Finite Group Databasebeta

← #26010469

Subgroups — #26010469

Order 11008.

10698 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149408C211yesmaximal, characteristic, complemented
2#19149407C211yesmaximal, characteristic, complemented
3#19149383C211yesmaximal, characteristic, complemented
4#19149380C218yesmaximal, complemented
5#19149379C216yesmaximal, complemented
6#19149378C216yesmaximal, complemented
7#19149377C218yesmaximal, complemented
8#19149368C216yesmaximal, complemented
9#19149367C218yesmaximal, complemented
10#19149366C211yesmaximal, characteristic, complemented
11C2×#14583715C216yesmaximal, complemented
12C2×#14583714C211yesmaximal, characteristic, complemented
13#578×D43C218yesmaximal, complemented
14#19149308C211yesmaximal, characteristic, complemented
15C43×#3586C211yesmaximal, characteristic, complemented
16#14583736—24no—
17#14583736C2218yescomplemented
18#14583735—24no—
19#14583735—26no—
20#14583735C2211yescharacteristic
21#14583735C2211yescharacteristic, complemented
22#14583735C2216yescomplemented
23#14583735C2216yescomplemented
24#14583734—26no—
25#14583734C2218yescomplemented
26C2×#13063373—22no—
27C2×#13063373C2216yescomplemented
28C2×#13063372—24no—
29C2×#13063372C2211yescharacteristic, complemented
30C2×#13063372C2216yescomplemented
312−1+4×D43—22no—
322−1+4×D43—24no—
332−1+4×D43C2218yescomplemented
342−1+4×D43C2218yescomplemented
35#14583716C2218yescomplemented
36#14583715C22112yescomplemented
37#14583715C22124yescomplemented
38#14583715C22112yescomplemented
39#14583715C22124yescomplemented
40#14583715C22124yescomplemented
41#14583714C2214yescomplemented
42#14583714C2218yescomplemented
43#14583714C2218yescomplemented
44#14583713C22124yescomplemented
45#14583712C22124yescomplemented
46#14583711C2218yescomplemented
47#14583710C2214yescomplemented
48#14583709C22112yescomplemented
49#14583709C22112yescomplemented
50#14583708C22112yescomplemented
51#14583708C22112yescomplemented
52#14583707C2214yescomplemented
53#14583706C22124yescomplemented
54#14583705C22124yescomplemented
55#14583703C22112yescomplemented
56#14583703C2214yescomplemented
57#14583702C2214yescomplemented
58#14583699C2216yescomplemented
59#14583698C22124yescomplemented
60#14583697C2216yescomplemented
61#14583696C22124yescomplemented
62#14583695C22124yescomplemented
63C2×#13063358C2216yescomplemented
64C2×#13063357C22112yescomplemented
65C2×#13063356C2213yescomplemented
66C2×#13063355C2213yescomplemented
67C2×#13063354C22112yescomplemented
68#137×D43C22124yescomplemented
69#137×D43C22124yescomplemented
70C2×#13063346C22112yescomplemented
71C2×#13063345C2213yescomplemented
72C2×#13063345C2216yescomplemented
73#135×D43C22124yescomplemented
74C22×#10621885C2213yescomplemented
75C2×Q16×D43C22112yescomplemented
76#14583665C2216yescomplemented
77#14583664C2218yescomplemented
78C2×#13063333C2216yescomplemented
79C2×#13063332C2211yescharacteristic, complemented
80#131×D43C2218yescomplemented
81C43×#585C2211yescharacteristic, complemented
82C2×2−1+4×C43C2211yescharacteristic, complemented
83C43×#578C2218yescomplemented
84C43×#577C2218yescomplemented
85C43×#575C2216yescomplemented
86C2×#137×C43C2216yescomplemented
87C43×#568C2211yescharacteristic, complemented
88#13063373—21no—
89#13063373—28no—
90#13063373—28no—
91#13063373—28no—
92#13063373—212no—
93#13063373—212no—
94#13063373D412yes—
95#13063373C23124yes—
96#13063373C23112yes—
97#13063373C23112yes—
98#13063372—24no—
99#13063372—28no—
100#13063372—224no—
101#13063372—224no—
102#13063372—212no—
103#13063372—212no—
104#13063372—26no—
105#13063372—26no—
106#13063372D414yes—
107#13063372C23124yes—
108#13063372C23112yes—
109#13063372C23112yes—
110#13063372C2314yes—
111#13063372C2318yes—
112#13063371—224no—
113#13063371—26no—
114#13063371—26no—
115#13063371D414yes—
116#13063371C23112yes—
117#13063371C2314yes—
118#13063371C2314yes—
119#13063370—23no—
120#13063370—212no—
121#13063370—212no—
122#13063370—224no—
123#13063370D416yes—
124#13063370C23112yes—
125#13063370C2314yes—
126C2×#10621902—28no—
127C2×#10621902—26no—
128C2×#10621902C23112yes—
129C2×#10621898—212no—
130C2×#10621898—212no—
131C2×#10621898—212no—
132C2×#10621898—26no—
133C2×#10621898C2316yes—
134C2×#10621898C2313yes—
135C2×#10621898C2316yes—
136C2×#10621900—23no—
137C2×#10621900—212no—
138C2×#10621900—224no—
139C2×#10621900C23112yes—
140#41×D43—24no—
141#41×D43—28no—
142#41×D43—224no—
143#41×D43—224no—
144#41×D43—224no—
145#41×D43—212no—
146#41×D43—212no—
147#41×D43C23124yes—
148#41×D43C23124yes—
149#41×D43C2318yes—
150C22×Dic86—26no—
151C22×Dic86C2313yes—
152C2×Q8×D43—21no—
153C2×Q8×D43—28no—
154C2×Q8×D43—28no—
155C2×Q8×D43—26no—
156C2×Q8×D43C23112yes—
157C2×Q8×D43C23112yes—
158#13063358C23112yes—
159#13063358C23124yes—
160#13063358C23112yes—
161#13063357C23124yes—
162#13063357C23148yes—
163#13063357C23124yes—
164#13063356C23112yes—
165#13063356C23124yes—
166#13063355C23112yes—
167#13063355C23124yes—
168#13063354C23124yes—
169#13063354C23148yes—
170#13063354C23124yes—
171#13063353C23112yes—
172#13063353C2314yes—
173#13063352C2318yes—
174#13063352C23124yes—
175#13063351C23112yes—
176#13063350C23112yes—
177#13063349C23124yes—
178#13063349C2318yes—
179#13063348C23124yes—
180#13063347C23124yes—
181#13063346C2318yes—
182#13063346C23124yes—
183#13063346C23148yes—
184#13063345C23112yes—
185#13063345C23112yes—
186#13063345C2314yes—
187#13063345C23112yes—
188#13063345C23112yes—
189#13063345C23112yes—
190#13063344C23124yes—
191C2×Dic172C23112yes—
192C2×#10621885C2316yes—
193C2×#10621885C23112yes—
194C2×#10621885C2313yes—
195C2×#10621885C23112yes—
196C2×#10621885C2316yes—
197Q16×D43C23124yes—
198Q16×D43C23148yes—
199C2×#10621873C23112yes—
200C2×#10621883C2316yes—
201C2×#10621883C2313yes—
202C2×#10621884C2313yes—
203C2×#10621884C2316yes—
204SD16×D43C23124yes—
205SD16×D43C23124yes—
206C2×#10621882C2311yescharacteristic
207C2×#10621882C2316yes—
208D8×D43C2318yes—
209#13063333C23112yes—
210#13063333C2314yes—
211#13063333C23112yes—
212#13063333C23112yes—
213#13063332C2314yes—
214#13063332C2314yes—
215#13063331C23124yes—
216C2×#10621877C2313yes—
217C2×#10621872C23112yes—
218M16×D43C23124yes—
219C22×C43⋊C8C2313yes—
220C2×C8×D43C23112yes—
2212−1+4×C43—24no—
2222−1+4×C43—21no—
2232−1+4×C43C2318yes—
2242−1+4×C43C2314yes—
225H(5,𝔽2)×C43—23no—
226H(5,𝔽2)×C43C2314yes—
227C2×#41×C43—24no—
228C2×#41×C43—23no—
229C2×#41×C43C2316yes—
230C2×#41×C43C2313yes—
231C2×#41×C43C2311yescharacteristic
232C22×Q8×C43—21no—
233C22×Q8×C43C2313yes—
234#137×C43C23112yes—
235#137×C43C23124yes—
236#137×C43C23112yes—
237AGL(1,ℤ/8)×C43C2314yes—
238AGL(1,ℤ/8)×C43C23112yes—
239#135×C43C23124yes—
240C2×Q16×C43C23112yes—
241C2×SD16×C43C23112yes—
242#131×C43C2318yes—
243C2×M16×C43C2316yes—
244#41×C43—24no—
245#41×C43—212no—
246#41×C43—224no—
247#41×C43—26no—
248#41×C43—26no—
249#41×C43—26no—
250#41×C43C2×D414yes—
251#41×C43C24112yes—
252#41×C43C24112yes—
253#41×C43C2414yes—
254#41×C43C2414yes—
255C2×Q8×C43—28no—
256C2×Q8×C43—24no—
257C2×Q8×C43—23no—
258C2×Q8×C43—26no—
259C2×Q8×C43C2×D411yescharacteristic
260C2×Q8×C43C24112yes—
261C2×Q8×C43C2416yes—
262C2×Q8×C43C2413yes—
263C2×D4×C43—212no—
264C2×D4×C43—23no—
265C2×D4×C43—26no—
266C2×D4×C43C2×D413yes—
267C2×D4×C43C2416yes—
268C2×D4×C43C2411yescharacteristic
269C22×C4×C43—23no—
270C22×C4×C43—26no—
271C22×C4×C43—23no—
272C22×C4×C43C2413yes—
273C2×C22⋊D43—224no—
274C2×C22⋊D43—28no—
275C2×C22⋊D43—23no—
276C2×C22⋊D43—26no—
277C2×C22⋊D43—212no—
278C2×C22⋊D43C2×D4112yes—
279C22×Dic43—212no—
280C22×Dic43—23no—
281#10621902—24no—
282#10621902—212no—
283#10621902—212no—
284#10621902—224no—
285#10621902—224no—
286#10621902C2×D418yes—
287#10621902C24124yes—
288#10621902C2418yes—
289Q8×D43—28no—
290Q8×D43—24no—
291Q8×D43—224no—
292Q8×D43—224no—
293Q8×D43—212no—
294Q8×D43—212no—
295Q8×D43—224no—
296Q8×D43C2×D418yes—
297Q8×D43C24124yes—
298Q8×D43C24124yes—
299#10621900—212no—
300#10621900—224no—
301#10621900—224no—
302#10621900—224no—
303#10621900—248no—
304#10621900—224no—
305#10621900—224no—
306#10621900—224no—
307#10621900—24no—
308#10621900—212no—
309#10621900C2×D4124yes—
310#10621900C2418yes—
311#10621900C24124yes—
312D4×D43—212no—
313D4×D43—28no—
314D4×D43—224no—
315D4×D43—212no—
316D4×D43—24no—
317D4×D43—224no—
318D4×D43—224no—
319D4×D43C2×D4124yes—
320D4×D43C2418yes—
321D4×D43C2418yes—
322#10621898—26no—
323#10621898—26no—
324#10621898—26no—
325#10621898—224no—
326#10621898—248no—
327#10621898—224no—
328#10621898—224no—
329#10621898—212no—
330#10621898—212no—
331#10621898—224no—
332#10621898—224no—
333#10621898—212no—
334#10621898—24no—
335#10621898C2×D4112yes—
336#10621898C2×D4112yes—
337#10621898C24112yes—
338#10621898C2414yes—
339#10621898C2414yes—
340#10621898C24112yes—
341#10621898C24112yes—
342C2×D172—24no—
343C2×D172—212no—
344C2×D172—212no—
345C2×D172C2×D416yes—
346C2×D172C2411yescharacteristic
347C2×D172C2416yes—
348C2×C4×D43—23no—
349C2×C4×D43—26no—
350C2×C4×D43—212no—
351C2×C4×D43—224no—
352C2×C4×D43—224no—
353C2×C4×D43—212no—
354C2×C4×D43—212no—
355C2×C4×D43C24112yes—
356C2×Dic86—23no—
357C2×Dic86—26no—
358C2×Dic86—212no—
359C2×Dic86—212no—
360C2×Dic86—212no—
361C2×Dic86—224no—
362C2×Dic86—212no—
363C2×Dic86C2×D416yes—
364C2×Dic86C2413yes—
365C2×Dic86C2416yes—
366C2×Dic86C24112yes—
367Q16×C43C24124yes—
368SD16×C43C24124yes—
369SD16×C43C2418yes—
370D8×C43C2418yes—
371M16×C43C2414yes—
372M16×C43C24112yes—
373C2×C8×C43C24112yes—
374#10621885C2414yes—
375#10621885C2416yes—
376#10621885C24112yes—
377#10621885C24124yes—
378#10621885C2416yes—
379#10621884C24112yes—
380#10621884C24112yes—
381#10621884C2414yes—
382#10621883C24112yes—
383#10621883C24112yes—
384#10621883C2414yes—
385#10621882C2412yes—
386#10621882C2414yes—
387#10621882C2412yes—
388#10621882C24112yes—
389#10621877C24112yes—
390C2×C43⋊C8C2416yes—
391C2×C43⋊C8C2411yescharacteristic
392C2×C43⋊C8C2416yes—
393C2×C43⋊C8C2413yes—
394Dic172C24124yes—
395D344C2418yes—
396#10621873C2418yes—
397#10621873C24124yes—
398#10621872C24124yes—
399#10621872C2418yes—
400C8×D43C2418yes—
401C8×D43C24124yes—
402C23×C43—26no—
403C23×C43—21no—
404C23×C43C22×D413yes—
405C22×D43—26no—
406C22×D43—21no—
407C22×D43—28no—
408C22×D43—28no—
409C22×D43C22×D4112yes—
410Q8×C43—26no—
411Q8×C43—23no—
412Q8×C43—212no—
413Q8×C43C22×D414yes—
414Q8×C43C2514yes—
415Q8×C43C2516yes—
416D4×C43—212no—
417D4×C43—212no—
418D4×C43—24no—
419D4×C43—21no—
420D4×C43—26no—
421D4×C43C22×D4112yes—
422D4×C43C2514yes—
423D4×C43C2512yes—
424C2×C4×C43—26no—
425C2×C4×C43—212no—
426C2×C4×C43—23no—
427C2×C4×C43—24no—
428C2×C4×C43—212no—
429C2×C4×C43—212no—
430C2×C4×C43C22×D416yes—
431C2×C4×C43C22×D413yes—
432C2×C4×C43C2511yescharacteristic
433C2×C4×C43C2516yes—
434C22⋊D43—24no—
435C22⋊D43—212no—
436C22⋊D43—212no—
437C22⋊D43—28no—
438C22⋊D43—224no—
439C22⋊D43—28no—
440C22⋊D43—28no—
441C22⋊D43C22×D418yes—
442C22⋊D43C22×D4124yes—
443C2×Dic43—26no—
444C2×Dic43—212no—
445C2×Dic43—23no—
446C2×Dic43—28no—
447C2×Dic43—224no—
448C2×Dic43C22×D4112yes—
449D172—224no—
450D172—28no—
451D172—21no—
452D172—26no—
453D172C22×D414yes—
454D172C22×D4112yes—
455D172C2514yes—
456D172C2512yes—
457C4×D43—224no—
458C4×D43—224no—
459C4×D43—212no—
460C4×D43—24no—
461C4×D43—212no—
462C4×D43—28no—
463C4×D43—224no—
464C4×D43C22×D4124yes—
465C4×D43C2518yes—
466Dic86—23no—
467Dic86—212no—
468Dic86—26no—
469Dic86—224no—
470Dic86—224no—
471Dic86C22×D414yes—
472Dic86C22×D4112yes—
473Dic86C2516yes—
474Dic86C2514yes—
475C8×C43C2518yes—
476C43⋊C8C2511yescharacteristic
477C43⋊C8C2516yes—
478C43⋊C8C2511yescharacteristic
479#63093—431nomaximal, Sylow
480C22×C43—22no—
481C22×C43—24no—
482C22×C43—43no—
483C22×C43—86no—
484C22×C43—81no—
485C22×C43C23×D416yes—
486C22×C43C23×D411yescharacteristic
487C2×D43—24no—
488C2×D43—22no—
489C2×D43—412no—
490C2×D43—88no—
491C2×D43—88no—
492C2×D43—86no—
493C2×D43—81no—
494C2×D43C23×D418yes—
495C4×C43—24no—
496C4×C43—26no—
497C4×C43C23×D411yescharacteristic
498C4×C43C23×D416yes—
499C4×C43C2611yescharacteristic
500Dic43—24no—
501Dic43—26no—
502Dic43C23×D418yes—
5032−1+6—431no—
5042−1+6—431no—
505#3586—438no—
506#3586—438no—
507#3586—436no—
508#3586—436no—
509#3586—431no—
510#3586D4311yescharacteristic, complemented
511#3584—431no—
512#3584—438no—
513#3584—436no—
514C2×#578—431no—
515C2×#578—438no—
516C2×#578—436no—
517#3573—431no—
518C2×C43—26no—
519C2×C43—21no—
520C2×C43—42no—
521C2×C43—44no—
522C2×C43C24×D411yescharacteristic
523D43—28no—
524D43—44no—
525D43—42no—
526#585—431no—
527#585—438no—
528#585—438no—
529#585—436no—
530#585—436no—
531#585—431no—
532#585—864no—
533#585—866no—
534#585—866no—
535#585—864no—
536#585C2×D4311yescharacteristic, complemented
537C2×2−1+4—438no—
538C2×2−1+4—438no—
539C2×2−1+4—436no—
540C2×2−1+4—431no—
541C2×2−1+4—436no—
542C2×2−1+4—862no—
543C2×2−1+4—864no—
544C2×2−1+4—864no—
545C2×2−1+4—862no—
546C2×2−1+4C2×D4311yescharacteristic, complemented
547#578—434no—
548#578—438no—
549#578—438no—
550#578—4312no—
551#578—4324no—
552#578—4312no—
553#578—4324no—
554#578—4324no—
555#578—4324no—
556#578—4324no—
557#578—438no—
558#578C2×D4318yescomplemented
559#577—434no—
560#577—434no—
561#577—4312no—
562#577—4312no—
563#577—4312no—
564#577—4312no—
565#577—4324no—
566#577—4324no—
567#577—438no—
568#577C2×D4318yescomplemented
569#576—434no—
570#576—4312no—
571#576—434no—
572#575—436no—
573#575—4324no—
574#575—4324no—
575#575—4324no—
576#575—436no—
577#575C2×D4316yescomplemented
578C2×#137—433no—
579C2×#137—433no—
580C2×#137—4324no—
581C2×#137—4324no—
582C2×#137—4312no—
583C2×#137—4312no—
584C2×#137—436no—
585C2×#137C2×D4316yescomplemented
586C2×#135—433no—
587C2×#135—436no—
588C2×#135—4324no—
589C2×#135—4312no—
590C22×Q16—433no—
591C22×Q16—4312no—
592#568—438no—
593#568—436no—
594#568C2×D4311yescharacteristic, complemented
595C2×#131—431no—
596C2×#131—438no—
597C2×#131—436no—
598C43#6309311yescharacteristic, complemented, Sylow
5992−1+4—24no—
6002−1+4—21no—
6012−1+4—434no—
6022−1+4—432no—
6032−1+4—4312no—
6042−1+4—4324no—
6052−1+4—4312no—
6062−1+4—434no—
6072−1+4—438no—
6082−1+4—4312no—
6092−1+4—4312no—
6102−1+4—4324no—
6112−1+4—868no—
6122−1+4—868no—
6132−1+4—868no—
6142−1+4—8612no—
6152−1+4—8612no—
6162−1+4—868no—
6172−1+4—866no—
6182−1+4—866no—
6192−1+4—8624no—
6202−1+4—8624no—
6212−1+4—8612no—
6222−1+4—8612no—
6232−1+4—864no—
6242−1+4—861no—
6252−1+4C22×D4314yes—
6262−1+4C22×D4318yes—
627H(5,𝔽2)—23no—
628H(5,𝔽2)—434no—
629H(5,𝔽2)—436no—
630H(5,𝔽2)—434no—
631H(5,𝔽2)—4312no—
632H(5,𝔽2)—434no—
633H(5,𝔽2)—434no—
634H(5,𝔽2)—4312no—
635H(5,𝔽2)—8612no—
636H(5,𝔽2)—8612no—
637H(5,𝔽2)—8624no—
638H(5,𝔽2)—8624no—
639H(5,𝔽2)—866no—
640H(5,𝔽2)—866no—
641H(5,𝔽2)—863no—
642H(5,𝔽2)C22×D4314yes—
643C2×#41—24no—
644C2×#41—23no—
645C2×#41—438no—
646C2×#41—436no—
647C2×#41—4324no—
648C2×#41—4324no—
649C2×#41—4312no—
650C2×#41—4312no—
651C2×#41—433no—
652C2×#41—436no—
653C2×#41—8612no—
654C2×#41—866no—
655C2×#41—8612no—
656C2×#41—8612no—
657C2×#41—8612no—
658C2×#41—8624no—
659C2×#41—866no—
660C2×#41—8624no—
661C2×#41—8624no—
662C2×#41—868no—
663C2×#41—868no—
664C2×#41—8624no—
665C2×#41—8612no—
666C2×#41—8612no—
667C2×#41—864no—
668C2×#41—863no—
669C2×#41C22×D4313yes—
670C2×#41C22×D4316yes—
671C2×#41C22×D4311yescharacteristic
672C22×Q8—21no—
673C22×Q8—4312no—
674C22×Q8—4312no—
675C22×Q8—433no—
676C22×Q8—866no—
677C22×Q8—868no—
678C22×Q8—868no—
679C22×Q8—866no—
680C22×Q8—861no—
681C22×Q8C22×D4313yes—
682#137—4312no—
683#137—4324no—
684#137—4312no—
685#137—4324no—
686#137—4324no—
687#137—4348no—
688#137—4324no—
689#137—4324no—
690#137—4348no—
691#137—4324no—
692#137—4312no—
693#137—4324no—
694#137—4312no—
695#137C22×D43112yes—
696#137C22×D43124yes—
697#137C22×D43112yes—
698AGL(1,ℤ/8)—4312no—
699AGL(1,ℤ/8)—4312no—
700AGL(1,ℤ/8)—438no—
701AGL(1,ℤ/8)—4324no—
702AGL(1,ℤ/8)—4324no—
703AGL(1,ℤ/8)—438no—
704AGL(1,ℤ/8)—4312no—
705AGL(1,ℤ/8)—434no—
706AGL(1,ℤ/8)C22×D43112yes—
707AGL(1,ℤ/8)C22×D4314yes—
708#135—434no—
709#135—4312no—
710#135—4312no—
711#135—4312no—
712#135—4312no—
713#135—4312no—
714#135—4324no—
715#135—438no—
716#135—4324no—
717#135—4348no—
718#135—4324no—
719#135—4324no—
720#135C22×D43124yes—
721C2×Q16—433no—
722C2×Q16—436no—
723C2×Q16—4312no—
724C2×Q16—436no—
725C2×Q16—4312no—
726C2×Q16—4324no—
727C2×Q16—4348no—
728C2×Q16—4312no—
729C2×Q16C22×D43112yes—
730C2×SD16—433no—
731C2×SD16—436no—
732C2×SD16—433no—
733C2×SD16—436no—
734C2×SD16—4324no—
735C2×SD16—4324no—
736C2×SD16—4312no—
737C2×SD16C22×D43112yes—
738C2×D8—431no—
739C2×D8—436no—
740C2×D8—438no—
741#131—434no—
742#131—434no—
743#131—4312no—
744#131—434no—
745#131—4312no—
746#131—4312no—
747#131—4324no—
748#131C22×D4318yes—
749C2×M16—433no—
750C2×M16—4324no—
751C2×M16—4312no—
752C2×M16C22×D4316yes—
753C22×C8—433no—
754C22×C8—4312no—
755#41—24no—
756#41—212no—
757#41—224no—
758#41—26no—
759#41—26no—
760#41—26no—
761#41—438no—
762#41—4324no—
763#41—4312no—
764#41—4312no—
765#41—434no—
766#41—4312no—
767#41—438no—
768#41—4324no—
769#41—4324no—
770#41—438no—
771#41—434no—
772#41—4312no—
773#41—4312no—
774#41—8624no—
775#41—8624no—
776#41—8624no—
777#41—8624no—
778#41—8648no—
779#41—8612no—
780#41—8624no—
781#41—8612no—
782#41—864no—
783#41—8612no—
784#41—8624no—
785#41—8624no—
786#41—8624no—
787#41—8624no—
788#41—8624no—
789#41—8648no—
790#41—8624no—
791#41—8612no—
792#41—864no—
793#41—8612no—
794#41—8624no—
795#41—8612no—
796#41—864no—
797#41—8624no—
798#41—8612no—
799#41—866no—
800#41—866no—
801#41—866no—
802#41D4×D4314yes—
803#41C23×D4314yes—
804#41C23×D43112yes—
805#41C23×D43112yes—
806#41C23×D4314yes—
807C2×Q8—28no—
808C2×Q8—24no—
809C2×Q8—23no—
810C2×Q8—26no—
811C2×Q8—438no—
812C2×Q8—436no—
813C2×Q8—4324no—
814C2×Q8—4324no—
815C2×Q8—433no—
816C2×Q8—436no—
817C2×Q8—4312no—
818C2×Q8—8612no—
819C2×Q8—8612no—
820C2×Q8—8612no—
821C2×Q8—8624no—
822C2×Q8—8612no—
823C2×Q8—8624no—
824C2×Q8—8624no—
825C2×Q8—8624no—
826C2×Q8—8612no—
827C2×Q8—8612no—
828C2×Q8—864no—
829C2×Q8—868no—
830C2×Q8—866no—
831C2×Q8—863no—
832C2×Q8D4×D4311yescharacteristic
833C2×Q8C23×D4313yes—
834C2×Q8C23×D4316yes—
835C2×Q8C23×D43112yes—
836C2×D4—23no—
837C2×D4—26no—
838C2×D4—212no—
839C2×D4—4312no—
840C2×D4—4324no—
841C2×D4—438no—
842C2×D4—438no—
843C2×D4—436no—
844C2×D4—431no—
845C2×D4—436no—
846C2×D4—864no—
847C2×D4—8612no—
848C2×D4—8612no—
849C2×D4—868no—
850C2×D4—8624no—
851C2×D4—8612no—
852C2×D4—864no—
853C2×D4—8624no—
854C2×D4—8624no—
855C2×D4—868no—
856C2×D4—8624no—
857C2×D4—8612no—
858C2×D4—866no—
859C2×D4—863no—
860C2×D4—8612no—
861C2×D4D4×D4313yes—
862C2×D4C23×D4311yescharacteristic
863C2×D4C23×D4316yes—
864C22×C4—23no—
865C22×C4—23no—
866C22×C4—26no—
867C22×C4—4312no—
868C22×C4—8612no—
869C22×C4—8624no—
870C22×C4—8624no—
871C22×C4—8612no—
872C22×C4—8612no—
873C22×C4—8612no—
874C22×C4—863no—
875C22×C4—866no—
876C22×C4—863no—
877C22×C4C23×D4313yes—
878Q16—434no—
879Q16—436no—
880Q16—4312no—
881Q16—436no—
882Q16—4324no—
883Q16—4324no—
884Q16C23×D43124yes—
885SD16—434no—
886SD16—4312no—
887SD16—4312no—
888SD16—434no—
889SD16—4312no—
890SD16—4312no—
891SD16—438no—
892SD16—4324no—
893SD16C23×D4318yes—
894SD16C23×D43124yes—
895D8—434no—
896D8—432no—
897D8—4312no—
898D8—432no—
899D8—438no—
900D8C23×D4318yes—
901M16—4312no—
902M16—4324no—
903M16—438no—
904M16C23×D43112yes—
905M16C23×D4314yes—
906C2×C8—431no—
907C2×C8—436no—
908C2×C8—433no—
909C2×C8—436no—
910C2×C8—438no—
911C2×C8—4324no—
912C2×C8C23×D43112yes—
913C23—21no—
914C23—26no—
915C23—4312no—
916C23—868no—
917C23—868no—
918C23—866no—
919C23—861no—
920C23C2×D4×D4313yes—
921Q8—212no—
922Q8—23no—
923Q8—26no—
924Q8—4312no—
925Q8—434no—
926Q8—434no—
927Q8—436no—
928Q8—8624no—
929Q8—8624no—
930Q8—866no—
931Q8—8612no—
932Q8—863no—
933Q8C2×D4×D4314yes—
934Q8C24×D4314yes—
935Q8C24×D4316yes—
936D4—212no—
937D4—24no—
938D4—212no—
939D4—26no—
940D4—21no—
941D4—4324no—
942D4—438no—
943D4—4312no—
944D4—434no—
945D4—434no—
946D4—432no—
947D4—868no—
948D4—8624no—
949D4—868no—
950D4—868no—
951D4—868no—
952D4—8624no—
953D4—8612no—
954D4—8612no—
955D4—864no—
956D4—866no—
957D4—861no—
958D4C2×D4×D43112yes—
959D4C24×D4314yes—
960D4C24×D4312yes—
961C2×C4—23no—
962C2×C4—26no—
963C2×C4—212no—
964C2×C4—24no—
965C2×C4—212no—
966C2×C4—212no—
967C2×C4—4312no—
968C2×C4—4324no—
969C2×C4—438no—
970C2×C4—868no—
971C2×C4—8624no—
972C2×C4—8624no—
973C2×C4—8624no—
974C2×C4—868no—
975C2×C4—8624no—
976C2×C4—866no—
977C2×C4—8612no—
978C2×C4—863no—
979C2×C4—8612no—
980C2×C4—8612no—
981C2×C4—864no—
982C2×C4C2×D4×D4316yes—
983C2×C4C2×D4×D4313yes—
984C2×C4C24×D4311yescharacteristic
985C2×C4C24×D4316yes—
986C8—431no—
987C8—431no—
988C8—436no—
989C8C24×D4318yes—
990C22—22no—
991C22—24no—
992C22—43no—
993C22—81no—
994C22—86no—
995C22—438no—
996C22—864no—
997C22—862no—
998C22—3441no—
999C22—3446no—
1000C22—3448no—
1001C22—3448no—
1002C22—17212no—
1003C22C22×D4×D4316yes—
1004C22C22×D4×D4311yescharacteristic
1005C4—24no—
1006C4—26no—
1007C4—438no—
1008C4—864no—
1009C4—866no—
1010C4C22×D4×D4316yes—
1011C4C22×D4×D4311yescharacteristic
1012C4C25×D4311yescharacteristic
1013C2—21no—
1014C2—26no—
1015C2—44no—
1016C2—42no—
1017C2—868no—
1018C2—1724no—
1019C2—1722no—
1020C2C23×D4×D4311yescharacteristic
subgroupG/H
centerC2C23×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC43×#3586C2
socleC2×C43C24×D4
hypercenter#3586D43
hypocenterC43#63093
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×#41 ◁ #3586

Complements

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

NH ≅ G/Ntype
1. #19149408C2semidirect
2. #19149407C2semidirect
3. #19149383C2semidirect
4. #19149380C2semidirect
5. #19149379C2semidirect
6. #19149378C2semidirect
7. #19149377C2semidirect
8. #19149368C2semidirect
9. #19149367C2semidirect
10. #19149366C2semidirect
11. C2×#14583715C2semidirect
12. C2×#14583714C2semidirect
13. #578×D43C2semidirect
14. #19149308C2semidirect
15. C43×#3586C2semidirect
17. #14583736C22semidirect
21. #14583735C22semidirect
22. #14583735C22semidirect
23. #14583735C22semidirect
25. #14583734C22semidirect
27. C2×#13063373C22semidirect
29. C2×#13063372C22semidirect
30. C2×#13063372C22semidirect
33. 2−1+4×D43C22semidirect
34. 2−1+4×D43C22semidirect
35. #14583716C22semidirect
36. #14583715C22semidirect
37. #14583715C22semidirect
38. #14583715C22semidirect
39. #14583715C22semidirect
40. #14583715C22semidirect
41. #14583714C22semidirect
42. #14583714C22semidirect
43. #14583714C22semidirect
44. #14583713C22semidirect
45. #14583712C22semidirect
46. #14583711C22semidirect
47. #14583710C22semidirect
48. #14583709C22semidirect
49. #14583709C22semidirect
50. #14583708C22semidirect
51. #14583708C22semidirect
52. #14583707C22semidirect
53. #14583706C22semidirect
54. #14583705C22semidirect
55. #14583703C22semidirect
56. #14583703C22semidirect
57. #14583702C22semidirect
58. #14583699C22semidirect
59. #14583698C22semidirect
60. #14583697C22semidirect
61. #14583696C22semidirect
62. #14583695C22semidirect
63. C2×#13063358C22semidirect
64. C2×#13063357C22semidirect
65. C2×#13063356C22semidirect
66. C2×#13063355C22semidirect
67. C2×#13063354C22semidirect
68. #137×D43C22semidirect
69. #137×D43C22semidirect
70. C2×#13063346C22semidirect
71. C2×#13063345C22semidirect
72. C2×#13063345C22semidirect
73. #135×D43C22semidirect
74. C22×#10621885C22semidirect
75. C2×Q16×D43C22semidirect
76. #14583665C22semidirect
77. #14583664C22semidirect
78. C2×#13063333C22semidirect
79. C2×#13063332C22semidirect
80. #131×D43C22semidirect
81. C43×#585C22semidirect
82. C2×2−1+4×C43C22semidirect
83. C43×#578C22semidirect
84. C43×#577C22semidirect
85. C43×#575C22semidirect
86. C2×#137×C43C22semidirect
87. C43×#568C22semidirect
510. #3586D43semidirect
536. #585C2×D43semidirect
546. C2×2−1+4C2×D43semidirect
558. #578C2×D43semidirect
568. #577C2×D43semidirect
577. #575C2×D43semidirect
585. C2×#137C2×D43semidirect
594. #568C2×D43semidirect
598. C43#63093semidirect

Maximal subgroups

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

subgroupindex
#191494082
#191494072
#191493832
#191493802
#191493792
#191493782
#191493772
#191493682
#191493672
#191493662
C2×#145837152
C2×#145837142
#578×D432
#191493082
C43×#35862
#6309343