Finite Group Databasebeta

← #15624527

Subgroups — #15624527

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
3#13079444C214yesmaximal, complemented
4#13079438C212yesmaximal, complemented
5#13079419C212yesmaximal, complemented
6#13079395C214yesmaximal, complemented
7#13079389C212yesmaximal, complemented
8#13079370C212yesmaximal, complemented
9#13078565C211yesmaximal, characteristic, complemented
10#13078560C211yesmaximal, characteristic, complemented
11#13078537C212yesmaximal, complemented
12#13078249C212yesmaximal, complemented
13#13078240C212yesmaximal, complemented
14#13077876C211yesmaximal, characteristic, complemented
15#13077848C212yesmaximal, complemented
16D11×#407C211yesmaximal, characteristic, complemented
17C11×#3007C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic, 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#10623359C2212yes—
30#10623359C2212yes—
31C2×#67004C2212yescomplemented
32C2×#66999C2211yescharacteristic
33C2×#66999C2211yescharacteristic
34C2×#66999C2211yescharacteristic, complemented
35C2×#66991C2211yescharacteristic
36C2×#66991C2211yescharacteristic
37C2×#66990—21no—
38C2×#66988—21no—
39C2×C4×C22⋊D11—21no—
40C2×C4×C22⋊D11—21no—
41C2×#66979C2211yescharacteristic
42C2×#66977C2211yescharacteristic
43C2×M16×D11C2212yescomplemented
44D11×C22⋊Q8—21no—
45D11×C22⋊Q8—21no—
46D11×C22⋊Q8—21no—
47D11×C22⋊Q8—21no—
48D11×C22⋊Q8C2212yes—
49D11×C22⋊Q8C2212yes—
50D11×C22⋊Q8C2212yescomplemented
51D11×C22⋊Q8C2212yescomplemented
52C2×#66950C2211yescharacteristic, complemented
53C2×#66949—21no—
54C2×C4⋊C4×D11—21no—
55C2×C4⋊C4×D11C2211yescharacteristic, complemented
56C2×C22⋊C4×D11—21no—
57C2×#66931—21no—
58C11×#452C2214yescomplemented
59C11×#451C2212yescomplemented
60C11×#450C2212yescomplemented
61C11×#417C2212yescomplemented
62C11×#407C2211yescharacteristic
63#10622852C2214yescomplemented
64#10622845C2212yescomplemented
65#10622841C2212yescomplemented
66#10622838C2212yescomplemented
67#10622831C2212yescomplemented
68#10622820C2211yescharacteristic
69#10622802C2214yescomplemented
70#10622801C2214yescomplemented
71#10622799C2214yescomplemented
72#10622799C2214yescomplemented
73#10622787C2214yescomplemented
74#10622784C2214yescomplemented
75#10622783C2214yescomplemented
76#10622783C2214yescomplemented
77#10622739C2212yescomplemented
78#10622734C2212yescomplemented
79#10622733C2212yescomplemented
80#10622658C2214yescomplemented
81#10622657C2212yescomplemented
82#10622656C2212yescomplemented
83#10622577C2212yescomplemented
84#10622429C2214yescomplemented
85#10622426C2214yescomplemented
86#10622422C2214yescomplemented
87#10622418C2214yescomplemented
88#10622393C2214yescomplemented
89#10622391C2214yescomplemented
90#10622390C2214yescomplemented
91#10622387C2214yescomplemented
92#10622339C2212yes—
93#10622339C2212yescomplemented
94D11×C22⋊C8C2212yes—
95D11×C22⋊C8C2212yescomplemented
96#10622336C2214yescomplemented
97#10622335C2212yescomplemented
98#10622334C2212yescomplemented
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—
113C23×Dic11D411yescharacteristic
114C2×Q8×D11—21no—
115C2×Q8×D11—21no—
116C2×Q8×D11—44no—
117C2×Q8×D11C2312yes—
118C2×Q8×D11C2312yes—
119C22×C4×D11—21no—
120C22×C4×D11—21no—
121C22×C4×D11—44no—
122C22×C4×D11D411yescharacteristic
123C22×C4×D11D411yescharacteristic
124C22×C4×D11D411yescharacteristic
125C22×C4×D11D411yescharacteristic
126C22×C4×D11D411yescharacteristic
127C22×C4×D11D411yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×Dic22—21no—
135C22×Dic22C2311yescharacteristic
136C11×#137—44no—
137C2×C11×Q16C2314yescomplemented
138C2×C11×SD16C2314yescomplemented
139C2×C11×M16C2312yes—
140C11×C22⋊Q8—21no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8C2312yes—
143C11×C22⋊Q8C2312yes—
144C2×C11×C4⋊C4—21no—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C22⋊C4—21no—
147C2×C22⋊Dic11—21no—
148C2×C22⋊Dic11—21no—
149C2×C22⋊Dic11—21no—
150C2×C22⋊Dic11—21no—
151#67004—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×#4326C2314yescomplemented
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×#4324C2314yescomplemented
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—
190C2×(C2×D11)⋊C4—21no—
191C2×(C2×D11)⋊C4—21no—
192C2×(C2×D11)⋊C4—21no—
193C2×(C2×D11)⋊C4—21no—
194#66979—21no—
195#66979—21no—
196#66979C2312yes—
197#66979C2312yes—
198C2×C4⋊Dic11—21no—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202#66977—21no—
203#66977—21no—
204#66977C2312yes—
205#66977C2312yes—
206C2×Dic11⋊C4—21no—
207C2×Dic11⋊C4—21no—
208C2×Dic11⋊C4—21no—
209C2×Dic11⋊C4—21no—
210C2×Dic11⋊C4—21no—
211C2×C4×Dic11—21no—
212C2×#4318C2312yes—
213M16×D11—44no—
214C2×#4313C2314yes—
215C2×C8×D11C2314yes—
216#66950—21no—
217#66950—21no—
218#66950C2312yes—
219#66950C2312yes—
220#66949—22no—
221#66949—22no—
222#66949—22no—
223#66949—22no—
224C4⋊C4×D11—22no—
225C4⋊C4×D11—22no—
226C4⋊C4×D11—22no—
227C4⋊C4×D11—22no—
228C4⋊C4×D11—21no—
229C4⋊C4×D11—21no—
230C4⋊C4×D11C2312yes—
231C4⋊C4×D11C2312yes—
232C22⋊C4×D11—22no—
233C22⋊C4×D11—22no—
234C22⋊C4×D11—22no—
235C22⋊C4×D11—22no—
236#66931—22no—
237#66931—22no—
238#66931—22no—
239#66931—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(C2×D11)⋊C8C2314yes—
251(C2×D11)⋊C8C2314yes—
252#66882C2314yescomplemented
253#66881C2314yescomplemented
254#66880C2314yescomplemented
255#66880C2314yescomplemented
256#66872C2314yescomplemented
257#66871C2314yescomplemented
258#60751—111nomaximal, Sylow
259C24×C11—21no—
260C24×C11C2×D411yescharacteristic
261C23×D11—24no—
262C23×D11—42no—
263C23×D11—42no—
264C23×D11C2×D411yescharacteristic
265C23×D11C2×D411yescharacteristic
266C23×D11C2×D411yescharacteristic
267C23×D11C2×D411yescharacteristic
268C23×D11C2×D411yescharacteristic
269C23×D11C2×D411yescharacteristic
270C11×#41—24no—
271C11×#41—24no—
272C11×#41—42no—
273C11×#41—42no—
274C11×#41—44no—
275C11×#41—44no—
276C2×Q8×C11—21no—
277C2×Q8×C11—21no—
278C2×Q8×C11—24no—
279C2×Q8×C11—42no—
280C2×Q8×C11C2412yes—
281C2×Q8×C11C2412yes—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—21no—
285C2×D4×C11—42no—
286C2×D4×C11—44no—
287C2×D4×C11C2412yes—
288C22×C4×C11—24no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—44no—
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—44no—
306C2×C22⋊D11—44no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—42no—
312C22×Dic11C2×D411yescharacteristic
313C22×Dic11C2×D411yescharacteristic
314C22×Dic11C2×D411yescharacteristic
315C22×Dic11C2×D411yescharacteristic
316C22×Dic11C2×D411yescharacteristic
317C22×Dic11C2×D411yescharacteristic
318Q8×D11—44no—
319Q8×D11—44no—
320Q8×D11—44no—
321Q8×D11—44no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—24no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—44no—
339C2×C4×D11—44no—
340C2×C4×D11C2×D411yescharacteristic
341C2×C4×D11C2×D411yescharacteristic
342C2×C4×D11C2×D411yescharacteristic
343C2×C4×D11C2×D411yescharacteristic
344C2×C4×D11C2×D411yescharacteristic
345C2×C4×D11C2×D411yescharacteristic
346C2×C4×D11C2×D411yescharacteristic
347C2×C4×D11C2×D411yescharacteristic
348C2×C4×D11C2×D411yescharacteristic
349C2×C4×D11C2×D411yescharacteristic
350C2×C4×D11C2×D411yescharacteristic
351C2×C4×D11C2×D411yescharacteristic
352C2×C4×D11C2411yescharacteristic
353C2×C4×D11C2411yescharacteristic
354C2×C4×D11C2411yescharacteristic
355C2×C4×D11C2411yescharacteristic
356C2×Dic22—22no—
357C2×Dic22—22no—
358C2×Dic22—21no—
359C2×Dic22—24no—
360C2×Dic22—44no—
361C2×Dic22C2412yes—
362C11×Q16—44no—
363C11×SD16—44no—
364C11×M16—24no—
365C2×C8×C11C2414yes—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—21no—
369C11×C4⋊C4C2412yes—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—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—
380#4326—44no—
381#4324—44no—
382(C2×D11)⋊C4—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—
390C4⋊Dic11—22no—
391C4⋊Dic11—22no—
392C4⋊Dic11—21no—
393C4⋊Dic11—21no—
394C4⋊Dic11—21no—
395C4⋊Dic11C2412yes—
396C4⋊Dic11C2412yes—
397C4⋊Dic11C2412yes—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410#4318—24no—
411C2×C11⋊C8C2414yes—
412#4313—44no—
413C8×D11—44no—
414C2×#525—111no—
415C22×C22⋊Q8—111no—
416#3196—114no—
417#3195—112no—
418#3193—112no—
419#3190—114no—
420#3189—112no—
421#3187—112no—
422#3095—111no—
423#3095—111no—
424#3092—112no—
425#3056—112no—
426#3056—112no—
427#3007—111no—
428#3007D1111yescharacteristic, complemented
429#3004—112no—
430C2×#407—111no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—41no—
435C23×C11—42no—
436C23×C11—42no—
437C23×C11—42no—
438C23×C11C22×D411yescharacteristic
439C23×C11C22×D411yescharacteristic
440C23×C11C22×D411yescharacteristic
441C22×D11—22no—
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—22no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—416no—
459C22×D11#13714yescomplemented
460C22×D11C22×D411yescharacteristic
461C22×D11C22×D411yescharacteristic
462C22×D11C22×D411yescharacteristic
463C22×D11C22×D411yescharacteristic
464Q8×C11—22no—
465Q8×C11—24no—
466Q8×C11—22no—
467Q8×C11—42no—
468Q8×C11—42no—
469D4×C11—22no—
470D4×C11—22no—
471D4×C11—42no—
472D4×C11—44no—
473D4×C11—44no—
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—44no—
483C2×C4×C11—42no—
484C2×C4×C11—42no—
485C2×C4×C11—42no—
486C2×C4×C11—44no—
487C2×C4×C11C22×D411yescharacteristic
488C2×C4×C11C22×D411yescharacteristic
489C2×C4×C11C22×D411yescharacteristic
490C2×C4×C11H(5,𝔽2)14yes—
491C2×C4×C11C2511yescharacteristic
492C22⋊D11—44no—
493C22⋊D11—44no—
494C22⋊D11—44no—
495C22⋊D11—44no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—42no—
507C2×Dic11—42no—
508C2×Dic11—42no—
509C2×Dic11—42no—
510C2×Dic11C22×D411yescharacteristic
511C2×Dic11C22×D411yescharacteristic
512C2×Dic11C22×D411yescharacteristic
513C2×Dic11C22×D411yescharacteristic
514C4×D11—22no—
515C4×D11—22no—
516C4×D11—22no—
517C4×D11—22no—
518C4×D11—22no—
519C4×D11—22no—
520C4×D11—22no—
521C4×D11—22no—
522C4×D11—41no—
523C4×D11—41no—
524C4×D11—41no—
525C4×D11—41no—
526C4×D11—41no—
527C4×D11—41no—
528C4×D11—41no—
529C4×D11—41no—
530C4×D11—44no—
531C4×D11—44no—
532C4×D11—44no—
533C4×D11—44no—
534Dic22—24no—
535Dic22—44no—
536Dic22—44no—
537Dic22—42no—
538C8×C11—24no—
539C11⋊C8—24no—
540C22×#41C2×D1111yescharacteristic
541C23×Q8—111no—
542C24×C4—111no—
543C2×#137—112no—
544C2×#137C2×D1112yescomplemented
545C22×M16—112no—
546#525—112no—
547#525—112no—
548#525—112no—
549#525—112no—
550#525—221no—
551#525—221no—
552#525—221no—
553#525—221no—
554C2×#123—221no—
555C2×C22⋊Q8—111no—
556C2×C22⋊Q8—111no—
557C2×C22⋊Q8—111no—
558C2×C22⋊Q8—111no—
559C2×C22⋊Q8—112no—
560C2×C22⋊Q8—112no—
561C2×C22⋊Q8—112no—
562C2×C22⋊Q8—112no—
563C2×C22⋊Q8—111no—
564C2×C22⋊Q8—221no—
565C2×C22⋊Q8—221no—
566C2×C22⋊Q8—221no—
567C2×C22⋊Q8—221no—
568C2×C22⋊Q8—221no—
569C2×C22⋊Q8—221no—
570C2×C22⋊Q8C2×D1111yescharacteristic
571C2×#121—111no—
572C2×#121—111no—
573C2×#120—221no—
574C2×C4×D4—221no—
575C2×C4×D4—221no—
576C2×#117—111no—
577C22×C4⋊C4—111no—
578C22×C4⋊C4—221no—
579C22×C22⋊C4—221no—
580#485—114no—
581#485—114no—
582#484—112no—
583#484—114no—
584#484—112no—
585#483—112no—
586#483—114no—
587#483—112no—
588#481—114no—
589#480—114no—
590#470—114no—
591#470—114no—
592#468—114no—
593#468—114no—
594#467—114no—
595#467—114no—
596#465—114no—
597#465—114no—
598#452—114no—
599#452C2×D1114yescomplemented
600#451—112no—
601#451—114no—
602#451—114no—
603#451C2×D1112yescomplemented
604#450—112no—
605#450C2×D1112yescomplemented
606#448—114no—
607#448—114no—
608#428—112no—
609#428—112no—
610#419—112no—
611#419—112no—
612#417—112no—
613#417C2×D1112yescomplemented
614#407—111no—
615#407—112no—
616#407—112no—
617#407—112no—
618#407C2×D1111yescharacteristic
619C2×C22⋊C8—112no—
620C2×C22⋊C8—112no—
621C22×C11—21no—
622C22×C11—21no—
623C22×C11—21no—
624C22×C11—21no—
625C22×C11—21no—
626C22×C11—21no—
627C22×C11—21no—
628C22×C11—44no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—84no—
633C22×C11#53412yes—
634C22×C11C2×#13712yes—
635C22×C11C23×D411yescharacteristic
636C2×D11—28no—
637C2×D11—21no—
638C2×D11—21no—
639C2×D11—21no—
640C2×D11—21no—
641C2×D11—21no—
642C2×D11—21no—
643C2×D11—21no—
644C2×D11—21no—
645C2×D11—21no—
646C2×D11—44no—
647C2×D11—44no—
648C2×D11—44no—
649C2×D11—44no—
650C2×D11—44no—
651C2×D11C2×#13712yes—
652C2×D11C2×#13712yes—
653C2×D11#57512yes—
654C4×C11—21no—
655C4×C11—21no—
656C4×C11—42no—
657C4×C11—42no—
658C4×C11—42no—
659C4×C11#53412yes—
660C4×C11C2×H(5,𝔽2)12yes—
661Dic11—21no—
662Dic11—21no—
663Dic11—21no—
664Dic11—21no—
665Dic11—42no—
666Dic11—42no—
667Dic11—42no—
668Dic11—42no—
669C25—111no—
670C2×#41—21no—
671C2×#41—21no—
672C2×#41—44no—
673C2×#41C22×D1112yes—
674C2×#41C22×D1112yes—
675C22×Q8—112no—
676C22×Q8—112no—
677C22×Q8—111no—
678C22×Q8—221no—
679C22×Q8—221no—
680C22×Q8—221no—
681C22×Q8—444no—
682C22×Q8C22×D1111yescharacteristic
683C22×Q8C22×D1111yescharacteristic
684C22×D4—21no—
685C22×D4—221no—
686C22×D4—221no—
687C22×D4C22×D1111yescharacteristic
688C23×C4—21no—
689C23×C4—111no—
690C23×C4—111no—
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—111no—
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—221no—
703C23×C4—221no—
704C23×C4—444no—
705C23×C4C22×D1111yescharacteristic
706#137—44no—
707#137—444no—
708C2×Q16—114no—
709C2×Q16C22×D1114yescomplemented
710C2×SD16—114no—
711C2×SD16C22×D1114yescomplemented
712C2×M16—112no—
713C2×M16—114no—
714C2×M16—444no—
715C2×M16C22×D1112yes—
716C22×C8—114no—
717#123—222no—
718#123—222no—
719#123—222no—
720#123—222no—
721C22⋊Q8—21no—
722C22⋊Q8—21no—
723C22⋊Q8—112no—
724C22⋊Q8—112no—
725C22⋊Q8—112no—
726C22⋊Q8—112no—
727C22⋊Q8—112no—
728C22⋊Q8—112no—
729C22⋊Q8—112no—
730C22⋊Q8—112no—
731C22⋊Q8—112no—
732C22⋊Q8—112no—
733C22⋊Q8—222no—
734C22⋊Q8—222no—
735C22⋊Q8—222no—
736C22⋊Q8—222no—
737C22⋊Q8—222no—
738C22⋊Q8—222no—
739C22⋊Q8—222no—
740C22⋊Q8—222no—
741C22⋊Q8—221no—
742C22⋊Q8—221no—
743C22⋊Q8—221no—
744C22⋊Q8—221no—
745C22⋊Q8—221no—
746C22⋊Q8—221no—
747C22⋊Q8—221no—
748C22⋊Q8—221no—
749C22⋊Q8—221no—
750C22⋊Q8—221no—
751C22⋊Q8C22×D1112yes—
752C22⋊Q8C22×D1112yes—
753#121—112no—
754#121—112no—
755#121—112no—
756#121—112no—
757#121—221no—
758#121—221no—
759#121—221no—
760#121—221no—
761#120—222no—
762#120—222no—
763#120—222no—
764#120—222no—
765C4×D4—222no—
766C4×D4—222no—
767C4×D4—222no—
768C4×D4—222no—
769C4×D4—222no—
770C4×D4—222no—
771C4×D4—222no—
772C4×D4—222no—
773#117—112no—
774#117—112no—
775#117—221no—
776#117—221no—
777C2×C4⋊C4—21no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—221no—
784C2×C4⋊C4—221no—
785C2×C4⋊C4—222no—
786C2×C4⋊C4—222no—
787C2×C4⋊C4—222no—
788C2×C4⋊C4—222no—
789C2×C4⋊C4—221no—
790C2×C4⋊C4—221no—
791C2×C4⋊C4—221no—
792C2×C4⋊C4—221no—
793C2×C4⋊C4—221no—
794C2×C4⋊C4—221no—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C22⋊C4—21no—
797C2×C22⋊C4—222no—
798C2×C22⋊C4—222no—
799C2×C22⋊C4—222no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—221no—
802C2×C22⋊C4—221no—
803C2×C22⋊C4—221no—
804C2×C22⋊C4—221no—
805C2×C22⋊C4—221no—
806C2×C22⋊C4—221no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C42—221no—
810#107—114no—
811#107—114no—
812#106—114no—
813#106—114no—
814#103—114no—
815#103—114no—
816#103—114no—
817#103—114no—
818#103—114no—
819#103C22×D1114yescomplemented
820#102—114no—
821#102C22×D1114yescomplemented
822C22⋊C8—112no—
823C22⋊C8—112no—
824C22⋊C8—114no—
825C22⋊C8—114no—
826C22⋊C8C22×D1112yes—
827C22⋊C8C22×D1112yes—
828C2×C11—22no—
829C2×C11—22no—
830C2×C11—41no—
831C2×C11—82no—
832C2×C11C2×#53411yescharacteristic
833C2×C11C22×#13711yescharacteristic
834C2×C11C2×#57511yescharacteristic
835D11—22no—
836D11—22no—
837D11—22no—
838D11—41no—
839C24—21no—
840C24—111no—
841C24—111no—
842C24—111no—
843C24—111no—
844C24—111no—
845C24—111no—
846C24—224no—
847C24—442no—
848C24—442no—
849C24D4×D1111yescharacteristic
850#41—24no—
851#41—24no—
852#41—42no—
853#41—42no—
854#41—44no—
855#41—44no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—24no—
859C2×Q8—42no—
860C2×Q8—112no—
861C2×Q8—222no—
862C2×Q8—222no—
863C2×Q8—221no—
864C2×Q8—224no—
865C2×Q8—444no—
866C2×Q8—444no—
867C2×Q8—444no—
868C2×Q8—444no—
869C2×Q8—444no—
870C2×Q8C23×D1112yes—
871C2×Q8C23×D1112yes—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—42no—
876C2×D4—44no—
877C2×D4—222no—
878C2×D4—222no—
879C2×D4—222no—
880C2×D4—222no—
881C2×D4—444no—
882C2×D4—444no—
883C2×D4C23×D1112yes—
884C22×C4—24no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—44no—
891C22×C4—111no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—111no—
898C22×C4—111no—
899C22×C4—111no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—111no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—221no—
920C22×C4—221no—
921C22×C4—221no—
922C22×C4—221no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—444no—
934C22×C4—444no—
935C22×C4—442no—
936C22×C4D4×D1111yescharacteristic
937C22×C4D4×D1111yescharacteristic
938C22×C4D4×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942Q16—44no—
943Q16—444no—
944SD16—44no—
945SD16—444no—
946M16—24no—
947M16—224no—
948M16—444no—
949C2×C8—114no—
950C2×C8—444no—
951C2×C8C23×D1114yes—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—112no—
956C4⋊C4—112no—
957C4⋊C4—112no—
958C4⋊C4—222no—
959C4⋊C4—222no—
960C4⋊C4—222no—
961C4⋊C4—222no—
962C4⋊C4—222no—
963C4⋊C4—222no—
964C4⋊C4—222no—
965C4⋊C4—222no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—221no—
969C4⋊C4—221no—
970C4⋊C4—221no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4C23×D1112yes—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—222no—
977C22⋊C4—222no—
978C22⋊C4—222no—
979C22⋊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—
992C42—222no—
993C42—222no—
994C11#6075111yescharacteristic, complemented, Sylow
995C23—22no—
996C23—22no—
997C23—22no—
998C23—41no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—111no—
1003C23—111no—
1004C23—111no—
1005C23—114no—
1006C23—111no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23—441no—
1021C23—441no—
1022C23—441no—
1023C23—441no—
1024C23—4416no—
1025C23C2×D4×D1111yescharacteristic
1026C23C2×D4×D1111yescharacteristic
1027C23C2×D4×D1111yescharacteristic
1028Q8—24no—
1029Q8—22no—
1030Q8—22no—
1031Q8—42no—
1032Q8—42no—
1033Q8—224no—
1034Q8—444no—
1035Q8—444no—
1036Q8—442no—
1037D4—22no—
1038D4—22no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—444no—
1043D4—444no—
1044D4—444no—
1045D4—444no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—44no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—44no—
1059C2×C4—111no—
1060C2×C4—111no—
1061C2×C4—111no—
1062C2×C4—111no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—444no—
1086C2×C4—444no—
1087C2×C4—444no—
1088C2×C4—444no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—442no—
1094C2×C4—442no—
1095C2×C4—442no—
1096C2×C4—442no—
1097C2×C4C2×D4×D1111yescharacteristic
1098C2×C4C2×D4×D1111yescharacteristic
1099C2×C4C2×D4×D1111yescharacteristic
1100C2×C4#6703714yes—
1101C2×C4C24×D1111yescharacteristic
1102C8—24no—
1103C8—224no—
1104C22—21no—
1105C22—21no—
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—44no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—84no—
1116C22—112no—
1117C22—112no—
1118C22—112no—
1119C22—228no—
1120C22—221no—
1121C22—221no—
1122C22—221no—
1123C22—221no—
1124C22—221no—
1125C22—221no—
1126C22—221no—
1127C22—221no—
1128C22—221no—
1129C22—444no—
1130C22—444no—
1131C22—444no—
1132C22—444no—
1133C22—444no—
1134C22#1062312012yes—
1135C22D11×#13712yes—
1136C22C22×D4×D1111yescharacteristic
1137C4—21no—
1138C4—21no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—221no—
1143C4—221no—
1144C4—221no—
1145C4—221no—
1146C4—442no—
1147C4—442no—
1148C4—442no—
1149C4—442no—
1150C4#1062312012yes—
1151C4C2×#6703712yes—
1152C2—22no—
1153C2—22no—
1154C2—41no—
1155C2—82no—
1156C2—222no—
1157C2—222no—
1158C2—222no—
1159C2—441no—
1160C2C2×#1062312011yescharacteristic
1161C2C2×D11×#13711yescharacteristic
1162C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3007C2
socleC22×C11C23×D4
prime radicalC2×#10623359C2
hypercenter#3007D11
hypocenterC11#60751
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
2. C2×D11×C22⋊Q8C2semidirect
3. #13079444C2semidirect
4. #13079438C2semidirect
5. #13079419C2semidirect
6. #13079395C2semidirect
7. #13079389C2semidirect
8. #13079370C2semidirect
9. #13078565C2semidirect
10. #13078560C2semidirect
11. #13078537C2semidirect
12. #13078249C2semidirect
13. #13078240C2semidirect
14. #13077876C2semidirect
15. #13077848C2semidirect
16. D11×#407C2semidirect
17. C11×#3007C2semidirect
19. C22×Q8×D11C22semidirect
21. C2×C11×#137C22semidirect
31. C2×#67004C22semidirect
34. C2×#66999C22semidirect
43. C2×M16×D11C22semidirect
50. D11×C22⋊Q8C22semidirect
51. D11×C22⋊Q8C22semidirect
52. C2×#66950C22semidirect
55. C2×C4⋊C4×D11C22semidirect
58. C11×#452C22semidirect
59. C11×#451C22semidirect
60. C11×#450C22semidirect
61. C11×#417C22semidirect
63. #10622852C22semidirect
64. #10622845C22semidirect
65. #10622841C22semidirect
66. #10622838C22semidirect
67. #10622831C22semidirect
69. #10622802C22semidirect
70. #10622801C22semidirect
71. #10622799C22semidirect
72. #10622799C22semidirect
73. #10622787C22semidirect
74. #10622784C22semidirect
75. #10622783C22semidirect
76. #10622783C22semidirect
77. #10622739C22semidirect
78. #10622734C22semidirect
79. #10622733C22semidirect
80. #10622658C22semidirect
81. #10622657C22semidirect
82. #10622656C22semidirect
83. #10622577C22semidirect
84. #10622429C22semidirect
85. #10622426C22semidirect
86. #10622422C22semidirect
87. #10622418C22semidirect
88. #10622393C22semidirect
89. #10622391C22semidirect
90. #10622390C22semidirect
91. #10622387C22semidirect
93. #10622339C22semidirect
95. D11×C22⋊C8C22semidirect
96. #10622336C22semidirect
97. #10622335C22semidirect
98. #10622334C22semidirect
137. C2×C11×Q16C23semidirect
138. C2×C11×SD16C23semidirect
164. C2×#4326C23semidirect
181. C2×#4324C23semidirect
240. C11×#103C23semidirect
241. C11×#102C23semidirect
244. #66899C23semidirect
245. #66899C23semidirect
246. #66899C23semidirect
247. #66896C23semidirect
252. #66882C23semidirect
253. #66881C23semidirect
254. #66880C23semidirect
255. #66880C23semidirect
256. #66872C23semidirect
257. #66871C23semidirect
428. #3007D11semidirect
459. C22×D11#137semidirect
544. C2×#137C2×D11semidirect
599. #452C2×D11semidirect
603. #451C2×D11semidirect
605. #450C2×D11semidirect
613. #417C2×D11semidirect
709. C2×Q16C22×D11semidirect
711. C2×SD16C22×D11semidirect
819. #103C22×D11semidirect
821. #102C22×D11semidirect
994. C11#60751semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×D11×C22⋊Q82
#130794442
#130794382
#130794192
#130793952
#130793892
#130793702
#130785652
#130785602
#130785372
#130782492
#130782402
#130778762
#130778482
D11×#4072
C11×#30072
#6075111