Finite Group Databasebeta

← #25968243

Subgroups — #25968243

Order 11008.

2108 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148324C211yesmaximal, characteristic, complemented
2#19147924C211yesmaximal, characteristic, complemented
3#19145702C212yesmaximal, complemented
4#19145685C212yesmaximal, complemented
5#19145652C212yesmaximal, complemented
6#19145641C212yesmaximal, complemented
7#19145630C212yesmaximal, complemented
8#19145587C212yesmaximal, complemented
9#19145568C212yesmaximal, complemented
10#19145526C212yesmaximal, complemented
11#19145080C211yesmaximal, characteristic, complemented
12#19145069C211yesmaximal, characteristic, complemented
13#19144963C211yesmaximal, characteristic, complemented
14#19144952C211yesmaximal, characteristic, complemented
15#19144144C211yesmaximal, characteristic, complemented
16#19144133C211yesmaximal, characteristic, complemented
17#19144109C211yesmaximal, characteristic, complemented
18#19144100C211yesmaximal, characteristic, complemented
19#19143840C211yesmaximal, characteristic, complemented
20#19143813C211yesmaximal, characteristic, complemented
21C2×#14583042C211yesmaximal, characteristic, complemented
22#19143255C211yesmaximal, characteristic, complemented
23C43×#3006C211yesmaximal, characteristic, complemented
24C22×#10621898C2211yescharacteristic
25C2×#13063358C2211yescharacteristic, complemented
26C2×#13063353C2211yescharacteristic, complemented
27C2×#13063345C2211yescharacteristic
28C2×#13063345C2211yescharacteristic
29C22×#10621883C2211yescharacteristic, complemented
30C22×#10621882C2211yescharacteristic, complemented
31#14583613—21no—
32#14583601—21no—
33#14583596—21no—
34#14583575—22no—
35#14583549—21no—
36#14583543—22no—
37#14583530C2211yescharacteristic, complemented
38#14583516C2212yescomplemented
39#14583502C2212yescomplemented
40#14583477—21no—
41#14583477—21no—
42#14583473C2212yescomplemented
43#14583470C2211yescharacteristic
44#14583470C2211yescharacteristic
45#14583466C2211yescharacteristic, complemented
46#14583466C2212yescomplemented
47#14583463C2211yescharacteristic
48#14583463C2211yescharacteristic
49#14583458—22no—
50#14583445C2212yescomplemented
51#14583445C2212yescomplemented
52#14583444C2212yescomplemented
53#14583430C2212yescomplemented
54#14583410—21no—
55#14583410—21no—
56#14583410C2211yescharacteristic
57#14583406—22no—
58#14583380C2211yescharacteristic, complemented
59#14583374C2211yescharacteristic, complemented
60C2×#13063284C2211yescharacteristic
61#14583290C2212yescomplemented
62#14583287C2212yescomplemented
63#14583287C2212yescomplemented
64#14583285C2212yescomplemented
65#14583282C2212yescomplemented
66#14583280C2212yescomplemented
67#14583274C2212yescomplemented
68#14583270C2212yescomplemented
69#14583266C2212yescomplemented
70#14583262C2212yescomplemented
71#14583260C2212yescomplemented
72#14583257C2212yescomplemented
73#14583255C2212yescomplemented
74#14583252C2212yescomplemented
75#14583248C2212yescomplemented
76#14583244C2212yescomplemented
77#14583124C2212yescomplemented
78#14583120C2212yescomplemented
79#14583117C2212yescomplemented
80#14583116C2212yescomplemented
81#14583116C2212yescomplemented
82#14583113C2212yescomplemented
83#14583112C2212yescomplemented
84#14583112C2212yescomplemented
85#14583108C2212yescomplemented
86#14583103C2212yescomplemented
87#14583102C2212yescomplemented
88#14583102C2212yescomplemented
89#14583098C2212yescomplemented
90#14583093C2212yescomplemented
91#14583092C2212yescomplemented
92#14583092C2212yescomplemented
93#14583063C2212yescomplemented
94#14583063C2212yescomplemented
95#14583061C2211yescharacteristic, complemented
96#14583061C2211yescharacteristic, complemented
97#14583055C2211yescharacteristic, complemented
98#14583050C2211yescharacteristic, complemented
99#14583046C2212yescomplemented
100#14583046C2212yescomplemented
101#14583044C2211yescharacteristic, complemented
102#14583044C2211yescharacteristic, complemented
103#14583042C2212yes—
104#14583042C2212yes—
105#14583042C2212yescomplemented
106#14583042C2212yescomplemented
107#14583038C2211yescharacteristic, complemented
108#14583033C2211yescharacteristic, complemented
109#14582957C2212yescomplemented
110#14582957C2212yescomplemented
111#14582953C2212yescomplemented
112#14582949C2212yescomplemented
113#14582927C2211yescharacteristic, complemented
114#14582927C2211yescharacteristic, complemented
115#14582909C2211yescharacteristic, complemented
116#14582905C2211yescharacteristic, complemented
117#14582895C2211yescharacteristic
118#14582895C2211yescharacteristic
119C2×#13063248C2211yescharacteristic, complemented
120C2×#13063245C2211yescharacteristic, complemented
121C2×C22⋊(C43⋊C8)C2211yescharacteristic
122#14582857C2211yescharacteristic, complemented
123#14582857C2211yescharacteristic, complemented
124C22×#41×C43C2211yescharacteristic
125C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
126C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
127C2×#121×C43C2211yescharacteristic
128C43×#449C2212yescomplemented
129C43×#449C2212yescomplemented
130C43×#448C2212yescomplemented
131C43×#447C2212yescomplemented
132C43×#417C2211yescharacteristic
133C43×#417C2211yescharacteristic
134C43×#407C2211yescharacteristic
135C2×#10621898—21no—
136C2×#10621898—21no—
137C2×#10621898—42no—
138C2×#10621898—42no—
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2312yes—
141C2×#10621898C2312yes—
142C2×#10621900—22no—
143C22×Dic86C2311yescharacteristic
144C22×D172C2311yescharacteristic
145C22×C22⋊D43—21no—
146C22×C4×D43—21no—
147#13063358—42no—
148#13063353—42no—
149#13063345—42no—
150#13063345—42no—
151C2×Dic172C2312yes—
152C2×#10621885C2311yescharacteristic
153C2×#10621885C2311yescharacteristic
154C2×#10621873C2312yes—
155C2×#10621873C2312yes—
156C2×#10621883—42no—
157C2×#10621883C2312yes—
158C2×#10621883C2312yes—
159C2×#10621883C2311yescharacteristic
160C2×#10621883C2311yescharacteristic
161C2×#10621884C2311yescharacteristic
162C2×#10621884C2311yescharacteristic
163C2×D344C2312yes—
164C2×#10621882—42no—
165C2×#10621882C2312yes—
166C2×#10621882C2312yes—
167C2×#10621882C2311yescharacteristic
168C2×#10621882C2311yescharacteristic
169C22×C43⋊C8C2311yescharacteristic
170C22×C43⋊C8C2311yescharacteristic
171#13063324—21no—
172#13063324C2312yes—
173#13063323C2312yes—
174#13063323C2312yes—
175#13063321C2312yes—
176#13063321C2312yes—
177#13063321C2312yes—
178#13063318—22no—
179#13063318—22no—
180#13063316—21no—
181#13063316C2312yes—
182#13063314C2312yes—
183#13063314C2312yes—
184#13063312—22no—
185#13063312C2312yes—
186#13063312C2312yes—
187#13063312C2312yes—
188#13063311—22no—
189#13063309—22no—
190#13063308—21no—
191#13063308—22no—
192#13063308—22no—
193#13063307—22no—
194#13063306—22no—
195#13063306—22no—
196#13063306—22no—
197#13063306—22no—
198#13063304—22no—
199#13063304—21no—
200#13063304—21no—
201#13063304—21no—
202#13063304—21no—
203#13063304C2311yescharacteristic
204#13063304C2311yescharacteristic
205#13063302—22no—
206#13063301—22no—
207#13063301—22no—
208#13063299—21no—
209#13063299—21no—
210#13063299—21no—
211#13063299—21no—
212#13063299C2311yescharacteristic
213#13063299C2311yescharacteristic
214#13063297—22no—
215#13063297—22no—
216#13063297—22no—
217#13063297—22no—
218#13063297—22no—
219#13063297—22no—
220#13063296—22no—
221#13063296—21no—
222#13063296—21no—
223#13063296—22no—
224#13063296—22no—
225#13063294—21no—
226#13063294—22no—
227#13063294—22no—
228#13063294—22no—
229#13063293—22no—
230#13063293—22no—
231#13063290C2312yes—
232D4×Dic43—22no—
233D4×Dic43—21no—
234D4×Dic43—21no—
235D4×Dic43C2312yes—
236D4×Dic43C2312yes—
237#13063287C2312yes—
238C4×C22⋊D43—21no—
239C4×C22⋊D43—21no—
240C4×C22⋊D43—22no—
241C4×C22⋊D43—22no—
242C4×C22⋊D43—22no—
243C4×C22⋊D43—22no—
244C4×C22⋊D43—22no—
245(C22⋊D43)⋊C4—22no—
246#13063284D412yes—
247#13063284D411yescharacteristic
248#13063284D411yescharacteristic
249#13063284C2311yescharacteristic
250#13063284C2311yescharacteristic
251#13063284C2311yescharacteristic
252#13063284C2312yes—
253#13063283—21no—
254#13063281—22no—
255C2×C4⋊Dic43D411yescharacteristic
256C2×C4⋊Dic43D411yescharacteristic
257C4⋊C4×D43—21no—
258C2×C22⋊Dic43—22no—
259C2×C22⋊Dic43D412yes—
260C2×C4×Dic43C2312yes—
261Dic43⋊C8C2312yes—
262Dic43⋊C8C2312yes—
263Dic43⋊C8C2312yes—
264Dic43⋊C8C2312yes—
265#13063250C2312yes—
266#13063250C2312yes—
267#13063249C2311yescharacteristic
268#13063249C2311yescharacteristic
269#13063249C2311yescharacteristic
270#13063249C2311yescharacteristic
271#13063248C2312yes—
272#13063248C2312yes—
273#13063247C2312yes—
274#13063247C2312yes—
275#13063246C2311yescharacteristic
276#13063246C2311yescharacteristic
277#13063246C2311yescharacteristic
278#13063246C2311yescharacteristic
279#13063245C2312yes—
280#13063245C2312yes—
281C22⋊(C43⋊C8)C2311yescharacteristic
282C22⋊(C43⋊C8)C2311yescharacteristic
283C22⋊(C43⋊C8)C2311yescharacteristic
284C22⋊(C43⋊C8)C2311yescharacteristic
285#13063235C2312yes—
286#13063235C2312yes—
287C8×Dic43C2312yes—
288C8×Dic43C2312yes—
289C2×#41×C43—21no—
290C2×#41×C43—21no—
291C2×#41×C43—42no—
292C2×#41×C43—42no—
293C2×#41×C43C2311yescharacteristic
294C2×#41×C43C2311yescharacteristic
295C2×#41×C43C2311yescharacteristic
296C2×#41×C43C2311yescharacteristic
297C22×Q8×C43C2311yescharacteristic
298C22×D4×C43—21no—
299C22×D4×C43—21no—
300C22×D4×C43C2311yescharacteristic
301C22×D4×C43C2311yescharacteristic
302C23×C4×C43—21no—
303C23×C4×C43C2311yescharacteristic
304AGL(1,ℤ/8)×C43—42no—
305AGL(1,ℤ/8)×C43—42no—
306C2×SD16×C43C2312yes—
307C2×SD16×C43C2312yes—
308C2×D8×C43C2312yes—
309C2×D8×C43C2312yes—
310C2×M16×C43C2311yescharacteristic
311C2×M16×C43C2311yescharacteristic
312#121×C43—21no—
313#121×C43—21no—
314#121×C43C2312yes—
315#121×C43C2312yes—
316C2×C4⋊C4×C43C2311yescharacteristic
317C2×C22⋊C4×C43—21no—
318#103×C43C2312yes—
319#103×C43C2312yes—
320#102×C43C2312yes—
321#102×C43C2312yes—
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C24×C43—21no—
325C24×C43—21no—
326C24×C43C2×D411yescharacteristic
327C23×D43—21no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—41no—
333#41×C43—41no—
334#41×C43—41no—
335#41×C43—41no—
336#41×C43—44no—
337#41×C43—44no—
338C2×Q8×C43—21no—
339C2×Q8×C43—41no—
340C2×Q8×C43—41no—
341C2×Q8×C43C2411yescharacteristic
342C2×Q8×C43C2411yescharacteristic
343C2×D4×C43—21no—
344C2×D4×C43—21no—
345C2×D4×C43—22no—
346C2×D4×C43—21no—
347C2×D4×C43—21no—
348C2×D4×C43—21no—
349C2×D4×C43—21no—
350C2×D4×C43—22no—
351C2×D4×C43—22no—
352C2×D4×C43—22no—
353C2×D4×C43—44no—
354C2×D4×C43—41no—
355C2×D4×C43—41no—
356C2×D4×C43—82no—
357C2×D4×C43C2411yescharacteristic
358C2×D4×C43C2411yescharacteristic
359C2×D4×C43C2412yes—
360C22×C4×C43—22no—
361C22×C4×C43—22no—
362C22×C4×C43—21no—
363C22×C4×C43—21no—
364C22×C4×C43—21no—
365C22×C4×C43—21no—
366C22×C4×C43—21no—
367C22×C4×C43—21no—
368C22×C4×C43—44no—
369C22×C4×C43C2×D411yescharacteristic
370C22×C4×C43C2×D411yescharacteristic
371C22×C4×C43C2×D411yescharacteristic
372C22×C4×C43C2411yescharacteristic
373C22×C4×C43C2411yescharacteristic
374C22×C4×C43C2411yescharacteristic
375C2×C22⋊D43—22no—
376C2×C22⋊D43—22no—
377C2×C22⋊D43—22no—
378C2×C22⋊D43—22no—
379C2×C22⋊D43—22no—
380C2×C22⋊D43—22no—
381C2×C22⋊D43—21no—
382C2×C22⋊D43—21no—
383C2×C22⋊D43—22no—
384C2×C22⋊D43—22no—
385C2×C22⋊D43—21no—
386C2×C22⋊D43—44no—
387C22×Dic43—22no—
388C22×Dic43—22no—
389C22×Dic43—21no—
390C22×Dic43C2×D412yes—
391C22×Dic43C2×D412yes—
392#10621900—84no—
393#10621898—22no—
394#10621898—22no—
395#10621898—42no—
396#10621898—42no—
397#10621898—42no—
398#10621898—42no—
399#10621898—44no—
400#10621898—44no—
401C2×D172—21no—
402C2×D172—22no—
403C2×D172—22no—
404C2×D172C2412yes—
405C2×D172C2411yescharacteristic
406C2×C4×D43—21no—
407C2×C4×D43—22no—
408C2×C4×D43—22no—
409C2×C4×D43—22no—
410C2×C4×D43—44no—
411C2×Dic86—22no—
412C2×Dic86—22no—
413C2×Dic86—21no—
414C2×Dic86—22no—
415C2×Dic86C2412yes—
416C2×Dic86C2411yescharacteristic
417SD16×C43—42no—
418SD16×C43—42no—
419D8×C43—42no—
420D8×C43—42no—
421M16×C43—22no—
422M16×C43—22no—
423C2×C8×C43C2412yes—
424C2×C8×C43C2412yes—
425C4⋊C4×C43—21no—
426C4⋊C4×C43C2412yes—
427C22⋊C4×C43—22no—
428C22⋊C4×C43—22no—
429C22⋊Dic43—22no—
430C22⋊Dic43—22no—
431C22⋊Dic43—22no—
432C22⋊Dic43—22no—
433C22⋊Dic43—22no—
434C22⋊Dic43—22no—
435C22⋊Dic43—22no—
436C22⋊Dic43—22no—
437C22⋊Dic43—21no—
438C22⋊Dic43—21no—
439C22⋊Dic43—21no—
440C22⋊Dic43C2×D412yes—
441C22⋊Dic43C2×D412yes—
442C22⋊Dic43C2×D412yes—
443C22⋊Dic43C2×D412yes—
444#10621885—41no—
445#10621885—41no—
446#10621884—41no—
447#10621884—41no—
448#10621883—42no—
449#10621883—42no—
450#10621883—41no—
451#10621883—41no—
452#10621882—42no—
453#10621882—42no—
454#10621882—41no—
455#10621882—41no—
456(C2×D43)⋊C4—21no—
457(C2×D43)⋊C4—21no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—22no—
460(C2×D43)⋊C4—22no—
461(C2×D43)⋊C4—22no—
462(C2×D43)⋊C4—22no—
463C4⋊Dic43—22no—
464C4⋊Dic43C2×D411yescharacteristic
465C4⋊Dic43C2×D411yescharacteristic
466C4⋊Dic43C2×D411yescharacteristic
467C4⋊Dic43C2×D411yescharacteristic
468C4⋊Dic43C2×D412yes—
469C4⋊Dic43C2×D412yes—
470C4⋊Dic43C2411yescharacteristic
471C4⋊Dic43C2411yescharacteristic
472Dic43⋊C4—21no—
473Dic43⋊C4—21no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—22no—
477Dic43⋊C4—22no—
478Dic43⋊C4—22no—
479Dic43⋊C4—22no—
480Dic43⋊C4—22no—
481C4×Dic43—21no—
482C4×Dic43—22no—
483C4×Dic43C2×D412yes—
484C4×Dic43C2×D412yes—
485C4×Dic43C2412yes—
486C4×Dic43C2412yes—
487C2×C43⋊C8—22no—
488C2×C43⋊C8—22no—
489C2×C43⋊C8C2411yescharacteristic
490C2×C43⋊C8C2411yescharacteristic
491C2×C43⋊C8C2411yescharacteristic
492C2×C43⋊C8C2411yescharacteristic
493Dic172—42no—
494D344—42no—
495#10621873—42no—
496#10621873—42no—
497C23×C43—22no—
498C23×C43—22no—
499C23×C43—21no—
500C23×C43—21no—
501C23×C43—41no—
502C23×C43—41no—
503C23×C43—42no—
504C23×C43—42no—
505C23×C43—81no—
506C23×C43—81no—
507C23×C43—81no—
508C23×C43—81no—
509C23×C43C22×D411yescharacteristic
510C23×C43C22×D411yescharacteristic
511C23×C43C22×D411yescharacteristic
512C22×D43—21no—
513C22×D43—22no—
514C22×D43—42no—
515C22×D43—81no—
516C22×D43—81no—
517Q8×C43—21no—
518Q8×C43—21no—
519Q8×C43—21no—
520Q8×C43—21no—
521Q8×C43—42no—
522D4×C43—22no—
523D4×C43—21no—
524D4×C43—21no—
525D4×C43—22no—
526D4×C43—21no—
527D4×C43—21no—
528D4×C43—42no—
529D4×C43—44no—
530D4×C43—42no—
531D4×C43—42no—
532D4×C43—42no—
533D4×C43—42no—
534D4×C43—42no—
535D4×C43—82no—
536C2×C4×C43—22no—
537C2×C4×C43—22no—
538C2×C4×C43—22no—
539C2×C4×C43—21no—
540C2×C4×C43—21no—
541C2×C4×C43—21no—
542C2×C4×C43—21no—
543C2×C4×C43—22no—
544C2×C4×C43—21no—
545C2×C4×C43—21no—
546C2×C4×C43—42no—
547C2×C4×C43—42no—
548C2×C4×C43—42no—
549C2×C4×C43—42no—
550C2×C4×C43—42no—
551C2×C4×C43—81no—
552C2×C4×C43C22×D411yescharacteristic
553C2×C4×C43C22×D411yescharacteristic
554C2×C4×C43C22×D411yescharacteristic
555C2×C4×C43H(5,𝔽2)12yes—
556C2×C4×C43H(5,𝔽2)12yes—
557C2×C4×C43C2511yescharacteristic
558C22⋊D43—44no—
559C22⋊D43—44no—
560C22⋊D43—42no—
561C22⋊D43—42no—
562C22⋊D43—82no—
563C22⋊D43—82no—
564C22⋊D43—82no—
565C22⋊D43—82no—
566C22⋊D43—82no—
567C22⋊D43—82no—
568C22⋊D43—81no—
569C2×Dic43—21no—
570C2×Dic43—21no—
571C2×Dic43—21no—
572C2×Dic43—22no—
573C2×Dic43—42no—
574C2×Dic43—42no—
575C2×Dic43—42no—
576C2×Dic43—82no—
577C2×Dic43—82no—
578C2×Dic43C22×D412yes—
579C2×Dic43C22×D412yes—
580C2×Dic43C22×D412yes—
581C2×Dic43C22×D412yes—
582D172—21no—
583D172—22no—
584D172—21no—
585D172—22no—
586D172—42no—
587C4×D43—44no—
588C4×D43—44no—
589C4×D43—42no—
590C4×D43—82no—
591Dic86—21no—
592Dic86—22no—
593Dic86—21no—
594Dic86—22no—
595Dic86—42no—
596Dic86—82no—
597C8×C43—22no—
598C8×C43—22no—
599C43⋊C8—21no—
600C43⋊C8—21no—
601C43⋊C8—21no—
602C43⋊C8—21no—
603#60815—431nomaximal, Sylow
604C22×C43—21no—
605C22×C43—21no—
606C22×C43—21no—
607C22×C43—21no—
608C22×C43—21no—
609C22×C43—21no—
610C22×C43—21no—
611C22×C43—21no—
612C22×C43—42no—
613C22×C43—41no—
614C22×C43—41no—
615C22×C43—42no—
616C22×C43—41no—
617C22×C43—41no—
618C22×C43—41no—
619C22×C43—41no—
620C22×C43—42no—
621C22×C43—82no—
622C22×C43—84no—
623C22×C43—162no—
624C22×C43#53512yes—
625C22×C43C23×D411yescharacteristic
626C2×D43—42no—
627C2×D43—41no—
628C2×D43—42no—
629C2×D43—41no—
630C2×D43—42no—
631C2×D43—41no—
632C2×D43—84no—
633C4×C43—21no—
634C4×C43—21no—
635C4×C43—42no—
636C4×C43—41no—
637C4×C43—41no—
638C4×C43#53512yes—
639C4×C43C2×H(5,𝔽2)11yescharacteristic
640C4×C43C2×H(5,𝔽2)11yescharacteristic
641Dic43—22no—
642Dic43—22no—
643Dic43—22no—
644Dic43—22no—
645Dic43—41no—
646Dic43—41no—
647Dic43—42no—
648Dic43—41no—
649#3494—431no—
650#3449—431no—
651#3225—432no—
652#3224—432no—
653#3221—432no—
654#3220—432no—
655#3219—432no—
656#3214—432no—
657#3212—432no—
658#3207—432no—
659#3155—431no—
660#3154—431no—
661#3137—431no—
662#3136—431no—
663#3046—431no—
664#3045—431no—
665#3042—431no—
666#3041—431no—
667#3006D4311yescharacteristic, complemented
668#3005—431no—
669#3002—431no—
670C2×#449—431no—
671#2924—431no—
672C2×C43—22no—
673C2×C43—41no—
674C2×C43—41no—
675C2×C43—81no—
676C2×C43—81no—
677C2×C43—82no—
678C2×C43C2×#53511yescharacteristic
679C2×C43#358411yescharacteristic
680C2×C43#358511yescharacteristic
681D43—81no—
682D43—82no—
683C22×#41—431no—
684C22×#41C2×D4311yescharacteristic
685C2×#137—431no—
686C2×AGL(1,ℤ/8)—431no—
687C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
688C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
689C2×#135—431no—
690C2×#135—431no—
691C22×SD16—431no—
692C22×D8—431no—
693#555—861no—
694#553—861no—
695#553—861no—
696#551—862no—
697#547—861no—
698#546—862no—
699#544—431no—
700#542—432no—
701#540—432no—
702#537—861no—
703#537—861no—
704#536—431no—
705#536—431no—
706#536—432no—
707#535—431no—
708#535—431no—
709#535—431no—
710#535—432no—
711#534—862no—
712#532—432no—
713#532—432no—
714#532—432no—
715#529—432no—
716#525—431no—
717#525—861no—
718#525—861no—
719#525—862no—
720C2×#121C2×D4311yescharacteristic
721#520—431no—
722#518—431no—
723C2×#117—431no—
724#497—432no—
725#496—432no—
726#496—432no—
727#496—432no—
728#495—432no—
729#495—432no—
730#493—432no—
731#492—432no—
732#491—432no—
733#490—432no—
734#489—432no—
735#489—432no—
736#488—432no—
737#488—432no—
738#487—432no—
739#486—432no—
740#464—432no—
741#464—432no—
742#463—432no—
743#463—432no—
744#463—432no—
745#463—432no—
746#463—432no—
747#463—432no—
748#462—432no—
749#461—432no—
750#461—432no—
751#461—432no—
752#460—432no—
753#459—432no—
754#459—432no—
755#459—432no—
756#452—431no—
757#452—431no—
758#452—432no—
759#452—432no—
760#451—431no—
761#450—431no—
762#449—431no—
763#449—431no—
764#449—432no—
765#449—432no—
766#449—432no—
767#449—432no—
768#449—432no—
769#449—432no—
770#449C2×D4312yescomplemented
771#449C2×D4312yescomplemented
772#448—431no—
773#448C2×D4312yescomplemented
774#447—431no—
775#447C2×D4312yescomplemented
776#433—432no—
777#433—432no—
778#432—432no—
779#431—432no—
780#424—431no—
781#424—431no—
782#419—431no—
783#418—431no—
784#417C2×D4311yescharacteristic
785#417C2×D4311yescharacteristic
786#416—431no—
787#416—431no—
788C2×#103—431no—
789C2×#102—431no—
790#407C2×D4311yescharacteristic
791C2×C22⋊C8—431no—
792#405—431no—
793#405—431no—
794C43#6081511yescharacteristic, complemented, Sylow
795C2×#41—21no—
796C2×#41—21no—
797C2×#41—42no—
798C2×#41—42no—
799C2×#41—431no—
800C2×#41—432no—
801C2×#41—432no—
802C2×#41—862no—
803C2×#41—861no—
804C2×#41—861no—
805C2×#41—1722no—
806C2×#41—1722no—
807C2×#41C22×D4311yescharacteristic
808C2×#41C22×D4311yescharacteristic
809C2×#41C22×D4311yescharacteristic
810C2×#41C22×D4311yescharacteristic
811C22×Q8—431no—
812C22×Q8C22×D4311yescharacteristic
813C22×D4—21no—
814C22×D4—21no—
815C22×D4—431no—
816C22×D4—861no—
817C22×D4C22×D4311yescharacteristic
818C22×D4C22×D4311yescharacteristic
819C23×C4—21no—
820C23×C4—861no—
821C23×C4C22×D4311yescharacteristic
822#137—1722no—
823AGL(1,ℤ/8)—42no—
824AGL(1,ℤ/8)—42no—
825AGL(1,ℤ/8)—1722no—
826#135—1722no—
827#135—1722no—
828C2×Q16—431no—
829C2×Q16—431no—
830C2×Q16—432no—
831C2×SD16—431no—
832C2×SD16—431no—
833C2×SD16—432no—
834C2×SD16—432no—
835C2×SD16—431no—
836C2×SD16—431no—
837C2×SD16—432no—
838C2×SD16—432no—
839C2×SD16—1722no—
840C2×SD16C22×D4312yes—
841C2×SD16C22×D4312yes—
842C2×D8—432no—
843C2×D8—432no—
844C2×D8—431no—
845C2×D8—431no—
846C2×D8—432no—
847C2×D8—1722no—
848C2×D8C22×D4312yes—
849C2×D8C22×D4312yes—
850C2×M16C22×D4311yescharacteristic
851C2×M16C22×D4311yescharacteristic
852C22×C8—431no—
853C22×C8—431no—
854C4⋊Q8—432no—
855C4⋊Q8—432no—
856C4⋊Q8—432no—
857C4⋊Q8—861no—
858#127—432no—
859#127—432no—
860#127—432no—
861#126—862no—
862#126—862no—
863#125—432no—
864#125—861no—
865#124—432no—
866#124—432no—
867#124—432no—
868#124—432no—
869#124—432no—
870#124—862no—
871#124—862no—
872#123—862no—
873#123—862no—
874#123—862no—
875#123—862no—
876#123—862no—
877#123—862no—
878#123—862no—
879#123—862no—
880#123—861no—
881C22⋊Q8—431no—
882C22⋊Q8—431no—
883C22⋊Q8—862no—
884C22⋊Q8—862no—
885C22⋊Q8—861no—
886C22⋊Q8—861no—
887C22⋊Q8—861no—
888C22⋊Q8—861no—
889C22⋊Q8—862no—
890C22⋊Q8—862no—
891#121—21no—
892#121—21no—
893#121—431no—
894#121—431no—
895#121—862no—
896#121—862no—
897#121—861no—
898#121—861no—
899#121—861no—
900#121—861no—
901#121—862no—
902#121—862no—
903#121—861no—
904#121—861no—
905#121—862no—
906#121—862no—
907#121—862no—
908#121—862no—
909#121—862no—
910#121C22×D4312yes—
911#121C22×D4312yes—
912#120—862no—
913#120—862no—
914#120—862no—
915#120—862no—
916#120—862no—
917#120—861no—
918C4×Q8—432no—
919C4×D4—432no—
920C4×D4—432no—
921C4×D4—432no—
922C4×D4—862no—
923C4×D4—862no—
924C4×D4—862no—
925C4×D4—862no—
926C4×D4—862no—
927C4×D4—862no—
928C4×D4—861no—
929C4×D4—861no—
930C4×D4—862no—
931C4×D4—861no—
932C4×D4—861no—
933#117—432no—
934#117—431no—
935#117—431no—
936#117—431no—
937#117—431no—
938#117—432no—
939#117—431no—
940#117—862no—
941#117—861no—
942C2×C4⋊C4—431no—
943C2×C4⋊C4—431no—
944C2×C4⋊C4—861no—
945C2×C4⋊C4C22×D4311yescharacteristic
946C2×C22⋊C4—21no—
947C2×C22⋊C4—432no—
948C2×C22⋊C4—862no—
949C2×C42—432no—
950C4⋊C8—432no—
951C4⋊C8—432no—
952C4⋊C8—432no—
953C4⋊C8—432no—
954#103—431no—
955#103—431no—
956#103—431no—
957#103—431no—
958#103—432no—
959#103—432no—
960#103—432no—
961#103—432no—
962#103C22×D4312yes—
963#103C22×D4312yes—
964#102—431no—
965#102—431no—
966#102—431no—
967#102—431no—
968#102—432no—
969#102—432no—
970#102—432no—
971#102—432no—
972#102C22×D4312yes—
973#102C22×D4312yes—
974C22⋊C8—431no—
975C22⋊C8—431no—
976C22⋊C8—431no—
977C22⋊C8—431no—
978C22⋊C8C22×D4312yes—
979C22⋊C8C22×D4312yes—
980#97—432no—
981#97—432no—
982C4×C8—432no—
983C4×C8—432no—
984C24—21no—
985C24—21no—
986C24—861no—
987C24D4×D4311yescharacteristic
988#41—22no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—41no—
993#41—41no—
994#41—41no—
995#41—41no—
996#41—44no—
997#41—44no—
998#41—862no—
999#41—862no—
1000#41—3444no—
1001#41—1722no—
1002#41—1722no—
1003#41—1722no—
1004#41—1722no—
1005#41—1724no—
1006#41—1724no—
1007C2×Q8—21no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—432no—
1011C2×Q8—431no—
1012C2×Q8—862no—
1013C2×Q8—861no—
1014C2×Q8—862no—
1015C2×Q8—862no—
1016C2×Q8C23×D4311yescharacteristic
1017C2×Q8C23×D4311yescharacteristic
1018C2×D4—22no—
1019C2×D4—21no—
1020C2×D4—21no—
1021C2×D4—21no—
1022C2×D4—21no—
1023C2×D4—22no—
1024C2×D4—21no—
1025C2×D4—21no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—41no—
1029C2×D4—41no—
1030C2×D4—44no—
1031C2×D4—82no—
1032C2×D4—432no—
1033C2×D4—431no—
1034C2×D4—862no—
1035C2×D4—862no—
1036C2×D4—862no—
1037C2×D4—862no—
1038C2×D4—862no—
1039C2×D4—862no—
1040C2×D4—861no—
1041C2×D4—861no—
1042C2×D4—861no—
1043C2×D4—862no—
1044C2×D4—862no—
1045C2×D4—861no—
1046C2×D4—862no—
1047C2×D4—862no—
1048C2×D4—1724no—
1049C2×D4C23×D4311yescharacteristic
1050C2×D4C23×D4311yescharacteristic
1051C2×D4C23×D4312yes—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—21no—
1055C22×C4—21no—
1056C22×C4—21no—
1057C22×C4—21no—
1058C22×C4—21no—
1059C22×C4—21no—
1060C22×C4—44no—
1061C22×C4—432no—
1062C22×C4—432no—
1063C22×C4—862no—
1064C22×C4—862no—
1065C22×C4—862no—
1066C22×C4—861no—
1067C22×C4—861no—
1068C22×C4—862no—
1069C22×C4—862no—
1070C22×C4—1724no—
1071C22×C4D4×D4311yescharacteristic
1072C22×C4D4×D4311yescharacteristic
1073C22×C4D4×D4311yescharacteristic
1074C22×C4C23×D4311yescharacteristic
1075C22×C4C23×D4311yescharacteristic
1076C22×C4C23×D4311yescharacteristic
1077Q16—1722no—
1078Q16—1721no—
1079Q16—1721no—
1080SD16—42no—
1081SD16—42no—
1082SD16—1722no—
1083SD16—1722no—
1084SD16—1722no—
1085SD16—1722no—
1086SD16—1721no—
1087SD16—1721no—
1088SD16—1721no—
1089SD16—1721no—
1090D8—42no—
1091D8—42no—
1092D8—1722no—
1093D8—1722no—
1094D8—1722no—
1095D8—1721no—
1096D8—1721no—
1097M16—22no—
1098M16—22no—
1099C2×C8—431no—
1100C2×C8—431no—
1101C2×C8—431no—
1102C2×C8—431no—
1103C2×C8—862no—
1104C2×C8—862no—
1105C2×C8C23×D4312yes—
1106C2×C8C23×D4312yes—
1107C4⋊C4—21no—
1108C4⋊C4—431no—
1109C4⋊C4—431no—
1110C4⋊C4—431no—
1111C4⋊C4—431no—
1112C4⋊C4—432no—
1113C4⋊C4—432no—
1114C4⋊C4—431no—
1115C4⋊C4—431no—
1116C4⋊C4—862no—
1117C4⋊C4—862no—
1118C4⋊C4—862no—
1119C4⋊C4—862no—
1120C4⋊C4—862no—
1121C4⋊C4—862no—
1122C4⋊C4—862no—
1123C4⋊C4—862no—
1124C4⋊C4—861no—
1125C4⋊C4—861no—
1126C4⋊C4C23×D4312yes—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—432no—
1130C22⋊C4—432no—
1131C22⋊C4—432no—
1132C22⋊C4—432no—
1133C22⋊C4—862no—
1134C22⋊C4—862no—
1135C22⋊C4—862no—
1136C22⋊C4—862no—
1137C22⋊C4—862no—
1138C22⋊C4—862no—
1139C22⋊C4—862no—
1140C22⋊C4—862no—
1141C22⋊C4—862no—
1142C22⋊C4—862no—
1143C22⋊C4—862no—
1144C22⋊C4—862no—
1145C22⋊C4—862no—
1146C22⋊C4—861no—
1147C22⋊C4—861no—
1148C22⋊C4—861no—
1149C22⋊C4—861no—
1150C22⋊C4—861no—
1151C42—432no—
1152C42—432no—
1153C42—432no—
1154C42—432no—
1155C42—862no—
1156C42—861no—
1157C23—22no—
1158C23—22no—
1159C23—21no—
1160C23—21no—
1161C23—41no—
1162C23—41no—
1163C23—42no—
1164C23—42no—
1165C23—81no—
1166C23—81no—
1167C23—81no—
1168C23—81no—
1169C23—861no—
1170C23—862no—
1171C23—3441no—
1172C23—3441no—
1173C23—1722no—
1174C23C2×D4×D4311yescharacteristic
1175C23C2×D4×D4311yescharacteristic
1176C23C2×D4×D4311yescharacteristic
1177Q8—21no—
1178Q8—21no—
1179Q8—21no—
1180Q8—21no—
1181Q8—42no—
1182Q8—861no—
1183Q8—862no—
1184Q8—861no—
1185Q8—862no—
1186Q8—3442no—
1187Q8—1722no—
1188D4—21no—
1189D4—21no—
1190D4—22no—
1191D4—22no—
1192D4—21no—
1193D4—21no—
1194D4—42no—
1195D4—42no—
1196D4—42no—
1197D4—44no—
1198D4—42no—
1199D4—42no—
1200D4—42no—
1201D4—82no—
1202D4—861no—
1203D4—862no—
1204D4—861no—
1205D4—862no—
1206D4—3442no—
1207D4—3442no—
1208D4—3442no—
1209D4—3442no—
1210D4—3442no—
1211D4—3442no—
1212D4—3441no—
1213D4—1724no—
1214D4—1724no—
1215D4—1722no—
1216D4—1722no—
1217D4—1722no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—81no—
1234C2×C4—432no—
1235C2×C4—432no—
1236C2×C4—432no—
1237C2×C4—432no—
1238C2×C4—861no—
1239C2×C4—861no—
1240C2×C4—861no—
1241C2×C4—862no—
1242C2×C4—3442no—
1243C2×C4—3442no—
1244C2×C4—3442no—
1245C2×C4—1724no—
1246C2×C4—1724no—
1247C2×C4—1722no—
1248C2×C4—1722no—
1249C2×C4—1722no—
1250C2×C4—1722no—
1251C2×C4C2×D4×D4311yescharacteristic
1252C2×C4C2×D4×D4311yescharacteristic
1253C2×C4C2×D4×D4311yescharacteristic
1254C2×C4#1306337012yes—
1255C2×C4#1306337012yes—
1256C2×C4C24×D4311yescharacteristic
1257C8—22no—
1258C8—22no—
1259C8—861no—
1260C8—861no—
1261C8—861no—
1262C8—861no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—82no—
1281C22—84no—
1282C22—162no—
1283C22—3444no—
1284C22—1721no—
1285C22—1722no—
1286C22—1721no—
1287C22—1722no—
1288C22—1722no—
1289C22—1721no—
1290C22#1458346412yes—
1291C22C22×D4×D4311yescharacteristic
1292C4—21no—
1293C4—21no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—862no—
1298C4—862no—
1299C4—862no—
1300C4—862no—
1301C4—1721no—
1302C4—1721no—
1303C4—1722no—
1304C4—1721no—
1305C4#1458346412yes—
1306C4C2×#1306337011yescharacteristic
1307C4C2×#1306337011yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—41no—
1311C2—81no—
1312C2—81no—
1313C2—82no—
1314C2—3442no—
1315C2—3441no—
1316C2C2×#1458346411yescharacteristic
1317C2#1914936811yescharacteristic
1318C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3006C2
socleC22×C43C23×D4
hypercenter#3006D43
hypocenterC43#60815
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. #19148324C2semidirect
2. #19147924C2semidirect
3. #19145702C2semidirect
4. #19145685C2semidirect
5. #19145652C2semidirect
6. #19145641C2semidirect
7. #19145630C2semidirect
8. #19145587C2semidirect
9. #19145568C2semidirect
10. #19145526C2semidirect
11. #19145080C2semidirect
12. #19145069C2semidirect
13. #19144963C2semidirect
14. #19144952C2semidirect
15. #19144144C2semidirect
16. #19144133C2semidirect
17. #19144109C2semidirect
18. #19144100C2semidirect
19. #19143840C2semidirect
20. #19143813C2semidirect
21. C2×#14583042C2semidirect
22. #19143255C2semidirect
23. C43×#3006C2semidirect
25. C2×#13063358C22semidirect
26. C2×#13063353C22semidirect
29. C22×#10621883C22semidirect
30. C22×#10621882C22semidirect
37. #14583530C22semidirect
38. #14583516C22semidirect
39. #14583502C22semidirect
42. #14583473C22semidirect
45. #14583466C22semidirect
46. #14583466C22semidirect
50. #14583445C22semidirect
51. #14583445C22semidirect
52. #14583444C22semidirect
53. #14583430C22semidirect
58. #14583380C22semidirect
59. #14583374C22semidirect
61. #14583290C22semidirect
62. #14583287C22semidirect
63. #14583287C22semidirect
64. #14583285C22semidirect
65. #14583282C22semidirect
66. #14583280C22semidirect
67. #14583274C22semidirect
68. #14583270C22semidirect
69. #14583266C22semidirect
70. #14583262C22semidirect
71. #14583260C22semidirect
72. #14583257C22semidirect
73. #14583255C22semidirect
74. #14583252C22semidirect
75. #14583248C22semidirect
76. #14583244C22semidirect
77. #14583124C22semidirect
78. #14583120C22semidirect
79. #14583117C22semidirect
80. #14583116C22semidirect
81. #14583116C22semidirect
82. #14583113C22semidirect
83. #14583112C22semidirect
84. #14583112C22semidirect
85. #14583108C22semidirect
86. #14583103C22semidirect
87. #14583102C22semidirect
88. #14583102C22semidirect
89. #14583098C22semidirect
90. #14583093C22semidirect
91. #14583092C22semidirect
92. #14583092C22semidirect
93. #14583063C22semidirect
94. #14583063C22semidirect
95. #14583061C22semidirect
96. #14583061C22semidirect
97. #14583055C22semidirect
98. #14583050C22semidirect
99. #14583046C22semidirect
100. #14583046C22semidirect
101. #14583044C22semidirect
102. #14583044C22semidirect
105. #14583042C22semidirect
106. #14583042C22semidirect
107. #14583038C22semidirect
108. #14583033C22semidirect
109. #14582957C22semidirect
110. #14582957C22semidirect
111. #14582953C22semidirect
112. #14582949C22semidirect
113. #14582927C22semidirect
114. #14582927C22semidirect
115. #14582909C22semidirect
116. #14582905C22semidirect
119. C2×#13063248C22semidirect
120. C2×#13063245C22semidirect
122. #14582857C22semidirect
123. #14582857C22semidirect
128. C43×#449C22semidirect
129. C43×#449C22semidirect
130. C43×#448C22semidirect
131. C43×#447C22semidirect
667. #3006D43semidirect
770. #449C2×D43semidirect
771. #449C2×D43semidirect
773. #448C2×D43semidirect
775. #447C2×D43semidirect
794. C43#60815semidirect

Maximal subgroups

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

subgroupindex
#191483242
#191479242
#191457022
#191456852
#191456522
#191456412
#191456302
#191455872
#191455682
#191455262
#191450802
#191450692
#191449632
#191449522
#191441442
#191441332
#191441092
#191441002
#191438402
#191438132
C2×#145830422
#191432552
C43×#30062
#6081543