Finite Group Databasebeta

← #25968522

Subgroups — #25968522

Order 11008.

2144 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148369C211yesmaximal, characteristic, complemented
2#19148023C211yesmaximal, characteristic, complemented
3#19145687C212yesmaximal, complemented
4#19145685C212yesmaximal, complemented
5#19145665C212yesmaximal, complemented
6#19145663C212yesmaximal, complemented
7#19145611C212yesmaximal, complemented
8#19145603C212yesmaximal, complemented
9#19145568C212yesmaximal, complemented
10#19145534C212yesmaximal, complemented
11#19145072C211yesmaximal, characteristic, complemented
12#19145069C211yesmaximal, characteristic, complemented
13#19144952C211yesmaximal, characteristic, complemented
14#19144947C211yesmaximal, characteristic, complemented
15#19144073C211yesmaximal, characteristic, complemented
16#19144066C211yesmaximal, characteristic, complemented
17#19144046C211yesmaximal, characteristic, complemented
18C2×#14583098C211yesmaximal, characteristic, complemented
19#19143896C211yesmaximal, characteristic, complemented
20#19143874C211yesmaximal, characteristic, complemented
21#19143872C211yesmaximal, characteristic, complemented
22#19143257C211yesmaximal, characteristic, complemented
23C43×#3012C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C2×#13063358C2211yescharacteristic, complemented
26C2×#13063355C2211yescharacteristic, complemented
27C2×#13063350C2211yescharacteristic, complemented
28C2×#13063345C2211yescharacteristic, complemented
29C22×#10621873C2211yescharacteristic, complemented
30C22×#10621883C2211yescharacteristic, complemented
31#14583568—21no—
32#14583568—21no—
33D4×C22⋊D43—22no—
34D4×C22⋊D43—21no—
35D4×C22⋊D43—22no—
36D4×C22⋊D43—21no—
37#14583530C2211yescharacteristic, complemented
38#14583516—21no—
39#14583516C2212yescomplemented
40#14583509—21no—
41#14583509C2212yescomplemented
42#14583494—22no—
43#14583470C2211yescharacteristic
44#14583470C2211yescharacteristic, complemented
45#14583466C2211yescharacteristic
46#14583466C2212yes—
47#14583463C2211yescharacteristic
48#14583463C2212yes—
49#14583451—21no—
50#14583451C2212yescomplemented
51#14583445C2212yes—
52#14583445C2211yescharacteristic
53C2×#13063321C2212yes—
54C2×#13063321C2211yescharacteristic
55#14583430—22no—
56#14583430—21no—
57#14583430C2212yescomplemented
58#41×Dic43C2211yescharacteristic
59#41×Dic43C2211yescharacteristic, complemented
60C2×#13063290C2211yescharacteristic, complemented
61#14583292C2212yescomplemented
62#14583290C2212yescomplemented
63#14583287C2212yescomplemented
64#14583287C2212yescomplemented
65#14583282C2212yescomplemented
66#14583280C2212yescomplemented
67#14583270C2212yescomplemented
68#14583270C2212yescomplemented
69#14583262C2212yescomplemented
70#14583262C2212yescomplemented
71#14583260C2212yescomplemented
72#14583257C2212yescomplemented
73#14583255C2212yescomplemented
74#14583252C2212yescomplemented
75#14583244C2212yescomplemented
76#14583244C2212yescomplemented
77#14583124C2212yescomplemented
78#14583123C2211yescharacteristic, complemented
79#14583120C2212yescomplemented
80#14583119C2211yescharacteristic, complemented
81#14583116C2211yescharacteristic, complemented
82#14583112C2211yescharacteristic, complemented
83#14583108C2212yescomplemented
84#14583107C2211yescharacteristic, complemented
85#14583102C2211yescharacteristic, complemented
86#14583098C2212yescomplemented
87#14583098C2212yescomplemented
88#14583098C2212yescomplemented
89#14583098C2212yescomplemented
90#14583098C2212yescomplemented
91#14583097C2211yescharacteristic, complemented
92#14583097C2212yescomplemented
93#14583097C2212yescomplemented
94#14583092C2212yescomplemented
95#14583092C2211yescharacteristic, complemented
96#14583092C2212yescomplemented
97#14583063C2212yescomplemented
98#14583063C2212yescomplemented
99#14583061C2212yescomplemented
100#14583061C2212yescomplemented
101#14583059C2212yescomplemented
102#14583052C2212yescomplemented
103#14583052C2212yescomplemented
104#14583050C2212yescomplemented
105#14583050C2212yescomplemented
106#14583049C2212yescomplemented
107#14583042C2212yescomplemented
108#14583032C2212yescomplemented
109#14582957C2212yescomplemented
110#14582957C2212yescomplemented
111#14582953C2212yescomplemented
112#14582949C2212yescomplemented
113#14582922C2211yescharacteristic, complemented
114C2×Dic43⋊C8C2211yescharacteristic, complemented
115#14582905C2211yescharacteristic, complemented
116#14582904C2211yescharacteristic, complemented
117#14582898C2211yescharacteristic, complemented
118#14582896C2211yescharacteristic, complemented
119#14582895C2211yescharacteristic, complemented
120C2×#13063245C2211yescharacteristic, complemented
121#14582866C2211yescharacteristic
122#14582857C2211yescharacteristic, complemented
123#14582854C2211yescharacteristic, complemented
124C2×H(5,𝔽2)×C43C2211yescharacteristic
125C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
126C2×#135×C43C2211yescharacteristic, complemented
127C43×#537C2211yescharacteristic
128C43×#452C2212yescomplemented
129C43×#450C2212yescomplemented
130C43×#449C2212yescomplemented
131C43×#447C2212yescomplemented
132C43×#417C2211yescharacteristic, complemented
133C2×#102×C43C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic
135#13063371—42no—
136#13063371—42no—
137C2×#10621902—21no—
138C2×#10621898C2311yescharacteristic
139C2×#10621898C2312yes—
140C22×Dic86C2311yescharacteristic
141C22×D172C2311yescharacteristic
142C22×D172C2312yes—
143C22×C22⋊D43—21no—
144C22×C22⋊D43—22no—
145C22×C22⋊D43—21no—
146C22×C22⋊D43—22no—
147C2×D4×D43—22no—
148C2×D4×D43—21no—
149#13063358—42no—
150#13063355—42no—
151#13063350—42no—
152#13063345—42no—
153C2×Dic172C2312yes—
154C2×#10621885C2311yescharacteristic
155C2×#10621885C2312yes—
156C2×#10621873—42no—
157C2×#10621873C2312yes—
158C2×#10621873C2312yes—
159C2×#10621873C2312yes—
160C2×#10621883—42no—
161C2×#10621883C2311yescharacteristic
162C2×#10621883C2312yes—
163C2×#10621883C2312yes—
164C2×#10621883C2312yes—
165C2×#10621884C2311yescharacteristic
166C2×#10621884C2312yes—
167C2×#10621882C2312yes—
168C2×#10621882C2311yescharacteristic
169C2×#10621877C2311yescharacteristic
170C22×C43⋊C8C2311yescharacteristic
171#13063324—21no—
172#13063324C2312yes—
173#13063323—21no—
174#13063323C2311yescharacteristic
175#13063323C2312yes—
176#13063321—21no—
177#13063321—22no—
178#13063321—21no—
179#13063321—22no—
180#13063321C2312yes—
181#13063321C2311yescharacteristic
182#13063321C2312yes—
183#13063321C2312yes—
184#13063321C2312yes—
185#13063318—22no—
186#13063318—22no—
187#13063318—22no—
188#13063318—22no—
189#13063316—22no—
190#13063316—21no—
191#13063316C2312yes—
192#13063315—22no—
193#13063315—22no—
194#13063314C2311yescharacteristic
195#13063314C2312yes—
196#13063312—21no—
197#13063312—22no—
198#13063312C2311yescharacteristic
199#13063312C2312yes—
200#13063312C2312yes—
201#13063306—22no—
202#13063306—22no—
203#13063306—22no—
204#13063306—22no—
205#13063304—22no—
206#13063304—21no—
207#13063304—21no—
208#13063304C2312yes—
209#13063304C2312yes—
210#13063302—22no—
211#13063302—22no—
212#13063299—22no—
213#13063299—21no—
214#13063299—21no—
215#13063299—22no—
216#13063297—21no—
217#13063297—22no—
218#13063297—21no—
219#13063297—22no—
220#13063296—22no—
221#13063296—21no—
222#13063296—21no—
223#13063296—22no—
224#13063294—22no—
225#13063294—22no—
226#13063294—22no—
227#13063293—22no—
228#13063293—22no—
229#13063293—22no—
230Q8×Dic43D411yescharacteristic
231Q8×Dic43D411yescharacteristic
232Q8×Dic43C2311yescharacteristic
233Q8×Dic43C2311yescharacteristic
234#13063290—21no—
235#13063290—21no—
236#13063290—22no—
237#13063290C2312yes—
238#13063290C2312yes—
239D4×Dic43—21no—
240D4×Dic43—21no—
241D4×Dic43—22no—
242D4×Dic43D411yescharacteristic
243D4×Dic43D412yes—
244D4×Dic43D412yes—
245D4×Dic43D411yescharacteristic
246D4×Dic43C2311yescharacteristic
247D4×Dic43C2311yescharacteristic
248C4×C22⋊D43—21no—
249C4×C22⋊D43—22no—
250C4×C22⋊D43—21no—
251C4×C22⋊D43—22no—
252#13063284—21no—
253#13063284C2311yescharacteristic
254#13063284C2311yescharacteristic
255#13063284C2312yes—
256#13063281—22no—
257#13063281—22no—
258C2×Dic43⋊C4—21no—
259C2×C4×Dic43—21no—
260C2×C4×Dic43—21no—
261C2×C4×Dic43C2311yescharacteristic
262C2×C4×Dic43C2312yes—
263Dic43⋊C8C2312yes—
264Dic43⋊C8C2312yes—
265Dic43⋊C8C2311yescharacteristic
266Dic43⋊C8C2311yescharacteristic
267Dic43⋊C8C2311yescharacteristic
268Dic43⋊C8C2311yescharacteristic
269#13063250C2311yescharacteristic
270#13063250C2311yescharacteristic
271#13063249C2311yescharacteristic
272#13063249C2311yescharacteristic
273#13063248C2312yes—
274#13063247C2311yescharacteristic
275#13063247C2311yescharacteristic
276#13063247C2312yes—
277#13063247C2312yes—
278#13063246C2311yescharacteristic
279#13063246C2311yescharacteristic
280#13063246C2312yes—
281#13063246C2312yes—
282#13063245C2312yes—
283#13063245C2312yes—
284#13063245C2312yes—
285C22⋊(C43⋊C8)C2312yes—
286C22⋊(C43⋊C8)C2312yes—
287#13063235C2312yes—
288#13063235C2312yes—
289C8×Dic43C2312yes—
290C8×Dic43C2312yes—
291H(5,𝔽2)×C43—42no—
292H(5,𝔽2)×C43—42no—
293C2×#41×C43—21no—
294C2×#41×C43C2311yescharacteristic
295C2×#41×C43C2311yescharacteristic
296C2×#41×C43C2312yes—
297C2×#41×C43C2311yescharacteristic
298C22×D4×C43—22no—
299C22×D4×C43—21no—
300C22×D4×C43C2311yescharacteristic
301C22×D4×C43C2312yes—
302AGL(1,ℤ/8)×C43—42no—
303#135×C43—42no—
304C2×Q16×C43C2311yescharacteristic
305C2×SD16×C43C2312yes—
306C2×SD16×C43C2311yescharacteristic
307C2×SD16×C43C2311yescharacteristic
308C2×D8×C43C2312yes—
309C2×D8×C43C2311yescharacteristic
310C2×M16×C43C2311yescharacteristic
311C22×C8×C43C2311yescharacteristic
312C22⋊Q8×C43—21no—
313C22⋊Q8×C43C2312yes—
314#121×C43—22no—
315#121×C43—21no—
316#121×C43C2312yes—
317C2×C4⋊C4×C43C2311yescharacteristic
318#103×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2312yes—
321#102×C43C2312yes—
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C24×C43—22no—
325C24×C43—21no—
326C23×D43—22no—
327C23×D43—21no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—22no—
333#41×C43—22no—
334#41×C43—42no—
335#41×C43—42no—
336#41×C43—44no—
337C2×Q8×C43C2×D411yescharacteristic
338C2×Q8×C43C2411yescharacteristic
339C2×Q8×C43C2411yescharacteristic
340C2×D4×C43—22no—
341C2×D4×C43—21no—
342C2×D4×C43—21no—
343C2×D4×C43—22no—
344C2×D4×C43—21no—
345C2×D4×C43—22no—
346C2×D4×C43—22no—
347C2×D4×C43—22no—
348C2×D4×C43—42no—
349C2×D4×C43—42no—
350C2×D4×C43—44no—
351C2×D4×C43—48no—
352C2×D4×C43C2×D412yes—
353C2×D4×C43C2×D411yescharacteristic
354C2×D4×C43C2412yes—
355C2×D4×C43C2411yescharacteristic
356C2×D4×C43C2411yescharacteristic
357C22×C4×C43—21no—
358C22×C4×C43—22no—
359C22×C4×C43—21no—
360C22×C4×C43—21no—
361C22×C4×C43C2412yes—
362C22×C4×C43C2411yescharacteristic
363C2×C22⋊D43—21no—
364C2×C22⋊D43—22no—
365C2×C22⋊D43—21no—
366C2×C22⋊D43—22no—
367C2×C22⋊D43—22no—
368C2×C22⋊D43—22no—
369C2×C22⋊D43—22no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43—22no—
372C2×C22⋊D43—22no—
373C2×C22⋊D43—22no—
374C2×C22⋊D43—21no—
375C2×C22⋊D43—82no—
376C2×C22⋊D43—84no—
377C2×C22⋊D43—82no—
378C2×C22⋊D43—84no—
379C22×Dic43—21no—
380C22×Dic43—21no—
381C22×Dic43—21no—
382C22×Dic43C2×D411yescharacteristic
383C22×Dic43C2×D412yes—
384C22×Dic43C2×D411yescharacteristic
385C22×Dic43C2×D412yes—
386#10621902—44no—
387D4×D43—44no—
388D4×D43—48no—
389#10621898—22no—
390#10621898—22no—
391#10621898—42no—
392#10621898—42no—
393C2×D172—22no—
394C2×D172—21no—
395C2×D172—22no—
396C2×D172—22no—
397C2×D172—42no—
398C2×D172—42no—
399C2×D172C2412yes—
400C2×D172C2411yescharacteristic
401C2×C4×D43—22no—
402C2×C4×D43—21no—
403C2×Dic86—22no—
404C2×Dic86—22no—
405C2×Dic86—21no—
406C2×Dic86—22no—
407C2×Dic86C2411yescharacteristic
408C2×Dic86C2412yes—
409Q16×C43—41no—
410SD16×C43—41no—
411SD16×C43—41no—
412SD16×C43—42no—
413D8×C43—41no—
414D8×C43—42no—
415M16×C43—22no—
416C2×C8×C43—22no—
417C2×C8×C43C2411yescharacteristic
418C2×C8×C43C2411yescharacteristic
419C2×C8×C43C2412yes—
420C4⋊C4×C43—21no—
421C4⋊C4×C43—22no—
422C4⋊C4×C43C2412yes—
423C22⋊C4×C43—22no—
424C22⋊C4×C43—22no—
425C22⋊Dic43—22no—
426C22⋊Dic43—21no—
427C22⋊Dic43—21no—
428C22⋊Dic43—21no—
429C22⋊Dic43—21no—
430C22⋊Dic43—22no—
431C22⋊Dic43—22no—
432C22⋊Dic43—22no—
433C22⋊Dic43—22no—
434C22⋊Dic43—21no—
435C22⋊Dic43—22no—
436C22⋊Dic43C2×D412yes—
437C22⋊Dic43C2×D412yes—
438C22⋊Dic43C2×D412yes—
439#10621885—41no—
440#10621885—42no—
441#10621884—41no—
442#10621884—42no—
443#10621883—42no—
444#10621883—42no—
445#10621883—41no—
446#10621883—42no—
447#10621882—41no—
448#10621882—42no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—22no—
452(C2×D43)⋊C4—22no—
453C4⋊Dic43—21no—
454C4⋊Dic43—21no—
455C4⋊Dic43—22no—
456C4⋊Dic43C2×D412yes—
457C4⋊Dic43C2×D411yescharacteristic
458C4⋊Dic43C2×D411yescharacteristic
459C4⋊Dic43C2×D412yes—
460C4⋊Dic43C2411yescharacteristic
461C4⋊Dic43C2411yescharacteristic
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—22no—
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—22no—
472C4×Dic43—21no—
473C4×Dic43—22no—
474C4×Dic43—21no—
475C4×Dic43—21no—
476C4×Dic43—22no—
477C4×Dic43C2×D411yescharacteristic
478C4×Dic43C2×D412yes—
479C4×Dic43C2×D411yescharacteristic
480C4×Dic43C2×D412yes—
481C4×Dic43C2412yes—
482C4×Dic43C2411yescharacteristic
483C4×Dic43C2411yescharacteristic
484#10621877—22no—
485C2×C43⋊C8—22no—
486C2×C43⋊C8C2411yescharacteristic
487C2×C43⋊C8C2412yes—
488C2×C43⋊C8C2411yescharacteristic
489Dic172—42no—
490#10621873—42no—
491#10621873—42no—
492#10621873—42no—
493C23×C43—21no—
494C23×C43—21no—
495C23×C43—22no—
496C23×C43—44no—
497C23×C43—42no—
498C23×C43—81no—
499C23×C43—81no—
500C23×C43—82no—
501C23×C43—82no—
502C23×C43C22×D412yes—
503C23×C43C22×D411yescharacteristic
504C22×D43—21no—
505C22×D43—22no—
506C22×D43—44no—
507C22×D43—42no—
508C22×D43—81no—
509C22×D43—82no—
510C22×D43—81no—
511C22×D43—82no—
512Q8×C43—22no—
513Q8×C43—21no—
514Q8×C43—21no—
515Q8×C43—21no—
516Q8×C43—21no—
517D4×C43—24no—
518D4×C43—22no—
519D4×C43—21no—
520D4×C43—21no—
521D4×C43—22no—
522D4×C43—21no—
523D4×C43—22no—
524D4×C43—21no—
525D4×C43—44no—
526D4×C43—44no—
527D4×C43—42no—
528D4×C43—42no—
529D4×C43—42no—
530D4×C43—82no—
531C2×C4×C43—22no—
532C2×C4×C43—22no—
533C2×C4×C43—21no—
534C2×C4×C43—22no—
535C2×C4×C43—21no—
536C2×C4×C43—44no—
537C2×C4×C43—42no—
538C2×C4×C43—42no—
539C2×C4×C43—81no—
540C2×C4×C43C22×D412yes—
541C2×C4×C43C22×D411yescharacteristic
542C2×C4×C43H(5,𝔽2)12yes—
543C2×C4×C43H(5,𝔽2)12yes—
544C2×C4×C43C2511yescharacteristic
545C22⋊D43—44no—
546C22⋊D43—42no—
547C22⋊D43—44no—
548C22⋊D43—42no—
549C22⋊D43—44no—
550C22⋊D43—42no—
551C22⋊D43—82no—
552C22⋊D43—82no—
553C22⋊D43—82no—
554C22⋊D43—82no—
555C22⋊D43—82no—
556C22⋊D43—82no—
557C2×Dic43—22no—
558C2×Dic43—24no—
559C2×Dic43—22no—
560C2×Dic43—21no—
561C2×Dic43—21no—
562C2×Dic43—21no—
563C2×Dic43—42no—
564C2×Dic43—41no—
565C2×Dic43—42no—
566C2×Dic43—42no—
567C2×Dic43—81no—
568C2×Dic43C22×D411yescharacteristic
569C2×Dic43C22×D411yescharacteristic
570C2×Dic43C22×D411yescharacteristic
571C2×Dic43C22×D412yes—
572C2×Dic43C22×D412yes—
573C2×Dic43C22×D411yescharacteristic
574D172—22no—
575D172—21no—
576D172—22no—
577D172—21no—
578D172—44no—
579D172—42no—
580C4×D43—44no—
581C4×D43—42no—
582Dic86—22no—
583Dic86—22no—
584Dic86—21no—
585Dic86—21no—
586Dic86—42no—
587Dic86—82no—
588C8×C43—21no—
589C8×C43—21no—
590C8×C43—22no—
591C43⋊C8—21no—
592C43⋊C8—21no—
593C43⋊C8—22no—
594#60833—431nomaximal, Sylow
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—22no—
598C22×C43—22no—
599C22×C43—22no—
600C22×C43—42no—
601C22×C43—41no—
602C22×C43—41no—
603C22×C43—41no—
604C22×C43—42no—
605C22×C43—41no—
606C22×C43—42no—
607C22×C43—41no—
608C22×C43—41no—
609C22×C43—162no—
610C22×C43—164no—
611C22×C43#53512yes—
612C22×C43C23×D411yescharacteristic
613C2×D43—42no—
614C2×D43—41no—
615C2×D43—41no—
616C2×D43—42no—
617C2×D43—42no—
618C2×D43—41no—
619C2×D43—162no—
620C2×D43—164no—
621C4×C43—22no—
622C4×C43—42no—
623C4×C43—41no—
624C4×C43—41no—
625C4×C43#53512yes—
626C4×C43C2×H(5,𝔽2)11yescharacteristic
627C4×C43C2×H(5,𝔽2)11yescharacteristic
628Dic43—22no—
629Dic43—21no—
630Dic43—21no—
631Dic43—21no—
632Dic43—22no—
633Dic43—41no—
634Dic43—42no—
635Dic43—41no—
636Dic43—41no—
637Dic43#57712yes—
638#3498—431no—
639#3461—431no—
640#3224—432no—
641#3224—432no—
642#3222—432no—
643#3222—432no—
644#3217—432no—
645#3216—432no—
646#3212—432no—
647#3208—432no—
648#3154—431no—
649#3154—431no—
650#3136—431no—
651#3136—431no—
652#3038—431no—
653#3037—431no—
654#3035—431no—
655C2×#460—431no—
656#3012—431no—
657#3012D4311yescharacteristic, complemented
658#3009—431no—
659#3009—431no—
660#2925—431no—
661C2×C43—22no—
662C2×C43—42no—
663C2×C43—81no—
664C2×C43—82no—
665C2×C43—81no—
666C2×C43C2×#53511yescharacteristic
667C2×C43C2×#57711yescharacteristic
668C2×C43#358511yescharacteristic
669D43—82no—
670D43—81no—
671C2×H(5,𝔽2)—431no—
672C2×H(5,𝔽2)C2×D4311yescharacteristic
673C2×#137—431no—
674C2×#137—431no—
675C2×AGL(1,ℤ/8)—431no—
676C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
677C2×#135—431no—
678C2×#135C2×D4311yescharacteristic, complemented
679C22×SD16—431no—
680C22×SD16—431no—
681#550—861no—
682#550—861no—
683D42—861no—
684D42—862no—
685D42—862no—
686D42—861no—
687#544—431no—
688#542—432no—
689#542—861no—
690#541—432no—
691#541—861no—
692#539—862no—
693#537C2×D4311yescharacteristic
694#536—431no—
695#536—431no—
696#535—431no—
697#535—432no—
698#535—431no—
699#535—432no—
700#533—432no—
701#533—861no—
702#532—432no—
703#532—431no—
704C2×#127—432no—
705C2×#127—431no—
706#529—432no—
707#529—861no—
708#529—862no—
709C4×#41—431no—
710C4×#41—431no—
711C2×C4×Q8—431no—
712#497—432no—
713#497—432no—
714#496—432no—
715#496—432no—
716#495—432no—
717#495—432no—
718#492—432no—
719#492—432no—
720#490—432no—
721#490—432no—
722#489—432no—
723#489—432no—
724#488—432no—
725#488—432no—
726#486—432no—
727#486—432no—
728#464—431no—
729#464—431no—
730#464—432no—
731#464—432no—
732#463—431no—
733#463—431no—
734#462—431no—
735#462—432no—
736#461—431no—
737#460—431no—
738#460—432no—
739#460—432no—
740#460—432no—
741#460—432no—
742#460—432no—
743#460—432no—
744#460—432no—
745#459—432no—
746#459—431no—
747#459—432no—
748#452—432no—
749#452—432no—
750#452—432no—
751#452—432no—
752#452—432no—
753#452C2×D4312yescomplemented
754#450—432no—
755#450—432no—
756#450—432no—
757#450—432no—
758#450—432no—
759#450C2×D4312yescomplemented
760#449—432no—
761#449C2×D4312yescomplemented
762#447—432no—
763#447C2×D4312yescomplemented
764#433—432no—
765#433—432no—
766#432—432no—
767#431—432no—
768#423—431no—
769C2×C4⋊C8—431no—
770#418—431no—
771#418—431no—
772#417—431no—
773#417C2×D4311yescharacteristic, complemented
774#416—431no—
775#416—431no—
776C2×#102—431no—
777C2×#102C2×D4311yescharacteristic, complemented
778#408—431no—
779#408C2×D4311yescharacteristic
780#405—431no—
781#405—431no—
782C43#6083311yescharacteristic, complemented, Sylow
783H(5,𝔽2)—42no—
784H(5,𝔽2)—42no—
785H(5,𝔽2)—1722no—
786H(5,𝔽2)—1722no—
787C2×#41—21no—
788C2×#41—431no—
789C2×#41—432no—
790C2×#41—861no—
791C2×#41C22×D4311yescharacteristic
792C2×#41C22×D4311yescharacteristic
793C2×#41C22×D4312yes—
794C2×#41C22×D4311yescharacteristic
795C22×Q8—431no—
796C22×D4—22no—
797C22×D4—21no—
798C22×D4—431no—
799C22×D4—432no—
800C22×D4—861no—
801C22×D4—862no—
802C22×D4—861no—
803C22×D4—862no—
804C22×D4—862no—
805C22×D4—861no—
806C22×D4C22×D4311yescharacteristic
807C22×D4C22×D4312yes—
808#137—1722no—
809#137—1722no—
810AGL(1,ℤ/8)—42no—
811AGL(1,ℤ/8)—1722no—
812#135—42no—
813#135—1722no—
814C2×Q16—431no—
815C2×Q16—432no—
816C2×Q16—432no—
817C2×Q16C22×D4311yescharacteristic
818C2×SD16—431no—
819C2×SD16—432no—
820C2×SD16—432no—
821C2×SD16—432no—
822C2×SD16—431no—
823C2×SD16—432no—
824C2×SD16—432no—
825C2×SD16—432no—
826C2×SD16—432no—
827C2×SD16—1722no—
828C2×SD16—1722no—
829C2×SD16C22×D4311yescharacteristic
830C2×SD16C22×D4311yescharacteristic
831C2×SD16C22×D4312yes—
832C2×D8—431no—
833C2×D8—432no—
834C2×D8C22×D4311yescharacteristic
835C2×D8C22×D4312yes—
836C2×M16—431no—
837C2×M16C22×D4311yescharacteristic
838C22×C8—431no—
839C22×C8C22×D4311yescharacteristic
840C4⋊Q8—432no—
841C4⋊Q8—431no—
842C4⋊Q8—432no—
843C4⋊Q8—861no—
844C4⋊Q8—861no—
845#127—431no—
846#127—432no—
847#127—432no—
848#127—432no—
849#127—432no—
850#127—861no—
851#127—862no—
852#127—861no—
853#127—862no—
854#126—862no—
855#126—862no—
856#126—862no—
857#126—862no—
858#125—432no—
859#125—862no—
860#125—862no—
861#125—861no—
862#125—862no—
863#124—431no—
864#124—432no—
865#124—432no—
866#124—431no—
867#124—432no—
868#124—862no—
869#124—861no—
870#123—862no—
871#123—862no—
872#123—862no—
873#123—862no—
874C22⋊Q8—21no—
875C22⋊Q8—432no—
876C22⋊Q8—432no—
877C22⋊Q8—862no—
878C22⋊Q8—862no—
879C22⋊Q8—862no—
880C22⋊Q8—861no—
881C22⋊Q8—861no—
882C22⋊Q8C22×D4312yes—
883#121—22no—
884#121—21no—
885#121—861no—
886#121—862no—
887#121—861no—
888#121—862no—
889#121—861no—
890#121—862no—
891#121—861no—
892#121—862no—
893#121—861no—
894#121—862no—
895#121—861no—
896#121—862no—
897#121C22×D4312yes—
898#120—862no—
899#120—862no—
900#120—862no—
901#120—862no—
902#120—862no—
903#120—862no—
904C4×Q8—431no—
905C4×Q8—431no—
906C4×Q8—431no—
907C4×Q8—431no—
908C4×Q8—432no—
909C4×Q8—432no—
910C4×Q8—861no—
911C4×Q8—861no—
912C4×Q8—862no—
913C4×D4—431no—
914C4×D4—432no—
915C4×D4—432no—
916C4×D4—431no—
917C4×D4—431no—
918C4×D4—431no—
919C4×D4—861no—
920C4×D4—862no—
921C4×D4—861no—
922C4×D4—862no—
923C4×D4—861no—
924C4×D4—861no—
925C4×D4—862no—
926#117—431no—
927#117—432no—
928#117—431no—
929#117—862no—
930#117—861no—
931#117—862no—
932C2×C4⋊C4—861no—
933C2×C4⋊C4C22×D4311yescharacteristic
934C2×C42—431no—
935C2×C42—432no—
936C2×C42—861no—
937C2×C42—861no—
938C4⋊C8—431no—
939C4⋊C8—431no—
940C4⋊C8—431no—
941C4⋊C8—431no—
942C4⋊C8—432no—
943C4⋊C8—432no—
944#103—431no—
945#103—431no—
946#103—431no—
947#103—431no—
948#103—432no—
949#103C22×D4312yes—
950#102—431no—
951#102—431no—
952#102—432no—
953#102—432no—
954#102—431no—
955#102—431no—
956#102—432no—
957#102—432no—
958#102—432no—
959#102—432no—
960#102—432no—
961#102C22×D4312yes—
962#102C22×D4312yes—
963#102C22×D4312yes—
964C22⋊C8—432no—
965C22⋊C8—432no—
966C22⋊C8C22×D4312yes—
967C22⋊C8C22×D4312yes—
968#97—432no—
969#97—432no—
970C4×C8—432no—
971C4×C8—432no—
972C24—22no—
973C24—21no—
974C24—862no—
975C24—861no—
976#41—22no—
977#41—22no—
978#41—22no—
979#41—22no—
980#41—22no—
981#41—22no—
982#41—42no—
983#41—42no—
984#41—44no—
985#41—862no—
986#41—862no—
987#41—1722no—
988#41—1722no—
989#41—1724no—
990C2×Q8—431no—
991C2×Q8—432no—
992C2×Q8—862no—
993C2×Q8—861no—
994C2×Q8—862no—
995C2×Q8—862no—
996C2×Q8D4×D4311yescharacteristic
997C2×Q8C23×D4311yescharacteristic
998C2×Q8C23×D4311yescharacteristic
999C2×D4—21no—
1000C2×D4—22no—
1001C2×D4—21no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—21no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—48no—
1010C2×D4—44no—
1011C2×D4—432no—
1012C2×D4—431no—
1013C2×D4—862no—
1014C2×D4—862no—
1015C2×D4—862no—
1016C2×D4—862no—
1017C2×D4—862no—
1018C2×D4—862no—
1019C2×D4—861no—
1020C2×D4—862no—
1021C2×D4—861no—
1022C2×D4—862no—
1023C2×D4—862no—
1024C2×D4—861no—
1025C2×D4—862no—
1026C2×D4—861no—
1027C2×D4—862no—
1028C2×D4—862no—
1029C2×D4—3442no—
1030C2×D4—3444no—
1031C2×D4—3442no—
1032C2×D4—3444no—
1033C2×D4—1722no—
1034C2×D4—1722no—
1035C2×D4—1728no—
1036C2×D4—1724no—
1037C2×D4D4×D4312yes—
1038C2×D4D4×D4311yescharacteristic
1039C2×D4C23×D4312yes—
1040C2×D4C23×D4311yescharacteristic
1041C2×D4C23×D4311yescharacteristic
1042C22×C4—21no—
1043C22×C4—21no—
1044C22×C4—22no—
1045C22×C4—21no—
1046C22×C4—431no—
1047C22×C4—432no—
1048C22×C4—431no—
1049C22×C4—432no—
1050C22×C4—861no—
1051C22×C4—861no—
1052C22×C4—861no—
1053C22×C4—862no—
1054C22×C4—861no—
1055C22×C4C23×D4312yes—
1056C22×C4C23×D4311yescharacteristic
1057Q16—41no—
1058Q16—1722no—
1059Q16—1721no—
1060Q16—1722no—
1061SD16—41no—
1062SD16—41no—
1063SD16—42no—
1064SD16—1722no—
1065SD16—1722no—
1066SD16—1722no—
1067SD16—1722no—
1068SD16—1722no—
1069SD16—1721no—
1070SD16—1722no—
1071SD16—1721no—
1072SD16—1722no—
1073D8—41no—
1074D8—42no—
1075D8—1721no—
1076D8—1722no—
1077M16—22no—
1078M16—862no—
1079C2×C8—22no—
1080C2×C8—431no—
1081C2×C8—432no—
1082C2×C8—431no—
1083C2×C8—862no—
1084C2×C8C23×D4311yescharacteristic
1085C2×C8C23×D4312yes—
1086C2×C8C23×D4311yescharacteristic
1087C4⋊C4—21no—
1088C4⋊C4—22no—
1089C4⋊C4—432no—
1090C4⋊C4—431no—
1091C4⋊C4—431no—
1092C4⋊C4—432no—
1093C4⋊C4—431no—
1094C4⋊C4—431no—
1095C4⋊C4—862no—
1096C4⋊C4—862no—
1097C4⋊C4—861no—
1098C4⋊C4—861no—
1099C4⋊C4—862no—
1100C4⋊C4—862no—
1101C4⋊C4—862no—
1102C4⋊C4—861no—
1103C4⋊C4—861no—
1104C4⋊C4—862no—
1105C4⋊C4—862no—
1106C4⋊C4—862no—
1107C4⋊C4—862no—
1108C4⋊C4C23×D4312yes—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—432no—
1112C22⋊C4—432no—
1113C22⋊C4—432no—
1114C22⋊C4—861no—
1115C22⋊C4—861no—
1116C22⋊C4—862no—
1117C22⋊C4—862no—
1118C22⋊C4—861no—
1119C22⋊C4—861no—
1120C22⋊C4—862no—
1121C22⋊C4—861no—
1122C22⋊C4—861no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C22⋊C4—862no—
1126C22⋊C4—861no—
1127C22⋊C4—862no—
1128C22⋊C4—862no—
1129C42—431no—
1130C42—432no—
1131C42—431no—
1132C42—432no—
1133C42—432no—
1134C42—431no—
1135C42—431no—
1136C42—861no—
1137C42—862no—
1138C42—861no—
1139C42—862no—
1140C42—861no—
1141C23—21no—
1142C23—22no—
1143C23—21no—
1144C23—44no—
1145C23—42no—
1146C23—81no—
1147C23—81no—
1148C23—82no—
1149C23—82no—
1150C23—862no—
1151C23—861no—
1152C23—3441no—
1153C23—3441no—
1154C23—3442no—
1155C23—3442no—
1156C23—1724no—
1157C23—1722no—
1158C23C2×D4×D4312yes—
1159C23C2×D4×D4311yescharacteristic
1160Q8—22no—
1161Q8—21no—
1162Q8—21no—
1163Q8—21no—
1164Q8—21no—
1165Q8—862no—
1166Q8—862no—
1167Q8—861no—
1168Q8—861no—
1169Q8—3442no—
1170Q8—1722no—
1171D4—24no—
1172D4—22no—
1173D4—21no—
1174D4—21no—
1175D4—22no—
1176D4—21no—
1177D4—22no—
1178D4—21no—
1179D4—44no—
1180D4—44no—
1181D4—42no—
1182D4—42no—
1183D4—42no—
1184D4—82no—
1185D4—862no—
1186D4—861no—
1187D4—862no—
1188D4—861no—
1189D4—3442no—
1190D4—3442no—
1191D4—3442no—
1192D4—3442no—
1193D4—3442no—
1194D4—3442no—
1195D4—1724no—
1196D4—1724no—
1197D4—1722no—
1198D4—1724no—
1199D4—1722no—
1200D4—1724no—
1201D4—1722no—
1202D4—1722no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—44no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—81no—
1212C2×C4—431no—
1213C2×C4—431no—
1214C2×C4—431no—
1215C2×C4—431no—
1216C2×C4—432no—
1217C2×C4—432no—
1218C2×C4—862no—
1219C2×C4—864no—
1220C2×C4—861no—
1221C2×C4—861no—
1222C2×C4—862no—
1223C2×C4—861no—
1224C2×C4—3441no—
1225C2×C4—1724no—
1226C2×C4—1722no—
1227C2×C4—1721no—
1228C2×C4—1722no—
1229C2×C4—1722no—
1230C2×C4—1722no—
1231C2×C4C2×D4×D4312yes—
1232C2×C4C2×D4×D4311yescharacteristic
1233C2×C4#1306337012yes—
1234C2×C4#1306337012yes—
1235C2×C4C24×D4311yescharacteristic
1236C8—21no—
1237C8—21no—
1238C8—22no—
1239C8—861no—
1240C8—861no—
1241C8—862no—
1242C22—21no—
1243C22—21no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—41no—
1248C22—42no—
1249C22—41no—
1250C22—41no—
1251C22—42no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—41no—
1256C22—162no—
1257C22—164no—
1258C22—1722no—
1259C22—1721no—
1260C22—1722no—
1261C22—1721no—
1262C22—1722no—
1263C22—1721no—
1264C22—6882no—
1265C22—6884no—
1266C22#1458346412yes—
1267C22C22×D4×D4311yescharacteristic
1268C4—22no—
1269C4—42no—
1270C4—41no—
1271C4—41no—
1272C4—432no—
1273C4—861no—
1274C4—862no—
1275C4—861no—
1276C4—861no—
1277C4—862no—
1278C4—1721no—
1279C4—1721no—
1280C4—1721no—
1281C4—1722no—
1282C4#1458346412yes—
1283C4C2×#1306337011yescharacteristic
1284C4C2×#1306337011yescharacteristic
1285C2—22no—
1286C2—42no—
1287C2—82no—
1288C2—81no—
1289C2—81no—
1290C2—3442no—
1291C2—3441no—
1292C2C2×#1458346411yescharacteristic
1293C2#577×D4311yescharacteristic
1294C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3012C2
socleC22×C43C23×D4
hypercenter#3012D43
hypocenterC43#60833
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3012

Complements

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

NH ≅ G/Ntype
1. #19148369C2semidirect
2. #19148023C2semidirect
3. #19145687C2semidirect
4. #19145685C2semidirect
5. #19145665C2semidirect
6. #19145663C2semidirect
7. #19145611C2semidirect
8. #19145603C2semidirect
9. #19145568C2semidirect
10. #19145534C2semidirect
11. #19145072C2semidirect
12. #19145069C2semidirect
13. #19144952C2semidirect
14. #19144947C2semidirect
15. #19144073C2semidirect
16. #19144066C2semidirect
17. #19144046C2semidirect
18. C2×#14583098C2semidirect
19. #19143896C2semidirect
20. #19143874C2semidirect
21. #19143872C2semidirect
22. #19143257C2semidirect
23. C43×#3012C2semidirect
25. C2×#13063358C22semidirect
26. C2×#13063355C22semidirect
27. C2×#13063350C22semidirect
28. C2×#13063345C22semidirect
29. C22×#10621873C22semidirect
30. C22×#10621883C22semidirect
37. #14583530C22semidirect
39. #14583516C22semidirect
41. #14583509C22semidirect
44. #14583470C22semidirect
50. #14583451C22semidirect
57. #14583430C22semidirect
59. #41×Dic43C22semidirect
60. C2×#13063290C22semidirect
61. #14583292C22semidirect
62. #14583290C22semidirect
63. #14583287C22semidirect
64. #14583287C22semidirect
65. #14583282C22semidirect
66. #14583280C22semidirect
67. #14583270C22semidirect
68. #14583270C22semidirect
69. #14583262C22semidirect
70. #14583262C22semidirect
71. #14583260C22semidirect
72. #14583257C22semidirect
73. #14583255C22semidirect
74. #14583252C22semidirect
75. #14583244C22semidirect
76. #14583244C22semidirect
77. #14583124C22semidirect
78. #14583123C22semidirect
79. #14583120C22semidirect
80. #14583119C22semidirect
81. #14583116C22semidirect
82. #14583112C22semidirect
83. #14583108C22semidirect
84. #14583107C22semidirect
85. #14583102C22semidirect
86. #14583098C22semidirect
87. #14583098C22semidirect
88. #14583098C22semidirect
89. #14583098C22semidirect
90. #14583098C22semidirect
91. #14583097C22semidirect
92. #14583097C22semidirect
93. #14583097C22semidirect
94. #14583092C22semidirect
95. #14583092C22semidirect
96. #14583092C22semidirect
97. #14583063C22semidirect
98. #14583063C22semidirect
99. #14583061C22semidirect
100. #14583061C22semidirect
101. #14583059C22semidirect
102. #14583052C22semidirect
103. #14583052C22semidirect
104. #14583050C22semidirect
105. #14583050C22semidirect
106. #14583049C22semidirect
107. #14583042C22semidirect
108. #14583032C22semidirect
109. #14582957C22semidirect
110. #14582957C22semidirect
111. #14582953C22semidirect
112. #14582949C22semidirect
113. #14582922C22semidirect
114. C2×Dic43⋊C8C22semidirect
115. #14582905C22semidirect
116. #14582904C22semidirect
117. #14582898C22semidirect
118. #14582896C22semidirect
119. #14582895C22semidirect
120. C2×#13063245C22semidirect
122. #14582857C22semidirect
123. #14582854C22semidirect
125. C2×AGL(1,ℤ/8)×C43C22semidirect
126. C2×#135×C43C22semidirect
128. C43×#452C22semidirect
129. C43×#450C22semidirect
130. C43×#449C22semidirect
131. C43×#447C22semidirect
132. C43×#417C22semidirect
133. C2×#102×C43C22semidirect
657. #3012D43semidirect
676. C2×AGL(1,ℤ/8)C2×D43semidirect
678. C2×#135C2×D43semidirect
753. #452C2×D43semidirect
759. #450C2×D43semidirect
761. #449C2×D43semidirect
763. #447C2×D43semidirect
773. #417C2×D43semidirect
777. C2×#102C2×D43semidirect
782. C43#60833semidirect

Maximal subgroups

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

subgroupindex
#191483692
#191480232
#191456872
#191456852
#191456652
#191456632
#191456112
#191456032
#191455682
#191455342
#191450722
#191450692
#191449522
#191449472
#191440732
#191440662
#191440462
C2×#145830982
#191438962
#191438742
#191438722
#191432572
C43×#30122
#6083343