Finite Group Databasebeta

← #25968559

Subgroups — #25968559

Order 11008.

2040 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148389C211yesmaximal, characteristic, complemented
2#19148019C211yesmaximal, characteristic, complemented
3#19145710C212yesmaximal, complemented
4#19145695C212yesmaximal, complemented
5#19145674C212yesmaximal, complemented
6#19145665C212yesmaximal, complemented
7#19145636C212yesmaximal, complemented
8#19145597C212yesmaximal, complemented
9#19145565C212yesmaximal, complemented
10#19145549C212yesmaximal, complemented
11#19145084C211yesmaximal, characteristic, complemented
12#19145074C211yesmaximal, characteristic, complemented
13#19144956C211yesmaximal, characteristic, complemented
14#19144953C211yesmaximal, characteristic, complemented
15#19144092C211yesmaximal, characteristic, complemented
16#19144064C211yesmaximal, characteristic, complemented
17#19144048C211yesmaximal, characteristic, complemented
18C2×#14583123C211yesmaximal, characteristic, complemented
19#19143910C211yesmaximal, characteristic, complemented
20#19143902C211yesmaximal, characteristic, complemented
21#19143870C211yesmaximal, characteristic, complemented
22#19143257C211yesmaximal, characteristic, complemented
23C43×#3011C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C2×#13063356C2211yescharacteristic
26C2×#13063356C2211yescharacteristic, complemented
27C2×#13063353C2211yescharacteristic
28C2×#13063347C2211yescharacteristic
29C2×#13063345C2211yescharacteristic, complemented
30C22×#10621884C2211yescharacteristic
31#14583560—21no—
32#14583560—21no—
33#14583537—22no—
34#14583537—21no—
35#14583537—22no—
36#14583537—21no—
37#14583527C2211yescharacteristic, complemented
38#14583522C2212yescomplemented
39#14583518—21no—
40#14583510—21no—
41#14583509C2212yescomplemented
42#14583493—22no—
43#14583477C2211yescharacteristic
44#14583473C2211yescharacteristic
45#14583473C2212yes—
46#14583473C2211yescharacteristic, complemented
47#14583463C2211yescharacteristic
48#14583463C2212yes—
49#14583454—21no—
50#14583451C2212yescomplemented
51#14583445C2212yes—
52#14583445C2211yescharacteristic
53#14583435C2212yescomplemented
54#14583428—21no—
55#14583426—22no—
56C2×#13063314C2212yes—
57C2×#13063314C2211yescharacteristic
58#41×Dic43C2211yescharacteristic
59#14583367C2211yescharacteristic, complemented
60C2×Q8×Dic43C2211yescharacteristic, complemented
61#14583292C2212yescomplemented
62#14583292C2212yescomplemented
63#14583292C2212yescomplemented
64#14583285C2212yescomplemented
65#14583284C2212yescomplemented
66#14583284C2212yescomplemented
67#14583277C2212yescomplemented
68#14583270C2212yescomplemented
69#14583266C2212yescomplemented
70#14583262C2212yescomplemented
71#14583260C2212yescomplemented
72#14583260C2212yescomplemented
73#14583255C2212yescomplemented
74#14583255C2212yescomplemented
75#14583248C2212yescomplemented
76#14583244C2212yescomplemented
77#14583124C2212yescomplemented
78#14583124C2211yescharacteristic, complemented
79#14583124C2212yescomplemented
80#14583123C2212yescomplemented
81#14583123C2212yescomplemented
82#14583123C2212yescomplemented
83#14583123C2212yescomplemented
84#14583123C2212yescomplemented
85#14583120C2211yescharacteristic, complemented
86#14583119C2212yescomplemented
87#14583117C2211yescharacteristic, complemented
88#14583117C2212yescomplemented
89#14583117C2212yescomplemented
90#14583113C2211yescharacteristic, complemented
91#14583108C2211yescharacteristic, complemented
92#14583107C2212yescomplemented
93#14583103C2211yescharacteristic, complemented
94#14583098C2211yescharacteristic, complemented
95#14583097C2212yescomplemented
96#14583093C2211yescharacteristic, complemented
97#14583063C2212yes—
98#14583061C2212yescomplemented
99#14583059C2212yes—
100#14583059C2212yes—
101#14583055C2212yescomplemented
102#14583052C2212yes—
103#14583049C2212yes—
104#14583049C2212yes—
105#14583046C2212yes—
106#14583044C2212yescomplemented
107#14583038C2212yescomplemented
108#14583035C2212yes—
109#14582957C2212yescomplemented
110#14582957C2212yescomplemented
111#14582953C2212yescomplemented
112#14582949C2212yescomplemented
113#14582922C2211yescharacteristic, complemented
114C2×Dic43⋊C8C2211yescharacteristic, complemented
115#14582903C2211yescharacteristic
116#14582901C2211yescharacteristic
117#14582900C2211yescharacteristic, complemented
118#14582893C2211yescharacteristic
119C2×#13063249C2211yescharacteristic, complemented
120C2×#13063247C2211yescharacteristic
121#14582866C2211yescharacteristic
122#14582857C2211yescharacteristic, complemented
123#14582854C2211yescharacteristic, complemented
124C2×2−1+4×C43C2211yescharacteristic
125C2×#137×C43C2211yescharacteristic, complemented
126C22×Q16×C43C2211yescharacteristic, complemented
127C43×#536C2211yescharacteristic
128C43×#452C2212yescomplemented
129C43×#452C2212yescomplemented
130C43×#451C2212yescomplemented
131C43×#451C2212yescomplemented
132C43×#419C2211yescharacteristic, complemented
133C43×#416C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic
135#13063371—42no—
136#13063371—42no—
137C2×#10621902—21no—
138C2×#10621898C2311yescharacteristic
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2312yes—
141C22×D172C2311yescharacteristic
142C22×D172C2312yes—
143C2×D4×D43—22no—
144C2×D4×D43—21no—
145#13063356—42no—
146#13063356—42no—
147#13063353—42no—
148#13063347—42no—
149#13063345—42no—
150C2×Dic172C2311yescharacteristic
151C2×#10621885C2311yescharacteristic
152C2×#10621885C2312yes—
153C2×#10621885C2312yes—
154C2×#10621873C2311yescharacteristic
155C2×#10621873C2311yescharacteristic
156C2×#10621873C2312yes—
157C2×#10621883C2311yescharacteristic
158C2×#10621884—42no—
159C2×#10621884C2312yes—
160C2×#10621884C2312yes—
161C2×#10621884C2312yes—
162C2×#10621884C2312yes—
163C2×#10621884C2311yescharacteristic
164C2×D344C2312yes—
165C2×D344C2311yescharacteristic
166C2×#10621882C2311yescharacteristic
167C2×#10621877C2311yescharacteristic
168C22×C43⋊C8C2311yescharacteristic
169#13063325—21no—
170#13063324C2312yes—
171#13063323C2311yescharacteristic
172#13063323C2312yes—
173#13063323C2312yes—
174#13063321C2311yescharacteristic
175#13063321C2312yes—
176#13063320—22no—
177#13063320—22no—
178#13063318—22no—
179#13063318—22no—
180#13063317—21no—
181#13063316—22no—
182#13063316C2312yes—
183#13063315—22no—
184#13063315—22no—
185#13063314—21no—
186#13063314—21no—
187#13063314—22no—
188#13063314—22no—
189#13063314C2311yescharacteristic
190#13063314C2312yes—
191#13063314C2312yes—
192#13063314C2312yes—
193#13063314C2312yes—
194#13063314C2312yes—
195#13063312C2311yescharacteristic
196#13063311—22no—
197#13063309—22no—
198#13063308—22no—
199#13063308—22no—
200#13063308—22no—
201#13063308—22no—
202#13063307—22no—
203#13063305—22no—
204#13063304C2312yes—
205#13063302—22no—
206#13063302—22no—
207#13063301—21no—
208#13063301—21no—
209#13063301—21no—
210#13063301—22no—
211#13063301—22no—
212#13063301—21no—
213#13063301—21no—
214#13063299—21no—
215#13063299—21no—
216#13063299—22no—
217#13063299—22no—
218#13063299C2312yes—
219#13063297—22no—
220#13063297—21no—
221#13063297—21no—
222#13063297—22no—
223#13063297—22no—
224#13063296—21no—
225#13063293—22no—
226#13063293—22no—
227#13063293—22no—
228Q8×Dic43—21no—
229Q8×Dic43—21no—
230Q8×Dic43D411yescharacteristic
231Q8×Dic43D411yescharacteristic
232Q8×Dic43C2312yes—
233Q8×Dic43C2312yes—
234#13063290—22no—
235#13063290C2311yescharacteristic
236#13063290C2311yescharacteristic
237D4×Dic43D412yes—
238D4×Dic43D411yescharacteristic
239D4×Dic43D412yes—
240D4×Dic43D411yescharacteristic
241#13063287C2311yescharacteristic
242#13063287C2311yescharacteristic
243C4×C22⋊D43—21no—
244C4×C22⋊D43—21no—
245C4×C22⋊D43—22no—
246C4×C22⋊D43—22no—
247(C22⋊D43)⋊C4—21no—
248(C22⋊D43)⋊C4—21no—
249(C22⋊D43)⋊C4—22no—
250#13063284C2311yescharacteristic
251#13063284C2312yes—
252#13063283—22no—
253#13063282—21no—
254#13063281—22no—
255C2×C4⋊Dic43—21no—
256C2×C4⋊Dic43C2311yescharacteristic
257C2×(C2×D43)⋊C4—21no—
258C2×(C2×D43)⋊C4—21no—
259C2×(C2×D43)⋊C4—22no—
260C2×(C2×D43)⋊C4—22no—
261C2×C4×Dic43—21no—
262C2×C4×Dic43C2311yescharacteristic
263C2×C4×Dic43C2312yes—
264C42×D43—21no—
265Dic43⋊C8C2311yescharacteristic
266Dic43⋊C8C2312yes—
267Dic43⋊C8C2311yescharacteristic
268Dic43⋊C8C2311yescharacteristic
269Dic43⋊C8C2312yes—
270Dic43⋊C8C2311yescharacteristic
271#13063250C2312yes—
272#13063249C2312yes—
273#13063249C2312yes—
274#13063249C2312yes—
275#13063248C2311yescharacteristic
276#13063248C2311yescharacteristic
277#13063247C2312yes—
278#13063247C2312yes—
279#13063247C2312yes—
280#13063246C2312yes—
281#13063245C2311yescharacteristic
282#13063245C2311yescharacteristic
283#13063245C2312yes—
284#13063245C2312yes—
285C22⋊(C43⋊C8)C2312yes—
286C22⋊(C43⋊C8)C2312yes—
287#13063235C2312yes—
288#13063235C2312yes—
289C8×Dic43C2312yes—
290C8×Dic43C2312yes—
2912−1+4×C43—42no—
2922−1+4×C43—42no—
293C2×#41×C43—22no—
294C2×#41×C43—21no—
295C2×#41×C43C2311yescharacteristic
296C2×#41×C43C2312yes—
297C2×#41×C43C2311yescharacteristic
298C22×Q8×C43—21no—
299C22×Q8×C43C2311yescharacteristic
300C22×Q8×C43C2311yescharacteristic
301C22×Q8×C43C2312yes—
302#137×C43—42no—
303C2×Q16×C43—42no—
304C2×Q16×C43C2312yes—
305C2×Q16×C43C2312yes—
306C2×Q16×C43C2312yes—
307C2×SD16×C43C2312yes—
308C2×M16×C43C2311yescharacteristic
309C22×C8×C43C2311yescharacteristic
310C4⋊Q8×C43—21no—
311#124×C43—21no—
312#123×C43—22no—
313C22⋊Q8×C43C2312yes—
314C22⋊Q8×C43C2312yes—
315#117×C43C2311yescharacteristic
316#103×C43C2311yescharacteristic
317#103×C43C2311yescharacteristic
318#103×C43C2312yes—
319#103×C43C2312yes—
320#102×C43C2311yescharacteristic
321#102×C43C2311yescharacteristic
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C23×D43—22no—
325C23×D43—21no—
326#41×C43—22no—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—42no—
331#41×C43—42no—
332#41×C43—48no—
333#41×C43—44no—
334C2×Q8×C43—21no—
335C2×Q8×C43—22no—
336C2×Q8×C43—21no—
337C2×Q8×C43—22no—
338C2×Q8×C43—22no—
339C2×Q8×C43—22no—
340C2×Q8×C43—22no—
341C2×Q8×C43—42no—
342C2×Q8×C43—42no—
343C2×Q8×C43—44no—
344C2×Q8×C43C2×D411yescharacteristic
345C2×Q8×C43C2412yes—
346C2×Q8×C43C2411yescharacteristic
347C2×Q8×C43C2412yes—
348C2×D4×C43—22no—
349C2×D4×C43—21no—
350C2×D4×C43C2×D412yes—
351C2×D4×C43C2×D411yescharacteristic
352C2×D4×C43C2411yescharacteristic
353C22×C4×C43—22no—
354C22×C4×C43—21no—
355C22×C4×C43—21no—
356C22×C4×C43—22no—
357C22×C4×C43—21no—
358C22×C4×C43C2412yes—
359C22×C4×C43C2411yescharacteristic
360C2×C22⋊D43—21no—
361C2×C22⋊D43—21no—
362C2×C22⋊D43—22no—
363C2×C22⋊D43—22no—
364C2×C22⋊D43—21no—
365C2×C22⋊D43—22no—
366C2×C22⋊D43—21no—
367C2×C22⋊D43—22no—
368C22×Dic43—21no—
369C22×Dic43C2×D411yescharacteristic
370C22×Dic43C2×D411yescharacteristic
371C22×Dic43C2×D412yes—
372C22×Dic43C2×D412yes—
373#10621902—44no—
374D4×D43—44no—
375D4×D43—48no—
376#10621898—22no—
377#10621898—22no—
378#10621898—22no—
379#10621898—22no—
380#10621898—42no—
381#10621898—42no—
382C2×D172—22no—
383C2×D172—21no—
384C2×D172—22no—
385C2×D172—22no—
386C2×D172—42no—
387C2×D172—42no—
388C2×D172C2412yes—
389C2×D172C2411yescharacteristic
390C2×D172C2411yescharacteristic
391C2×C4×D43—21no—
392C2×C4×D43—22no—
393C2×C4×D43—21no—
394C2×C4×D43—21no—
395C2×C4×D43—21no—
396C2×Dic86—22no—
397C2×Dic86C2411yescharacteristic
398C2×Dic86C2411yescharacteristic
399Q16×C43—42no—
400Q16×C43—42no—
401Q16×C43—42no—
402SD16×C43—42no—
403M16×C43—22no—
404C2×C8×C43—22no—
405C2×C8×C43C2411yescharacteristic
406C2×C8×C43C2411yescharacteristic
407C2×C8×C43C2412yes—
408C4⋊C4×C43—22no—
409C4⋊C4×C43—22no—
410C4⋊C4×C43C2411yescharacteristic
411C4⋊C4×C43C2411yescharacteristic
412C22⋊C4×C43—21no—
413C22⋊C4×C43—22no—
414C22⋊C4×C43—22no—
415C42×C43—21no—
416C22⋊Dic43—21no—
417C22⋊Dic43—21no—
418C22⋊Dic43—22no—
419C22⋊Dic43C2×D412yes—
420C22⋊Dic43C2×D412yes—
421C22⋊Dic43C2×D412yes—
422#10621885—41no—
423#10621885—42no—
424#10621885—42no—
425#10621884—42no—
426#10621884—42no—
427#10621884—41no—
428#10621884—42no—
429#10621884—42no—
430#10621883—41no—
431#10621882—41no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—22no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4—21no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4—21no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447C4⋊Dic43—21no—
448C4⋊Dic43—22no—
449C4⋊Dic43—22no—
450C4⋊Dic43—22no—
451C4⋊Dic43C2×D411yescharacteristic
452C4⋊Dic43C2×D411yescharacteristic
453C4⋊Dic43C2×D412yes—
454C4⋊Dic43C2×D412yes—
455C4⋊Dic43C2412yes—
456Dic43⋊C4—22no—
457Dic43⋊C4—22no—
458Dic43⋊C4—22no—
459Dic43⋊C4—21no—
460Dic43⋊C4—21no—
461Dic43⋊C4—22no—
462Dic43⋊C4—21no—
463Dic43⋊C4—21no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467C4×Dic43—21no—
468C4×Dic43—21no—
469C4×Dic43—22no—
470C4×Dic43—22no—
471C4×Dic43C2×D411yescharacteristic
472C4×Dic43C2×D411yescharacteristic
473C4×Dic43C2×D412yes—
474C4×Dic43C2×D412yes—
475C4×Dic43C2412yes—
476C4×Dic43C2411yescharacteristic
477C4×Dic43C2411yescharacteristic
478#10621877—22no—
479C2×C43⋊C8—22no—
480C2×C43⋊C8C2411yescharacteristic
481C2×C43⋊C8C2412yes—
482C2×C43⋊C8C2411yescharacteristic
483Dic172—41no—
484D344—41no—
485D344—42no—
486#10621873—41no—
487#10621873—41no—
488#10621873—42no—
489C23×C43—21no—
490C23×C43C22×D412yes—
491C23×C43C22×D411yescharacteristic
492C22×D43—21no—
493C22×D43—21no—
494C22×D43—22no—
495C22×D43—44no—
496C22×D43—42no—
497C22×D43—81no—
498C22×D43—82no—
499C22×D43—81no—
500C22×D43—82no—
501Q8×C43—22no—
502Q8×C43—22no—
503Q8×C43—22no—
504Q8×C43—22no—
505Q8×C43—21no—
506Q8×C43—22no—
507Q8×C43—21no—
508Q8×C43—44no—
509Q8×C43—42no—
510Q8×C43—42no—
511D4×C43—24no—
512D4×C43—22no—
513D4×C43—21no—
514D4×C43—21no—
515D4×C43—44no—
516D4×C43—42no—
517C2×C4×C43—22no—
518C2×C4×C43—22no—
519C2×C4×C43—22no—
520C2×C4×C43—21no—
521C2×C4×C43—21no—
522C2×C4×C43—22no—
523C2×C4×C43—21no—
524C2×C4×C43—44no—
525C2×C4×C43—44no—
526C2×C4×C43—42no—
527C2×C4×C43—42no—
528C2×C4×C43—42no—
529C2×C4×C43C22×D412yes—
530C2×C4×C43C22×D411yescharacteristic
531C2×C4×C43H(5,𝔽2)12yes—
532C2×C4×C43H(5,𝔽2)12yes—
533C2×C4×C43C2511yescharacteristic
534C22⋊D43—44no—
535C22⋊D43—42no—
536C22⋊D43—42no—
537C22⋊D43—82no—
538C22⋊D43—81no—
539C22⋊D43—81no—
540C22⋊D43—82no—
541C22⋊D43—82no—
542C2×Dic43—21no—
543C2×Dic43—22no—
544C2×Dic43—21no—
545C2×Dic43—42no—
546C2×Dic43—41no—
547C2×Dic43—41no—
548C2×Dic43—42no—
549C2×Dic43—81no—
550C2×Dic43C22×D411yescharacteristic
551C2×Dic43C22×D411yescharacteristic
552C2×Dic43C22×D411yescharacteristic
553C2×Dic43C22×D411yescharacteristic
554C2×Dic43C22×D412yes—
555C2×Dic43C22×D412yes—
556D172—21no—
557D172—22no—
558D172—21no—
559D172—21no—
560D172—22no—
561D172—21no—
562D172—44no—
563D172—42no—
564C4×D43—42no—
565C4×D43—44no—
566C4×D43—42no—
567C4×D43—42no—
568C4×D43—81no—
569Dic86—21no—
570Dic86—21no—
571Dic86—21no—
572Dic86—21no—
573Dic86—82no—
574C8×C43—21no—
575C8×C43—22no—
576C8×C43—21no—
577C43⋊C8—21no—
578C43⋊C8—21no—
579C43⋊C8—22no—
580#60835—431nomaximal, Sylow
581C22×C43—21no—
582C22×C43—21no—
583C22×C43—22no—
584C22×C43—22no—
585C22×C43—22no—
586C22×C43—41no—
587C22×C43—41no—
588C22×C43—41no—
589C22×C43#53512yes—
590C22×C43C23×D411yescharacteristic
591C2×D43—42no—
592C2×D43—41no—
593C2×D43—41no—
594C2×D43—42no—
595C2×D43—41no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—42no—
599C2×D43—41no—
600C2×D43—162no—
601C2×D43—164no—
602C4×C43—22no—
603C4×C43—41no—
604C4×C43—41no—
605C4×C43—42no—
606C4×C43—41no—
607C4×C43—42no—
608C4×C43#53512yes—
609C4×C43C2×H(5,𝔽2)11yescharacteristic
610C4×C43C2×H(5,𝔽2)11yescharacteristic
611Dic43—22no—
612Dic43—21no—
613Dic43—21no—
614Dic43—21no—
615Dic43—21no—
616Dic43—22no—
617Dic43—42no—
618Dic43—41no—
619Dic43—41no—
620#3500—431no—
621#3461—431no—
622#3225—432no—
623#3224—432no—
624#3223—432no—
625#3222—432no—
626#3219—432no—
627#3215—432no—
628#3211—432no—
629#3210—432no—
630#3156—431no—
631#3154—431no—
632#3137—431no—
633#3136—431no—
634#3040—431no—
635#3037—431no—
636#3035—431no—
637C2×#464—431no—
638#3013—431no—
639#3012—431no—
640#3011D4311yescharacteristic, complemented
641#3009—431no—
642#2925—431no—
643C2×C43—22no—
644C2×C43—42no—
645C2×C43—81no—
646C2×C43C2×#53511yescharacteristic
647C2×C43#358411yescharacteristic
648C2×C43#358611yescharacteristic
649D43—81no—
650D43—82no—
651D43—81no—
652C2×2−1+4C2×D4311yescharacteristic
653C2×H(5,𝔽2)—431no—
654C2×#137—431no—
655C2×#137—431no—
656C2×#137C2×D4311yescharacteristic, complemented
657C2×AGL(1,ℤ/8)—431no—
658C2×#135—431no—
659C2×#135—431no—
660C22×Q16C2×D4311yescharacteristic, complemented
661C22×SD16—431no—
662#548—861no—
663#548—861no—
664#546—862no—
665#546—861no—
666#546—862no—
667#546—861no—
668#544—431no—
669#542—432no—
670#542—861no—
671#541—432no—
672#541—861no—
673#539—862no—
674#537—431no—
675#536—431no—
676#536—431no—
677#536—432no—
678#536C2×D4311yescharacteristic
679#535—431no—
680#535—432no—
681#533—432no—
682#533—861no—
683#532—432no—
684#532—431no—
685#529—432no—
686#529—862no—
687#529—861no—
688C2×#124—432no—
689C2×#124—431no—
690C4×#41—431no—
691C4×#41—431no—
692C2×C4×Q8—431no—
693#497—432no—
694#497—432no—
695#497—432no—
696#496—432no—
697#495—432no—
698#495—432no—
699#494—432no—
700#492—432no—
701#491—432no—
702#490—432no—
703#489—432no—
704#489—432no—
705#488—432no—
706#488—432no—
707#487—432no—
708#486—432no—
709#464—432no—
710#464—432no—
711#464—432no—
712#464—432no—
713#464—432no—
714#464—432no—
715#464—432no—
716#464—431no—
717#464—432no—
718#464—431no—
719#463—431no—
720#463—432no—
721#463—432no—
722#463—431no—
723#462—432no—
724#462—431no—
725#461—431no—
726#460—432no—
727#460—431no—
728#459—431no—
729#452—432no—
730#452—432no—
731#452—432no—
732#452—432no—
733#452C2×D4312yescomplemented
734#452C2×D4312yescomplemented
735#451—432no—
736#451C2×D4312yescomplemented
737#451C2×D4312yescomplemented
738#450—432no—
739#450—432no—
740#450—432no—
741#449—432no—
742#449—432no—
743#448—432no—
744#447—432no—
745#433—432no—
746#433—432no—
747#432—432no—
748#431—432no—
749#423—431no—
750C2×C4⋊C8—431no—
751#419C2×D4311yescharacteristic, complemented
752#418—431no—
753#417—431no—
754#417—431no—
755#416—431no—
756#416C2×D4311yescharacteristic, complemented
757C2×#103—431no—
758C2×#102—431no—
759#408—431no—
760#408C2×D4311yescharacteristic
761#405—431no—
762#405—431no—
763C43#6083511yescharacteristic, complemented, Sylow
7642−1+4—42no—
7652−1+4—42no—
766H(5,𝔽2)—1722no—
767H(5,𝔽2)—1722no—
768C2×#41—22no—
769C2×#41—21no—
770C2×#41—431no—
771C2×#41—431no—
772C2×#41—432no—
773C2×#41—861no—
774C2×#41C22×D4311yescharacteristic
775C2×#41C22×D4312yes—
776C2×#41C22×D4311yescharacteristic
777C22×Q8—21no—
778C22×Q8C22×D4311yescharacteristic
779C22×Q8C22×D4311yescharacteristic
780C22×Q8C22×D4312yes—
781C22×D4—431no—
782C22×D4—432no—
783C22×D4—862no—
784C22×D4—861no—
785#137—42no—
786#137—1722no—
787#137—1722no—
788AGL(1,ℤ/8)—1722no—
789#135—1722no—
790#135—1722no—
791C2×Q16—42no—
792C2×Q16—431no—
793C2×Q16—432no—
794C2×Q16—432no—
795C2×Q16—431no—
796C2×Q16C22×D4312yes—
797C2×Q16C22×D4312yes—
798C2×Q16C22×D4312yes—
799C2×SD16—432no—
800C2×SD16—432no—
801C2×SD16—431no—
802C2×SD16—432no—
803C2×SD16—432no—
804C2×SD16—431no—
805C2×SD16—431no—
806C2×SD16—431no—
807C2×SD16—432no—
808C2×SD16—1722no—
809C2×SD16C22×D4312yes—
810C2×D8—431no—
811C2×D8—431no—
812C2×D8—432no—
813C2×M16—431no—
814C2×M16C22×D4311yescharacteristic
815C22×C8—431no—
816C22×C8C22×D4311yescharacteristic
817C4⋊Q8—21no—
818C4⋊Q8—432no—
819C4⋊Q8—431no—
820C4⋊Q8—432no—
821C4⋊Q8—432no—
822C4⋊Q8—861no—
823#127—431no—
824#127—432no—
825#126—862no—
826#126—862no—
827#126—862no—
828#126—862no—
829#125—432no—
830#125—861no—
831#125—862no—
832#125—862no—
833#125—862no—
834#124—21no—
835#124—431no—
836#124—432no—
837#124—432no—
838#124—432no—
839#124—432no—
840#124—432no—
841#124—431no—
842#124—861no—
843#124—862no—
844#124—861no—
845#124—862no—
846#124—862no—
847#123—22no—
848#123—862no—
849#123—862no—
850#123—862no—
851#123—862no—
852#123—862no—
853#123—862no—
854C22⋊Q8—432no—
855C22⋊Q8—862no—
856C22⋊Q8—862no—
857C22⋊Q8—862no—
858C22⋊Q8—861no—
859C22⋊Q8—861no—
860C22⋊Q8—861no—
861C22⋊Q8—862no—
862C22⋊Q8—861no—
863C22⋊Q8—862no—
864C22⋊Q8—861no—
865C22⋊Q8C22×D4312yes—
866C22⋊Q8C22×D4312yes—
867#121—432no—
868#121—861no—
869#121—862no—
870#121—861no—
871#121—862no—
872#121—861no—
873#121—861no—
874#121—862no—
875#121—862no—
876#121—862no—
877#121—861no—
878#120—862no—
879#120—862no—
880#120—862no—
881C4×Q8—431no—
882C4×Q8—431no—
883C4×Q8—432no—
884C4×Q8—432no—
885C4×Q8—431no—
886C4×Q8—431no—
887C4×Q8—862no—
888C4×Q8—861no—
889C4×Q8—861no—
890C4×D4—431no—
891C4×D4—432no—
892C4×D4—432no—
893C4×D4—431no—
894C4×D4—431no—
895C4×D4—431no—
896C4×D4—861no—
897C4×D4—862no—
898C4×D4—861no—
899C4×D4—862no—
900C4×D4—861no—
901C4×D4—861no—
902C4×D4—862no—
903#117—431no—
904#117—432no—
905#117—861no—
906#117—862no—
907#117—862no—
908#117C22×D4311yescharacteristic
909C2×C4⋊C4—431no—
910C2×C4⋊C4—861no—
911C2×C22⋊C4—861no—
912C2×C22⋊C4—861no—
913C2×C22⋊C4—862no—
914C2×C22⋊C4—862no—
915C2×C42—431no—
916C2×C42—432no—
917C2×C42—861no—
918C2×C42—861no—
919C4⋊C8—431no—
920C4⋊C8—431no—
921C4⋊C8—431no—
922C4⋊C8—431no—
923C4⋊C8—432no—
924C4⋊C8—432no—
925#103—432no—
926#103—432no—
927#103—432no—
928#103—432no—
929#103—431no—
930#103—431no—
931#103C22×D4311yescharacteristic
932#103C22×D4311yescharacteristic
933#103C22×D4312yes—
934#103C22×D4312yes—
935#102—432no—
936#102—432no—
937#102—432no—
938#102—432no—
939#102—431no—
940#102—431no—
941#102—432no—
942#102—432no—
943#102C22×D4311yescharacteristic
944#102C22×D4311yescharacteristic
945C22⋊C8—432no—
946C22⋊C8—432no—
947C22⋊C8C22×D4312yes—
948C22⋊C8C22×D4312yes—
949#97—432no—
950#97—432no—
951C4×C8—432no—
952C4×C8—432no—
953C24—862no—
954C24—861no—
955#41—22no—
956#41—22no—
957#41—22no—
958#41—22no—
959#41—42no—
960#41—42no—
961#41—48no—
962#41—44no—
963#41—862no—
964#41—862no—
965#41—862no—
966#41—862no—
967#41—1722no—
968#41—1722no—
969#41—1724no—
970C2×Q8—21no—
971C2×Q8—22no—
972C2×Q8—21no—
973C2×Q8—22no—
974C2×Q8—22no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—42no—
978C2×Q8—42no—
979C2×Q8—44no—
980C2×Q8—431no—
981C2×Q8—431no—
982C2×Q8—862no—
983C2×Q8D4×D4311yescharacteristic
984C2×Q8C23×D4312yes—
985C2×Q8C23×D4311yescharacteristic
986C2×Q8C23×D4312yes—
987C2×D4—22no—
988C2×D4—21no—
989C2×D4—432no—
990C2×D4—431no—
991C2×D4—431no—
992C2×D4—861no—
993C2×D4—861no—
994C2×D4—862no—
995C2×D4—862no—
996C2×D4—862no—
997C2×D4—861no—
998C2×D4—862no—
999C2×D4—861no—
1000C2×D4—862no—
1001C2×D4—861no—
1002C2×D4—862no—
1003C2×D4—862no—
1004C2×D4—1722no—
1005C2×D4—1722no—
1006C2×D4—1728no—
1007C2×D4—1724no—
1008C2×D4D4×D4312yes—
1009C2×D4D4×D4311yescharacteristic
1010C2×D4C23×D4311yescharacteristic
1011C22×C4—21no—
1012C22×C4—22no—
1013C22×C4—21no—
1014C22×C4—22no—
1015C22×C4—21no—
1016C22×C4—431no—
1017C22×C4—431no—
1018C22×C4—432no—
1019C22×C4—432no—
1020C22×C4—861no—
1021C22×C4—861no—
1022C22×C4—861no—
1023C22×C4—861no—
1024C22×C4—862no—
1025C22×C4—861no—
1026C22×C4C23×D4312yes—
1027C22×C4C23×D4311yescharacteristic
1028Q16—42no—
1029Q16—42no—
1030Q16—42no—
1031Q16—1721no—
1032Q16—1721no—
1033Q16—1722no—
1034Q16—1722no—
1035SD16—42no—
1036SD16—1721no—
1037SD16—1721no—
1038SD16—1722no—
1039SD16—1721no—
1040SD16—1722no—
1041SD16—1722no—
1042SD16—1721no—
1043SD16—1722no—
1044SD16—1722no—
1045D8—1721no—
1046D8—1722no—
1047D8—1721no—
1048M16—22no—
1049M16—862no—
1050C2×C8—22no—
1051C2×C8—431no—
1052C2×C8—432no—
1053C2×C8—431no—
1054C2×C8—862no—
1055C2×C8C23×D4311yescharacteristic
1056C2×C8C23×D4312yes—
1057C2×C8C23×D4311yescharacteristic
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—432no—
1061C4⋊C4—431no—
1062C4⋊C4—431no—
1063C4⋊C4—432no—
1064C4⋊C4—432no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—862no—
1072C4⋊C4—861no—
1073C4⋊C4—861no—
1074C4⋊C4—862no—
1075C4⋊C4—862no—
1076C4⋊C4—862no—
1077C4⋊C4—862no—
1078C4⋊C4—861no—
1079C4⋊C4—862no—
1080C4⋊C4C23×D4311yescharacteristic
1081C4⋊C4C23×D4311yescharacteristic
1082C22⋊C4—22no—
1083C22⋊C4—21no—
1084C22⋊C4—22no—
1085C22⋊C4—432no—
1086C22⋊C4—432no—
1087C22⋊C4—432no—
1088C22⋊C4—862no—
1089C22⋊C4—861no—
1090C22⋊C4—862no—
1091C22⋊C4—861no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—862no—
1095C22⋊C4—862no—
1096C22⋊C4—862no—
1097C22⋊C4—862no—
1098C22⋊C4—861no—
1099C22⋊C4—861no—
1100C22⋊C4—862no—
1101C22⋊C4—862no—
1102C22⋊C4—861no—
1103C22⋊C4—861no—
1104C22⋊C4—862no—
1105C22⋊C4—862no—
1106C42—21no—
1107C42—431no—
1108C42—432no—
1109C42—431no—
1110C42—432no—
1111C42—432no—
1112C42—431no—
1113C42—431no—
1114C42—861no—
1115C42—862no—
1116C42—861no—
1117C42—862no—
1118C23—21no—
1119C23—861no—
1120C23—862no—
1121C23—861no—
1122C23—3441no—
1123C23—3441no—
1124C23—3442no—
1125C23—3442no—
1126C23—1724no—
1127C23—1722no—
1128C23C2×D4×D4312yes—
1129C23C2×D4×D4311yescharacteristic
1130Q8—22no—
1131Q8—22no—
1132Q8—22no—
1133Q8—22no—
1134Q8—21no—
1135Q8—22no—
1136Q8—21no—
1137Q8—44no—
1138Q8—42no—
1139Q8—42no—
1140Q8—861no—
1141Q8—861no—
1142Q8—861no—
1143Q8—861no—
1144Q8—3442no—
1145D4—24no—
1146D4—22no—
1147D4—21no—
1148D4—21no—
1149D4—44no—
1150D4—42no—
1151D4—861no—
1152D4—861no—
1153D4—862no—
1154D4—861no—
1155D4—862no—
1156D4—861no—
1157D4—3441no—
1158D4—3442no—
1159D4—3441no—
1160D4—3442no—
1161D4—3442no—
1162D4—1724no—
1163D4—1724no—
1164D4—1722no—
1165D4—1722no—
1166D4—1722no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—44no—
1175C2×C4—44no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—431no—
1180C2×C4—431no—
1181C2×C4—431no—
1182C2×C4—431no—
1183C2×C4—432no—
1184C2×C4—432no—
1185C2×C4—862no—
1186C2×C4—861no—
1187C2×C4—861no—
1188C2×C4—3441no—
1189C2×C4—3441no—
1190C2×C4—1724no—
1191C2×C4—1722no—
1192C2×C4—1721no—
1193C2×C4—1722no—
1194C2×C4—1721no—
1195C2×C4—1722no—
1196C2×C4—1722no—
1197C2×C4—1722no—
1198C2×C4C2×D4×D4312yes—
1199C2×C4C2×D4×D4311yescharacteristic
1200C2×C4#1306337012yes—
1201C2×C4#1306337012yes—
1202C2×C4C24×D4311yescharacteristic
1203C8—21no—
1204C8—21no—
1205C8—22no—
1206C8—861no—
1207C8—861no—
1208C8—862no—
1209C22—21no—
1210C22—21no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—1721no—
1218C22—1722no—
1219C22—1721no—
1220C22—1721no—
1221C22—1722no—
1222C22—1721no—
1223C22—1722no—
1224C22—1721no—
1225C22—1721no—
1226C22—6882no—
1227C22—6884no—
1228C22#1458346412yes—
1229C22C22×D4×D4311yescharacteristic
1230C4—22no—
1231C4—41no—
1232C4—41no—
1233C4—42no—
1234C4—41no—
1235C4—42no—
1236C4—861no—
1237C4—861no—
1238C4—862no—
1239C4—861no—
1240C4—861no—
1241C4—862no—
1242C4—1722no—
1243C4—1721no—
1244C4—1721no—
1245C4#1458346412yes—
1246C4C2×#1306337011yescharacteristic
1247C4C2×#1306337011yescharacteristic
1248C2—22no—
1249C2—42no—
1250C2—81no—
1251C2—3442no—
1252C2—3441no—
1253C2—3441no—
1254C2C2×#1458346411yescharacteristic
1255C2#1914936511yescharacteristic
1256C2#1914938011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3011C2
socleC22×C43C23×D4
hypercenter#3011D43
hypocenterC43#60835
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3011

Complements

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

NH ≅ G/Ntype
1. #19148389C2semidirect
2. #19148019C2semidirect
3. #19145710C2semidirect
4. #19145695C2semidirect
5. #19145674C2semidirect
6. #19145665C2semidirect
7. #19145636C2semidirect
8. #19145597C2semidirect
9. #19145565C2semidirect
10. #19145549C2semidirect
11. #19145084C2semidirect
12. #19145074C2semidirect
13. #19144956C2semidirect
14. #19144953C2semidirect
15. #19144092C2semidirect
16. #19144064C2semidirect
17. #19144048C2semidirect
18. C2×#14583123C2semidirect
19. #19143910C2semidirect
20. #19143902C2semidirect
21. #19143870C2semidirect
22. #19143257C2semidirect
23. C43×#3011C2semidirect
26. C2×#13063356C22semidirect
29. C2×#13063345C22semidirect
37. #14583527C22semidirect
38. #14583522C22semidirect
41. #14583509C22semidirect
46. #14583473C22semidirect
50. #14583451C22semidirect
53. #14583435C22semidirect
59. #14583367C22semidirect
60. C2×Q8×Dic43C22semidirect
61. #14583292C22semidirect
62. #14583292C22semidirect
63. #14583292C22semidirect
64. #14583285C22semidirect
65. #14583284C22semidirect
66. #14583284C22semidirect
67. #14583277C22semidirect
68. #14583270C22semidirect
69. #14583266C22semidirect
70. #14583262C22semidirect
71. #14583260C22semidirect
72. #14583260C22semidirect
73. #14583255C22semidirect
74. #14583255C22semidirect
75. #14583248C22semidirect
76. #14583244C22semidirect
77. #14583124C22semidirect
78. #14583124C22semidirect
79. #14583124C22semidirect
80. #14583123C22semidirect
81. #14583123C22semidirect
82. #14583123C22semidirect
83. #14583123C22semidirect
84. #14583123C22semidirect
85. #14583120C22semidirect
86. #14583119C22semidirect
87. #14583117C22semidirect
88. #14583117C22semidirect
89. #14583117C22semidirect
90. #14583113C22semidirect
91. #14583108C22semidirect
92. #14583107C22semidirect
93. #14583103C22semidirect
94. #14583098C22semidirect
95. #14583097C22semidirect
96. #14583093C22semidirect
98. #14583061C22semidirect
101. #14583055C22semidirect
106. #14583044C22semidirect
107. #14583038C22semidirect
109. #14582957C22semidirect
110. #14582957C22semidirect
111. #14582953C22semidirect
112. #14582949C22semidirect
113. #14582922C22semidirect
114. C2×Dic43⋊C8C22semidirect
117. #14582900C22semidirect
119. C2×#13063249C22semidirect
122. #14582857C22semidirect
123. #14582854C22semidirect
125. C2×#137×C43C22semidirect
126. C22×Q16×C43C22semidirect
128. C43×#452C22semidirect
129. C43×#452C22semidirect
130. C43×#451C22semidirect
131. C43×#451C22semidirect
132. C43×#419C22semidirect
133. C43×#416C22semidirect
640. #3011D43semidirect
656. C2×#137C2×D43semidirect
660. C22×Q16C2×D43semidirect
733. #452C2×D43semidirect
734. #452C2×D43semidirect
736. #451C2×D43semidirect
737. #451C2×D43semidirect
751. #419C2×D43semidirect
756. #416C2×D43semidirect
763. C43#60835semidirect

Maximal subgroups

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

subgroupindex
#191483892
#191480192
#191457102
#191456952
#191456742
#191456652
#191456362
#191455972
#191455652
#191455492
#191450842
#191450742
#191449562
#191449532
#191440922
#191440642
#191440482
C2×#145831232
#191439102
#191439022
#191438702
#191432572
C43×#30112
#6083543