Finite Group Databasebeta

← #72343015

Subgroups — #72343015

Order 1024.

2545 conjugacy classes of subgroups.

The subgroup lattice has 1135 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623096C211yesmaximal, characteristic
2#6345726C211yesmaximal, characteristic, complemented
3C2×#18044C211yesmaximal, characteristic, complemented
4#484110C214yesmaximal, complemented
5#484106C214yesmaximal, complemented
6#484058C214yesmaximal, complemented
7#484057C214yesmaximal, complemented
8#483924C214yesmaximal, complemented
9#483878C214yesmaximal, complemented
10#483443C211yesmaximal, characteristic, complemented
11#481386C211yesmaximal, characteristic, complemented
12#481279C211yesmaximal, characteristic, complemented
13#479974C211yesmaximal, characteristic, complemented
14#60673C2211yescharacteristic
15#60292—21no—
16C22×C4×D8C2211yescharacteristic
17C2×D4×M16—21no—
18#33674C2212yes—
19#33674C2212yes—
20#33670C2212yes—
21#33669C2212yes—
22#33665C414yes—
23#33661C411yescharacteristic
24#33661C411yescharacteristic
25#33660C411yescharacteristic
26#33660C411yescharacteristic
27#33646C412yes—
28#33627C412yes—
29#33580C412yes—
30#33517C412yes—
31C4×#509C2214yes—
32#33418C2211yescharacteristic
33#33418C2211yescharacteristic
34#18091C2212yescomplemented
35#18090C2212yescomplemented
36#18089—22no—
37#18065C2212yescomplemented
38#18063C2212yescomplemented
39#18061—22no—
40#18044—22no—
41#18044—22no—
42#18044C2214yes—
43#18044C2214yes—
44#17978—22no—
45#17963C2214yescomplemented
46C2×#1594C2212yes—
47C2×#1586—22no—
48C2×#1580C2212yes—
49#17793C2211yescharacteristic
50C2×#1566C2211yescharacteristic
51#17503—21no—
52C2×#1486—21no—
53C2×#1451C2211yescharacteristic
54#12089C2218yescomplemented
55#12087C2218yescomplemented
56#12080C2218yescomplemented
57#12078C2218yescomplemented
58#12078C2218yescomplemented
59#12077C2218yescomplemented
60#12067C2218yescomplemented
61#12065C2218yescomplemented
62#12029C2214yescomplemented
63#12028C2214yescomplemented
64#12020C2212yescomplemented
65#12020C2212yescomplemented
66#11681C2212yescomplemented
67#11680C2212yescomplemented
68#11667C2212yes—
69#11667C2212yes—
70#11666C2214yescomplemented
71#11663C2212yes—
72#11663C2212yes—
73#11651C2214yescomplemented
74#11599C2214yes—
75#11415C2214yescomplemented
76#11414C2214yescomplemented
77#11414C2214yescomplemented
78C23×D8C2×C411yescharacteristic
79C23×M16—41no—
80#3444—21no—
81C22×C4×D4—21no—
82C2×#509C2×C414yes—
83#3170C2×C411yescharacteristic
84#3170C2311yescharacteristic
85#3169C2×C411yescharacteristic
86#3169C2311yescharacteristic
87#3168—21no—
88#3168—21no—
89#3168C2×C412yes—
90#3168C2312yes—
91#3167—21no—
92#3167—21no—
93#3160C2×C411yescharacteristic
94#3147C2×C411yescharacteristic
95#3131—21no—
96#3050—21no—
97#3050C2×C412yes—
98#2991—22no—
99#2990—22no—
100#2989—41no—
101#2988—41no—
102#2986—22no—
103#2979—22no—
104#2976—42no—
105#2969—42no—
106#2966—24no—
107C4×#135—21no—
108C4×#135C2312yes—
109C2×C4×D8—21no—
110C2×C4×D8—21no—
111C2×C4×D8—21no—
112C2×C4×D8—21no—
113C2×C4×D8—21no—
114C2×C4×D8—21no—
115C2×C4×D8C2×C412yes—
116C2×C4×D8C2×C411yescharacteristic
117C2×C4×D8C2×C411yescharacteristic
118C2×C4×D8C2×C412yes—
119C2×C4×D8C2312yes—
120C2×C4×D8C2312yes—
121C2×C4×D8C2311yescharacteristic
122C2×C4×D8C2311yescharacteristic
123D4×M16—24no—
124D4×M16—24no—
125D4×M16—42no—
126D4×M16—42no—
127C2×#436—22no—
128C2×#435—42no—
129C2×C8×D4—22no—
130#2925—42no—
131#2920—21no—
132C2×#431D411yescharacteristic
133C22×#107C2×C411yescharacteristic
134C2×#423—21no—
135C22×#102—21no—
136C2×#407—41no—
137C2×C4×M16D411yescharacteristic
138C22×C4×C8C2311yescharacteristic
139#2236C2×C414yes—
140#2235C2×C412yes—
141#2235C2×C412yes—
142#2233C2×C414yes—
143#2232C2×C412yes—
144#2232C2×C412yes—
145#2228C2×C414yes—
146#2228C2×C414yes—
147#2226C2×C412yes—
148#2226C2×C412yes—
149#2224C2×C412yes—
150#2224C2×C412yes—
151#2210C2×C414yes—
152#2210C2×C414yes—
153#2208C2×C412yes—
154#2208C2×C412yes—
155#2206C2×C412yes—
156#2206C2×C412yes—
157#2187C2×C412yes—
158#2187C2×C412yes—
159#2187C2×C414yes—
160#2184C2×C412yes—
161#2184C2×C412yes—
162#2184C2×C414yes—
163#2177C2314yes—
164#2177C2314yes—
165#2175C2314yes—
166#2175C2314yes—
167C4×SD32C2×C414yes—
168C4×SD32C2×C414yes—
169C4×D16C2×C414yes—
170C4×D16C2×C414yes—
171#2163C2312yes—
172#2163C2312yes—
173#2163C2312yes—
174#2163C2312yes—
175#2162—21no—
176#2162—21no—
177#2162C2×C411yescharacteristic
178#2162C2×C411yescharacteristic
179#2162C2×C412yes—
180#2159C2×C414yes—
181#2150—21no—
182#2150C2×C412yes—
183#2140C2×C414yes—
184#2139C2×C414yes—
185#2112—21no—
186#2112C2×C412yes—
187C4×M32C2312yes—
188C4×M32C2312yes—
189#1594—24no—
190#1594C2318yes—
191#1594C2314yescomplemented
192#1593C2314yescomplemented
193#1592—24no—
194#1586—28no—
195#1586—28no—
196#1584—24no—
197#1583—24no—
198#1582—24no—
199#1581—24no—
200#1580—24no—
201#1580C2318yes—
202#1580C2314yescomplemented
203#1579C2314yescomplemented
204SD16⋊C8—24no—
205#1568—21no—
206#1568C2312yes—
207#1567—21no—
208#1566—21no—
209#1566—21no—
210#1566C2312yes—
211#1566C2312yes—
212#1566C2311yescharacteristic
213#1566C2311yescharacteristic
214#1564—21no—
215#1564C2312yes—
216C2×#334—21no—
217C2×#334C2312yes—
218#1494—24no—
219#1489—22no—
220#1489—22no—
221#1486—24no—
222#1486—24no—
223#1485—22no—
224#1484—22no—
225C2×D4⋊C8—22no—
226C2×D4⋊C8—22no—
227#1451D412yes—
228#1451D412yes—
229#1451C2312yes—
230#1451C2312yes—
231C2×#322D412yes—
232C2×#322C2312yes—
233#1368C2318yescomplemented
234#1368C2318yescomplemented
235#1334C2318yescomplemented
236#1333C2314yes—
237#1333C2314yes—
238#1333C2314yes—
239#1333C2314yes—
240#1333C2318yescomplemented
241#1313C2318yescomplemented
242#1313C2318yescomplemented
243C23×D4—21no—
244C24×C4—41no—
245C2×#135—21no—
246C2×#135C22×C412yes—
247C22×D8—21no—
248C22×D8—21no—
249C22×D8—21no—
250C22×D8—44no—
251C22×D8C22×C411yescharacteristic
252C22×D8C22×C412yes—
253C22×D8C22×C412yes—
254C22×D8C22×C411yescharacteristic
255C22×M16—21no—
256C22×M16—42no—
257C22×M16—44no—
258C22×M16—44no—
259C22×M16—41no—
260C22×M16—88no—
261C23×C8—42no—
262C23×C8C22×C411yescharacteristic
263C23×C8#4111yescharacteristic
264#533—21no—
265#533—21no—
266#533—21no—
267#532—21no—
268#532—21no—
269#532—21no—
270#529—22no—
271#529—22no—
272#529—41no—
273#529—41no—
274#529—41no—
275#529—41no—
276#525—22no—
277#525—41no—
278#525—41no—
279C4×#41—22no—
280C4×#41—41no—
281C4×#41—41no—
282C2×C4×D4—22no—
283C2×C4×D4—21no—
284C2×C4×D4—21no—
285C2×C4×D4—22no—
286C2×C4×D4—21no—
287C2×C4×D4—21no—
288C2×C4×D4—22no—
289C2×C4×D4—22no—
290C2×C4×D4—41no—
291C2×C4×D4—41no—
292C2×C4×D4—41no—
293C2×C4×D4—41no—
294C2×C4×D4—41no—
295C2×C4×D4—41no—
296C22×C4⋊C4—21no—
297C22×C22⋊C4—41no—
298C22×C42C2×D411yescharacteristic
299#509—48no—
300C2×SD32C22×C414yes—
301C2×SD32C22×C414yes—
302C2×D16C22×C414yes—
303C2×D16C22×C414yes—
304C2×M32—22no—
305C2×M32C22×C414yes—
306#500C22×C411yescharacteristic
307#500C22×C411yescharacteristic
308#499—21no—
309#499C22×C412yes—
310#498—21no—
311#495—21no—
312#495C22×C412yes—
313#494C22×C411yescharacteristic
314#493C22×C411yescharacteristic
315#492—21no—
316#488—22no—
317#488—22no—
318#487—21no—
319#487—21no—
320#486—21no—
321#486—21no—
322#467—21no—
323#467—21no—
324#467C22×C412yes—
325#467C22×C412yes—
326#466—21no—
327#466—21no—
328#466C22×C412yes—
329#466C22×C412yes—
330#465—22no—
331#465—22no—
332#465—22no—
333#465—22no—
334#446—24no—
335#446—42no—
336C8×Q8—24no—
337C8×Q8—42no—
338C4×Q16—21no—
339C4×Q16—21no—
340C4×Q16C22×C412yes—
341C4×Q16C2412yes—
342C4×SD16—22no—
343C4×SD16—22no—
344C4×SD16—22no—
345C4×SD16—22no—
346C4×D8—21no—
347C4×D8—21no—
348C4×D8—21no—
349C4×D8—22no—
350C4×D8—21no—
351C4×D8—21no—
352C4×D8—22no—
353C4×D8—22no—
354C4×D8—22no—
355C4×D8—21no—
356C4×D8—21no—
357C4×D8—22no—
358C4×D8—22no—
359C4×D8—21no—
360C4×D8—22no—
361C4×D8—22no—
362C4×D8—21no—
363C4×D8—21no—
364C4×D8C22×C412yes—
365C4×D8C22×C412yes—
366C4×D8C22×C412yes—
367C4×D8C22×C412yes—
368C4×D8C22×C412yes—
369C4×D8C22×C412yes—
370C4×D8C22×C412yes—
371C4×D8C2412yes—
372C4×D8C2412yes—
373C4×D8C2412yes—
374#436—24no—
375#436—28no—
376#436—44no—
377#436—44no—
378#436—42no—
379#435—48no—
380#435—48no—
381#435—44no—
382#435—44no—
383C8×D4—24no—
384C8×D4—28no—
385C8×D4—44no—
386C8×D4—42no—
387C8×D4—44no—
388#433—44no—
389#433—44no—
390#432—22no—
391#432—42no—
392#432—41no—
393#431—21no—
394#431—21no—
395#431—22no—
396#431—42no—
397#431—41no—
398#431C2×D412yes—
399#431C2×D412yes—
400#427—21no—
401#427C22×C412yes—
402C2×#107—21no—
403C2×#107—21no—
404C2×#107—21no—
405C2×#107C22×C412yes—
406C2×#107C22×C411yescharacteristic
407C2×#107C22×C411yescharacteristic
408C2×#107C22×C412yes—
409#423—22no—
410#423—22no—
411#423—21no—
412#423—21no—
413#423—42no—
414#423—41no—
415#423—41no—
416C2×C4⋊C8—21no—
417C2×C4⋊C8—22no—
418C2×C4⋊C8—42no—
419C2×C4⋊C8—41no—
420#416—22no—
421#416—22no—
422C2×#102—22no—
423C2×#102—22no—
424C2×#102—21no—
425C2×#102—21no—
426C2×#102—22no—
427C2×#102—21no—
428C2×#102—21no—
429C2×#102—22no—
430#408—44no—
431#407—44no—
432#407—44no—
433#407—41no—
434C2×C22⋊C8—21no—
435C2×C22⋊C8—42no—
436C2×C22⋊C8—42no—
437#405—44no—
438C4×M16—21no—
439C4×M16—21no—
440C4×M16—41no—
441C4×M16C2×D412yes—
442C4×M16C2×D412yes—
443C2×#97—21no—
444C2×C4×C8C22×C411yescharacteristic
445C2×C4×C8C22×C411yescharacteristic
446C2×C4×C8C22×C411yescharacteristic
447C2×C4×C8C2×D412yes—
448C2×C4×C8C2×D412yes—
449C2×C4×C8C2×D411yescharacteristic
450C2×C4×C8C2×D411yescharacteristic
451C2×C4×C8C2×D411yescharacteristic
452C2×C4×C8#4111yescharacteristic
453C2×C4×C8#4111yescharacteristic
454C2×C4×C8#4111yescharacteristic
455C2×C4×C8C2411yescharacteristic
456C2×C4×C8C2411yescharacteristic
457C2×C4×C8C2411yescharacteristic
458#367C22×C414yes—
459#367C22×C414yes—
460#366C22×C414yes—
461#366C22×C414yes—
462C4⋊C16—22no—
463C4⋊C16—22no—
464C4⋊C16C22×C412yes—
465C4⋊C16C22×C412yes—
466C4⋊C16C22×C414yes—
467#358C22×C414yes—
468#358C22×C414yes—
469#357C22×C414yes—
470#357C22×C414yes—
471#357C22×C414yes—
472#357C22×C414yes—
473#357C22×C414yes—
474#357C22×C414yes—
475C22⋊C16—22no—
476C22⋊C16—22no—
477C22⋊C16C22×C412yes—
478C22⋊C16C22×C412yes—
479C22⋊C16C22×C414yes—
480#346C2414yes—
481#346C2414yes—
482C4×C16—22no—
483C4×C16C22×C412yes—
484C4×C16C22×C412yes—
485#335—22no—
486#335—22no—
487#334—22no—
488#334—22no—
489#334—22no—
490#334—21no—
491#334—21no—
492#334C2414yes—
493#334C2412yes—
494#334C2412yes—
495Q8⋊C8—24no—
496Q8⋊C8—24no—
497D4⋊C8—24no—
498D4⋊C8—28no—
499D4⋊C8—24no—
500D4⋊C8—28no—
501#322C2×D414yes—
502#322C2×D414yes—
503#322C2×D414yes—
504#322C2414yes—
505C25—41no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—44no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—82no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4—42no—
522C23×C4—42no—
523C23×C4—42no—
524C23×C4—42no—
525C23×C4—41no—
526C23×C4—41no—
527C23×C4—84no—
528C23×C4—84no—
529C23×C4C4×D411yescharacteristic
530C23×C4AGL(1,ℤ/8)11yescharacteristic
531C23×C4AGL(1,ℤ/8)11yescharacteristic
532#135—44no—
533#135—82no—
534C2×Q16—21no—
535C2×Q16C23×C412yes—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×D8—24no—
539C2×D8—24no—
540C2×D8—24no—
541C2×D8—21no—
542C2×D8—22no—
543C2×D8—21no—
544C2×D8—22no—
545C2×D8—21no—
546C2×D8—42no—
547C2×D8—42no—
548C2×D8—42no—
549C2×D8—44no—
550C2×D8—44no—
551C2×D8—44no—
552C2×D8C23×C412yes—
553C2×D8C23×C412yes—
554C2×D8C23×C412yes—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—48no—
558C2×M16—44no—
559C2×M16—44no—
560C2×M16—42no—
561C2×M16—42no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—88no—
565C2×M16—816no—
566C2×M16—816no—
567C2×M16—84no—
568C22×C8—22no—
569C22×C8—22no—
570C22×C8—42no—
571C22×C8—48no—
572C22×C8—44no—
573C22×C8—42no—
574C22×C8—81no—
575C22×C8—88no—
576C22×C8C4×D411yescharacteristic
577C22×C8C4×D411yescharacteristic
578C22×C8C4×D411yescharacteristic
579C22×C8C4×D411yescharacteristic
580C22×C8C4×D411yescharacteristic
581C22×C8C4×D411yescharacteristic
582C22×C8C23×C411yescharacteristic
583C22×C8C23×C411yescharacteristic
584C22×C8C23×C411yescharacteristic
585C22×C8C2×#4111yescharacteristic
586C22×C8C2×#4111yescharacteristic
587C22×C8C2×#4111yescharacteristic
588C4⋊Q8—21no—
589C4⋊Q8—21no—
590C4⋊Q8—21no—
591#127—21no—
592#126—42no—
593#126—42no—
594#125—22no—
595#125—41no—
596#125—41no—
597#124—22no—
598#124—41no—
599#124—41no—
600#123—42no—
601#123—42no—
602#123—42no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609#121—22no—
610#121—22no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#120—42no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—42no—
633C4×D4—42no—
634C4×D4—42no—
635C4×D4—42no—
636C4×D4—42no—
637C4×D4—42no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—42no—
641C4×D4—42no—
642C4×D4—41no—
643C4×D4—42no—
644C4×D4—42no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—42no—
648C4×D4—41no—
649C4×D4—42no—
650C4×D4—42no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—42no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—41no—
658#117—22no—
659#117—41no—
660#117—41no—
661#117—42no—
662#117—42no—
663#117—42no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C22⋊C4—42no—
672C2×C22⋊C4—42no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—42no—
678C2×C22⋊C4—42no—
679C2×C42—42no—
680C2×C42C4×D411yescharacteristic
681C2×C42C4×D411yescharacteristic
682C2×C42C4×D411yescharacteristic
683C2×C42AGL(1,ℤ/8)11yescharacteristic
684C2×C42AGL(1,ℤ/8)11yescharacteristic
685C2×C42AGL(1,ℤ/8)11yescharacteristic
686C2×C42AGL(1,ℤ/8)11yescharacteristic
687C2×C42AGL(1,ℤ/8)11yescharacteristic
688C2×C42AGL(1,ℤ/8)11yescharacteristic
689C2×C42C22×D411yescharacteristic
690C2×C42C22×D411yescharacteristic
691C2×C42C22×D411yescharacteristic
692SD32—28no—
693SD32—44no—
694D16—28no—
695D16—44no—
696M32—44no—
697M32—82no—
698C2×C16—24no—
699C2×C16C23×C414yes—
700C2×C16C23×C414yes—
701#107—21no—
702#107—21no—
703#107—22no—
704#107—22no—
705#107—21no—
706#107—21no—
707#107C23×C412yes—
708#107C23×C412yes—
709#107C23×C412yes—
710#107C23×C412yes—
711#106—22no—
712#106—22no—
713C4⋊C8—22no—
714C4⋊C8—22no—
715C4⋊C8—24no—
716C4⋊C8—22no—
717C4⋊C8—22no—
718C4⋊C8—44no—
719C4⋊C8—44no—
720C4⋊C8—42no—
721C4⋊C8—41no—
722C4⋊C8—42no—
723C4⋊C8—42no—
724C4⋊C8—41no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—48no—
744C22⋊C8—48no—
745C22⋊C8—44no—
746C22⋊C8—44no—
747C22⋊C8—42no—
748C22⋊C8—42no—
749#97—22no—
750#97—22no—
751#97—44no—
752#97—42no—
753C4×C8—22no—
754C4×C8—22no—
755C4×C8—44no—
756C4×C8—42no—
757C4×C8C4×D411yescharacteristic
758C4×C8C4×D411yescharacteristic
759C4×C8C4×D411yescharacteristic
760C4×C8C4×D411yescharacteristic
761C4×C8C4×D411yescharacteristic
762C4×C8C4×D411yescharacteristic
763C4×C8C23×C411yescharacteristic
764C4×C8C23×C411yescharacteristic
765C4×C8C23×C411yescharacteristic
766C4×C8C22×D414yes—
767C4×C8C22×D414yes—
768C4×C8C22×D411yescharacteristic
769C4×C8C22×D411yescharacteristic
770C4×C8C22×D411yescharacteristic
771C4×C8C2×#4111yescharacteristic
772C4×C8C2×#4111yescharacteristic
773C4×C8C2×#4111yescharacteristic
774C4×C8C2511yescharacteristic
775C24—41no—
776C24—41no—
777C24—42no—
778C24—42no—
779C24—84no—
780C24—84no—
781C24—162no—
782C24#44211yescharacteristic
783#41—82no—
784#41—82no—
785#41—84no—
786#41—161no—
787#41—161no—
788C2×Q8—22no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—41no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—41no—
807C2×D4—41no—
808C2×D4—41no—
809C2×D4—82no—
810C2×D4—82no—
811C2×D4—84no—
812C2×D4—84no—
813C2×D4—84no—
814C22×C4—24no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—82no—
833C22×C4—82no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—82no—
837C22×C4—82no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—88no—
841C22×C4—88no—
842C22×C4—81no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4#44211yescharacteristic
847C22×C4#44211yescharacteristic
848C22×C4#44211yescharacteristic
849C22×C4#44211yescharacteristic
850C22×C4#44211yescharacteristic
851C22×C4#44211yescharacteristic
852C22×C4#44211yescharacteristic
853C22×C4#44211yescharacteristic
854C22×C4#44211yescharacteristic
855C22×C4C2×C4×D411yescharacteristic
856C22×C4C2×C4×D411yescharacteristic
857C22×C4C2×C4×D411yescharacteristic
858C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
859C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
860C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
861C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
862C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
863C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
864Q16—24no—
865Q16—81no—
866SD16—44no—
867SD16—82no—
868D8—24no—
869D8—22no—
870D8—24no—
871D8—22no—
872D8—22no—
873D8—44no—
874D8—44no—
875D8—42no—
876D8—81no—
877D8#56814yes—
878M16—44no—
879M16—44no—
880M16—816no—
881M16—84no—
882M16—84no—
883M16—164no—
884M16—161no—
885M16—161no—
886C2×C8—22no—
887C2×C8—22no—
888C2×C8—22no—
889C2×C8—24no—
890C2×C8—24no—
891C2×C8—41no—
892C2×C8—41no—
893C2×C8—41no—
894C2×C8—41no—
895C2×C8—41no—
896C2×C8—41no—
897C2×C8—41no—
898C2×C8—41no—
899C2×C8—41no—
900C2×C8—44no—
901C2×C8—42no—
902C2×C8—42no—
903C2×C8—44no—
904C2×C8—82no—
905C2×C8—816no—
906C2×C8—84no—
907C2×C8—164no—
908C2×C8C2×C4×D411yescharacteristic
909C2×C8C2×C4×D411yescharacteristic
910C2×C8C2×C4×D411yescharacteristic
911C2×C8C2×C4×D411yescharacteristic
912C2×C8C2×C4×D411yescharacteristic
913C2×C8C2×C4×D411yescharacteristic
914C2×C8C24×C411yescharacteristic
915C2×C8C22×#4111yescharacteristic
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—42no—
921C4⋊C4—41no—
922C4⋊C4—42no—
923C4⋊C4—41no—
924C4⋊C4—42no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C42—42no—
952C42—42no—
953C42—42no—
954C42#44211yescharacteristic
955C42#44211yescharacteristic
956C42#44211yescharacteristic
957C42#44211yescharacteristic
958C42#44211yescharacteristic
959C42#44211yescharacteristic
960C42C2×C4×D411yescharacteristic
961C42C2×C4×D411yescharacteristic
962C42C2×C4×D411yescharacteristic
963C42C2×AGL(1,ℤ/8)11yescharacteristic
964C42C2×AGL(1,ℤ/8)11yescharacteristic
965C42C2×AGL(1,ℤ/8)11yescharacteristic
966C42C2×AGL(1,ℤ/8)11yescharacteristic
967C42C2×AGL(1,ℤ/8)11yescharacteristic
968C42C2×AGL(1,ℤ/8)11yescharacteristic
969C42C23×D411yescharacteristic
970C16—24no—
971C16—24no—
972C16—44no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—44no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—84no—
981C23—84no—
982C23—82no—
983C23—84no—
984C23—84no—
985C23—82no—
986C23—82no—
987C23—82no—
988C23—82no—
989C23—162no—
990C23—162no—
991C23—1616no—
992C23C2×#44211yescharacteristic
993C23C2×#44211yescharacteristic
994C23C2×#44211yescharacteristic
995Q8—42no—
996Q8—42no—
997Q8—82no—
998Q8—161no—
999D4—24no—
1000D4—44no—
1001D4—42no—
1002D4—42no—
1003D4—42no—
1004D4—42no—
1005D4—42no—
1006D4—84no—
1007D4—84no—
1008D4—82no—
1009D4—84no—
1010D4—82no—
1011D4—161no—
1012D4—162no—
1013D4—162no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4—82no—
1044C2×C4—82no—
1045C2×C4—84no—
1046C2×C4—84no—
1047C2×C4—84no—
1048C2×C4—84no—
1049C2×C4—82no—
1050C2×C4—82no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4—84no—
1054C2×C4—84no—
1055C2×C4—84no—
1056C2×C4—162no—
1057C2×C4AGL(1,ℤ/16)14yes—
1058C2×C4C2×#44211yescharacteristic
1059C2×C4C2×#44211yescharacteristic
1060C2×C4C2×#44211yescharacteristic
1061C2×C4C2×#44211yescharacteristic
1062C2×C4C2×#44211yescharacteristic
1063C2×C4C2×#44211yescharacteristic
1064C2×C4C2×#44211yescharacteristic
1065C2×C4C2×#44211yescharacteristic
1066C2×C4C2×#44211yescharacteristic
1067C2×C4C22×C4×D411yescharacteristic
1068C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1069C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1070C8—21no—
1071C8—21no—
1072C8—21no—
1073C8—21no—
1074C8—21no—
1075C8—21no—
1076C8—21no—
1077C8—44no—
1078C8—44no—
1079C8—84no—
1080C8—82no—
1081C8—82no—
1082C8C2×#56812yes—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—21no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—44no—
1093C22—88no—
1094C22—82no—
1095C22—82no—
1096C22—82no—
1097C22—82no—
1098C22—82no—
1099C22—82no—
1100C22—82no—
1101C22—82no—
1102C22—164no—
1103C22—168no—
1104C22—168no—
1105C22C2×AGL(1,ℤ/16)12yes—
1106C22C22×#44211yescharacteristic
1107C4—21no—
1108C4—21no—
1109C4—21no—
1110C4—21no—
1111C4—21no—
1112C4—21no—
1113C4—21no—
1114C4—21no—
1115C4—21no—
1116C4—82no—
1117C4—82no—
1118C4—82no—
1119C4—82no—
1120C4—82no—
1121C4C2×AGL(1,ℤ/16)12yes—
1122C4C2×AGL(1,ℤ/16)12yes—
1123C4#6014111yescharacteristic
1124C4#6018211yescharacteristic
1125C2—22no—
1126C2—41no—
1127C2—41no—
1128C2—84no—
1129C2—162no—
1130C2—162no—
1131C2#634528711yescharacteristic
1132C2C22×AGL(1,ℤ/16)11yescharacteristic
1133C2#762263511yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623096C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#1451 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6345726C2semidirect
3. C2×#18044C2semidirect
4. #484110C2semidirect
5. #484106C2semidirect
6. #484058C2semidirect
7. #484057C2semidirect
8. #483924C2semidirect
9. #483878C2semidirect
10. #483443C2semidirect
11. #481386C2semidirect
12. #481279C2semidirect
13. #479974C2semidirect
34. #18091C22semidirect
35. #18090C22semidirect
37. #18065C22semidirect
38. #18063C22semidirect
45. #17963C22semidirect
54. #12089C22semidirect
55. #12087C22semidirect
56. #12080C22semidirect
57. #12078C22semidirect
58. #12078C22semidirect
59. #12077C22semidirect
60. #12067C22semidirect
61. #12065C22semidirect
62. #12029C22semidirect
63. #12028C22semidirect
64. #12020C22semidirect
65. #12020C22semidirect
66. #11681C22semidirect
67. #11680C22semidirect
70. #11666C22semidirect
73. #11651C22semidirect
75. #11415C22semidirect
76. #11414C22semidirect
77. #11414C22semidirect
191. #1594C23semidirect
192. #1593C23semidirect
202. #1580C23semidirect
203. #1579C23semidirect
233. #1368C23semidirect
234. #1368C23semidirect
235. #1334C23semidirect
240. #1333C23semidirect
241. #1313C23semidirect
242. #1313C23semidirect

Maximal subgroups

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

subgroupindex
#76230962
#63457262
C2×#180442
#4841102
#4841062
#4840582
#4840572
#4839242
#4838782
#4834432
#4813862
#4812792
#4799742