Finite Group Databasebeta

← #10581625

Subgroups — #10581625

Order 512.

6090 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62837C211yesmaximal, characteristic, complemented
2C2×#3548C211yesmaximal, characteristic, complemented
3#62401C218yesmaximal, complemented
4#62381C214yesmaximal, complemented
5#62371C214yesmaximal, complemented
6#61935C214yesmaximal, complemented
7#61914C214yesmaximal, complemented
8#61901C214yesmaximal, complemented
9#61890C212yesmaximal, complemented
10#61881C212yesmaximal, complemented
11#61868C214yesmaximal, complemented
12#61851C214yesmaximal, complemented
13#61841C214yesmaximal, complemented
14#61826C212yesmaximal, complemented
15#61819C212yesmaximal, complemented
16#60979C218yesmaximal, complemented
17#60969C211yesmaximal, characteristic, complemented
18#60951C211yesmaximal, characteristic, complemented
19#60946C211yesmaximal, characteristic, complemented
20#60941C211yesmaximal, characteristic, complemented
21#60250C211yesmaximal, characteristic, complemented
22#3563—22no—
23#3563—22no—
24#3556C2212yescomplemented
25#3555—22no—
26#3555C2214yescomplemented
27#3550C2212yescomplemented
28#3548—22no—
29#3548—22no—
30#3548—22no—
31#3548—22no—
32#3548C2214yes—
33#3548C2214yes—
34#3548C2214yes—
35#3548C2214yes—
36#3538—22no—
37C2×#562—22no—
38#3523—22no—
39#3523C2214yes—
40#3509—22no—
41#3509—21no—
42#3509C2212yescomplemented
43#3507C2212yes—
44#3507C2212yescomplemented
45#3503—21no—
46#3503C2212yescomplemented
47#3502C2212yes—
48#3502C2212yescomplemented
49#3495—22no—
50#3495C2214yes—
51C2×#554C2212yes—
52C2×#554C2212yes—
53C2×#550C2212yes—
54C2×#550C2212yes—
55C2×#547—21no—
56C2×#547—21no—
57C2×#540C2214yes—
58C2×#537—22no—
59C2×#537—22no—
60#3444C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#533C2211yescharacteristic
63C2×#532C2211yescharacteristic
64C2×#532C2211yescharacteristic
65#3399C2218yescomplemented
66#3397C2218yescomplemented
67#3397C2218yescomplemented
68#3397C22116yescomplemented
69#3392C2218yescomplemented
70#3392C2218yescomplemented
71#3392C2218yescomplemented
72#3388C22116yescomplemented
73#3385C2218yescomplemented
74#3385C2218yescomplemented
75#3384C2218yescomplemented
76#3381C2218yescomplemented
77#3381C2218yescomplemented
78#3380C2218yescomplemented
79#3376C22116yescomplemented
80#3372C2218yescomplemented
81#3372C2218yescomplemented
82#3372C2218yescomplemented
83#3368C2218yescomplemented
84#3368C22116yescomplemented
85#3368C2218yescomplemented
86#3366C2218yescomplemented
87#3362C2218yescomplemented
88#3362C2218yescomplemented
89#3361C2218yescomplemented
90#3360C2218yescomplemented
91#3360C2218yescomplemented
92#3358C2218yescomplemented
93#3260C22116yescomplemented
94#3257C22116yescomplemented
95#3254C2212yescomplemented
96#3254C2214yescomplemented
97#3253C2212yescomplemented
98#3247C2214yescomplemented
99#3246C2214yescomplemented
100#3241C22116yescomplemented
101#3238C2212yes—
102#3236C2218yes—
103#3235C2212yescomplemented
104#3232C2218yes—
105#3230C2211yescharacteristic
106#3230C2212yes—
107#3229C2212yes—
108#3228C2212yescomplemented
109#3227C2211yescharacteristic
110#3227C2212yescomplemented
111#3226C2212yescomplemented
112#3221C22116yescomplemented
113#3217C2212yes—
114#3217C2218yes—
115#3214C2212yescomplemented
116#3208C2212yes—
117#3208C2211yescharacteristic
118#3208C2212yes—
119#3208C2218yes—
120#3207C2212yescomplemented
121#3206C2212yescomplemented
122#3206C2212yescomplemented
123#3205C2211yescharacteristic
124#3194C2214yes—
125#3193C2214yes—
126#3188C2214yes—
127#3187C2214yes—
128#3182C2214yescomplemented
129#3179C22116yescomplemented
130#3174C22116yescomplemented
131#3171C2214yescomplemented
132#3169C2212yescomplemented
133#3167C2214yescomplemented
134#3167C2212yescomplemented
135#3126C22116yescomplemented
136#3119C22116yescomplemented
137#3114C2218yes—
138#3112C2214yescomplemented
139#3110C2214yes—
140#3110C2218yes—
141#3106C2214yescomplemented
142#3106C2214yescomplemented
143#3105C2214yes—
144#3105C2218yes—
145#3103C2214yescomplemented
146#3101C2212yes—
147#3101C2212yes—
148#3101C2212yes—
149#3101C2218yes—
150#3100C2212yes—
151#2986C2214yescomplemented
152#2985C2214yescomplemented
153#2984C2214yes—
154#2983C2212yes—
155#2982C2212yes—
156#2962C2214yescomplemented
157#2960C2214yescomplemented
158#2924C2214yes—
159#2920C2211yescharacteristic
160C2×#431C2211yescharacteristic
161C22×#41—22no—
162C22×#41—22no—
163C22×#41—21no—
164C22×#41—21no—
165#564—24no—
166#563—24no—
167#563—28no—
168#562—28no—
169#562—28no—
170#562—28no—
171#562—28no—
172#559C2314yes—
173Q82—22no—
174Q82C2314yes—
175Q82C2314yes—
176#557—22no—
177#557—22no—
178#557—22no—
179#557—24no—
180#557—24no—
181#557—24no—
182#557C2314yes—
183#557C2314yes—
184#557C2314yes—
185#557C2314yes—
186#557C2314yes—
187#557C2318yes—
188#556—22no—
189#556—22no—
190#556—24no—
191#556—24no—
192#556—24no—
193#556C2314yes—
194#556C2314yes—
195#556C2318yes—
196#554—22no—
197#554—24no—
198#554—24no—
199#554—24no—
200#554—24no—
201#554—24no—
202#554—24no—
203#554C2318yes—
204#554C2318yes—
205#554C2318yes—
206#554C2314yes—
207#554C2318yes—
208#552—24no—
209#552—24no—
210#552—24no—
211#552—24no—
212#552—24no—
213#552—24no—
214#552—28no—
215#552—28no—
216#552—24no—
217#552—24no—
218#551—28no—
219#550—24no—
220#550—24no—
221#550—24no—
222#550—24no—
223#550C2318yes—
224#550C2318yes—
225#550C2318yes—
226#550C2318yes—
227D4×Q8—24no—
228D4×Q8—22no—
229D4×Q8—24no—
230D4×Q8C2314yes—
231#547—24no—
232#547—24no—
233#547—24no—
234#547—24no—
235#547—24no—
236#547—24no—
237#547—24no—
238#547—24no—
239#544—24no—
240#544—24no—
241#544—24no—
242#544—22no—
243#544—24no—
244#544C2314yes—
245#542—24no—
246#542C2318yes—
247#541—24no—
248#541—24no—
249#541—28no—
250#541—24no—
251#541—24no—
252#541—24no—
253#541—28no—
254#541C2318yes—
255#540—28no—
256#540—28no—
257#540C23116yes—
258#540C23116yes—
259#539—24no—
260#539—24no—
261#537—28no—
262#537—28no—
263#537—28no—
264#537—28no—
265#537—28no—
266#537—28no—
267#537—28no—
268#537—28no—
269#536—22no—
270#536—24no—
271#536C2314yes—
272#533—22no—
273#533—22no—
274#533—22no—
275#533—24no—
276#533—21no—
277#533—21no—
278#533—21no—
279#533—21no—
280#533D412yes—
281#533D412yes—
282#533D412yes—
283#533D412yes—
284#533C2312yes—
285#533C2311yescharacteristic
286#533C2318yes—
287#533C2312yes—
288#533C2312yes—
289#533C2311yescharacteristic
290#533C2312yes—
291#533C2311yescharacteristic
292#533C2312yes—
293#533C2312yes—
294#533C2312yes—
295#533C2312yes—
296#532—21no—
297#532—21no—
298#532—21no—
299#532—21no—
300#532—21no—
301#532—21no—
302#532—21no—
303#532—21no—
304#532C2311yescharacteristic
305#532C2311yescharacteristic
306#532C2312yes—
307#532C2312yes—
308#532C2312yes—
309#532C2312yes—
310#532C2312yes—
311#532C2312yes—
312#532C2311yescharacteristic
313#532C2312yes—
314#532C2312yes—
315C2×C4⋊Q8—22no—
316C2×C4⋊Q8D411yescharacteristic
317C2×C4⋊Q8D411yescharacteristic
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2311yescharacteristic
320C2×C4⋊Q8C2311yescharacteristic
321C2×C4⋊Q8C2311yescharacteristic
322C2×#127C2311yescharacteristic
323C2×#127C2311yescharacteristic
324C2×#127C2314yes—
325#529—24no—
326#529—21no—
327#529—21no—
328#529—21no—
329#529—21no—
330#529C2312yes—
331#529C2318yes—
332#529C2312yes—
333C2×#125—21no—
334C2×#125D412yes—
335C2×#125C2314yes—
336C2×#124—21no—
337C2×#124—21no—
338#525—21no—
339#525—21no—
340#525C2312yes—
341C2×#123—24no—
342C2×#123—24no—
343C2×C22⋊Q8—22no—
344C2×C22⋊Q8—22no—
345C2×C22⋊Q8—21no—
346C2×C22⋊Q8—24no—
347C2×C22⋊Q8—24no—
348C2×C22⋊Q8D412yes—
349C2×C22⋊Q8D412yes—
350C2×C22⋊Q8C2312yes—
351C2×#121—21no—
352C2×#121—21no—
353C2×#121—22no—
354C2×#121—22no—
355C2×#121—24no—
356C2×#121—24no—
357C2×#121—24no—
358C2×#121—24no—
359C2×#121C2312yes—
360C2×#121C2312yes—
361#520—22no—
362#520C2314yes—
363#519—22no—
364#519—24no—
365#519C2314yes—
366C4×#41—21no—
367C4×#41—21no—
368C4×#41C2312yes—
369C2×C4×Q8—21no—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2312yes—
373C2×C4×D4—21no—
374C2×C4×D4—21no—
375C2×C4×D4C2312yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2314yes—
379C2×#117—21no—
380C2×#117C2312yes—
381C22×C4⋊C4—22no—
382C22×C4⋊C4—22no—
383C22×C42C2311yescharacteristic
384#501C23116yes—
385#501C2314yes—
386#500C2314yes—
387#500C2312yes—
388#499C23116yes—
389#498C2312yes—
390#498C2314yes—
391#496C2314yes—
392#496C23116yes—
393#493C2312yes—
394#492C2312yes—
395#492C23116yes—
396#492C2314yes—
397#492C2314yes—
398#491C23116yes—
399#490C23116yes—
400#490C2314yes—
401#489C2314yes—
402#488C23116yes—
403#487C2314yes—
404#487C2314yes—
405#487C2312yes—
406#486C2314yes—
407#486C23116yes—
408#486C2312yes—
409#486C2312yes—
410#486C2314yes—
411#486C2312yes—
412#484C2314yes—
413#484C2318yes—
414#483C2314yes—
415#483C2314yes—
416#483C2314yes—
417#482C2318yes—
418#482C2318yes—
419#481C2318yes—
420#481C2314yes—
421#480C2314yes—
422#480C2318yes—
423#479C23116yes—
424#479C23116yes—
425#479C23116yes—
426#478C23116yes—
427#478C2318yes—
428#478C23116yes—
429#478C23116yes—
430#477C2318yes—
431#477C2314yes—
432#477C2314yes—
433#476C2314yes—
434#476C23116yes—
435#476C2314yes—
436#476C2314yes—
437#476C2314yes—
438#476C2314yes—
439#475C2318yes—
440#474C2314yes—
441#474C2318yes—
442#474C23116yes—
443#469C2318yes—
444#468C2318yes—
445#468C23116yes—
446#466C2318yes—
447#465C2318yes—
448#465C2318yes—
449#465C2318yes—
450#463C23116yes—
451#463C23116yes—
452#463C2318yes—
453#461C2314yes—
454#461C2314yes—
455#461C2314yes—
456#461C23116yes—
457#461C2318yes—
458#461C23116yes—
459#460C2318yes—
460#460C2314yes—
461#460C2314yes—
462#460C2318yes—
463#460C23116yes—
464#460C23116yes—
465#460C23116yes—
466#459C2314yes—
467#459C2314yes—
468#459C23116yes—
469#459C2314yes—
470#450C2314yes—
471#450C2314yes—
472#450C2314yes—
473#450C2314yes—
474#450C2318yes—
475#449C2318yes—
476#449C2318yes—
477#448C2318yes—
478#448C2318yes—
479#447C2314yes—
480#447C2314yes—
481#446C2318yes—
482#446C2318yes—
483#446C2318yes—
484#446C23116yes—
485C8×Q8C2318yes—
486C8×Q8C2318yes—
487C8×Q8C2318yes—
488#442C23116yes—
489#440C23116yes—
490#440C23116yes—
491#440C23116yes—
492#440C23116yes—
493C4×SD16C2318yes—
494C4×SD16C2318yes—
495C4×SD16C23116yes—
496C4×SD16C2318yes—
497C4×SD16C23116yes—
498C4×SD16C23116yes—
499C4×SD16C2318yes—
500C4×D8C2318yes—
501C4×D8C2318yes—
502C4×D8C23116yes—
503#433C23116yes—
504#432C2312yes—
505#432C2318yes—
506#432C2312yes—
507#431C2312yes—
508#431C2311yescharacteristic
509#431C2311yescharacteristic
510#431C2318yes—
511#431C2312yes—
512#431C2312yes—
513#431C2312yes—
514#431C2312yes—
515#424C2318yes—
516#423C2312yes—
517C2×C4⋊C8C2312yes—
518#407C2312yes—
519C2×C22⋊C8C2312yes—
520#405C2318yes—
521C4×M16C2312yes—
522C2×C4×C8C2312yes—
523C2×#41—28no—
524C2×#41—28no—
525C2×#41—28no—
526C2×#41—28no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—84no—
538C2×#41—84no—
539C2×#41—88no—
540C2×#41—88no—
541C2×#41C2412yes—
542C22×Q8—24no—
543C22×Q8—21no—
544C22×Q8—21no—
545C22×Q8—21no—
546C22×Q8C2×D412yes—
547C22×Q8C2×D412yes—
548C22×Q8C2412yes—
549C22×D4—22no—
550C22×D4—22no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—24no—
554C22×D4—24no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4C2412yes—
558C22×D4C2412yes—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—24no—
562C23×C4—24no—
563C23×C4C2×D411yescharacteristic
564C23×C4C2×D411yescharacteristic
565C23×C4C2411yescharacteristic
566C2×SD16C2418yes—
567C2×SD16C2418yes—
568C2×SD16C2418yes—
569C2×SD16C24116yes—
570C2×SD16C2418yes—
571C2×D8C2418yes—
572C2×D8C2418yes—
573C2×M16C2414yes—
574C22×C8C2414yes—
575C4⋊Q8—24no—
576C4⋊Q8—24no—
577C4⋊Q8—28no—
578C4⋊Q8—24no—
579C4⋊Q8—24no—
580C4⋊Q8—24no—
581C4⋊Q8—28no—
582C4⋊Q8—28no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586C4⋊Q8—21no—
587C4⋊Q8—21no—
588C4⋊Q8—21no—
589C4⋊Q8—21no—
590C4⋊Q8—21no—
591C4⋊Q8C2×D412yes—
592C4⋊Q8C2×D412yes—
593C4⋊Q8C2×D412yes—
594C4⋊Q8C2×D412yes—
595C4⋊Q8C2×D412yes—
596C4⋊Q8C2×D412yes—
597C4⋊Q8C2×D412yes—
598C4⋊Q8C2×D412yes—
599C4⋊Q8C2412yes—
600C4⋊Q8C2412yes—
601C4⋊Q8C2411yescharacteristic
602C4⋊Q8C2418yes—
603C4⋊Q8C2412yes—
604C4⋊Q8C2412yes—
605C4⋊Q8C2412yes—
606C4⋊Q8C2412yes—
607C4⋊Q8C2412yes—
608C4⋊Q8C2412yes—
609C4⋊Q8C2411yescharacteristic
610C4⋊Q8C2411yescharacteristic
611C4⋊Q8C2418yes—
612#127—21no—
613#127—21no—
614#127—21no—
615#127—21no—
616#127—28no—
617#127C2412yes—
618#127C2412yes—
619#127C2412yes—
620#127C2412yes—
621#127C24116yes—
622#127C2411yescharacteristic
623#126—28no—
624#126—28no—
625#126—28no—
626#126—28no—
627#126—28no—
628#126—28no—
629#126—28no—
630#126—22no—
631#126—22no—
632#126—28no—
633#125—24no—
634#125—28no—
635#125—24no—
636#125—24no—
637#125—24no—
638#125—28no—
639#125—28no—
640#125—28no—
641#125—28no—
642#125—28no—
643#125—28no—
644#125—28no—
645#125—28no—
646#125—22no—
647#125—22no—
648#125—22no—
649#125—22no—
650#125—28no—
651#125—21no—
652#125—21no—
653#125—28no—
654#125C2×D414yes—
655#125C2×D414yes—
656#125C2×D414yes—
657#125C2×D414yes—
658#125C24116yes—
659#125C2412yes—
660#125C2418yes—
661#124—24no—
662#124—28no—
663#124—22no—
664#124—22no—
665#124—22no—
666#124—22no—
667#124—22no—
668#124—22no—
669#124—22no—
670#124—22no—
671#124—21no—
672#124—21no—
673#124C2412yes—
674#124C2418yes—
675#123—22no—
676#123—22no—
677#123—22no—
678#123—28no—
679#123—216no—
680#123—216no—
681#123—216no—
682#123—216no—
683#123—28no—
684#123—28no—
685#123—28no—
686C22⋊Q8—28no—
687C22⋊Q8—28no—
688C22⋊Q8—28no—
689C22⋊Q8—28no—
690C22⋊Q8—24no—
691C22⋊Q8—24no—
692C22⋊Q8—24no—
693C22⋊Q8—28no—
694C22⋊Q8—22no—
695C22⋊Q8—22no—
696C22⋊Q8—22no—
697C22⋊Q8—22no—
698C22⋊Q8—22no—
699C22⋊Q8—22no—
700C22⋊Q8—21no—
701C22⋊Q8—21no—
702C22⋊Q8—21no—
703C22⋊Q8—21no—
704C22⋊Q8—28no—
705C22⋊Q8—216no—
706C22⋊Q8—216no—
707C22⋊Q8—216no—
708C22⋊Q8—216no—
709C22⋊Q8—24no—
710C22⋊Q8—24no—
711C22⋊Q8—24no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8C2×D414yes—
717C22⋊Q8C2×D414yes—
718C22⋊Q8C2×D414yes—
719C22⋊Q8C2×D414yes—
720C22⋊Q8C2×D414yes—
721C22⋊Q8C2×D414yes—
722C22⋊Q8C2×D414yes—
723C22⋊Q8C2×D414yes—
724C22⋊Q8C2414yes—
725C22⋊Q8C2414yes—
726C22⋊Q8C2412yes—
727C22⋊Q8C2412yes—
728#121—22no—
729#121—22no—
730#121—22no—
731#121—22no—
732#121—22no—
733#121—22no—
734#121—22no—
735#121—22no—
736#121—22no—
737#121—22no—
738#121—22no—
739#121—22no—
740#121—21no—
741#121—21no—
742#121—21no—
743#121—21no—
744#121—28no—
745#121—28no—
746#121—28no—
747#121—28no—
748#121—216no—
749#121—216no—
750#121—216no—
751#121—216no—
752#121—216no—
753#121—216no—
754#121—216no—
755#121—216no—
756#121C2414yes—
757#121C2414yes—
758#121C2414yes—
759#121C2414yes—
760#121C2412yes—
761#121C2412yes—
762#120—22no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—24no—
766C4×Q8—24no—
767C4×Q8—24no—
768C4×Q8—24no—
769C4×Q8—28no—
770C4×Q8—24no—
771C4×Q8—24no—
772C4×Q8—24no—
773C4×Q8—22no—
774C4×Q8—22no—
775C4×Q8—22no—
776C4×Q8—22no—
777C4×Q8—22no—
778C4×Q8—22no—
779C4×Q8—21no—
780C4×Q8—21no—
781C4×Q8—21no—
782C4×Q8—21no—
783C4×Q8—28no—
784C4×Q8C2×D414yes—
785C4×Q8C2×D414yes—
786C4×Q8C2×D414yes—
787C4×Q8C2×D414yes—
788C4×Q8C2414yes—
789C4×Q8C2414yes—
790C4×Q8C2412yes—
791C4×Q8C2412yes—
792C4×Q8C2418yes—
793C4×Q8C2418yes—
794C4×Q8C2418yes—
795C4×Q8C2414yes—
796C4×Q8C2414yes—
797C4×Q8C2414yes—
798C4×Q8C2414yes—
799C4×D4—22no—
800C4×D4—22no—
801C4×D4—22no—
802C4×D4—22no—
803C4×D4—22no—
804C4×D4—22no—
805C4×D4—28no—
806C4×D4—24no—
807C4×D4—28no—
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—22no—
811C4×D4—22no—
812C4×D4—22no—
813C4×D4—22no—
814C4×D4—22no—
815C4×D4—22no—
816C4×D4—22no—
817C4×D4—22no—
818C4×D4—22no—
819C4×D4—22no—
820C4×D4—28no—
821C4×D4—28no—
822C4×D4—21no—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—21no—
826C4×D4C2414yes—
827C4×D4C2414yes—
828C4×D4C2414yes—
829C4×D4C2414yes—
830C4×D4C24116yes—
831C4×D4C24116yes—
832C4×D4C2412yes—
833C4×D4C2412yes—
834C4×D4C2418yes—
835#117—22no—
836#117—22no—
837#117—22no—
838#117—22no—
839#117—21no—
840#117—21no—
841#117—28no—
842#117—28no—
843#117—24no—
844#117—24no—
845#117—24no—
846#117—28no—
847#117—22no—
848#117—22no—
849#117—22no—
850#117—28no—
851#117C2×D414yes—
852#117C2×D414yes—
853#117C2412yes—
854#117C2414yes—
855#117C2414yes—
856C2×C4⋊C4—21no—
857C2×C4⋊C4—21no—
858C2×C4⋊C4—24no—
859C2×C4⋊C4—24no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—21no—
862C2×C4⋊C4—21no—
863C2×C4⋊C4—22no—
864C2×C4⋊C4—22no—
865C2×C4⋊C4—28no—
866C2×C4⋊C4—28no—
867C2×C4⋊C4—28no—
868C2×C4⋊C4—28no—
869C2×C4⋊C4—24no—
870C2×C4⋊C4—24no—
871C2×C4⋊C4C2×D412yes—
872C2×C4⋊C4C2×D412yes—
873C2×C4⋊C4C2×D412yes—
874C2×C4⋊C4C2×D412yes—
875C2×C4⋊C4C2×D414yes—
876C2×C4⋊C4C2×D414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C22⋊C4—22no—
881C2×C22⋊C4—22no—
882C2×C22⋊C4—22no—
883C2×C22⋊C4—24no—
884C2×C22⋊C4—24no—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—22no—
887C2×C22⋊C4C2×D414yes—
888C2×C42—22no—
889C2×C42—22no—
890C2×C42C2×D411yescharacteristic
891C2×C42C2×D411yescharacteristic
892C2×C42C2×D411yescharacteristic
893C2×C42C2×D411yescharacteristic
894C2×C42C2×D411yescharacteristic
895C2×C42C2×D411yescharacteristic
896C2×C42C2414yes—
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903#107C2418yes—
904#107C24116yes—
905#107C2418yes—
906#106C2418yes—
907#106C2418yes—
908#106C2418yes—
909#106C2418yes—
910C4⋊C8C2412yes—
911C4⋊C8C2412yes—
912C4⋊C8C2414yes—
913C4⋊C8C2414yes—
914C4⋊C8C2414yes—
915C4⋊C8C24116yes—
916C4⋊C8C24116yes—
917#103C2418yes—
918#103C2418yes—
919#103C24116yes—
920#103C2418yes—
921#103C2418yes—
922#102C2418yes—
923#102C2418yes—
924#102C2418yes—
925#102C2418yes—
926#102C2418yes—
927#102C2418yes—
928#102C2418yes—
929#102C2418yes—
930#102C24116yes—
931C22⋊C8C2412yes—
932C22⋊C8C2412yes—
933C22⋊C8C2414yes—
934C22⋊C8C2414yes—
935C22⋊C8C2414yes—
936#97C2414yes—
937#97C24116yes—
938C4×C8C2414yes—
939C4×C8C2412yes—
940C4×C8C2412yes—
941C4×C8C2414yes—
942C4×C8C24116yes—
943C24—22no—
944C24—22no—
945C24C22×D411yescharacteristic
946#41—44no—
947#41—44no—
948#41—82no—
949#41—84no—
950#41—84no—
951#41—84no—
952#41—84no—
953#41—84no—
954#41—84no—
955#41—84no—
956#41—84no—
957#41—816no—
958#41—816no—
959#41—816no—
960#41—816no—
961C2×Q8—28no—
962C2×Q8—22no—
963C2×Q8—21no—
964C2×Q8—22no—
965C2×Q8—22no—
966C2×Q8—28no—
967C2×Q8—21no—
968C2×Q8—22no—
969C2×Q8—22no—
970C2×Q8—22no—
971C2×Q8—22no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—82no—
975C2×Q8—82no—
976C2×Q8—82no—
977C2×Q8—88no—
978C2×Q8C22×D414yes—
979C2×Q8C22×D414yes—
980C2×Q8C22×D414yes—
981C2×Q8C22×D414yes—
982C2×Q8C2514yes—
983C2×Q8C2512yes—
984C2×D4—22no—
985C2×D4—22no—
986C2×D4—22no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—21no—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—22no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—21no—
999C2×D4—216no—
1000C2×D4—216no—
1001C2×D4—22no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—22no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—82no—
1010C2×D4—88no—
1011C2×D4—84no—
1012C2×D4—82no—
1013C2×D4—88no—
1014C2×D4—84no—
1015C2×D4C2512yes—
1016C2×D4C2514yes—
1017C2×D4C2514yes—
1018C22×C4—24no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—28no—
1031C22×C4—216no—
1032C22×C4—216no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—48no—
1036C22×C4—48no—
1037C22×C4—88no—
1038C22×C4—88no—
1039C22×C4C22×D411yescharacteristic
1040C22×C4C22×D411yescharacteristic
1041C22×C4C22×D411yescharacteristic
1042C22×C4C22×D411yescharacteristic
1043C22×C4C22×D411yescharacteristic
1044C22×C4C22×D411yescharacteristic
1045C22×C4C22×D411yescharacteristic
1046C22×C4C22×D411yescharacteristic
1047C22×C4C22×D414yes—
1048C22×C4C22×D411yescharacteristic
1049C22×C4C22×D411yescharacteristic
1050C22×C4C22×D411yescharacteristic
1051C22×C4C22×D411yescharacteristic
1052C22×C4C22×D411yescharacteristic
1053C22×C4C22×D411yescharacteristic
1054C22×C4C22×D414yes—
1055C22×C4C22×D411yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059SD16—48no—
1060SD16—48no—
1061SD16—48no—
1062SD16—416no—
1063SD16—48no—
1064D8—48no—
1065D8—48no—
1066M16—44no—
1067C2×C8—44no—
1068C2×C8C2514yes—
1069C2×C8C2518yes—
1070C2×C8C2514yes—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—216no—
1077C4⋊C4—216no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—24no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—22no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—21no—
1093C4⋊C4—21no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—21no—
1097C4⋊C4—21no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4C22×D414yes—
1109C4⋊C4C22×D414yes—
1110C4⋊C4C22×D414yes—
1111C4⋊C4C22×D414yes—
1112C4⋊C4C22×D414yes—
1113C4⋊C4C22×D414yes—
1114C4⋊C4C22×D418yes—
1115C4⋊C4C22×D414yes—
1116C4⋊C4C22×D414yes—
1117C4⋊C4C22×D418yes—
1118C4⋊C4C22×D418yes—
1119C4⋊C4C22×D418yes—
1120C4⋊C4C2514yes—
1121C4⋊C4C2512yes—
1122C4⋊C4C2512yes—
1123C4⋊C4C2514yes—
1124C4⋊C4C2514yes—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—22no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—24no—
1134C22⋊C4—216no—
1135C22⋊C4—216no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—22no—
1141C22⋊C4—22no—
1142C22⋊C4—28no—
1143C22⋊C4—22no—
1144C22⋊C4—22no—
1145C22⋊C4—28no—
1146C22⋊C4—22no—
1147C22⋊C4—22no—
1148C22⋊C4—28no—
1149C22⋊C4C22×D418yes—
1150C22⋊C4C22×D418yes—
1151C42—24no—
1152C42—22no—
1153C42—22no—
1154C42—24no—
1155C42—22no—
1156C42—28no—
1157C42—28no—
1158C42—28no—
1159C42C22×D411yescharacteristic
1160C42C22×D411yescharacteristic
1161C42C22×D411yescharacteristic
1162C42C22×D411yescharacteristic
1163C42C22×D411yescharacteristic
1164C42C22×D411yescharacteristic
1165C42C22×D411yescharacteristic
1166C42C22×D411yescharacteristic
1167C42C22×D411yescharacteristic
1168C42C22×D411yescharacteristic
1169C42C22×D411yescharacteristic
1170C42C22×D411yescharacteristic
1171C42C22×D418yes—
1172C42C2511yescharacteristic
1173C42C2511yescharacteristic
1174C42C2511yescharacteristic
1175C42C2518yes—
1176C42C2511yescharacteristic
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—41no—
1182C23—41no—
1183C23—44no—
1184C23—44no—
1185C23—44no—
1186C23—44no—
1187C23—44no—
1188C23—44no—
1189C23C23×D411yescharacteristic
1190C23C23×D411yescharacteristic
1191C23C23×D411yescharacteristic
1192Q8—28no—
1193Q8—28no—
1194Q8—28no—
1195Q8—28no—
1196Q8—24no—
1197Q8—44no—
1198Q8—44no—
1199Q8—44no—
1200Q8—42no—
1201Q8—82no—
1202Q8—88no—
1203Q8—82no—
1204Q8—82no—
1205Q8—82no—
1206Q8—82no—
1207Q8—81no—
1208D4—24no—
1209D4—24no—
1210D4—28no—
1211D4—24no—
1212D4—44no—
1213D4—44no—
1214D4—44no—
1215D4—44no—
1216D4—44no—
1217D4—44no—
1218D4—44no—
1219D4—44no—
1220D4—42no—
1221D4—82no—
1222D4—82no—
1223D4—816no—
1224D4—82no—
1225D4—82no—
1226D4—816no—
1227D4—81no—
1228D4—84no—
1229D4—84no—
1230D4—84no—
1231D4—84no—
1232D4—82no—
1233C2×C4—22no—
1234C2×C4—28no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—44no—
1259C2×C4—48no—
1260C2×C4—44no—
1261C2×C4—44no—
1262C2×C4—44no—
1263C2×C4—44no—
1264C2×C4—48no—
1265C2×C4—44no—
1266C2×C4—48no—
1267C2×C4—48no—
1268C2×C4—44no—
1269C2×C4—816no—
1270C2×C4—816no—
1271C2×C4—88no—
1272C2×C4—82no—
1273C2×C4#57714yes—
1274C2×C4C23×D411yescharacteristic
1275C2×C4C23×D411yescharacteristic
1276C2×C4C23×D418yes—
1277C2×C4C23×D418yes—
1278C2×C4C23×D411yescharacteristic
1279C2×C4C23×D411yescharacteristic
1280C2×C4C23×D411yescharacteristic
1281C2×C4C23×D411yescharacteristic
1282C2×C4C23×D411yescharacteristic
1283C2×C4C23×D411yescharacteristic
1284C2×C4C23×D411yescharacteristic
1285C2×C4C23×D411yescharacteristic
1286C2×C4C23×D411yescharacteristic
1287C2×C4C2611yescharacteristic
1288C8—24no—
1289C8—24no—
1290C8—28no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—21no—
1297C22—21no—
1298C22—21no—
1299C22—44no—
1300C22—42no—
1301C22—44no—
1302C22—44no—
1303C22—42no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—44no—
1308C22—82no—
1309C22—88no—
1310C22—88no—
1311C22C2×#57712yes—
1312C22C24×D411yescharacteristic
1313C4—21no—
1314C4—21no—
1315C4—28no—
1316C4—21no—
1317C4—21no—
1318C4—21no—
1319C4—28no—
1320C4—21no—
1321C4—21no—
1322C4—21no—
1323C4—44no—
1324C4—42no—
1325C4—44no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—44no—
1330C4C2×#57712yes—
1331C4C2×#57712yes—
1332C4#358512yes—
1333C42−1+612yes—
1334C2—22no—
1335C2—41no—
1336C2—41no—
1337C2—82no—
1338C2—84no—
1339C2—84no—
1340C2#6284811yescharacteristic
1341C2C22×#57711yescharacteristic
1342C2C2×#358511yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62837C2semidirect
2. C2×#3548C2semidirect
3. #62401C2semidirect
4. #62381C2semidirect
5. #62371C2semidirect
6. #61935C2semidirect
7. #61914C2semidirect
8. #61901C2semidirect
9. #61890C2semidirect
10. #61881C2semidirect
11. #61868C2semidirect
12. #61851C2semidirect
13. #61841C2semidirect
14. #61826C2semidirect
15. #61819C2semidirect
16. #60979C2semidirect
17. #60969C2semidirect
18. #60951C2semidirect
19. #60946C2semidirect
20. #60941C2semidirect
21. #60250C2semidirect
24. #3556C22semidirect
26. #3555C22semidirect
27. #3550C22semidirect
42. #3509C22semidirect
44. #3507C22semidirect
46. #3503C22semidirect
48. #3502C22semidirect
65. #3399C22semidirect
66. #3397C22semidirect
67. #3397C22semidirect
68. #3397C22semidirect
69. #3392C22semidirect
70. #3392C22semidirect
71. #3392C22semidirect
72. #3388C22semidirect
73. #3385C22semidirect
74. #3385C22semidirect
75. #3384C22semidirect
76. #3381C22semidirect
77. #3381C22semidirect
78. #3380C22semidirect
79. #3376C22semidirect
80. #3372C22semidirect
81. #3372C22semidirect
82. #3372C22semidirect
83. #3368C22semidirect
84. #3368C22semidirect
85. #3368C22semidirect
86. #3366C22semidirect
87. #3362C22semidirect
88. #3362C22semidirect
89. #3361C22semidirect
90. #3360C22semidirect
91. #3360C22semidirect
92. #3358C22semidirect
93. #3260C22semidirect
94. #3257C22semidirect
95. #3254C22semidirect
96. #3254C22semidirect
97. #3253C22semidirect
98. #3247C22semidirect
99. #3246C22semidirect
100. #3241C22semidirect
103. #3235C22semidirect
108. #3228C22semidirect
110. #3227C22semidirect
111. #3226C22semidirect
112. #3221C22semidirect
115. #3214C22semidirect
120. #3207C22semidirect
121. #3206C22semidirect
122. #3206C22semidirect
128. #3182C22semidirect
129. #3179C22semidirect
130. #3174C22semidirect
131. #3171C22semidirect
132. #3169C22semidirect
133. #3167C22semidirect
134. #3167C22semidirect
135. #3126C22semidirect
136. #3119C22semidirect
138. #3112C22semidirect
141. #3106C22semidirect
142. #3106C22semidirect
145. #3103C22semidirect
151. #2986C22semidirect
152. #2985C22semidirect
156. #2962C22semidirect
157. #2960C22semidirect

Maximal subgroups

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

subgroupindex
#628372
C2×#35482
#624012
#623812
#623712
#619352
#619142
#619012
#618902
#618812
#618682
#618512
#618412
#618262
#618192
#609792
#609692
#609512
#609462
#609412
#602502