Finite Group Databasebeta

← #25974473

Subgroups — #25974473

Order 11008.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148316C211yesmaximal, characteristic, complemented
2#19148265C211yesmaximal, characteristic, complemented
3#19146845C212yesmaximal, complemented
4#19146823C212yesmaximal, complemented
5#19146748C212yesmaximal, complemented
6#19146733C212yesmaximal, complemented
7#19146718C212yesmaximal, complemented
8#19146658C212yesmaximal, complemented
9#19146542C212yesmaximal, complemented
10#19146427C212yesmaximal, complemented
11#19144954C211yesmaximal, characteristic, complemented
12#19144588C211yesmaximal, characteristic, complemented
13C2×#14583226C211yesmaximal, characteristic, complemented
14#19144267C211yesmaximal, characteristic, complemented
15#19144215C211yesmaximal, characteristic, complemented
16#19144136C211yesmaximal, characteristic, complemented
17#19143901C211yesmaximal, characteristic, complemented
18#19143815C211yesmaximal, characteristic, complemented
19#19143476C211yesmaximal, characteristic, complemented
20#19143319C211yesmaximal, characteristic, complemented
21#19143117C211yesmaximal, characteristic, complemented
22#19143111C211yesmaximal, characteristic, complemented
23C43×#3083C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C2×#41×D43C2211yescharacteristic
26C2×#13063353C2211yescharacteristic, complemented
27C2×#13063347C2211yescharacteristic, complemented
28C2×#13063345C2211yescharacteristic
29C2×#13063331C2211yescharacteristic, complemented
30C2×M16×D43C2211yescharacteristic, complemented
31#14583623—21no—
32#14583623C2212yescomplemented
33#14583615—21no—
34#14583615C2212yescomplemented
35#14583602—21no—
36#14583602C2212yescomplemented
37#14583587—21no—
38#14583587C2212yescomplemented
39#14583571C2212yes—
40#14583561C2212yes—
41#14583544—22no—
42#14583544C2212yes—
43D4×D172—22no—
44D4×D172C2212yes—
45#14583489—22no—
46#14583480—21no—
47#14583480C2211yescharacteristic
48#14583480C2211yescharacteristic, complemented
49#14583468—21no—
50#14583468C2211yescharacteristic
51#14583435—22no—
52#14583411—21no—
53#14583411C2211yescharacteristic
54#14583411C2211yescharacteristic, complemented
55C2×#13063300—21no—
56C2×#13063300C2211yescharacteristic
57#14583379C2211yescharacteristic, complemented
58#14583379C2211yescharacteristic, complemented
59C2×#13063283C2211yescharacteristic, complemented
60#14583265C2212yescomplemented
61#14583261C2212yescomplemented
62#14583256C2212yescomplemented
63#14583247C2212yescomplemented
64#14583242C2212yescomplemented
65#14583231C2212yescomplemented
66#14583226C2212yescomplemented
67#14583226C2212yescomplemented
68#14583226C2212yescomplemented
69#14583226C2212yescomplemented
70#14583226C2212yescomplemented
71#14583219C2212yescomplemented
72#14583153C2212yescomplemented
73#14583146C2212yescomplemented
74#14583146C2212yescomplemented
75#14583146C2212yescomplemented
76#14583141C2212yescomplemented
77#14583136C2212yescomplemented
78#14583136C2212yescomplemented
79#14583129C2212yescomplemented
80#14583122C2212yescomplemented
81#14583115C2212yescomplemented
82#14583100C2212yescomplemented
83#14583095C2212yescomplemented
84#14583064C2211yescharacteristic, complemented
85#14583064C2212yescomplemented
86#14583062C2211yescharacteristic, complemented
87#14583056C2211yescharacteristic, complemented
88#14583051C2211yescharacteristic, complemented
89#14583051C2212yescomplemented
90#14583047C2211yescharacteristic, complemented
91#14583047C2212yescomplemented
92#14583045C2211yescharacteristic, complemented
93#14583039C2211yescharacteristic, complemented
94#14583034C2211yescharacteristic, complemented
95#14583034C2212yescomplemented
96#14583009C2212yescomplemented
97#14583004C2212yescomplemented
98C4×#10621884C2212yescomplemented
99C4×#10621883C2212yescomplemented
100#14582976C2212yescomplemented
101#14582969C2212yescomplemented
102#14582969C2212yescomplemented
103#14582964C2212yescomplemented
104C2×#13063256C2211yescharacteristic, complemented
105#14582906C2212yescomplemented
106#14582903C2211yescharacteristic, complemented
107#14582902C2212yescomplemented
108#14582902C2212yescomplemented
109#14582901C2211yescharacteristic, complemented
110#14582900C2211yescharacteristic
111#14582899C2212yescomplemented
112#14582898C2211yescharacteristic, complemented
113#14582898C2211yescharacteristic, complemented
114#14582894C2212yescomplemented
115#14582894C2212yescomplemented
116#14582893C2211yescharacteristic, complemented
117#14582892C2212yescomplemented
118C2×#13063247C2211yescharacteristic, complemented
119C2×#13063245C2211yescharacteristic, complemented
120#102×D43C2212yescomplemented
121#14582867C2211yescharacteristic, complemented
122C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
123#14582855C2211yescharacteristic, complemented
124C43×#544C2211yescharacteristic, complemented
125C43×#520C2211yescharacteristic
126C43×#479C2212yescomplemented
127C43×#478C2212yescomplemented
128C43×#477C2212yescomplemented
129C43×#474C2212yescomplemented
130C43×#428C2211yescharacteristic, complemented
131C2×#107×C43C2211yescharacteristic, complemented
132C43×#424C2211yescharacteristic, complemented
133C43×#417C2211yescharacteristic
134C43×#416C2211yescharacteristic
135#13063371—24no—
136#13063371—42no—
137C2×#10621902C2312yes—
138C2×#10621902C2311yescharacteristic
139C2×#10621898—21no—
140C2×#10621898—21no—
141C2×#10621898C2311yescharacteristic
142C2×#10621898C2311yescharacteristic
143C2×#10621898C2311yescharacteristic
144C2×#10621900—21no—
145C2×#10621900C2311yescharacteristic
146#41×D43—24no—
147#41×D43—42no—
148C2×Q8×D43C2311yescharacteristic
149C22×D172—21no—
150C22×D172—21no—
151C22×D172—22no—
152C22×D172C2311yescharacteristic
153C2×D4×D43—21no—
154C2×D4×D43—22no—
155C2×D4×D43C2312yes—
156C2×D4×D43C2311yescharacteristic
157C22×C4×D43—21no—
158C22×C4×D43C2311yescharacteristic
159#13063353—42no—
160#13063347—42no—
161#13063345—24no—
162C2×Dic172C2311yescharacteristic
163C2×#10621885C2311yescharacteristic
164C2×#10621873C2311yescharacteristic
165C2×#10621873C2311yescharacteristic
166C2×#10621873C2312yes—
167C2×#10621883C2311yescharacteristic
168C2×#10621884C2311yescharacteristic
169C2×D344C2311yescharacteristic
170C2×D344C2312yes—
171C2×#10621882C2311yescharacteristic
172#13063331—42no—
173C2×#10621877C2311yescharacteristic
174C2×#10621872C2312yes—
175C2×#10621872C2312yes—
176M16×D43—42no—
177C22×C43⋊C8C2311yescharacteristic
178C2×C8×D43C2312yes—
179C2×C8×D43C2312yes—
180#13063322—22no—
181#13063322C2312yes—
182#13063320—22no—
183#13063320—22no—
184#13063320—22no—
185#13063320—22no—
186#13063316—22no—
187#13063314—22no—
188#13063314—22no—
189#13063314—22no—
190#13063313—22no—
191#13063313C2312yes—
192#13063310—22no—
193#13063310—22no—
194#13063309—21no—
195#13063309—22no—
196#13063309D412yes—
197#13063305—21no—
198#13063305—21no—
199#13063305—22no—
200#13063305D411yescharacteristic
201#13063305D411yescharacteristic
202#13063305C2312yes—
203#13063305C2311yescharacteristic
204#13063305C2312yes—
205#13063305C2311yescharacteristic
206#13063300—22no—
207#13063300—21no—
208#13063300—22no—
209#13063300—22no—
210#13063300—21no—
211#13063300—21no—
212#13063300—21no—
213#13063300—21no—
214#13063300—21no—
215#13063300—22no—
216#13063300—22no—
217#13063300D411yescharacteristic
218#13063300D411yescharacteristic
219#13063300C2311yescharacteristic
220#13063300C2312yes—
221#13063300C2312yes—
222#13063300C2312yes—
223#13063300C2312yes—
224#13063300C2311yescharacteristic
225#13063299—22no—
226#13063299—22no—
227#13063299—22no—
228#13063299—22no—
229#13063295—21no—
230#13063295—22no—
231#13063295—22no—
232#13063295—22no—
233#13063295—22no—
234#13063295D412yes—
235Q8×Dic43—22no—
236C4×Dic86—21no—
237C4×Dic86C2312yes—
238C4×D172—21no—
239C4×D172—21no—
240C4×D172—21no—
241C4×D172—22no—
242C4×D172—22no—
243C4×D172C2312yes—
244C4×D172C2312yes—
245C4×D172C2312yes—
246#13063287—22no—
247(C22⋊D43)⋊C4—22no—
248(C22⋊D43)⋊C4—22no—
249#13063283—21no—
250#13063283—21no—
251#13063283—21no—
252#13063283—22no—
253#13063283—22no—
254#13063283C2312yes—
255#13063283C2312yes—
256#13063283C2312yes—
257C2×C4⋊Dic43C2311yescharacteristic
258C4⋊C4×D43—21no—
259C4⋊C4×D43C2312yes—
260C2×(C2×D43)⋊C4—21no—
261C2×(C2×D43)⋊C4—21no—
262C2×(C2×D43)⋊C4—22no—
263C2×C4×Dic43—21no—
264#13063256C2312yes—
265#13063256C2312yes—
266#13063250C2312yes—
267#13063249C2312yes—
268#13063248C2311yescharacteristic
269#13063248C2311yescharacteristic
270#13063248C2312yes—
271#13063248C2312yes—
272#13063247C2312yes—
273#13063247C2312yes—
274#13063247C2312yes—
275#13063246C2312yes—
276#13063245C2312yes—
277#13063245C2311yescharacteristic
278#13063245C2312yes—
279#13063245C2311yescharacteristic
280#13063245C2312yes—
281#13063245C2312yes—
282#13063245C2312yes—
283#13063245C2312yes—
284(C2×D43)⋊C8C2311yescharacteristic
285(C2×D43)⋊C8C2312yes—
286(C2×D43)⋊C8C2311yescharacteristic
287(C2×D43)⋊C8C2311yescharacteristic
288(C2×D43)⋊C8C2311yescharacteristic
289(C2×D43)⋊C8C2312yes—
290#13063236C2312yes—
291C4×C43⋊C8C2312yes—
292C2×#41×C43C2311yescharacteristic
293C2×M16×C43C2311yescharacteristic
294C22×C8×C43C2311yescharacteristic
295C4⋊Q8×C43—21no—
296C4⋊Q8×C43C2312yes—
297#125×C43—21no—
298#125×C43C2312yes—
299C22⋊Q8×C43—22no—
300C4×Q8×C43C2312yes—
301C4×D4×C43—22no—
302C4×D4×C43C2312yes—
303#117×C43—21no—
304#117×C43C2311yescharacteristic
305#117×C43C2311yescharacteristic
306C2×C4⋊C4×C43—21no—
307C2×C4⋊C4×C43C2311yescharacteristic
308C2×C4⋊C4×C43C2311yescharacteristic
309#107×C43C2312yes—
310#107×C43C2312yes—
311#107×C43C2312yes—
312#106×C43C2312yes—
313C4⋊C8×C43C2312yes—
314C4⋊C8×C43C2312yes—
315#103×C43C2311yescharacteristic
316#103×C43C2312yes—
317#103×C43C2311yescharacteristic
318#102×C43C2311yescharacteristic
319#102×C43C2312yes—
320#102×C43C2311yescharacteristic
321C23×D43—21no—
322C23×D43—21no—
323C23×D43—22no—
324C23×D43C2×D411yescharacteristic
325#41×C43—22no—
326#41×C43#4114yes—
327C2×Q8×C43—22no—
328C2×Q8×C43C2411yescharacteristic
329C2×D4×C43—21no—
330C2×D4×C43C2411yescharacteristic
331C22×C4×C43—21no—
332C22×C4×C43—22no—
333C22×C4×C43—21no—
334C22×C4×C43—21no—
335C22×C4×C43C2411yescharacteristic
336C2×C22⋊D43—21no—
337C2×C22⋊D43—22no—
338C2×C22⋊D43—21no—
339C2×C22⋊D43—21no—
340C2×C22⋊D43—21no—
341C2×C22⋊D43C2×D412yes—
342C22×Dic43—21no—
343C22×Dic43—21no—
344C22×Dic43C2×D411yescharacteristic
345#10621902—22no—
346#10621902—24no—
347#10621902—41no—
348#10621902—42no—
349Q8×D43—22no—
350Q8×D43—41no—
351#10621900—22no—
352#10621900—41no—
353#10621900—44no—
354D4×D43—22no—
355D4×D43—24no—
356D4×D43—44no—
357D4×D43—41no—
358D4×D43—42no—
359D4×D43—48no—
360#10621898—22no—
361#10621898—22no—
362#10621898—22no—
363#10621898—22no—
364#10621898—22no—
365#10621898—22no—
366#10621898—44no—
367#10621898—44no—
368C2×D172—21no—
369C2×D172—22no—
370C2×D172—22no—
371C2×D172—22no—
372C2×D172—22no—
373C2×D172—21no—
374C2×D172—22no—
375C2×D172—21no—
376C2×D172—21no—
377C2×D172—22no—
378C2×D172—22no—
379C2×D172—22no—
380C2×D172—22no—
381C2×D172—44no—
382C2×D172—82no—
383C2×D172—84no—
384C2×D172C2×D411yescharacteristic
385C2×D172C2×D412yes—
386C2×D172C2×D412yes—
387C2×D172C2412yes—
388C2×D172C2411yescharacteristic
389C2×D172C2411yescharacteristic
390C2×C4×D43—22no—
391C2×C4×D43—22no—
392C2×C4×D43—21no—
393C2×C4×D43—21no—
394C2×C4×D43—21no—
395C2×C4×D43—22no—
396C2×C4×D43—22no—
397C2×C4×D43—21no—
398C2×C4×D43—22no—
399C2×C4×D43—44no—
400C2×C4×D43C2×D411yescharacteristic
401C2×C4×D43C2×D411yescharacteristic
402C2×C4×D43C2412yes—
403C2×C4×D43C2411yescharacteristic
404C2×C4×D43C2411yescharacteristic
405C2×Dic86—21no—
406C2×Dic86C2×D411yescharacteristic
407C2×Dic86C2411yescharacteristic
408C2×Dic86C2411yescharacteristic
409M16×C43—22no—
410C2×C8×C43—22no—
411C2×C8×C43C2412yes—
412C2×C8×C43C2411yescharacteristic
413C2×C8×C43C2411yescharacteristic
414C4⋊C4×C43—21no—
415C4⋊C4×C43—22no—
416C4⋊C4×C43—21no—
417C4⋊C4×C43—22no—
418C4⋊C4×C43—22no—
419C4⋊C4×C43—22no—
420C4⋊C4×C43C2×D411yescharacteristic
421C4⋊C4×C43C2×D411yescharacteristic
422C4⋊C4×C43C2411yescharacteristic
423C4⋊C4×C43C2412yes—
424C4⋊C4×C43C2411yescharacteristic
425C4⋊C4×C43C2412yes—
426C22⋊C4×C43—22no—
427C22⋊C4×C43—21no—
428C22⋊C4×C43C2×D412yes—
429C42×C43—22no—
430C42×C43—21no—
431C42×C43C2412yes—
432#10621885—22no—
433#10621884—22no—
434#10621883—22no—
435#10621882—22no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—21no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4—22no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—22no—
449(C2×D43)⋊C4—22no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—21no—
452(C2×D43)⋊C4C2×D412yes—
453(C2×D43)⋊C4C2×D412yes—
454(C2×D43)⋊C4C2×D412yes—
455(C2×D43)⋊C4C2×D412yes—
456C4⋊Dic43—21no—
457C4⋊Dic43—21no—
458C4⋊Dic43—21no—
459C4⋊Dic43—22no—
460C4⋊Dic43—22no—
461C4⋊Dic43C2×D412yes—
462C4⋊Dic43C2×D412yes—
463C4⋊Dic43C2412yes—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466C4×Dic43—22no—
467C4×Dic43—22no—
468C4×Dic43—22no—
469C4×Dic43—22no—
470#10621877—22no—
471C2×C43⋊C8—22no—
472C2×C43⋊C8C2411yescharacteristic
473C2×C43⋊C8C2412yes—
474C2×C43⋊C8C2411yescharacteristic
475Dic172—41no—
476D344—41no—
477D344—42no—
478#10621873—41no—
479#10621873—41no—
480#10621873—42no—
481#10621872—42no—
482#10621872—42no—
483C8×D43—42no—
484C8×D43—42no—
485C23×C43—21no—
486C23×C43C22×D411yescharacteristic
487C22×D43—22no—
488C22×D43—21no—
489C22×D43—22no—
490C22×D43—21no—
491C22×D43—41no—
492C22×D43—41no—
493C22×D43—42no—
494C22×D43—42no—
495C22×D43—44no—
496C22×D43—42no—
497C22×D43—81no—
498C22×D43—82no—
499C22×D43—82no—
500C22×D43—81no—
501C22×D43—81no—
502C22×D43C22×D411yescharacteristic
503C22×D43C22×D412yes—
504C22×D43C22×D411yescharacteristic
505Q8×C43—21no—
506Q8×C43—82no—
507Q8×C43C2×#4112yes—
508D4×C43—24no—
509D4×C43—21no—
510D4×C43C2×#4112yes—
511C2×C4×C43—21no—
512C2×C4×C43—24no—
513C2×C4×C43—21no—
514C2×C4×C43—22no—
515C2×C4×C43—21no—
516C2×C4×C43—22no—
517C2×C4×C43—82no—
518C2×C4×C43—81no—
519C2×C4×C43—81no—
520C2×C4×C43C22×D412yes—
521C2×C4×C43C22×D412yes—
522C2×C4×C43C22×D411yescharacteristic
523C2×C4×C43C2×#4112yes—
524C2×C4×C43H(5,𝔽2)12yes—
525C2×C4×C43C2511yescharacteristic
526C22⋊D43—24no—
527C22⋊D43—44no—
528C22⋊D43—42no—
529C22⋊D43—42no—
530C22⋊D43—42no—
531C22⋊D43—42no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—21no—
535C2×Dic43—21no—
536C2×Dic43—42no—
537C2×Dic43—81no—
538C2×Dic43C22×D411yescharacteristic
539C2×Dic43C22×D411yescharacteristic
540C2×Dic43C22×D412yes—
541D172—22no—
542D172—21no—
543D172—22no—
544D172—21no—
545D172—21no—
546D172—22no—
547D172—21no—
548D172—42no—
549D172—42no—
550D172—44no—
551D172—42no—
552D172—44no—
553D172—42no—
554D172—82no—
555D172—82no—
556D172—81no—
557D172—82no—
558D172—81no—
559D172—82no—
560D172—82no—
561C4×D43—22no—
562C4×D43—22no—
563C4×D43—21no—
564C4×D43—21no—
565C4×D43—22no—
566C4×D43—21no—
567C4×D43—22no—
568C4×D43—21no—
569C4×D43—42no—
570C4×D43—44no—
571C4×D43—42no—
572C4×D43—42no—
573C4×D43—42no—
574C4×D43—82no—
575C4×D43—82no—
576Dic86—22no—
577Dic86—21no—
578Dic86—21no—
579Dic86—21no—
580Dic86—21no—
581Dic86—42no—
582C8×C43—21no—
583C8×C43—22no—
584C8×C43—21no—
585C43⋊C8—21no—
586C43⋊C8—21no—
587C43⋊C8—22no—
588#61196—431nomaximal, Sylow
589C22×C43—21no—
590C22×C43—21no—
591C22×C43—22no—
592C22×C43—41no—
593C22×C43—41no—
594C22×C43#54612yes—
595C22×C43C23×D411yescharacteristic
596C2×D43—21no—
597C2×D43—21no—
598C2×D43—22no—
599C2×D43—21no—
600C2×D43—21no—
601C2×D43—22no—
602C2×D43—21no—
603C2×D43—21no—
604C2×D43—22no—
605C2×D43—42no—
606C2×D43—41no—
607C2×D43—41no—
608C2×D43—41no—
609C2×D43—42no—
610C2×D43—41no—
611C2×D43—42no—
612C2×D43—41no—
613C2×D43—41no—
614C2×D43—82no—
615C2×D43—84no—
616C2×D43—164no—
617C2×D43—162no—
618C4×C43—22no—
619C4×C43—22no—
620C4×C43—22no—
621C4×C43—41no—
622C4×C43—42no—
623C4×C43—42no—
624C4×C43—41no—
625C4×C43#54612yes—
626C4×C43C22×#4111yescharacteristic
627C4×C43C2×H(5,𝔽2)11yescharacteristic
628Dic43—22no—
629Dic43—21no—
630Dic43—21no—
631Dic43—42no—
632Dic43—41no—
633Dic43—41no—
634#3493—431no—
635#3488—431no—
636#3326—432no—
637#3324—432no—
638#3319—432no—
639#3318—432no—
640#3317—432no—
641#3313—432no—
642#3305—432no—
643#3296—432no—
644#3136—431no—
645#3099—431no—
646C2×#482—431no—
647#3083D4311yescharacteristic, complemented
648#3061—431no—
649#3055—431no—
650#3045—431no—
651#3012—431no—
652#3002—431no—
653#2952—431no—
654#2933—431no—
655#2897—431no—
656#2896—431no—
657C2×C43—22no—
658C2×C43—42no—
659C2×C43C2×#54611yescharacteristic
660C2×C43#358411yescharacteristic
661C2×C43#358511yescharacteristic
662D43—41no—
663D43—41no—
664D43—42no—
665D43—81no—
666D43—81no—
667D43—82no—
668C2×H(5,𝔽2)—431no—
669C22×#41—431no—
670C2×AGL(1,ℤ/8)—431no—
671C2×#135—431no—
672C2×#135—431no—
673C2×#131—431no—
674C22×M16—431no—
675#556—432no—
676#556—861no—
677#555—432no—
678#555—861no—
679#553—432no—
680#553—861no—
681#552—432no—
682#552—861no—
683#550—432no—
684#548—432no—
685#546—432no—
686#546—862no—
687D42—432no—
688D42—862no—
689#544C2×D4311yescharacteristic, complemented
690#538—862no—
691#537—431no—
692#537—431no—
693#537—861no—
694#535—431no—
695#535—861no—
696#529—862no—
697#525—431no—
698#525—431no—
699#525—861no—
700C2×#121—431no—
701C2×#121—861no—
702#520—431no—
703#520—431no—
704#520C2×D4311yescharacteristic
705C2×#117—431no—
706#490—432no—
707#489—432no—
708#488—432no—
709#486—432no—
710#485—432no—
711#483—432no—
712#482—432no—
713#482—432no—
714#482—432no—
715#482—432no—
716#482—432no—
717#481—432no—
718#479C2×D4312yescomplemented
719#478C2×D4312yescomplemented
720#477C2×D4312yescomplemented
721#474C2×D4312yescomplemented
722#469—432no—
723#468—432no—
724#468—432no—
725#468—432no—
726#467—432no—
727#466—432no—
728#466—432no—
729#465—432no—
730#464—432no—
731#463—432no—
732#460—432no—
733#459—432no—
734#452—431no—
735#452—432no—
736#452—431no—
737#451—431no—
738#450—431no—
739#450—432no—
740#449—431no—
741#449—432no—
742#449—431no—
743#448—431no—
744#447—431no—
745#447—432no—
746#442—432no—
747#441—432no—
748C4×SD16—432no—
749C4×SD16—432no—
750#436—432no—
751#435—432no—
752#435—432no—
753C8×D4—432no—
754#428C2×D4311yescharacteristic, complemented
755C2×#107C2×D4311yescharacteristic, complemented
756C2×#106—431no—
757#424C2×D4311yescharacteristic, complemented
758#419—432no—
759#418—431no—
760#418—432no—
761#418—432no—
762#417—431no—
763#417—431no—
764#417—431no—
765#417—431no—
766#417—432no—
767#417C2×D4311yescharacteristic
768#416—431no—
769#416—432no—
770#416—432no—
771#416—432no—
772#416C2×D4311yescharacteristic
773C2×#102—431no—
774C2×#102—431no—
775C2×#102—432no—
776#408—431no—
777C2×C22⋊C8—431no—
778#405—431no—
779C43#6119611yescharacteristic, complemented, Sylow
780H(5,𝔽2)—864no—
781H(5,𝔽2)—1722no—
782C2×#41—431no—
783C2×#41—432no—
784C2×#41—431no—
785C2×#41—431no—
786C2×#41—431no—
787C2×#41—431no—
788C2×#41—861no—
789C2×#41—861no—
790C2×#41—861no—
791C2×#41—864no—
792C2×#41—1722no—
793C2×#41C22×D4311yescharacteristic
794C22×Q8—431no—
795C22×D4—431no—
796C22×D4—432no—
797C22×D4—431no—
798C22×D4—862no—
799C22×D4—861no—
800C22×D4—861no—
801C22×D4—862no—
802C22×D4—861no—
803C23×C4—431no—
804C23×C4—861no—
805AGL(1,ℤ/8)—1722no—
806#135—864no—
807#135—1722no—
808C2×Q16—431no—
809C2×Q16—431no—
810C2×SD16—431no—
811C2×SD16—431no—
812C2×SD16—431no—
813C2×SD16—431no—
814C2×SD16—432no—
815C2×D8—431no—
816C2×D8—431no—
817C2×D8—432no—
818#131—1722no—
819C2×M16—431no—
820C2×M16—432no—
821C2×M16—432no—
822C2×M16—1722no—
823C2×M16C22×D4311yescharacteristic
824C22×C8—431no—
825C22×C8—432no—
826C22×C8—432no—
827C22×C8C22×D4311yescharacteristic
828C4⋊Q8—21no—
829C4⋊Q8C22×D4312yes—
830#127—432no—
831#127—862no—
832#126—862no—
833#126—862no—
834#126—862no—
835#126—862no—
836#125—21no—
837#125—862no—
838#125C22×D4312yes—
839#124—432no—
840#124—862no—
841#124—862no—
842#124—862no—
843#124—862no—
844#123—432no—
845#123—862no—
846#123—861no—
847#123—862no—
848#123—862no—
849C22⋊Q8—22no—
850C22⋊Q8—431no—
851C22⋊Q8—431no—
852C22⋊Q8—431no—
853C22⋊Q8—431no—
854C22⋊Q8—432no—
855C22⋊Q8—432no—
856C22⋊Q8—862no—
857C22⋊Q8—861no—
858C22⋊Q8—861no—
859#121—431no—
860#121—431no—
861#121—432no—
862#121—432no—
863#121—431no—
864#121—431no—
865#121—432no—
866#121—432no—
867#121—862no—
868#121—862no—
869#121—862no—
870#121—861no—
871#121—861no—
872#121—861no—
873#121—862no—
874#121—861no—
875#121—862no—
876#121—862no—
877#121—862no—
878#121—862no—
879#121—862no—
880#121—861no—
881#121—861no—
882#120—432no—
883#120—862no—
884#120—862no—
885#120—862no—
886#120—861no—
887#120—862no—
888C4×Q8—432no—
889C4×Q8—861no—
890C4×Q8—862no—
891C4×Q8C22×D4312yes—
892C4×D4—22no—
893C4×D4—432no—
894C4×D4—432no—
895C4×D4—432no—
896C4×D4—862no—
897C4×D4—862no—
898C4×D4—861no—
899C4×D4—861no—
900C4×D4—861no—
901C4×D4—862no—
902C4×D4—862no—
903C4×D4—862no—
904C4×D4C22×D4312yes—
905#117—21no—
906#117—432no—
907#117—432no—
908#117—432no—
909#117—862no—
910#117—862no—
911#117—861no—
912#117—861no—
913#117—861no—
914#117C22×D4311yescharacteristic
915#117C22×D4311yescharacteristic
916C2×C4⋊C4—21no—
917C2×C4⋊C4—431no—
918C2×C4⋊C4—432no—
919C2×C4⋊C4—861no—
920C2×C4⋊C4C22×D4311yescharacteristic
921C2×C4⋊C4C22×D4311yescharacteristic
922C2×C22⋊C4—862no—
923C2×C22⋊C4—861no—
924C2×C22⋊C4—861no—
925C2×C42—861no—
926#107C22×D4312yes—
927#107C22×D4312yes—
928#107C22×D4312yes—
929#106—432no—
930#106—432no—
931#106C22×D4312yes—
932C4⋊C8C22×D4312yes—
933C4⋊C8C22×D4312yes—
934#103—432no—
935#103—432no—
936#103—432no—
937#103—431no—
938#103—431no—
939#103—432no—
940#103C22×D4311yescharacteristic
941#103C22×D4312yes—
942#103C22×D4311yescharacteristic
943#102—432no—
944#102—432no—
945#102—432no—
946#102—432no—
947#102—432no—
948#102—432no—
949#102—432no—
950#102—432no—
951#102—432no—
952#102—431no—
953#102—431no—
954#102—432no—
955#102C22×D4311yescharacteristic
956#102C22×D4312yes—
957#102C22×D4311yescharacteristic
958C22⋊C8—431no—
959C22⋊C8—431no—
960C22⋊C8—431no—
961C22⋊C8—431no—
962C22⋊C8—432no—
963C22⋊C8—432no—
964#97—432no—
965C4×C8—432no—
966C24—431no—
967C24—862no—
968C24—861no—
969C24—861no—
970#41—22no—
971#41—862no—
972#41—862no—
973#41—862no—
974#41—864no—
975#41—862no—
976#41—862no—
977#41—862no—
978#41—862no—
979#41—862no—
980#41—1724no—
981#41—1724no—
982#41—1721no—
983#41—1724no—
984#41—1721no—
985#41—1722no—
986#41#1062190214yes—
987C2×Q8—22no—
988C2×Q8—431no—
989C2×Q8—431no—
990C2×Q8—431no—
991C2×Q8—861no—
992C2×Q8—862no—
993C2×Q8—1721no—
994C2×Q8C23×D4311yescharacteristic
995C2×D4—21no—
996C2×D4—432no—
997C2×D4—431no—
998C2×D4—432no—
999C2×D4—432no—
1000C2×D4—432no—
1001C2×D4—431no—
1002C2×D4—431no—
1003C2×D4—861no—
1004C2×D4—861no—
1005C2×D4—862no—
1006C2×D4—862no—
1007C2×D4—862no—
1008C2×D4—862no—
1009C2×D4—862no—
1010C2×D4—861no—
1011C2×D4—861no—
1012C2×D4—862no—
1013C2×D4—862no—
1014C2×D4—864no—
1015C2×D4—861no—
1016C2×D4—861no—
1017C2×D4—861no—
1018C2×D4—862no—
1019C2×D4—862no—
1020C2×D4—861no—
1021C2×D4—862no—
1022C2×D4—862no—
1023C2×D4—3444no—
1024C2×D4—3442no—
1025C2×D4—1724no—
1026C2×D4—1721no—
1027C2×D4—1722no—
1028C2×D4—1728no—
1029C2×D4—1724no—
1030C2×D4C23×D4311yescharacteristic
1031C22×C4—21no—
1032C22×C4—21no—
1033C22×C4—21no—
1034C22×C4—22no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—431no—
1038C22×C4—432no—
1039C22×C4—431no—
1040C22×C4—431no—
1041C22×C4—861no—
1042C22×C4—862no—
1043C22×C4—862no—
1044C22×C4—861no—
1045C22×C4—861no—
1046C22×C4—862no—
1047C22×C4—862no—
1048C22×C4—861no—
1049C22×C4—862no—
1050C22×C4—861no—
1051C22×C4—861no—
1052C22×C4—1724no—
1053C22×C4C23×D4311yescharacteristic
1054Q16—862no—
1055Q16—1721no—
1056SD16—862no—
1057SD16—862no—
1058SD16—1721no—
1059SD16—1721no—
1060SD16—1722no—
1061D8—862no—
1062D8—1721no—
1063D8—1722no—
1064M16—22no—
1065M16—862no—
1066M16—1722no—
1067M16—1722no—
1068C2×C8—22no—
1069C2×C8—431no—
1070C2×C8—432no—
1071C2×C8—431no—
1072C2×C8—862no—
1073C2×C8—1722no—
1074C2×C8—1722no—
1075C2×C8C23×D4311yescharacteristic
1076C2×C8C23×D4311yescharacteristic
1077C2×C8C23×D4312yes—
1078C4⋊C4—21no—
1079C4⋊C4—22no—
1080C4⋊C4—21no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—432no—
1085C4⋊C4—432no—
1086C4⋊C4—432no—
1087C4⋊C4—862no—
1088C4⋊C4—861no—
1089C4⋊C4—861no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—861no—
1093C4⋊C4—862no—
1094C4⋊C4D4×D4311yescharacteristic
1095C4⋊C4D4×D4311yescharacteristic
1096C4⋊C4C23×D4311yescharacteristic
1097C4⋊C4C23×D4312yes—
1098C4⋊C4C23×D4311yescharacteristic
1099C4⋊C4C23×D4312yes—
1100C22⋊C4—21no—
1101C22⋊C4—22no—
1102C22⋊C4—432no—
1103C22⋊C4—432no—
1104C22⋊C4—432no—
1105C22⋊C4—432no—
1106C22⋊C4—862no—
1107C22⋊C4—862no—
1108C22⋊C4—861no—
1109C22⋊C4—862no—
1110C22⋊C4—861no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—862no—
1117C22⋊C4—861no—
1118C22⋊C4—861no—
1119C22⋊C4—862no—
1120C22⋊C4—862no—
1121C22⋊C4—862no—
1122C22⋊C4D4×D4312yes—
1123C42—22no—
1124C42—21no—
1125C42—862no—
1126C42—862no—
1127C42—862no—
1128C42—862no—
1129C42C23×D4312yes—
1130C23—21no—
1131C23—431no—
1132C23—431no—
1133C23—432no—
1134C23—862no—
1135C23—861no—
1136C23—862no—
1137C23—861no—
1138C23—3441no—
1139C23—3441no—
1140C23—3441no—
1141C23—3442no—
1142C23—3442no—
1143C23—1721no—
1144C23—1721no—
1145C23—1722no—
1146C23—1724no—
1147C23—1722no—
1148C23—1722no—
1149C23C2×D4×D4311yescharacteristic
1150Q8—21no—
1151Q8—82no—
1152Q8—862no—
1153Q8—861no—
1154Q8—861no—
1155Q8—861no—
1156Q8—861no—
1157Q8—1722no—
1158Q8C2×#1062190212yes—
1159D4—24no—
1160D4—21no—
1161D4—864no—
1162D4—861no—
1163D4—862no—
1164D4—861no—
1165D4—861no—
1166D4—862no—
1167D4—861no—
1168D4—862no—
1169D4—3442no—
1170D4—3442no—
1171D4—3442no—
1172D4—3442no—
1173D4—3441no—
1174D4—3442no—
1175D4—3441no—
1176D4—1722no—
1177D4—1722no—
1178D4—1724no—
1179D4—1722no—
1180D4—1724no—
1181D4—1724no—
1182D4—1722no—
1183D4—1722no—
1184D4—1722no—
1185D4—1722no—
1186D4—1722no—
1187D4C2×#1062190212yes—
1188C2×C4—21no—
1189C2×C4—24no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—82no—
1195C2×C4—81no—
1196C2×C4—81no—
1197C2×C4—431no—
1198C2×C4—431no—
1199C2×C4—432no—
1200C2×C4—862no—
1201C2×C4—861no—
1202C2×C4—861no—
1203C2×C4—862no—
1204C2×C4—861no—
1205C2×C4—862no—
1206C2×C4—861no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—862no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—3442no—
1213C2×C4—3442no—
1214C2×C4—3441no—
1215C2×C4—1722no—
1216C2×C4—1724no—
1217C2×C4—1722no—
1218C2×C4—1722no—
1219C2×C4—1722no—
1220C2×C4—1722no—
1221C2×C4C2×D4×D4312yes—
1222C2×C4C2×D4×D4312yes—
1223C2×C4C2×D4×D4311yescharacteristic
1224C2×C4C2×#1062190212yes—
1225C2×C4#1306337112yes—
1226C2×C4C24×D4311yescharacteristic
1227C8—21no—
1228C8—21no—
1229C8—22no—
1230C8—861no—
1231C8—861no—
1232C8—862no—
1233C22—21no—
1234C22—21no—
1235C22—22no—
1236C22—41no—
1237C22—41no—
1238C22—861no—
1239C22—861no—
1240C22—862no—
1241C22—862no—
1242C22—861no—
1243C22—861no—
1244C22—861no—
1245C22—862no—
1246C22—861no—
1247C22—3442no—
1248C22—3444no—
1249C22—1721no—
1250C22—1722no—
1251C22—1721no—
1252C22—1721no—
1253C22—1721no—
1254C22—1722no—
1255C22—1721no—
1256C22—1721no—
1257C22—1722no—
1258C22—6882no—
1259C22—6884no—
1260C22#1458354012yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—41no—
1266C4—42no—
1267C4—42no—
1268C4—41no—
1269C4—861no—
1270C4—861no—
1271C4—862no—
1272C4—1721no—
1273C4—1721no—
1274C4—1722no—
1275C4#1458354012yes—
1276C4C22×#1062190211yescharacteristic
1277C4C2×#1306337111yescharacteristic
1278C2—22no—
1279C2—42no—
1280C2—3441no—
1281C2—3442no—
1282C2—3441no—
1283C2—1721no—
1284C2—1721no—
1285C2—1722no—
1286C2C2×#1458354011yescharacteristic
1287C2#1914936511yescharacteristic
1288C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3083C2
socleC22×C43C23×D4
hypercenter#3083D43
hypocenterC43#61196
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #3083

Complements

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

NH ≅ G/Ntype
1. #19148316C2semidirect
2. #19148265C2semidirect
3. #19146845C2semidirect
4. #19146823C2semidirect
5. #19146748C2semidirect
6. #19146733C2semidirect
7. #19146718C2semidirect
8. #19146658C2semidirect
9. #19146542C2semidirect
10. #19146427C2semidirect
11. #19144954C2semidirect
12. #19144588C2semidirect
13. C2×#14583226C2semidirect
14. #19144267C2semidirect
15. #19144215C2semidirect
16. #19144136C2semidirect
17. #19143901C2semidirect
18. #19143815C2semidirect
19. #19143476C2semidirect
20. #19143319C2semidirect
21. #19143117C2semidirect
22. #19143111C2semidirect
23. C43×#3083C2semidirect
26. C2×#13063353C22semidirect
27. C2×#13063347C22semidirect
29. C2×#13063331C22semidirect
30. C2×M16×D43C22semidirect
32. #14583623C22semidirect
34. #14583615C22semidirect
36. #14583602C22semidirect
38. #14583587C22semidirect
48. #14583480C22semidirect
54. #14583411C22semidirect
57. #14583379C22semidirect
58. #14583379C22semidirect
59. C2×#13063283C22semidirect
60. #14583265C22semidirect
61. #14583261C22semidirect
62. #14583256C22semidirect
63. #14583247C22semidirect
64. #14583242C22semidirect
65. #14583231C22semidirect
66. #14583226C22semidirect
67. #14583226C22semidirect
68. #14583226C22semidirect
69. #14583226C22semidirect
70. #14583226C22semidirect
71. #14583219C22semidirect
72. #14583153C22semidirect
73. #14583146C22semidirect
74. #14583146C22semidirect
75. #14583146C22semidirect
76. #14583141C22semidirect
77. #14583136C22semidirect
78. #14583136C22semidirect
79. #14583129C22semidirect
80. #14583122C22semidirect
81. #14583115C22semidirect
82. #14583100C22semidirect
83. #14583095C22semidirect
84. #14583064C22semidirect
85. #14583064C22semidirect
86. #14583062C22semidirect
87. #14583056C22semidirect
88. #14583051C22semidirect
89. #14583051C22semidirect
90. #14583047C22semidirect
91. #14583047C22semidirect
92. #14583045C22semidirect
93. #14583039C22semidirect
94. #14583034C22semidirect
95. #14583034C22semidirect
96. #14583009C22semidirect
97. #14583004C22semidirect
98. C4×#10621884C22semidirect
99. C4×#10621883C22semidirect
100. #14582976C22semidirect
101. #14582969C22semidirect
102. #14582969C22semidirect
103. #14582964C22semidirect
104. C2×#13063256C22semidirect
105. #14582906C22semidirect
106. #14582903C22semidirect
107. #14582902C22semidirect
108. #14582902C22semidirect
109. #14582901C22semidirect
111. #14582899C22semidirect
112. #14582898C22semidirect
113. #14582898C22semidirect
114. #14582894C22semidirect
115. #14582894C22semidirect
116. #14582893C22semidirect
117. #14582892C22semidirect
118. C2×#13063247C22semidirect
119. C2×#13063245C22semidirect
120. #102×D43C22semidirect
121. #14582867C22semidirect
122. C2×(C2×D43)⋊C8C22semidirect
123. #14582855C22semidirect
124. C43×#544C22semidirect
126. C43×#479C22semidirect
127. C43×#478C22semidirect
128. C43×#477C22semidirect
129. C43×#474C22semidirect
130. C43×#428C22semidirect
131. C2×#107×C43C22semidirect
132. C43×#424C22semidirect
647. #3083D43semidirect
689. #544C2×D43semidirect
718. #479C2×D43semidirect
719. #478C2×D43semidirect
720. #477C2×D43semidirect
721. #474C2×D43semidirect
754. #428C2×D43semidirect
755. C2×#107C2×D43semidirect
757. #424C2×D43semidirect
779. C43#61196semidirect

Maximal subgroups

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

subgroupindex
#191483162
#191482652
#191468452
#191468232
#191467482
#191467332
#191467182
#191466582
#191465422
#191464272
#191449542
#191445882
C2×#145832262
#191442672
#191442152
#191441362
#191439012
#191438152
#191434762
#191433192
#191431172
#191431112
C43×#30832
#6119643