Finite Group Databasebeta

← #25968350

Subgroups — #25968350

Order 11008.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148504C211yesmaximal, characteristic, complemented
2#19148369C211yesmaximal, characteristic, complemented
3#19145695C212yesmaximal, complemented
4#19145693C212yesmaximal, complemented
5#19145687C212yesmaximal, complemented
6#19145685C212yesmaximal, complemented
7#19145549C212yesmaximal, complemented
8#19145534C212yesmaximal, complemented
9#19145526C212yesmaximal, complemented
10#19145511C212yesmaximal, complemented
11#19145043C211yesmaximal, characteristic, complemented
12#19145019C211yesmaximal, characteristic, complemented
13#19144986C211yesmaximal, characteristic, complemented
14C2×#14583244C211yesmaximal, characteristic, complemented
15#19144139C211yesmaximal, characteristic, complemented
16#19144138C211yesmaximal, characteristic, complemented
17#19144133C211yesmaximal, characteristic, complemented
18#19144132C211yesmaximal, characteristic, complemented
19#19143902C211yesmaximal, characteristic, complemented
20#19143899C211yesmaximal, characteristic, complemented
21#19143896C211yesmaximal, characteristic, complemented
22#19143235C211yesmaximal, characteristic, complemented
23C43×#3012C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C2×#13063353C2211yescharacteristic, complemented
26C2×#13063351C2211yescharacteristic, complemented
27C2×#13063350C2211yescharacteristic, complemented
28C2×#13063347C2211yescharacteristic, complemented
29C2×#13063345C2211yescharacteristic, complemented
30C2×#13063345C2211yescharacteristic, complemented
31#14583620—21no—
32#14583613—21no—
33#14583607—21no—
34#14583592—22no—
35#14583568—21no—
36#14583568—21no—
37#14583555—22no—
38#14583549—21no—
39D4×C22⋊D43—22no—
40D4×C22⋊D43—22no—
41D4×C22⋊D43—21no—
42D4×C22⋊D43—21no—
43#14583522C2212yescomplemented
44#14583516C2212yescomplemented
45#14583477C2211yescharacteristic
46#14583466C2211yescharacteristic
47#14583466C2212yes—
48#14583463C2211yescharacteristic
49#14583463C2212yes—
50#14583451C2212yescomplemented
51#14583445C2211yescharacteristic
52#14583445C2212yes—
53#14583445C2211yescharacteristic, complemented
54#14583444C2212yescomplemented
55C2×#13063324C2211yescharacteristic, complemented
56C2×#13063321C2212yes—
57C2×#13063321C2211yescharacteristic
58#14583382C2211yescharacteristic, complemented
59#14583380C2211yescharacteristic, complemented
60#41×Dic43C2211yescharacteristic
61#14583287C2212yescomplemented
62#14583285C2212yescomplemented
63#14583284C2211yescharacteristic, complemented
64#14583282C2211yescharacteristic, complemented
65#14583280C2211yescharacteristic, complemented
66#14583280C2211yescharacteristic, complemented
67#14583277C2211yescharacteristic, complemented
68#14583274C2211yescharacteristic, complemented
69#14583274C2212yescomplemented
70#14583270C2211yescharacteristic, complemented
71#14583270C2211yescharacteristic, complemented
72#14583270C2212yescomplemented
73#14583260C2212yescomplemented
74#14583257C2212yescomplemented
75#14583248C2212yescomplemented
76#14583244C2212yescomplemented
77#14583244C2212yescomplemented
78#14583244C2212yescomplemented
79#14583244C2212yescomplemented
80#14583244C2212yescomplemented
81#14583124C2212yescomplemented
82#14583123C2212yescomplemented
83#14583120C2212yescomplemented
84#14583119C2212yescomplemented
85#14583117C2212yescomplemented
86#14583116C2212yescomplemented
87#14583113C2212yescomplemented
88#14583112C2212yescomplemented
89#14583098C2212yescomplemented
90#14583098C2212yescomplemented
91#14583097C2212yescomplemented
92#14583097C2212yescomplemented
93#14583093C2212yescomplemented
94#14583093C2212yescomplemented
95#14583092C2212yescomplemented
96#14583092C2212yescomplemented
97#14583063C2212yescomplemented
98#14583061C2212yescomplemented
99#14583059C2212yescomplemented
100#14583052C2212yescomplemented
101#14583050C2212yescomplemented
102#14583049C2212yescomplemented
103#14583046C2212yescomplemented
104#14583044C2212yescomplemented
105#14583042C2212yescomplemented
106#14583035C2212yescomplemented
107#14583033C2212yescomplemented
108#14583032C2212yescomplemented
109#14582957C2212yescomplemented
110#14582957C2212yescomplemented
111#14582949C2212yescomplemented
112#14582949C2212yescomplemented
113#14582927C2211yescharacteristic, complemented
114#14582925C2211yescharacteristic, complemented
115#14582901C2211yescharacteristic, complemented
116#14582900C2211yescharacteristic, complemented
117#14582898C2211yescharacteristic, complemented
118C2×#13063247C2211yescharacteristic, complemented
119C2×#13063246C2211yescharacteristic, complemented
120C2×#13063245C2211yescharacteristic, complemented
121#14582866C2211yescharacteristic
122M16×Dic43C2211yescharacteristic, complemented
123C2×C8×Dic43C2211yescharacteristic, 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×#10621898C2311yescharacteristic
140C2×#10621898C2312yes—
141C2×#10621900—22no—
142C22×Dic86—21no—
143C22×D172C2311yescharacteristic
144C22×D172C2312yes—
145C22×C22⋊D43—21no—
146C22×C22⋊D43—22no—
147C22×C22⋊D43—21no—
148C22×C22⋊D43—22no—
149C2×D4×D43—21no—
150C2×D4×D43—22no—
151#13063353—42no—
152#13063351—42no—
153#13063350—42no—
154#13063347—42no—
155#13063345—42no—
156#13063345—42no—
157C2×Dic172C2311yescharacteristic
158C2×#10621885C2311yescharacteristic
159C2×#10621885C2311yescharacteristic
160C2×#10621873C2311yescharacteristic
161C2×#10621873C2311yescharacteristic
162C2×#10621873C2312yes—
163C2×#10621883C2311yescharacteristic
164C2×#10621883C2311yescharacteristic
165C2×#10621883C2312yes—
166C2×#10621884C2311yescharacteristic
167C2×#10621884C2311yescharacteristic
168C2×#10621884C2312yes—
169C2×D344C2312yes—
170C2×D344C2311yescharacteristic
171C2×#10621882C2312yes—
172C2×#10621882C2312yes—
173C2×#10621882C2311yescharacteristic
174C2×#10621882C2311yescharacteristic
175C2×#10621877C2311yescharacteristic
176C22×C43⋊C8C2311yescharacteristic
177#13063324—21no—
178#13063324—21no—
179#13063324C2312yes—
180#13063324C2312yes—
181#13063323C2311yescharacteristic
182#13063323C2311yescharacteristic
183#13063321—22no—
184#13063321—21no—
185#13063321—21no—
186#13063321—22no—
187#13063321C2312yes—
188#13063321C2312yes—
189#13063321C2311yescharacteristic
190#13063321C2312yes—
191#13063321C2312yes—
192#13063321C2311yescharacteristic
193#13063320—22no—
194#13063318—22no—
195#13063315—22no—
196#13063314C2312yes—
197#13063314C2311yescharacteristic
198#13063314C2311yescharacteristic
199#13063312—22no—
200#13063312C2312yes—
201#13063312C2311yescharacteristic
202#13063312C2311yescharacteristic
203#13063311—22no—
204#13063311—22no—
205#13063307—22no—
206#13063306—22no—
207#13063305—22no—
208#13063304C2312yes—
209#13063302—22no—
210#13063302—22no—
211#13063301—21no—
212#13063299—21no—
213#13063299—21no—
214#13063299—22no—
215#13063299—22no—
216#13063299C2312yes—
217#13063297—22no—
218#13063297—21no—
219#13063297—21no—
220#13063297—22no—
221#13063297—21no—
222#13063297—22no—
223#13063297—21no—
224#13063297—22no—
225#13063296—21no—
226#13063296—21no—
227#13063296—21no—
228#13063296—22no—
229#13063296—22no—
230#13063294—22no—
231#13063294—22no—
232#13063294—22no—
233#13063293—22no—
234#13063293—22no—
235#13063293—22no—
236Q8×Dic43D411yescharacteristic
237Q8×Dic43D411yescharacteristic
238Q8×Dic43C2312yes—
239#13063290—22no—
240#13063290C2312yes—
241D4×Dic43—22no—
242D4×Dic43D412yes—
243D4×Dic43D412yes—
244D4×Dic43D411yescharacteristic
245D4×Dic43D411yescharacteristic
246D4×Dic43C2312yes—
247#13063287C2312yes—
248C4×C22⋊D43—22no—
249C4×C22⋊D43—22no—
250C4×C22⋊D43—21no—
251C4×C22⋊D43—21no—
252C4×C22⋊D43—22no—
253C4×C22⋊D43—21no—
254C4×C22⋊D43—21no—
255(C22⋊D43)⋊C4—22no—
256#13063284—21no—
257#13063284C2311yescharacteristic
258#13063284C2312yes—
259#13063283—21no—
260#13063281—22no—
261C2×C4⋊Dic43—21no—
262C2×C4⋊Dic43C2311yescharacteristic
263C2×Dic43⋊C4—21no—
264C4⋊C4×D43—21no—
265C2×C4×Dic43C2311yescharacteristic
266C2×C4×Dic43C2312yes—
267Dic43⋊C8C2312yes—
268Dic43⋊C8C2312yes—
269Dic43⋊C8C2312yes—
270Dic43⋊C8C2312yes—
271#13063250C2312yes—
272#13063249C2312yes—
273#13063248C2312yes—
274#13063247C2312yes—
275#13063247C2312yes—
276#13063247C2312yes—
277#13063246C2312yes—
278#13063246C2312yes—
279#13063246C2312yes—
280#13063245C2312yes—
281#13063245C2312yes—
282#13063245C2312yes—
283C22⋊(C43⋊C8)C2312yes—
284C22⋊(C43⋊C8)C2312yes—
285#13063235C2312yes—
286C8×Dic43C2311yescharacteristic
287C8×Dic43C2311yescharacteristic
288C8×Dic43C2311yescharacteristic
289C8×Dic43C2311yescharacteristic
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—21no—
299C22×D4×C43—22no—
300C22×D4×C43C2311yescharacteristic
301C22×D4×C43C2312yes—
302AGL(1,ℤ/8)×C43—42no—
303#135×C43—42no—
304C2×Q16×C43C2311yescharacteristic
305C2×SD16×C43C2311yescharacteristic
306C2×SD16×C43C2312yes—
307C2×SD16×C43C2311yescharacteristic
308C2×D8×C43C2311yescharacteristic
309C2×D8×C43C2312yes—
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×D411yescharacteristic
353C2×D4×C43C2×D412yes—
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—21no—
365C2×C22⋊D43—21no—
366C2×C22⋊D43—22no—
367C2×C22⋊D43—22no—
368C2×C22⋊D43—21no—
369C2×C22⋊D43—22no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43—22no—
372C2×C22⋊D43—22no—
373C2×C22⋊D43—22no—
374C2×C22⋊D43—22no—
375C2×C22⋊D43—21no—
376C2×C22⋊D43—22no—
377C2×C22⋊D43—21no—
378C2×C22⋊D43—22no—
379C2×C22⋊D43—82no—
380C2×C22⋊D43—84no—
381C2×C22⋊D43—82no—
382C2×C22⋊D43—84no—
383C22×Dic43—22no—
384C22×Dic43—21no—
385C22×Dic43C2×D411yescharacteristic
386C22×Dic43C2×D412yes—
387C22×Dic43C2×D411yescharacteristic
388C22×Dic43C2×D412yes—
389#10621902—44no—
390#10621900—84no—
391D4×D43—44no—
392D4×D43—48no—
393#10621898—22no—
394#10621898—22no—
395#10621898—22no—
396#10621898—22no—
397#10621898—42no—
398#10621898—42no—
399C2×D172—22no—
400C2×D172—21no—
401C2×D172—22no—
402C2×D172—22no—
403C2×D172—42no—
404C2×D172—42no—
405C2×D172C2412yes—
406C2×D172C2411yescharacteristic
407C2×D172C2411yescharacteristic
408C2×C4×D43—21no—
409C2×C4×D43—22no—
410C2×C4×D43—21no—
411C2×C4×D43—22no—
412C2×Dic86—22no—
413C2×Dic86—22no—
414C2×Dic86—82no—
415C2×Dic86C2411yescharacteristic
416C2×Dic86C2411yescharacteristic
417Q16×C43—41no—
418SD16×C43—41no—
419SD16×C43—41no—
420SD16×C43—42no—
421D8×C43—41no—
422D8×C43—42no—
423M16×C43—22no—
424C2×C8×C43—22no—
425C2×C8×C43C2411yescharacteristic
426C2×C8×C43C2411yescharacteristic
427C2×C8×C43C2412yes—
428C4⋊C4×C43—21no—
429C4⋊C4×C43—22no—
430C4⋊C4×C43C2412yes—
431C22⋊C4×C43—22no—
432C22⋊C4×C43—22no—
433C22⋊Dic43—22no—
434C22⋊Dic43—22no—
435C22⋊Dic43—21no—
436C22⋊Dic43—22no—
437C22⋊Dic43—21no—
438C22⋊Dic43—21no—
439C22⋊Dic43—21no—
440C22⋊Dic43—22no—
441C22⋊Dic43C2×D412yes—
442C22⋊Dic43C2×D412yes—
443C22⋊Dic43C2×D412yes—
444#10621885—41no—
445#10621885—41no—
446#10621884—41no—
447#10621884—41no—
448#10621884—42no—
449#10621883—41no—
450#10621883—41no—
451#10621883—42no—
452#10621882—41no—
453#10621882—41no—
454#10621882—42no—
455#10621882—42no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—21no—
460(C2×D43)⋊C4—22no—
461(C2×D43)⋊C4—21no—
462(C2×D43)⋊C4—21no—
463(C2×D43)⋊C4—21no—
464C4⋊Dic43—21no—
465C4⋊Dic43—22no—
466C4⋊Dic43C2×D411yescharacteristic
467C4⋊Dic43C2×D411yescharacteristic
468C4⋊Dic43C2×D412yes—
469C4⋊Dic43C2×D412yes—
470C4⋊Dic43C2412yes—
471Dic43⋊C4—22no—
472Dic43⋊C4—22no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—21no—
476Dic43⋊C4—21no—
477Dic43⋊C4—21no—
478Dic43⋊C4—21no—
479C4×Dic43—22no—
480C4×Dic43—22no—
481C4×Dic43C2×D412yes—
482C4×Dic43C2×D411yescharacteristic
483C4×Dic43C2×D411yescharacteristic
484C4×Dic43C2×D412yes—
485C4×Dic43C2411yescharacteristic
486C4×Dic43C2411yescharacteristic
487C4×Dic43C2412yes—
488#10621877—22no—
489C2×C43⋊C8—22no—
490C2×C43⋊C8C2411yescharacteristic
491C2×C43⋊C8C2411yescharacteristic
492C2×C43⋊C8C2412yes—
493Dic172—41no—
494D344—41no—
495D344—42no—
496#10621873—41no—
497#10621873—41no—
498#10621873—42no—
499C23×C43—21no—
500C23×C43—21no—
501C23×C43—22no—
502C23×C43—44no—
503C23×C43—42no—
504C23×C43—81no—
505C23×C43—81no—
506C23×C43—82no—
507C23×C43—82no—
508C23×C43C22×D412yes—
509C23×C43C22×D411yescharacteristic
510C22×D43—21no—
511C22×D43—21no—
512C22×D43—22no—
513C22×D43—44no—
514C22×D43—42no—
515C22×D43—81no—
516C22×D43—82no—
517C22×D43—81no—
518C22×D43—82no—
519Q8×C43—22no—
520Q8×C43—21no—
521Q8×C43—21no—
522Q8×C43—21no—
523Q8×C43—21no—
524D4×C43—24no—
525D4×C43—22no—
526D4×C43—21no—
527D4×C43—21no—
528D4×C43—22no—
529D4×C43—21no—
530D4×C43—22no—
531D4×C43—21no—
532D4×C43—44no—
533D4×C43—44no—
534D4×C43—42no—
535D4×C43—42no—
536D4×C43—42no—
537D4×C43—82no—
538C2×C4×C43—22no—
539C2×C4×C43—22no—
540C2×C4×C43—21no—
541C2×C4×C43—22no—
542C2×C4×C43—21no—
543C2×C4×C43—44no—
544C2×C4×C43—42no—
545C2×C4×C43—42no—
546C2×C4×C43—81no—
547C2×C4×C43C22×D412yes—
548C2×C4×C43C22×D411yescharacteristic
549C2×C4×C43H(5,𝔽2)12yes—
550C2×C4×C43H(5,𝔽2)12yes—
551C2×C4×C43C2511yescharacteristic
552C22⋊D43—44no—
553C22⋊D43—42no—
554C22⋊D43—42no—
555C22⋊D43—42no—
556C22⋊D43—44no—
557C22⋊D43—42no—
558C22⋊D43—42no—
559C22⋊D43—44no—
560C22⋊D43—42no—
561C22⋊D43—82no—
562C22⋊D43—82no—
563C22⋊D43—82no—
564C22⋊D43—82no—
565C22⋊D43—82no—
566C22⋊D43—82no—
567C22⋊D43—82no—
568C2×Dic43—22no—
569C2×Dic43—24no—
570C2×Dic43—22no—
571C2×Dic43—24no—
572C2×Dic43—21no—
573C2×Dic43—22no—
574C2×Dic43—21no—
575C2×Dic43—82no—
576C2×Dic43—81no—
577C2×Dic43C22×D412yes—
578C2×Dic43C22×D411yescharacteristic
579C2×Dic43C22×D412yes—
580C2×Dic43C22×D411yescharacteristic
581C2×Dic43C22×D411yescharacteristic
582C2×Dic43C22×D411yescharacteristic
583D172—21no—
584D172—22no—
585D172—21no—
586D172—21no—
587D172—22no—
588D172—21no—
589D172—44no—
590D172—42no—
591C4×D43—44no—
592C4×D43—42no—
593C4×D43—42no—
594C4×D43—82no—
595Dic86—21no—
596Dic86—21no—
597Dic86—21no—
598Dic86—21no—
599Dic86—44no—
600Dic86—82no—
601C8×C43—21no—
602C8×C43—22no—
603C8×C43—21no—
604C43⋊C8—21no—
605C43⋊C8—21no—
606C43⋊C8—22no—
607#60822—431nomaximal, Sylow
608C22×C43—21no—
609C22×C43—21no—
610C22×C43—22no—
611C22×C43—22no—
612C22×C43—22no—
613C22×C43—41no—
614C22×C43—42no—
615C22×C43—41no—
616C22×C43—42no—
617C22×C43—41no—
618C22×C43—41no—
619C22×C43—42no—
620C22×C43—41no—
621C22×C43—41no—
622C22×C43—162no—
623C22×C43—164no—
624C22×C43#53512yes—
625C22×C43C23×D411yescharacteristic
626C2×D43—41no—
627C2×D43—42no—
628C2×D43—41no—
629C2×D43—42no—
630C2×D43—41no—
631C2×D43—41no—
632C2×D43—42no—
633C2×D43—41no—
634C2×D43—41no—
635C2×D43—162no—
636C2×D43—164no—
637C4×C43—22no—
638C4×C43—41no—
639C4×C43—41no—
640C4×C43—42no—
641C4×C43#53512yes—
642C4×C43C2×H(5,𝔽2)11yescharacteristic
643C4×C43C2×H(5,𝔽2)11yescharacteristic
644Dic43—21no—
645Dic43—22no—
646Dic43—22no—
647Dic43—21no—
648Dic43—41no—
649Dic43—41no—
650Dic43—42no—
651Dic43#57612yes—
652Dic43#57712yes—
653#3511—431no—
654#3498—431no—
655#3224—432no—
656#3224—432no—
657#3224—432no—
658#3224—432no—
659#3210—432no—
660#3208—432no—
661#3207—432no—
662#3205—432no—
663#3151—431no—
664#3147—431no—
665#3141—431no—
666C2×#486—431no—
667#3045—431no—
668#3045—431no—
669#3045—431no—
670#3045—431no—
671#3012—431no—
672#3012—431no—
673#3012—431no—
674#3012D4311yescharacteristic, complemented
675#2922—431no—
676C2×C43—22no—
677C2×C43—42no—
678C2×C43—81no—
679C2×C43—82no—
680C2×C43—81no—
681C2×C43C2×#53511yescharacteristic
682C2×C43C2×#57611yescharacteristic
683C2×C43C2×#57711yescharacteristic
684D43—81no—
685D43—82no—
686D43—81no—
687C2×H(5,𝔽2)—431no—
688C2×H(5,𝔽2)C2×D4311yescharacteristic
689C2×AGL(1,ℤ/8)—431no—
690C2×AGL(1,ℤ/8)—431no—
691C2×AGL(1,ℤ/8)—431no—
692C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
693C2×#135—431no—
694C2×#135—431no—
695C2×#135—431no—
696C2×#135C2×D4311yescharacteristic, complemented
697#556—861no—
698#555—861no—
699#554—861no—
700#553—862no—
701#550—861no—
702#550—861no—
703#548—862no—
704#547—861no—
705D42—861no—
706D42—862no—
707D42—862no—
708D42—861no—
709#542—432no—
710#542—432no—
711#537—431no—
712#537C2×D4311yescharacteristic
713#535—432no—
714#535—431no—
715#535—432no—
716#535—431no—
717#533—432no—
718#532—432no—
719#532—431no—
720#532—431no—
721#532—432no—
722C2×C4⋊Q8—431no—
723C2×#127—431no—
724C2×#127—432no—
725#520—431no—
726#520—431no—
727C4×#41—431no—
728#496—432no—
729#496—432no—
730#495—431no—
731#495—431no—
732#495—431no—
733#495—431no—
734#494—431no—
735#493—431no—
736#493—432no—
737#492—431no—
738#492—431no—
739#492—432no—
740#489—432no—
741#489—432no—
742#487—432no—
743#486—432no—
744#486—432no—
745#486—432no—
746#486—432no—
747#486—432no—
748#464—432no—
749#464—432no—
750#464—432no—
751#464—432no—
752#463—432no—
753#463—432no—
754#463—432no—
755#463—432no—
756#460—432no—
757#460—432no—
758#460—432no—
759#460—432no—
760#459—432no—
761#459—432no—
762#459—432no—
763#459—432no—
764#452—432no—
765#452—432no—
766#452—432no—
767#452C2×D4312yescomplemented
768#450—432no—
769#450—432no—
770#450—432no—
771#450C2×D4312yescomplemented
772#449—432no—
773#449—432no—
774#449—432no—
775#449C2×D4312yescomplemented
776#447—432no—
777#447—432no—
778#447—432no—
779#447C2×D4312yescomplemented
780#433—432no—
781#433—432no—
782#431—432no—
783#431—432no—
784#424—431no—
785#424—431no—
786#417—431no—
787#417—431no—
788#417—431no—
789#417C2×D4311yescharacteristic, complemented
790C2×#102—431no—
791C2×#102—431no—
792C2×#102—431no—
793C2×#102C2×D4311yescharacteristic, complemented
794#408—431no—
795#408C2×D4311yescharacteristic
796C4×M16—431no—
797C2×C4×C8—431no—
798C43#6082211yescharacteristic, complemented, Sylow
799H(5,𝔽2)—42no—
800H(5,𝔽2)—42no—
801H(5,𝔽2)—1722no—
802H(5,𝔽2)—1722no—
803C2×#41—21no—
804C2×#41—431no—
805C2×#41—431no—
806C2×#41—432no—
807C2×#41—862no—
808C2×#41—861no—
809C2×#41C22×D4311yescharacteristic
810C2×#41C22×D4311yescharacteristic
811C2×#41C22×D4312yes—
812C2×#41C22×D4311yescharacteristic
813C22×Q8—861no—
814C22×D4—22no—
815C22×D4—21no—
816C22×D4—431no—
817C22×D4—432no—
818C22×D4—861no—
819C22×D4—862no—
820C22×D4—861no—
821C22×D4—862no—
822C22×D4—862no—
823C22×D4—861no—
824C22×D4C22×D4311yescharacteristic
825C22×D4C22×D4312yes—
826AGL(1,ℤ/8)—42no—
827AGL(1,ℤ/8)—1722no—
828AGL(1,ℤ/8)—1722no—
829AGL(1,ℤ/8)—1722no—
830#135—42no—
831#135—1722no—
832#135—1722no—
833#135—1722no—
834C2×Q16—431no—
835C2×Q16—431no—
836C2×Q16—431no—
837C2×Q16C22×D4311yescharacteristic
838C2×SD16—431no—
839C2×SD16—431no—
840C2×SD16—432no—
841C2×SD16—431no—
842C2×SD16—431no—
843C2×SD16—432no—
844C2×SD16—431no—
845C2×SD16—431no—
846C2×SD16—432no—
847C2×SD16C22×D4311yescharacteristic
848C2×SD16C22×D4311yescharacteristic
849C2×SD16C22×D4312yes—
850C2×D8—431no—
851C2×D8—431no—
852C2×D8—432no—
853C2×D8—432no—
854C2×D8—431no—
855C2×D8—432no—
856C2×D8C22×D4311yescharacteristic
857C2×D8C22×D4312yes—
858C2×M16—431no—
859C2×M16C22×D4311yescharacteristic
860C22×C8—431no—
861C22×C8C22×D4311yescharacteristic
862C4⋊Q8—432no—
863C4⋊Q8—432no—
864C4⋊Q8—431no—
865C4⋊Q8—431no—
866C4⋊Q8—861no—
867C4⋊Q8—861no—
868#127—432no—
869#127—431no—
870#127—432no—
871#127—432no—
872#127—432no—
873#127—431no—
874#127—862no—
875#127—861no—
876#127—861no—
877#127—862no—
878#126—862no—
879#126—862no—
880#125—862no—
881#124—432no—
882#124—431no—
883#124—431no—
884#124—432no—
885#124—431no—
886#124—431no—
887#124—862no—
888#124—862no—
889#124—862no—
890#123—862no—
891#123—862no—
892C22⋊Q8—21no—
893C22⋊Q8—432no—
894C22⋊Q8—862no—
895C22⋊Q8—862no—
896C22⋊Q8—862no—
897C22⋊Q8—861no—
898C22⋊Q8C22×D4312yes—
899#121—21no—
900#121—22no—
901#121—432no—
902#121—861no—
903#121—861no—
904#121—862no—
905#121—862no—
906#121—861no—
907#121—861no—
908#121—862no—
909#121—862no—
910#121—861no—
911#121—862no—
912#121—861no—
913#121—862no—
914#121—861no—
915#121—861no—
916#121—862no—
917#121—861no—
918#121—862no—
919#121C22×D4312yes—
920#120—862no—
921#120—862no—
922#120—862no—
923#120—862no—
924#120—862no—
925#120—862no—
926C4×Q8—431no—
927C4×Q8—431no—
928C4×Q8—432no—
929C4×Q8—432no—
930C4×Q8—862no—
931C4×D4—431no—
932C4×D4—432no—
933C4×D4—432no—
934C4×D4—431no—
935C4×D4—432no—
936C4×D4—432no—
937C4×D4—862no—
938C4×D4—862no—
939C4×D4—861no—
940C4×D4—861no—
941C4×D4—862no—
942C4×D4—861no—
943C4×D4—861no—
944C4×D4—862no—
945C4×D4—862no—
946#117—431no—
947#117—432no—
948#117—862no—
949#117—861no—
950#117—861no—
951C2×C4⋊C4—431no—
952C2×C4⋊C4—861no—
953C2×C4⋊C4—861no—
954C2×C4⋊C4—861no—
955C2×C4⋊C4C22×D4311yescharacteristic
956C2×C42—431no—
957C2×C42—432no—
958C4⋊C8—432no—
959C4⋊C8—432no—
960C4⋊C8—432no—
961C4⋊C8—432no—
962#103—432no—
963#103—432no—
964#103—432no—
965#103C22×D4312yes—
966#102—432no—
967#102—432no—
968#102—432no—
969#102—432no—
970#102—432no—
971#102—432no—
972#102—432no—
973#102—432no—
974#102—432no—
975#102C22×D4312yes—
976#102C22×D4312yes—
977#102C22×D4312yes—
978C22⋊C8—432no—
979C22⋊C8—432no—
980C22⋊C8C22×D4312yes—
981C22⋊C8C22×D4312yes—
982#97—432no—
983C4×C8—431no—
984C4×C8—431no—
985C4×C8—431no—
986C4×C8—431no—
987C4×C8—432no—
988C24—22no—
989C24—21no—
990C24—862no—
991C24—861no—
992#41—22no—
993#41—22no—
994#41—22no—
995#41—22no—
996#41—22no—
997#41—22no—
998#41—42no—
999#41—42no—
1000#41—44no—
1001#41—862no—
1002#41—862no—
1003#41—862no—
1004#41—862no—
1005#41—3444no—
1006#41—1722no—
1007#41—1722no—
1008#41—1724no—
1009C2×Q8—431no—
1010C2×Q8—431no—
1011C2×Q8—862no—
1012C2×Q8—862no—
1013C2×Q8—3442no—
1014C2×Q8D4×D4311yescharacteristic
1015C2×Q8C23×D4311yescharacteristic
1016C2×Q8C23×D4311yescharacteristic
1017C2×D4—21no—
1018C2×D4—22no—
1019C2×D4—21no—
1020C2×D4—22no—
1021C2×D4—22no—
1022C2×D4—21no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—42no—
1026C2×D4—42no—
1027C2×D4—48no—
1028C2×D4—44no—
1029C2×D4—432no—
1030C2×D4—431no—
1031C2×D4—431no—
1032C2×D4—862no—
1033C2×D4—862no—
1034C2×D4—862no—
1035C2×D4—862no—
1036C2×D4—862no—
1037C2×D4—862no—
1038C2×D4—861no—
1039C2×D4—861no—
1040C2×D4—862no—
1041C2×D4—861no—
1042C2×D4—861no—
1043C2×D4—862no—
1044C2×D4—862no—
1045C2×D4—861no—
1046C2×D4—862no—
1047C2×D4—861no—
1048C2×D4—862no—
1049C2×D4—861no—
1050C2×D4—862no—
1051C2×D4—862no—
1052C2×D4—3442no—
1053C2×D4—3444no—
1054C2×D4—3442no—
1055C2×D4—3444no—
1056C2×D4—1722no—
1057C2×D4—1722no—
1058C2×D4—1728no—
1059C2×D4—1724no—
1060C2×D4D4×D4312yes—
1061C2×D4D4×D4311yescharacteristic
1062C2×D4C23×D4312yes—
1063C2×D4C23×D4311yescharacteristic
1064C2×D4C23×D4311yescharacteristic
1065C22×C4—21no—
1066C22×C4—21no—
1067C22×C4—22no—
1068C22×C4—21no—
1069C22×C4—431no—
1070C22×C4—432no—
1071C22×C4—431no—
1072C22×C4—432no—
1073C22×C4—862no—
1074C22×C4—862no—
1075C22×C4—861no—
1076C22×C4—861no—
1077C22×C4—862no—
1078C22×C4—861no—
1079C22×C4C23×D4312yes—
1080C22×C4C23×D4311yescharacteristic
1081Q16—41no—
1082Q16—1721no—
1083Q16—1721no—
1084Q16—1721no—
1085SD16—41no—
1086SD16—41no—
1087SD16—42no—
1088SD16—1721no—
1089SD16—1721no—
1090SD16—1722no—
1091SD16—1721no—
1092SD16—1721no—
1093SD16—1722no—
1094SD16—1721no—
1095SD16—1721no—
1096SD16—1722no—
1097D8—41no—
1098D8—42no—
1099D8—1721no—
1100D8—1722no—
1101D8—1721no—
1102D8—1721no—
1103D8—1722no—
1104D8—1722no—
1105M16—22no—
1106M16—862no—
1107C2×C8—22no—
1108C2×C8—431no—
1109C2×C8—431no—
1110C2×C8—432no—
1111C2×C8—862no—
1112C2×C8C23×D4311yescharacteristic
1113C2×C8C23×D4311yescharacteristic
1114C2×C8C23×D4312yes—
1115C4⋊C4—21no—
1116C4⋊C4—22no—
1117C4⋊C4—431no—
1118C4⋊C4—431no—
1119C4⋊C4—432no—
1120C4⋊C4—432no—
1121C4⋊C4—432no—
1122C4⋊C4—862no—
1123C4⋊C4—862no—
1124C4⋊C4—862no—
1125C4⋊C4—862no—
1126C4⋊C4—861no—
1127C4⋊C4—861no—
1128C4⋊C4—861no—
1129C4⋊C4—861no—
1130C4⋊C4—861no—
1131C4⋊C4—862no—
1132C4⋊C4C23×D4312yes—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—432no—
1136C22⋊C4—432no—
1137C22⋊C4—432no—
1138C22⋊C4—862no—
1139C22⋊C4—862no—
1140C22⋊C4—861no—
1141C22⋊C4—861no—
1142C22⋊C4—862no—
1143C22⋊C4—861no—
1144C22⋊C4—861no—
1145C22⋊C4—862no—
1146C22⋊C4—862no—
1147C22⋊C4—861no—
1148C22⋊C4—861no—
1149C22⋊C4—862no—
1150C22⋊C4—861no—
1151C22⋊C4—861no—
1152C22⋊C4—862no—
1153C22⋊C4—862no—
1154C42—432no—
1155C42—431no—
1156C42—431no—
1157C42—432no—
1158C42—431no—
1159C42—431no—
1160C42—432no—
1161C42—862no—
1162C42—862no—
1163C23—21no—
1164C23—22no—
1165C23—21no—
1166C23—44no—
1167C23—42no—
1168C23—81no—
1169C23—81no—
1170C23—82no—
1171C23—82no—
1172C23—861no—
1173C23—862no—
1174C23—861no—
1175C23—3441no—
1176C23—3441no—
1177C23—3442no—
1178C23—3442no—
1179C23—1724no—
1180C23—1722no—
1181C23C2×D4×D4312yes—
1182C23C2×D4×D4311yescharacteristic
1183Q8—22no—
1184Q8—21no—
1185Q8—21no—
1186Q8—21no—
1187Q8—21no—
1188Q8—861no—
1189Q8—861no—
1190Q8—861no—
1191Q8—861no—
1192Q8—3442no—
1193Q8—1724no—
1194D4—24no—
1195D4—22no—
1196D4—21no—
1197D4—21no—
1198D4—22no—
1199D4—21no—
1200D4—22no—
1201D4—21no—
1202D4—44no—
1203D4—44no—
1204D4—42no—
1205D4—42no—
1206D4—42no—
1207D4—82no—
1208D4—861no—
1209D4—861no—
1210D4—862no—
1211D4—862no—
1212D4—861no—
1213D4—861no—
1214D4—3442no—
1215D4—3442no—
1216D4—3442no—
1217D4—3442no—
1218D4—3442no—
1219D4—3442no—
1220D4—3442no—
1221D4—1724no—
1222D4—1724no—
1223D4—1722no—
1224D4—1724no—
1225D4—1722no—
1226D4—1722no—
1227D4—1722no—
1228D4—1724no—
1229D4—1722no—
1230D4—1722no—
1231D4—1722no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—44no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—81no—
1241C2×C4—431no—
1242C2×C4—431no—
1243C2×C4—432no—
1244C2×C4—431no—
1245C2×C4—431no—
1246C2×C4—432no—
1247C2×C4—862no—
1248C2×C4—864no—
1249C2×C4—862no—
1250C2×C4—864no—
1251C2×C4—861no—
1252C2×C4—862no—
1253C2×C4—861no—
1254C2×C4—3442no—
1255C2×C4—3442no—
1256C2×C4—3441no—
1257C2×C4—1724no—
1258C2×C4—1722no—
1259C2×C4—1722no—
1260C2×C4C2×D4×D4312yes—
1261C2×C4C2×D4×D4311yescharacteristic
1262C2×C4#1306337012yes—
1263C2×C4#1306337012yes—
1264C2×C4C24×D4311yescharacteristic
1265C8—21no—
1266C8—21no—
1267C8—22no—
1268C8—861no—
1269C8—861no—
1270C8—862no—
1271C22—21no—
1272C22—21no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—41no—
1277C22—42no—
1278C22—41no—
1279C22—42no—
1280C22—41no—
1281C22—41no—
1282C22—42no—
1283C22—41no—
1284C22—41no—
1285C22—162no—
1286C22—164no—
1287C22—1721no—
1288C22—1722no—
1289C22—1721no—
1290C22—1722no—
1291C22—1721no—
1292C22—1721no—
1293C22—1722no—
1294C22—1721no—
1295C22—1721no—
1296C22—6882no—
1297C22—6884no—
1298C22#1458346412yes—
1299C22C22×D4×D4311yescharacteristic
1300C4—22no—
1301C4—42no—
1302C4—41no—
1303C4—41no—
1304C4—432no—
1305C4—432no—
1306C4—862no—
1307C4—861no—
1308C4—862no—
1309C4—861no—
1310C4—1722no—
1311C4—1721no—
1312C4—1721no—
1313C4#1458346412yes—
1314C4C2×#1306337011yescharacteristic
1315C4C2×#1306337011yescharacteristic
1316C2—22no—
1317C2—42no—
1318C2—82no—
1319C2—81no—
1320C2—81no—
1321C2—3442no—
1322C2—3441no—
1323C2—3441no—
1324C2C2×#1458346411yescharacteristic
1325C2#576×D4311yescharacteristic
1326C2#577×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3012C2
socleC22×C43C23×D4
hypercenter#3012D43
hypocenterC43#60822
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. #19148504C2semidirect
2. #19148369C2semidirect
3. #19145695C2semidirect
4. #19145693C2semidirect
5. #19145687C2semidirect
6. #19145685C2semidirect
7. #19145549C2semidirect
8. #19145534C2semidirect
9. #19145526C2semidirect
10. #19145511C2semidirect
11. #19145043C2semidirect
12. #19145019C2semidirect
13. #19144986C2semidirect
14. C2×#14583244C2semidirect
15. #19144139C2semidirect
16. #19144138C2semidirect
17. #19144133C2semidirect
18. #19144132C2semidirect
19. #19143902C2semidirect
20. #19143899C2semidirect
21. #19143896C2semidirect
22. #19143235C2semidirect
23. C43×#3012C2semidirect
25. C2×#13063353C22semidirect
26. C2×#13063351C22semidirect
27. C2×#13063350C22semidirect
28. C2×#13063347C22semidirect
29. C2×#13063345C22semidirect
30. C2×#13063345C22semidirect
43. #14583522C22semidirect
44. #14583516C22semidirect
50. #14583451C22semidirect
53. #14583445C22semidirect
54. #14583444C22semidirect
55. C2×#13063324C22semidirect
58. #14583382C22semidirect
59. #14583380C22semidirect
61. #14583287C22semidirect
62. #14583285C22semidirect
63. #14583284C22semidirect
64. #14583282C22semidirect
65. #14583280C22semidirect
66. #14583280C22semidirect
67. #14583277C22semidirect
68. #14583274C22semidirect
69. #14583274C22semidirect
70. #14583270C22semidirect
71. #14583270C22semidirect
72. #14583270C22semidirect
73. #14583260C22semidirect
74. #14583257C22semidirect
75. #14583248C22semidirect
76. #14583244C22semidirect
77. #14583244C22semidirect
78. #14583244C22semidirect
79. #14583244C22semidirect
80. #14583244C22semidirect
81. #14583124C22semidirect
82. #14583123C22semidirect
83. #14583120C22semidirect
84. #14583119C22semidirect
85. #14583117C22semidirect
86. #14583116C22semidirect
87. #14583113C22semidirect
88. #14583112C22semidirect
89. #14583098C22semidirect
90. #14583098C22semidirect
91. #14583097C22semidirect
92. #14583097C22semidirect
93. #14583093C22semidirect
94. #14583093C22semidirect
95. #14583092C22semidirect
96. #14583092C22semidirect
97. #14583063C22semidirect
98. #14583061C22semidirect
99. #14583059C22semidirect
100. #14583052C22semidirect
101. #14583050C22semidirect
102. #14583049C22semidirect
103. #14583046C22semidirect
104. #14583044C22semidirect
105. #14583042C22semidirect
106. #14583035C22semidirect
107. #14583033C22semidirect
108. #14583032C22semidirect
109. #14582957C22semidirect
110. #14582957C22semidirect
111. #14582949C22semidirect
112. #14582949C22semidirect
113. #14582927C22semidirect
114. #14582925C22semidirect
115. #14582901C22semidirect
116. #14582900C22semidirect
117. #14582898C22semidirect
118. C2×#13063247C22semidirect
119. C2×#13063246C22semidirect
120. C2×#13063245C22semidirect
122. M16×Dic43C22semidirect
123. C2×C8×Dic43C22semidirect
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
674. #3012D43semidirect
692. C2×AGL(1,ℤ/8)C2×D43semidirect
696. C2×#135C2×D43semidirect
767. #452C2×D43semidirect
771. #450C2×D43semidirect
775. #449C2×D43semidirect
779. #447C2×D43semidirect
789. #417C2×D43semidirect
793. C2×#102C2×D43semidirect
798. C43#60822semidirect

Maximal subgroups

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

subgroupindex
#191485042
#191483692
#191456952
#191456932
#191456872
#191456852
#191455492
#191455342
#191455262
#191455112
#191450432
#191450192
#191449862
C2×#145832442
#191441392
#191441382
#191441332
#191441322
#191439022
#191438992
#191438962
#191432352
C43×#30122
#6082243