Finite Group Databasebeta

← #25963128

Subgroups — #25963128

Order 11008.

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×#13063371C211yesmaximal, characteristic, complemented
2C2×#14583703C212yesmaximal, complemented
3#19148260C211yesmaximal, characteristic, complemented
4#19143901C212yesmaximal, complemented
5#19143897C214yesmaximal, complemented
6#19143862C212yesmaximal, complemented
7#19143860C214yesmaximal, complemented
8#19143846C212yesmaximal, complemented
9#19143825C211yesmaximal, characteristic, complemented
10#19143819C212yesmaximal, complemented
11#19143813C211yesmaximal, characteristic, complemented
12#19143812C212yesmaximal, complemented
13C2×#14583032C211yesmaximal, characteristic, complemented
14#447×D43C212yesmaximal, complemented
15#19143119C212yesmaximal, complemented
16#19143045C211yesmaximal, characteristic, complemented
17C43×#3006C211yesmaximal, characteristic, complemented
18C2×#13063371—216no—
19C2×#13063371—22no—
20C2×#13063371—21no—
21C2×#13063371—21no—
22C2×#13063371C2212yes—
23C2×#13063371C2214yescomplemented
24C2×#13063371C2212yescomplemented
25C2×#13063370C2211yescharacteristic, complemented
26C22×#10621902C2212yescomplemented
27C22×#10621898—21no—
28C22×#10621898C2211yescharacteristic
29C23×D172—21no—
30C23×D172C2211yescharacteristic, complemented
31C22×D4×D43—22no—
32C22×D4×D43C2212yescomplemented
33#14583703—216no—
34C2×#13063353C2212yescomplemented
35C2×#13063352C2214yescomplemented
36C2×#13063349C2214yescomplemented
37C2×#13063346C2214yescomplemented
38C2×#13063345C2212yescomplemented
39C22×#10621882C2212yescomplemented
40C2×D8×D43C2214yescomplemented
41C2×#13063333C2212yescomplemented
42#14583567—21no—
43#14583555—21no—
44#14583546—21no—
45#14583539—22no—
46#14583533—21no—
47D4×C22⋊D43—22no—
48#14583480C2211yescharacteristic, complemented
49#14583478C2212yescomplemented
50#14583466C2211yescharacteristic, complemented
51#14583465C2212yescomplemented
52#14583410C2211yescharacteristic, complemented
53#14583409C2212yescomplemented
54#121×D43C2212yescomplemented
55#14583380C2211yescharacteristic, complemented
56#14583064C2214yescomplemented
57#14583061C2212yescomplemented
58#14583055C2211yescharacteristic, complemented
59#14583052C2212yescomplemented
60#14583052C2212yescomplemented
61#14583051C2214yescomplemented
62#14583050C2211yescharacteristic, complemented
63#14583047C2214yescomplemented
64#14583044C2212yescomplemented
65#14583043C2214yescomplemented
66#14583043C2214yescomplemented
67#14583038C2211yescharacteristic, complemented
68#14583035C2212yescomplemented
69#14583035C2212yescomplemented
70#14583034C2214yescomplemented
71#14583033C2211yescharacteristic, complemented
72#14583032C2212yescomplemented
73#14583032C2212yescomplemented
74#14583032C2214yescomplemented
75#14583031C2214yescomplemented
76#14583031C2214yescomplemented
77#14582905C2212yescomplemented
78#14582902C2214yescomplemented
79#14582899C2214yescomplemented
80#14582895C2212yescomplemented
81#14582894C2214yescomplemented
82C2×#13063245C2212yescomplemented
83#102×D43C2214yescomplemented
84#14582867C2212yescomplemented
85#14582864C2214yescomplemented
86#14582861C2212yescomplemented
87C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
88C22⋊C8×D43C2212yescomplemented
89C22×#41×C43C2211yescharacteristic, complemented
90C2×AGL(1,ℤ/8)×C43C2212yescomplemented
91C2×#121×C43C2211yescharacteristic, complemented
92C43×#449C2214yescomplemented
93C43×#448C2212yescomplemented
94C43×#447C2212yescomplemented
95C43×#417C2212yescomplemented
96C43×#407C2211yescharacteristic, complemented
97C24×D43—21no—
98C24×D43—22no—
99#13063371—232no—
100#13063371—216no—
101#13063371—216no—
102#13063371—28no—
103#13063371—216no—
104#13063371—216no—
105#13063371—28no—
106#13063371—28no—
107#13063371D4116yescomplemented
108#13063370—28no—
109C2×#10621902—216no—
110C2×#10621902—22no—
111C2×#10621902—22no—
112C2×#10621902C2314yes—
113C2×#10621902C2314yes—
114C2×#10621898—216no—
115C2×#10621898—28no—
116C2×#10621898—22no—
117C2×#10621898—24no—
118C2×#10621898—22no—
119C2×#10621898D411yescharacteristic
120C2×#10621898D412yes—
121C2×#10621898D411yescharacteristic
122C2×#10621898C2312yes—
123C2×#10621898C2311yescharacteristic
124C2×#10621898C2311yescharacteristic
125C2×#10621898C2311yescharacteristic, complemented
126C2×#10621900—21no—
127C2×#10621900C2312yescomplemented
128C22×Dic86D411yescharacteristic
129C22×D172—216no—
130C22×D172—22no—
131C22×D172—21no—
132C22×D172—21no—
133C22×D172—21no—
134C22×D172—22no—
135C22×D172—24no—
136C22×D172—22no—
137C22×D172—28no—
138C22×D172D411yescharacteristic
139C22×D172C2312yes—
140C22×D172C2312yes—
141C22×D172C2312yes—
142C22×C22⋊D43—22no—
143C22×C22⋊D43—22no—
144C22×C22⋊D43D412yes—
145C2×D4×D43—232no—
146C2×D4×D43—24no—
147C2×D4×D43—24no—
148C2×D4×D43—24no—
149C2×D4×D43—24no—
150C2×D4×D43—216no—
151C2×D4×D43—22no—
152C2×D4×D43—21no—
153C2×D4×D43—22no—
154C2×D4×D43—22no—
155C2×D4×D43C2314yes—
156C2×D4×D43C2314yes—
157C2×D4×D43C2312yescomplemented
158C22×C4×D43—22no—
159C22×C4×D43C2312yes—
160#13063353—28no—
161#13063352—216no—
162#13063349—216no—
163#13063346—216no—
164#13063345—28no—
165C2×#10621885C2312yescomplemented
166C2×#10621873C2314yescomplemented
167C2×#10621883C2312yescomplemented
168C2×#10621884C2312yescomplemented
169C2×D344C2314yescomplemented
170C2×#10621882—28no—
171C2×#10621882C2314yescomplemented
172C2×#10621882C2314yescomplemented
173C2×#10621882C2312yescomplemented
174D8×D43—216no—
175#13063333—28no—
176C2×#10621872C2314yescomplemented
177C22×C43⋊C8C2312yescomplemented
178C2×C8×D43C2314yescomplemented
179#13063321—22no—
180#13063321—21no—
181#13063312—21no—
182#13063311—22no—
183#13063308—21no—
184#13063307—22no—
185#13063305—21no—
186#13063305C2312yescomplemented
187#13063304C2311yescharacteristic
188#13063304C2311yescharacteristic, complemented
189#13063302—22no—
190#13063300—21no—
191#13063300C2312yescomplemented
192#13063299—22no—
193#13063299C2311yescharacteristic
194#13063299C2311yescharacteristic, complemented
195#13063298—22no—
196#13063298—22no—
197#13063297—22no—
198#13063297—22no—
199#13063296—22no—
200#13063296C2312yescomplemented
201#13063296C2312yescomplemented
202#13063295—22no—
203#13063294—21no—
204#13063294—22no—
205#13063293—22no—
206#13063293—22no—
207#13063290—21no—
208D4×Dic43—22no—
209#13063287—21no—
210C4×C22⋊D43—21no—
211C4×C22⋊D43—21no—
212C4×C22⋊D43—22no—
213(C22⋊D43)⋊C4—22no—
214#13063284C2311yescharacteristic, complemented
215#13063283C2312yescomplemented
216C4⋊C4×D43C2312yescomplemented
217C22⋊C4×D43—22no—
218#13063249C2312yescomplemented
219#13063249C2312yescomplemented
220#13063247C2314yescomplemented
221#13063247C2314yescomplemented
222#13063246C2312yescomplemented
223#13063246C2312yescomplemented
224#13063245C2314yescomplemented
225#13063245C2314yescomplemented
226C22⋊(C43⋊C8)C2311yescharacteristic
227C22⋊(C43⋊C8)C2311yescharacteristic
228C22⋊(C43⋊C8)C2312yescomplemented
229(C2×D43)⋊C8C2314yescomplemented
230(C2×D43)⋊C8C2314yescomplemented
231C2×#41×C43—28no—
232C2×#41×C43—21no—
233C2×#41×C43—21no—
234C2×#41×C43C2312yes—
235C2×#41×C43C2312yes—
236C22×Q8×C43C2311yescharacteristic
237C22×D4×C43—21no—
238C22×D4×C43—21no—
239C22×D4×C43C2311yescharacteristic
240C22×D4×C43C2311yescharacteristic, complemented
241C23×C4×C43—21no—
242C23×C4×C43C2311yescharacteristic
243AGL(1,ℤ/8)×C43—28no—
244C2×SD16×C43C2314yescomplemented
245C2×D8×C43C2314yescomplemented
246C2×M16×C43C2312yescomplemented
247#121×C43—21no—
248#121×C43—21no—
249#121×C43C2312yes—
250#121×C43C2312yescomplemented
251C2×C4⋊C4×C43C2311yescharacteristic, complemented
252C2×C22⋊C4×C43—21no—
253#103×C43C2314yescomplemented
254#102×C43C2314yescomplemented
255C22⋊C8×C43C2312yes—
256C22⋊C8×C43C2312yescomplemented
257C24×C43—21no—
258C24×C43—21no—
259C24×C43C2×D411yescharacteristic
260C23×D43—22no—
261C23×D43—28no—
262C23×D43—216no—
263C23×D43—22no—
264C23×D43—22no—
265C23×D43—24no—
266C23×D43—24no—
267C23×D43—22no—
268C23×D43—84no—
269C23×D43—82no—
270C23×D43—84no—
271C23×D43—82no—
272C23×D43C2×D412yes—
273#41×C43—28no—
274#41×C43—28no—
275#41×C43—24no—
276#41×C43—24no—
277#41×C43—24no—
278#41×C43C2×D418yescomplemented
279C2×Q8×C43—24no—
280C2×Q8×C43—21no—
281C2×Q8×C43C2412yes—
282C2×D4×C43—28no—
283C2×D4×C43—24no—
284C2×D4×C43—21no—
285C2×D4×C43—21no—
286C2×D4×C43—22no—
287C2×D4×C43—22no—
288C2×D4×C43—22no—
289C2×D4×C43—22no—
290C2×D4×C43—24no—
291C2×D4×C43—82no—
292C2×D4×C43C2412yes—
293C2×D4×C43C2412yes—
294C22×C4×C43—28no—
295C22×C4×C43—22no—
296C22×C4×C43—22no—
297C22×C4×C43—24no—
298C22×C4×C43—21no—
299C22×C4×C43—21no—
300C22×C4×C43C2×D411yescharacteristic
301C22×C4×C43C2×D411yescharacteristic
302C22×C4×C43C2×D411yescharacteristic
303C22×C4×C43C2411yescharacteristic
304C22×C4×C43C2411yescharacteristic
305C22×C4×C43C2411yescharacteristic
306C2×C22⋊D43—216no—
307C2×C22⋊D43—28no—
308C2×C22⋊D43—24no—
309C2×C22⋊D43—24no—
310C2×C22⋊D43—22no—
311C2×C22⋊D43—21no—
312C2×C22⋊D43—21no—
313C2×C22⋊D43—21no—
314C2×C22⋊D43—22no—
315C2×C22⋊D43—22no—
316C2×C22⋊D43—22no—
317C2×C22⋊D43—48no—
318C2×C22⋊D43C2×D412yes—
319C2×C22⋊D43C2×D412yes—
320C2×C22⋊D43C2×D412yes—
321C2×C22⋊D43C2×D412yes—
322C22×Dic43—22no—
323C22×Dic43C2×D412yes—
324#10621902—216no—
325#10621902—216no—
326#10621902—28no—
327#10621902—28no—
328#10621902—28no—
329#10621902C2×D4116yescomplemented
330#10621900—28no—
331#10621900—44no—
332D4×D43—232no—
333D4×D43—216no—
334D4×D43—232no—
335D4×D43—232no—
336D4×D43—216no—
337D4×D43—28no—
338D4×D43—232no—
339D4×D43—28no—
340D4×D43—28no—
341D4×D43—28no—
342D4×D43—44no—
343D4×D43—84no—
344D4×D43C2×D4116yescomplemented
345#10621898—216no—
346#10621898—232no—
347#10621898—24no—
348#10621898—28no—
349#10621898—24no—
350#10621898—28no—
351#10621898—24no—
352#10621898—216no—
353#10621898—24no—
354#10621898C2×D418yes—
355C2×D172—216no—
356C2×D172—28no—
357C2×D172—216no—
358C2×D172—28no—
359C2×D172—232no—
360C2×D172—28no—
361C2×D172—22no—
362C2×D172—22no—
363C2×D172—22no—
364C2×D172—24no—
365C2×D172—24no—
366C2×D172—216no—
367C2×D172—28no—
368C2×D172—28no—
369C2×D172—24no—
370C2×D172—24no—
371C2×D172—22no—
372C2×D172C2×D412yes—
373C2×D172C2×D411yescharacteristic
374C2×D172C2×D411yescharacteristic
375C2×D172C2×D418yescomplemented
376C2×D172C2411yescharacteristic
377C2×D172C2414yes—
378C2×C4×D43—216no—
379C2×C4×D43—24no—
380C2×C4×D43—24no—
381C2×C4×D43—28no—
382C2×C4×D43—21no—
383C2×C4×D43—22no—
384C2×C4×D43C2×D412yes—
385C2×C4×D43C2×D412yes—
386C2×C4×D43C2412yes—
387C2×C4×D43C2412yes—
388C2×Dic86—24no—
389C2×Dic86C2×D412yes—
390C2×Dic86C2×D411yescharacteristic
391C2×Dic86C2×D411yescharacteristic
392C2×Dic86C2411yescharacteristic
393SD16×C43—28no—
394D8×C43—28no—
395M16×C43—24no—
396C2×C8×C43C2414yes—
397C4⋊C4×C43—21no—
398C4⋊C4×C43C2412yes—
399C22⋊C4×C43—22no—
400C22⋊C4×C43—22no—
401C22⋊Dic43—22no—
402C22⋊Dic43—22no—
403C22⋊Dic43—21no—
404C22⋊Dic43—21no—
405C22⋊Dic43—21no—
406#10621885—24no—
407#10621884—24no—
408#10621883—24no—
409#10621882—24no—
410#10621882—28no—
411#10621882—28no—
412(C2×D43)⋊C4—21no—
413(C2×D43)⋊C4—21no—
414(C2×D43)⋊C4—22no—
415(C2×D43)⋊C4—22no—
416(C2×D43)⋊C4—22no—
417C4⋊Dic43—22no—
418C4⋊Dic43C2411yescharacteristic
419C4⋊Dic43C2411yescharacteristic
420Dic43⋊C4—21no—
421Dic43⋊C4—21no—
422Dic43⋊C4—22no—
423C4×Dic43—21no—
424C4×Dic43—22no—
425C2×C43⋊C8—24no—
426C2×C43⋊C8C2412yes—
427C2×C43⋊C8C2412yes—
428D344—28no—
429#10621873—28no—
430#10621872—28no—
431C8×D43—28no—
432C23×C43—24no—
433C23×C43—22no—
434C23×C43—22no—
435C23×C43—22no—
436C23×C43—22no—
437C23×C43—41no—
438C23×C43—42no—
439C23×C43—42no—
440C23×C43—42no—
441C23×C43—81no—
442C23×C43—81no—
443C23×C43C22×D411yescharacteristic
444C23×C43C22×D411yescharacteristic
445C23×C43C22×D411yescharacteristic
446C22×D43—28no—
447C22×D43—24no—
448C22×D43—24no—
449C22×D43—28no—
450C22×D43—216no—
451C22×D43—28no—
452C22×D43—24no—
453C22×D43—216no—
454C22×D43—21no—
455C22×D43—42no—
456C22×D43—44no—
457C22×D43—44no—
458C22×D43—44no—
459C22×D43—84no—
460C22×D43—84no—
461C22×D43—84no—
462C22×D43—84no—
463C22×D43—82no—
464C22×D43—82no—
465C22×D43—82no—
466C22×D43—82no—
467C22×D43—82no—
468C22×D43—82no—
469C22×D43—832no—
470C22×D43—816no—
471C22×D43C22×D412yes—
472C22×D43C22×D412yes—
473Q8×C43—24no—
474Q8×C43—22no—
475Q8×C43C22×D414yes—
476D4×C43—28no—
477D4×C43—24no—
478D4×C43—28no—
479D4×C43—22no—
480D4×C43—24no—
481D4×C43—44no—
482D4×C43—42no—
483D4×C43—82no—
484D4×C43C22×D414yes—
485C2×C4×C43—24no—
486C2×C4×C43—28no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—28no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—81no—
496C2×C4×C43C22×D411yescharacteristic
497C2×C4×C43C22×D411yescharacteristic
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C22×D414yes—
500C2×C4×C43C2511yescharacteristic
501C22⋊D43—216no—
502C22⋊D43—24no—
503C22⋊D43—24no—
504C22⋊D43—24no—
505C22⋊D43—216no—
506C22⋊D43—42no—
507C22⋊D43—42no—
508C22⋊D43—44no—
509C22⋊D43—44no—
510C22⋊D43—82no—
511C22⋊D43—82no—
512C22⋊D43—81no—
513C22⋊D43#12018yes—
514C2×Dic43—24no—
515C2×Dic43—21no—
516C2×Dic43—21no—
517C2×Dic43—21no—
518C2×Dic43—44no—
519C2×Dic43C22×D412yes—
520C2×Dic43C22×D412yes—
521D172—28no—
522D172—216no—
523D172—28no—
524D172—24no—
525D172—216no—
526D172—22no—
527D172—28no—
528D172—24no—
529D172—22no—
530D172—82no—
531D172#12014yes—
532D172C22×D418yes—
533C4×D43—216no—
534C4×D43—24no—
535C4×D43—24no—
536C4×D43—216no—
537C4×D43—24no—
538C4×D43—42no—
539C4×D43—82no—
540C4×D43C22×D418yes—
541Dic86—22no—
542Dic86—24no—
543Dic86—22no—
544Dic86#12014yes—
545C8×C43—24no—
546C43⋊C8—22no—
547C43⋊C8—22no—
548#60372—431nomaximal, Sylow
549C22×C43—21no—
550C22×C43—21no—
551C22×C43—21no—
552C22×C43—21no—
553C22×C43—21no—
554C22×C43—24no—
555C22×C43—21no—
556C22×C43—21no—
557C22×C43—44no—
558C22×C43—48no—
559C22×C43—42no—
560C22×C43—42no—
561C22×C43—42no—
562C22×C43—42no—
563C22×C43—42no—
564C22×C43—162no—
565C22×C43C2×#12012yes—
566C22×C43#57612yescomplemented
567C22×C43C23×D411yescharacteristic
568C2×D43—22no—
569C2×D43—22no—
570C2×D43—22no—
571C2×D43—28no—
572C2×D43—22no—
573C2×D43—22no—
574C2×D43—48no—
575C2×D43—416no—
576C2×D43—44no—
577C2×D43—44no—
578C2×D43—41no—
579C2×D43—41no—
580C2×D43—41no—
581C2×D43—816no—
582C2×D43—88no—
583C2×D43—816no—
584C2×D43—88no—
585C2×D43—164no—
586C2×D43C2×#12014yes—
587C4×C43—21no—
588C4×C43—24no—
589C4×C43—21no—
590C4×C43—42no—
591C4×C43C2×#12012yes—
592C4×C43C23×D412yes—
593Dic43—22no—
594Dic43—41no—
595Dic43—41no—
596Dic43—41no—
597Dic43C2×#12014yes—
598C22×H(5,𝔽2)—431no—
599C2×#576—432no—
600#3488—431no—
601#3012—434no—
602#3012—432no—
603#3008—434no—
604#3008—432no—
605#3006—432no—
606#3006D4311yescharacteristic, complemented
607#3003—432no—
608#3003—431no—
609#3002—432no—
610#3002—431no—
611C2×#447—432no—
612C2×#447—431no—
613#2897—432no—
614#2880—431no—
615C2×C43—22no—
616C2×C43—22no—
617C2×C43—41no—
618C2×C43—44no—
619C2×C43—82no—
620C2×C43C22×#12011yescharacteristic
621C2×C43C2×#57611yescharacteristic
622C2×C43#358511yescharacteristic
623D43—24no—
624D43—42no—
625D43—48no—
626D43—81no—
627C2×H(5,𝔽2)—432no—
628C2×H(5,𝔽2)—434no—
629C2×H(5,𝔽2)—432no—
630C2×H(5,𝔽2)—431no—
631C2×H(5,𝔽2)—861no—
632C2×H(5,𝔽2)—862no—
633C2×H(5,𝔽2)—861no—
634C2×H(5,𝔽2)—8616no—
635C22×#41—431no—
636C22×#41—432no—
637C22×#41—861no—
638C22×#41C2×D4311yescharacteristic, complemented
639C23×D4—432no—
640C23×D4—431no—
641C23×D4—861no—
642C23×D4—862no—
643#576—8616no—
644C2×AGL(1,ℤ/8)—434no—
645C2×AGL(1,ℤ/8)—434no—
646C2×AGL(1,ℤ/8)—432no—
647C2×AGL(1,ℤ/8)C2×D4312yescomplemented
648C2×#135—432no—
649C2×#135—434no—
650C22×D8—432no—
651C22×D8—434no—
652C2×#131—432no—
653#550—861no—
654#548—861no—
655#546—862no—
656#546—861no—
657D42—861no—
658D42—862no—
659#537—432no—
660#537—431no—
661#535—431no—
662#535—432no—
663#525—431no—
664#525—432no—
665C2×#121—432no—
666C2×#121C2×D4311yescharacteristic, complemented
667#520—431no—
668#452—432no—
669#452—434no—
670#451—431no—
671#450—431no—
672#450—434no—
673#450—432no—
674#450—432no—
675#449—432no—
676#449—434no—
677#449—434no—
678#449—434no—
679#449C2×D4314yescomplemented
680#448—431no—
681#448C2×D4312yescomplemented
682#447—431no—
683#447—434no—
684#447—434no—
685#447—432no—
686#447—432no—
687#447—434no—
688#447—434no—
689#447—432no—
690#447—432no—
691#447C2×D4312yescomplemented
692#418—432no—
693#418—434no—
694#417—434no—
695#417C2×D4312yescomplemented
696#416—432no—
697#416—434no—
698C2×#102—432no—
699C2×#102—434no—
700#408—432no—
701#408—434no—
702#407—432no—
703#407C2×D4311yescharacteristic, complemented
704C2×C22⋊C8—431no—
705C2×C22⋊C8—432no—
706C43#6037211yescharacteristic, complemented, Sylow
707C25—862no—
708C25—861no—
709H(5,𝔽2)—4316no—
710H(5,𝔽2)—868no—
711H(5,𝔽2)—8616no—
712H(5,𝔽2)—868no—
713H(5,𝔽2)—8616no—
714H(5,𝔽2)—868no—
715H(5,𝔽2)—8616no—
716H(5,𝔽2)—8632no—
717H(5,𝔽2)—8616no—
718H(5,𝔽2)—868no—
719C2×#41—28no—
720C2×#41—21no—
721C2×#41—21no—
722C2×#41—431no—
723C2×#41—432no—
724C2×#41—431no—
725C2×#41—431no—
726C2×#41—432no—
727C2×#41—431no—
728C2×#41—434no—
729C2×#41—434no—
730C2×#41—432no—
731C2×#41—431no—
732C2×#41—862no—
733C2×#41—864no—
734C2×#41—862no—
735C2×#41—868no—
736C2×#41—8616no—
737C2×#41—862no—
738C2×#41—862no—
739C2×#41—861no—
740C2×#41—8616no—
741C2×#41C22×D4312yes—
742C2×#41C22×D4312yes—
743C22×Q8—431no—
744C22×Q8C22×D4311yescharacteristic
745C22×D4—21no—
746C22×D4—21no—
747C22×D4—434no—
748C22×D4—432no—
749C22×D4—432no—
750C22×D4—434no—
751C22×D4—431no—
752C22×D4—432no—
753C22×D4—432no—
754C22×D4—432no—
755C22×D4—868no—
756C22×D4—862no—
757C22×D4—864no—
758C22×D4—862no—
759C22×D4—862no—
760C22×D4—8616no—
761C22×D4—862no—
762C22×D4—862no—
763C22×D4—862no—
764C22×D4—8616no—
765C22×D4—864no—
766C22×D4—864no—
767C22×D4—864no—
768C22×D4—864no—
769C22×D4—861no—
770C22×D4—8632no—
771C22×D4—862no—
772C22×D4—862no—
773C22×D4—861no—
774C22×D4—861no—
775C22×D4—861no—
776C22×D4C22×D4311yescharacteristic
777C22×D4C22×D4311yescharacteristic, complemented
778C23×C4—21no—
779C23×C4—432no—
780C23×C4—862no—
781C23×C4C22×D4311yescharacteristic
782AGL(1,ℤ/8)—28no—
783AGL(1,ℤ/8)—868no—
784AGL(1,ℤ/8)—8616no—
785AGL(1,ℤ/8)—8616no—
786#135—8616no—
787#135—868no—
788C2×Q16—432no—
789C2×SD16—432no—
790C2×SD16—432no—
791C2×SD16—434no—
792C2×SD16C22×D4314yescomplemented
793C2×D8—434no—
794C2×D8—432no—
795C2×D8—434no—
796C2×D8—434no—
797C2×D8—8616no—
798C2×D8—868no—
799C2×D8C22×D4314yescomplemented
800#131—868no—
801C2×M16—434no—
802C2×M16C22×D4312yescomplemented
803C22×C8—432no—
804C22×C8—434no—
805#127—862no—
806#127—861no—
807#124—862no—
808#124—861no—
809#123—862no—
810#123—861no—
811C22⋊Q8—431no—
812C22⋊Q8—431no—
813C22⋊Q8—432no—
814C22⋊Q8—862no—
815C22⋊Q8—861no—
816#121—21no—
817#121—21no—
818#121—432no—
819#121—432no—
820#121—431no—
821#121—431no—
822#121—432no—
823#121—862no—
824#121—862no—
825#121—861no—
826#121—862no—
827#121—862no—
828#121—862no—
829#121—862no—
830#121C22×D4312yes—
831#121C22×D4312yescomplemented
832#120—862no—
833#120—862no—
834#120—862no—
835#120—862no—
836#120—861no—
837C4×Q8—861no—
838C4×D4—862no—
839C4×D4—861no—
840C4×D4—862no—
841C4×D4—862no—
842C4×D4—861no—
843C4×D4—861no—
844#117—431no—
845#117—432no—
846C2×C4⋊C4—432no—
847C2×C4⋊C4C22×D4311yescharacteristic, complemented
848C2×C22⋊C4—21no—
849C2×C22⋊C4—862no—
850#103—432no—
851#103—432no—
852#103C22×D4314yescomplemented
853#102—432no—
854#102—432no—
855#102—434no—
856#102—434no—
857#102—434no—
858#102—434no—
859#102C22×D4314yescomplemented
860C22⋊C8—431no—
861C22⋊C8—431no—
862C22⋊C8—432no—
863C22⋊C8—434no—
864C22⋊C8—434no—
865C22⋊C8C22×D4312yes—
866C22⋊C8C22×D4312yescomplemented
867C24—21no—
868C24—21no—
869C24—432no—
870C24—864no—
871C24—864no—
872C24—862no—
873C24—8616no—
874C24—868no—
875C24—862no—
876C24—862no—
877C24—862no—
878C24—3442no—
879C24—3444no—
880C24—3442no—
881C24—3444no—
882C24D4×D4311yescharacteristic
883#41—28no—
884#41—28no—
885#41—24no—
886#41—24no—
887#41—24no—
888#41—438no—
889#41—4316no—
890#41—868no—
891#41—868no—
892#41—864no—
893#41—864no—
894#41—8616no—
895#41—8632no—
896#41—8616no—
897#41—868no—
898#41—868no—
899#41—868no—
900#41—8616no—
901#41—8616no—
902#41—868no—
903#41—864no—
904#41—864no—
905#41—1724no—
906#41D4×D4318yescomplemented
907C2×Q8—24no—
908C2×Q8—21no—
909C2×Q8—431no—
910C2×Q8—432no—
911C2×Q8—431no—
912C2×Q8—431no—
913C2×Q8—864no—
914C2×Q8C23×D4312yes—
915C2×D4—28no—
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—24no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—21no—
922C2×D4—24no—
923C2×D4—21no—
924C2×D4—82no—
925C2×D4—432no—
926C2×D4—4316no—
927C2×D4—432no—
928C2×D4—432no—
929C2×D4—432no—
930C2×D4—431no—
931C2×D4—438no—
932C2×D4—432no—
933C2×D4—431no—
934C2×D4—434no—
935C2×D4—431no—
936C2×D4—864no—
937C2×D4—868no—
938C2×D4—868no—
939C2×D4—8616no—
940C2×D4—864no—
941C2×D4—864no—
942C2×D4—8616no—
943C2×D4—868no—
944C2×D4—8632no—
945C2×D4—868no—
946C2×D4—8616no—
947C2×D4—868no—
948C2×D4—862no—
949C2×D4—868no—
950C2×D4—868no—
951C2×D4—864no—
952C2×D4—864no—
953C2×D4—862no—
954C2×D4—868no—
955C2×D4—8632no—
956C2×D4—8616no—
957C2×D4—8632no—
958C2×D4—8616no—
959C2×D4—8632no—
960C2×D4—8632no—
961C2×D4—868no—
962C2×D4—8616no—
963C2×D4—868no—
964C2×D4—862no—
965C2×D4—862no—
966C2×D4—861no—
967C2×D4—862no—
968C2×D4—861no—
969C2×D4—861no—
970C2×D4—862no—
971C2×D4—862no—
972C2×D4—862no—
973C2×D4—864no—
974C2×D4—3444no—
975C2×D4—1724no—
976C2×D4—1728no—
977C2×D4C23×D4312yes—
978C2×D4C23×D4312yes—
979C22×C4—28no—
980C22×C4—21no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—24no—
984C22×C4—21no—
985C22×C4—432no—
986C22×C4—432no—
987C22×C4—432no—
988C22×C4—432no—
989C22×C4—432no—
990C22×C4—868no—
991C22×C4—864no—
992C22×C4—864no—
993C22×C4—8616no—
994C22×C4—862no—
995C22×C4—862no—
996C22×C4—861no—
997C22×C4D4×D4311yescharacteristic
998C22×C4D4×D4311yescharacteristic
999C22×C4D4×D4311yescharacteristic
1000C22×C4C23×D4311yescharacteristic
1001C22×C4C23×D4311yescharacteristic
1002C22×C4C23×D4311yescharacteristic
1003Q16—864no—
1004SD16—28no—
1005SD16—868no—
1006SD16—864no—
1007SD16—864no—
1008D8—28no—
1009D8—868no—
1010D8—868no—
1011D8—868no—
1012D8—864no—
1013M16—24no—
1014M16—868no—
1015C2×C8—432no—
1016C2×C8—432no—
1017C2×C8—868no—
1018C2×C8—864no—
1019C2×C8C23×D4314yes—
1020C4⋊C4—21no—
1021C4⋊C4—431no—
1022C4⋊C4—431no—
1023C4⋊C4—862no—
1024C4⋊C4—862no—
1025C4⋊C4—861no—
1026C4⋊C4—861no—
1027C4⋊C4C23×D4312yes—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—862no—
1031C22⋊C4—862no—
1032C22⋊C4—862no—
1033C22⋊C4—862no—
1034C22⋊C4—862no—
1035C22⋊C4—861no—
1036C22⋊C4—861no—
1037C22⋊C4—861no—
1038C22⋊C4—861no—
1039C22⋊C4—861no—
1040C42—862no—
1041C42—861no—
1042C23—24no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—81no—
1052C23—81no—
1053C23—432no—
1054C23—432no—
1055C23—8616no—
1056C23—864no—
1057C23—868no—
1058C23—8616no—
1059C23—868no—
1060C23—868no—
1061C23—864no—
1062C23—864no—
1063C23—861no—
1064C23—3442no—
1065C23—3442no—
1066C23—3442no—
1067C23—3442no—
1068C23—3444no—
1069C23—3444no—
1070C23—3444no—
1071C23—3444no—
1072C23—3442no—
1073C23—3442no—
1074C23—34416no—
1075C23—34432no—
1076C23—1722no—
1077C23—1724no—
1078C23—1724no—
1079C23—1724no—
1080C23C2×D4×D4311yescharacteristic
1081C23C2×D4×D4311yescharacteristic
1082C23C2×D4×D4311yescharacteristic
1083Q8—24no—
1084Q8—22no—
1085Q8—434no—
1086Q8—864no—
1087Q8—862no—
1088Q8—862no—
1089Q8C2×D4×D4314yes—
1090D4—28no—
1091D4—24no—
1092D4—28no—
1093D4—22no—
1094D4—24no—
1095D4—44no—
1096D4—42no—
1097D4—82no—
1098D4—438no—
1099D4—434no—
1100D4—438no—
1101D4—864no—
1102D4—8616no—
1103D4—868no—
1104D4—8616no—
1105D4—868no—
1106D4—864no—
1107D4—8616no—
1108D4—864no—
1109D4—8616no—
1110D4—864no—
1111D4—868no—
1112D4—862no—
1113D4—864no—
1114D4—862no—
1115D4—3442no—
1116D4—3441no—
1117D4—3442no—
1118D4—3442no—
1119D4—1724no—
1120D4—1724no—
1121D4—1722no—
1122D4—1722no—
1123D4C2×D4×D4314yes—
1124C2×C4—24no—
1125C2×C4—28no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—28no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—81no—
1135C2×C4—432no—
1136C2×C4—438no—
1137C2×C4—432no—
1138C2×C4—864no—
1139C2×C4—8616no—
1140C2×C4—864no—
1141C2×C4—8616no—
1142C2×C4—864no—
1143C2×C4—864no—
1144C2×C4—861no—
1145C2×C4—861no—
1146C2×C4—861no—
1147C2×C4—3442no—
1148C2×C4—1724no—
1149C2×C4—1722no—
1150C2×C4C2×D4×D4311yescharacteristic
1151C2×C4C2×D4×D4311yescharacteristic
1152C2×C4C2×D4×D4311yescharacteristic
1153C2×C4C2×D4×D4314yes—
1154C2×C4C24×D4311yescharacteristic
1155C8—24no—
1156C8—862no—
1157C8—862no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—24no—
1164C22—21no—
1165C22—21no—
1166C22—44no—
1167C22—48no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—162no—
1174C22—434no—
1175C22—862no—
1176C22—862no—
1177C22—868no—
1178C22—862no—
1179C22—862no—
1180C22—862no—
1181C22—3448no—
1182C22—34416no—
1183C22—3448no—
1184C22—34416no—
1185C22—1728no—
1186C22—17216no—
1187C22—1721no—
1188C22—1721no—
1189C22—1721no—
1190C22—1724no—
1191C22—1724no—
1192C22—6884no—
1193C22#120×D4312yes—
1194C22#1458370312yescomplemented
1195C22C22×D4×D4311yescharacteristic
1196C4—21no—
1197C4—24no—
1198C4—21no—
1199C4—42no—
1200C4—434no—
1201C4—862no—
1202C4—1721no—
1203C4—1721no—
1204C4—1721no—
1205C4#120×D4312yes—
1206C4C22×D4×D4312yes—
1207C2—22no—
1208C2—22no—
1209C2—41no—
1210C2—44no—
1211C2—82no—
1212C2—864no—
1213C2—3441no—
1214C2—1722no—
1215C2—1728no—
1216C2C2×#120×D4311yescharacteristic
1217C2C2×#1458370311yescharacteristic
1218C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3006C2
socleC22×C43C23×D4
hypercenter#3006D43
hypocenterC43#60372
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. C22×#13063371C2semidirect
2. C2×#14583703C2semidirect
3. #19148260C2semidirect
4. #19143901C2semidirect
5. #19143897C2semidirect
6. #19143862C2semidirect
7. #19143860C2semidirect
8. #19143846C2semidirect
9. #19143825C2semidirect
10. #19143819C2semidirect
11. #19143813C2semidirect
12. #19143812C2semidirect
13. C2×#14583032C2semidirect
14. #447×D43C2semidirect
15. #19143119C2semidirect
16. #19143045C2semidirect
17. C43×#3006C2semidirect
23. C2×#13063371C22semidirect
24. C2×#13063371C22semidirect
25. C2×#13063370C22semidirect
26. C22×#10621902C22semidirect
30. C23×D172C22semidirect
32. C22×D4×D43C22semidirect
34. C2×#13063353C22semidirect
35. C2×#13063352C22semidirect
36. C2×#13063349C22semidirect
37. C2×#13063346C22semidirect
38. C2×#13063345C22semidirect
39. C22×#10621882C22semidirect
40. C2×D8×D43C22semidirect
41. C2×#13063333C22semidirect
48. #14583480C22semidirect
49. #14583478C22semidirect
50. #14583466C22semidirect
51. #14583465C22semidirect
52. #14583410C22semidirect
53. #14583409C22semidirect
54. #121×D43C22semidirect
55. #14583380C22semidirect
56. #14583064C22semidirect
57. #14583061C22semidirect
58. #14583055C22semidirect
59. #14583052C22semidirect
60. #14583052C22semidirect
61. #14583051C22semidirect
62. #14583050C22semidirect
63. #14583047C22semidirect
64. #14583044C22semidirect
65. #14583043C22semidirect
66. #14583043C22semidirect
67. #14583038C22semidirect
68. #14583035C22semidirect
69. #14583035C22semidirect
70. #14583034C22semidirect
71. #14583033C22semidirect
72. #14583032C22semidirect
73. #14583032C22semidirect
74. #14583032C22semidirect
75. #14583031C22semidirect
76. #14583031C22semidirect
77. #14582905C22semidirect
78. #14582902C22semidirect
79. #14582899C22semidirect
80. #14582895C22semidirect
81. #14582894C22semidirect
82. C2×#13063245C22semidirect
83. #102×D43C22semidirect
84. #14582867C22semidirect
85. #14582864C22semidirect
86. #14582861C22semidirect
87. C2×C22⋊(C43⋊C8)C22semidirect
88. C22⋊C8×D43C22semidirect
89. C22×#41×C43C22semidirect
90. C2×AGL(1,ℤ/8)×C43C22semidirect
91. C2×#121×C43C22semidirect
92. C43×#449C22semidirect
93. C43×#448C22semidirect
94. C43×#447C22semidirect
95. C43×#417C22semidirect
96. C43×#407C22semidirect
107. #13063371D4semidirect
125. C2×#10621898C23semidirect
127. C2×#10621900C23semidirect
157. C2×D4×D43C23semidirect
165. C2×#10621885C23semidirect
166. C2×#10621873C23semidirect
167. C2×#10621883C23semidirect
168. C2×#10621884C23semidirect
169. C2×D344C23semidirect
171. C2×#10621882C23semidirect
172. C2×#10621882C23semidirect
173. C2×#10621882C23semidirect
176. C2×#10621872C23semidirect
177. C22×C43⋊C8C23semidirect
178. C2×C8×D43C23semidirect
186. #13063305C23semidirect
188. #13063304C23semidirect
191. #13063300C23semidirect
194. #13063299C23semidirect
200. #13063296C23semidirect
201. #13063296C23semidirect
214. #13063284C23semidirect
215. #13063283C23semidirect
216. C4⋊C4×D43C23semidirect
218. #13063249C23semidirect
219. #13063249C23semidirect
220. #13063247C23semidirect
221. #13063247C23semidirect
222. #13063246C23semidirect
223. #13063246C23semidirect
224. #13063245C23semidirect
225. #13063245C23semidirect
228. C22⋊(C43⋊C8)C23semidirect
229. (C2×D43)⋊C8C23semidirect
230. (C2×D43)⋊C8C23semidirect
240. C22×D4×C43C23semidirect
244. C2×SD16×C43C23semidirect
245. C2×D8×C43C23semidirect
246. C2×M16×C43C23semidirect
250. #121×C43C23semidirect
251. C2×C4⋊C4×C43C23semidirect
253. #103×C43C23semidirect
254. #102×C43C23semidirect
256. C22⋊C8×C43C23semidirect
278. #41×C43C2×D4semidirect
329. #10621902C2×D4semidirect
344. D4×D43C2×D4semidirect
375. C2×D172C2×D4semidirect
566. C22×C43#576semidirect
606. #3006D43semidirect
638. C22×#41C2×D43semidirect
647. C2×AGL(1,ℤ/8)C2×D43semidirect
666. C2×#121C2×D43semidirect
679. #449C2×D43semidirect
681. #448C2×D43semidirect
691. #447C2×D43semidirect
695. #417C2×D43semidirect
703. #407C2×D43semidirect
706. C43#60372semidirect
777. C22×D4C22×D43semidirect
792. C2×SD16C22×D43semidirect
799. C2×D8C22×D43semidirect
802. C2×M16C22×D43semidirect
831. #121C22×D43semidirect
847. C2×C4⋊C4C22×D43semidirect
852. #103C22×D43semidirect
859. #102C22×D43semidirect
866. C22⋊C8C22×D43semidirect
906. #41D4×D43semidirect
1194. C22#14583703semidirect

Maximal subgroups

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

subgroupindex
C22×#130633712
C2×#145837032
#191482602
#191439012
#191438972
#191438622
#191438602
#191438462
#191438252
#191438192
#191438132
#191438122
C2×#145830322
#447×D432
#191431192
#191430452
C43×#30062
#6037243