Finite Group Databasebeta

← #25968496

Subgroups — #25968496

Order 11008.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148369C211yesmaximal, characteristic, complemented
2#19148008C211yesmaximal, characteristic, complemented
3#19145687C212yesmaximal, complemented
4#19145685C212yesmaximal, complemented
5#19145643C212yesmaximal, complemented
6#19145641C212yesmaximal, complemented
7#19145611C212yesmaximal, complemented
8#19145587C212yesmaximal, complemented
9#19145568C212yesmaximal, complemented
10#19145511C212yesmaximal, complemented
11#19145080C211yesmaximal, characteristic, complemented
12#19145076C211yesmaximal, characteristic, complemented
13#19144953C211yesmaximal, characteristic, complemented
14#19144945C211yesmaximal, characteristic, complemented
15#19144074C211yesmaximal, characteristic, complemented
16#19144056C211yesmaximal, characteristic, complemented
17#19144048C211yesmaximal, characteristic, complemented
18C2×#14583092C211yesmaximal, characteristic, complemented
19#19143902C211yesmaximal, characteristic, complemented
20#19143899C211yesmaximal, characteristic, complemented
21#19143861C211yesmaximal, characteristic, complemented
22#19143257C211yesmaximal, characteristic, complemented
23C43×#3008C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C2×#13063353C2211yescharacteristic, complemented
26C2×#13063351C2211yescharacteristic, complemented
27C2×#13063351C2211yescharacteristic, complemented
28C2×#13063347C2211yescharacteristic, complemented
29C2×#13063345C2211yescharacteristic, complemented
30C22×#10621882C2211yescharacteristic, complemented
31#14583568—21no—
32#14583568—21no—
33D4×C22⋊D43—21no—
34D4×C22⋊D43—21no—
35D4×C22⋊D43—22no—
36D4×C22⋊D43—22no—
37#14583527C2211yescharacteristic, complemented
38#14583518—21no—
39#14583516C2212yescomplemented
40#14583503—21no—
41#14583502C2212yescomplemented
42#14583484—22no—
43#14583477C2211yescharacteristic
44#14583466C2211yescharacteristic
45#14583466C2212yescomplemented
46#14583466C2211yescharacteristic, complemented
47#14583463C2211yescharacteristic
48#14583463C2212yescomplemented
49#14583447—21no—
50#14583445C2211yescharacteristic
51#14583445C2212yescomplemented
52#14583444C2212yescomplemented
53C2×#13063321C2211yescharacteristic
54C2×#13063321C2212yescomplemented
55#14583430C2212yescomplemented
56#14583428—21no—
57#14583405—22no—
58#41×Dic43C2211yescharacteristic
59#14583367C2211yescharacteristic, complemented
60C2×D4×Dic43C2211yescharacteristic, complemented
61#14583287C2212yescomplemented
62#14583287C2212yescomplemented
63#14583287C2212yescomplemented
64#14583285C2212yescomplemented
65#14583282C2212yescomplemented
66#14583280C2212yescomplemented
67#14583274C2212yescomplemented
68#14583274C2212yescomplemented
69#14583262C2212yescomplemented
70#14583262C2212yescomplemented
71#14583260C2212yescomplemented
72#14583257C2212yescomplemented
73#14583255C2212yescomplemented
74#14583252C2212yescomplemented
75#14583244C2212yescomplemented
76#14583244C2212yescomplemented
77#14583124C2211yescharacteristic, complemented
78#14583120C2211yescharacteristic, complemented
79#14583117C2211yescharacteristic, complemented
80#14583116C2212yescomplemented
81#14583113C2211yescharacteristic, complemented
82#14583112C2212yescomplemented
83#14583108C2211yescharacteristic, complemented
84#14583103C2211yescharacteristic, complemented
85#14583102C2212yescomplemented
86#14583098C2212yescomplemented
87#14583098C2211yescharacteristic, complemented
88#14583098C2212yescomplemented
89#14583093C2211yescharacteristic, complemented
90#14583093C2212yescomplemented
91#14583093C2212yescomplemented
92#14583092C2212yescomplemented
93#14583092C2212yescomplemented
94#14583092C2212yescomplemented
95#14583092C2212yescomplemented
96#14583092C2212yescomplemented
97#14583063C2212yescomplemented
98#14583061C2212yescomplemented
99#14583052C2212yescomplemented
100#14583050C2212yescomplemented
101#14583046C2212yescomplemented
102#14583044C2212yescomplemented
103#14583042C2212yescomplemented
104#14583042C2212yescomplemented
105#14583035C2212yescomplemented
106#14583033C2212yescomplemented
107#14583032C2212yescomplemented
108#14583032C2212yescomplemented
109#14582957C2212yescomplemented
110#14582957C2212yescomplemented
111#14582953C2212yescomplemented
112#14582949C2212yescomplemented
113#14582922C2211yescharacteristic, complemented
114C2×Dic43⋊C8C2211yescharacteristic, complemented
115#14582903C2211yescharacteristic, complemented
116#14582901C2211yescharacteristic, complemented
117#14582900C2211yescharacteristic, complemented
118#14582893C2211yescharacteristic, complemented
119C2×#13063247C2211yescharacteristic, complemented
120C2×#13063246C2211yescharacteristic, complemented
121#14582866C2211yescharacteristic
122#14582857C2211yescharacteristic, complemented
123#14582854C2211yescharacteristic, complemented
124C2×H(5,𝔽2)×C43C2211yescharacteristic
125C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
126C22×D8×C43C2211yescharacteristic, complemented
127C43×#535C2211yescharacteristic
128C43×#449C2212yescomplemented
129C43×#449C2212yescomplemented
130C43×#447C2212yescomplemented
131C43×#447C2212yescomplemented
132C43×#418C2211yescharacteristic, complemented
133C43×#416C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic
135#13063371—42no—
136#13063371—42no—
137C2×#10621902—21no—
138C2×#10621898C2311yescharacteristic
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2312yes—
141C2×#10621900—22no—
142C22×D172C2311yescharacteristic
143C22×D172C2312yes—
144C22×C22⋊D43—21no—
145C22×C22⋊D43—21no—
146C22×C22⋊D43—22no—
147C22×C22⋊D43—22no—
148C2×D4×D43—22no—
149C2×D4×D43—21no—
150C23×Dic43—21no—
151#13063353—42no—
152#13063351—42no—
153#13063351—42no—
154#13063347—42no—
155#13063345—42no—
156C2×Dic172C2311yescharacteristic
157C2×#10621885C2311yescharacteristic
158C2×#10621873C2311yescharacteristic
159C2×#10621873C2311yescharacteristic
160C2×#10621873C2312yes—
161C2×#10621883C2312yes—
162C2×#10621883C2311yescharacteristic
163C2×#10621883C2312yes—
164C2×#10621884C2311yescharacteristic
165C2×D344C2312yes—
166C2×D344C2311yescharacteristic
167C2×#10621882—42no—
168C2×#10621882C2312yes—
169C2×#10621882C2312yes—
170C2×#10621882C2312yes—
171C2×#10621882C2312yes—
172C2×#10621882C2311yescharacteristic
173C2×#10621877C2311yescharacteristic
174C22×C43⋊C8C2311yescharacteristic
175#13063325—21no—
176#13063324C2312yes—
177#13063323C2311yescharacteristic
178#13063321—21no—
179#13063321—21no—
180#13063321—22no—
181#13063321—22no—
182#13063321C2312yes—
183#13063321C2312yes—
184#13063321C2311yescharacteristic
185#13063321C2312yes—
186#13063321C2312yes—
187#13063321C2312yes—
188#13063318—22no—
189#13063318—22no—
190#13063317—21no—
191#13063316C2312yes—
192#13063314C2311yescharacteristic
193#13063314C2312yes—
194#13063312—22no—
195#13063312C2311yescharacteristic
196#13063312C2312yes—
197#13063312C2312yes—
198#13063311—22no—
199#13063309—22no—
200#13063307—22no—
201#13063306—22no—
202#13063306—22no—
203#13063304C2312yes—
204#13063302—22no—
205#13063302—22no—
206#13063301—21no—
207#13063299—21no—
208#13063299—21no—
209#13063299—22no—
210#13063299—22no—
211#13063299C2312yes—
212#13063297—22no—
213#13063297—22no—
214#13063297—21no—
215#13063297—21no—
216#13063297—22no—
217#13063297—22no—
218#13063297—22no—
219#13063296—21no—
220#13063296—22no—
221#13063296—21no—
222#13063296—21no—
223#13063296—22no—
224#13063296—22no—
225#13063296—21no—
226#13063296—21no—
227#13063294—22no—
228#13063294—22no—
229#13063294—22no—
230#13063294—22no—
231#13063293—22no—
232#13063293—22no—
233#13063293—22no—
234Q8×Dic43D411yescharacteristic
235Q8×Dic43D411yescharacteristic
236#13063290C2311yescharacteristic
237#13063290C2311yescharacteristic
238D4×Dic43—22no—
239D4×Dic43—21no—
240D4×Dic43—21no—
241D4×Dic43D412yes—
242D4×Dic43D411yescharacteristic
243D4×Dic43D412yes—
244D4×Dic43D411yescharacteristic
245D4×Dic43C2312yes—
246D4×Dic43C2312yes—
247#13063287C2311yescharacteristic
248#13063287C2311yescharacteristic
249C4×C22⋊D43—21no—
250C4×C22⋊D43—21no—
251C4×C22⋊D43—22no—
252C4×C22⋊D43—22no—
253(C22⋊D43)⋊C4—21no—
254(C22⋊D43)⋊C4—21no—
255(C22⋊D43)⋊C4—22no—
256#13063284C2311yescharacteristic
257#13063284C2312yes—
258#13063282—21no—
259#13063281—22no—
260C2×C4⋊Dic43C2311yescharacteristic
261C2×C22⋊Dic43—21no—
262C2×C4×Dic43C2311yescharacteristic
263C2×C4×Dic43C2312yes—
264C42×D43—21no—
265Dic43⋊C8C2311yescharacteristic
266Dic43⋊C8C2311yescharacteristic
267Dic43⋊C8C2311yescharacteristic
268Dic43⋊C8C2311yescharacteristic
269Dic43⋊C8C2312yes—
270Dic43⋊C8C2312yes—
271#13063250C2312yes—
272#13063249C2312yes—
273#13063248C2311yescharacteristic
274#13063248C2311yescharacteristic
275#13063247C2312yes—
276#13063247C2312yes—
277#13063247C2312yes—
278#13063246C2312yes—
279#13063246C2312yes—
280#13063246C2312yes—
281#13063245C2312yes—
282#13063245C2312yes—
283#13063245C2311yescharacteristic
284#13063245C2311yescharacteristic
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×C43C2312yes—
296C2×#41×C43C2311yescharacteristic
297C22×D4×C43—22no—
298C22×D4×C43—21no—
299C22×D4×C43C2311yescharacteristic
300C22×D4×C43C2311yescharacteristic
301C22×D4×C43C2312yes—
302AGL(1,ℤ/8)×C43—42no—
303C2×SD16×C43C2312yes—
304C2×D8×C43—42no—
305C2×D8×C43C2312yes—
306C2×D8×C43C2312yes—
307C2×D8×C43C2312yes—
308C2×M16×C43C2311yescharacteristic
309C22×C8×C43C2311yescharacteristic
310#127×C43—21no—
311#124×C43—21no—
312#121×C43C2312yes—
313#121×C43C2312yes—
314#120×C43—22no—
315#117×C43C2311yescharacteristic
316#103×C43C2311yescharacteristic
317#103×C43C2311yescharacteristic
318#102×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2311yescharacteristic
321#102×C43C2311yescharacteristic
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C24×C43—21no—
325C24×C43—22no—
326C24×C43—21no—
327C23×D43—22no—
328C23×D43—21no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—22no—
333#41×C43—42no—
334#41×C43—42no—
335#41×C43—44no—
336C2×Q8×C43C2×D411yescharacteristic
337C2×Q8×C43C2411yescharacteristic
338C2×D4×C43—21no—
339C2×D4×C43—22no—
340C2×D4×C43—21no—
341C2×D4×C43—22no—
342C2×D4×C43—21no—
343C2×D4×C43—22no—
344C2×D4×C43—22no—
345C2×D4×C43—22no—
346C2×D4×C43—22no—
347C2×D4×C43—22no—
348C2×D4×C43—22no—
349C2×D4×C43—42no—
350C2×D4×C43—42no—
351C2×D4×C43—44no—
352C2×D4×C43—48no—
353C2×D4×C43C2×D412yes—
354C2×D4×C43C2×D411yescharacteristic
355C2×D4×C43C2412yes—
356C2×D4×C43C2411yescharacteristic
357C2×D4×C43C2412yes—
358C22×C4×C43—22no—
359C22×C4×C43—21no—
360C22×C4×C43C2412yes—
361C22×C4×C43C2411yescharacteristic
362C2×C22⋊D43—21no—
363C2×C22⋊D43—22no—
364C2×C22⋊D43—21no—
365C2×C22⋊D43—22no—
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—22no—
376C2×C22⋊D43—21no—
377C2×C22⋊D43—22no—
378C2×C22⋊D43—84no—
379C2×C22⋊D43—82no—
380C2×C22⋊D43—82no—
381C2×C22⋊D43—84no—
382C22×Dic43—22no—
383C22×Dic43—22no—
384C22×Dic43—21no—
385C22×Dic43—82no—
386C22×Dic43C2×D411yescharacteristic
387C22×Dic43C2×D412yes—
388C22×Dic43C2×D411yescharacteristic
389C22×Dic43C2×D412yes—
390#10621902—44no—
391#10621900—84no—
392D4×D43—44no—
393D4×D43—48no—
394#10621898—22no—
395#10621898—22no—
396#10621898—22no—
397#10621898—22no—
398#10621898—42no—
399#10621898—42no—
400C2×D172—22no—
401C2×D172—21no—
402C2×D172—22no—
403C2×D172—22no—
404C2×D172—42no—
405C2×D172—42no—
406C2×D172C2412yes—
407C2×D172C2411yescharacteristic
408C2×D172C2411yescharacteristic
409C2×C4×D43—21no—
410C2×C4×D43—22no—
411C2×C4×D43—21no—
412C2×C4×D43—21no—
413C2×C4×D43—21no—
414C2×Dic86—22no—
415C2×Dic86C2411yescharacteristic
416C2×Dic86C2411yescharacteristic
417SD16×C43—42no—
418D8×C43—42no—
419D8×C43—42no—
420D8×C43—42no—
421M16×C43—22no—
422C2×C8×C43—22no—
423C2×C8×C43C2412yes—
424C2×C8×C43C2411yescharacteristic
425C2×C8×C43C2411yescharacteristic
426C4⋊C4×C43C2411yescharacteristic
427C4⋊C4×C43C2411yescharacteristic
428C22⋊C4×C43—22no—
429C22⋊C4×C43—22no—
430C22⋊C4×C43—21no—
431C42×C43—21no—
432C22⋊Dic43—22no—
433C22⋊Dic43—22no—
434C22⋊Dic43—22no—
435C22⋊Dic43—21no—
436C22⋊Dic43—22no—
437C22⋊Dic43—21no—
438C22⋊Dic43—22no—
439C22⋊Dic43—22no—
440C22⋊Dic43—22no—
441C22⋊Dic43C2×D412yes—
442C22⋊Dic43C2×D412yes—
443C22⋊Dic43C2×D412yes—
444#10621885—41no—
445#10621884—41no—
446#10621883—41no—
447#10621883—42no—
448#10621883—42no—
449#10621882—42no—
450#10621882—42no—
451#10621882—41no—
452#10621882—42no—
453#10621882—42no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—21no—
456(C2×D43)⋊C4—21no—
457(C2×D43)⋊C4—21no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—21no—
460(C2×D43)⋊C4—22no—
461C4⋊Dic43—21no—
462C4⋊Dic43—22no—
463C4⋊Dic43C2×D411yescharacteristic
464C4⋊Dic43C2×D411yescharacteristic
465C4⋊Dic43C2×D412yes—
466C4⋊Dic43C2×D412yes—
467C4⋊Dic43C2412yes—
468Dic43⋊C4—22no—
469Dic43⋊C4—22no—
470Dic43⋊C4—21no—
471Dic43⋊C4—21no—
472Dic43⋊C4—22no—
473Dic43⋊C4—21no—
474Dic43⋊C4—21no—
475C4×Dic43—21no—
476C4×Dic43—21no—
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—41no—
490D344—41no—
491D344—42no—
492#10621873—41no—
493#10621873—41no—
494#10621873—42no—
495C23×C43—22no—
496C23×C43—21no—
497C23×C43—22no—
498C23×C43—44no—
499C23×C43—42no—
500C23×C43—42no—
501C23×C43—81no—
502C23×C43—81no—
503C23×C43—81no—
504C23×C43—81no—
505C23×C43—82no—
506C23×C43—82no—
507C23×C43C22×D412yes—
508C23×C43C22×D411yescharacteristic
509C22×D43—21no—
510C22×D43—21no—
511C22×D43—22no—
512C22×D43—44no—
513C22×D43—42no—
514C22×D43—81no—
515C22×D43—82no—
516C22×D43—81no—
517C22×D43—82no—
518Q8×C43—22no—
519Q8×C43—21no—
520Q8×C43—21no—
521D4×C43—24no—
522D4×C43—22no—
523D4×C43—22no—
524D4×C43—22no—
525D4×C43—22no—
526D4×C43—21no—
527D4×C43—22no—
528D4×C43—21no—
529D4×C43—44no—
530D4×C43—44no—
531D4×C43—42no—
532D4×C43—42no—
533D4×C43—42no—
534D4×C43—82no—
535D4×C43—82no—
536C2×C4×C43—22no—
537C2×C4×C43—22no—
538C2×C4×C43—21no—
539C2×C4×C43—21no—
540C2×C4×C43—21no—
541C2×C4×C43—44no—
542C2×C4×C43—42no—
543C2×C4×C43C22×D412yes—
544C2×C4×C43C22×D411yescharacteristic
545C2×C4×C43H(5,𝔽2)12yes—
546C2×C4×C43H(5,𝔽2)12yes—
547C2×C4×C43C2511yescharacteristic
548C22⋊D43—42no—
549C22⋊D43—44no—
550C22⋊D43—44no—
551C22⋊D43—42no—
552C22⋊D43—42no—
553C22⋊D43—42no—
554C22⋊D43—44no—
555C22⋊D43—82no—
556C22⋊D43—82no—
557C22⋊D43—82no—
558C22⋊D43—82no—
559C22⋊D43—82no—
560C22⋊D43—82no—
561C22⋊D43—82no—
562C22⋊D43—82no—
563C22⋊D43—82no—
564C2×Dic43—24no—
565C2×Dic43—22no—
566C2×Dic43—21no—
567C2×Dic43—22no—
568C2×Dic43—21no—
569C2×Dic43—41no—
570C2×Dic43—42no—
571C2×Dic43—44no—
572C2×Dic43—82no—
573C2×Dic43—81no—
574C2×Dic43C22×D411yescharacteristic
575C2×Dic43C22×D411yescharacteristic
576C2×Dic43C22×D412yes—
577C2×Dic43C22×D411yescharacteristic
578C2×Dic43C22×D412yes—
579C2×Dic43C22×D411yescharacteristic
580D172—21no—
581D172—22no—
582D172—21no—
583D172—21no—
584D172—22no—
585D172—21no—
586D172—44no—
587D172—42no—
588C4×D43—44no—
589C4×D43—42no—
590C4×D43—42no—
591C4×D43—42no—
592C4×D43—81no—
593Dic86—21no—
594Dic86—21no—
595Dic86—21no—
596Dic86—21no—
597Dic86—82no—
598C8×C43—21no—
599C8×C43—22no—
600C8×C43—21no—
601C43⋊C8—21no—
602C43⋊C8—21no—
603C43⋊C8—22no—
604#60832—431nomaximal, Sylow
605C22×C43—21no—
606C22×C43—21no—
607C22×C43—22no—
608C22×C43—22no—
609C22×C43—22no—
610C22×C43—42no—
611C22×C43—41no—
612C22×C43—42no—
613C22×C43—41no—
614C22×C43—42no—
615C22×C43—42no—
616C22×C43—42no—
617C22×C43—41no—
618C22×C43—42no—
619C22×C43—84no—
620C22×C43—162no—
621C22×C43—164no—
622C22×C43#53512yes—
623C22×C43C23×D411yescharacteristic
624C2×D43—42no—
625C2×D43—41no—
626C2×D43—41no—
627C2×D43—41no—
628C2×D43—42no—
629C2×D43—41no—
630C2×D43—42no—
631C2×D43—41no—
632C2×D43—41no—
633C2×D43—162no—
634C2×D43—164no—
635C4×C43—22no—
636C4×C43—41no—
637C4×C43—41no—
638C4×C43—41no—
639C4×C43#53512yes—
640C4×C43C2×H(5,𝔽2)11yescharacteristic
641C4×C43C2×H(5,𝔽2)11yescharacteristic
642Dic43—21no—
643Dic43—21no—
644Dic43—22no—
645Dic43—22no—
646Dic43—21no—
647Dic43—41no—
648Dic43—41no—
649Dic43—42no—
650Dic43#57612yes—
651#3498—431no—
652#3460—431no—
653#3224—432no—
654#3224—432no—
655#3220—432no—
656#3220—432no—
657#3217—432no—
658#3214—432no—
659#3212—432no—
660#3205—432no—
661#3155—431no—
662#3155—431no—
663#3136—431no—
664#3136—431no—
665#3038—431no—
666#3036—431no—
667#3035—431no—
668C2×#459—431no—
669#3012—431no—
670#3012—431no—
671#3008—431no—
672#3008D4311yescharacteristic, complemented
673#2925—431no—
674C2×C43—22no—
675C2×C43—42no—
676C2×C43—82no—
677C2×C43—82no—
678C2×C43—81no—
679C2×C43C2×#53511yescharacteristic
680C2×C43C2×#57611yescharacteristic
681C2×C43#358511yescharacteristic
682D43—81no—
683D43—82no—
684D43—81no—
685C2×H(5,𝔽2)—431no—
686C2×H(5,𝔽2)C2×D4311yescharacteristic
687C2×AGL(1,ℤ/8)—431no—
688C2×AGL(1,ℤ/8)—431no—
689C2×AGL(1,ℤ/8)—431no—
690C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
691C2×#135—431no—
692C2×#135—431no—
693C22×D8—431no—
694C22×D8C2×D4311yescharacteristic, complemented
695#550—861no—
696#550—861no—
697D42—862no—
698D42—861no—
699D42—862no—
700D42—861no—
701#544—431no—
702#542—432no—
703#542—861no—
704#540—432no—
705#540—861no—
706#538—862no—
707#537—431no—
708#535—431no—
709#535—432no—
710#535—431no—
711#535—431no—
712#535—432no—
713#535C2×D4311yescharacteristic
714#532—432no—
715#532—432no—
716#532—431no—
717#532—861no—
718C2×#127—432no—
719C2×#127—431no—
720#529—432no—
721#529—861no—
722#525—862no—
723C4×#41—431no—
724C4×#41—431no—
725C2×C4×D4—431no—
726#496—432no—
727#496—432no—
728#496—432no—
729#496—432no—
730#495—432no—
731#495—432no—
732#493—432no—
733#493—432no—
734#490—432no—
735#490—432no—
736#489—432no—
737#489—432no—
738#488—432no—
739#488—432no—
740#486—432no—
741#486—432no—
742#464—431no—
743#464—431no—
744#463—432no—
745#463—432no—
746#463—431no—
747#463—431no—
748#462—431no—
749#461—432no—
750#461—431no—
751#460—432no—
752#460—431no—
753#460—432no—
754#459—432no—
755#459—432no—
756#459—432no—
757#459—432no—
758#459—432no—
759#459—431no—
760#459—432no—
761#459—432no—
762#452—432no—
763#452—432no—
764#450—432no—
765#450—432no—
766#449—432no—
767#449—432no—
768#449—432no—
769#449—432no—
770#449C2×D4312yescomplemented
771#449C2×D4312yescomplemented
772#447—432no—
773#447—432no—
774#447—432no—
775#447—432no—
776#447C2×D4312yescomplemented
777#447C2×D4312yescomplemented
778#433—432no—
779#433—432no—
780#432—432no—
781#431—432no—
782#423—431no—
783C2×C4⋊C8—431no—
784#418—431no—
785#418C2×D4311yescharacteristic, complemented
786#417—431no—
787#417—431no—
788#416—431no—
789#416C2×D4311yescharacteristic, complemented
790C2×#102—431no—
791C2×#102—431no—
792#408—431no—
793#408C2×D4311yescharacteristic
794#405—431no—
795#405—431no—
796C43#6083211yescharacteristic, complemented, Sylow
797H(5,𝔽2)—42no—
798H(5,𝔽2)—42no—
799H(5,𝔽2)—1722no—
800H(5,𝔽2)—1722no—
801C2×#41—21no—
802C2×#41—431no—
803C2×#41—431no—
804C2×#41—432no—
805C2×#41—862no—
806C2×#41—861no—
807C2×#41C22×D4311yescharacteristic
808C2×#41C22×D4312yes—
809C2×#41C22×D4311yescharacteristic
810C22×D4—22no—
811C22×D4—21no—
812C22×D4—431no—
813C22×D4—432no—
814C22×D4—861no—
815C22×D4—862no—
816C22×D4—861no—
817C22×D4—862no—
818C22×D4—862no—
819C22×D4—861no—
820C22×D4C22×D4311yescharacteristic
821C22×D4C22×D4311yescharacteristic
822C22×D4C22×D4312yes—
823C23×C4—861no—
824AGL(1,ℤ/8)—42no—
825AGL(1,ℤ/8)—1722no—
826AGL(1,ℤ/8)—1722no—
827AGL(1,ℤ/8)—1722no—
828#135—1722no—
829#135—1722no—
830C2×Q16—431no—
831C2×Q16—431no—
832C2×SD16—431no—
833C2×SD16—431no—
834C2×SD16—432no—
835C2×SD16—432no—
836C2×SD16—431no—
837C2×SD16—431no—
838C2×SD16—432no—
839C2×SD16C22×D4312yes—
840C2×D8—42no—
841C2×D8—432no—
842C2×D8—432no—
843C2×D8—431no—
844C2×D8—432no—
845C2×D8—432no—
846C2×D8—431no—
847C2×D8—432no—
848C2×D8—1722no—
849C2×D8C22×D4312yes—
850C2×D8C22×D4312yes—
851C2×D8C22×D4312yes—
852C2×M16—431no—
853C2×M16C22×D4311yescharacteristic
854C22×C8—431no—
855C22×C8C22×D4311yescharacteristic
856C4⋊Q8—432no—
857C4⋊Q8—431no—
858C4⋊Q8—861no—
859#127—21no—
860#127—431no—
861#127—432no—
862#127—432no—
863#127—432no—
864#127—432no—
865#127—432no—
866#127—861no—
867#127—862no—
868#127—861no—
869#127—862no—
870#126—862no—
871#126—862no—
872#125—432no—
873#125—861no—
874#124—21no—
875#124—431no—
876#124—432no—
877#124—432no—
878#124—431no—
879#124—432no—
880#124—862no—
881#124—862no—
882#123—862no—
883#123—862no—
884#123—862no—
885#123—862no—
886C22⋊Q8—432no—
887C22⋊Q8—862no—
888C22⋊Q8—862no—
889C22⋊Q8—861no—
890#121—432no—
891#121—862no—
892#121—862no—
893#121—861no—
894#121—861no—
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—862no—
904#121—861no—
905#121—862no—
906#121—861no—
907#121—862no—
908#121—862no—
909#121—861no—
910#121C22×D4312yes—
911#121C22×D4312yes—
912#120—22no—
913#120—862no—
914#120—862no—
915#120—862no—
916#120—862no—
917#120—862no—
918#120—862no—
919#120—862no—
920C4×Q8—431no—
921C4×Q8—431no—
922C4×Q8—431no—
923C4×Q8—431no—
924C4×D4—432no—
925C4×D4—431no—
926C4×D4—432no—
927C4×D4—431no—
928C4×D4—432no—
929C4×D4—432no—
930C4×D4—431no—
931C4×D4—431no—
932C4×D4—862no—
933C4×D4—861no—
934C4×D4—862no—
935C4×D4—861no—
936C4×D4—862no—
937C4×D4—861no—
938C4×D4—861no—
939C4×D4—861no—
940C4×D4—861no—
941C4×D4—862no—
942#117—431no—
943#117—432no—
944#117—861no—
945#117—862no—
946#117C22×D4311yescharacteristic
947C2×C4⋊C4—431no—
948C2×C22⋊C4—861no—
949C2×C42—431no—
950C2×C42—432no—
951C2×C42—861no—
952C4⋊C8—431no—
953C4⋊C8—431no—
954C4⋊C8—431no—
955C4⋊C8—431no—
956C4⋊C8—432no—
957C4⋊C8—432no—
958#103—432no—
959#103—432no—
960#103—431no—
961#103—431no—
962#103C22×D4311yescharacteristic
963#103C22×D4311yescharacteristic
964#102—432no—
965#102—432no—
966#102—432no—
967#102—432no—
968#102—432no—
969#102—432no—
970#102—431no—
971#102—431no—
972#102—432no—
973#102—432no—
974#102C22×D4311yescharacteristic
975#102C22×D4311yescharacteristic
976#102C22×D4312yes—
977#102C22×D4312yes—
978C22⋊C8—432no—
979C22⋊C8—432no—
980C22⋊C8C22×D4312yes—
981C22⋊C8C22×D4312yes—
982#97—432no—
983#97—432no—
984C4×C8—432no—
985C4×C8—432no—
986C24—21no—
987C24—22no—
988C24—21no—
989C24—862no—
990C24—861no—
991#41—22no—
992#41—22no—
993#41—22no—
994#41—22no—
995#41—42no—
996#41—42no—
997#41—44no—
998#41—862no—
999#41—862no—
1000#41—862no—
1001#41—862no—
1002#41—3444no—
1003#41—1722no—
1004#41—1722no—
1005#41—1724no—
1006C2×Q8—431no—
1007C2×Q8—431no—
1008C2×Q8—862no—
1009C2×Q8D4×D4311yescharacteristic
1010C2×Q8C23×D4311yescharacteristic
1011C2×D4—22no—
1012C2×D4—21no—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—21no—
1016C2×D4—22no—
1017C2×D4—21no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C2×D4—22no—
1021C2×D4—22no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4—48no—
1025C2×D4—44no—
1026C2×D4—432no—
1027C2×D4—431no—
1028C2×D4—431no—
1029C2×D4—862no—
1030C2×D4—862no—
1031C2×D4—862no—
1032C2×D4—862no—
1033C2×D4—862no—
1034C2×D4—862no—
1035C2×D4—862no—
1036C2×D4—862no—
1037C2×D4—861no—
1038C2×D4—862no—
1039C2×D4—861no—
1040C2×D4—862no—
1041C2×D4—862no—
1042C2×D4—861no—
1043C2×D4—862no—
1044C2×D4—861no—
1045C2×D4—862no—
1046C2×D4—861no—
1047C2×D4—862no—
1048C2×D4—862no—
1049C2×D4—3442no—
1050C2×D4—3444no—
1051C2×D4—3442no—
1052C2×D4—3444no—
1053C2×D4—1722no—
1054C2×D4—1722no—
1055C2×D4—1728no—
1056C2×D4—1724no—
1057C2×D4D4×D4312yes—
1058C2×D4D4×D4311yescharacteristic
1059C2×D4C23×D4312yes—
1060C2×D4C23×D4311yescharacteristic
1061C2×D4C23×D4312yes—
1062C22×C4—22no—
1063C22×C4—21no—
1064C22×C4—431no—
1065C22×C4—432no—
1066C22×C4—431no—
1067C22×C4—432no—
1068C22×C4—861no—
1069C22×C4—861no—
1070C22×C4—862no—
1071C22×C4—862no—
1072C22×C4—861no—
1073C22×C4—861no—
1074C22×C4—862no—
1075C22×C4—861no—
1076C22×C4—3442no—
1077C22×C4C23×D4312yes—
1078C22×C4C23×D4311yescharacteristic
1079Q16—1721no—
1080Q16—1721no—
1081SD16—42no—
1082SD16—1721no—
1083SD16—1721no—
1084SD16—1722no—
1085SD16—1721no—
1086SD16—1722no—
1087SD16—1722no—
1088SD16—1721no—
1089D8—42no—
1090D8—42no—
1091D8—42no—
1092D8—1721no—
1093D8—1722no—
1094D8—1722no—
1095D8—1722no—
1096D8—1721no—
1097D8—1722no—
1098D8—1722no—
1099M16—22no—
1100M16—862no—
1101C2×C8—22no—
1102C2×C8—431no—
1103C2×C8—432no—
1104C2×C8—431no—
1105C2×C8—862no—
1106C2×C8C23×D4311yescharacteristic
1107C2×C8C23×D4312yes—
1108C2×C8C23×D4311yescharacteristic
1109C4⋊C4—431no—
1110C4⋊C4—431no—
1111C4⋊C4—432no—
1112C4⋊C4—432no—
1113C4⋊C4—432no—
1114C4⋊C4—861no—
1115C4⋊C4—861no—
1116C4⋊C4—862no—
1117C4⋊C4—861no—
1118C4⋊C4—861no—
1119C4⋊C4—862no—
1120C4⋊C4—862no—
1121C4⋊C4—861no—
1122C4⋊C4—862no—
1123C4⋊C4C23×D4311yescharacteristic
1124C4⋊C4C23×D4311yescharacteristic
1125C22⋊C4—21no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—432no—
1129C22⋊C4—432no—
1130C22⋊C4—432no—
1131C22⋊C4—861no—
1132C22⋊C4—861no—
1133C22⋊C4—861no—
1134C22⋊C4—862no—
1135C22⋊C4—861no—
1136C22⋊C4—862no—
1137C22⋊C4—862no—
1138C22⋊C4—862no—
1139C22⋊C4—862no—
1140C22⋊C4—861no—
1141C22⋊C4—862no—
1142C22⋊C4—861no—
1143C22⋊C4—862no—
1144C22⋊C4—862no—
1145C22⋊C4—862no—
1146C22⋊C4—862no—
1147C42—21no—
1148C42—431no—
1149C42—432no—
1150C42—431no—
1151C42—432no—
1152C42—432no—
1153C42—431no—
1154C42—431no—
1155C42—861no—
1156C42—861no—
1157C23—22no—
1158C23—22no—
1159C23—21no—
1160C23—44no—
1161C23—42no—
1162C23—42no—
1163C23—81no—
1164C23—81no—
1165C23—81no—
1166C23—81no—
1167C23—82no—
1168C23—82no—
1169C23—861no—
1170C23—862no—
1171C23—861no—
1172C23—3441no—
1173C23—3441no—
1174C23—3442no—
1175C23—3442no—
1176C23—1724no—
1177C23—1722no—
1178C23C2×D4×D4312yes—
1179C23C2×D4×D4311yescharacteristic
1180Q8—22no—
1181Q8—21no—
1182Q8—21no—
1183Q8—861no—
1184Q8—861no—
1185Q8—861no—
1186Q8—861no—
1187Q8—3442no—
1188D4—24no—
1189D4—22no—
1190D4—22no—
1191D4—22no—
1192D4—21no—
1193D4—22no—
1194D4—22no—
1195D4—21no—
1196D4—44no—
1197D4—44no—
1198D4—42no—
1199D4—42no—
1200D4—42no—
1201D4—82no—
1202D4—82no—
1203D4—861no—
1204D4—861no—
1205D4—862no—
1206D4—861no—
1207D4—862no—
1208D4—861no—
1209D4—3442no—
1210D4—3442no—
1211D4—3442no—
1212D4—3442no—
1213D4—3442no—
1214D4—3442no—
1215D4—3442no—
1216D4—3442no—
1217D4—3442no—
1218D4—1724no—
1219D4—1724no—
1220D4—1722no—
1221D4—1724no—
1222D4—1722no—
1223D4—1724no—
1224D4—1722no—
1225D4—1722no—
1226D4—1722no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—44no—
1233C2×C4—42no—
1234C2×C4—431no—
1235C2×C4—431no—
1236C2×C4—431no—
1237C2×C4—432no—
1238C2×C4—431no—
1239C2×C4—432no—
1240C2×C4—862no—
1241C2×C4—864no—
1242C2×C4—861no—
1243C2×C4—861no—
1244C2×C4—862no—
1245C2×C4—3441no—
1246C2×C4—3442no—
1247C2×C4—3441no—
1248C2×C4—1724no—
1249C2×C4—1722no—
1250C2×C4—1724no—
1251C2×C4—1721no—
1252C2×C4—1722no—
1253C2×C4—1722no—
1254C2×C4—1722no—
1255C2×C4C2×D4×D4312yes—
1256C2×C4C2×D4×D4311yescharacteristic
1257C2×C4#1306337012yes—
1258C2×C4#1306337012yes—
1259C2×C4C24×D4311yescharacteristic
1260C8—21no—
1261C8—21no—
1262C8—22no—
1263C8—861no—
1264C8—861no—
1265C8—862no—
1266C22—21no—
1267C22—21no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—42no—
1272C22—42no—
1273C22—41no—
1274C22—42no—
1275C22—42no—
1276C22—41no—
1277C22—42no—
1278C22—41no—
1279C22—42no—
1280C22—84no—
1281C22—162no—
1282C22—164no—
1283C22—1721no—
1284C22—1722no—
1285C22—1721no—
1286C22—1721no—
1287C22—1722no—
1288C22—1721no—
1289C22—1722no—
1290C22—1721no—
1291C22—1721no—
1292C22—6882no—
1293C22—6884no—
1294C22#1458346412yes—
1295C22C22×D4×D4311yescharacteristic
1296C4—22no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—432no—
1301C4—861no—
1302C4—862no—
1303C4—861no—
1304C4—861no—
1305C4—862no—
1306C4—1722no—
1307C4—1721no—
1308C4—1721no—
1309C4#1458346412yes—
1310C4C2×#1306337011yescharacteristic
1311C4C2×#1306337011yescharacteristic
1312C2—22no—
1313C2—42no—
1314C2—82no—
1315C2—82no—
1316C2—81no—
1317C2—3442no—
1318C2—3441no—
1319C2—3441no—
1320C2C2×#1458346411yescharacteristic
1321C2#576×D4311yescharacteristic
1322C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3008C2
socleC22×C43C23×D4
hypercenter#3008D43
hypocenterC43#60832
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3008

Complements

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

NH ≅ G/Ntype
1. #19148369C2semidirect
2. #19148008C2semidirect
3. #19145687C2semidirect
4. #19145685C2semidirect
5. #19145643C2semidirect
6. #19145641C2semidirect
7. #19145611C2semidirect
8. #19145587C2semidirect
9. #19145568C2semidirect
10. #19145511C2semidirect
11. #19145080C2semidirect
12. #19145076C2semidirect
13. #19144953C2semidirect
14. #19144945C2semidirect
15. #19144074C2semidirect
16. #19144056C2semidirect
17. #19144048C2semidirect
18. C2×#14583092C2semidirect
19. #19143902C2semidirect
20. #19143899C2semidirect
21. #19143861C2semidirect
22. #19143257C2semidirect
23. C43×#3008C2semidirect
25. C2×#13063353C22semidirect
26. C2×#13063351C22semidirect
27. C2×#13063351C22semidirect
28. C2×#13063347C22semidirect
29. C2×#13063345C22semidirect
30. C22×#10621882C22semidirect
37. #14583527C22semidirect
39. #14583516C22semidirect
41. #14583502C22semidirect
45. #14583466C22semidirect
46. #14583466C22semidirect
48. #14583463C22semidirect
51. #14583445C22semidirect
52. #14583444C22semidirect
54. C2×#13063321C22semidirect
55. #14583430C22semidirect
59. #14583367C22semidirect
60. C2×D4×Dic43C22semidirect
61. #14583287C22semidirect
62. #14583287C22semidirect
63. #14583287C22semidirect
64. #14583285C22semidirect
65. #14583282C22semidirect
66. #14583280C22semidirect
67. #14583274C22semidirect
68. #14583274C22semidirect
69. #14583262C22semidirect
70. #14583262C22semidirect
71. #14583260C22semidirect
72. #14583257C22semidirect
73. #14583255C22semidirect
74. #14583252C22semidirect
75. #14583244C22semidirect
76. #14583244C22semidirect
77. #14583124C22semidirect
78. #14583120C22semidirect
79. #14583117C22semidirect
80. #14583116C22semidirect
81. #14583113C22semidirect
82. #14583112C22semidirect
83. #14583108C22semidirect
84. #14583103C22semidirect
85. #14583102C22semidirect
86. #14583098C22semidirect
87. #14583098C22semidirect
88. #14583098C22semidirect
89. #14583093C22semidirect
90. #14583093C22semidirect
91. #14583093C22semidirect
92. #14583092C22semidirect
93. #14583092C22semidirect
94. #14583092C22semidirect
95. #14583092C22semidirect
96. #14583092C22semidirect
97. #14583063C22semidirect
98. #14583061C22semidirect
99. #14583052C22semidirect
100. #14583050C22semidirect
101. #14583046C22semidirect
102. #14583044C22semidirect
103. #14583042C22semidirect
104. #14583042C22semidirect
105. #14583035C22semidirect
106. #14583033C22semidirect
107. #14583032C22semidirect
108. #14583032C22semidirect
109. #14582957C22semidirect
110. #14582957C22semidirect
111. #14582953C22semidirect
112. #14582949C22semidirect
113. #14582922C22semidirect
114. C2×Dic43⋊C8C22semidirect
115. #14582903C22semidirect
116. #14582901C22semidirect
117. #14582900C22semidirect
118. #14582893C22semidirect
119. C2×#13063247C22semidirect
120. C2×#13063246C22semidirect
122. #14582857C22semidirect
123. #14582854C22semidirect
125. C2×AGL(1,ℤ/8)×C43C22semidirect
126. C22×D8×C43C22semidirect
128. C43×#449C22semidirect
129. C43×#449C22semidirect
130. C43×#447C22semidirect
131. C43×#447C22semidirect
132. C43×#418C22semidirect
133. C43×#416C22semidirect
672. #3008D43semidirect
690. C2×AGL(1,ℤ/8)C2×D43semidirect
694. C22×D8C2×D43semidirect
770. #449C2×D43semidirect
771. #449C2×D43semidirect
776. #447C2×D43semidirect
777. #447C2×D43semidirect
785. #418C2×D43semidirect
789. #416C2×D43semidirect
796. C43#60832semidirect

Maximal subgroups

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

subgroupindex
#191483692
#191480082
#191456872
#191456852
#191456432
#191456412
#191456112
#191455872
#191455682
#191455112
#191450802
#191450762
#191449532
#191449452
#191440742
#191440562
#191440482
C2×#145830922
#191439022
#191438992
#191438612
#191432572
C43×#30082
#6083243