Finite Group Databasebeta

← #15624520

Subgroups — #15624520

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×#10623158C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic, complemented
3#13079431C214yesmaximal, complemented
4#13079418C211yesmaximal, characteristic, complemented
5#13079416C211yesmaximal, characteristic, complemented
6#13079413C211yesmaximal, characteristic, complemented
7#13079386C212yesmaximal, complemented
8#13079384C212yesmaximal, complemented
9#13079371C212yesmaximal, complemented
10#13079366C212yesmaximal, complemented
11#13078551C212yesmaximal, complemented
12#13078543C212yesmaximal, complemented
13#13078230C214yesmaximal, complemented
14#13077867C212yesmaximal, complemented
15#13077844C212yesmaximal, complemented
16D11×#407C211yesmaximal, characteristic, complemented
17C11×#3193C211yesmaximal, characteristic, complemented
18C22×#4343C2211yescharacteristic, complemented
19C22×D4×D11—21no—
20C22×D4×D11C2211yescharacteristic, complemented
21C23×C4×D11C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic, complemented
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic, complemented
25C2×#66992—21no—
26C2×#66991C2211yescharacteristic, complemented
27C2×#66983C2211yescharacteristic
28C2×#66983C2211yescharacteristic, complemented
29C2×#66967C2214yescomplemented
30C2×M16×D11C2212yescomplemented
31#10623158—21no—
32#10623158—21no—
33#10623158—21no—
34#10623158—21no—
35#10623158C2212yes—
36#10623158C2212yescomplemented
37#10623158C2212yescomplemented
38#10623158C2212yescomplemented
39D11×#121—21no—
40D11×#121—21no—
41D11×#121—21no—
42D11×#121—21no—
43D11×#121C2212yes—
44D11×#121C2212yes—
45D11×#121C2212yescomplemented
46D11×#121C2212yescomplemented
47C2×#66948C2211yescharacteristic, complemented
48C2×#66948C2211yescharacteristic, complemented
49C2×#66947—21no—
50C2×#66946—21no—
51C2×#66945C2211yescharacteristic, complemented
52C2×C4⋊C4×D11C2211yescharacteristic, complemented
53C2×#66937—21no—
54C2×#66935—21no—
55C2×(C22⋊D11)⋊C4—21no—
56C2×C22⋊C4×D11—21no—
57C11×#484C2212yescomplemented
58C11×#480C2212yescomplemented
59C11×#468C2214yescomplemented
60C11×#450C2212yescomplemented
61C11×#448C2212yescomplemented
62C11×#407C2211yescharacteristic, complemented
63#10622840C2212yescomplemented
64#10622830C2212yescomplemented
65#10622820C2211yescharacteristic, complemented
66#10622785C2214yescomplemented
67#10622784C2214yescomplemented
68#10622782C2214yescomplemented
69#10622748C2214yescomplemented
70#10622739C2212yescomplemented
71#10622662C2214yescomplemented
72#10622659C2212yescomplemented
73#10622657C2212yescomplemented
74#10622652C2214yescomplemented
75#10622649C2212yescomplemented
76#10622647C2212yescomplemented
77#10622581C2212yescomplemented
78#10622580C2212yescomplemented
79#10622498C2214yescomplemented
80#10622496C2214yescomplemented
81#10622495C2214yescomplemented
82#10622494C2214yescomplemented
83#10622424C2214yescomplemented
84#10622420C2214yescomplemented
85#10622418C2214yescomplemented
86#10622416C2214yescomplemented
87#10622392C2214yescomplemented
88#10622388C2214yescomplemented
89#10622386C2214yescomplemented
90#10622383C2214yescomplemented
91#10622348C2212yescomplemented
92#10622348C2212yescomplemented
93#10622345C2212yescomplemented
94#10622345C2212yescomplemented
95#10622339C2212yescomplemented
96#10622339C2212yescomplemented
97D11×C22⋊C8C2212yescomplemented
98D11×C22⋊C8C2212yescomplemented
99C24×D11—21no—
100C24×D11D411yescharacteristic
101C22×Q8×C11C2311yescharacteristic, complemented
102C22×D4×C11—21no—
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C22×C22⋊D11—21no—
106C22×C22⋊D11—21no—
107C22×C22⋊D11—21no—
108C22×C22⋊D11—21no—
109C23×Dic11D411yescharacteristic
110C2×#4343—21no—
111C2×#4343—21no—
112C2×#4343—44no—
113C2×#4343C2312yes—
114C2×#4343C2312yescomplemented
115C2×D4×D11—22no—
116C2×D4×D11—22no—
117C2×D4×D11—22no—
118C2×D4×D11—22no—
119C2×D4×D11—21no—
120C2×D4×D11—21no—
121C2×D4×D11—44no—
122C2×D4×D11—48no—
123C2×D4×D11C2312yes—
124C2×D4×D11C2312yes—
125C22×D44—21no—
126C22×D44—21no—
127C22×D44—21no—
128C22×D44C2311yescharacteristic
129C22×D44C2311yescharacteristic, complemented
130C22×C4×D11—21no—
131C22×C4×D11—21no—
132C22×C4×D11—44no—
133C22×C4×D11D411yescharacteristic
134C22×C4×D11D411yescharacteristic
135C22×C4×D11D411yescharacteristic
136C22×C4×D11D411yescharacteristic
137C22×C4×D11D411yescharacteristic
138C22×C4×D11D411yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C2×C11×SD16C2314yescomplemented
146C2×C11×M16C2312yescomplemented
147C11×C22⋊Q8—21no—
148C11×C22⋊Q8—21no—
149C11×C22⋊Q8C2312yes—
150C11×C22⋊Q8C2312yescomplemented
151C11×#121—21no—
152C11×#121—21no—
153C11×#121C2312yes—
154C11×#121C2312yes—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic, complemented
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C22⋊Dic11—21no—
161#66999—21no—
162#66999—21no—
163#66999C2312yes—
164#66999C2312yescomplemented
165C2×#4325C2314yescomplemented
166#66992—22no—
167#66992—22no—
168#66992—22no—
169#66992—22no—
170#66991—21no—
171#66991—21no—
172#66991C2312yes—
173#66991C2312yes—
174C2×#4323C2314yescomplemented
175#66983—21no—
176#66983—21no—
177#66983—21no—
178#66983—21no—
179#66983C2312yes—
180#66983C2312yes—
181#66983C2312yes—
182#66983C2312yescomplemented
183C2×(C2×D11)⋊C4—21no—
184C2×(C2×D11)⋊C4—21no—
185C2×(C2×D11)⋊C4—21no—
186C2×(C2×D11)⋊C4—21no—
187C2×(C2×D11)⋊C4—21no—
188C2×(C2×D11)⋊C4—21no—
189C2×C4⋊Dic11C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic, complemented
191C2×Dic11⋊C4—21no—
192C2×Dic11⋊C4—21no—
193C2×C4×Dic11—21no—
194C2×#4318C2312yescomplemented
195#66967—48no—
196M16×D11—44no—
197C2×D88C2314yescomplemented
198C2×#4313C2314yes—
199C2×C8×D11C2314yescomplemented
200#66948—21no—
201#66948—21no—
202#66948—21no—
203#66948—21no—
204#66948C2312yes—
205#66948C2312yes—
206#66948C2312yes—
207#66948C2312yescomplemented
208#66947—22no—
209#66947—22no—
210#66947—22no—
211#66947—22no—
212#66946—22no—
213#66946—22no—
214#66946—22no—
215#66946—22no—
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#66935—22no—
229#66935—22no—
230#66935—22no—
231#66935—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×#103C2314yescomplemented
242C11×#102C2314yescomplemented
243C11×C22⋊C8C2312yes—
244C11×C22⋊C8C2312yescomplemented
245#66899C2314yescomplemented
246#66896C2314yescomplemented
247C22⋊(C11⋊C8)C2312yes—
248C22⋊(C11⋊C8)C2312yescomplemented
249#66885C2314yescomplemented
250#66885C2314yescomplemented
251(C2×D11)⋊C8C2314yes—
252(C2×D11)⋊C8C2314yescomplemented
253#66881C2314yescomplemented
254#66873C2314yescomplemented
255#66873C2314yescomplemented
256#66872C2314yescomplemented
257#66871C2314yescomplemented
258#60750—111nomaximal, Sylow
259C24×C11—21no—
260C24×C11C2×D411yescharacteristic
261C23×D11—24no—
262C23×D11—21no—
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×Q8×C11—21no—
278C2×Q8×C11—42no—
279C2×Q8×C11C2412yes—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—21no—
283C2×D4×C11—42no—
284C2×D4×C11—44no—
285C2×D4×C11C2412yes—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—42no—
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2×D411yescharacteristic
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C2×C22⋊D11—22no—
297C2×C22⋊D11—22no—
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—44no—
305C2×C22⋊D11—44no—
306C2×C22⋊D11—44no—
307C2×C22⋊D11—44no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—42no—
311C22×Dic11C2×D411yescharacteristic
312C22×Dic11C2×D411yescharacteristic
313C22×Dic11C2×D411yescharacteristic
314C22×Dic11C2×D411yescharacteristic
315C22×Dic11C2×D411yescharacteristic
316C22×Dic11C2×D411yescharacteristic
317#4343—28no—
318#4343—44no—
319#4343—44no—
320#4343—44no—
321D4×D11—28no—
322D4×D11—44no—
323D4×D11—48no—
324D4×D11—48no—
325D4×D11—48no—
326D4×D11—44no—
327D4×D11—44no—
328D4×D11—48no—
329C2×D44—22no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—22no—
333C2×D44—22no—
334C2×D44—22no—
335C2×D44—21no—
336C2×D44—21no—
337C2×D44—42no—
338C2×D44—42no—
339C2×D44—44no—
340C2×D44—44no—
341C2×D44—44no—
342C2×D44C2412yes—
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—22no—
350C2×C4×D11—22no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—44no—
358C2×C4×D11—42no—
359C2×C4×D11—42no—
360C2×C4×D11—42no—
361C2×C4×D11—44no—
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×D11C2×D411yescharacteristic
372C2×C4×D11C2×D411yescharacteristic
373C2×C4×D11C2×D411yescharacteristic
374C2×C4×D11C2411yescharacteristic
375C2×C4×D11C2411yescharacteristic
376C2×C4×D11C2411yescharacteristic
377C2×C4×D11C2411yescharacteristic
378C11×SD16—44no—
379C11×M16—42no—
380C2×C8×C11C2414yes—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—21no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4C2412yes—
386C11×C4⋊C4C2412yes—
387C11×C22⋊C4—22no—
388C11×C22⋊C4—22no—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—22no—
391C22⋊Dic11—22no—
392C22⋊Dic11—22no—
393#4325—44no—
394#4323—44no—
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—22no—
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—
405(C2×D11)⋊C4—22no—
406(C2×D11)⋊C4—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—
417#4318—42no—
418C2×C11⋊C8C2414yes—
419D88—44no—
420#4313—28no—
421C8×D11—44no—
422C2×#525—111no—
423C22×#121—111no—
424#3194—114no—
425#3193—111no—
426#3193D1111yescharacteristic, complemented
427#3192—111no—
428#3192—111no—
429#3188—112no—
430#3188—112no—
431#3187—112no—
432#3186—112no—
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—22no—
442C23×C11—41no—
443C23×C11—42no—
444C23×C11—42no—
445C23×C11—42no—
446C23×C11C22×D411yescharacteristic
447C23×C11C22×D411yescharacteristic
448C23×C11C22×D411yescharacteristic
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
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—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—416no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11—42no—
474C22×D11—42no—
475C22×D11—42no—
476C22×D11—42no—
477C22×D11—42no—
478C22×D11—42no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11—816no—
482C22×D11AGL(1,ℤ/8)14yescomplemented
483C22×D11C22×D411yescharacteristic
484C22×D11C22×D411yescharacteristic
485C22×D11C22×D411yescharacteristic
486C22×D11C22×D411yescharacteristic
487Q8×C11—24no—
488Q8×C11—42no—
489D4×C11—24no—
490D4×C11—42no—
491D4×C11—44no—
492D4×C11—44no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—42no—
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—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—42no—
526C2×Dic11—42no—
527C2×Dic11C22×D411yescharacteristic
528C2×Dic11C22×D411yescharacteristic
529C2×Dic11C22×D411yescharacteristic
530C2×Dic11C22×D411yescharacteristic
531D44—24no—
532D44—24no—
533D44—42no—
534D44—42no—
535D44—44no—
536D44—44no—
537D44—44no—
538D44—44no—
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×D11—44no—
559C4×D11—44no—
560C4×D11H(5,𝔽2)14yes—
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⋊Q8C2×D1111yescharacteristic, complemented
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—111no—
589C2×#121—221no—
590C2×#121—221no—
591C2×#121—221no—
592C2×#121—221no—
593C2×#121—221no—
594C2×#121—221no—
595C2×#121C2×D1111yescharacteristic
596C2×#120—221no—
597C2×C4×D4—221no—
598C2×C4×D4—221no—
599C2×#117—111no—
600C22×C4⋊C4—111no—
601C22×C22⋊C4—221no—
602#484—112no—
603#484C2×D1112yescomplemented
604#483—114no—
605#482—114no—
606#482—114no—
607#481—112no—
608#481—112no—
609#481—112no—
610#481—112no—
611#480—112no—
612#480—114no—
613#480C2×D1112yescomplemented
614#469—114no—
615#469—114no—
616#468—114no—
617#468C2×D1114yescomplemented
618#466—114no—
619#466—114no—
620#465—114no—
621#465—114no—
622#450—114no—
623#450—112no—
624#450C2×D1112yescomplemented
625#449—114no—
626#449—114no—
627#448—112no—
628#448C2×D1112yescomplemented
629#447—112no—
630#447—112no—
631#447—114no—
632#447—112no—
633#447—112no—
634#428—114no—
635#418—114no—
636#417—114no—
637#407—111no—
638#407—112no—
639#407—112no—
640#407—112no—
641#407C2×D1111yescharacteristic, complemented
642C2×C22⋊C8—112no—
643C2×C22⋊C8—112no—
644C22×C11—21no—
645C22×C11—21no—
646C22×C11—21no—
647C22×C11—21no—
648C22×C11—21no—
649C22×C11—21no—
650C22×C11—21no—
651C22×C11—44no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—84no—
656C22×C11C2×AGL(1,ℤ/8)12yes—
657C22×C11#57512yes—
658C22×C11C23×D411yescharacteristic
659C2×D11—28no—
660C2×D11—21no—
661C2×D11—21no—
662C2×D11—21no—
663C2×D11—21no—
664C2×D11—21no—
665C2×D11—21no—
666C2×D11—21no—
667C2×D11—21no—
668C2×D11—21no—
669C2×D11—44no—
670C2×D11—44no—
671C2×D11—44no—
672C2×D11—44no—
673C2×D11—44no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—88no—
681C2×D11—88no—
682C2×D11—84no—
683C2×D11—84no—
684C2×D11#53412yes—
685C2×D11C2×AGL(1,ℤ/8)12yes—
686C2×D11C2×AGL(1,ℤ/8)12yes—
687C4×C11—21no—
688C4×C11—21no—
689C4×C11—21no—
690C4×C11—42no—
691C4×C11—42no—
692C4×C11—42no—
693C4×C11C2×H(5,𝔽2)12yes—
694Dic11—21no—
695Dic11—21no—
696Dic11—21no—
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×Q8C22×D1111yescharacteristic, complemented
708C22×D4—21no—
709C22×D4—112no—
710C22×D4—112no—
711C22×D4—111no—
712C22×D4—111no—
713C22×D4—221no—
714C22×D4—221no—
715C22×D4—221no—
716C22×D4—221no—
717C22×D4—221no—
718C22×D4—221no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—222no—
722C22×D4—222no—
723C22×D4—221no—
724C22×D4—221no—
725C22×D4—221no—
726C22×D4—444no—
727C22×D4—448no—
728C22×D4C22×D1111yescharacteristic
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×SD16C22×D1114yescomplemented
749C2×D8—114no—
750C2×D8—114no—
751C2×M16—112no—
752C2×M16—114no—
753C2×M16—444no—
754C2×M16C22×D1112yescomplemented
755C22×C8—114no—
756#123—222no—
757#123—222no—
758#123—222no—
759#123—222no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—112no—
763C22⋊Q8—112no—
764C22⋊Q8—221no—
765C22⋊Q8—221no—
766C22⋊Q8C22×D1112yes—
767C22⋊Q8C22×D1112yescomplemented
768#121—21no—
769#121—21no—
770#121—112no—
771#121—112no—
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—221no—
789#121—221no—
790#121—222no—
791#121—222no—
792#121—222no—
793#121—222no—
794#121—221no—
795#121—221no—
796#121—221no—
797#121—221no—
798#121C22×D1112yes—
799#121C22×D1112yes—
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—21no—
817C2×C4⋊C4—111no—
818C2×C4⋊C4—111no—
819C2×C4⋊C4—112no—
820C2×C4⋊C4—112no—
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#103C22×D1114yescomplemented
847#102—114no—
848#102—114no—
849#102—114no—
850#102—114no—
851#102—114no—
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—41no—
862C2×C11—82no—
863C2×C11C2×#53411yescharacteristic
864C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
865C2×C11C2×#57511yescharacteristic
866D11—22no—
867D11—22no—
868D11—22no—
869D11—41no—
870D11—82no—
871D11—82no—
872C24—21no—
873C24—111no—
874C24—111no—
875C24—111no—
876C24—111no—
877C24—111no—
878C24—111no—
879C24—224no—
880C24—222no—
881C24—222no—
882C24—221no—
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—21no—
895C2×Q8—42no—
896C2×Q8C23×D1112yes—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—21no—
900C2×D4—42no—
901C2×D4—44no—
902C2×D4—112no—
903C2×D4—112no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—222no—
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—221no—
920C2×D4—221no—
921C2×D4—442no—
922C2×D4—442no—
923C2×D4—444no—
924C2×D4—444no—
925C2×D4—444no—
926C2×D4—444no—
927C2×D4—444no—
928C2×D4—444no—
929C2×D4—444no—
930C2×D4—448no—
931C2×D4—448no—
932C2×D4—448no—
933C2×D4—448no—
934C2×D4—444no—
935C2×D4—444no—
936C2×D4—444no—
937C2×D4C23×D1112yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—42no—
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—111no—
964C22×C4—224no—
965C22×C4—224no—
966C22×C4—224no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—222no—
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—444no—
984C22×C4—442no—
985C22×C4D4×D1111yescharacteristic
986C22×C4D4×D1111yescharacteristic
987C22×C4D4×D1111yescharacteristic
988C22×C4C23×D1111yescharacteristic
989C22×C4C23×D1111yescharacteristic
990C22×C4C23×D1111yescharacteristic
991SD16—44no—
992SD16—444no—
993D8—444no—
994D8—444no—
995M16—42no—
996M16—228no—
997M16—442no—
998C2×C8—114no—
999C2×C8—444no—
1000C2×C8C23×D1114yes—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—112no—
1006C4⋊C4—112no—
1007C4⋊C4—222no—
1008C4⋊C4—222no—
1009C4⋊C4—222no—
1010C4⋊C4—222no—
1011C4⋊C4—221no—
1012C4⋊C4—221no—
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—22no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—111no—
1044C23—111no—
1045C23—111no—
1046C23—114no—
1047C23—111no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—441no—
1061C23—441no—
1062C23—441no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—442no—
1068C23—442no—
1069C23—442no—
1070C23—442no—
1071C23—444no—
1072C23—444no—
1073C23—4416no—
1074C23—444no—
1075C23—444no—
1076C23—444no—
1077C23—444no—
1078C23—442no—
1079C23—442no—
1080C23—8816no—
1081C23C2×D4×D1111yescharacteristic
1082C23C2×D4×D1111yescharacteristic
1083C23C2×D4×D1111yescharacteristic
1084Q8—24no—
1085Q8—42no—
1086D4—24no—
1087D4—42no—
1088D4—44no—
1089D4—44no—
1090D4—224no—
1091D4—224no—
1092D4—442no—
1093D4—442no—
1094D4—444no—
1095D4—444no—
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—22no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—111no—
1121C2×C4—114no—
1122C2×C4—111no—
1123C2×C4—111no—
1124C2×C4—111no—
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—222no—
1139C2×C4—441no—
1140C2×C4—441no—
1141C2×C4—441no—
1142C2×C4—441no—
1143C2×C4—441no—
1144C2×C4—441no—
1145C2×C4—444no—
1146C2×C4—444no—
1147C2×C4—444no—
1148C2×C4—444no—
1149C2×C4—441no—
1150C2×C4—441no—
1151C2×C4—441no—
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—21no—
1167C22—44no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—84no—
1172C22—112no—
1173C22—112no—
1174C22—112no—
1175C22—228no—
1176C22—221no—
1177C22—221no—
1178C22—221no—
1179C22—221no—
1180C22—221no—
1181C22—221no—
1182C22—221no—
1183C22—221no—
1184C22—221no—
1185C22—444no—
1186C22—444no—
1187C22—444no—
1188C22—444no—
1189C22—444no—
1190C22—442no—
1191C22—442no—
1192C22—442no—
1193C22—442no—
1194C22—442no—
1195C22—442no—
1196C22—884no—
1197C22—884no—
1198C22—888no—
1199C22—888no—
1200C22D11×AGL(1,ℤ/8)12yes—
1201C22#1062330812yes—
1202C22C22×D4×D1111yescharacteristic
1203C4—21no—
1204C4—21no—
1205C4—21no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—112no—
1210C4—221no—
1211C4—221no—
1212C4—221no—
1213C4—442no—
1214C4—442no—
1215C4D11×H(5,𝔽2)12yes—
1216C2—22no—
1217C2—22no—
1218C2—41no—
1219C2—82no—
1220C2—222no—
1221C2—222no—
1222C2—222no—
1223C2—441no—
1224C2—882no—
1225C2—882no—
1226C2D11×#53411yescharacteristic
1227C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1228C2C2×#1062330811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3193C2
socleC22×C11C23×D4
hypercenter#3193D11
hypocenterC11#60750
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C2×D11×#121C2semidirect
3. #13079431C2semidirect
4. #13079418C2semidirect
5. #13079416C2semidirect
6. #13079413C2semidirect
7. #13079386C2semidirect
8. #13079384C2semidirect
9. #13079371C2semidirect
10. #13079366C2semidirect
11. #13078551C2semidirect
12. #13078543C2semidirect
13. #13078230C2semidirect
14. #13077867C2semidirect
15. #13077844C2semidirect
16. D11×#407C2semidirect
17. C11×#3193C2semidirect
18. C22×#4343C22semidirect
20. C22×D4×D11C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
24. C2×#66999C22semidirect
26. C2×#66991C22semidirect
28. C2×#66983C22semidirect
29. C2×#66967C22semidirect
30. C2×M16×D11C22semidirect
36. #10623158C22semidirect
37. #10623158C22semidirect
38. #10623158C22semidirect
45. D11×#121C22semidirect
46. D11×#121C22semidirect
47. C2×#66948C22semidirect
48. C2×#66948C22semidirect
51. C2×#66945C22semidirect
52. C2×C4⋊C4×D11C22semidirect
57. C11×#484C22semidirect
58. C11×#480C22semidirect
59. C11×#468C22semidirect
60. C11×#450C22semidirect
61. C11×#448C22semidirect
62. C11×#407C22semidirect
63. #10622840C22semidirect
64. #10622830C22semidirect
65. #10622820C22semidirect
66. #10622785C22semidirect
67. #10622784C22semidirect
68. #10622782C22semidirect
69. #10622748C22semidirect
70. #10622739C22semidirect
71. #10622662C22semidirect
72. #10622659C22semidirect
73. #10622657C22semidirect
74. #10622652C22semidirect
75. #10622649C22semidirect
76. #10622647C22semidirect
77. #10622581C22semidirect
78. #10622580C22semidirect
79. #10622498C22semidirect
80. #10622496C22semidirect
81. #10622495C22semidirect
82. #10622494C22semidirect
83. #10622424C22semidirect
84. #10622420C22semidirect
85. #10622418C22semidirect
86. #10622416C22semidirect
87. #10622392C22semidirect
88. #10622388C22semidirect
89. #10622386C22semidirect
90. #10622383C22semidirect
91. #10622348C22semidirect
92. #10622348C22semidirect
93. #10622345C22semidirect
94. #10622345C22semidirect
95. #10622339C22semidirect
96. #10622339C22semidirect
97. D11×C22⋊C8C22semidirect
98. D11×C22⋊C8C22semidirect
101. C22×Q8×C11C23semidirect
114. C2×#4343C23semidirect
129. C22×D44C23semidirect
145. C2×C11×SD16C23semidirect
146. C2×C11×M16C23semidirect
150. C11×C22⋊Q8C23semidirect
157. C2×C11×C4⋊C4C23semidirect
164. #66999C23semidirect
165. C2×#4325C23semidirect
174. C2×#4323C23semidirect
182. #66983C23semidirect
190. C2×C4⋊Dic11C23semidirect
194. C2×#4318C23semidirect
197. C2×D88C23semidirect
199. C2×C8×D11C23semidirect
207. #66948C23semidirect
219. #66945C23semidirect
240. C11×#107C23semidirect
241. C11×#103C23semidirect
242. C11×#102C23semidirect
244. C11×C22⋊C8C23semidirect
245. #66899C23semidirect
246. #66896C23semidirect
248. C22⋊(C11⋊C8)C23semidirect
249. #66885C23semidirect
250. #66885C23semidirect
252. (C2×D11)⋊C8C23semidirect
253. #66881C23semidirect
254. #66873C23semidirect
255. #66873C23semidirect
256. #66872C23semidirect
257. #66871C23semidirect
426. #3193D11semidirect
482. C22×D11AGL(1,ℤ/8)semidirect
579. C2×C22⋊Q8C2×D11semidirect
603. #484C2×D11semidirect
613. #480C2×D11semidirect
617. #468C2×D11semidirect
624. #450C2×D11semidirect
628. #448C2×D11semidirect
641. #407C2×D11semidirect
707. C22×Q8C22×D11semidirect
748. C2×SD16C22×D11semidirect
754. C2×M16C22×D11semidirect
767. C22⋊Q8C22×D11semidirect
826. C2×C4⋊C4C22×D11semidirect
842. #107C22×D11semidirect
846. #103C22×D11semidirect
852. #102C22×D11semidirect
858. C22⋊C8C22×D11semidirect
1035. C11#60750semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×D11×#1212
#130794312
#130794182
#130794162
#130794132
#130793862
#130793842
#130793712
#130793662
#130785512
#130785432
#130782302
#130778672
#130778442
D11×#4072
C11×#31932
#6075011