Finite Group Databasebeta

← #15624548

Subgroups — #15624548

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2C2×#10623322C211yesmaximal, characteristic, complemented
3#13079458C214yesmaximal, complemented
4#13079448C212yesmaximal, complemented
5#13079432C212yesmaximal, complemented
6#13079409C214yesmaximal, complemented
7#13079399C212yesmaximal, complemented
8#13079383C212yesmaximal, complemented
9#13078565C211yesmaximal, characteristic, complemented
10#13078557C211yesmaximal, characteristic, complemented
11#13078549C212yesmaximal, complemented
12#13078246C212yesmaximal, complemented
13#13078235C212yesmaximal, complemented
14#13077878C211yesmaximal, characteristic, complemented
15#13077870C211yesmaximal, characteristic, complemented
16#13077861C212yesmaximal, complemented
17C2×C11×#407C211yesmaximal, characteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×#4339C2211yescharacteristic, complemented
21C22×C11×M16C2212yescomplemented
22C2×#67006—21no—
23C2×#67006—21no—
24#10623322—21no—
25#10623322—21no—
26#10623322—21no—
27#10623322—21no—
28#10623322—21no—
29#10623322—21no—
30#10623322—21no—
31#10623322—21no—
32#10623322C2212yes—
33#10623322C2212yes—
34#10623322C2212yes—
35#10623322C2212yes—
36#10623322C2212yescomplemented
37#10623322C2212yescomplemented
38#10623322C2212yescomplemented
39#10623322C2212yescomplemented
40C2×#66983C2211yescharacteristic
41C2×#66983C2211yescharacteristic, complemented
42C2×#66983C2211yescharacteristic, complemented
43C2×#66983C2211yescharacteristic, complemented
44C2×#66982—21no—
45C2×#66982—21no—
46C2×C4×C22⋊D11—21no—
47C2×C4×C22⋊D11—21no—
48C2×C4×C22⋊D11—21no—
49C2×C4×C22⋊D11—21no—
50C2×#66979C2211yescharacteristic
51C2×#66979C2211yescharacteristic, complemented
52C2×#66977C2211yescharacteristic
53C2×#66977C2211yescharacteristic, complemented
54C2×#66977C2211yescharacteristic, complemented
55C2×#66977C2211yescharacteristic, complemented
56C2×#66962C2212yescomplemented
57C2×#66961C2212yescomplemented
58C11×#407C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C11×#407C2212yescomplemented
61C11×#407C2212yescomplemented
62C11×#407C2212yescomplemented
63C2×C11×C22⋊C8C2212yescomplemented
64C2×C11×C22⋊C8C2212yescomplemented
65#10622750C2214yescomplemented
66#10622748C2214yescomplemented
67#10622747C2214yescomplemented
68#10622747C2214yescomplemented
69#10622746C2212yescomplemented
70#10622746C2212yescomplemented
71#10622744C2212yescomplemented
72#10622734C2212yescomplemented
73#10622734C2212yescomplemented
74#10622733C2212yescomplemented
75#10622729C2214yescomplemented
76#10622728C2214yescomplemented
77#10622727C2214yescomplemented
78#10622727C2214yescomplemented
79#10622352C2212yescomplemented
80#10622351C2212yescomplemented
81#10622350C2214yescomplemented
82#10622350C2214yescomplemented
83#10622350C2214yescomplemented
84#10622349C2212yescomplemented
85#10622348C2212yescomplemented
86#10622347C2214yescomplemented
87#10622347C2214yescomplemented
88#10622347C2214yescomplemented
89#10622346C2214yescomplemented
90#10622346C2214yescomplemented
91#10622346C2214yescomplemented
92#10622345C2212yescomplemented
93#10622344C2212yescomplemented
94#10622336C2214yescomplemented
95#10622336C2214yescomplemented
96#10622336C2214yescomplemented
97#10622335C2212yescomplemented
98#10622334C2212yescomplemented
99C25×C11D411yescharacteristic
100C23×C4×C11—44no—
101C23×C4×C11D411yescharacteristic
102C23×C4×C11D411yescharacteristic
103C23×C4×C11D411yescharacteristic
104C23×C4×C11D411yescharacteristic
105C23×C4×C11D411yescharacteristic
106C23×C4×C11D411yescharacteristic
107C23×C4×C11D411yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2311yescharacteristic
115C22×C22⋊D11—21no—
116C22×C22⋊D11—21no—
117C22×C22⋊D11—21no—
118C22×C22⋊D11—21no—
119C22×C22⋊D11—21no—
120C22×C22⋊D11—21no—
121C2×#4339—21no—
122C2×#4339—21no—
123C2×#4339—21no—
124C2×#4339—21no—
125C2×#4339—44no—
126C2×#4339—44no—
127C2×#4339C2312yes—
128C2×#4339C2312yes—
129C2×#4339C2312yes—
130C2×#4339C2312yes—
131C22×D44C2311yescharacteristic
132C22×D44C2311yescharacteristic
133C22×C4×D11—21no—
134C22×C4×D11—21no—
135C22×Dic22C2311yescharacteristic
136C22×Dic22C2311yescharacteristic
137C2×C11×M16—44no—
138C2×C11×M16C2312yes—
139C2×C11×M16C2312yes—
140C2×C11×M16C2314yes—
141C22×C8×C11C2314yes—
142#67006—22no—
143#67006—22no—
144#67006—22no—
145#67006—22no—
146#67006—22no—
147#67006—22no—
148#67006—22no—
149#67006—22no—
150C2×C22⋊Dic11—21no—
151C2×C22⋊Dic11—21no—
152C2×C22⋊Dic11—21no—
153C2×C22⋊Dic11—21no—
154C2×C22⋊Dic11—21no—
155C2×C22⋊Dic11—21no—
156#66983—21no—
157#66983—21no—
158#66983—21no—
159#66983—21no—
160#66983—21no—
161#66983—21no—
162#66983—21no—
163#66983—21no—
164#66983C2312yes—
165#66983C2312yes—
166#66983C2312yes—
167#66983C2312yes—
168#66983C2312yes—
169#66983C2312yes—
170#66983C2312yes—
171#66983C2312yes—
172#66982—22no—
173#66982—22no—
174#66982—22no—
175#66982—22no—
176#66982—22no—
177#66982—22no—
178#66982—22no—
179#66982—22no—
180C4×C22⋊D11—22no—
181C4×C22⋊D11—22no—
182C4×C22⋊D11—22no—
183C4×C22⋊D11—22no—
184C4×C22⋊D11—22no—
185C4×C22⋊D11—22no—
186C4×C22⋊D11—22no—
187C4×C22⋊D11—22no—
188C4×C22⋊D11—22no—
189C4×C22⋊D11—22no—
190C4×C22⋊D11—22no—
191C4×C22⋊D11—22no—
192C4×C22⋊D11—22no—
193C4×C22⋊D11—22no—
194C4×C22⋊D11—22no—
195C4×C22⋊D11—22no—
196C2×(C2×D11)⋊C4—21no—
197C2×(C2×D11)⋊C4—21no—
198C2×(C2×D11)⋊C4—21no—
199C2×(C2×D11)⋊C4—21no—
200#66979—21no—
201#66979—21no—
202#66979—21no—
203#66979—21no—
204#66979C2312yes—
205#66979C2312yes—
206#66979C2312yes—
207#66979C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212#66977—21no—
213#66977—21no—
214#66977—21no—
215#66977—21no—
216#66977—21no—
217#66977—21no—
218#66977—21no—
219#66977—21no—
220#66977C2312yes—
221#66977C2312yes—
222#66977C2312yes—
223#66977C2312yes—
224#66977C2312yes—
225#66977C2312yes—
226#66977C2312yes—
227#66977C2312yes—
228C2×Dic11⋊C4—21no—
229C2×Dic11⋊C4—21no—
230C2×Dic11⋊C4—21no—
231C2×Dic11⋊C4—21no—
232C2×C4×Dic11—21no—
233C2×C4×Dic11—21no—
234#66962—44no—
235#66961—44no—
236C2×Dic44C2314yescomplemented
237C2×D88C2314yescomplemented
238C2×#4314C2314yescomplemented
239C2×#4314C2314yescomplemented
240C11×C22⋊C8C2312yes—
241C11×C22⋊C8C2312yes—
242C11×C22⋊C8C2314yes—
243C11×C22⋊C8C2314yes—
244C11×C22⋊C8C2312yes—
245C11×C22⋊C8C2312yes—
246#66885C2314yescomplemented
247#66885C2314yescomplemented
248#66885C2314yescomplemented
249#66885C2314yescomplemented
250#66882C2314yescomplemented
251#66882C2314yescomplemented
252#66881C2314yescomplemented
253#66881C2314yescomplemented
254#66880C2314yescomplemented
255#66880C2314yescomplemented
256#66880C2314yescomplemented
257#66880C2314yescomplemented
258#60752—111nomaximal, Sylow
259C24×C11—42no—
260C24×C11—42no—
261C24×C11—42no—
262C24×C11C2×D411yescharacteristic
263C24×C11C2×D411yescharacteristic
264C24×C11C2×D411yescharacteristic
265C24×C11C2×D411yescharacteristic
266C24×C11C2×D411yescharacteristic
267C24×C11C2×D411yescharacteristic
268C24×C11C2×D411yescharacteristic
269C23×D11—21no—
270C23×D11—21no—
271C22×C4×C11—24no—
272C22×C4×C11—24no—
273C22×C4×C11—24no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2×D411yescharacteristic
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2×D411yescharacteristic
305C22×C4×C11C2×D411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—22no—
322C2×C22⋊D11—22no—
323C2×C22⋊D11—22no—
324C2×C22⋊D11—22no—
325C2×C22⋊D11—44no—
326C2×C22⋊D11—44no—
327C2×C22⋊D11—44no—
328C2×C22⋊D11—44no—
329C2×C22⋊D11—44no—
330C2×C22⋊D11—44no—
331C22×Dic11—21no—
332C22×Dic11—21no—
333C22×Dic11—21no—
334C22×Dic11—21no—
335C22×Dic11—21no—
336C22×Dic11—21no—
337#4339—24no—
338#4339—24no—
339#4339—42no—
340#4339—44no—
341#4339—44no—
342#4339—42no—
343#4339—44no—
344#4339—44no—
345#4339—44no—
346#4339—44no—
347C2×D44—21no—
348C2×D44—21no—
349C2×D44—24no—
350C2×D44—42no—
351C2×D44C2412yes—
352C2×D44C2412yes—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—22no—
356C2×C4×D11—22no—
357C2×C4×D11—44no—
358C2×C4×D11—44no—
359C2×Dic22—21no—
360C2×Dic22—21no—
361C2×Dic22—24no—
362C2×Dic22—42no—
363C2×Dic22C2412yes—
364C2×Dic22C2412yes—
365C11×M16—24no—
366C11×M16—24no—
367C11×M16—44no—
368C2×C8×C11—44no—
369C2×C8×C11C2414yes—
370C2×C8×C11C2414yes—
371C22⋊Dic11—22no—
372C22⋊Dic11—22no—
373C22⋊Dic11—22no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—22no—
377C22⋊Dic11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—22no—
380C22⋊Dic11—22no—
381C22⋊Dic11—22no—
382C22⋊Dic11—22no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—22no—
391C4⋊Dic11—21no—
392C4⋊Dic11—21no—
393C4⋊Dic11—21no—
394C4⋊Dic11—21no—
395C4⋊Dic11C2412yes—
396C4⋊Dic11C2412yes—
397C4⋊Dic11C2412yes—
398C4⋊Dic11C2412yes—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407C4×Dic11—22no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411Dic44—44no—
412D88—44no—
413#4314—44no—
414#4314—44no—
415C2×#525—111no—
416C2×#525—111no—
417#3197—114no—
418#3196—112no—
419#3194—112no—
420#3191—114no—
421#3190—112no—
422#3188—112no—
423#3095—111no—
424#3094—111no—
425#3093—112no—
426#3056—112no—
427#3055—112no—
428#3007—111no—
429#3006—111no—
430#3005—112no—
431C2×#407D1111yescharacteristic, complemented
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—416no—
454C23×C11C22×D411yescharacteristic
455C23×C11C22×D411yescharacteristic
456C23×C11C22×D411yescharacteristic
457C23×C11C22×D411yescharacteristic
458C23×C11C22×D411yescharacteristic
459C23×C11C22×D411yescharacteristic
460C23×C11C22×D411yescharacteristic
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—42no—
464C22×D11—42no—
465C22×D11—42no—
466C22×D11—42no—
467C22×D11—42no—
468C22×D11—42no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11C22×D411yescharacteristic
497C2×C4×C11C22×D411yescharacteristic
498C2×C4×C11C22×D411yescharacteristic
499C2×C4×C11C22×D411yescharacteristic
500C2×C4×C11C22×D411yescharacteristic
501C2×C4×C11C22×D411yescharacteristic
502C2×C4×C11C22×D411yescharacteristic
503C2×C4×C11H(5,𝔽2)14yes—
504C2×C4×C11C2511yescharacteristic
505C22⋊D11—44no—
506C22⋊D11—44no—
507C22⋊D11—44no—
508C22⋊D11—44no—
509C22⋊D11—44no—
510C22⋊D11—44no—
511C22⋊D11—44no—
512C22⋊D11—44no—
513C22⋊D11—44no—
514C22⋊D11—44no—
515C22⋊D11—44no—
516C22⋊D11—44no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—42no—
524C2×Dic11—42no—
525C2×Dic11—42no—
526C2×Dic11—42no—
527C2×Dic11—42no—
528C2×Dic11—42no—
529D44—22no—
530D44—24no—
531D44—22no—
532D44—42no—
533D44—42no—
534C4×D11—44no—
535C4×D11—44no—
536C4×D11—44no—
537C4×D11—44no—
538Dic22—22no—
539Dic22—24no—
540Dic22—22no—
541Dic22—42no—
542Dic22—42no—
543C8×C11—24no—
544C8×C11—24no—
545C22×#41—111no—
546C22×#41—111no—
547C24×C4C2×D1111yescharacteristic
548C2×#137—112no—
549C2×AGL(1,ℤ/8)—112no—
550C22×M16C2×D1112yescomplemented
551#525—112no—
552#525—112no—
553#525—112no—
554#525—112no—
555#525—112no—
556#525—112no—
557#525—112no—
558#525—112no—
559#525—221no—
560#525—221no—
561#525—221no—
562#525—221no—
563#525—221no—
564#525—221no—
565#525—221no—
566#525—221no—
567C2×#123—221no—
568C2×#123—221no—
569C2×C22⋊Q8—111no—
570C2×C22⋊Q8—111no—
571C2×C22⋊Q8—111no—
572C2×C22⋊Q8—111no—
573C2×#121—111no—
574C2×#121—111no—
575C2×#121—111no—
576C2×#121—111no—
577C2×#120—221no—
578C2×#120—221no—
579C2×C4×D4—221no—
580C2×C4×D4—221no—
581C2×C4×D4—221no—
582C2×C4×D4—221no—
583C2×#117—111no—
584C2×#117—111no—
585#485—114no—
586#485—114no—
587#485—114no—
588#484—112no—
589#483—112no—
590#482—114no—
591#482—114no—
592#482—114no—
593#481—112no—
594#480—112no—
595#470—114no—
596#469—114no—
597#468—114no—
598#468—114no—
599#467—114no—
600#466—114no—
601#465—114no—
602#465—114no—
603#452—114no—
604#452—114no—
605#452—114no—
606#451—112no—
607#450—112no—
608#449—114no—
609#449—114no—
610#449—114no—
611#448—112no—
612#447—112no—
613#428—112no—
614#428—112no—
615#419—112no—
616#418—112no—
617#417—112no—
618#417—112no—
619#407C2×D1111yescharacteristic
620#407C2×D1111yescharacteristic
621#407C2×D1112yescomplemented
622#407C2×D1112yescomplemented
623#407C2×D1112yescomplemented
624C2×C22⋊C8C2×D1112yescomplemented
625C2×C22⋊C8C2×D1112yescomplemented
626C22×C11—21no—
627C22×C11—21no—
628C22×C11—21no—
629C22×C11—21no—
630C22×C11—21no—
631C22×C11—21no—
632C22×C11—21no—
633C22×C11—21no—
634C22×C11—21no—
635C22×C11—21no—
636C22×C11—21no—
637C22×C11—21no—
638C22×C11—21no—
639C22×C11—21no—
640C22×C11—21no—
641C22×C11—21no—
642C22×C11—21no—
643C22×C11—21no—
644C22×C11—44no—
645C22×C11—44no—
646C22×C11—44no—
647C22×C11—44no—
648C22×C11—44no—
649C22×C11—44no—
650C22×C11—44no—
651C22×C11#53412yes—
652C22×C11#57512yes—
653C22×C11#57512yes—
654C22×C11C23×D411yescharacteristic
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—84no—
662C2×D11—84no—
663C4×C11—21no—
664C4×C11—21no—
665C4×C11—21no—
666C4×C11—21no—
667C4×C11—21no—
668C4×C11—21no—
669C4×C11#53412yes—
670C4×C11C2×H(5,𝔽2)12yes—
671Dic11—42no—
672Dic11—42no—
673Dic11—42no—
674Dic11—42no—
675Dic11—42no—
676Dic11—42no—
677C25D4411yescharacteristic
678C2×#41—112no—
679C2×#41—112no—
680C2×#41—112no—
681C2×#41—112no—
682C2×#41—221no—
683C2×#41—221no—
684C2×#41—221no—
685C2×#41—221no—
686C2×#41—444no—
687C2×#41—444no—
688C22×Q8—111no—
689C22×Q8—111no—
690C22×D4—111no—
691C22×D4—111no—
692C22×D4—221no—
693C22×D4—221no—
694C22×D4—221no—
695C22×D4—221no—
696C22×D4—221no—
697C22×D4—221no—
698C23×C4—44no—
699C23×C4—221no—
700C23×C4—221no—
701C23×C4D4411yescharacteristic
702C23×C4D4411yescharacteristic
703C23×C4D4411yescharacteristic
704C23×C4D4411yescharacteristic
705C23×C4D4411yescharacteristic
706C23×C4D4411yescharacteristic
707C23×C4D4411yescharacteristic
708C23×C4C22×D1111yescharacteristic
709C23×C4C22×D1111yescharacteristic
710C23×C4C22×D1111yescharacteristic
711C23×C4C22×D1111yescharacteristic
712C23×C4C22×D1111yescharacteristic
713C23×C4C22×D1111yescharacteristic
714C23×C4C22×D1111yescharacteristic
715#137—444no—
716AGL(1,ℤ/8)—444no—
717C2×Q16—114no—
718C2×SD16—114no—
719C2×SD16—114no—
720C2×D8—114no—
721C2×M16—44no—
722C2×M16C22×D1112yes—
723C2×M16C22×D1112yes—
724C2×M16C22×D1114yes—
725C22×C8C22×D1114yes—
726#123—222no—
727#123—222no—
728#123—222no—
729#123—222no—
730#123—222no—
731#123—222no—
732#123—222no—
733#123—222no—
734C22⋊Q8—112no—
735C22⋊Q8—112no—
736C22⋊Q8—112no—
737C22⋊Q8—112no—
738C22⋊Q8—112no—
739C22⋊Q8—112no—
740C22⋊Q8—112no—
741C22⋊Q8—112no—
742C22⋊Q8—221no—
743C22⋊Q8—221no—
744C22⋊Q8—221no—
745C22⋊Q8—221no—
746C22⋊Q8—221no—
747C22⋊Q8—221no—
748C22⋊Q8—221no—
749C22⋊Q8—221no—
750#121—112no—
751#121—112no—
752#121—112no—
753#121—112no—
754#121—112no—
755#121—112no—
756#121—112no—
757#121—112no—
758#121—221no—
759#121—221no—
760#121—221no—
761#121—221no—
762#121—221no—
763#121—221no—
764#121—221no—
765#121—221no—
766#120—222no—
767#120—222no—
768#120—222no—
769#120—222no—
770#120—222no—
771#120—222no—
772#120—222no—
773#120—222no—
774C4×D4—222no—
775C4×D4—222no—
776C4×D4—222no—
777C4×D4—222no—
778C4×D4—222no—
779C4×D4—222no—
780C4×D4—222no—
781C4×D4—222no—
782C4×D4—222no—
783C4×D4—222no—
784C4×D4—222no—
785C4×D4—222no—
786C4×D4—222no—
787C4×D4—222no—
788C4×D4—222no—
789C4×D4—222no—
790#117—112no—
791#117—112no—
792#117—112no—
793#117—112no—
794#117—221no—
795#117—221no—
796#117—221no—
797#117—221no—
798C2×C4⋊C4—111no—
799C2×C4⋊C4—111no—
800C2×C4⋊C4—111no—
801C2×C4⋊C4—111no—
802C2×C4⋊C4—221no—
803C2×C4⋊C4—221no—
804C2×C4⋊C4—221no—
805C2×C4⋊C4—221no—
806C2×C22⋊C4—221no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C22⋊C4—221no—
810C2×C22⋊C4—221no—
811C2×C22⋊C4—221no—
812C2×C22⋊C4—221no—
813C2×C22⋊C4—221no—
814C2×C22⋊C4—221no—
815C2×C22⋊C4—221no—
816C2×C42—221no—
817C2×C42—221no—
818#107—114no—
819#107—114no—
820#106—114no—
821#106—114no—
822#103—114no—
823#103—114no—
824#103—114no—
825#103—114no—
826#102—114no—
827#102—114no—
828#102—114no—
829#102—114no—
830C22⋊C8C22×D1112yes—
831C22⋊C8C22×D1112yes—
832C22⋊C8C22×D1112yes—
833C22⋊C8C22×D1112yes—
834C22⋊C8C22×D1114yes—
835C22⋊C8C22×D1114yes—
836C2×C11—22no—
837C2×C11—22no—
838C2×C11—22no—
839C2×C11—41no—
840C2×C11—41no—
841C2×C11—41no—
842C2×C11—41no—
843C2×C11C2×#53411yescharacteristic
844C2×C11C2×#57511yescharacteristic
845C2×C11C2×#57511yescharacteristic
846D11—82no—
847D11—82no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—221no—
852C24—221no—
853C24C2×D4411yescharacteristic
854C24C2×D4411yescharacteristic
855C24C2×D4411yescharacteristic
856C24C2×D4411yescharacteristic
857C24C2×D4411yescharacteristic
858C24C2×D4411yescharacteristic
859C24C2×D4411yescharacteristic
860#41—224no—
861#41—224no—
862#41—442no—
863#41—444no—
864#41—444no—
865#41—442no—
866#41—444no—
867#41—444no—
868#41—444no—
869#41—444no—
870C2×Q8—112no—
871C2×Q8—112no—
872C2×Q8—221no—
873C2×Q8—221no—
874C2×Q8—224no—
875C2×Q8—442no—
876C2×D4—112no—
877C2×D4—112no—
878C2×D4—222no—
879C2×D4—222no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—222no—
887C2×D4—222no—
888C2×D4—222no—
889C2×D4—222no—
890C2×D4—221no—
891C2×D4—221no—
892C2×D4—224no—
893C2×D4—442no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—221no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4C2×D4411yescharacteristic
927C22×C4C2×D4411yescharacteristic
928C22×C4C2×D4411yescharacteristic
929C22×C4C2×D4411yescharacteristic
930C22×C4C2×D4411yescharacteristic
931C22×C4C2×D4411yescharacteristic
932C22×C4C2×D4411yescharacteristic
933C22×C4C2×D4411yescharacteristic
934C22×C4C2×D4411yescharacteristic
935C22×C4C2×D4411yescharacteristic
936C22×C4C2×D4411yescharacteristic
937C22×C4C2×D4411yescharacteristic
938C22×C4C2×D4411yescharacteristic
939C22×C4C2×D4411yescharacteristic
940C22×C4C2×D4411yescharacteristic
941C22×C4C2×D4411yescharacteristic
942C22×C4C2×D4411yescharacteristic
943C22×C4C2×D4411yescharacteristic
944C22×C4C2×D4411yescharacteristic
945C22×C4C2×D4411yescharacteristic
946C22×C4C2×D4411yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1111yescharacteristic
949C22×C4C23×D1111yescharacteristic
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954Q16—444no—
955SD16—444no—
956SD16—444no—
957D8—444no—
958M16—24no—
959M16—24no—
960M16—44no—
961C2×C8—44no—
962C2×C8C23×D1114yes—
963C2×C8C23×D1114yes—
964C4⋊C4—112no—
965C4⋊C4—112no—
966C4⋊C4—112no—
967C4⋊C4—112no—
968C4⋊C4—221no—
969C4⋊C4—221no—
970C4⋊C4—221no—
971C4⋊C4—221no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—222no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C22⋊C4—222no—
993C22⋊C4—222no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—222no—
998C22⋊C4—222no—
999C22⋊C4—222no—
1000C42—222no—
1001C42—222no—
1002C42—222no—
1003C42—222no—
1004C11#6075211yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—416no—
1027C23—222no—
1028C23—222no—
1029C23—442no—
1030C23—442no—
1031C23—442no—
1032C23—442no—
1033C23—442no—
1034C23—442no—
1035C23C22×D4411yescharacteristic
1036C23C22×D4411yescharacteristic
1037C23C22×D4411yescharacteristic
1038C23C22×D4411yescharacteristic
1039C23C22×D4411yescharacteristic
1040C23C22×D4411yescharacteristic
1041C23C22×D4411yescharacteristic
1042Q8—222no—
1043Q8—224no—
1044Q8—222no—
1045Q8—442no—
1046Q8—442no—
1047D4—222no—
1048D4—224no—
1049D4—222no—
1050D4—442no—
1051D4—444no—
1052D4—444no—
1053D4—444no—
1054D4—444no—
1055D4—444no—
1056D4—444no—
1057D4—444no—
1058D4—444no—
1059D4—444no—
1060D4—444no—
1061D4—444no—
1062D4—444no—
1063D4—442no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—444no—
1098C2×C4—444no—
1099C2×C4—444no—
1100C2×C4—442no—
1101C2×C4—442no—
1102C2×C4—442no—
1103C2×C4—442no—
1104C2×C4—442no—
1105C2×C4—442no—
1106C2×C4—444no—
1107C2×C4C22×D4411yescharacteristic
1108C2×C4C22×D4411yescharacteristic
1109C2×C4C22×D4411yescharacteristic
1110C2×C4C22×D4411yescharacteristic
1111C2×C4C22×D4411yescharacteristic
1112C2×C4C22×D4411yescharacteristic
1113C2×C4C22×D4411yescharacteristic
1114C2×C4#6703714yes—
1115C2×C4C24×D1111yescharacteristic
1116C8—24no—
1117C8—24no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22—442no—
1147C22—442no—
1148C22—442no—
1149C22—884no—
1150C22—884no—
1151C22#1062302412yes—
1152C22#1062327912yes—
1153C22#1062327912yes—
1154C22C23×D4411yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—442no—
1162C4—442no—
1163C4—442no—
1164C4—442no—
1165C4—442no—
1166C4—442no—
1167C4#1062302412yes—
1168C4C2×#6703712yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—882no—
1177C2—882no—
1178C2C2×#1062302411yescharacteristic
1179C2C2×#1062327911yescharacteristic
1180C2C2×#1062327911yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC22×C11C23×D4
hypercenterC2×#407D11
hypocenterC11#60752
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. C2×#10623322C2semidirect
3. #13079458C2semidirect
4. #13079448C2semidirect
5. #13079432C2semidirect
6. #13079409C2semidirect
7. #13079399C2semidirect
8. #13079383C2semidirect
9. #13078565C2semidirect
10. #13078557C2semidirect
11. #13078549C2semidirect
12. #13078246C2semidirect
13. #13078235C2semidirect
14. #13077878C2semidirect
15. #13077870C2semidirect
16. #13077861C2semidirect
17. C2×C11×#407C2semidirect
20. C22×#4339C22semidirect
21. C22×C11×M16C22semidirect
36. #10623322C22semidirect
37. #10623322C22semidirect
38. #10623322C22semidirect
39. #10623322C22semidirect
41. C2×#66983C22semidirect
42. C2×#66983C22semidirect
43. C2×#66983C22semidirect
51. C2×#66979C22semidirect
53. C2×#66977C22semidirect
54. C2×#66977C22semidirect
55. C2×#66977C22semidirect
56. C2×#66962C22semidirect
57. C2×#66961C22semidirect
60. C11×#407C22semidirect
61. C11×#407C22semidirect
62. C11×#407C22semidirect
63. C2×C11×C22⋊C8C22semidirect
64. C2×C11×C22⋊C8C22semidirect
65. #10622750C22semidirect
66. #10622748C22semidirect
67. #10622747C22semidirect
68. #10622747C22semidirect
69. #10622746C22semidirect
70. #10622746C22semidirect
71. #10622744C22semidirect
72. #10622734C22semidirect
73. #10622734C22semidirect
74. #10622733C22semidirect
75. #10622729C22semidirect
76. #10622728C22semidirect
77. #10622727C22semidirect
78. #10622727C22semidirect
79. #10622352C22semidirect
80. #10622351C22semidirect
81. #10622350C22semidirect
82. #10622350C22semidirect
83. #10622350C22semidirect
84. #10622349C22semidirect
85. #10622348C22semidirect
86. #10622347C22semidirect
87. #10622347C22semidirect
88. #10622347C22semidirect
89. #10622346C22semidirect
90. #10622346C22semidirect
91. #10622346C22semidirect
92. #10622345C22semidirect
93. #10622344C22semidirect
94. #10622336C22semidirect
95. #10622336C22semidirect
96. #10622336C22semidirect
97. #10622335C22semidirect
98. #10622334C22semidirect
236. C2×Dic44C23semidirect
237. C2×D88C23semidirect
238. C2×#4314C23semidirect
239. C2×#4314C23semidirect
246. #66885C23semidirect
247. #66885C23semidirect
248. #66885C23semidirect
249. #66885C23semidirect
250. #66882C23semidirect
251. #66882C23semidirect
252. #66881C23semidirect
253. #66881C23semidirect
254. #66880C23semidirect
255. #66880C23semidirect
256. #66880C23semidirect
257. #66880C23semidirect
431. C2×#407D11semidirect
550. C22×M16C2×D11semidirect
621. #407C2×D11semidirect
622. #407C2×D11semidirect
623. #407C2×D11semidirect
624. C2×C22⋊C8C2×D11semidirect
625. C2×C22⋊C8C2×D11semidirect
1004. C11#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130794582
#130794482
#130794322
#130794092
#130793992
#130793832
#130785652
#130785572
#130785492
#130782462
#130782352
#130778782
#130778702
#130778612
C2×C11×#4072
#6075211