Finite Group Databasebeta

← #10581623

Subgroups — #10581623

Order 512.

5906 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62837C211yesmaximal, characteristic, complemented
2C2×#3550C211yesmaximal, characteristic, complemented
3#62404C218yesmaximal, complemented
4#62382C214yesmaximal, complemented
5#62375C214yesmaximal, complemented
6#61934C214yesmaximal, complemented
7#61917C214yesmaximal, complemented
8#61905C214yesmaximal, complemented
9#61892C212yesmaximal, complemented
10#61885C212yesmaximal, complemented
11#61870C214yesmaximal, complemented
12#61854C214yesmaximal, complemented
13#61837C214yesmaximal, complemented
14#61830C212yesmaximal, complemented
15#61821C212yesmaximal, complemented
16#60981C218yesmaximal, complemented
17#60969C211yesmaximal, characteristic, complemented
18#60952C211yesmaximal, characteristic, complemented
19#60946C211yesmaximal, characteristic
20#60943C211yesmaximal, characteristic, complemented
21#60250C211yesmaximal, characteristic, complemented
22#3563—22no—
23#3563—22no—
24#3556C2212yescomplemented
25#3555—22no—
26#3555C2214yescomplemented
27#3550—22no—
28#3550—22no—
29#3550—22no—
30#3550—22no—
31#3550C2214yes—
32#3550C2214yes—
33#3550C2214yes—
34#3550C2214yes—
35#3550C2212yescomplemented
36#3538—22no—
37C2×#563—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×#559C2212yes—
52C2×Q82C2212yes—
53C2×#556—21no—
54C2×#556C2212yes—
55C2×D4×Q8—21no—
56C2×D4×Q8C2212yes—
57C2×#542—22no—
58C2×#542C2214yes—
59C2×#536—22no—
60#3444C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#533C2211yescharacteristic
63C2×#533C2211yescharacteristic
64C2×#532C2211yescharacteristic
65#3402C22116yescomplemented
66#3400C2218yescomplemented
67#3400C2218yescomplemented
68#3398C2218yescomplemented
69#3396C2218yescomplemented
70#3394C2218yescomplemented
71#3393C2218yescomplemented
72#3387C2218yescomplemented
73#3386C22116yescomplemented
74#3386C2218yescomplemented
75#3385C2218yescomplemented
76Q8×Q16C2218yescomplemented
77Q8×Q16C2218yescomplemented
78Q8×D8C2218yescomplemented
79#3377C22116yescomplemented
80#3375C2218yescomplemented
81#3375C2218yescomplemented
82#3375C2218yescomplemented
83#3369C2218yescomplemented
84#3367C2218yescomplemented
85#3367C22116yescomplemented
86#3367C2218yescomplemented
87#3365C2218yescomplemented
88#3364C2218yescomplemented
89#3363C2218yescomplemented
90#3363C2218yescomplemented
91#3361C2218yescomplemented
92#3359C2218yescomplemented
93#3262C22116yescomplemented
94#3258C22116yescomplemented
95#3255C2212yescomplemented
96#3254C2214yes—
97#3254C2212yescomplemented
98#3249C2214yescomplemented
99#3247C2214yes—
100#3243C22116yescomplemented
101#3239C2212yes—
102#3239C2218yes—
103#3237C2212yescomplemented
104#3230C2212yes—
105#3230C2211yescharacteristic
106#3230C2212yes—
107#3230C2218yes—
108#3230C2212yescomplemented
109#3228C2212yes—
110#3227C2211yescharacteristic
111#3226C2212yes—
112#3225C22116yescomplemented
113#3218C2212yes—
114#3216C2212yescomplemented
115#3215C2218yes—
116#3211C2218yes—
117#3209C2212yes—
118#3209C2212yescomplemented
119#3208C2211yescharacteristic
120#3208C2212yes—
121#3207C2212yes—
122#3206C2212yes—
123#3205C2211yescharacteristic
124#3196C2214yes—
125#3193C2214yes—
126#3189C2214yes—
127#3188C2214yes—
128#3182C2214yes—
129#3178C22116yescomplemented
130#3175C22116yescomplemented
131#3172C2214yescomplemented
132#3170C2214yescomplemented
133#3169C2212yes—
134#3167C2212yes—
135#3124C22116yescomplemented
136#3121C22116yescomplemented
137#3117C2218yes—
138#3112C2214yes—
139#3110C2214yes—
140#3110C2218yes—
141#3107C2214yescomplemented
142#3106C2214yes—
143#3105C2214yes—
144#3105C2218yes—
145#3104C2212yes—
146#3104C2212yes—
147#3104C2212yes—
148#3104C2218yes—
149#3104C2214yescomplemented
150#3103C2212yes—
151#2986C2214yescomplemented
152#2985C2214yescomplemented
153#2984C2214yes—
154#2983C2212yes—
155#2982C2212yes—
156#2962C2214yescomplemented
157#2960C2214yescomplemented
158#2924C2214yes—
159#2920C2211yescharacteristic
160C2×#431C2211yescharacteristic
161C22×#41—21no—
162C23×Q8—22no—
163#564—24no—
164#563—28no—
165#563—28no—
166#563—28no—
167#563—28no—
168#563—24no—
169#563—28no—
170#559—24no—
171#559—24no—
172#559C2318yes—
173#559C2318yes—
174#559C2314yes—
175Q82—22no—
176Q82—24no—
177Q82—24no—
178Q82C2318yes—
179Q82C2318yes—
180Q82C2314yes—
181Q82C2314yes—
182#557—22no—
183#557—22no—
184#557—22no—
185#557—24no—
186#557—24no—
187#557—24no—
188#557C2314yes—
189#557C2314yes—
190#557C2314yes—
191#557C2314yes—
192#557C2314yes—
193#557C2318yes—
194#556—24no—
195#556—24no—
196#556—24no—
197#556—24no—
198#556—22no—
199#556—22no—
200#556—24no—
201#556—24no—
202#556—24no—
203#556—24no—
204#556—24no—
205#556C2318yes—
206#556C2314yes—
207#556C2318yes—
208#556C2314yes—
209#556C2318yes—
210#554—22no—
211#554—24no—
212#554—24no—
213#554C2314yes—
214#552—24no—
215#552—24no—
216#552—24no—
217#552—24no—
218#552—24no—
219#552—24no—
220#552—28no—
221#552—28no—
222#552—24no—
223#552—24no—
224#551—28no—
225D4×Q8—24no—
226D4×Q8—24no—
227D4×Q8—24no—
228D4×Q8—24no—
229D4×Q8—24no—
230D4×Q8—22no—
231D4×Q8—24no—
232D4×Q8—24no—
233D4×Q8—24no—
234D4×Q8C2318yes—
235D4×Q8C2314yes—
236D4×Q8C2318yes—
237#544—24no—
238#544—24no—
239#544—24no—
240#544—22no—
241#544—24no—
242#544C2314yes—
243#542—28no—
244#542—28no—
245#542—28no—
246#542—28no—
247#542—24no—
248#542—28no—
249#542—28no—
250#542C23116yes—
251#542C2318yes—
252#542C23116yes—
253#541—24no—
254#541—24no—
255#541—28no—
256#541—24no—
257#541—24no—
258#541—24no—
259#541—28no—
260#541C2318yes—
261#539—24no—
262#539—24no—
263#536—22no—
264#536—28no—
265#536—28no—
266#536—28no—
267#536—28no—
268#536—24no—
269#536C2314yes—
270#533—22no—
271#533—22no—
272#533—22no—
273#533—24no—
274#533—21no—
275#533—21no—
276#533—21no—
277#533—21no—
278#533—21no—
279#533—21no—
280#533—21no—
281#533—21no—
282#533D412yes—
283#533D412yes—
284#533D412yes—
285#533D412yes—
286#533C2312yes—
287#533C2311yescharacteristic
288#533C2318yes—
289#533C2312yes—
290#533C2312yes—
291#533C2312yes—
292#533C2311yescharacteristic
293#533C2312yes—
294#533C2312yes—
295#533C2312yes—
296#533C2312yes—
297#533C2311yescharacteristic
298#533C2312yes—
299#533C2312yes—
300#533C2312yes—
301#533C2312yes—
302#532—21no—
303#532—21no—
304#532—21no—
305#532—21no—
306#532C2311yescharacteristic
307#532C2311yescharacteristic
308#532C2312yes—
309#532C2312yes—
310#532C2312yes—
311#532C2311yescharacteristic
312#532C2312yes—
313C2×C4⋊Q8—22no—
314C2×C4⋊Q8—24no—
315C2×C4⋊Q8—22no—
316C2×C4⋊Q8D411yescharacteristic
317C2×C4⋊Q8D411yescharacteristic
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2311yescharacteristic
320C2×C4⋊Q8C2311yescharacteristic
321C2×C4⋊Q8C2311yescharacteristic
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2314yes—
324C2×#127C2311yescharacteristic
325#529—24no—
326#529—21no—
327#529—21no—
328#529—21no—
329#529—21no—
330#529C2312yes—
331#529C2318yes—
332#529C2312yes—
333C2×#126—24no—
334C2×#126—24no—
335C2×#125—21no—
336C2×#125—21no—
337C2×#125D412yes—
338C2×#124—22no—
339C2×#124—24no—
340C2×#124—21no—
341C2×#124C2314yes—
342#525—21no—
343#525—21no—
344#525C2312yes—
345C2×#123—24no—
346C2×#123—24no—
347C2×C22⋊Q8—22no—
348C2×C22⋊Q8—21no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—22no—
351C2×C22⋊Q8—24no—
352C2×C22⋊Q8—24no—
353C2×C22⋊Q8D412yes—
354C2×C22⋊Q8D412yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×#121—21no—
358C2×#121C2312yes—
359#520—22no—
360#520C2314yes—
361#519—22no—
362#519—24no—
363#519C2314yes—
364C4×#41—21no—
365C4×#41—21no—
366C4×#41C2312yes—
367C2×C4×Q8—22no—
368C2×C4×Q8—21no—
369C2×C4×Q8—21no—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2314yes—
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×D4—22no—
376C2×C4×D4—21no—
377C2×C4×D4C2312yes—
378C2×C4×D4C2314yes—
379C2×#117—21no—
380C2×#117—21no—
381C2×#117—22no—
382C2×#117C2312yes—
383C22×C42C2311yescharacteristic
384#501C23116yes—
385#501C2314yes—
386#500C2314yes—
387#500C23116yes—
388#500C2312yes—
389#500C2314yes—
390#498C2312yes—
391#497C23116yes—
392#497C2314yes—
393#495C23116yes—
394#494C2314yes—
395#493C2312yes—
396#492C2314yes—
397#492C2312yes—
398#491C2314yes—
399#489C2314yes—
400#489C23116yes—
401#489C23116yes—
402#488C23116yes—
403#487C2314yes—
404#487C23116yes—
405#487C2312yes—
406#487C2314yes—
407#487C2314yes—
408#486C2314yes—
409#486C2312yes—
410#486C2312yes—
411#486C2312yes—
412#485C2318yes—
413#484C2314yes—
414#484C2314yes—
415#484C2314yes—
416#484C2314yes—
417#484C2318yes—
418#484C2318yes—
419#482C2318yes—
420#481C2314yes—
421#481C2314yes—
422#480C2318yes—
423#479C23116yes—
424#478C23116yes—
425#478C2318yes—
426#477C2314yes—
427#477C23116yes—
428#477C2314yes—
429#477C2314yes—
430#477C2318yes—
431#477C2314yes—
432#477C23116yes—
433#477C23116yes—
434#477C2318yes—
435#476C2314yes—
436#475C2314yes—
437#475C2314yes—
438#475C23116yes—
439#474C2314yes—
440#474C2318yes—
441#474C23116yes—
442#474C23116yes—
443#470C2318yes—
444#468C2318yes—
445#468C23116yes—
446#467C2318yes—
447#467C2318yes—
448#466C2318yes—
449#465C2318yes—
450#464C23116yes—
451#464C23116yes—
452#464C23116yes—
453#464C23116yes—
454#463C23116yes—
455#463C2318yes—
456#463C23116yes—
457#462C2314yes—
458#462C23116yes—
459#462C2314yes—
460#462C2314yes—
461#462C2318yes—
462#462C2314yes—
463#461C2318yes—
464#461C23116yes—
465#461C2314yes—
466#460C2314yes—
467#460C2314yes—
468#460C2318yes—
469#459C2314yes—
470#452C2318yes—
471#451C2314yes—
472#451C2314yes—
473#451C2314yes—
474#451C2318yes—
475#450C2314yes—
476#450C2318yes—
477#449C2318yes—
478#448C2314yes—
479#448C2318yes—
480#447C2314yes—
481#446C2318yes—
482#446C23116yes—
483#446C2318yes—
484#446C2318yes—
485C8×Q8C2318yes—
486C8×Q8C2318yes—
487C8×Q8C2318yes—
488#441C23116yes—
489#440C23116yes—
490#440C23116yes—
491#440C23116yes—
492#440C23116yes—
493C4×Q16C2318yes—
494C4×Q16C2318yes—
495C4×Q16C2318yes—
496C4×Q16C23116yes—
497C4×Q16C23116yes—
498C4×SD16C2318yes—
499C4×SD16C2318yes—
500C4×SD16C23116yes—
501C4×D8C23116yes—
502C4×D8C2318yes—
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—21no—
524C2×#41—21no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—84no—
530C2×#41C2412yes—
531C22×Q8—24no—
532C22×Q8—28no—
533C22×Q8—28no—
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8—24no—
537C22×Q8—21no—
538C22×Q8—88no—
539C22×Q8C2×D412yes—
540C22×Q8C2×D412yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4C2412yes—
547C23×C4—22no—
548C23×C4—24no—
549C23×C4C2×D411yescharacteristic
550C23×C4C2×D411yescharacteristic
551C23×C4C2411yescharacteristic
552C2×Q16C2418yes—
553C2×Q16C2418yes—
554C2×Q16C2418yes—
555C2×SD16C24116yes—
556C2×SD16C2418yes—
557C2×SD16C2418yes—
558C2×D8C2418yes—
559C2×M16C2414yes—
560C22×C8C2414yes—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—28no—
564C4⋊Q8—216no—
565C4⋊Q8—216no—
566C4⋊Q8—28no—
567C4⋊Q8—28no—
568C4⋊Q8—24no—
569C4⋊Q8—24no—
570C4⋊Q8—24no—
571C4⋊Q8—28no—
572C4⋊Q8—28no—
573C4⋊Q8—21no—
574C4⋊Q8—21no—
575C4⋊Q8—21no—
576C4⋊Q8—21no—
577C4⋊Q8—21no—
578C4⋊Q8—21no—
579C4⋊Q8—21no—
580C4⋊Q8—21no—
581C4⋊Q8—21no—
582C4⋊Q8—21no—
583C4⋊Q8—28no—
584C4⋊Q8C2×D412yes—
585C4⋊Q8C2×D412yes—
586C4⋊Q8C2×D412yes—
587C4⋊Q8C2×D412yes—
588C4⋊Q8C2×D412yes—
589C4⋊Q8C2×D412yes—
590C4⋊Q8C2×D412yes—
591C4⋊Q8C2×D412yes—
592C4⋊Q8C2412yes—
593C4⋊Q8C2412yes—
594C4⋊Q8C2412yes—
595C4⋊Q8C2412yes—
596C4⋊Q8C2411yescharacteristic
597C4⋊Q8C2418yes—
598C4⋊Q8C2412yes—
599C4⋊Q8C2412yes—
600C4⋊Q8C2412yes—
601C4⋊Q8C2412yes—
602C4⋊Q8C2412yes—
603C4⋊Q8C2412yes—
604C4⋊Q8C24116yes—
605C4⋊Q8C2411yescharacteristic
606C4⋊Q8C2411yescharacteristic
607C4⋊Q8C2418yes—
608#127—21no—
609#127—21no—
610#127C2412yes—
611#127C2412yes—
612#127C2411yescharacteristic
613#126—216no—
614#126—216no—
615#126—216no—
616#126—216no—
617#126—28no—
618#126—28no—
619#126—28no—
620#126—28no—
621#126—28no—
622#126—28no—
623#126—28no—
624#126—22no—
625#126—22no—
626#126—28no—
627#125—24no—
628#125—28no—
629#125—24no—
630#125—24no—
631#125—24no—
632#125—28no—
633#125—28no—
634#125—28no—
635#125—28no—
636#125—28no—
637#125—28no—
638#125—28no—
639#125—28no—
640#125—22no—
641#125—22no—
642#125—22no—
643#125—22no—
644#125—22no—
645#125—22no—
646#125—22no—
647#125—22no—
648#125—21no—
649#125—21no—
650#125—28no—
651#125C2×D414yes—
652#125C2×D414yes—
653#125C2×D414yes—
654#125C2×D414yes—
655#125C2412yes—
656#125C2418yes—
657#124—28no—
658#124—28no—
659#124—24no—
660#124—216no—
661#124—216no—
662#124—28no—
663#124—22no—
664#124—22no—
665#124—22no—
666#124—22no—
667#124—28no—
668#124—21no—
669#124—21no—
670#124C24116yes—
671#124C2412yes—
672#124C2418yes—
673#123—22no—
674#123—22no—
675#123—22no—
676#123—28no—
677#123—216no—
678#123—216no—
679#123—28no—
680#123—216no—
681#123—216no—
682#123—28no—
683#123—28no—
684C22⋊Q8—28no—
685C22⋊Q8—28no—
686C22⋊Q8—24no—
687C22⋊Q8—24no—
688C22⋊Q8—24no—
689C22⋊Q8—28no—
690C22⋊Q8—22no—
691C22⋊Q8—22no—
692C22⋊Q8—22no—
693C22⋊Q8—22no—
694C22⋊Q8—22no—
695C22⋊Q8—22no—
696C22⋊Q8—22no—
697C22⋊Q8—22no—
698C22⋊Q8—22no—
699C22⋊Q8—22no—
700C22⋊Q8—22no—
701C22⋊Q8—22no—
702C22⋊Q8—21no—
703C22⋊Q8—21no—
704C22⋊Q8—21no—
705C22⋊Q8—21no—
706C22⋊Q8—28no—
707C22⋊Q8—28no—
708C22⋊Q8—28no—
709C22⋊Q8—216no—
710C22⋊Q8—216no—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—24no—
714C22⋊Q8—24no—
715C22⋊Q8—24no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—28no—
719C22⋊Q8—28no—
720C22⋊Q8C2×D414yes—
721C22⋊Q8C2×D414yes—
722C22⋊Q8C2×D414yes—
723C22⋊Q8C2×D414yes—
724C22⋊Q8C2×D414yes—
725C22⋊Q8C2×D414yes—
726C22⋊Q8C2×D414yes—
727C22⋊Q8C2×D414yes—
728C22⋊Q8C2414yes—
729C22⋊Q8C2414yes—
730C22⋊Q8C2414yes—
731C22⋊Q8C2414yes—
732C22⋊Q8C2412yes—
733C22⋊Q8C2412yes—
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#121C2414yes—
745#121C2414yes—
746#121C2412yes—
747#121C2412yes—
748#120—22no—
749C4×Q8—28no—
750C4×Q8—28no—
751C4×Q8—24no—
752C4×Q8—24no—
753C4×Q8—24no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—28no—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—24no—
761C4×Q8—22no—
762C4×Q8—22no—
763C4×Q8—22no—
764C4×Q8—22no—
765C4×Q8—22no—
766C4×Q8—22no—
767C4×Q8—22no—
768C4×Q8—22no—
769C4×Q8—22no—
770C4×Q8—22no—
771C4×Q8—22no—
772C4×Q8—22no—
773C4×Q8—28no—
774C4×Q8—21no—
775C4×Q8—21no—
776C4×Q8—21no—
777C4×Q8—21no—
778C4×Q8—28no—
779C4×Q8C2×D414yes—
780C4×Q8C2×D414yes—
781C4×Q8C2×D414yes—
782C4×Q8C2×D414yes—
783C4×Q8C2414yes—
784C4×Q8C2414yes—
785C4×Q8C2414yes—
786C4×Q8C2414yes—
787C4×Q8C24116yes—
788C4×Q8C2412yes—
789C4×Q8C2412yes—
790C4×Q8C2418yes—
791C4×Q8C2418yes—
792C4×Q8C2418yes—
793C4×Q8C2414yes—
794C4×Q8C2414yes—
795C4×Q8C2414yes—
796C4×Q8C2414yes—
797C4×D4—22no—
798C4×D4—22no—
799C4×D4—22no—
800C4×D4—22no—
801C4×D4—22no—
802C4×D4—22no—
803C4×D4—28no—
804C4×D4—28no—
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—28no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4C2414yes—
820C4×D4C2414yes—
821C4×D4C24116yes—
822C4×D4C2412yes—
823C4×D4C2412yes—
824C4×D4C2418yes—
825#117—22no—
826#117—22no—
827#117—22no—
828#117—22no—
829#117—22no—
830#117—22no—
831#117—22no—
832#117—22no—
833#117—21no—
834#117—21no—
835#117—28no—
836#117—28no—
837#117—28no—
838#117—28no—
839#117—24no—
840#117—24no—
841#117—24no—
842#117—28no—
843#117—22no—
844#117—22no—
845#117—22no—
846#117—28no—
847#117C2×D414yes—
848#117C2×D414yes—
849#117C2412yes—
850#117C2414yes—
851#117C2414yes—
852C2×C4⋊C4—21no—
853C2×C4⋊C4—21no—
854C2×C4⋊C4—21no—
855C2×C4⋊C4—21no—
856C2×C4⋊C4—21no—
857C2×C4⋊C4—21no—
858C2×C4⋊C4—22no—
859C2×C4⋊C4—24no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—22no—
862C2×C4⋊C4—24no—
863C2×C4⋊C4—22no—
864C2×C4⋊C4—22no—
865C2×C4⋊C4—24no—
866C2×C4⋊C4—24no—
867C2×C4⋊C4C2×D412yes—
868C2×C4⋊C4C2×D412yes—
869C2×C4⋊C4C2×D412yes—
870C2×C4⋊C4C2×D412yes—
871C2×C4⋊C4C2×D414yes—
872C2×C4⋊C4C2×D414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C22⋊C4—22no—
877C2×C22⋊C4—22no—
878C2×C22⋊C4—24no—
879C2×C22⋊C4—22no—
880C2×C22⋊C4—24no—
881C2×C22⋊C4—22no—
882C2×C22⋊C4—24no—
883C2×C22⋊C4C2×D414yes—
884C2×C42—22no—
885C2×C42—24no—
886C2×C42—22no—
887C2×C42—22no—
888C2×C42C2×D411yescharacteristic
889C2×C42C2×D411yescharacteristic
890C2×C42C2×D411yescharacteristic
891C2×C42C2×D411yescharacteristic
892C2×C42C2×D411yescharacteristic
893C2×C42C2×D411yescharacteristic
894C2×C42C2414yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901#107C2418yes—
902#107C2418yes—
903#107C2418yes—
904#107C2418yes—
905#107C24116yes—
906#106C2418yes—
907#106C2418yes—
908C4⋊C8C2412yes—
909C4⋊C8C2412yes—
910C4⋊C8C2414yes—
911C4⋊C8C2414yes—
912C4⋊C8C2414yes—
913C4⋊C8C24116yes—
914C4⋊C8C24116yes—
915#103C2418yes—
916#103C2418yes—
917#103C2418yes—
918#103C2418yes—
919#103C2418yes—
920#103C2418yes—
921#103C2418yes—
922#103C2418yes—
923#103C24116yes—
924#102C2418yes—
925#102C2418yes—
926#102C24116yes—
927#102C2418yes—
928#102C2418yes—
929C22⋊C8C2412yes—
930C22⋊C8C2412yes—
931C22⋊C8C2414yes—
932C22⋊C8C2414yes—
933C22⋊C8C2414yes—
934#97C2414yes—
935#97C24116yes—
936C4×C8C2414yes—
937C4×C8C2412yes—
938C4×C8C2412yes—
939C4×C8C2414yes—
940C4×C8C24116yes—
941C24—22no—
942C24C22×D411yescharacteristic
943#41—44no—
944#41—44no—
945#41—82no—
946#41—84no—
947#41—84no—
948#41—84no—
949#41—84no—
950C2×Q8—28no—
951C2×Q8—22no—
952C2×Q8—22no—
953C2×Q8—21no—
954C2×Q8—22no—
955C2×Q8—22no—
956C2×Q8—22no—
957C2×Q8—22no—
958C2×Q8—28no—
959C2×Q8—21no—
960C2×Q8—216no—
961C2×Q8—22no—
962C2×Q8—22no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—82no—
968C2×Q8—88no—
969C2×Q8—82no—
970C2×Q8—88no—
971C2×Q8—816no—
972C2×Q8—816no—
973C2×Q8C22×D414yes—
974C2×Q8C22×D414yes—
975C2×Q8C22×D414yes—
976C2×Q8C22×D414yes—
977C2×Q8C2514yes—
978C2×Q8C2514yes—
979C2×Q8C2512yes—
980C2×D4—22no—
981C2×D4—22no—
982C2×D4—22no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—21no—
986C2×D4—22no—
987C2×D4—22no—
988C2×D4—22no—
989C2×D4—21no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—82no—
995C2×D4—84no—
996C2×D4C2512yes—
997C2×D4C2514yes—
998C22×C4—24no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—28no—
1010C22×C4—216no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—48no—
1014C22×C4—88no—
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D414yes—
1017C22×C4C22×D411yescharacteristic
1018C22×C4C22×D411yescharacteristic
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C22×D411yescharacteristic
1022C22×C4C22×D411yescharacteristic
1023C22×C4C22×D411yescharacteristic
1024C22×C4C22×D411yescharacteristic
1025C22×C4C22×D411yescharacteristic
1026C22×C4C22×D411yescharacteristic
1027C22×C4C22×D411yescharacteristic
1028C22×C4C22×D411yescharacteristic
1029C22×C4C22×D411yescharacteristic
1030C22×C4C22×D414yes—
1031C22×C4C22×D411yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035Q16—48no—
1036Q16—48no—
1037Q16—48no—
1038SD16—48no—
1039SD16—48no—
1040SD16—416no—
1041D8—48no—
1042M16—44no—
1043C2×C8—44no—
1044C2×C8C2514yes—
1045C2×C8C2518yes—
1046C2×C8C2514yes—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—22no—
1053C4⋊C4—24no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—216no—
1067C4⋊C4—24no—
1068C4⋊C4—22no—
1069C4⋊C4—216no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4C22×D414yes—
1093C4⋊C4C22×D414yes—
1094C4⋊C4C22×D414yes—
1095C4⋊C4C22×D414yes—
1096C4⋊C4C22×D414yes—
1097C4⋊C4C22×D418yes—
1098C4⋊C4C22×D414yes—
1099C4⋊C4C22×D414yes—
1100C4⋊C4C22×D414yes—
1101C4⋊C4C22×D418yes—
1102C4⋊C4C22×D418yes—
1103C4⋊C4C22×D418yes—
1104C4⋊C4C2512yes—
1105C4⋊C4C2514yes—
1106C4⋊C4C2512yes—
1107C4⋊C4C2514yes—
1108C4⋊C4C2514yes—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—216no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—216no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—216no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—28no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—28no—
1129C22⋊C4—22no—
1130C22⋊C4—22no—
1131C22⋊C4—28no—
1132C22⋊C4C22×D418yes—
1133C22⋊C4C22×D418yes—
1134C42—24no—
1135C42—24no—
1136C42—24no—
1137C42—22no—
1138C42—22no—
1139C42—24no—
1140C42—216no—
1141C42—22no—
1142C42—28no—
1143C42—28no—
1144C42—28no—
1145C42C22×D411yescharacteristic
1146C42C22×D411yescharacteristic
1147C42C22×D411yescharacteristic
1148C42C22×D411yescharacteristic
1149C42C22×D411yescharacteristic
1150C42C22×D411yescharacteristic
1151C42C22×D411yescharacteristic
1152C42C22×D411yescharacteristic
1153C42C22×D411yescharacteristic
1154C42C22×D411yescharacteristic
1155C42C22×D411yescharacteristic
1156C42C22×D411yescharacteristic
1157C42C22×D418yes—
1158C42C2511yescharacteristic
1159C42C2511yescharacteristic
1160C42C2511yescharacteristic
1161C42C2518yes—
1162C42C2511yescharacteristic
1163C23—22no—
1164C23—22no—
1165C23—24no—
1166C23—41no—
1167C23—41no—
1168C23—44no—
1169C23—44no—
1170C23—44no—
1171C23C23×D411yescharacteristic
1172C23C23×D411yescharacteristic
1173C23C23×D411yescharacteristic
1174Q8—28no—
1175Q8—28no—
1176Q8—28no—
1177Q8—24no—
1178Q8—28no—
1179Q8—24no—
1180Q8—24no—
1181Q8—44no—
1182Q8—44no—
1183Q8—44no—
1184Q8—44no—
1185Q8—44no—
1186Q8—44no—
1187Q8—42no—
1188Q8—82no—
1189Q8—88no—
1190Q8—816no—
1191Q8—82no—
1192Q8—82no—
1193Q8—81no—
1194D4—24no—
1195D4—28no—
1196D4—44no—
1197D4—44no—
1198D4—44no—
1199D4—44no—
1200D4—44no—
1201D4—42no—
1202D4—82no—
1203D4—82no—
1204D4—81no—
1205D4—84no—
1206D4—84no—
1207D4—82no—
1208C2×C4—22no—
1209C2×C4—28no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—44no—
1235C2×C4—48no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—44no—
1241C2×C4—48no—
1242C2×C4—44no—
1243C2×C4—44no—
1244C2×C4—816no—
1245C2×C4—88no—
1246C2×C4—82no—
1247C2×C4#57814yes—
1248C2×C4C23×D411yescharacteristic
1249C2×C4C23×D418yes—
1250C2×C4C23×D411yescharacteristic
1251C2×C4C23×D418yes—
1252C2×C4C23×D411yescharacteristic
1253C2×C4C23×D411yescharacteristic
1254C2×C4C23×D411yescharacteristic
1255C2×C4C23×D411yescharacteristic
1256C2×C4C23×D411yescharacteristic
1257C2×C4C23×D411yescharacteristic
1258C2×C4C23×D411yescharacteristic
1259C2×C4C23×D411yescharacteristic
1260C2×C4C23×D411yescharacteristic
1261C2×C4C2611yescharacteristic
1262C8—24no—
1263C8—24no—
1264C8—28no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—21no—
1272C22—21no—
1273C22—42no—
1274C22—44no—
1275C22—44no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—82no—
1280C22—88no—
1281C22C2×#57812yes—
1282C22C24×D411yescharacteristic
1283C4—21no—
1284C4—21no—
1285C4—28no—
1286C4—21no—
1287C4—21no—
1288C4—21no—
1289C4—28no—
1290C4—21no—
1291C4—21no—
1292C4—21no—
1293C4—42no—
1294C4—44no—
1295C4—44no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C4C2×#57812yes—
1302C4C2×#57812yes—
1303C4#358512yes—
1304C42−1+612yes—
1305C2—22no—
1306C2—41no—
1307C2—41no—
1308C2—82no—
1309C2—84no—
1310C2#6284811yescharacteristic
1311C2C22×#57811yescharacteristic
1312C2C2×#358511yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#60946C2
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×#3550C2semidirect
3. #62404C2semidirect
4. #62382C2semidirect
5. #62375C2semidirect
6. #61934C2semidirect
7. #61917C2semidirect
8. #61905C2semidirect
9. #61892C2semidirect
10. #61885C2semidirect
11. #61870C2semidirect
12. #61854C2semidirect
13. #61837C2semidirect
14. #61830C2semidirect
15. #61821C2semidirect
16. #60981C2semidirect
17. #60969C2semidirect
18. #60952C2semidirect
20. #60943C2semidirect
21. #60250C2semidirect
24. #3556C22semidirect
26. #3555C22semidirect
35. #3550C22semidirect
42. #3509C22semidirect
44. #3507C22semidirect
46. #3503C22semidirect
48. #3502C22semidirect
65. #3402C22semidirect
66. #3400C22semidirect
67. #3400C22semidirect
68. #3398C22semidirect
69. #3396C22semidirect
70. #3394C22semidirect
71. #3393C22semidirect
72. #3387C22semidirect
73. #3386C22semidirect
74. #3386C22semidirect
75. #3385C22semidirect
76. Q8×Q16C22semidirect
77. Q8×Q16C22semidirect
78. Q8×D8C22semidirect
79. #3377C22semidirect
80. #3375C22semidirect
81. #3375C22semidirect
82. #3375C22semidirect
83. #3369C22semidirect
84. #3367C22semidirect
85. #3367C22semidirect
86. #3367C22semidirect
87. #3365C22semidirect
88. #3364C22semidirect
89. #3363C22semidirect
90. #3363C22semidirect
91. #3361C22semidirect
92. #3359C22semidirect
93. #3262C22semidirect
94. #3258C22semidirect
95. #3255C22semidirect
97. #3254C22semidirect
98. #3249C22semidirect
100. #3243C22semidirect
103. #3237C22semidirect
108. #3230C22semidirect
112. #3225C22semidirect
114. #3216C22semidirect
118. #3209C22semidirect
129. #3178C22semidirect
130. #3175C22semidirect
131. #3172C22semidirect
132. #3170C22semidirect
135. #3124C22semidirect
136. #3121C22semidirect
141. #3107C22semidirect
149. #3104C22semidirect
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×#35502
#624042
#623822
#623752
#619342
#619172
#619052
#618922
#618852
#618702
#618542
#618372
#618302
#618212
#609812
#609692
#609522
#609462
#609432
#602502