Finite Group Databasebeta

← #72343009

Subgroups — #72343009

Order 1024.

2395 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623520C211yesmaximal, characteristic
2#6345726C211yesmaximal, characteristic, complemented
3C2×#18073C211yesmaximal, characteristic, complemented
4#484148C214yesmaximal, complemented
5#484147C214yesmaximal, complemented
6#484056C214yesmaximal, complemented
7#484053C214yesmaximal, complemented
8#483924C214yesmaximal, complemented
9#483878C214yesmaximal, complemented
10#483421C211yesmaximal, characteristic, complemented
11#481384C211yesmaximal, characteristic, complemented
12#481317C211yesmaximal, characteristic, complemented
13#479974C211yesmaximal, characteristic, complemented
14#60673C2211yescharacteristic
15C2×#3169C2211yescharacteristic
16#60292—21no—
17C2×#2935—21no—
18#33817C414yes—
19#33795C411yescharacteristic
20#33794C412yes—
21#33792C411yescharacteristic
22#33774C411yescharacteristic
23#33773C412yes—
24#33771C411yescharacteristic
25#33760C414yes—
26#33751C2212yes—
27#33748C2212yes—
28#33675C2214yes—
29#33674C2214yes—
30#33418C2211yescharacteristic
31#33418C2211yescharacteristic
32#18091C2212yescomplemented
33#18090C2212yescomplemented
34#18089—22no—
35#18073—22no—
36#18073—22no—
37#18073C2214yes—
38#18073C2214yes—
39#18065C2212yescomplemented
40#18063C2212yescomplemented
41#18061—22no—
42#17978—22no—
43#17963C2214yes—
44C2×#1594C2212yes—
45C2×#1586—22no—
46C2×#1580C2212yes—
47#17793C2211yescharacteristic
48C22×#334C2211yescharacteristic
49#17503—21no—
50C2×#1480—21no—
51C2×#1451C2211yescharacteristic
52#12089C2218yescomplemented
53#12087C2218yescomplemented
54#12080C2218yescomplemented
55#12078C2218yescomplemented
56#12078C2218yescomplemented
57#12077C2218yescomplemented
58#12067C2218yescomplemented
59#12065C2218yescomplemented
60#12030C2212yescomplemented
61#12030C2212yescomplemented
62#12028C2212yes—
63#12028C2212yes—
64#12000C2214yescomplemented
65#11680C2212yes—
66#11680C2212yes—
67#11667C2214yes—
68#11655C2212yescomplemented
69#11654C2212yescomplemented
70#11652C2214yes—
71#11651C2212yes—
72#11651C2212yes—
73#11598C2214yescomplemented
74#11415C2214yes—
75#11414C2214yescomplemented
76#11414C2214yescomplemented
77C22×#131—41no—
78#3444—21no—
79C2×#532—21no—
80#3170C2×C411yescharacteristic
81#3170C2311yescharacteristic
82#3169—21no—
83#3169—21no—
84#3169—21no—
85#3169—21no—
86#3169C2×C411yescharacteristic
87#3169C2×C412yes—
88#3169C2×C412yes—
89#3169C2311yescharacteristic
90#3169C2312yes—
91#3169C2312yes—
92#3168—21no—
93#3168—21no—
94#3168C2×C412yes—
95#3168C2312yes—
96#3167—21no—
97#3167—21no—
98#3160C2×C411yescharacteristic
99C2×#500C2×C411yescharacteristic
100#3147C2×C411yescharacteristic
101C2×#493C2×C411yescharacteristic
102#3131—21no—
103C2×#486—21no—
104#3050—21no—
105#3050C2×C412yes—
106C2×#466—21no—
107C2×#466C2×C412yes—
108#2991—22no—
109#2990—22no—
110#2989—41no—
111#2988—41no—
112#2986—22no—
113#2979—22no—
114#2976—42no—
115#2969—42no—
116#2966—24no—
117C4×#135—21no—
118C4×#135C2312yes—
119C2×C4×D8—21no—
120C2×C4×D8C2312yes—
121#2935—24no—
122#2935—24no—
123#2935—42no—
124#2935—42no—
125C2×#436—22no—
126C2×#435—42no—
127C2×C8×D4—22no—
128#2925—42no—
129#2920—21no—
130C2×#431D411yescharacteristic
131C22×C4⋊C8—21no—
132C2×#408—41no—
133C2×C4×M16D411yescharacteristic
134C22×C4×C8C2311yescharacteristic
135#2254C2×C412yes—
136#2252C2×C412yes—
137#2248C2×C412yes—
138#2246C2×C412yes—
139#2241C2×C412yes—
140#2240C2×C412yes—
141#2240C2×C412yes—
142#2240C2×C412yes—
143#2235C2×C414yes—
144#2234C2×C418yes—
145#2232C2×C414yes—
146#2228C2×C418yes—
147#2225C2×C414yes—
148#2224C2×C414yes—
149#2220C2×C418yes—
150#2218C2×C418yes—
151#2210C2×C418yes—
152#2207C2×C414yes—
153#2206C2×C414yes—
154#2187C2×C414yes—
155#2186C2×C418yes—
156#2184C2×C414yes—
157#2177C2318yes—
158#2175C2318yes—
159#2163C2312yes—
160#2163C2312yes—
161#2163C2312yes—
162#2163C2312yes—
163#2162—21no—
164#2162—21no—
165#2162C2×C411yescharacteristic
166#2162C2×C412yes—
167#2162C2×C411yescharacteristic
168#2150—21no—
169#2150C2×C412yes—
170#2112—21no—
171#2112C2×C412yes—
172C4×M32C2312yes—
173C4×M32C2312yes—
174#1594—24no—
175#1594C2314yes—
176#1594C2318yes—
177#1593C2314yes—
178#1592—24no—
179#1586—28no—
180#1586—28no—
181#1584—24no—
182#1583—24no—
183#1582—24no—
184#1581—24no—
185#1580—24no—
186#1580C2318yes—
187#1580C2314yes—
188#1579C2314yes—
189SD16⋊C8—24no—
190#1568—21no—
191#1568C2312yes—
192#1567—21no—
193#1566C2311yescharacteristic
194#1566C2311yescharacteristic
195#1564—21no—
196#1564C2312yes—
197C2×#334—21no—
198C2×#334—21no—
199C2×#334—21no—
200C2×#334C2312yes—
201C2×#334C2311yescharacteristic
202C2×#334C2311yescharacteristic
203C2×#334C2312yes—
204#1494—24no—
205#1489—22no—
206#1489—22no—
207#1485—22no—
208#1484—22no—
209#1480—24no—
210#1480—24no—
211C2×D4⋊C8—22no—
212C2×D4⋊C8—22no—
213#1451D412yes—
214#1451D412yes—
215#1451C2312yes—
216#1451C2312yes—
217C2×#322D412yes—
218C2×#322C2312yes—
219#1368C2314yes—
220#1368C2314yes—
221#1368C2314yes—
222#1368C2314yes—
223#1334C2314yes—
224#1334C2314yes—
225#1333C2318yes—
226#1333C2314yes—
227#1333C2318yes—
228#1333C2314yes—
229#1313C2318yes—
230#1313C2318yes—
231C22×#41—41no—
232C2×#135—21no—
233C2×#135C22×C412yes—
234C22×D8—21no—
235C22×D8C22×C412yes—
236C2×#131—44no—
237C2×#131—44no—
238C2×#131—88no—
239C22×M16—21no—
240C22×M16—42no—
241C23×C8—42no—
242C23×C8—41no—
243C23×C8C22×C411yescharacteristic
244C23×C8#4111yescharacteristic
245#533—21no—
246#533—21no—
247#533—21no—
248#532—21no—
249#532—22no—
250#532—22no—
251#532—21no—
252#532—21no—
253#532—22no—
254#532—22no—
255#532—41no—
256#532—41no—
257#532—41no—
258#532—41no—
259C2×C4⋊Q8—21no—
260C2×#127—21no—
261#529—22no—
262#529—22no—
263#529—41no—
264#529—41no—
265#529—41no—
266#529—41no—
267C2×#124—41no—
268#525—22no—
269#525—41no—
270#525—41no—
271C2×#121—22no—
272C2×#121—41no—
273C4×#41—22no—
274C4×#41—41no—
275C4×#41—41no—
276C2×C4×D4—22no—
277C2×C4×D4—41no—
278C22×C42C2×D411yescharacteristic
279C2×SD32C22×C418yes—
280C2×D16C22×C418yes—
281C2×M32—22no—
282C2×M32C22×C414yes—
283#500—21no—
284#500—21no—
285#500C22×C412yes—
286#500C22×C412yes—
287#500C22×C411yescharacteristic
288#500C22×C411yescharacteristic
289#499—21no—
290#499C22×C412yes—
291#498—21no—
292#495—21no—
293#495C22×C412yes—
294#494C22×C411yescharacteristic
295#493—21no—
296#493—21no—
297#493C22×C412yes—
298#493C22×C412yes—
299#493C22×C411yescharacteristic
300#492—21no—
301#488—22no—
302#488—22no—
303#487—21no—
304#487—21no—
305#486—22no—
306#486—22no—
307#486—21no—
308#486—22no—
309#486—22no—
310#486—21no—
311#467—21no—
312#467—21no—
313#467C22×C412yes—
314#467C22×C412yes—
315#466—21no—
316#466—22no—
317#466—22no—
318#466—22no—
319#466—22no—
320#466—21no—
321#466—22no—
322#466—22no—
323#466C22×C412yes—
324#466C22×C412yes—
325#466C22×C414yes—
326#466C22×C414yes—
327#465—22no—
328#465—22no—
329#465—22no—
330#465—22no—
331#446—24no—
332#446—42no—
333C8×Q8—24no—
334C8×Q8—42no—
335C4×Q16—21no—
336C4×Q16—21no—
337C4×Q16C22×C412yes—
338C4×Q16C2412yes—
339C4×SD16—22no—
340C4×SD16—22no—
341C4×SD16—22no—
342C4×SD16—22no—
343C4×D8—21no—
344C4×D8—22no—
345C4×D8—22no—
346C4×D8—22no—
347C4×D8—21no—
348C4×D8—22no—
349C4×D8—22no—
350C4×D8—22no—
351C4×D8C22×C412yes—
352C4×D8C22×C414yes—
353C4×D8C2412yes—
354C4×D8C2414yes—
355#436—24no—
356#436—28no—
357#436—44no—
358#436—44no—
359#436—42no—
360#435—48no—
361#435—48no—
362#435—44no—
363#435—44no—
364C8×D4—24no—
365C8×D4—28no—
366C8×D4—44no—
367C8×D4—42no—
368C8×D4—44no—
369#433—44no—
370#433—44no—
371#432—22no—
372#432—42no—
373#432—41no—
374#431—21no—
375#431—21no—
376#431—22no—
377#431—42no—
378#431—41no—
379#431C2×D412yes—
380#431C2×D412yes—
381#427—21no—
382#427C22×C412yes—
383C2×#107—21no—
384C2×#107C22×C412yes—
385#423—21no—
386#423—21no—
387#423—42no—
388C2×C4⋊C8—21no—
389C2×C4⋊C8—21no—
390C2×C4⋊C8—21no—
391C2×C4⋊C8—22no—
392C2×C4⋊C8—22no—
393C2×C4⋊C8—42no—
394C2×C4⋊C8—41no—
395C2×C4⋊C8—41no—
396C2×C4⋊C8—41no—
397#416—22no—
398#416—22no—
399C2×#102—22no—
400C2×#102—22no—
401#408—44no—
402#408—44no—
403#408—44no—
404#407—41no—
405C2×C22⋊C8—21no—
406C2×C22⋊C8—42no—
407C2×C22⋊C8—42no—
408#405—44no—
409C4×M16—21no—
410C4×M16—21no—
411C4×M16—41no—
412C4×M16C2×D412yes—
413C4×M16C2×D412yes—
414C2×#97—21no—
415C2×C4×C8C22×C411yescharacteristic
416C2×C4×C8C22×C411yescharacteristic
417C2×C4×C8C22×C411yescharacteristic
418C2×C4×C8C2×D412yes—
419C2×C4×C8C2×D412yes—
420C2×C4×C8C2×D411yescharacteristic
421C2×C4×C8C2×D411yescharacteristic
422C2×C4×C8C2×D411yescharacteristic
423C2×C4×C8#4111yescharacteristic
424C2×C4×C8#4111yescharacteristic
425C2×C4×C8#4111yescharacteristic
426C2×C4×C8C2411yescharacteristic
427C2×C4×C8C2411yescharacteristic
428C2×C4×C8C2411yescharacteristic
429#367C22×C418yes—
430#366C22×C418yes—
431C4⋊C16—22no—
432C4⋊C16—22no—
433C4⋊C16C22×C412yes—
434C4⋊C16C22×C412yes—
435C4⋊C16C22×C414yes—
436#358C22×C418yes—
437#357C22×C418yes—
438#357C22×C418yes—
439#357C22×C418yes—
440C22⋊C16—22no—
441C22⋊C16—22no—
442C22⋊C16C22×C412yes—
443C22⋊C16C22×C414yes—
444C22⋊C16C22×C412yes—
445#346C2414yes—
446#346C2414yes—
447C4×C16—22no—
448C4×C16C22×C412yes—
449C4×C16C22×C412yes—
450#335—22no—
451#335—22no—
452#334—21no—
453#334—22no—
454#334—22no—
455#334—21no—
456#334—21no—
457#334—21no—
458#334C2412yes—
459#334C2412yes—
460#334C2412yes—
461#334C2412yes—
462Q8⋊C8—24no—
463Q8⋊C8—24no—
464D4⋊C8—24no—
465D4⋊C8—28no—
466D4⋊C8—24no—
467D4⋊C8—28no—
468#322C2×D414yes—
469#322C2×D414yes—
470#322C2×D414yes—
471#322C2414yes—
472C2×#41—22no—
473C2×#41—42no—
474C2×#41—42no—
475C2×#41—41no—
476C2×#41—41no—
477C2×#41—42no—
478C2×#41—42no—
479C2×#41—84no—
480C2×#41—84no—
481C22×Q8—41no—
482C22×D4—22no—
483C22×D4—42no—
484C22×D4—41no—
485C22×D4—41no—
486C23×C4—42no—
487C23×C4C4×D411yescharacteristic
488C23×C4AGL(1,ℤ/8)11yescharacteristic
489C23×C4AGL(1,ℤ/8)11yescharacteristic
490#135—44no—
491#135—82no—
492C2×Q16—21no—
493C2×Q16C23×C412yes—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—21no—
500C2×D8—44no—
501C2×D8—82no—
502C2×D8C23×C414yes—
503C2×D8C23×C412yes—
504#131—816no—
505#131—816no—
506C2×M16—22no—
507C2×M16—22no—
508C2×M16—48no—
509C2×M16—44no—
510C2×M16—44no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—88no—
514C22×C8—22no—
515C22×C8—22no—
516C22×C8—42no—
517C22×C8—48no—
518C22×C8—44no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8—42no—
522C22×C8—42no—
523C22×C8—81no—
524C22×C8—88no—
525C22×C8—84no—
526C22×C8C4×D411yescharacteristic
527C22×C8C4×D411yescharacteristic
528C22×C8C4×D411yescharacteristic
529C22×C8C4×D411yescharacteristic
530C22×C8C4×D411yescharacteristic
531C22×C8C4×D411yescharacteristic
532C22×C8C23×C411yescharacteristic
533C22×C8C23×C411yescharacteristic
534C22×C8C23×C411yescharacteristic
535C22×C8C2×#4111yescharacteristic
536C22×C8C2×#4111yescharacteristic
537C22×C8C2×#4111yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—21no—
541C4⋊Q8—21no—
542C4⋊Q8—21no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545#127—22no—
546#127—22no—
547#127—21no—
548#127—41no—
549#127—41no—
550#126—42no—
551#126—42no—
552#125—22no—
553#125—41no—
554#125—41no—
555#124—22no—
556#124—42no—
557#124—42no—
558#124—41no—
559#124—42no—
560#124—42no—
561#124—41no—
562#123—42no—
563#123—42no—
564#123—42no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571#121—24no—
572#121—24no—
573#121—22no—
574#121—22no—
575#121—42no—
576#121—42no—
577#121—41no—
578#121—42no—
579#121—42no—
580#121—42no—
581#121—42no—
582#121—41no—
583#121—41no—
584#121—41no—
585#120—42no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×D4—24no—
593C4×D4—22no—
594C4×D4—24no—
595C4×D4—22no—
596C4×D4—42no—
597C4×D4—42no—
598C4×D4—42no—
599C4×D4—42no—
600C4×D4—42no—
601C4×D4—42no—
602C4×D4—42no—
603C4×D4—42no—
604C4×D4—42no—
605C4×D4—42no—
606C4×D4—41no—
607C4×D4—42no—
608C4×D4—42no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612#117—22no—
613#117—41no—
614#117—41no—
615#117—42no—
616#117—42no—
617#117—42no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—41no—
620C2×C22⋊C4—42no—
621C2×C22⋊C4—42no—
622C2×C42—42no—
623C2×C42C4×D411yescharacteristic
624C2×C42C4×D411yescharacteristic
625C2×C42C4×D411yescharacteristic
626C2×C42AGL(1,ℤ/8)11yescharacteristic
627C2×C42AGL(1,ℤ/8)11yescharacteristic
628C2×C42AGL(1,ℤ/8)11yescharacteristic
629C2×C42AGL(1,ℤ/8)11yescharacteristic
630C2×C42AGL(1,ℤ/8)11yescharacteristic
631C2×C42AGL(1,ℤ/8)11yescharacteristic
632C2×C42C22×D411yescharacteristic
633C2×C42C22×D411yescharacteristic
634C2×C42C22×D411yescharacteristic
635SD32—48no—
636D16—48no—
637M32—44no—
638M32—82no—
639C2×C16—24no—
640C2×C16C23×C414yes—
641C2×C16C23×C414yes—
642#107—22no—
643#107—22no—
644#107—22no—
645#107—21no—
646#107—21no—
647#107C23×C412yes—
648#107C23×C412yes—
649#107C23×C414yes—
650#106—22no—
651#106—22no—
652C4⋊C8—22no—
653C4⋊C8—22no—
654C4⋊C8—22no—
655C4⋊C8—22no—
656C4⋊C8—22no—
657C4⋊C8—22no—
658C4⋊C8—44no—
659C4⋊C8—44no—
660C4⋊C8—41no—
661C4⋊C8—42no—
662C4⋊C8—42no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#102—24no—
671#102—24no—
672#102—24no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—24no—
677#102—22no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—48no—
681C22⋊C8—48no—
682C22⋊C8—44no—
683C22⋊C8—44no—
684C22⋊C8—42no—
685C22⋊C8—42no—
686#97—22no—
687#97—22no—
688#97—44no—
689#97—42no—
690C4×C8—22no—
691C4×C8—22no—
692C4×C8—44no—
693C4×C8—42no—
694C4×C8C4×D411yescharacteristic
695C4×C8C4×D411yescharacteristic
696C4×C8C4×D411yescharacteristic
697C4×C8C4×D411yescharacteristic
698C4×C8C4×D411yescharacteristic
699C4×C8C4×D411yescharacteristic
700C4×C8C23×C411yescharacteristic
701C4×C8C23×C411yescharacteristic
702C4×C8C23×C411yescharacteristic
703C4×C8C22×D414yes—
704C4×C8C22×D414yes—
705C4×C8C22×D411yescharacteristic
706C4×C8C22×D411yescharacteristic
707C4×C8C22×D411yescharacteristic
708C4×C8C2×#4111yescharacteristic
709C4×C8C2×#4111yescharacteristic
710C4×C8C2×#4111yescharacteristic
711C4×C8C2511yescharacteristic
712C24—42no—
713C24#44211yescharacteristic
714#41—84no—
715#41—84no—
716#41—84no—
717#41—84no—
718#41—88no—
719#41—88no—
720#41—82no—
721#41—82no—
722#41—84no—
723#41—161no—
724#41—161no—
725C2×Q8—22no—
726C2×Q8—41no—
727C2×Q8—42no—
728C2×Q8—42no—
729C2×Q8—41no—
730C2×Q8—84no—
731C2×D4—22no—
732C2×D4—24no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—42no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—41no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—41no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—88no—
748C2×D4—84no—
749C2×D4—162no—
750C22×C4—24no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—44no—
756C22×C4—42no—
757C22×C4—44no—
758C22×C4—42no—
759C22×C4—84no—
760C22×C4—84no—
761C22×C4—81no—
762C22×C4#44211yescharacteristic
763C22×C4#44211yescharacteristic
764C22×C4#44211yescharacteristic
765C22×C4#44211yescharacteristic
766C22×C4#44211yescharacteristic
767C22×C4#44211yescharacteristic
768C22×C4#44211yescharacteristic
769C22×C4#44211yescharacteristic
770C22×C4#44211yescharacteristic
771C22×C4C2×C4×D411yescharacteristic
772C22×C4C2×C4×D411yescharacteristic
773C22×C4C2×C4×D411yescharacteristic
774C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
775C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
776C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
777C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
778C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
779C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
780Q16—24no—
781Q16—81no—
782SD16—44no—
783SD16—82no—
784D8—24no—
785D8—28no—
786D8—44no—
787D8—82no—
788D8—82no—
789D8—81no—
790M16—44no—
791M16—44no—
792M16—816no—
793M16—164no—
794M16—161no—
795M16—161no—
796C2×C8—22no—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—24no—
800C2×C8—24no—
801C2×C8—41no—
802C2×C8—41no—
803C2×C8—41no—
804C2×C8—41no—
805C2×C8—41no—
806C2×C8—41no—
807C2×C8—41no—
808C2×C8—41no—
809C2×C8—41no—
810C2×C8—44no—
811C2×C8—42no—
812C2×C8—42no—
813C2×C8—42no—
814C2×C8—42no—
815C2×C8—82no—
816C2×C8—816no—
817C2×C8—82no—
818C2×C8—82no—
819C2×C8—84no—
820C2×C8—84no—
821C2×C8—164no—
822C2×C8C2×C4×D411yescharacteristic
823C2×C8C2×C4×D411yescharacteristic
824C2×C8C2×C4×D411yescharacteristic
825C2×C8C2×C4×D411yescharacteristic
826C2×C8C2×C4×D411yescharacteristic
827C2×C8C2×C4×D411yescharacteristic
828C2×C8C24×C411yescharacteristic
829C2×C8C22×#4111yescharacteristic
830C4⋊C4—24no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—41no—
838C4⋊C4—41no—
839C4⋊C4—41no—
840C4⋊C4—41no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—42no—
853C22⋊C4—42no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—44no—
858C22⋊C4—42no—
859C42—42no—
860C42—42no—
861C42—42no—
862C42#44211yescharacteristic
863C42#44211yescharacteristic
864C42#44211yescharacteristic
865C42#44211yescharacteristic
866C42#44211yescharacteristic
867C42#44211yescharacteristic
868C42C2×C4×D411yescharacteristic
869C42C2×C4×D411yescharacteristic
870C42C2×C4×D411yescharacteristic
871C42C2×AGL(1,ℤ/8)11yescharacteristic
872C42C2×AGL(1,ℤ/8)11yescharacteristic
873C42C2×AGL(1,ℤ/8)11yescharacteristic
874C42C2×AGL(1,ℤ/8)11yescharacteristic
875C42C2×AGL(1,ℤ/8)11yescharacteristic
876C42C2×AGL(1,ℤ/8)11yescharacteristic
877C42C23×D411yescharacteristic
878C16—24no—
879C16—24no—
880C16—44no—
881C23—22no—
882C23—41no—
883C23—41no—
884C23—42no—
885C23—44no—
886C23—84no—
887C23—84no—
888C23—84no—
889C23C2×#44211yescharacteristic
890C23C2×#44211yescharacteristic
891C23C2×#44211yescharacteristic
892Q8—42no—
893Q8—42no—
894Q8—84no—
895Q8—84no—
896Q8—82no—
897Q8—161no—
898D4—44no—
899D4—42no—
900D4—44no—
901D4—42no—
902D4—84no—
903D4—88no—
904D4—88no—
905D4—84no—
906D4—84no—
907D4—84no—
908D4—82no—
909D4—162no—
910D4—162no—
911D4—161no—
912D4—162no—
913D4—162no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—44no—
938C2×C4—84no—
939C2×C4—82no—
940C2×C4—82no—
941C2×C4—84no—
942C2×C4—88no—
943C2×C4—84no—
944C2×C4—84no—
945C2×C4—162no—
946C2×C4AGL(1,ℤ/16)14yes—
947C2×C4C2×#44211yescharacteristic
948C2×C4C2×#44211yescharacteristic
949C2×C4C2×#44211yescharacteristic
950C2×C4C2×#44211yescharacteristic
951C2×C4C2×#44211yescharacteristic
952C2×C4C2×#44211yescharacteristic
953C2×C4C2×#44211yescharacteristic
954C2×C4C2×#44211yescharacteristic
955C2×C4C2×#44211yescharacteristic
956C2×C4C22×C4×D411yescharacteristic
957C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
958C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
959C8—21no—
960C8—21no—
961C8—21no—
962C8—21no—
963C8—21no—
964C8—21no—
965C8—21no—
966C8—44no—
967C8—44no—
968C8—82no—
969C8—82no—
970C8—82no—
971C8—82no—
972C8#357312yes—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—44no—
982C22—84no—
983C22—82no—
984C22—82no—
985C22—84no—
986C22—82no—
987C22—84no—
988C22—168no—
989C22C2×AGL(1,ℤ/16)12yes—
990C22C22×#44211yescharacteristic
991C4—21no—
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—84no—
1001C4—82no—
1002C4—82no—
1003C4—82no—
1004C4C2×AGL(1,ℤ/16)12yes—
1005C4C2×AGL(1,ℤ/16)12yes—
1006C4#6014211yescharacteristic
1007C4#6018211yescharacteristic
1008C2—22no—
1009C2—41no—
1010C2—41no—
1011C2—162no—
1012C2—164no—
1013C2#634545811yescharacteristic
1014C2C22×AGL(1,ℤ/16)11yescharacteristic
1015C2#762263511yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623520C2
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×#18073C2semidirect
4. #484148C2semidirect
5. #484147C2semidirect
6. #484056C2semidirect
7. #484053C2semidirect
8. #483924C2semidirect
9. #483878C2semidirect
10. #483421C2semidirect
11. #481384C2semidirect
12. #481317C2semidirect
13. #479974C2semidirect
32. #18091C22semidirect
33. #18090C22semidirect
39. #18065C22semidirect
40. #18063C22semidirect
52. #12089C22semidirect
53. #12087C22semidirect
54. #12080C22semidirect
55. #12078C22semidirect
56. #12078C22semidirect
57. #12077C22semidirect
58. #12067C22semidirect
59. #12065C22semidirect
60. #12030C22semidirect
61. #12030C22semidirect
64. #12000C22semidirect
68. #11655C22semidirect
69. #11654C22semidirect
73. #11598C22semidirect
75. #11414C22semidirect
76. #11414C22semidirect

Maximal subgroups

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

subgroupindex
#76235202
#63457262
C2×#180732
#4841482
#4841472
#4840562
#4840532
#4839242
#4838782
#4834212
#4813842
#4813172
#4799742