Finite Group Databasebeta

← #15620305

Subgroups — #15620305

Order 2816.

5126 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67037C211yesmaximal, characteristic, complemented
2C2×#10623305C212yesmaximal, complemented
3#13082277C211yesmaximal, characteristic, complemented
4#13077921C214yesmaximal, complemented
5#13077919C212yesmaximal, complemented
6#13077885C212yesmaximal, complemented
7#13077879C214yesmaximal, complemented
8#13077870C211yesmaximal, characteristic, complemented
9#13077863C212yesmaximal, complemented
10#13077844C212yesmaximal, complemented
11#13077835C212yesmaximal, complemented
12#13077832C211yesmaximal, characteristic, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14D11×#447C212yesmaximal, complemented
15#13077141C212yesmaximal, complemented
16#13077066C211yesmaximal, characteristic, complemented
17C11×#3003C211yesmaximal, characteristic, complemented
18C23×D4×C11C2211yescharacteristic, complemented
19C23×C22⋊D11—22no—
20C2×#67042C2211yescharacteristic, complemented
21C2×#67037—216no—
22C2×#67037—21no—
23C2×#67037—21no—
24C2×#67037—22no—
25C2×#67037C2212yes—
26C2×#67037C2214yescomplemented
27C2×#67037C2212yescomplemented
28C22×#4341—21no—
29C22×#4341C2212yescomplemented
30C22×D4×D11—21no—
31C22×D4×D11C2212yescomplemented
32C22×#4339C2211yescharacteristic
33C22×#4339C2211yescharacteristic, complemented
34C2×C11×AGL(1,ℤ/8)C2212yescomplemented
35C11×#525C2211yescharacteristic, complemented
36#10623364C2211yescharacteristic, complemented
37C2×#67003C2212yescomplemented
38C22×#4323C2212yescomplemented
39C2×#66983C2211yescharacteristic, complemented
40#10623305—216no—
41C2×#66969C2214yescomplemented
42C2×#66967C2214yescomplemented
43C2×#66964C2214yescomplemented
44C2×D8×D11C2214yescomplemented
45C2×#66961C2212yescomplemented
46C2×#66960C2212yescomplemented
47#10623185—22no—
48#10623160C2212yescomplemented
49#10623158C2212yescomplemented
50#10623138C2212yescomplemented
51D11×#121C2212yescomplemented
52#10623121—22no—
53#10623084—21no—
54#10623083—21no—
55#10623081—21no—
56D4×D44—21no—
57#10623056C2211yescharacteristic, complemented
58#10623054C2211yescharacteristic, complemented
59C11×#450C2212yescomplemented
60C11×#450C2212yescomplemented
61C11×#447C2212yescomplemented
62C11×#447C2212yescomplemented
63C11×#418C2212yescomplemented
64C11×#407C2211yescharacteristic, complemented
65#10622830C2212yescomplemented
66#10622830C2212yescomplemented
67#10622830C2214yescomplemented
68C2×#66896C2212yescomplemented
69C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
70#10622786C2214yescomplemented
71#10622782C2214yescomplemented
72#10622771C2214yescomplemented
73#10622769C2214yescomplemented
74#10622746C2212yescomplemented
75#10622742C2212yescomplemented
76#10622663C2211yescharacteristic, complemented
77#10622660C2212yescomplemented
78#10622659C2211yescharacteristic, complemented
79#10622653C2211yescharacteristic, complemented
80#10622650C2212yescomplemented
81#10622649C2211yescharacteristic, complemented
82#10622615C2212yescomplemented
83#10622394C2214yescomplemented
84#10622394C2214yescomplemented
85#10622386C2214yescomplemented
86#10622386C2214yescomplemented
87#10622385C2214yescomplemented
88#10622384C2214yescomplemented
89#10622383C2214yescomplemented
90D11×#102C2214yescomplemented
91#10622351C2212yescomplemented
92#10622347C2214yescomplemented
93#10622345C2212yescomplemented
94#10622340C2214yescomplemented
95#10622339C2212yescomplemented
96D11×C22⋊C8C2212yescomplemented
97C25×C11—21no—
98C24×D11—22no—
99C2×C11×#41C2311yescharacteristic, complemented
100C22×D4×C11—28no—
101C22×D4×C11—21no—
102C22×D4×C11—21no—
103C22×D4×C11—21no—
104C22×D4×C11C2312yes—
105C22×D4×C11C2312yes—
106C22×D4×C11C2312yes—
107C23×C4×C11C2311yescharacteristic
108C22×C22⋊D11—232no—
109C22×C22⋊D11—21no—
110C22×C22⋊D11—22no—
111C22×C22⋊D11—24no—
112C22×C22⋊D11—24no—
113C22×C22⋊D11—24no—
114C22×C22⋊D11—24no—
115C22×C22⋊D11—21no—
116C22×C22⋊D11—22no—
117C22×C22⋊D11D412yes—
118C23×Dic11—22no—
119#67042—28no—
120C2×#4343C2312yescomplemented
121#67037—232no—
122#67037—216no—
123#67037—216no—
124#67037—28no—
125#67037—216no—
126#67037—216no—
127#67037—28no—
128#67037—28no—
129#67037D4116yescomplemented
130C2×#4341—216no—
131C2×#4341—216no—
132C2×#4341—22no—
133C2×#4341—22no—
134C2×#4341—22no—
135C2×#4341—22no—
136C2×#4341—24no—
137C2×#4341C2314yes—
138C2×#4341C2314yes—
139C2×D4×D11—216no—
140C2×D4×D11—216no—
141C2×D4×D11—22no—
142C2×D4×D11—22no—
143C2×D4×D11—22no—
144C2×D4×D11—22no—
145C2×D4×D11—24no—
146C2×D4×D11—22no—
147C2×D4×D11—22no—
148C2×D4×D11C2314yes—
149C2×D4×D11C2314yes—
150C2×D4×D11C2312yescomplemented
151C2×#4339—21no—
152C2×#4339—21no—
153C2×#4339—28no—
154C2×#4339—28no—
155C2×#4339—21no—
156C2×#4339D411yescharacteristic
157C2×#4339D411yescharacteristic
158C2×#4339D412yes—
159C2×#4339C2311yescharacteristic
160C2×#4339C2312yes—
161C2×#4339C2311yescharacteristic
162C2×#4339C2312yes—
163C2×#4339C2312yes—
164C22×D44—21no—
165C22×D44D411yescharacteristic
166C22×D44C2311yescharacteristic
167C22×D44C2311yescharacteristic, complemented
168C22×C4×D11—21no—
169C22×C4×D11C2312yes—
170C22×Dic22D411yescharacteristic
171C22×Dic22C2311yescharacteristic
172C11×AGL(1,ℤ/8)—28no—
173C2×C11×SD16C2314yescomplemented
174C2×C11×D8C2314yescomplemented
175C2×C11×M16C2312yescomplemented
176C11×#123—21no—
177C11×C22⋊Q8C2311yescharacteristic
178C11×C22⋊Q8C2311yescharacteristic, complemented
179C11×#121C2311yescharacteristic
180C11×#121C2311yescharacteristic, complemented
181C11×#120—21no—
182C4×D4×C11—21no—
183C4×D4×C11—21no—
184C11×#117C2311yescharacteristic, complemented
185#67003—28no—
186#66999C2312yescomplemented
187C2×#4326C2312yescomplemented
188C2×#4325C2312yescomplemented
189#66993—22no—
190#66992—22no—
191#66992—22no—
192#66991C2312yescomplemented
193#66990—22no—
194C2×#4324C2312yescomplemented
195C2×#4323—28no—
196C2×#4323C2312yescomplemented
197C2×#4323C2314yescomplemented
198C2×#4323C2314yescomplemented
199#66983—21no—
200#66983—21no—
201#66983—21no—
202#66983C2312yes—
203#66983C2312yescomplemented
204C2×(C2×D11)⋊C4—21no—
205C2×C4⋊Dic11C2311yescharacteristic, complemented
206#66977—21no—
207C22×C11⋊C8C2312yescomplemented
208#66969—216no—
209#66967—216no—
210#66964—216no—
211D8×D11—216no—
212#66961—28no—
213#66960—28no—
214C2×D88C2314yescomplemented
215C2×#4314C2314yescomplemented
216C2×#4313C2314yescomplemented
217C2×C8×D11C2314yescomplemented
218#66949—22no—
219#66948—22no—
220#66948C2312yescomplemented
221#66948C2312yescomplemented
222#66947—22no—
223#66946—22no—
224#66945C2312yescomplemented
225C4⋊C4×D11C2312yescomplemented
226#66938—22no—
227#66937—22no—
228#66937—22no—
229#66937—22no—
230#66935—22no—
231#66935—22no—
232#66935—22no—
233(C22⋊D11)⋊C4—22no—
234(C22⋊D11)⋊C4—22no—
235C22⋊C4×D11—22no—
236#66928—21no—
237#66927—21no—
238C4×D44—21no—
239C4×Dic22—21no—
240C11×#102C2314yescomplemented
241C11×#102C2314yescomplemented
242C11×C22⋊C8C2312yes—
243C11×C22⋊C8C2312yescomplemented
244#66896C2314yescomplemented
245#66896C2314yescomplemented
246C22⋊(C11⋊C8)C2311yescharacteristic
247C22⋊(C11⋊C8)C2311yescharacteristic
248C22⋊(C11⋊C8)C2312yescomplemented
249#66885C2314yescomplemented
250(C2×D11)⋊C8C2314yescomplemented
251(C2×D11)⋊C8C2314yescomplemented
252#66880C2314yescomplemented
253#66874C2312yescomplemented
254#66874C2312yescomplemented
255#66873C2312yescomplemented
256#66873C2312yescomplemented
257#60372—111nomaximal, Sylow
258C24×C11—28no—
259C24×C11—22no—
260C24×C11—22no—
261C24×C11—22no—
262C24×C11—82no—
263C24×C11—82no—
264C24×C11C2×D411yescharacteristic
265C23×D11—21no—
266C23×D11—216no—
267C23×D11—24no—
268C23×D11—24no—
269C23×D11—21no—
270C23×D11—22no—
271C23×D11—84no—
272C23×D11—84no—
273C23×D11C2×D412yes—
274C11×#41—24no—
275C2×Q8×C11C2411yescharacteristic
276C2×D4×C11—28no—
277C2×D4×C11—28no—
278C2×D4×C11—28no—
279C2×D4×C11—28no—
280C2×D4×C11—28no—
281C2×D4×C11—21no—
282C2×D4×C11—21no—
283C2×D4×C11—21no—
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11—22no—
287C2×D4×C11—24no—
288C2×D4×C11C2×D418yescomplemented
289C2×D4×C11C2411yescharacteristic
290C2×D4×C11C2414yes—
291C22×C4×C11—24no—
292C22×C4×C11—21no—
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—28no—
300C2×C22⋊D11—216no—
301C2×C22⋊D11—216no—
302C2×C22⋊D11—232no—
303C2×C22⋊D11—232no—
304C2×C22⋊D11—232no—
305C2×C22⋊D11—28no—
306C2×C22⋊D11—232no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—82no—
318C2×C22⋊D11C2×D412yes—
319C2×C22⋊D11C2×D412yes—
320C2×C22⋊D11C2×D412yes—
321C2×C22⋊D11C2×D412yes—
322C22×Dic11—216no—
323C22×Dic11—24no—
324C22×Dic11—24no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11C2×D412yes—
328#4343—28no—
329#4341—216no—
330#4341—216no—
331#4341—232no—
332#4341—216no—
333#4341—28no—
334#4341—216no—
335#4341—28no—
336#4341—28no—
337#4341C2×D4116yescomplemented
338D4×D11—216no—
339D4×D11—232no—
340D4×D11—216no—
341D4×D11—216no—
342D4×D11—216no—
343D4×D11—28no—
344D4×D11—28no—
345D4×D11—28no—
346D4×D11—28no—
347D4×D11—48no—
348D4×D11—84no—
349D4×D11C2×D4116yescomplemented
350#4339—28no—
351#4339—28no—
352#4339—28no—
353#4339—24no—
354#4339—24no—
355#4339—28no—
356#4339—24no—
357#4339—24no—
358#4339—24no—
359#4339—24no—
360#4339—44no—
361#4339C2×D418yes—
362#4339C2×D418yescomplemented
363C2×D44—24no—
364C2×D44—24no—
365C2×D44—22no—
366C2×D44—22no—
367C2×D44—22no—
368C2×D44—21no—
369C2×D44—21no—
370C2×D44—24no—
371C2×D44—44no—
372C2×D44C2×D411yescharacteristic
373C2×D44C2×D412yes—
374C2×D44C2×D411yescharacteristic
375C2×D44C2412yes—
376C2×D44C2412yes—
377C2×C4×D11—28no—
378C2×C4×D11—28no—
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—22no—
382C2×C4×D11—22no—
383C2×C4×D11C2×D412yes—
384C2×C4×D11C2×D412yes—
385C2×C4×D11C2412yes—
386C2×C4×D11C2412yes—
387C2×Dic22—24no—
388C2×Dic22—24no—
389C2×Dic22—21no—
390C2×Dic22C2×D411yescharacteristic
391C2×Dic22C2×D412yes—
392C2×Dic22C2×D411yescharacteristic
393C2×Dic22C2412yes—
394C11×SD16—28no—
395C11×D8—28no—
396C11×M16—24no—
397C2×C8×C11C2414yes—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4C2411yescharacteristic
401C11×C4⋊C4C2411yescharacteristic
402C11×C22⋊C4—21no—
403C11×C22⋊C4—21no—
404C11×C22⋊C4—21no—
405C11×C22⋊C4—21no—
406C11×C22⋊C4—21no—
407C42×C11—21no—
408C22⋊Dic11—22no—
409#4326—24no—
410#4325—24no—
411#4324—24no—
412#4323—24no—
413#4323—28no—
414#4323—28no—
415(C2×D11)⋊C4—22no—
416(C2×D11)⋊C4—22no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—22no—
420(C2×D11)⋊C4—22no—
421C4⋊Dic11—21no—
422C4⋊Dic11C2412yes—
423Dic11⋊C4—22no—
424Dic11⋊C4—22no—
425C4×Dic11—22no—
426C2×C11⋊C8—24no—
427C2×C11⋊C8C2412yes—
428C2×C11⋊C8C2412yes—
429D88—28no—
430#4314—28no—
431#4313—28no—
432C8×D11—28no—
433C22×H(5,𝔽2)—111no—
434C2×#576—112no—
435#3488—111no—
436#3012—114no—
437#3012—112no—
438#3008—114no—
439#3008—112no—
440#3006—112no—
441#3006—111no—
442#3003—112no—
443#3003D1111yescharacteristic, complemented
444#3002—112no—
445#3002—111no—
446C2×#447—112no—
447C2×#447—111no—
448#2897—112no—
449#2880—111no—
450C23×C11—28no—
451C23×C11—28no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—24no—
455C23×C11—28no—
456C23×C11—21no—
457C23×C11—41no—
458C23×C11—44no—
459C23×C11—44no—
460C23×C11—82no—
461C23×C11—82no—
462C23×C11—82no—
463C23×C11—82no—
464C23×C11—816no—
465C23×C11C22×D411yescharacteristic
466C23×C11C22×D411yescharacteristic
467C23×C11C22×D411yescharacteristic
468C22×D11—24no—
469C22×D11—24no—
470C22×D11—22no—
471C22×D11—216no—
472C22×D11—24no—
473C22×D11—216no—
474C22×D11—22no—
475C22×D11—42no—
476C22×D11—42no—
477C22×D11—42no—
478C22×D11—42no—
479C22×D11—44no—
480C22×D11—84no—
481C22×D11—84no—
482C22×D11—84no—
483C22×D11—84no—
484C22×D11—82no—
485C22×D11—82no—
486C22×D11—832no—
487C22×D11—81no—
488C22×D11—81no—
489C22×D11C22×D412yes—
490C22×D11C22×D412yes—
491Q8×C11—22no—
492D4×C11—28no—
493D4×C11—28no—
494D4×C11—28no—
495D4×C11—24no—
496D4×C11—22no—
497D4×C11—42no—
498D4×C11—42no—
499D4×C11—81no—
500D4×C11C22×D418yes—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—42no—
510C2×C4×C11C22×D411yescharacteristic
511C2×C4×C11C22×D411yescharacteristic
512C2×C4×C11C22×D411yescharacteristic
513C2×C4×C11C22×D414yes—
514C2×C4×C11C2511yescharacteristic
515C22⋊D11—28no—
516C22⋊D11—216no—
517C22⋊D11—216no—
518C22⋊D11—24no—
519C22⋊D11—28no—
520C22⋊D11—24no—
521C22⋊D11—216no—
522C22⋊D11—24no—
523C22⋊D11—216no—
524C22⋊D11—44no—
525C22⋊D11—44no—
526C22⋊D11—82no—
527C22⋊D11—82no—
528C22⋊D11#12018yes—
529C2×Dic11—24no—
530C2×Dic11—216no—
531C2×Dic11—22no—
532C2×Dic11—24no—
533C2×Dic11—216no—
534C2×Dic11—22no—
535C2×Dic11—81no—
536C2×Dic11C22×D412yes—
537C2×Dic11C22×D412yes—
538D44—24no—
539D44—24no—
540D44—22no—
541D44—22no—
542D44—24no—
543D44—44no—
544D44—42no—
545D44—82no—
546D44—82no—
547D44#12014yes—
548D44C22×D414yes—
549C4×D11—28no—
550C4×D11—24no—
551C4×D11—28no—
552C4×D11—24no—
553C4×D11—24no—
554C4×D11—44no—
555C4×D11—82no—
556C4×D11C22×D418yes—
557Dic22—24no—
558Dic22—22no—
559Dic22—22no—
560Dic22—24no—
561Dic22#12014yes—
562Dic22C22×D414yes—
563C8×C11—24no—
564C11⋊C8—22no—
565C11⋊C8—22no—
566C2×H(5,𝔽2)—111no—
567C2×H(5,𝔽2)—112no—
568C2×H(5,𝔽2)—114no—
569C2×H(5,𝔽2)—112no—
570C2×H(5,𝔽2)—222no—
571C2×H(5,𝔽2)—221no—
572C2×H(5,𝔽2)—221no—
573C2×H(5,𝔽2)—2216no—
574C22×#41—111no—
575C22×#41—112no—
576C22×#41—111no—
577C22×#41—221no—
578C23×D4—112no—
579C23×D4—221no—
580C23×D4—222no—
581C23×D4C2×D1111yescharacteristic, complemented
582#576—2216no—
583C2×AGL(1,ℤ/8)—114no—
584C2×AGL(1,ℤ/8)—114no—
585C2×AGL(1,ℤ/8)—112no—
586C2×AGL(1,ℤ/8)C2×D1112yescomplemented
587C2×#135—112no—
588C2×#135—114no—
589C22×D8—112no—
590C22×D8—114no—
591C2×#131—112no—
592#550—221no—
593#548—221no—
594#546—221no—
595#546—222no—
596D42—221no—
597D42—222no—
598#537—111no—
599#537—112no—
600#535—112no—
601#535—111no—
602#525—112no—
603#525C2×D1111yescharacteristic, complemented
604C2×#121—111no—
605C2×#121—112no—
606#520—111no—
607#452—114no—
608#452—112no—
609#451—111no—
610#450—114no—
611#450—111no—
612#450C2×D1112yescomplemented
613#450C2×D1112yescomplemented
614#449—114no—
615#449—112no—
616#449—114no—
617#449—114no—
618#449—114no—
619#448—111no—
620#448—112no—
621#447—112no—
622#447—112no—
623#447—114no—
624#447—114no—
625#447—111no—
626#447—114no—
627#447—114no—
628#447—112no—
629#447C2×D1112yescomplemented
630#447C2×D1112yescomplemented
631#418—114no—
632#418C2×D1112yescomplemented
633#417—112no—
634#417—114no—
635#416—112no—
636#416—114no—
637C2×#102—112no—
638C2×#102—114no—
639#408—112no—
640#408—114no—
641#407—112no—
642#407C2×D1111yescharacteristic, complemented
643C2×C22⋊C8—111no—
644C2×C22⋊C8—112no—
645C22×C11—21no—
646C22×C11—21no—
647C22×C11—21no—
648C22×C11—21no—
649C22×C11—21no—
650C22×C11—21no—
651C22×C11—28no—
652C22×C11—21no—
653C22×C11—44no—
654C22×C11—416no—
655C22×C11—44no—
656C22×C11—44no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11—88no—
661C22×C11—88no—
662C22×C11C2×#12012yes—
663C22×C11#57612yescomplemented
664C22×C11C23×D411yescharacteristic
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—24no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—48no—
672C2×D11—48no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—816no—
679C2×D11—816no—
680C2×D11—164no—
681C2×D11—162no—
682C2×D11C2×#12014yes—
683C4×C11—21no—
684C4×C11—21no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11—41no—
688C4×C11C2×#12012yes—
689C4×C11C23×D412yes—
690Dic11—22no—
691Dic11—24no—
692Dic11—42no—
693Dic11C2×#12014yes—
694C25—21no—
695C25—222no—
696H(5,𝔽2)—1116no—
697H(5,𝔽2)—2216no—
698H(5,𝔽2)—2216no—
699H(5,𝔽2)—228no—
700H(5,𝔽2)—228no—
701H(5,𝔽2)—2216no—
702H(5,𝔽2)—2232no—
703H(5,𝔽2)—2216no—
704H(5,𝔽2)—228no—
705H(5,𝔽2)—228no—
706C2×#41—111no—
707C2×#41—112no—
708C2×#41—111no—
709C2×#41—111no—
710C2×#41—112no—
711C2×#41—111no—
712C2×#41—112no—
713C2×#41—114no—
714C2×#41—114no—
715C2×#41—112no—
716C2×#41—112no—
717C2×#41—221no—
718C2×#41—228no—
719C2×#41—228no—
720C2×#41—222no—
721C2×#41—222no—
722C2×#41—222no—
723C2×#41—224no—
724C2×#41—222no—
725C2×#41—2216no—
726C2×#41—2216no—
727C2×#41—221no—
728C2×#41—221no—
729C2×#41C22×D1111yescharacteristic, complemented
730C22×Q8—111no—
731C22×Q8—111no—
732C22×D4—28no—
733C22×D4—21no—
734C22×D4—21no—
735C22×D4—21no—
736C22×D4—114no—
737C22×D4—112no—
738C22×D4—112no—
739C22×D4—114no—
740C22×D4—111no—
741C22×D4—111no—
742C22×D4—111no—
743C22×D4—221no—
744C22×D4—222no—
745C22×D4—222no—
746C22×D4—222no—
747C22×D4—2216no—
748C22×D4—222no—
749C22×D4—224no—
750C22×D4—222no—
751C22×D4—222no—
752C22×D4—2216no—
753C22×D4—222no—
754C22×D4—224no—
755C22×D4—224no—
756C22×D4—224no—
757C22×D4—224no—
758C22×D4—222no—
759C22×D4—2232no—
760C22×D4—221no—
761C22×D4—221no—
762C22×D4C22×D1112yes—
763C22×D4C22×D1112yes—
764C22×D4C22×D1112yes—
765C23×C4—112no—
766C23×C4—222no—
767C23×C4—221no—
768C23×C4C22×D1111yescharacteristic
769AGL(1,ℤ/8)—28no—
770AGL(1,ℤ/8)—228no—
771AGL(1,ℤ/8)—2216no—
772AGL(1,ℤ/8)—2216no—
773#135—2216no—
774#135—228no—
775C2×Q16—112no—
776C2×SD16—112no—
777C2×SD16—112no—
778C2×SD16—114no—
779C2×SD16C22×D1114yescomplemented
780C2×D8—112no—
781C2×D8—114no—
782C2×D8—114no—
783C2×D8—114no—
784C2×D8—2216no—
785C2×D8—228no—
786C2×D8C22×D1114yescomplemented
787#131—228no—
788C2×M16—114no—
789C2×M16C22×D1112yescomplemented
790C22×C8—112no—
791C22×C8—114no—
792#127—221no—
793#127—222no—
794#124—221no—
795#124—222no—
796#123—21no—
797#123—222no—
798C22⋊Q8—112no—
799C22⋊Q8—222no—
800C22⋊Q8—221no—
801C22⋊Q8C22×D1111yescharacteristic
802C22⋊Q8C22×D1111yescharacteristic, complemented
803#121—112no—
804#121—112no—
805#121—112no—
806#121—112no—
807#121—112no—
808#121—222no—
809#121—222no—
810#121—222no—
811#121—222no—
812#121—221no—
813#121—222no—
814#121—222no—
815#121—221no—
816#121—221no—
817#121C22×D1111yescharacteristic
818#121C22×D1111yescharacteristic, complemented
819#120—21no—
820#120—222no—
821#120—222no—
822#120—222no—
823#120—222no—
824C4×Q8—221no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—221no—
828C4×D4—222no—
829C4×D4—222no—
830C4×D4—222no—
831#117—112no—
832#117C22×D1111yescharacteristic, complemented
833C2×C4⋊C4—111no—
834C2×C4⋊C4—112no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—221no—
837#103—114no—
838#103—112no—
839#103—112no—
840#102—114no—
841#102—114no—
842#102—114no—
843#102—112no—
844#102—112no—
845#102C22×D1114yescomplemented
846#102C22×D1114yescomplemented
847C22⋊C8—111no—
848C22⋊C8—111no—
849C22⋊C8—112no—
850C22⋊C8—114no—
851C22⋊C8—114no—
852C22⋊C8C22×D1112yes—
853C22⋊C8C22×D1112yescomplemented
854C2×C11—22no—
855C2×C11—22no—
856C2×C11—48no—
857C2×C11—41no—
858C2×C11—81no—
859C2×C11C22×#12011yescharacteristic
860C2×C11C2×#57611yescharacteristic
861C2×C11#358511yescharacteristic
862D11—24no—
863D11—42no—
864D11—44no—
865D11—82no—
866C24—28no—
867C24—22no—
868C24—22no—
869C24—22no—
870C24—82no—
871C24—82no—
872C24—112no—
873C24—224no—
874C24—224no—
875C24—222no—
876C24—2216no—
877C24—221no—
878C24—221no—
879C24—884no—
880C24—884no—
881C24D4×D1111yescharacteristic
882#41—24no—
883#41—118no—
884#41—1116no—
885#41—118no—
886#41—228no—
887#41—228no—
888#41—224no—
889#41—224no—
890#41—224no—
891#41—224no—
892#41—228no—
893#41—228no—
894#41—228no—
895#41—228no—
896#41—228no—
897#41—2216no—
898#41—2216no—
899#41—2216no—
900#41—2232no—
901#41—2216no—
902#41—228no—
903#41—224no—
904#41—224no—
905#41—444no—
906C2×Q8—111no—
907C2×Q8—112no—
908C2×Q8—111no—
909C2×Q8—112no—
910C2×Q8—224no—
911C2×Q8—224no—
912C2×Q8—221no—
913C2×Q8C23×D1111yescharacteristic
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—24no—
926C2×D4—112no—
927C2×D4—1116no—
928C2×D4—112no—
929C2×D4—112no—
930C2×D4—112no—
931C2×D4—111no—
932C2×D4—112no—
933C2×D4—111no—
934C2×D4—112no—
935C2×D4—112no—
936C2×D4—224no—
937C2×D4—224no—
938C2×D4—222no—
939C2×D4—222no—
940C2×D4—222no—
941C2×D4—228no—
942C2×D4—228no—
943C2×D4—224no—
944C2×D4—224no—
945C2×D4—222no—
946C2×D4—228no—
947C2×D4—2216no—
948C2×D4—2216no—
949C2×D4—2216no—
950C2×D4—2232no—
951C2×D4—2216no—
952C2×D4—228no—
953C2×D4—2232no—
954C2×D4—224no—
955C2×D4—224no—
956C2×D4—2216no—
957C2×D4—2216no—
958C2×D4—228no—
959C2×D4—2232no—
960C2×D4—2232no—
961C2×D4—2232no—
962C2×D4—222no—
963C2×D4—222no—
964C2×D4—228no—
965C2×D4—222no—
966C2×D4—222no—
967C2×D4—222no—
968C2×D4—221no—
969C2×D4—224no—
970C2×D4—221no—
971C2×D4—444no—
972C2×D4—448no—
973C2×D4—884no—
974C2×D4—882no—
975C2×D4D4×D1118yescomplemented
976C2×D4C23×D1111yescharacteristic
977C2×D4C23×D1114yes—
978C22×C4—24no—
979C22×C4—21no—
980C22×C4—112no—
981C22×C4—112no—
982C22×C4—112no—
983C22×C4—112no—
984C22×C4—112no—
985C22×C4—228no—
986C22×C4—222no—
987C22×C4—228no—
988C22×C4—222no—
989C22×C4—224no—
990C22×C4—224no—
991C22×C4—2216no—
992C22×C4—221no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—221no—
996C22×C4D4×D1111yescharacteristic
997C22×C4D4×D1111yescharacteristic
998C22×C4D4×D1111yescharacteristic
999C22×C4C23×D1111yescharacteristic
1000C22×C4C23×D1111yescharacteristic
1001C22×C4C23×D1111yescharacteristic
1002Q16—224no—
1003SD16—28no—
1004SD16—228no—
1005SD16—224no—
1006SD16—224no—
1007D8—28no—
1008D8—228no—
1009D8—224no—
1010D8—228no—
1011D8—228no—
1012M16—24no—
1013M16—228no—
1014C2×C8—112no—
1015C2×C8—112no—
1016C2×C8—228no—
1017C2×C8—224no—
1018C2×C8C23×D1114yes—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—112no—
1022C4⋊C4—222no—
1023C4⋊C4—222no—
1024C4⋊C4—221no—
1025C4⋊C4C23×D1111yescharacteristic
1026C4⋊C4C23×D1111yescharacteristic
1027C22⋊C4—21no—
1028C22⋊C4—21no—
1029C22⋊C4—21no—
1030C22⋊C4—21no—
1031C22⋊C4—21no—
1032C22⋊C4—222no—
1033C22⋊C4—222no—
1034C22⋊C4—222no—
1035C22⋊C4—222no—
1036C22⋊C4—222no—
1037C22⋊C4—222no—
1038C22⋊C4—222no—
1039C42—21no—
1040C42—222no—
1041C11#6037211yescharacteristic, complemented, Sylow
1042C23—28no—
1043C23—28no—
1044C23—22no—
1045C23—22no—
1046C23—24no—
1047C23—28no—
1048C23—21no—
1049C23—41no—
1050C23—44no—
1051C23—44no—
1052C23—82no—
1053C23—82no—
1054C23—82no—
1055C23—82no—
1056C23—816no—
1057C23—112no—
1058C23—112no—
1059C23—224no—
1060C23—2216no—
1061C23—224no—
1062C23—2216no—
1063C23—224no—
1064C23—222no—
1065C23—222no—
1066C23—442no—
1067C23—442no—
1068C23—444no—
1069C23—442no—
1070C23—442no—
1071C23—881no—
1072C23—881no—
1073C23—884no—
1074C23—884no—
1075C23—884no—
1076C23—884no—
1077C23—882no—
1078C23—882no—
1079C23—8832no—
1080C23C2×D4×D1111yescharacteristic
1081C23C2×D4×D1111yescharacteristic
1082C23C2×D4×D1111yescharacteristic
1083Q8—22no—
1084Q8—114no—
1085Q8—114no—
1086Q8—224no—
1087Q8—224no—
1088Q8—222no—
1089Q8—222no—
1090D4—28no—
1091D4—28no—
1092D4—28no—
1093D4—24no—
1094D4—22no—
1095D4—42no—
1096D4—42no—
1097D4—81no—
1098D4—118no—
1099D4—114no—
1100D4—114no—
1101D4—224no—
1102D4—224no—
1103D4—224no—
1104D4—2216no—
1105D4—224no—
1106D4—2216no—
1107D4—2216no—
1108D4—228no—
1109D4—2216no—
1110D4—224no—
1111D4—228no—
1112D4—222no—
1113D4—222no—
1114D4—224no—
1115D4—444no—
1116D4—444no—
1117D4—444no—
1118D4—442no—
1119D4—882no—
1120D4—882no—
1121D4—882no—
1122D4—882no—
1123D4C2×D4×D1118yes—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—42no—
1133C2×C4—112no—
1134C2×C4—118no—
1135C2×C4—112no—
1136C2×C4—224no—
1137C2×C4—224no—
1138C2×C4—228no—
1139C2×C4—224no—
1140C2×C4—2216no—
1141C2×C4—224no—
1142C2×C4—2216no—
1143C2×C4—222no—
1144C2×C4—228no—
1145C2×C4—224no—
1146C2×C4—222no—
1147C2×C4—444no—
1148C2×C4—882no—
1149C2×C4—881no—
1150C2×C4C2×D4×D1111yescharacteristic
1151C2×C4C2×D4×D1111yescharacteristic
1152C2×C4C2×D4×D1111yescharacteristic
1153C2×C4C2×D4×D1114yes—
1154C2×C4C24×D1111yescharacteristic
1155C8—24no—
1156C8—222no—
1157C8—222no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—28no—
1165C22—21no—
1166C22—44no—
1167C22—416no—
1168C22—44no—
1169C22—44no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—88no—
1174C22—88no—
1175C22—114no—
1176C22—222no—
1177C22—222no—
1178C22—222no—
1179C22—224no—
1180C22—222no—
1181C22—222no—
1182C22—448no—
1183C22—448no—
1184C22—442no—
1185C22—442no—
1186C22—442no—
1187C22—442no—
1188C22—442no—
1189C22—8816no—
1190C22—8816no—
1191C22—1762no—
1192C22—1764no—
1193C22D11×#12012yes—
1194C22#1062330512yescomplemented
1195C22C22×D4×D1111yescharacteristic
1196C4—21no—
1197C4—21no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—114no—
1202C4—222no—
1203C4—224no—
1204C4—442no—
1205C4D11×#12012yes—
1206C4C22×D4×D1112yes—
1207C2—22no—
1208C2—22no—
1209C2—41no—
1210C2—48no—
1211C2—81no—
1212C2—224no—
1213C2—442no—
1214C2—444no—
1215C2—882no—
1216C2C2×D11×#12011yescharacteristic
1217C2C2×#1062330511yescharacteristic
1218C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3003C2
socleC22×C11C23×D4
hypercenter#3003D11
hypocenterC11#60372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3003

Complements

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

NH ≅ G/Ntype
1. C22×#67037C2semidirect
2. C2×#10623305C2semidirect
3. #13082277C2semidirect
4. #13077921C2semidirect
5. #13077919C2semidirect
6. #13077885C2semidirect
7. #13077879C2semidirect
8. #13077870C2semidirect
9. #13077863C2semidirect
10. #13077844C2semidirect
11. #13077835C2semidirect
12. #13077832C2semidirect
13. C2×#10622830C2semidirect
14. D11×#447C2semidirect
15. #13077141C2semidirect
16. #13077066C2semidirect
17. C11×#3003C2semidirect
18. C23×D4×C11C22semidirect
20. C2×#67042C22semidirect
26. C2×#67037C22semidirect
27. C2×#67037C22semidirect
29. C22×#4341C22semidirect
31. C22×D4×D11C22semidirect
33. C22×#4339C22semidirect
34. C2×C11×AGL(1,ℤ/8)C22semidirect
35. C11×#525C22semidirect
36. #10623364C22semidirect
37. C2×#67003C22semidirect
38. C22×#4323C22semidirect
39. C2×#66983C22semidirect
41. C2×#66969C22semidirect
42. C2×#66967C22semidirect
43. C2×#66964C22semidirect
44. C2×D8×D11C22semidirect
45. C2×#66961C22semidirect
46. C2×#66960C22semidirect
48. #10623160C22semidirect
49. #10623158C22semidirect
50. #10623138C22semidirect
51. D11×#121C22semidirect
57. #10623056C22semidirect
58. #10623054C22semidirect
59. C11×#450C22semidirect
60. C11×#450C22semidirect
61. C11×#447C22semidirect
62. C11×#447C22semidirect
63. C11×#418C22semidirect
64. C11×#407C22semidirect
65. #10622830C22semidirect
66. #10622830C22semidirect
67. #10622830C22semidirect
68. C2×#66896C22semidirect
69. C2×C22⋊(C11⋊C8)C22semidirect
70. #10622786C22semidirect
71. #10622782C22semidirect
72. #10622771C22semidirect
73. #10622769C22semidirect
74. #10622746C22semidirect
75. #10622742C22semidirect
76. #10622663C22semidirect
77. #10622660C22semidirect
78. #10622659C22semidirect
79. #10622653C22semidirect
80. #10622650C22semidirect
81. #10622649C22semidirect
82. #10622615C22semidirect
83. #10622394C22semidirect
84. #10622394C22semidirect
85. #10622386C22semidirect
86. #10622386C22semidirect
87. #10622385C22semidirect
88. #10622384C22semidirect
89. #10622383C22semidirect
90. D11×#102C22semidirect
91. #10622351C22semidirect
92. #10622347C22semidirect
93. #10622345C22semidirect
94. #10622340C22semidirect
95. #10622339C22semidirect
96. D11×C22⋊C8C22semidirect
99. C2×C11×#41C23semidirect
120. C2×#4343C23semidirect
129. #67037D4semidirect
150. C2×D4×D11C23semidirect
167. C22×D44C23semidirect
173. C2×C11×SD16C23semidirect
174. C2×C11×D8C23semidirect
175. C2×C11×M16C23semidirect
178. C11×C22⋊Q8C23semidirect
180. C11×#121C23semidirect
184. C11×#117C23semidirect
186. #66999C23semidirect
187. C2×#4326C23semidirect
188. C2×#4325C23semidirect
192. #66991C23semidirect
194. C2×#4324C23semidirect
196. C2×#4323C23semidirect
197. C2×#4323C23semidirect
198. C2×#4323C23semidirect
203. #66983C23semidirect
205. C2×C4⋊Dic11C23semidirect
207. C22×C11⋊C8C23semidirect
214. C2×D88C23semidirect
215. C2×#4314C23semidirect
216. C2×#4313C23semidirect
217. C2×C8×D11C23semidirect
220. #66948C23semidirect
221. #66948C23semidirect
224. #66945C23semidirect
225. C4⋊C4×D11C23semidirect
240. C11×#102C23semidirect
241. C11×#102C23semidirect
243. C11×C22⋊C8C23semidirect
244. #66896C23semidirect
245. #66896C23semidirect
248. C22⋊(C11⋊C8)C23semidirect
249. #66885C23semidirect
250. (C2×D11)⋊C8C23semidirect
251. (C2×D11)⋊C8C23semidirect
252. #66880C23semidirect
253. #66874C23semidirect
254. #66874C23semidirect
255. #66873C23semidirect
256. #66873C23semidirect
288. C2×D4×C11C2×D4semidirect
337. #4341C2×D4semidirect
349. D4×D11C2×D4semidirect
362. #4339C2×D4semidirect
443. #3003D11semidirect
581. C23×D4C2×D11semidirect
586. C2×AGL(1,ℤ/8)C2×D11semidirect
603. #525C2×D11semidirect
612. #450C2×D11semidirect
613. #450C2×D11semidirect
629. #447C2×D11semidirect
630. #447C2×D11semidirect
632. #418C2×D11semidirect
642. #407C2×D11semidirect
663. C22×C11#576semidirect
729. C2×#41C22×D11semidirect
779. C2×SD16C22×D11semidirect
786. C2×D8C22×D11semidirect
789. C2×M16C22×D11semidirect
802. C22⋊Q8C22×D11semidirect
818. #121C22×D11semidirect
832. #117C22×D11semidirect
845. #102C22×D11semidirect
846. #102C22×D11semidirect
853. C22⋊C8C22×D11semidirect
975. C2×D4D4×D11semidirect
1041. C11#60372semidirect
1194. C22#10623305semidirect

Maximal subgroups

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

subgroupindex
C22×#670372
C2×#106233052
#130822772
#130779212
#130779192
#130778852
#130778792
#130778702
#130778632
#130778442
#130778352
#130778322
C2×#106228302
D11×#4472
#130771412
#130770662
C11×#30032
#6037211