Finite Group Databasebeta

← #15624507

Subgroups — #15624507

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic, complemented
3#13079429C212yesmaximal, complemented
4#13079427C212yesmaximal, complemented
5#13079424C212yesmaximal, complemented
6#13079414C212yesmaximal, complemented
7#13079376C214yesmaximal, complemented
8#13079374C211yesmaximal, characteristic, complemented
9#13079373C211yesmaximal, characteristic, complemented
10#13079364C211yesmaximal, characteristic, complemented
11#13078551C212yesmaximal, complemented
12#13078535C212yesmaximal, complemented
13#13078232C214yesmaximal, complemented
14#13077863C212yesmaximal, complemented
15#13077840C212yesmaximal, complemented
16C2×#10622339C211yesmaximal, characteristic, complemented
17C11×#3186C211yesmaximal, characteristic, complemented
18C22×#4341C2211yescharacteristic, complemented
19C22×D4×D11—21no—
20C22×D4×D11C2211yescharacteristic, complemented
21C23×C4×D11C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic, complemented
24C2×#66992—21no—
25C2×#66991C2211yescharacteristic, complemented
26C2×#66991C2211yescharacteristic, complemented
27C2×#66990—21no—
28C2×D4×Dic11—21no—
29C2×#66983C2211yescharacteristic
30C2×#66977C2211yescharacteristic, complemented
31C2×#66964C2214yescomplemented
32C22×#4313C2212yescomplemented
33#10623137—21no—
34#10623137—21no—
35#10623137—21no—
36#10623137—21no—
37#10623137C2212yes—
38#10623137C2212yescomplemented
39#10623137C2212yescomplemented
40#10623137C2212yescomplemented
41D11×#121—21no—
42D11×#121—21no—
43D11×#121—21no—
44D11×#121—21no—
45D11×#121C2212yes—
46D11×#121C2212yes—
47D11×#121C2212yescomplemented
48D11×#121C2212yescomplemented
49C2×#66950C2211yescharacteristic, complemented
50C2×#66948C2211yescharacteristic, complemented
51C2×#66945C2211yescharacteristic, complemented
52C2×C4⋊C4×D11C2211yescharacteristic, complemented
53C2×#66937—21no—
54C2×#66936—21no—
55C2×(C22⋊D11)⋊C4—21no—
56C2×C22⋊C4×D11—21no—
57C11×#480C2212yescomplemented
58C11×#480C2212yescomplemented
59C11×#466C2214yescomplemented
60C11×#447C2212yescomplemented
61C11×#447C2212yescomplemented
62C2×C11×C22⋊C8C2211yescharacteristic, complemented
63#10622831C2212yescomplemented
64#10622830C2212yescomplemented
65C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
66#10622772C2214yescomplemented
67#10622771C2214yescomplemented
68#10622769C2214yescomplemented
69#10622727C2214yescomplemented
70C2×(C2×D11)⋊C8C2212yescomplemented
71#10622654C2214yescomplemented
72#10622653C2212yescomplemented
73#10622651C2214yescomplemented
74#10622649C2212yescomplemented
75#10622647C2212yescomplemented
76#10622646C2212yescomplemented
77#10622584C2212yescomplemented
78#10622580C2212yescomplemented
79#10622499C2214yescomplemented
80#10622498C2214yescomplemented
81#10622497C2214yescomplemented
82#10622494C2214yescomplemented
83#10622395C2214yescomplemented
84#10622394C2214yescomplemented
85#10622393C2214yescomplemented
86#10622392C2214yescomplemented
87#10622390C2214yescomplemented
88#10622389C2214yescomplemented
89#10622384C2214yescomplemented
90#10622383C2214yescomplemented
91#10622351C2212yescomplemented
92#10622348C2212yescomplemented
93#10622344C2212yescomplemented
94#10622339C2212yescomplemented
95#10622339C2212yescomplemented
96#10622339C2212yescomplemented
97#10622339C2212yescomplemented
98#10622334C2212yescomplemented
99C24×D11—21no—
100C24×D11D411yescharacteristic
101C22×D4×C11—21no—
102C22×D4×C11—21no—
103C22×D4×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic, complemented
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—21no—
107C22×C22⋊D11—21no—
108C22×C22⋊D11—21no—
109C22×C22⋊D11—21no—
110C22×C22⋊D11—21no—
111C23×Dic11—21no—
112C23×Dic11D411yescharacteristic
113C2×#4341—21no—
114C2×#4341—21no—
115C2×#4341—44no—
116C2×#4341C2312yes—
117C2×#4341C2312yescomplemented
118C2×D4×D11—22no—
119C2×D4×D11—22no—
120C2×D4×D11—22no—
121C2×D4×D11—22no—
122C2×D4×D11—21no—
123C2×D4×D11—21no—
124C2×D4×D11—44no—
125C2×D4×D11—48no—
126C2×D4×D11C2312yes—
127C2×D4×D11C2312yes—
128C22×D44—21no—
129C22×D44C2311yescharacteristic
130C22×C4×D11—21no—
131C22×C4×D11—44no—
132C22×C4×D11D411yescharacteristic
133C22×C4×D11D411yescharacteristic
134C22×C4×D11D411yescharacteristic
135C22×C4×D11D411yescharacteristic
136C22×C4×D11D411yescharacteristic
137C22×C4×D11D411yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×Dic22C2311yescharacteristic, complemented
145C2×C11×D8C2314yescomplemented
146C22×C8×C11C2312yescomplemented
147C11×#121—21no—
148C11×#121—21no—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121C2312yes—
152C11×#121C2312yes—
153C11×#121C2312yes—
154C11×#121C2312yescomplemented
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic, complemented
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C22⋊Dic11—21no—
160C2×C22⋊Dic11—21no—
161C2×C22⋊Dic11—21no—
162#66992—22no—
163#66992—22no—
164#66992—22no—
165#66992—22no—
166#66991—21no—
167#66991—21no—
168#66991—21no—
169#66991—21no—
170#66991C2312yes—
171#66991C2312yes—
172#66991C2312yes—
173#66991C2312yescomplemented
174#66990—22no—
175#66990—22no—
176#66990—22no—
177#66990—22no—
178D4×Dic11—22no—
179D4×Dic11—22no—
180D4×Dic11—22no—
181D4×Dic11—22no—
182C2×#4324C2314yescomplemented
183C2×#4323C2314yescomplemented
184#66983—21no—
185#66983—21no—
186#66983C2312yes—
187#66983C2312yes—
188C2×(C2×D11)⋊C4—21no—
189C2×(C2×D11)⋊C4—21no—
190C2×(C2×D11)⋊C4—21no—
191C2×(C2×D11)⋊C4—21no—
192C2×C4⋊Dic11—21no—
193C2×C4⋊Dic11C2311yescharacteristic
194C2×C4⋊Dic11C2311yescharacteristic, complemented
195#66977—21no—
196#66977—21no—
197#66977C2312yes—
198#66977C2312yescomplemented
199C2×Dic11⋊C4—21no—
200C2×Dic11⋊C4—21no—
201C2×C4×Dic11—21no—
202C22×C11⋊C8C2312yescomplemented
203#66964—48no—
204C2×#4314C2314yescomplemented
205C2×#4313—44no—
206C2×#4313C2314yes—
207C2×#4313C2314yescomplemented
208#66950—21no—
209#66950—21no—
210#66950C2312yes—
211#66950C2312yescomplemented
212#66948—21no—
213#66948—21no—
214#66948C2312yes—
215#66948C2312yes—
216#66945—21no—
217#66945—21no—
218#66945C2312yes—
219#66945C2312yescomplemented
220C4⋊C4×D11—21no—
221C4⋊C4×D11—21no—
222C4⋊C4×D11C2312yes—
223C4⋊C4×D11C2312yes—
224#66937—22no—
225#66937—22no—
226#66937—22no—
227#66937—22no—
228#66936—22no—
229#66936—22no—
230#66936—22no—
231#66936—22no—
232(C22⋊D11)⋊C4—22no—
233(C22⋊D11)⋊C4—22no—
234(C22⋊D11)⋊C4—22no—
235(C22⋊D11)⋊C4—22no—
236C22⋊C4×D11—22no—
237C22⋊C4×D11—22no—
238C22⋊C4×D11—22no—
239C22⋊C4×D11—22no—
240C11×#107C2314yescomplemented
241C11×#102C2314yescomplemented
242C11×#102C2314yescomplemented
243C11×C22⋊C8C2312yes—
244C11×C22⋊C8C2312yescomplemented
245#66896C2314yescomplemented
246#66896C2314yescomplemented
247C22⋊(C11⋊C8)C2312yes—
248C22⋊(C11⋊C8)C2312yescomplemented
249#66885C2314yescomplemented
250(C2×D11)⋊C8C2314yes—
251(C2×D11)⋊C8C2314yescomplemented
252#66881C2314yescomplemented
253#66880C2314yescomplemented
254#66874C2314yescomplemented
255#66873C2314yescomplemented
256#66872C2314yescomplemented
257#66871C2314yescomplemented
258#60750—111nomaximal, Sylow
259C24×C11—21no—
260C24×C11—21no—
261C24×C11C2×D411yescharacteristic
262C23×D11—24no—
263C23×D11—21no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—44no—
269C23×D11—44no—
270C23×D11—44no—
271C23×D11C2×D411yescharacteristic
272C23×D11C2×D411yescharacteristic
273C23×D11C2×D411yescharacteristic
274C23×D11C2×D411yescharacteristic
275C23×D11C2×D411yescharacteristic
276C23×D11C2×D411yescharacteristic
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—21no—
282C2×D4×C11—21no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—44no—
286C2×D4×C11—44no—
287C2×D4×C11C2412yes—
288C2×D4×C11C2412yes—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—42no—
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—44no—
309C2×C22⋊D11—44no—
310C2×C22⋊D11—44no—
311C2×C22⋊D11—44no—
312C2×C22⋊D11—44no—
313C22×Dic11—22no—
314C22×Dic11—22no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—42no—
319C22×Dic11—44no—
320C22×Dic11C2×D411yescharacteristic
321C22×Dic11C2×D411yescharacteristic
322C22×Dic11C2×D411yescharacteristic
323C22×Dic11C2×D411yescharacteristic
324C22×Dic11C2×D411yescharacteristic
325C22×Dic11C2×D411yescharacteristic
326#4341—28no—
327#4341—44no—
328#4341—44no—
329#4341—44no—
330D4×D11—28no—
331D4×D11—44no—
332D4×D11—48no—
333D4×D11—48no—
334D4×D11—48no—
335D4×D11—48no—
336D4×D11—44no—
337D4×D11—44no—
338C2×D44—22no—
339C2×D44—22no—
340C2×D44—21no—
341C2×D44—42no—
342C2×D44—44no—
343C2×D44C2412yes—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—44no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11C2×D411yescharacteristic
360C2×C4×D11C2×D411yescharacteristic
361C2×C4×D11C2×D411yescharacteristic
362C2×C4×D11C2×D411yescharacteristic
363C2×C4×D11C2×D411yescharacteristic
364C2×C4×D11C2×D411yescharacteristic
365C2×C4×D11C2×D411yescharacteristic
366C2×C4×D11C2×D411yescharacteristic
367C2×C4×D11C2×D411yescharacteristic
368C2×C4×D11C2×D411yescharacteristic
369C2×C4×D11C2×D411yescharacteristic
370C2×C4×D11C2×D411yescharacteristic
371C2×C4×D11C2411yescharacteristic
372C2×C4×D11C2411yescharacteristic
373C2×C4×D11C2411yescharacteristic
374C2×C4×D11C2411yescharacteristic
375C2×Dic22—21no—
376C2×Dic22—42no—
377C2×Dic22C2412yes—
378C11×D8—44no—
379C2×C8×C11—42no—
380C2×C8×C11C2414yes—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—21no—
383C11×C4⋊C4C2412yes—
384C11×C4⋊C4C2412yes—
385C11×C22⋊C4—22no—
386C11×C22⋊C4—22no—
387C11×C22⋊C4—22no—
388C11×C22⋊C4—22no—
389C22⋊Dic11—22no—
390C22⋊Dic11—22no—
391C22⋊Dic11—22no—
392C22⋊Dic11—22no—
393C22⋊Dic11—22no—
394C22⋊Dic11—22no—
395#4324—44no—
396#4323—44no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—22no—
399(C2×D11)⋊C4—22no—
400(C2×D11)⋊C4—22no—
401(C2×D11)⋊C4—22no—
402(C2×D11)⋊C4—22no—
403(C2×D11)⋊C4—22no—
404(C2×D11)⋊C4—22no—
405C4⋊Dic11—22no—
406C4⋊Dic11—22no—
407C4⋊Dic11—21no—
408C4⋊Dic11—21no—
409C4⋊Dic11C2412yes—
410C4⋊Dic11C2412yes—
411Dic11⋊C4—22no—
412Dic11⋊C4—22no—
413Dic11⋊C4—22no—
414Dic11⋊C4—22no—
415C4×Dic11—22no—
416C4×Dic11—22no—
417C2×C11⋊C8—42no—
418C2×C11⋊C8C2414yes—
419#4314—44no—
420#4313—28no—
421#4313—44no—
422C2×#525—111no—
423C22×#121—111no—
424#3194—112no—
425#3194—112no—
426#3193—112no—
427#3192—112no—
428#3188—114no—
429#3187—111no—
430#3187—111no—
431#3186—111no—
432#3186D1111yescharacteristic, complemented
433#3094—112no—
434#3092—112no—
435#3055—114no—
436#3006—112no—
437#3003—112no—
438C2×#407—111no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—42no—
444C23×C11—42no—
445C23×C11—42no—
446C23×C11—42no—
447C23×C11—42no—
448C23×C11—42no—
449C23×C11AGL(1,ℤ/8)14yescomplemented
450C23×C11C22×D411yescharacteristic
451C23×C11C22×D411yescharacteristic
452C23×C11C22×D411yescharacteristic
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—416no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—44no—
477C22×D11—42no—
478C22×D11—42no—
479C22×D11—42no—
480C22×D11—44no—
481C22×D11—44no—
482C22×D11—816no—
483C22×D11C22×D411yescharacteristic
484C22×D11C22×D411yescharacteristic
485C22×D11C22×D411yescharacteristic
486C22×D11C22×D411yescharacteristic
487D4×C11—24no—
488D4×C11—24no—
489D4×C11—42no—
490D4×C11—42no—
491D4×C11—44no—
492D4×C11—44no—
493D4×C11—44no—
494D4×C11—44no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—42no—
504C2×C4×C11—42no—
505C2×C4×C11C22×D411yescharacteristic
506C2×C4×C11C22×D411yescharacteristic
507C2×C4×C11C22×D411yescharacteristic
508C2×C4×C11C2511yescharacteristic
509C22⋊D11—44no—
510C22⋊D11—44no—
511C22⋊D11—44no—
512C22⋊D11—44no—
513C22⋊D11—44no—
514C22⋊D11—44no—
515C22⋊D11—44no—
516C22⋊D11—44no—
517C22⋊D11—44no—
518C22⋊D11—44no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—44no—
529C2×Dic11—42no—
530C2×Dic11—42no—
531C2×Dic11—42no—
532C2×Dic11—44no—
533C2×Dic11C22×D411yescharacteristic
534C2×Dic11C22×D411yescharacteristic
535C2×Dic11C22×D411yescharacteristic
536C2×Dic11C22×D411yescharacteristic
537D44—24no—
538D44—42no—
539D44—44no—
540D44—44no—
541C4×D11—22no—
542C4×D11—22no—
543C4×D11—22no—
544C4×D11—22no—
545C4×D11—22no—
546C4×D11—22no—
547C4×D11—22no—
548C4×D11—22no—
549C4×D11—22no—
550C4×D11—41no—
551C4×D11—41no—
552C4×D11—41no—
553C4×D11—41no—
554C4×D11—41no—
555C4×D11—41no—
556C4×D11—44no—
557C4×D11—44no—
558C4×D11H(5,𝔽2)14yes—
559Dic22—24no—
560Dic22—42no—
561C8×C11—24no—
562C11⋊C8—24no—
563C22×#41—111no—
564C23×D4—111no—
565C23×D4—221no—
566C24×C4—111no—
567C2×AGL(1,ℤ/8)—114no—
568C22×M16—112no—
569#525—112no—
570#525—112no—
571#525—112no—
572#525—112no—
573#525—221no—
574#525—221no—
575#525—221no—
576#525—221no—
577C2×#123—221no—
578C2×C22⋊Q8—111no—
579C2×C22⋊Q8—111no—
580C2×#121—111no—
581C2×#121—111no—
582C2×#121—111no—
583C2×#121—112no—
584C2×#121—112no—
585C2×#121—112no—
586C2×#121—112no—
587C2×#121—111no—
588C2×#121—221no—
589C2×#121—221no—
590C2×#121—221no—
591C2×#121—221no—
592C2×#121—221no—
593C2×#121—221no—
594C2×#121C2×D1111yescharacteristic
595C2×#121C2×D1111yescharacteristic, complemented
596C2×#120—221no—
597C2×C4×D4—221no—
598C2×C4×D4—221no—
599C2×#117—111no—
600C22×C4⋊C4—111no—
601C22×C22⋊C4—221no—
602#484—114no—
603#483—112no—
604#483—112no—
605#482—114no—
606#482—114no—
607#481—112no—
608#481—114no—
609#481—112no—
610#480—112no—
611#480—112no—
612#480C2×D1112yescomplemented
613#480C2×D1112yescomplemented
614#469—114no—
615#469—114no—
616#468—114no—
617#468—114no—
618#466—114no—
619#466C2×D1114yescomplemented
620#465—114no—
621#465—114no—
622#450—112no—
623#450—114no—
624#450—112no—
625#449—114no—
626#449—114no—
627#448—112no—
628#448—112no—
629#447—112no—
630#447—114no—
631#447—112no—
632#447C2×D1112yescomplemented
633#447C2×D1112yescomplemented
634#428—114no—
635#418—114no—
636#417—114no—
637#407—112no—
638#407—112no—
639#407—112no—
640#407—112no—
641C2×C22⋊C8—111no—
642C2×C22⋊C8—112no—
643C2×C22⋊C8C2×D1111yescharacteristic, complemented
644C22×C11—21no—
645C22×C11—21no—
646C22×C11—21no—
647C22×C11—21no—
648C22×C11—21no—
649C22×C11—21no—
650C22×C11—44no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—84no—
658C22×C11—84no—
659C22×C11C2×AGL(1,ℤ/8)12yes—
660C22×C11C2×AGL(1,ℤ/8)12yes—
661C22×C11C2×AGL(1,ℤ/8)12yes—
662C22×C11C23×D411yescharacteristic
663C2×D11—28no—
664C2×D11—21no—
665C2×D11—21no—
666C2×D11—21no—
667C2×D11—21no—
668C2×D11—21no—
669C2×D11—21no—
670C2×D11—21no—
671C2×D11—21no—
672C2×D11—21no—
673C2×D11—21no—
674C2×D11—44no—
675C2×D11—44no—
676C2×D11—44no—
677C2×D11—44no—
678C2×D11—44no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—88no—
683C2×D11—88no—
684C2×D11—84no—
685C2×D11#53412yes—
686C2×D11#57512yes—
687C4×C11—21no—
688C4×C11—21no—
689C4×C11—21no—
690C4×C11—42no—
691C4×C11—42no—
692C4×C11C2×H(5,𝔽2)12yes—
693Dic11—21no—
694Dic11—21no—
695Dic11—21no—
696Dic11—42no—
697Dic11—42no—
698Dic11—42no—
699Dic11#53412yes—
700C25—111no—
701C25—221no—
702C2×#41—112no—
703C2×#41—112no—
704C2×#41—221no—
705C2×#41—221no—
706C2×#41—444no—
707C22×Q8—111no—
708C22×D4—21no—
709C22×D4—21no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—111no—
713C22×D4—221no—
714C22×D4—221no—
715C22×D4—221no—
716C22×D4—221no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—221no—
722C22×D4—221no—
723C22×D4—221no—
724C22×D4—221no—
725C22×D4—444no—
726C22×D4—448no—
727C22×D4C22×D1111yescharacteristic
728C22×D4C22×D1111yescharacteristic, complemented
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—221no—
743C23×C4—221no—
744C23×C4—444no—
745C23×C4C22×D1111yescharacteristic
746AGL(1,ℤ/8)—448no—
747C2×SD16—114no—
748C2×SD16—114no—
749C2×D8—114no—
750C2×D8C22×D1114yescomplemented
751C2×M16—114no—
752C2×M16—114no—
753C2×M16—444no—
754C22×C8—112no—
755C22×C8C22×D1112yescomplemented
756#123—222no—
757#123—222no—
758#123—222no—
759#123—222no—
760C22⋊Q8—112no—
761C22⋊Q8—112no—
762C22⋊Q8—112no—
763C22⋊Q8—112no—
764C22⋊Q8—221no—
765C22⋊Q8—221no—
766C22⋊Q8—221no—
767C22⋊Q8—221no—
768#121—21no—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—112no—
773#121—112no—
774#121—112no—
775#121—112no—
776#121—112no—
777#121—112no—
778#121—112no—
779#121—112no—
780#121—222no—
781#121—222no—
782#121—222no—
783#121—222no—
784#121—221no—
785#121—221no—
786#121—221no—
787#121—221no—
788#121—222no—
789#121—222no—
790#121—222no—
791#121—222no—
792#121—221no—
793#121—221no—
794#121—221no—
795#121—221no—
796#121C22×D1112yes—
797#121C22×D1112yes—
798#121C22×D1112yes—
799#121C22×D1112yescomplemented
800#120—222no—
801#120—222no—
802#120—222no—
803#120—222no—
804C4×D4—222no—
805C4×D4—222no—
806C4×D4—222no—
807C4×D4—222no—
808C4×D4—222no—
809C4×D4—222no—
810C4×D4—222no—
811C4×D4—222no—
812#117—112no—
813#117—112no—
814#117—221no—
815#117—221no—
816C2×C4⋊C4—111no—
817C2×C4⋊C4—111no—
818C2×C4⋊C4—112no—
819C2×C4⋊C4—112no—
820C2×C4⋊C4—221no—
821C2×C4⋊C4—221no—
822C2×C4⋊C4—221no—
823C2×C4⋊C4—221no—
824C2×C4⋊C4—221no—
825C2×C4⋊C4C22×D1111yescharacteristic
826C2×C4⋊C4C22×D1111yescharacteristic, complemented
827C2×C22⋊C4—21no—
828C2×C22⋊C4—21no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—221no—
834C2×C22⋊C4—221no—
835C2×C22⋊C4—221no—
836C2×C22⋊C4—221no—
837C2×C22⋊C4—221no—
838C2×C22⋊C4—221no—
839C2×C22⋊C4—221no—
840C2×C42—221no—
841#107—114no—
842#107C22×D1114yescomplemented
843#106—114no—
844#106—114no—
845#103—114no—
846#103—114no—
847#102—114no—
848#102—114no—
849#102—114no—
850#102—114no—
851#102C22×D1114yescomplemented
852#102C22×D1114yescomplemented
853C22⋊C8—112no—
854C22⋊C8—112no—
855C22⋊C8—114no—
856C22⋊C8—114no—
857C22⋊C8C22×D1112yes—
858C22⋊C8C22×D1112yescomplemented
859C2×C11—22no—
860C2×C11—22no—
861C2×C11—22no—
862C2×C11—82no—
863C2×C11—82no—
864C2×C11C2×#53411yescharacteristic
865C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
866C2×C11C2×#57511yescharacteristic
867D11—22no—
868D11—22no—
869D11—41no—
870D11—41no—
871D11—82no—
872C24—21no—
873C24—21no—
874C24—111no—
875C24—111no—
876C24—111no—
877C24—111no—
878C24—111no—
879C24—111no—
880C24—222no—
881C24—222no—
882C24—224no—
883C24—221no—
884C24—442no—
885C24—442no—
886C24—444no—
887C24—444no—
888C24—444no—
889C24D4×D1111yescharacteristic
890#41—228no—
891#41—444no—
892#41—444no—
893#41—444no—
894C2×Q8—112no—
895C2×Q8—221no—
896C2×Q8—442no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—112no—
908C2×D4—222no—
909C2×D4—222no—
910C2×D4—228no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—222no—
915C2×D4—222no—
916C2×D4—222no—
917C2×D4—222no—
918C2×D4—222no—
919C2×D4—222no—
920C2×D4—222no—
921C2×D4—221no—
922C2×D4—442no—
923C2×D4—444no—
924C2×D4—444no—
925C2×D4—444no—
926C2×D4—444no—
927C2×D4—444no—
928C2×D4—448no—
929C2×D4—448no—
930C2×D4—448no—
931C2×D4—448no—
932C2×D4—444no—
933C2×D4—444no—
934C2×D4—444no—
935C2×D4—444no—
936C2×D4C23×D1112yes—
937C2×D4C23×D1112yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—42no—
941C22×C4—111no—
942C22×C4—111no—
943C22×C4—111no—
944C22×C4—111no—
945C22×C4—111no—
946C22×C4—111no—
947C22×C4—111no—
948C22×C4—111no—
949C22×C4—111no—
950C22×C4—111no—
951C22×C4—111no—
952C22×C4—111no—
953C22×C4—111no—
954C22×C4—111no—
955C22×C4—111no—
956C22×C4—111no—
957C22×C4—111no—
958C22×C4—111no—
959C22×C4—111no—
960C22×C4—111no—
961C22×C4—111no—
962C22×C4—111no—
963C22×C4—224no—
964C22×C4—224no—
965C22×C4—224no—
966C22×C4—222no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—442no—
974C22×C4—442no—
975C22×C4—442no—
976C22×C4—442no—
977C22×C4—442no—
978C22×C4—442no—
979C22×C4—442no—
980C22×C4—442no—
981C22×C4—442no—
982C22×C4—444no—
983C22×C4—442no—
984C22×C4—444no—
985C22×C4D4×D1111yescharacteristic
986C22×C4D4×D1111yescharacteristic
987C22×C4D4×D1111yescharacteristic
988C22×C4C23×D1111yescharacteristic
989C22×C4C23×D1111yescharacteristic
990C22×C4C23×D1111yescharacteristic
991SD16—444no—
992SD16—444no—
993D8—44no—
994D8—444no—
995M16—228no—
996M16—444no—
997C2×C8—42no—
998C2×C8—114no—
999C2×C8—442no—
1000C2×C8C23×D1114yes—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—112no—
1004C4⋊C4—112no—
1005C4⋊C4—222no—
1006C4⋊C4—222no—
1007C4⋊C4—222no—
1008C4⋊C4—222no—
1009C4⋊C4—221no—
1010C4⋊C4—221no—
1011C4⋊C4—222no—
1012C4⋊C4—222no—
1013C4⋊C4C23×D1112yes—
1014C4⋊C4C23×D1112yes—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—222no—
1020C22⋊C4—222no—
1021C22⋊C4—222no—
1022C22⋊C4—222no—
1023C22⋊C4—222no—
1024C22⋊C4—222no—
1025C22⋊C4—222no—
1026C22⋊C4—222no—
1027C22⋊C4—222no—
1028C22⋊C4—222no—
1029C22⋊C4—222no—
1030C22⋊C4—222no—
1031C22⋊C4—222no—
1032C22⋊C4—222no—
1033C42—222no—
1034C42—222no—
1035C11#6075011yescharacteristic, complemented, Sylow
1036C23—22no—
1037C23—22no—
1038C23—41no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—111no—
1047C23—111no—
1048C23—111no—
1049C23—111no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—441no—
1068C23—441no—
1069C23—442no—
1070C23—442no—
1071C23—444no—
1072C23—444no—
1073C23—4416no—
1074C23—444no—
1075C23—444no—
1076C23—444no—
1077C23—444no—
1078C23—442no—
1079C23—8816no—
1080C23#6696414yescomplemented
1081C23C2×D4×D1111yescharacteristic
1082C23C2×D4×D1111yescharacteristic
1083C23C2×D4×D1111yescharacteristic
1084Q8—224no—
1085Q8—442no—
1086D4—24no—
1087D4—24no—
1088D4—42no—
1089D4—42no—
1090D4—44no—
1091D4—44no—
1092D4—44no—
1093D4—44no—
1094D4—224no—
1095D4—442no—
1096D4—444no—
1097D4—444no—
1098D4—444no—
1099D4—444no—
1100D4—444no—
1101D4—444no—
1102D4—444no—
1103D4—444no—
1104D4—444no—
1105D4—444no—
1106D4—444no—
1107D4—444no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—111no—
1119C2×C4—114no—
1120C2×C4—111no—
1121C2×C4—111no—
1122C2×C4—111no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—441no—
1139C2×C4—441no—
1140C2×C4—441no—
1141C2×C4—441no—
1142C2×C4—441no—
1143C2×C4—441no—
1144C2×C4—444no—
1145C2×C4—444no—
1146C2×C4—444no—
1147C2×C4—441no—
1148C2×C4—441no—
1149C2×C4—441no—
1150C2×C4—444no—
1151C2×C4—442no—
1152C2×C4—442no—
1153C2×C4—442no—
1154C2×C4C2×D4×D1111yescharacteristic
1155C2×C4C2×D4×D1111yescharacteristic
1156C2×C4C2×D4×D1111yescharacteristic
1157C2×C4C24×D1111yescharacteristic
1158C8—24no—
1159C8—224no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—21no—
1166C22—44no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—84no—
1174C22—84no—
1175C22—112no—
1176C22—112no—
1177C22—228no—
1178C22—221no—
1179C22—221no—
1180C22—221no—
1181C22—221no—
1182C22—221no—
1183C22—221no—
1184C22—221no—
1185C22—221no—
1186C22—221no—
1187C22—221no—
1188C22—444no—
1189C22—444no—
1190C22—444no—
1191C22—444no—
1192C22—444no—
1193C22—442no—
1194C22—442no—
1195C22—442no—
1196C22—884no—
1197C22—888no—
1198C22—888no—
1199C22C2×#6696412yes—
1200C22C2×#6696412yes—
1201C22C2×#6696412yes—
1202C22C22×D4×D1111yescharacteristic
1203C4—21no—
1204C4—21no—
1205C4—21no—
1206C4—42no—
1207C4—42no—
1208C4—112no—
1209C4—221no—
1210C4—221no—
1211C4—221no—
1212C4—442no—
1213C4—442no—
1214C4—442no—
1215C4D11×H(5,𝔽2)12yes—
1216C2—22no—
1217C2—22no—
1218C2—22no—
1219C2—82no—
1220C2—82no—
1221C2—222no—
1222C2—222no—
1223C2—441no—
1224C2—441no—
1225C2—882no—
1226C2D11×#53411yescharacteristic
1227C2C22×#6696411yescharacteristic
1228C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3186C2
socleC22×C11C23×D4
hypercenter#3186D11
hypocenterC11#60750
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. C2×#10623137C2semidirect
2. C2×D11×#121C2semidirect
3. #13079429C2semidirect
4. #13079427C2semidirect
5. #13079424C2semidirect
6. #13079414C2semidirect
7. #13079376C2semidirect
8. #13079374C2semidirect
9. #13079373C2semidirect
10. #13079364C2semidirect
11. #13078551C2semidirect
12. #13078535C2semidirect
13. #13078232C2semidirect
14. #13077863C2semidirect
15. #13077840C2semidirect
16. C2×#10622339C2semidirect
17. C11×#3186C2semidirect
18. C22×#4341C22semidirect
20. C22×D4×D11C22semidirect
23. C2×C11×#121C22semidirect
25. C2×#66991C22semidirect
26. C2×#66991C22semidirect
30. C2×#66977C22semidirect
31. C2×#66964C22semidirect
32. C22×#4313C22semidirect
38. #10623137C22semidirect
39. #10623137C22semidirect
40. #10623137C22semidirect
47. D11×#121C22semidirect
48. D11×#121C22semidirect
49. C2×#66950C22semidirect
50. C2×#66948C22semidirect
51. C2×#66945C22semidirect
52. C2×C4⋊C4×D11C22semidirect
57. C11×#480C22semidirect
58. C11×#480C22semidirect
59. C11×#466C22semidirect
60. C11×#447C22semidirect
61. C11×#447C22semidirect
62. C2×C11×C22⋊C8C22semidirect
63. #10622831C22semidirect
64. #10622830C22semidirect
65. C2×C22⋊(C11⋊C8)C22semidirect
66. #10622772C22semidirect
67. #10622771C22semidirect
68. #10622769C22semidirect
69. #10622727C22semidirect
70. C2×(C2×D11)⋊C8C22semidirect
71. #10622654C22semidirect
72. #10622653C22semidirect
73. #10622651C22semidirect
74. #10622649C22semidirect
75. #10622647C22semidirect
76. #10622646C22semidirect
77. #10622584C22semidirect
78. #10622580C22semidirect
79. #10622499C22semidirect
80. #10622498C22semidirect
81. #10622497C22semidirect
82. #10622494C22semidirect
83. #10622395C22semidirect
84. #10622394C22semidirect
85. #10622393C22semidirect
86. #10622392C22semidirect
87. #10622390C22semidirect
88. #10622389C22semidirect
89. #10622384C22semidirect
90. #10622383C22semidirect
91. #10622351C22semidirect
92. #10622348C22semidirect
93. #10622344C22semidirect
94. #10622339C22semidirect
95. #10622339C22semidirect
96. #10622339C22semidirect
97. #10622339C22semidirect
98. #10622334C22semidirect
104. C22×D4×C11C23semidirect
117. C2×#4341C23semidirect
144. C22×Dic22C23semidirect
145. C2×C11×D8C23semidirect
146. C22×C8×C11C23semidirect
154. C11×#121C23semidirect
156. C2×C11×C4⋊C4C23semidirect
173. #66991C23semidirect
182. C2×#4324C23semidirect
183. C2×#4323C23semidirect
194. C2×C4⋊Dic11C23semidirect
198. #66977C23semidirect
202. C22×C11⋊C8C23semidirect
204. C2×#4314C23semidirect
207. C2×#4313C23semidirect
211. #66950C23semidirect
219. #66945C23semidirect
240. C11×#107C23semidirect
241. C11×#102C23semidirect
242. C11×#102C23semidirect
244. C11×C22⋊C8C23semidirect
245. #66896C23semidirect
246. #66896C23semidirect
248. C22⋊(C11⋊C8)C23semidirect
249. #66885C23semidirect
251. (C2×D11)⋊C8C23semidirect
252. #66881C23semidirect
253. #66880C23semidirect
254. #66874C23semidirect
255. #66873C23semidirect
256. #66872C23semidirect
257. #66871C23semidirect
432. #3186D11semidirect
449. C23×C11AGL(1,ℤ/8)semidirect
595. C2×#121C2×D11semidirect
612. #480C2×D11semidirect
613. #480C2×D11semidirect
619. #466C2×D11semidirect
632. #447C2×D11semidirect
633. #447C2×D11semidirect
643. C2×C22⋊C8C2×D11semidirect
728. C22×D4C22×D11semidirect
750. C2×D8C22×D11semidirect
755. C22×C8C22×D11semidirect
799. #121C22×D11semidirect
826. C2×C4⋊C4C22×D11semidirect
842. #107C22×D11semidirect
851. #102C22×D11semidirect
852. #102C22×D11semidirect
858. C22⋊C8C22×D11semidirect
1035. C11#60750semidirect
1080. C23#66964semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
C2×D11×#1212
#130794292
#130794272
#130794242
#130794142
#130793762
#130793742
#130793732
#130793642
#130785512
#130785352
#130782322
#130778632
#130778402
C2×#106223392
C11×#31862
#6075011