4⋊Dic11C2311yescharacteristic
177#66977—22no—
178#66977C2314yes—
179C2×Dic11⋊C4—21no—
180C2×Dic11⋊C4—21no—
181C2×C4×Dic11—21no—
182C2×#4318C2314yes—
183C22×C11⋊C8C2314yes—
184#66949—24no—
185#66949—24no—
186#66938—24no—
187#66938—24no—
188(C22⋊D11)⋊C4—24no—
189(C22⋊D11)⋊C4—24no—
190#66928—21no—
191#66928—21no—
192#66928C2312yes—
193#66928C2312yes—
194C4×Dic22—21no—
195C4×Dic22—21no—
196C4×Dic22C2312yes—
197C4×Dic22C2312yes—
198#66899C2314yes—
199#66896C2314yes—
200C22⋊(C11⋊C8)C2312yes—
201C22⋊(C11⋊C8)C2312yes—
202C22⋊(C11⋊C8)C2314yes—
203C22⋊(C11⋊C8)C2314yes—
204#66874C2314yes—
205#66874C2314yes—
206#66874C2314yes—
207#66874C2314yes—
208#66873C2314yes—
209#66873C2314yes—
210#66872C2314yes—
211#66871C2314yes—
212C4⋊(C11⋊C8)C2312yes—
213C4⋊(C11⋊C8)C2312yes—
214#66867C2312yes—
215#66867C2312yes—
216#61578—111nomaximal, Sylow
217C24×C11C2×D411yescharacteristic
218C24×C11C2×D411yescharacteristic
219C23×D11—21no—
220C11×#41—44no—
221C11×#41—44no—
222C11×#41—44no—
223C2×Q8×C11—21no—
224C2×Q8×C11—21no—
225C2×Q8×C11C2412yes—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—42no—
234C2×D4×C11C2×D412yes—
235C2×D4×C11C2×D412yes—
236C2×D4×C11C2412yes—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
255C22×Dic11—21no—
256C22×Dic11—24no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—44no—
260#4339—28no—
261#4339—44no—
262#4339—48no—
263C2×D44—21no—
264C2×D44—42no—
265C2×D44C2412yes—
266C2×C4×D11—24no—
267C2×C4×D11—44no—
268C2×Dic22—24no—
269C2×Dic22—28no—
270C2×Dic22—21no—
271C2×Dic22—21no—
272C2×Dic22—24no—
273C2×Dic22—44no—
274C2×Dic22—42no—
275C2×Dic22—48no—
276C2×Dic22—44no—
277C2×Dic22C2412yes—
278C2×Dic22C2412yes—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4C2×D412yes—
288C11×C4⋊C4C2×D412yes—
289C11×C4⋊C4C2412yes—
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4C2×D412yes—
301C11×C22⋊C4C2×D412yes—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C42×C11—22no—
305C42×C11—22no—
306C42×C11—22no—
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2411yescharacteristic
310C42×C11C2411yescharacteristic
311C22⋊Dic11—24no—
312#4326—28no—
313#4326—44no—
314#4325—44no—
315#4324—28no—
316#4324—44no—
317#4323—44no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—24no—
323C4⋊Dic11—21no—
324C4⋊Dic11C2412yes—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—24no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330#4318—44no—
331C2×C11⋊C8—44no—
332C2×C11⋊C8C2414yes—
333C2×C11⋊C8C2414yes—
334#3506D1111yescharacteristic, complemented
335C2×#548—111no—
336#3321—114no—
337#3313—114no—
338#3271—114no—
339#3269—114no—
340#3215—111no—
341#3213—111no—
342#3194—112no—
343#3190—112no—
344#3113—111no—
345#3112—111no—
346#3004—112no—
347#3002—112no—
348#2973—111no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11C22×D412yes—
357C23×C11C22×D412yes—
358C23×C11C22×D411yescharacteristic
359C22×D11—22no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—42no—
363Q8×C11—24no—
364Q8×C11—42no—
365Q8×C11—81no—
366D4×C11—24no—
367D4×C11—42no—
368D4×C11—42no—
369D4×C11—42no—
370D4×C11—44no—
371D4×C11—81no—
372D4×C11—82no—
373D4×C11—82no—
374D4×C11—82no—
375D4×C11—82no—
376C2×C4×C11—22no—
377C2×C4×C11—24no—
378C2×C4×C11—24no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—42no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—42no—
387C2×C4×C11—41no—
388C2×C4×C11—44no—
389C2×C4×C11—82no—
390C2×C4×C11—82no—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D412yes—
398C2×C4×C11C2511yescharacteristic
399C22⋊D11—48no—
400C22⋊D11—48no—
401C2×Dic11—24no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—48no—
406C2×Dic11—42no—
407C2×Dic11—42no—
408D44—24no—
409D44—42no—
410C4×D11—48no—
411Dic22—24no—
412Dic22—22no—
413Dic22—24no—
414Dic22—48no—
415Dic22—42no—
416Dic22H(5,𝔽2)14yes—
417C11⋊C8—24no—
418C11⋊C8—24no—
419C22×#41—111no—
420C23×Q8—111no—
421C2×#137—114no—
422C2×#135—114no—
423#559—22no—
424#556C2×D1112yescomplemented
425#555C2×D1112yescomplemented
426#553—22no—
427#550C2×D1112yescomplemented
428#548—114no—
429#548—114no—
430#548—222no—
431#548—222no—
432#547C2×D1112yescomplemented
433#538—21no—
434#538—21no—
435#535—21no—
436#533C2×D1111yescharacteristic
437#532C2×D1111yescharacteristic
438C2×#124—111no—
439C2×#124—221no—
440#525C2×D1112yes—
441#525C2×D1112yes—
442C2×C22⋊Q8—111no—
443C2×C22⋊Q8—221no—
444C2×#121—111no—
445C2×#121—221no—
446#520—21no—
447C2×C4×Q8—111no—
448C2×C4×D4—221no—
449C2×C4×D4C2×D1111yescharacteristic
450#497—112no—
451#496—112no—
452#489—112no—
453#489—112no—
454#485—114no—
455#483—112no—
456#482—114no—
457#480—112no—
458#477—112no—
459#475—112no—
460#469—114no—
461#468—114no—
462#467—114no—
463#465—114no—
464#464—114no—
465#463—114no—
466#462—112no—
467#460—112no—
468#452—114no—
469#452—114no—
470#451—112no—
471#451—112no—
472#451—114no—
473#450—112no—
474#449—114no—
475#449—114no—
476#448—112no—
477#448—112no—
478#448—114no—
479#447—112no—
480#441—114no—
481#440—114no—
482#435—114no—
483#435—114no—
484#432—111no—
485#432—111no—
486#419—114no—
487#416—114no—
488#407—112no—
489C2×C22⋊C8—112no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—22no—
498C22×C11—44no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—82no—
503C22×C11#57512yes—
504C22×C11C23×D411yescharacteristic
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—84no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—22no—
513C4×C11—22no—
514C4×C11—21no—
515C4×C11—21no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11C2×H(5,𝔽2)12yes—
520Dic11—24no—
521Dic11—42no—
522Dic11—42no—
523C2×#41—21no—
524C2×#41—114no—
525C2×#41—222no—
526C2×#41—444no—
527C2×#41C22×D1112yes—
528C2×#41C22×D1112yes—
529C22×Q8—111no—
530C22×Q8—114no—
531C22×Q8—111no—
532C22×Q8—221no—
533C22×Q8—222no—
534C22×Q8—444no—
535C22×D4—111no—
536C22×D4—221no—
537C22×D4—221no—
538C22×D4C22⋊D1111yescharacteristic
539C23×C4—221no—
540C23×C4—221no—
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543#137—448no—
544#135—448no—
545C2×Q16—114no—
546C2×Q16—114no—
547C2×SD16—114no—
548C2×SD16—114no—
549C2×SD16—114no—
550C2×D8—114no—
551C2×M16—114no—
552C22×C8—114no—
553C4⋊Q8C22×D1111yescharacteristic
554C4⋊Q8C22×D1111yescharacteristic
555C4⋊Q8C22×D1111yescharacteristic
556#127—22no—
557#127C22×D1111yescharacteristic
558#126—22no—
559#126—22no—
560#125—21no—
561#124—22no—
562#124—22no—
563#124—22no—
564#124—21no—
565#124—112no—
566#124—112no—
567#124—224no—
568#124—224no—
569#124—221no—
570#124—221no—
571#123—22no—
572#123—22no—
573#123—22no—
574#123—22no—
575C22⋊Q8—21no—
576C22⋊Q8—114no—
577C22⋊Q8—222no—
578C22⋊Q8—224no—
579C22⋊Q8—224no—
580C22⋊Q8C22×D1112yes—
581C22⋊Q8C22×D1112yes—
582C22⋊Q8C22×D1112yes—
583#121—22no—
584#121—22no—
585#121—21no—
586#121—22no—
587#121—22no—
588#121—114no—
589#121—224no—
590#121—224no—
591#121—222no—
592#121C22×D1112yes—
593#121C22×D1112yes—
594#121C22×D1112yes—
595#120—22no—
596#120—22no—
597C4×Q8—22no—
598C4×Q8—21no—
599C4×Q8—112no—
600C4×Q8—112no—
601C4×Q8—221no—
602C4×Q8—221no—
603C4×Q8C22×D1112yes—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—21no—
610C4×D4—224no—
611C4×D4—224no—
612C4×D4C22⋊D1112yes—
613C4×D4C22⋊D1112yes—
614C4×D4C22×D1112yes—
615C4×D4C22×D1112yes—
616C4×D4C22×D1112yes—
617#117—21no—
618#117—22no—
619#117C22×D1112yes—
620#117C22×D1112yes—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—221no—
624C2×C4⋊C4—221no—
625C2×C4⋊C4C22⋊D1111yescharacteristic
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4C22⋊D1111yescharacteristic
631C2×C22⋊C4C22⋊D1111yescharacteristic
632C2×C42—221no—
633C2×C42C22×D1111yescharacteristic
634#107—114no—
635#106—114no—
636C4⋊C8—112no—
637C4⋊C8—112no—
638#103—114no—
639#103—114no—
640#103—114no—
641#103—114no—
642#103—114no—
643#102—114no—
644#102—114no—
645#102—114no—
646C22⋊C8—112no—
647C22⋊C8—112no—
648C22⋊C8—114no—
649C22⋊C8—114no—
650#97—112no—
651#97—112no—
652C2×C11—22no—
653C2×C11—42no—
654C2×C11—42no—
655C2×C11—82no—
656C2×C11#348411yescharacteristic
657C2×C11C2×#57511yescharacteristic
658C2×C11#358611yescharacteristic
659D11—82no—
660C24—221no—
661C24C2×C22⋊D1111yescharacteristic
662C24C2×C22⋊D1111yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—228no—
667#41—444no—
668#41—448no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—112no—
672C2×Q8—112no—
673C2×Q8—224no—
674C2×Q8—228no—
675C2×Q8—221no—
676C2×Q8—224no—
677C2×Q8—221no—
678C2×Q8—444no—
679C2×Q8—442no—
680C2×Q8—444no—
681C2×Q8—448no—
682C2×Q8C23×D1112yes—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—42no—
691C2×D4—112no—
692C2×D4—224no—
693C2×D4—224no—
694C2×D4—221no—
695C2×D4—442no—
696C2×D4—444no—
697C2×D4—444no—
698C2×D4C2×C22⋊D1112yes—
699C2×D4C2×C22⋊D1112yes—
700C2×D4C23×D1112yes—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—224no—
710C22×C4—224no—
711C22×C4—444no—
712C22×C4—444no—
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1112yes—
718C22×C4C2×C22⋊D1112yes—
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722Q16—228no—
723Q16—444no—
724SD16—228no—
725SD16—444no—
726SD16—444no—
727D8—444no—
728M16—444no—
729C2×C8—114no—
730C2×C8—114no—
731C2×C8—444no—
732C4⋊C4—21no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—22no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—22no—
740C4⋊C4—112no—
741C4⋊C4—221no—
742C4⋊C4—224no—
743C4⋊C4—222no—
744C4⋊C4—222no—
745C4⋊C4C2×C22⋊D1112yes—
746C4⋊C4C2×C22⋊D1112yes—
747C4⋊C4C23×D1112yes—
748C4⋊C4C23×D1112yes—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—224no—
759C22⋊C4—222no—
760C22⋊C4—222no—
761C22⋊C4—224no—
762C22⋊C4—222no—
763C22⋊C4—222no—
764C22⋊C4C2×C22⋊D1112yes—
765C22⋊C4C2×C22⋊D1112yes—
766C22⋊C4C2×C22⋊D1112yes—
767C22⋊C4C2×C22⋊D1112yes—
768C42—22no—
769C42—22no—
770C42—22no—
771C42—222no—
772C42—222no—
773C42C2×C22⋊D1111yescharacteristic
774C42C2×C22⋊D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C42C23×D1111yescharacteristic
777C11#6157811yescharacteristic, complemented, Sylow
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—222no—
786C23—442no—
787C23—442no—
788C23—442no—
789C23C22×C22⋊D1112yes—
790C23C22×C22⋊D1112yes—
791C23C22×C22⋊D1111yescharacteristic
792Q8—24no—
793Q8—42no—
794Q8—81no—
795Q8—114no—
796Q8—224no—
797Q8—222no—
798Q8—224no—
799Q8—448no—
800Q8—442no—
801D4—24no—
802D4—42no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—81no—
807D4—82no—
808D4—82no—
809D4—82no—
810D4—82no—
811D4—224no—
812D4—442no—
813D4—448no—
814D4—448no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—44no—
828C2×C4—82no—
829C2×C4—82no—
830C2×C4—224no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—448no—
835C2×C4—448no—
836C2×C4—442no—
837C2×C4—442no—
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1112yes—
840C2×C4C22×C22⋊D1112yes—
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C24×D1111yescharacteristic
846C8—224no—
847C8—224no—
848C22—21no—
849C22—21no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—44no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—82no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—884no—
865C22#1062335312yes—
866C22C23×C22⋊D1111yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—22no—
871C4—22no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—224no—
878C4—442no—
879C4—442no—
880C4D11×H(5,𝔽2)12yes—
881C2—22no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—882no—
886C2#1308224711yescharacteristic
887C2C2×#1062335311yescharacteristic
888C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3506C2
socleC22×C11C23×D4
hypercenter#3506D11
hypocenterC11#61578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. C2×#10623083C2semidirect
2. #13080796C2semidirect
3. #13080676C2semidirect
4. #13080197C2semidirect
5. #13080167C2semidirect
6. #13079615C2semidirect
7. #13079599C2semidirect
8. #13079426C2semidirect
9. #13079393C2semidirect
10. #13078742C2semidirect
11. #13078734C2semidirect
12. #13077849C2semidirect
13. #13077832C2semidirect
14. #13077645C2semidirect
15. C11×#3506C2semidirect
19. C11×#556C22semidirect
20. C11×#555C22semidirect
22. C11×#550C22semidirect
23. C11×#547C22semidirect
33. C2×#67004C22semidirect
34. C2×#67003C22semidirect
47. #10622852C22semidirect
48. #10622851C22semidirect
51. #10622707C22semidirect
52. #10622704C22semidirect
53. #10622703C22semidirect
54. #10622702C22semidirect
55. #10622702C22semidirect
56. #10622699C22semidirect
57. #10622688C22semidirect
58. #10622687C22semidirect
59. #10622664C22semidirect
62. #10622663C22semidirect
63. #10622662C22semidirect
64. #10622660C22semidirect
67. #10622654C22semidirect
70. #10622653C22semidirect
71. #10622652C22semidirect
72. #10622650C22semidirect
75. #10622643C22semidirect
76. #10622641C22semidirect
77. #10622631C22semidirect
78. #10622629C22semidirect
79. #10622624C22semidirect
80. #10622624C22semidirect
81. #10622617C22semidirect
82. #10622616C22semidirect
83. #10622615C22semidirect
84. #10622609C22semidirect
334. #3506D11semidirect
424. #556C2×D11semidirect
425. #555C2×D11semidirect
427. #550C2×D11semidirect
432. #547C2×D11semidirect
777. C11#61578semidirect

Maximal subgroups

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

subgroupindex
C2×#106230832
#130807962
#130806762
#130801972
#130801672
#130796152
#130795992
#130794262
#130793932
#130787422
#130787342
#130778492
#130778322
#130776452
C11×#35062
#6157811