Finite Group Databasebeta

← #10578512

Subgroups — #10578512

Order 512.

5952 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62962C212yesmaximal, complemented
2#62411C218yesmaximal, complemented
3#62408C214yesmaximal, complemented
4#62400C214yesmaximal, complemented
5#62379C212yesmaximal, complemented
6#62379C214yesmaximal, complemented
7#62377C214yesmaximal, complemented
8#62375C212yesmaximal, complemented
9#62363C212yesmaximal, complemented
10#62361C212yesmaximal, complemented
11#61413C212yesmaximal, complemented
12#61409C211yesmaximal, characteristic, complemented
13C2×#3396C211yesmaximal, characteristic, complemented
14#61372C211yesmaximal, characteristic, complemented
15#61370C212yesmaximal, complemented
16Q8×#135C211yesmaximal, characteristic, complemented
17#61343C214yesmaximal, complemented
18#61341C212yesmaximal, complemented
19#61324C212yesmaximal, complemented
20#60926C214yesmaximal, complemented
21#60924C212yesmaximal, complemented
22#60714C211yesmaximal, characteristic, complemented
23#60713C212yesmaximal, complemented
24#60696C211yesmaximal, characteristic, complemented
25#60695C212yesmaximal, complemented
26Q8×#131C211yesmaximal, characteristic, complemented
27#3561—24no—
28#3557—24no—
29#3557C2218yescomplemented
30#3554—24no—
31#3554—22no—
32#3554C2214yescomplemented
33#3554C2218yescomplemented
34#3550—22no—
35#3550C2214yescomplemented
36#3535—28no—
37#3522—22no—
38#3522C2214yescomplemented
39#3520—24no—
40#3510C2214yes—
41#3510C2214yes—
42#3508C2212yes—
43#3508C2212yes—
44#3507—22no—
45#3507C2214yescomplemented
46#3502C2212yes—
47#3501C2214yes—
48C2×#559C2212yes—
49Q8×#41C2212yes—
50Q8×#41C2211yescharacteristic
51#3461C2212yes—
52#3460C2214yes—
53#3401C2218yescomplemented
54#3401C2218yescomplemented
55#3399C2214yes—
56#3399C2214yes—
57#3396C2212yes—
58#3396C2212yes—
59#3396C2212yes—
60#3396C2212yes—
61#3396C2214yes—
62#3396C2212yes—
63#3396C2212yes—
64#3396C2214yes—
65#3396C2214yescomplemented
66#3396C2214yescomplemented
67#3393C2214yescomplemented
68#3393C2214yescomplemented
69#3391C2212yes—
70#3391C2212yes—
71#3390C2214yescomplemented
72#3389C2218yescomplemented
73#3387C2214yescomplemented
74#3384C2218yescomplemented
75#3383C2211yescharacteristic, complemented
76#3383C2212yescomplemented
77#3383C2212yescomplemented
78#3383C2214yescomplemented
79Q8×Q16C2212yescomplemented
80Q8×Q16C2211yescharacteristic, complemented
81#3381C2212yescomplemented
82#3381C2214yescomplemented
83#3380C2214yescomplemented
84#3380C2211yescharacteristic, complemented
85#3380C2214yescomplemented
86#3380C2214yescomplemented
87#3380C2212yescomplemented
88Q8×SD16C2212yescomplemented
89Q8×D8C2214yescomplemented
90Q8×D8C2211yescharacteristic, complemented
91#3376C2218yescomplemented
92#3376C2218yescomplemented
93#3375C2214yescomplemented
94#3375C2214yescomplemented
95#3373C2214yescomplemented
96#3373C2218yescomplemented
97#3371C2218yescomplemented
98#3371C2218yescomplemented
99#3370C2218yescomplemented
100#3370C2218yescomplemented
101#3370C2218yescomplemented
102#3368C2214yescomplemented
103#3368C2218yescomplemented
104#3367C2218yescomplemented
105#3365C2214yescomplemented
106#3365C2214yescomplemented
107#3362C2214yescomplemented
108#3361C2214yescomplemented
109#3361C2218yescomplemented
110#3360C2218yescomplemented
111#3263C2218yescomplemented
112#3262C2218yescomplemented
113#3260C2218yescomplemented
114#3257C2218yescomplemented
115#3257C2218yescomplemented
116#3257C2218yescomplemented
117#3256C2218yescomplemented
118#3254C2214yescomplemented
119#3251C2214yescomplemented
120#3251C2218yescomplemented
121#3250C2218yescomplemented
122#3247C2214yescomplemented
123#3247C2218yescomplemented
124#3246C2214yescomplemented
125#3184C2214yes—
126#3183C2218yescomplemented
127#3179C2218yescomplemented
128#3178C2214yescomplemented
129#3177C2212yescomplemented
130#3176C2214yes—
131#3176C2214yes—
132#3176C2214yescomplemented
133#3175C2214yescomplemented
134#3175C2212yescomplemented
135#3175C2214yescomplemented
136#3175C2214yescomplemented
137#3173C2218yescomplemented
138#3172C2214yescomplemented
139#3171C2218yescomplemented
140#3170C2212yescomplemented
141#3169C2212yes—
142#3169C2212yes—
143#3169C2214yescomplemented
144#3168C2214yescomplemented
145#3168C2212yescomplemented
146#3168C2214yescomplemented
147#3168C2214yescomplemented
148#3164C2212yes—
149#3164C2211yescharacteristic
150#3160C2212yes—
151#3160C2211yescharacteristic
152#3156C2211yescharacteristic
153#3155C2212yes—
154C2×#495C2212yes—
155C2×#493C2211yescharacteristic
156#3140C2214yes—
157#3138C2212yes—
158#3137C2212yes—
159#3136C2214yes—
160#3082C2214yes—
161#3081C2214yes—
162#3081C2214yes—
163#3078C2212yes—
164#3077C2214yes—
165#3076C2212yes—
166#3076C2214yes—
167#3063C2212yes—
168#3062C2214yes—
169#3061C2211yescharacteristic
170#3059C2211yescharacteristic
171#3058C2212yes—
172#3058C2212yes—
173#3057C2214yes—
174#3043C2214yes—
175#3042C2214yes—
176#3041C2214yes—
177#3040C2214yes—
178#3038C2212yes—
179C2×#460C2212yes—
180C2×#463C2214yes—
181Q8×M16C2211yescharacteristic
182Q8×M16C2212yescomplemented
183#2962C2211yescharacteristic
184#2962C2212yes—
185#2962C2212yescomplemented
186#2962C2214yescomplemented
187#2960C2212yes—
188#2960C2211yescharacteristic
189#2960C2212yescomplemented
190#2960C2214yescomplemented
191C2×C8×Q8C2211yescharacteristic
192C2×C8×Q8C2212yescomplemented
193#2950C2212yes—
194#2949C2214yes—
195#2948C2212yes—
196#2948C2212yes—
197#2948C2212yes—
198C4×#137C2212yes—
199C4×AGL(1,ℤ/8)C2214yes—
200C4×#135C2212yes—
201C4×#135C2211yescharacteristic
202C2×C4×Q16C2211yescharacteristic
203C2×C4×D8C2212yes—
204#2906C2211yescharacteristic
205#2906C2212yes—
206C4×#131C2212yes—
207C4×#131C2211yescharacteristic
208C2×#137C2312yes—
209C2×AGL(1,ℤ/8)C2314yes—
210C2×#135C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2314yes—
213C22×D8C2312yes—
214C22×D8C2312yes—
215C2×#131C2311yescharacteristic
216C2×#131C2312yes—
217C2×#131C2311yescharacteristic
218#563—28no—
219#563—28no—
220#563—28no—
221#562—28no—
222#562—28no—
223#562—28no—
224#559—22no—
225#559—22no—
226#559—24no—
227#559—22no—
228#559—22no—
229#559—24no—
230#559—24no—
231#559C2314yes—
232#559C2318yes—
233#559C2314yes—
234#559C2318yes—
235#559C2318yes—
236#559C2314yes—
237#559C2314yes—
238Q82—22no—
239Q82D411yescharacteristic
240Q82C2314yes—
241Q82C2312yes—
242#557—22no—
243#557—24no—
244#557D411yescharacteristic
245#557D412yes—
246#557C2312yes—
247#557C2314yes—
248#557C2318yes—
249#557C2314yes—
250#556—24no—
251#556—24no—
252#556—24no—
253#556—24no—
254#556—24no—
255#556C2318yes—
256#556C2318yes—
257#554—24no—
258#554—24no—
259#554—24no—
260#554—22no—
261#554—24no—
262#554D412yes—
263#554D411yescharacteristic
264#554D414yes—
265#554D412yes—
266#554C2318yes—
267#554C2312yes—
268#554C2318yes—
269#554C2314yes—
270#554C2318yes—
271#552—28no—
272#552—28no—
273#552—28no—
274#551—28no—
275#551—28no—
276#551—28no—
277#551—28no—
278#550—22no—
279#550—22no—
280#550C2314yes—
281#550C2314yes—
282D4×Q8—22no—
283D4×Q8—24no—
284D4×Q8—24no—
285D4×Q8D411yescharacteristic
286D4×Q8D412yes—
287D4×Q8C2318yes—
288D4×Q8C2312yes—
289#548—24no—
290#548—28no—
291#548—24no—
292#547—24no—
293#547—28no—
294#547—24no—
295#547—28no—
296#546—24no—
297#546—24no—
298#546—24no—
299#546—24no—
300#544—24no—
301#544C2312yes—
302#544C2314yes—
303#543—28no—
304#542—24no—
305#542—24no—
306#542—24no—
307#542—28no—
308#542—24no—
309#542—28no—
310#542—24no—
311#542—28no—
312#542—24no—
313#542—28no—
314#542—24no—
315#542—22no—
316#542C2318yes—
317#542C2318yes—
318#542C2314yes—
319#542C2318yes—
320#541—22no—
321#541C2314yes—
322#540—24no—
323#540—24no—
324#540C2318yes—
325#540C2318yes—
326#539—28no—
327#539—28no—
328#539—28no—
329#539—28no—
330#539—28no—
331#539—24no—
332#539—28no—
333#538—28no—
334#537C2312yes—
335#536—24no—
336#536—24no—
337#536—28no—
338#536—28no—
339#536C2312yes—
340#536C2312yes—
341#535C2314yes—
342#535C2314yes—
343#533—24no—
344#533—22no—
345#533—22no—
346#533—24no—
347#533C2314yes—
348#533C2314yes—
349#533C2312yes—
350#533C2312yes—
351#533C2311yescharacteristic
352#533C2312yes—
353#533C2314yes—
354#532—22no—
355#532—22no—
356#532—24no—
357#532C2314yes—
358#532C2314yes—
359#532C2318yes—
360C2×#127C2312yes—
361#529—24no—
362#529—24no—
363#529—24no—
364#529—24no—
365#529—22no—
366#529C2318yes—
367#529C2314yes—
368#529C2318yes—
369#529C2318yes—
370C2×#124—22no—
371C2×#124C2314yes—
372#525—28no—
373C2×#123—24no—
374C2×C22⋊Q8—28no—
375#520—24no—
376#520—24no—
377#519C2314yes—
378#518C2314yes—
379#518C2314yes—
380C4×#41C2314yes—
381C4×#41C2312yes—
382C4×#41C2312yes—
383C4×#41C2311yescharacteristic
384C2×C4×Q8—22no—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2311yescharacteristic
387C2×C4×Q8C2312yes—
388C2×C4×D4—22no—
389C2×C4×D4C2314yes—
390#501C2314yes—
391#501C2318yes—
392#500C2312yes—
393#500C2312yes—
394#500C2312yes—
395#500C2314yes—
396#500C2311yescharacteristic
397#500C2311yescharacteristic
398#499C2312yes—
399#499C2312yes—
400#499C2312yes—
401#499C2314yes—
402#499C2312yes—
403#499C2314yes—
404#499C2312yes—
405#498C2314yes—
406#498C2312yes—
407#497C2314yes—
408#496C2318yes—
409#495C2314yes—
410#495C2314yes—
411#495C2314yes—
412#495C2314yes—
413#495C2314yes—
414#495C2312yes—
415#494C2312yes—
416#493C2314yes—
417#493C2312yes—
418#493C2312yes—
419#493C2312yes—
420#493C2312yes—
421#491C2314yes—
422#490C2318yes—
423#490C2318yes—
424#489C2318yes—
425#489C2318yes—
426#489C2314yes—
427#489C2318yes—
428#488C2318yes—
429#488C2318yes—
430#488C2314yes—
431#488C2318yes—
432#487C2314yes—
433#486C2318yes—
434#486C2314yes—
435#486C2314yes—
436#479C2314yes—
437#479C2314yes—
438#479C2314yes—
439#479C2318yes—
440#479C2318yes—
441#479C2318yes—
442#478C2314yes—
443#478C2314yes—
444#478C2314yes—
445#478C2318yes—
446#478C2318yes—
447#478C2318yes—
448#478C2318yes—
449#478C2318yes—
450#478C2318yes—
451#477C2314yes—
452#477C2312yes—
453#477C2314yes—
454#477C2318yes—
455#476C2312yes—
456#476C2314yes—
457#476C2318yes—
458#476C2318yes—
459#476C2318yes—
460#475C2312yes—
461#475C2314yes—
462#475C2314yes—
463#475C2318yes—
464#474C2312yes—
465#474C2314yes—
466#474C2318yes—
467#474C2318yes—
468#474C2318yes—
469#470C2314yes—
470#470C2314yes—
471#469C2318yes—
472#469C2318yes—
473#469C2318yes—
474#468C2314yes—
475#468C2318yes—
476#468C2314yes—
477#468C2318yes—
478#468C2318yes—
479#467C2312yes—
480#467C2312yes—
481#467C2312yes—
482#467C2314yes—
483#466C2314yes—
484#466C2314yes—
485#466C2312yes—
486#466C2314yes—
487#466C2314yes—
488#466C2318yes—
489#465C2318yes—
490#465C2318yes—
491#465C2314yes—
492#465C2318yes—
493#464C2318yes—
494#464C2318yes—
495#464C2318yes—
496#464C2318yes—
497#463C2318yes—
498#463C2318yes—
499#463C2318yes—
500#463C2318yes—
501#463C2318yes—
502#463C2318yes—
503#463C2318yes—
504#463C2318yes—
505#463C2318yes—
506#463C2318yes—
507#461C2318yes—
508#461C2318yes—
509#460C2314yes—
510#460C2318yes—
511#460C2314yes—
512#460C2318yes—
513#460C2318yes—
514#460C2314yes—
515#460C2314yes—
516#459C2318yes—
517#459C2314yes—
518#459C2314yes—
519#459C2318yes—
520#446C2314yes—
521#446C2314yes—
522#446C2312yes—
523#446C2314yes—
524#446C2314yes—
525#446C2312yes—
526#446C2314yes—
527#446C2314yes—
528#446C2312yes—
529#446C2314yes—
530#446C2312yes—
531C8×Q8C2314yes—
532C8×Q8C2312yes—
533C8×Q8C2312yes—
534C8×Q8C2314yes—
535C8×Q8C2311yescharacteristic
536C8×Q8C2311yescharacteristic
537C8×Q8C2314yes—
538C8×Q8C2311yescharacteristic
539C8×Q8C2312yes—
540C8×Q8C2312yes—
541C8×Q8C2311yescharacteristic
542C8×Q8C2312yes—
543C8×Q8C2312yes—
544#442C2318yes—
545#442C2318yes—
546#442C2318yes—
547#442C2318yes—
548#441C2314yes—
549#441C2318yes—
550#440C2318yes—
551#440C2318yes—
552#440C2314yes—
553#440C2318yes—
554C4×Q16C2314yes—
555C4×Q16C2312yes—
556C4×Q16C2314yes—
557C4×Q16C2312yes—
558C4×Q16C2311yescharacteristic
559C4×Q16C2312yes—
560C4×Q16C2314yes—
561C4×Q16C2312yes—
562C4×Q16C2311yescharacteristic
563C4×Q16C2312yes—
564C4×Q16C2312yes—
565C4×SD16C2318yes—
566C4×SD16C2318yes—
567C4×SD16C2314yes—
568C4×SD16C2318yes—
569C4×SD16C2312yes—
570C4×SD16C2314yes—
571C4×SD16C2312yes—
572C4×SD16C2314yes—
573C4×D8C2314yes—
574C4×D8C2314yes—
575C4×D8C2318yes—
576C4×D8C2311yescharacteristic
577C4×D8C2314yes—
578C4×D8C2314yes—
579C4×D8C2314yes—
580C4×D8C2312yes—
581C4×D8C2311yescharacteristic
582C4×D8C2314yes—
583C4×D8C2314yes—
584C4×D8C2314yes—
585C4×D8C2312yes—
586C4×D8C2314yes—
587C4×D8C2314yes—
588#428C2312yes—
589#428C2314yes—
590#427C2314yes—
591#427C2312yes—
592#427C2311yescharacteristic
593#427C2312yes—
594C2×#107C2311yescharacteristic
595#424C2312yes—
596#424C2312yes—
597#424C2312yes—
598#424C2314yes—
599#424C2314yes—
600#424C2314yes—
601#423C2312yes—
602#423C2311yescharacteristic
603#423C2312yes—
604#423C2314yes—
605C2×C4⋊C8C2312yes—
606C2×C4⋊C8C2311yescharacteristic
607C2×C4⋊C8C2312yes—
608C2×C4⋊C8C2314yes—
609#419C2314yes—
610#419C2312yes—
611#418C2314yes—
612#418C2314yes—
613#418C2314yes—
614#417C2312yes—
615#416C2314yes—
616#416C2312yes—
617C2×#103C2312yes—
618C2×#102C2314yes—
619#405C2312yes—
620#405C2311yescharacteristic
621#405C2312yes—
622#405C2311yescharacteristic
623#405C2314yes—
624#405C2314yes—
625#405C2312yes—
626#405C2312yes—
627C4×M16C2311yescharacteristic
628C4×M16C2312yes—
629C4×M16C2314yes—
630C4×M16C2312yes—
631C2×C4×C8C2311yescharacteristic
632C2×C4×C8C2312yes—
633C2×C4×C8C2314yes—
634C2×C4×C8C2312yes—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—28no—
639C2×#41—24no—
640C2×#41C2412yes—
641C2×#41C2411yescharacteristic
642C22×Q8—22no—
643C22×Q8—28no—
644C22×Q8C2×D411yescharacteristic
645C22×Q8C2×D412yes—
646C22×Q8C2412yes—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4C2414yes—
650C23×C4—24no—
651#137—44no—
652AGL(1,ℤ/8)—48no—
653#135—24no—
654C2×Q16—24no—
655C2×Q16C2412yes—
656C2×Q16C2412yes—
657C2×Q16C2411yescharacteristic
658C2×Q16C2414yes—
659C2×SD16—48no—
660C2×SD16C2412yes—
661C2×SD16C2418yes—
662C2×SD16C2418yes—
663C2×SD16C2418yes—
664C2×SD16C2414yes—
665C2×D8—28no—
666C2×D8—44no—
667C2×D8C2414yes—
668C2×D8C2414yes—
669C2×D8C2411yescharacteristic
670C2×D8C2414yes—
671C2×D8C2414yes—
672C2×D8C2418yes—
673#131—24no—
674#131—42no—
675#131—44no—
676C2×M16C2412yes—
677C2×M16C2411yescharacteristic
678C2×M16C2411yescharacteristic
679C2×M16C2412yes—
680C2×M16C2414yes—
681C2×M16C2412yes—
682C22×C8C2411yescharacteristic
683C22×C8C2412yes—
684C22×C8C2412yes—
685C22×C8C2414yes—
686C22×C8C2412yes—
687C22×C8C2411yescharacteristic
688C4⋊Q8—24no—
689C4⋊Q8—22no—
690C4⋊Q8—22no—
691C4⋊Q8—24no—
692C4⋊Q8—28no—
693C4⋊Q8—24no—
694C4⋊Q8—24no—
695C4⋊Q8—24no—
696C4⋊Q8—22no—
697C4⋊Q8—22no—
698C4⋊Q8—28no—
699C4⋊Q8C2×D411yescharacteristic
700C4⋊Q8C2×D411yescharacteristic
701C4⋊Q8C2×D412yes—
702C4⋊Q8C2×D414yes—
703C4⋊Q8C2×D412yes—
704C4⋊Q8C2×D412yes—
705C4⋊Q8C2×D412yes—
706C4⋊Q8C2×D414yes—
707C4⋊Q8C2414yes—
708C4⋊Q8C2412yes—
709C4⋊Q8C2412yes—
710C4⋊Q8C2418yes—
711C4⋊Q8C2414yes—
712C4⋊Q8C2414yes—
713C4⋊Q8C2414yes—
714#127—24no—
715#127—22no—
716#127—22no—
717#127C2414yes—
718#127C2414yes—
719#127C2418yes—
720#126—28no—
721#126—24no—
722#126—28no—
723#126—28no—
724#126—28no—
725#126—28no—
726#126—28no—
727#126—28no—
728#126—24no—
729#126—24no—
730#126—28no—
731#126—24no—
732#126—28no—
733#126—28no—
734#125—24no—
735#125—24no—
736#125—22no—
737#125—24no—
738#125—24no—
739#125—24no—
740#125—28no—
741#125—24no—
742#125—28no—
743#125—28no—
744#125—24no—
745#125C2×D412yes—
746#125C2×D412yes—
747#125C2×D414yes—
748#125C2×D414yes—
749#125C2×D414yes—
750#125C2×D412yes—
751#125C2414yes—
752#125C2414yes—
753#125C2418yes—
754#125C2414yes—
755#125C2414yes—
756#124—24no—
757#124—24no—
758#124—28no—
759#124—24no—
760#124—24no—
761#124—24no—
762#124—28no—
763#124—28no—
764#124—22no—
765#124—24no—
766#124—28no—
767#124—28no—
768#124—28no—
769#124—24no—
770#124—24no—
771#124—28no—
772#124—24no—
773#124—24no—
774#124C2418yes—
775#124C2418yes—
776#124C2418yes—
777#124C2414yes—
778#123—24no—
779#123—28no—
780#123—28no—
781#123—28no—
782#123—24no—
783#123—28no—
784#123—28no—
785#123—28no—
786#123—28no—
787#123—28no—
788#123—28no—
789#123—28no—
790#123—28no—
791#123—28no—
792#123—28no—
793#123—28no—
794#123—28no—
795#123—28no—
796#123—28no—
797#123—28no—
798#123—24no—
799#123—24no—
800#123—28no—
801#123—28no—
802C22⋊Q8—28no—
803C22⋊Q8—22no—
804C22⋊Q8—22no—
805C22⋊Q8—24no—
806C22⋊Q8—28no—
807C22⋊Q8—28no—
808C22⋊Q8—28no—
809C22⋊Q8—28no—
810C22⋊Q8—24no—
811C22⋊Q8—22no—
812C22⋊Q8—24no—
813C22⋊Q8—24no—
814C22⋊Q8—22no—
815C22⋊Q8—28no—
816C22⋊Q8—28no—
817C22⋊Q8—28no—
818C22⋊Q8—28no—
819C22⋊Q8—22no—
820C22⋊Q8—22no—
821C22⋊Q8—24no—
822C22⋊Q8—24no—
823C22⋊Q8—24no—
824C22⋊Q8—24no—
825C22⋊Q8—22no—
826C22⋊Q8—24no—
827C22⋊Q8—28no—
828C22⋊Q8—28no—
829C22⋊Q8—28no—
830C22⋊Q8—28no—
831C22⋊Q8—28no—
832C22⋊Q8—28no—
833C22⋊Q8—28no—
834C22⋊Q8—28no—
835C22⋊Q8—24no—
836C22⋊Q8—28no—
837C22⋊Q8C2×D414yes—
838C22⋊Q8C2×D412yes—
839C22⋊Q8C2×D414yes—
840C22⋊Q8C2×D414yes—
841C22⋊Q8C2×D414yes—
842C22⋊Q8C2×D412yes—
843C22⋊Q8C2×D414yes—
844C22⋊Q8C2×D412yes—
845C22⋊Q8C2×D414yes—
846C22⋊Q8C2×D414yes—
847C22⋊Q8C2×D412yes—
848C22⋊Q8C2414yes—
849C22⋊Q8C2414yes—
850C22⋊Q8C2414yes—
851#121—24no—
852#121—22no—
853#121—28no—
854#121—24no—
855#121—24no—
856#121—24no—
857#121—24no—
858#121—24no—
859#121—24no—
860#121—28no—
861#121—28no—
862#121—28no—
863#121—28no—
864#121—28no—
865#121—28no—
866#121C2418yes—
867#121C2418yes—
868#121C2414yes—
869#120—28no—
870#120—28no—
871C4×Q8—22no—
872C4×Q8—24no—
873C4×Q8—22no—
874C4×Q8—24no—
875C4×Q8—24no—
876C4×Q8—24no—
877C4×Q8—24no—
878C4×Q8—28no—
879C4×Q8—22no—
880C4×Q8—24no—
881C4×Q8—22no—
882C4×Q8—22no—
883C4×Q8—24no—
884C4×Q8—24no—
885C4×Q8—22no—
886C4×Q8C2×D411yescharacteristic
887C4×Q8C2×D412yes—
888C4×Q8C2×D411yescharacteristic
889C4×Q8C2×D412yes—
890C4×Q8C2×D412yes—
891C4×Q8C2×D414yes—
892C4×Q8C2×D412yes—
893C4×Q8C2×D411yescharacteristic
894C4×Q8C2×D411yescharacteristic
895C4×Q8C2×D412yes—
896C4×Q8C2414yes—
897C4×Q8C2414yes—
898C4×Q8C2414yes—
899C4×Q8C2412yes—
900C4×Q8C2412yes—
901C4×Q8C2414yes—
902C4×Q8C2418yes—
903C4×Q8C2418yes—
904C4×Q8C2411yescharacteristic
905C4×Q8C2411yescharacteristic
906C4×Q8C2412yes—
907C4×Q8C2414yes—
908C4×Q8C2412yes—
909C4×Q8C2414yes—
910C4×Q8C2412yes—
911C4×D4—24no—
912C4×D4—22no—
913C4×D4—24no—
914C4×D4—22no—
915C4×D4—28no—
916C4×D4—28no—
917C4×D4—24no—
918C4×D4—28no—
919C4×D4—24no—
920C4×D4—28no—
921C4×D4—24no—
922C4×D4—24no—
923C4×D4—24no—
924C4×D4—24no—
925C4×D4—24no—
926C4×D4—28no—
927C4×D4—24no—
928C4×D4—28no—
929C4×D4—24no—
930C4×D4—24no—
931C4×D4—24no—
932C4×D4—28no—
933C4×D4—24no—
934C4×D4—24no—
935C4×D4C2×D414yes—
936C4×D4C2×D412yes—
937C4×D4C2×D411yescharacteristic
938C4×D4C2×D412yes—
939C4×D4C2×D414yes—
940C4×D4C2×D412yes—
941C4×D4C2×D412yes—
942C4×D4C2×D411yescharacteristic
943C4×D4C2418yes—
944C4×D4C2418yes—
945C4×D4C2412yes—
946C4×D4C2414yes—
947C4×D4C2414yes—
948C4×D4C2412yes—
949C4×D4C2418yes—
950C4×D4C2418yes—
951C4×D4C2418yes—
952C4×D4C2418yes—
953#117—24no—
954#117—28no—
955#117—28no—
956#117—28no—
957#117—22no—
958#117—24no—
959#117—24no—
960#117—28no—
961#117—28no—
962#117—28no—
963#117C2412yes—
964#117C2414yes—
965#117C2411yescharacteristic
966#117C2412yes—
967#117C2412yes—
968#117C2414yes—
969C2×C4⋊C4—22no—
970C2×C4⋊C4—22no—
971C2×C4⋊C4—24no—
972C2×C4⋊C4—28no—
973C2×C4⋊C4—28no—
974C2×C4⋊C4—28no—
975C2×C4⋊C4C2×D411yescharacteristic
976C2×C4⋊C4C2×D412yes—
977C2×C4⋊C4C2×D412yes—
978C2×C4⋊C4C2×D414yes—
979C2×C4⋊C4C2412yes—
980C2×C22⋊C4—24no—
981C2×C22⋊C4—24no—
982C2×C22⋊C4—24no—
983C2×C22⋊C4—28no—
984C2×C22⋊C4—28no—
985C2×C42—22no—
986C2×C42—24no—
987C2×C42—22no—
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2414yes—
991C2×C42C2412yes—
992#107C2412yes—
993#107C2412yes—
994#107C2411yescharacteristic
995#107C2411yescharacteristic
996#107C2412yes—
997#107C2412yes—
998#107C2412yes—
999#107C2412yes—
1000#107C2414yes—
1001#107C2414yes—
1002#107C2418yes—
1003#107C2414yes—
1004#106C2414yes—
1005#106C2412yes—
1006#106C2414yes—
1007#106C2414yes—
1008#106C2414yes—
1009#106C2414yes—
1010#106C2418yes—
1011C4⋊C8C2411yescharacteristic
1012C4⋊C8C2412yes—
1013C4⋊C8C2412yes—
1014C4⋊C8C2411yescharacteristic
1015C4⋊C8C2412yes—
1016C4⋊C8C2414yes—
1017C4⋊C8C2414yes—
1018C4⋊C8C2412yes—
1019C4⋊C8C2414yes—
1020C4⋊C8C2414yes—
1021C4⋊C8C2412yes—
1022C4⋊C8C2412yes—
1023C4⋊C8C2412yes—
1024C4⋊C8C2414yes—
1025C4⋊C8C2414yes—
1026C4⋊C8C2414yes—
1027C4⋊C8C2414yes—
1028#103C2414yes—
1029#103C2414yes—
1030#103C2414yes—
1031#103C2414yes—
1032#103C2412yes—
1033#103C2412yes—
1034#103C2414yes—
1035#103C2414yes—
1036#103C2414yes—
1037#103C2418yes—
1038#103C2418yes—
1039#102C2418yes—
1040#102C2418yes—
1041#102C2412yes—
1042#102C2412yes—
1043#102C2414yes—
1044#102C2414yes—
1045#102C2414yes—
1046#102C2418yes—
1047#102C2418yes—
1048#102C2418yes—
1049#102C2418yes—
1050#102C2418yes—
1051#102C2418yes—
1052#97C2414yes—
1053#97C2412yes—
1054#97C2414yes—
1055#97C2414yes—
1056#97C2412yes—
1057#97C2412yes—
1058C4×C8C2412yes—
1059C4×C8C2411yescharacteristic
1060C4×C8C2414yes—
1061C4×C8C2412yes—
1062C4×C8C2412yes—
1063C4×C8C2411yescharacteristic
1064C4×C8C2412yes—
1065C4×C8C2412yes—
1066C4×C8C2412yes—
1067C4×C8C2412yes—
1068C4×C8C2414yes—
1069C4×C8C2411yescharacteristic
1070C4×C8C2414yes—
1071C4×C8C2411yescharacteristic
1072C24—24no—
1073#41—22no—
1074#41—22no—
1075#41—24no—
1076#41—24no—
1077#41—88no—
1078#41—88no—
1079#41—168no—
1080#41—164no—
1081#41—164no—
1082C2×Q8—22no—
1083C2×Q8—22no—
1084C2×Q8—24no—
1085C2×Q8—24no—
1086C2×Q8—24no—
1087C2×Q8—28no—
1088C2×Q8—22no—
1089C2×Q8—24no—
1090C2×Q8—24no—
1091C2×Q8—42no—
1092C2×Q8—44no—
1093C2×Q8—84no—
1094C2×Q8—168no—
1095C2×Q8C22×D411yescharacteristic
1096C2×Q8C22×D412yes—
1097C2×Q8C22×D411yescharacteristic
1098C2×Q8C22×D411yescharacteristic
1099C2×Q8C22×D414yes—
1100C2×Q8C22×D412yes—
1101C2×Q8C22×D414yes—
1102C2×Q8C22×D412yes—
1103C2×Q8C2514yes—
1104C2×Q8C2512yes—
1105C2×D4—22no—
1106C2×D4—28no—
1107C2×D4—28no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4—24no—
1111C2×D4—28no—
1112C2×D4—24no—
1113C2×D4—28no—
1114C2×D4—24no—
1115C2×D4—24no—
1116C2×D4—28no—
1117C2×D4—28no—
1118C2×D4—84no—
1119C2×D4—162no—
1120C2×D4C22×D412yes—
1121C2×D4C22×D411yescharacteristic
1122C2×D4C2518yes—
1123C2×D4C2512yes—
1124C22×C4—22no—
1125C22×C4—22no—
1126C22×C4—22no—
1127C22×C4—22no—
1128C22×C4—24no—
1129C22×C4—22no—
1130C22×C4—24no—
1131C22×C4—28no—
1132C22×C4—28no—
1133C22×C4—28no—
1134C22×C4—28no—
1135C22×C4—28no—
1136C22×C4—28no—
1137C22×C4—164no—
1138C22×C4C22×D411yescharacteristic
1139C22×C4C22×D412yes—
1140C22×C4C22×D412yes—
1141C22×C4C22×D412yes—
1142C22×C4C22×D411yescharacteristic
1143C22×C4C22×D414yes—
1144C22×C4C22×D412yes—
1145C22×C4C22×D414yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148Q16—24no—
1149Q16—24no—
1150Q16—22no—
1151Q16—44no—
1152SD16—24no—
1153SD16—48no—
1154SD16—48no—
1155SD16—48no—
1156SD16—44no—
1157D8—28no—
1158D8—28no—
1159D8—22no—
1160D8—44no—
1161D8—44no—
1162D8—48no—
1163M16—22no—
1164M16—24no—
1165M16—22no—
1166M16—24no—
1167M16—42no—
1168M16—44no—
1169C2×C8—22no—
1170C2×C8—24no—
1171C2×C8—24no—
1172C2×C8—42no—
1173C2×C8—44no—
1174C2×C82−1+414yes—
1175C2×C8C2512yes—
1176C2×C8C2512yes—
1177C2×C8C2511yescharacteristic
1178C2×C8C2512yes—
1179C2×C8C2512yes—
1180C2×C8C2514yes—
1181C2×C8C2511yescharacteristic
1182C2×C8C2511yescharacteristic
1183C2×C8C2511yescharacteristic
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—22no—
1192C4⋊C4—28no—
1193C4⋊C4—28no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—22no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—22no—
1207C4⋊C4—24no—
1208C4⋊C4—22no—
1209C4⋊C4—28no—
1210C4⋊C4—28no—
1211C4⋊C4—22no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4C22×D411yescharacteristic
1215C4⋊C4C22×D414yes—
1216C4⋊C4C22×D414yes—
1217C4⋊C4C22×D412yes—
1218C4⋊C4C22×D414yes—
1219C4⋊C4C22×D412yes—
1220C4⋊C4C22×D412yes—
1221C4⋊C4C22×D411yescharacteristic
1222C4⋊C4C22×D412yes—
1223C4⋊C4C22×D414yes—
1224C4⋊C4C22×D414yes—
1225C4⋊C4C22×D412yes—
1226C4⋊C4C22×D412yes—
1227C4⋊C4C22×D414yes—
1228C4⋊C4C22×D411yescharacteristic
1229C4⋊C4C22×D411yescharacteristic
1230C4⋊C4C22×D412yes—
1231C4⋊C4C22×D412yes—
1232C4⋊C4C22×D414yes—
1233C4⋊C4C22×D412yes—
1234C4⋊C4C22×D414yes—
1235C4⋊C4C22×D412yes—
1236C4⋊C4C22×D412yes—
1237C4⋊C4C22×D414yes—
1238C4⋊C4C22×D414yes—
1239C4⋊C4C2512yes—
1240C4⋊C4C2514yes—
1241C4⋊C4C2514yes—
1242C4⋊C4C2512yes—
1243C4⋊C4C2514yes—
1244C22⋊C4—22no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—28no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—24no—
1264C22⋊C4—24no—
1265C22⋊C4—22no—
1266C22⋊C4—22no—
1267C22⋊C4—24no—
1268C22⋊C4—24no—
1269C22⋊C4—24no—
1270C22⋊C4C22×D412yes—
1271C22⋊C4C22×D414yes—
1272C22⋊C4C22×D412yes—
1273C22⋊C4C22×D412yes—
1274C22⋊C4C22×D414yes—
1275C22⋊C4C22×D414yes—
1276C42—24no—
1277C42—24no—
1278C42—22no—
1279C42—24no—
1280C42—22no—
1281C42—24no—
1282C42—22no—
1283C42—24no—
1284C42—28no—
1285C42—28no—
1286C42C22×D412yes—
1287C42C22×D411yescharacteristic
1288C42C22×D414yes—
1289C42C22×D412yes—
1290C42C22×D412yes—
1291C42C22×D411yescharacteristic
1292C42C22×D414yes—
1293C42C22×D412yes—
1294C42C2512yes—
1295C42C2511yescharacteristic
1296C42C2512yes—
1297C42C2512yes—
1298C42C2514yes—
1299C42C2511yescharacteristic
1300C23—28no—
1301C23—22no—
1302C23—48no—
1303C23—84no—
1304C23—84no—
1305C23C23×D412yes—
1306C23C23×D411yescharacteristic
1307Q8—22no—
1308Q8—22no—
1309Q8—24no—
1310Q8—22no—
1311Q8—22no—
1312Q8—24no—
1313Q8—24no—
1314Q8—22no—
1315Q8—44no—
1316Q8—42no—
1317Q8—44no—
1318Q8—42no—
1319Q8—44no—
1320Q8—44no—
1321Q8—84no—
1322Q8—84no—
1323Q8—84no—
1324Q8—88no—
1325Q8—82no—
1326D4—24no—
1327D4—28no—
1328D4—22no—
1329D4—22no—
1330D4—28no—
1331D4—22no—
1332D4—44no—
1333D4—48no—
1334D4—48no—
1335D4—84no—
1336D4—84no—
1337D4—84no—
1338D4—88no—
1339D4—88no—
1340D4—88no—
1341D4—84no—
1342D4—88no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—42no—
1355C2×C4—41no—
1356C2×C4—44no—
1357C2×C4—42no—
1358C2×C4—44no—
1359C2×C4—42no—
1360C2×C4—44no—
1361C2×C4—44no—
1362C2×C4—44no—
1363C2×C4—88no—
1364C2×C4—88no—
1365C2×C4—84no—
1366C2×C4—88no—
1367C2×C4—88no—
1368C2×C4—88no—
1369C2×C4—88no—
1370C2×C4—84no—
1371C2×C4—82no—
1372C2×C4—82no—
1373C2×C4C23×D411yescharacteristic
1374C2×C4C23×D412yes—
1375C2×C4C23×D412yes—
1376C2×C4C23×D414yes—
1377C2×C4C23×D414yes—
1378C2×C4C23×D411yescharacteristic
1379C2×C4C23×D412yes—
1380C2×C4C23×D412yes—
1381C2×C4C23×D411yescharacteristic
1382C2×C4C23×D412yes—
1383C2×C4C23×D412yes—
1384C2×C4C23×D412yes—
1385C2×C4C23×D411yescharacteristic
1386C2×C4C23×D411yescharacteristic
1387C2×C4C2×2−1+412yes—
1388C2×C4#58512yes—
1389C2×C4C2611yescharacteristic
1390C8—22no—
1391C8—21no—
1392C8—22no—
1393C8—21no—
1394C8—22no—
1395C8—24no—
1396C8—22no—
1397C8C2×2−1+412yes—
1398C8C2×2−1+412yes—
1399C22—21no—
1400C22—21no—
1401C22—22no—
1402C22—22no—
1403C22—22no—
1404C22—42no—
1405C22—48no—
1406C22—42no—
1407C22—48no—
1408C22—48no—
1409C22—42no—
1410C22—168no—
1411C22#349712yes—
1412C22C24×D411yescharacteristic
1413C4—22no—
1414C4—22no—
1415C4—21no—
1416C4—22no—
1417C4—24no—
1418C4—22no—
1419C4—22no—
1420C4—21no—
1421C4—22no—
1422C4—22no—
1423C4—21no—
1424C4—24no—
1425C4—42no—
1426C4—44no—
1427C4—42no—
1428C4—44no—
1429C4—44no—
1430C4—42no—
1431C4—44no—
1432C4#349712yes—
1433C4#358412yes—
1434C4C22×2−1+411yescharacteristic
1435C4C2×#58511yescharacteristic
1436C2—22no—
1437C2—42no—
1438C2—82no—
1439C2—88no—
1440C2C2×#349711yescharacteristic
1441C2C2×#358411yescharacteristic
1442C2#6309111yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ Q8×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62962C2semidirect
2. #62411C2semidirect
3. #62408C2semidirect
4. #62400C2semidirect
5. #62379C2semidirect
6. #62379C2semidirect
7. #62377C2semidirect
8. #62375C2semidirect
9. #62363C2semidirect
10. #62361C2semidirect
11. #61413C2semidirect
12. #61409C2semidirect
13. C2×#3396C2semidirect
14. #61372C2semidirect
15. #61370C2semidirect
16. Q8×#135C2semidirect
17. #61343C2semidirect
18. #61341C2semidirect
19. #61324C2semidirect
20. #60926C2semidirect
21. #60924C2semidirect
22. #60714C2semidirect
23. #60713C2semidirect
24. #60696C2semidirect
25. #60695C2semidirect
26. Q8×#131C2semidirect
29. #3557C22semidirect
32. #3554C22semidirect
33. #3554C22semidirect
35. #3550C22semidirect
38. #3522C22semidirect
45. #3507C22semidirect
53. #3401C22semidirect
54. #3401C22semidirect
65. #3396C22semidirect
66. #3396C22semidirect
67. #3393C22semidirect
68. #3393C22semidirect
71. #3390C22semidirect
72. #3389C22semidirect
73. #3387C22semidirect
74. #3384C22semidirect
75. #3383C22semidirect
76. #3383C22semidirect
77. #3383C22semidirect
78. #3383C22semidirect
79. Q8×Q16C22semidirect
80. Q8×Q16C22semidirect
81. #3381C22semidirect
82. #3381C22semidirect
83. #3380C22semidirect
84. #3380C22semidirect
85. #3380C22semidirect
86. #3380C22semidirect
87. #3380C22semidirect
88. Q8×SD16C22semidirect
89. Q8×D8C22semidirect
90. Q8×D8C22semidirect
91. #3376C22semidirect
92. #3376C22semidirect
93. #3375C22semidirect
94. #3375C22semidirect
95. #3373C22semidirect
96. #3373C22semidirect
97. #3371C22semidirect
98. #3371C22semidirect
99. #3370C22semidirect
100. #3370C22semidirect
101. #3370C22semidirect
102. #3368C22semidirect
103. #3368C22semidirect
104. #3367C22semidirect
105. #3365C22semidirect
106. #3365C22semidirect
107. #3362C22semidirect
108. #3361C22semidirect
109. #3361C22semidirect
110. #3360C22semidirect
111. #3263C22semidirect
112. #3262C22semidirect
113. #3260C22semidirect
114. #3257C22semidirect
115. #3257C22semidirect
116. #3257C22semidirect
117. #3256C22semidirect
118. #3254C22semidirect
119. #3251C22semidirect
120. #3251C22semidirect
121. #3250C22semidirect
122. #3247C22semidirect
123. #3247C22semidirect
124. #3246C22semidirect
126. #3183C22semidirect
127. #3179C22semidirect
128. #3178C22semidirect
129. #3177C22semidirect
132. #3176C22semidirect
133. #3175C22semidirect
134. #3175C22semidirect
135. #3175C22semidirect
136. #3175C22semidirect
137. #3173C22semidirect
138. #3172C22semidirect
139. #3171C22semidirect
140. #3170C22semidirect
143. #3169C22semidirect
144. #3168C22semidirect
145. #3168C22semidirect
146. #3168C22semidirect
147. #3168C22semidirect
182. Q8×M16C22semidirect
185. #2962C22semidirect
186. #2962C22semidirect
189. #2960C22semidirect
190. #2960C22semidirect
192. C2×C8×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#629622
#624112
#624082
#624002
#623792
#623772
#623752
#623632
#623612
#614132
#614092
C2×#33962
#613722
#613702
Q8×#1352
#613432
#613412
#613242
#609262
#609242
#607142
#607132
#606962
#606952
Q8×#1312