Finite Group Databasebeta

← #15624545

Subgroups — #15624545

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×#10623158C211yesmaximal, characteristic, complemented
2C2×#10623359C211yesmaximal, characteristic, complemented
3#13079457C214yesmaximal, complemented
4#13079449C212yesmaximal, complemented
5#13079433C212yesmaximal, complemented
6#13079408C214yesmaximal, complemented
7#13079400C212yesmaximal, complemented
8#13079384C212yesmaximal, complemented
9#13078560C211yesmaximal, characteristic, complemented
10#13078557C211yesmaximal, characteristic, complemented
11#13078546C212yesmaximal, complemented
12#13078240C212yesmaximal, complemented
13#13078238C212yesmaximal, complemented
14#13077868C211yesmaximal, characteristic, complemented
15#13077857C212yesmaximal, complemented
16D11×#407C211yesmaximal, characteristic, complemented
17C11×#3007C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C22×#4343C2211yescharacteristic, complemented
20C23×C4×D11C2211yescharacteristic
21C2×C11×#137C2212yescomplemented
22C2×C11×C22⋊Q8C2211yescharacteristic
23#10623359—21no—
24#10623359—21no—
25#10623359—21no—
26#10623359—21no—
27#10623359C2212yes—
28#10623359C2212yes—
29#10623359C2212yescomplemented
30#10623359C2212yescomplemented
31C2×#67002C2212yescomplemented
32C2×#66999C2211yescharacteristic, complemented
33C2×#66999C2211yescharacteristic, complemented
34C2×#66999C2211yescharacteristic, complemented
35C2×#66991C2211yescharacteristic, complemented
36C2×#66991C2211yescharacteristic, complemented
37C2×#66990—21no—
38C2×#66988—21no—
39C2×#66983C2211yescharacteristic
40C2×C4×C22⋊D11—21no—
41C2×C4×C22⋊D11—21no—
42C2×#66979C2211yescharacteristic
43C2×M16×D11C2212yescomplemented
44#10623158—21no—
45#10623158—21no—
46#10623158—21no—
47#10623158—21no—
48#10623158C2212yes—
49#10623158C2212yes—
50#10623158C2212yescomplemented
51#10623158C2212yescomplemented
52C2×#66948C2211yescharacteristic, complemented
53C2×#66947—21no—
54C2×#66946—21no—
55C2×#66945C2211yescharacteristic, complemented
56C2×#66935—21no—
57C2×(C22⋊D11)⋊C4—21no—
58C11×#452C2214yescomplemented
59C11×#451C2212yescomplemented
60C11×#450C2212yescomplemented
61C11×#417C2212yescomplemented
62C11×#407C2211yescharacteristic
63#10622851C2214yescomplemented
64#10622845C2212yescomplemented
65#10622840C2212yescomplemented
66#10622838C2212yescomplemented
67#10622830C2212yescomplemented
68#10622820C2211yescharacteristic
69#10622802C2214yescomplemented
70#10622801C2214yescomplemented
71#10622800C2214yescomplemented
72#10622800C2214yescomplemented
73#10622787C2214yescomplemented
74#10622785C2214yescomplemented
75#10622785C2214yescomplemented
76#10622784C2214yescomplemented
77#10622744C2212yescomplemented
78#10622739C2212yescomplemented
79#10622734C2212yescomplemented
80#10622658C2214yescomplemented
81#10622657C2212yescomplemented
82#10622656C2212yescomplemented
83#10622577C2212yescomplemented
84#10622428C2214yescomplemented
85#10622427C2214yescomplemented
86#10622425C2214yescomplemented
87#10622420C2214yescomplemented
88#10622397C2214yescomplemented
89#10622395C2214yescomplemented
90#10622392C2214yescomplemented
91#10622388C2214yescomplemented
92#10622350C2214yescomplemented
93#10622349C2212yescomplemented
94#10622348C2212yescomplemented
95#10622339C2212yescomplemented
96#10622339C2212yescomplemented
97D11×C22⋊C8C2212yescomplemented
98D11×C22⋊C8C2212yescomplemented
99C24×D11D411yescharacteristic
100C2×C11×#41—21no—
101C2×C11×#41—21no—
102C2×C11×#41—44no—
103C2×C11×#41C2312yes—
104C2×C11×#41C2312yes—
105C22×Q8×C11C2311yescharacteristic
106C22×Q8×C11C2311yescharacteristic
107C22×D4×C11—21no—
108C22×D4×C11C2311yescharacteristic
109C23×C4×C11—21no—
110C23×C4×C11C2311yescharacteristic
111C22×C22⋊D11—21no—
112C22×C22⋊D11—21no—
113C22×C22⋊D11—21no—
114C23×Dic11D411yescharacteristic
115C2×#4343—21no—
116C2×#4343—21no—
117C2×#4343—44no—
118C2×#4343C2312yes—
119C2×#4343C2312yes—
120C22×D44—21no—
121C22×D44—21no—
122C22×D44C2311yescharacteristic
123C22×C4×D11—21no—
124C22×C4×D11—44no—
125C22×C4×D11D411yescharacteristic
126C22×C4×D11D411yescharacteristic
127C22×C4×D11D411yescharacteristic
128C22×C4×D11D411yescharacteristic
129C22×C4×D11D411yescharacteristic
130C22×C4×D11D411yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C11×#137—44no—
138C2×C11×Q16C2314yescomplemented
139C2×C11×SD16C2314yescomplemented
140C2×C11×M16C2312yes—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8—21no—
143C11×C22⋊Q8C2312yes—
144C11×C22⋊Q8C2312yes—
145C2×C11×C4⋊C4—21no—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4—21no—
148C2×C22⋊Dic11—21no—
149C2×C22⋊Dic11—21no—
150C2×C22⋊Dic11—21no—
151#67002—44no—
152#66999—21no—
153#66999—21no—
154#66999—21no—
155#66999—21no—
156#66999—21no—
157#66999—21no—
158#66999C2312yes—
159#66999C2312yes—
160#66999C2312yes—
161#66999C2312yes—
162#66999C2312yes—
163#66999C2312yes—
164C2×#4325C2314yescomplemented
165#66991—21no—
166#66991—21no—
167#66991—21no—
168#66991—21no—
169#66991C2312yes—
170#66991C2312yes—
171#66991C2312yes—
172#66991C2312yes—
173#66990—22no—
174#66990—22no—
175#66990—22no—
176#66990—22no—
177#66988—22no—
178#66988—22no—
179#66988—22no—
180#66988—22no—
181C2×#4323C2314yescomplemented
182#66983—21no—
183#66983—21no—
184#66983C2312yes—
185#66983C2312yes—
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—
194C2×(C2×D11)⋊C4—21no—
195C2×(C2×D11)⋊C4—21no—
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#66979C2312yes—
203#66979C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×Dic11⋊C4—21no—
208C2×Dic11⋊C4—21no—
209C2×Dic11⋊C4—21no—
210C2×C4×Dic11—21no—
211C2×C4×Dic11—21no—
212C2×#4318C2312yes—
213M16×D11—44no—
214C2×#4313C2314yes—
215C2×C8×D11C2314yes—
216#66948—21no—
217#66948—21no—
218#66948C2312yes—
219#66948C2312yes—
220#66947—22no—
221#66947—22no—
222#66947—22no—
223#66947—22no—
224#66946—22no—
225#66946—22no—
226#66946—22no—
227#66946—22no—
228#66945—21no—
229#66945—21no—
230#66945C2312yes—
231#66945C2312yes—
232#66935—22no—
233#66935—22no—
234#66935—22no—
235#66935—22no—
236(C22⋊D11)⋊C4—22no—
237(C22⋊D11)⋊C4—22no—
238(C22⋊D11)⋊C4—22no—
239(C22⋊D11)⋊C4—22no—
240C11×#103C2314yescomplemented
241C11×#102C2314yescomplemented
242C11×C22⋊C8C2312yes—
243C11×C22⋊C8C2312yes—
244#66899C2314yescomplemented
245#66899C2314yescomplemented
246#66899C2314yescomplemented
247#66896C2314yescomplemented
248C22⋊(C11⋊C8)C2312yes—
249C22⋊(C11⋊C8)C2312yes—
250#66885C2314yescomplemented
251#66885C2314yescomplemented
252(C2×D11)⋊C8C2314yes—
253(C2×D11)⋊C8C2314yes—
254#66882C2314yescomplemented
255#66881C2314yescomplemented
256#66872C2314yescomplemented
257#66871C2314yescomplemented
258#60752—111nomaximal, Sylow
259C24×C11—21no—
260C24×C11C2×D411yescharacteristic
261C23×D11—21no—
262C23×D11—42no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11C2×D411yescharacteristic
266C23×D11C2×D411yescharacteristic
267C23×D11C2×D411yescharacteristic
268C23×D11C2×D411yescharacteristic
269C23×D11C2×D411yescharacteristic
270C23×D11C2×D411yescharacteristic
271C11×#41—24no—
272C11×#41—24no—
273C11×#41—42no—
274C11×#41—42no—
275C11×#41—44no—
276C11×#41—44no—
277C2×Q8×C11—21no—
278C2×Q8×C11—21no—
279C2×Q8×C11—24no—
280C2×Q8×C11—42no—
281C2×Q8×C11C2412yes—
282C2×Q8×C11C2412yes—
283C2×D4×C11—22no—
284C2×D4×C11—22no—
285C2×D4×C11—21no—
286C2×D4×C11—42no—
287C2×D4×C11—44no—
288C2×D4×C11C2412yes—
289C22×C4×C11—24no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—44no—
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
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—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—42no—
315C22×Dic11C2×D411yescharacteristic
316C22×Dic11C2×D411yescharacteristic
317C22×Dic11C2×D411yescharacteristic
318C22×Dic11C2×D411yescharacteristic
319C22×Dic11C2×D411yescharacteristic
320C22×Dic11C2×D411yescharacteristic
321#4343—44no—
322#4343—44no—
323#4343—44no—
324#4343—44no—
325C2×D44—22no—
326C2×D44—22no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—21no—
330C2×D44—24no—
331C2×D44—44no—
332C2×D44—44no—
333C2×D44C2412yes—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—44no—
349C2×C4×D11C2×D411yescharacteristic
350C2×C4×D11C2×D411yescharacteristic
351C2×C4×D11C2×D411yescharacteristic
352C2×C4×D11C2×D411yescharacteristic
353C2×C4×D11C2×D411yescharacteristic
354C2×C4×D11C2×D411yescharacteristic
355C2×C4×D11C2×D411yescharacteristic
356C2×C4×D11C2×D411yescharacteristic
357C2×C4×D11C2×D411yescharacteristic
358C2×C4×D11C2×D411yescharacteristic
359C2×C4×D11C2×D411yescharacteristic
360C2×C4×D11C2×D411yescharacteristic
361C2×C4×D11C2411yescharacteristic
362C2×C4×D11C2411yescharacteristic
363C2×C4×D11C2411yescharacteristic
364C2×C4×D11C2411yescharacteristic
365C11×Q16—44no—
366C11×SD16—44no—
367C11×M16—24no—
368C2×C8×C11C2414yes—
369C11×C4⋊C4—21no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—22no—
372C11×C4⋊C4C2412yes—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—22no—
377C22⋊Dic11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—22no—
380C22⋊Dic11—22no—
381#4325—44no—
382#4323—44no—
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—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—22no—
395C4⋊Dic11—21no—
396C4⋊Dic11—21no—
397C4⋊Dic11—21no—
398C4⋊Dic11C2412yes—
399C4⋊Dic11C2412yes—
400C4⋊Dic11C2412yes—
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—
411#4318—24no—
412C2×C11⋊C8C2414yes—
413#4313—44no—
414C8×D11—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#3007D1111yescharacteristic, complemented
429#3006—111no—
430#3005—112no—
431C2×#407—111no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—41no—
436C23×C11—42no—
437C23×C11—42no—
438C23×C11—42no—
439C23×C11C22×D411yescharacteristic
440C23×C11C22×D411yescharacteristic
441C23×C11C22×D411yescharacteristic
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—416no—
462C22×D11—42no—
463C22×D11—42no—
464C22×D11—42no—
465C22×D11C22×D411yescharacteristic
466C22×D11C22×D411yescharacteristic
467C22×D11C22×D411yescharacteristic
468C22×D11C22×D411yescharacteristic
469Q8×C11—22no—
470Q8×C11—24no—
471Q8×C11—22no—
472Q8×C11—42no—
473Q8×C11—42no—
474D4×C11—22no—
475D4×C11—22no—
476D4×C11—42no—
477D4×C11—44no—
478D4×C11—44no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—44no—
488C2×C4×C11—42no—
489C2×C4×C11—42no—
490C2×C4×C11—42no—
491C2×C4×C11—44no—
492C2×C4×C11C22×D411yescharacteristic
493C2×C4×C11C22×D411yescharacteristic
494C2×C4×C11C22×D411yescharacteristic
495C2×C4×C11H(5,𝔽2)14yes—
496C2×C4×C11C2511yescharacteristic
497C22⋊D11—44no—
498C22⋊D11—44no—
499C22⋊D11—44no—
500C22⋊D11—44no—
501C22⋊D11—44no—
502C22⋊D11—44no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—42no—
513C2×Dic11—42no—
514C2×Dic11—42no—
515C2×Dic11C22×D411yescharacteristic
516C2×Dic11C22×D411yescharacteristic
517C2×Dic11C22×D411yescharacteristic
518C2×Dic11C22×D411yescharacteristic
519D44—24no—
520D44—44no—
521D44—44no—
522D44—44no—
523D44—44no—
524D44—42no—
525C4×D11—22no—
526C4×D11—22no—
527C4×D11—22no—
528C4×D11—22no—
529C4×D11—22no—
530C4×D11—22no—
531C4×D11—22no—
532C4×D11—22no—
533C4×D11—41no—
534C4×D11—41no—
535C4×D11—41no—
536C4×D11—41no—
537C4×D11—41no—
538C4×D11—41no—
539C4×D11—41no—
540C4×D11—41no—
541C4×D11—44no—
542C4×D11—44no—
543C8×C11—24no—
544C11⋊C8—24no—
545C22×#41—111no—
546C22×#41C2×D1111yescharacteristic
547C24×C4—111no—
548C2×#137C2×D1112yescomplemented
549C2×AGL(1,ℤ/8)—112no—
550C22×M16—112no—
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⋊Q8C2×D1111yescharacteristic
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#452C2×D1114yescomplemented
606#451C2×D1112yescomplemented
607#450C2×D1112yescomplemented
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#417C2×D1112yescomplemented
619#407—111no—
620#407—112no—
621#407—112no—
622#407—112no—
623#407C2×D1111yescharacteristic
624C2×C22⋊C8—112no—
625C2×C22⋊C8—112no—
626C22×C11—21no—
627C22×C11—21no—
628C22×C11—21no—
629C22×C11—21no—
630C22×C11—21no—
631C22×C11—21no—
632C22×C11—21no—
633C22×C11—44no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—84no—
638C22×C11#53412yes—
639C22×C11#57512yes—
640C22×C11C23×D411yescharacteristic
641C2×D11—21no—
642C2×D11—21no—
643C2×D11—21no—
644C2×D11—21no—
645C2×D11—21no—
646C2×D11—21no—
647C2×D11—21no—
648C2×D11—21no—
649C2×D11—21no—
650C2×D11—21no—
651C2×D11—21no—
652C2×D11—44no—
653C2×D11—44no—
654C2×D11—44no—
655C2×D11—44no—
656C2×D11—44no—
657C2×D11—44no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—84no—
662C2×D11#57512yes—
663C4×C11—21no—
664C4×C11—21no—
665C4×C11—42no—
666C4×C11—42no—
667C4×C11—42no—
668C4×C11#53412yes—
669C4×C11C2×H(5,𝔽2)12yes—
670Dic11—21no—
671Dic11—21no—
672Dic11—21no—
673Dic11—21no—
674Dic11—42no—
675Dic11—42no—
676Dic11—42no—
677C25—111no—
678C2×#41—21no—
679C2×#41—21no—
680C2×#41—44no—
681C2×#41—112no—
682C2×#41—112no—
683C2×#41—221no—
684C2×#41—221no—
685C2×#41—444no—
686C2×#41C22×D1112yes—
687C2×#41C22×D1112yes—
688C22×Q8C22×D1111yescharacteristic
689C22×Q8C22×D1111yescharacteristic
690C22×D4—21no—
691C22×D4—111no—
692C22×D4—221no—
693C22×D4—221no—
694C22×D4—221no—
695C22×D4—221no—
696C22×D4—221no—
697C22×D4C22×D1111yescharacteristic
698C23×C4—21no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—111no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—221no—
713C23×C4—444no—
714C23×C4C22×D1111yescharacteristic
715#137—44no—
716AGL(1,ℤ/8)—444no—
717C2×Q16C22×D1114yescomplemented
718C2×SD16—114no—
719C2×SD16C22×D1114yescomplemented
720C2×D8—114no—
721C2×M16—112no—
722C2×M16—114no—
723C2×M16—444no—
724C2×M16C22×D1112yes—
725C22×C8—114no—
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—21no—
735C22⋊Q8—21no—
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⋊Q8C22×D1112yes—
749C22⋊Q8C22×D1112yes—
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—21no—
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⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4—21no—
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#103C22×D1114yescomplemented
826#102—114no—
827#102—114no—
828#102—114no—
829#102C22×D1114yescomplemented
830C22⋊C8—112no—
831C22⋊C8—112no—
832C22⋊C8—114no—
833C22⋊C8—114no—
834C22⋊C8C22×D1112yes—
835C22⋊C8C22×D1112yes—
836C2×C11—22no—
837C2×C11—22no—
838C2×C11—41no—
839C2×C11—82no—
840C2×C11C2×#53411yescharacteristic
841C2×C11C2×#57511yescharacteristic
842C2×C11C2×#57511yescharacteristic
843D11—22no—
844D11—41no—
845D11—41no—
846D11—41no—
847D11—82no—
848C24—21no—
849C24—111no—
850C24—111no—
851C24—111no—
852C24—111no—
853C24—111no—
854C24—111no—
855C24—221no—
856C24—442no—
857C24—442no—
858C24—442no—
859C24D4×D1111yescharacteristic
860#41—24no—
861#41—24no—
862#41—42no—
863#41—42no—
864#41—44no—
865#41—44no—
866#41—444no—
867#41—444no—
868#41—444no—
869#41—444no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—24no—
873C2×Q8—42no—
874C2×Q8C23×D1112yes—
875C2×Q8C23×D1112yes—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—21no—
879C2×D4—42no—
880C2×D4—44no—
881C2×D4—112no—
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—222no—
891C2×D4—222no—
892C2×D4—221no—
893C2×D4—224no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4C23×D1112yes—
900C22×C4—24no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—44no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—111no—
913C22×C4—111no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—111no—
919C22×C4—111no—
920C22×C4—111no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—224no—
932C22×C4—224no—
933C22×C4—221no—
934C22×C4—221no—
935C22×C4—221no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4—442no—
942C22×C4—442no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—444no—
947C22×C4—442no—
948C22×C4D4×D1111yescharacteristic
949C22×C4D4×D1111yescharacteristic
950C22×C4D4×D1111yescharacteristic
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954Q16—44no—
955SD16—44no—
956SD16—444no—
957D8—444no—
958M16—24no—
959M16—224no—
960M16—444no—
961C2×C8—114no—
962C2×C8—444no—
963C2×C8C23×D1114yes—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—112no—
968C4⋊C4—112no—
969C4⋊C4—112no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—221no—
977C4⋊C4—221no—
978C4⋊C4—221no—
979C4⋊C4C23×D1112yes—
980C22⋊C4—22no—
981C22⋊C4—22no—
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—41no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—111no—
1013C23—111no—
1014C23—111no—
1015C23—111no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—222no—
1023C23—222no—
1024C23—441no—
1025C23—441no—
1026C23—441no—
1027C23—441no—
1028C23—441no—
1029C23—441no—
1030C23—441no—
1031C23—441no—
1032C23—441no—
1033C23—441no—
1034C23—441no—
1035C23—442no—
1036C23—442no—
1037C23—4416no—
1038C23—442no—
1039C23C2×D4×D1111yescharacteristic
1040C23C2×D4×D1111yescharacteristic
1041C23C2×D4×D1111yescharacteristic
1042Q8—24no—
1043Q8—22no—
1044Q8—22no—
1045Q8—42no—
1046Q8—42no—
1047D4—22no—
1048D4—22no—
1049D4—42no—
1050D4—44no—
1051D4—44no—
1052D4—224no—
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—44no—
1073C2×C4—42no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—44no—
1077C2×C4—111no—
1078C2×C4—111no—
1079C2×C4—111no—
1080C2×C4—111no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—442no—
1109C2×C4—442no—
1110C2×C4—442no—
1111C2×C4C2×D4×D1111yescharacteristic
1112C2×C4C2×D4×D1111yescharacteristic
1113C2×C4C2×D4×D1111yescharacteristic
1114C2×C4#6703714yes—
1115C2×C4C24×D1111yescharacteristic
1116C8—24no—
1117C8—224no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—44no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—84no—
1130C22—112no—
1131C22—221no—
1132C22—221no—
1133C22—221no—
1134C22—221no—
1135C22—221no—
1136C22—221no—
1137C22—221no—
1138C22—221no—
1139C22—221no—
1140C22—221no—
1141C22—221no—
1142C22—444no—
1143C22—444no—
1144C22—444no—
1145C22—444no—
1146C22—444no—
1147C22—444no—
1148C22—442no—
1149C22—442no—
1150C22—442no—
1151C22—884no—
1152C22#1062312012yes—
1153C22#1062330812yes—
1154C22C22×D4×D1111yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—221no—
1161C4—221no—
1162C4—221no—
1163C4—221no—
1164C4—442no—
1165C4—442no—
1166C4—442no—
1167C4#1062312012yes—
1168C4C2×#6703712yes—
1169C2—22no—
1170C2—22no—
1171C2—41no—
1172C2—82no—
1173C2—222no—
1174C2—441no—
1175C2—441no—
1176C2—441no—
1177C2—882no—
1178C2C2×#1062312011yescharacteristic
1179C2D11×#57511yescharacteristic
1180C2C2×#1062330811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3007C2
socleC22×C11C23×D4
hypercenter#3007D11
hypocenterC11#60752
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C2×#10623359C2semidirect
3. #13079457C2semidirect
4. #13079449C2semidirect
5. #13079433C2semidirect
6. #13079408C2semidirect
7. #13079400C2semidirect
8. #13079384C2semidirect
9. #13078560C2semidirect
10. #13078557C2semidirect
11. #13078546C2semidirect
12. #13078240C2semidirect
13. #13078238C2semidirect
14. #13077868C2semidirect
15. #13077857C2semidirect
16. D11×#407C2semidirect
17. C11×#3007C2semidirect
19. C22×#4343C22semidirect
21. C2×C11×#137C22semidirect
29. #10623359C22semidirect
30. #10623359C22semidirect
31. C2×#67002C22semidirect
32. C2×#66999C22semidirect
33. C2×#66999C22semidirect
34. C2×#66999C22semidirect
35. C2×#66991C22semidirect
36. C2×#66991C22semidirect
43. C2×M16×D11C22semidirect
50. #10623158C22semidirect
51. #10623158C22semidirect
52. C2×#66948C22semidirect
55. C2×#66945C22semidirect
58. C11×#452C22semidirect
59. C11×#451C22semidirect
60. C11×#450C22semidirect
61. C11×#417C22semidirect
63. #10622851C22semidirect
64. #10622845C22semidirect
65. #10622840C22semidirect
66. #10622838C22semidirect
67. #10622830C22semidirect
69. #10622802C22semidirect
70. #10622801C22semidirect
71. #10622800C22semidirect
72. #10622800C22semidirect
73. #10622787C22semidirect
74. #10622785C22semidirect
75. #10622785C22semidirect
76. #10622784C22semidirect
77. #10622744C22semidirect
78. #10622739C22semidirect
79. #10622734C22semidirect
80. #10622658C22semidirect
81. #10622657C22semidirect
82. #10622656C22semidirect
83. #10622577C22semidirect
84. #10622428C22semidirect
85. #10622427C22semidirect
86. #10622425C22semidirect
87. #10622420C22semidirect
88. #10622397C22semidirect
89. #10622395C22semidirect
90. #10622392C22semidirect
91. #10622388C22semidirect
92. #10622350C22semidirect
93. #10622349C22semidirect
94. #10622348C22semidirect
95. #10622339C22semidirect
96. #10622339C22semidirect
97. D11×C22⋊C8C22semidirect
98. D11×C22⋊C8C22semidirect
138. C2×C11×Q16C23semidirect
139. C2×C11×SD16C23semidirect
164. C2×#4325C23semidirect
181. C2×#4323C23semidirect
240. C11×#103C23semidirect
241. C11×#102C23semidirect
244. #66899C23semidirect
245. #66899C23semidirect
246. #66899C23semidirect
247. #66896C23semidirect
250. #66885C23semidirect
251. #66885C23semidirect
254. #66882C23semidirect
255. #66881C23semidirect
256. #66872C23semidirect
257. #66871C23semidirect
428. #3007D11semidirect
548. C2×#137C2×D11semidirect
605. #452C2×D11semidirect
606. #451C2×D11semidirect
607. #450C2×D11semidirect
618. #417C2×D11semidirect
717. C2×Q16C22×D11semidirect
719. C2×SD16C22×D11semidirect
825. #103C22×D11semidirect
829. #102C22×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×#106231582
C2×#106233592
#130794572
#130794492
#130794332
#130794082
#130794002
#130793842
#130785602
#130785572
#130785462
#130782402
#130782382
#130778682
#130778572
D11×#4072
C11×#30072
#6075211