Finite Group Databasebeta

← #10581396

Subgroups — #10581396

Order 512.

6514 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62834C211yesmaximal, characteristic, complemented
2C2×#3548C211yesmaximal, characteristic, complemented
3#62353C218yesmaximal, complemented
4#62342C214yesmaximal, complemented
5#62332C214yesmaximal, complemented
6#61807C214yesmaximal, complemented
7#61791C214yesmaximal, complemented
8#61726C214yesmaximal, complemented
9#61717C212yesmaximal, complemented
10#61694C212yesmaximal, complemented
11#61684C214yesmaximal, complemented
12#61668C214yesmaximal, complemented
13#61605C214yesmaximal, complemented
14#61585C212yesmaximal, complemented
15#61565C212yesmaximal, complemented
16#60969C211yesmaximal, characteristic, complemented
17#60951C211yesmaximal, characteristic, complemented
18#60947C211yesmaximal, characteristic, complemented
19#60940C211yesmaximal, characteristic, complemented
20#60762C218yesmaximal, complemented
21#60236C211yesmaximal, characteristic, complemented
22#3558—22no—
23#3558—22no—
24#3549C2212yescomplemented
25#3548—22no—
26#3548—22no—
27#3548—22no—
28#3548—22no—
29#3548C2214yescomplemented
30#3548C2214yescomplemented
31#3548C2214yescomplemented
32#3548C2214yescomplemented
33#3548C2212yescomplemented
34#3546—22no—
35#3546C2214yescomplemented
36#3537—22no—
37C2×#562—22no—
38#3519—22no—
39#3519C2214yes—
40#3511—21no—
41#3511C2212yescomplemented
42#3508—22no—
43#3506C2212yes—
44#3506C2212yescomplemented
45#3498—21no—
46#3498C2212yescomplemented
47#3496C2212yes—
48#3496C2212yescomplemented
49#3488—22no—
50#3488C2214yes—
51C2×#554—21no—
52C2×#554C2212yescomplemented
53C2×#550—21no—
54C2×#550C2212yescomplemented
55C2×#547C2212yescomplemented
56C2×#547C2212yescomplemented
57C2×#540—22no—
58C2×#537—22no—
59C2×#537C2214yescomplemented
60#3444C2211yescharacteristic
61C2×#533C2211yescharacteristic, complemented
62C2×#532C2211yescharacteristic
63C2×#532C2211yescharacteristic
64C2×#532C2211yescharacteristic, complemented
65#3357C2218yescomplemented
66#3354C2218yescomplemented
67#3353C2218yescomplemented
68#3346C22116yescomplemented
69#3338C2218yescomplemented
70#3334C2218yescomplemented
71#3334C2218yescomplemented
72#3333C2218yescomplemented
73#3333C2218yescomplemented
74#3332C2218yescomplemented
75#3330C2218yescomplemented
76#3330C2218yescomplemented
77#3330C2218yescomplemented
78#3314C22116yescomplemented
79#3309C22116yescomplemented
80#3305C2218yescomplemented
81#3303C2218yescomplemented
82#3302C2218yescomplemented
83#3295C2218yescomplemented
84#3294C2218yescomplemented
85#3294C2218yescomplemented
86#3287C2218yescomplemented
87#3284C2218yescomplemented
88#3283C2218yescomplemented
89#3274C2218yescomplemented
90#3272C2218yescomplemented
91#3272C2218yescomplemented
92#3268C22116yescomplemented
93#3254C2212yescomplemented
94#3254C2214yescomplemented
95#3253C2212yescomplemented
96#3248C2214yescomplemented
97#3245C2214yescomplemented
98#3238C2212yescomplemented
99#3235C2212yescomplemented
100#3231C2212yescomplemented
101#3230C2212yescomplemented
102#3229C2211yescharacteristic, complemented
103#3226C2212yescomplemented
104#3226C2212yescomplemented
105#3226C2211yescharacteristic, complemented
106#3226C2212yescomplemented
107#3217C2212yescomplemented
108#3214C2212yescomplemented
109#3210C2212yescomplemented
110#3209C2211yescharacteristic, complemented
111#3208C2212yescomplemented
112#3206C2211yescharacteristic, complemented
113#3206C2212yescomplemented
114#3205C2212yescomplemented
115#3205C2212yescomplemented
116#3203C22116yescomplemented
117#3203C22116yescomplemented
118#3198C22116yescomplemented
119#3198C22116yescomplemented
120#3194C2218yescomplemented
121#3194C2214yescomplemented
122#3193C2218yescomplemented
123#3193C2214yescomplemented
124#3190C2214yescomplemented
125#3190C2218yescomplemented
126#3186C2214yescomplemented
127#3186C2218yescomplemented
128#3182C2214yescomplemented
129#3171C2214yescomplemented
130#3170C2212yescomplemented
131#3169C2214yescomplemented
132#3167C2212yescomplemented
133#3112C2214yescomplemented
134#3110C2214yescomplemented
135#3108C2214yescomplemented
136#3107C2214yescomplemented
137#3106C2214yescomplemented
138#3101C2212yescomplemented
139#3100C2212yescomplemented
140#3100C2214yescomplemented
141#3100C2212yescomplemented
142#3100C2212yescomplemented
143#3098C22116yescomplemented
144#3092C2218yescomplemented
145C2×#480C2218yescomplemented
146#3062C22116yescomplemented
147#3061C22116yescomplemented
148#3012C22116yescomplemented
149#3006C2218yescomplemented
150#3002C2218yescomplemented
151#2981C2214yescomplemented
152#2979C2214yescomplemented
153#2975C2212yescomplemented
154#2974C2214yescomplemented
155#2972C2212yescomplemented
156#2935C2214yescomplemented
157#2931C2214yescomplemented
158#2920C2211yescharacteristic, complemented
159C2×#431C2211yescharacteristic, complemented
160#2880C2214yescomplemented
161C2×H(5,𝔽2)—22no—
162C2×H(5,𝔽2)C2314yes—
163C22×#41—22no—
164C22×#41—21no—
165C22×#41—21no—
166C22×#41C2314yes—
167C22×#41C2312yes—
168C2×AGL(1,ℤ/8)C23116yes—
169C2×#135C23116yes—
170C2×#131C2318yes—
171#562—28no—
172#562—28no—
173#562—28no—
174#562—28no—
175#562—24no—
176H(3,𝔽4)—24no—
177#560—28no—
178#559—24no—
179#559—24no—
180#556—22no—
181#556C2314yes—
182#555—22no—
183#555C2314yes—
184#555C2314yes—
185#554—24no—
186#554—24no—
187#554—24no—
188#554—24no—
189#554—22no—
190#554—24no—
191#554—24no—
192#554C2314yes—
193#554C2318yes—
194#554C2318yes—
195#553—24no—
196#553—24no—
197#553—24no—
198#553C2318yes—
199#550—24no—
200#550—24no—
201#550—24no—
202#550—24no—
203#550—24no—
204#550—22no—
205#550—22no—
206#550—24no—
207#550—24no—
208#550—24no—
209#550C2314yes—
210#550C2314yes—
211#550C2318yes—
212#550C2318yes—
213#548—24no—
214#548—24no—
215#547—22no—
216#547—24no—
217#547—24no—
218#547—24no—
219#547—24no—
220#547C2314yes—
221#547C2318yes—
222#547C2318yes—
223#547C2314yes—
224#547C2314yes—
225#547C2318yes—
226#547C2318yes—
227#546—24no—
228#546—28no—
229#546—24no—
230#546—24no—
231#546—24no—
232#546—24no—
233#546—28no—
234#546C2318yes—
235D42—28no—
236D42—24no—
237D42—24no—
238D42—22no—
239D42—22no—
240D42—24no—
241D42—24no—
242D42C2314yes—
243D42C2314yes—
244D42C2314yes—
245#542—24no—
246#542—24no—
247#540—28no—
248#540—28no—
249#540—28no—
250#540—28no—
251#540—24no—
252#540—24no—
253#538—28no—
254#538—24no—
255#538—28no—
256#538—24no—
257#537—28no—
258#537—28no—
259#537—28no—
260#537—28no—
261#537—28no—
262#537—28no—
263#537—24no—
264#537—22no—
265#537C23116yes—
266#537C23116yes—
267#537C2314yes—
268#537C2318yes—
269#535—22no—
270#535—24no—
271#535—24no—
272#535—24no—
273#535—24no—
274#535C2314yes—
275#535C2318yes—
276#534—24no—
277#534—24no—
278#533—22no—
279#533—21no—
280#533—21no—
281#533—21no—
282#533—21no—
283#533C2311yescharacteristic
284#533C2312yes—
285#533C2312yes—
286#533C2312yes—
287#533C2311yescharacteristic
288#533C2312yes—
289#533C2311yescharacteristic
290#532—22no—
291#532—22no—
292#532—21no—
293#532—21no—
294#532—21no—
295#532—21no—
296#532—21no—
297#532—21no—
298#532—21no—
299#532—21no—
300#532D412yes—
301#532D412yes—
302#532D412yes—
303#532D412yes—
304#532C2311yescharacteristic
305#532C2312yes—
306#532C2312yes—
307#532C2311yescharacteristic
308#532C2312yes—
309#532C2312yes—
310#532C2311yescharacteristic
311#532C2312yes—
312#532C2312yes—
313#532C2312yes—
314#532C2312yes—
315#532C2312yes—
316#532C2312yes—
317#532C2312yes—
318#532C2312yes—
319C2×C4⋊Q8D411yescharacteristic
320C2×C4⋊Q8C2311yescharacteristic
321C2×C4⋊Q8C2311yescharacteristic
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2311yescharacteristic
324C2×#127—22no—
325C2×#127—22no—
326C2×#127D411yescharacteristic
327C2×#127C2311yescharacteristic
328C2×#127C2311yescharacteristic
329#529—21no—
330#529—21no—
331#529—21no—
332#529—21no—
333#529C2312yes—
334#529C2312yes—
335C2×#125—22no—
336C2×#125—21no—
337C2×#124—21no—
338C2×#124—21no—
339C2×#124D412yes—
340#525—21no—
341#525—21no—
342#525—24no—
343#525C2318yes—
344#525C2312yes—
345C2×#123—24no—
346C2×#123—24no—
347C2×C22⋊Q8—24no—
348C2×C22⋊Q8—21no—
349C2×C22⋊Q8—22no—
350C2×C22⋊Q8—24no—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2314yes—
353C2×#121—24no—
354C2×#121—24no—
355C2×#121—22no—
356C2×#121—24no—
357C2×#121—21no—
358C2×#121—21no—
359C2×#121—24no—
360C2×#121—24no—
361C2×#121D412yes—
362C2×#121D412yes—
363C2×#121C2318yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2314yes—
367#520—22no—
368#520C2314yes—
369#518—24no—
370C4×#41—21no—
371C4×#41—21no—
372C4×#41C2312yes—
373C2×C4×Q8—21no—
374C2×C4×Q8C2312yes—
375C2×C4×D4—22no—
376C2×C4×D4—22no—
377C2×C4×D4—21no—
378C2×C4×D4—21no—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×#117—21no—
384C22×C4⋊C4—22no—
385C22×C4⋊C4C2314yes—
386C22×C42C2311yescharacteristic
387#501C2314yes—
388#500C2312yes—
389#500C2314yes—
390#500C2314yes—
391#498C2312yes—
392#496C2314yes—
393#494C2312yes—
394#493C2314yes—
395#492C2312yes—
396#492C2314yes—
397#490C2314yes—
398#489C2314yes—
399#487C2312yes—
400#487C2312yes—
401#487C2314yes—
402#487C2312yes—
403#486C2314yes—
404#486C2314yes—
405#486C2314yes—
406#486C2312yes—
407#485C23116yes—
408#485C2318yes—
409#484C23116yes—
410#484C23116yes—
411#484C2318yes—
412#483C2314yes—
413#483C2314yes—
414#482C23116yes—
415#482C2318yes—
416#481C23116yes—
417#480C23116yes—
418#480C23116yes—
419#480C23116yes—
420#480C2314yes—
421#480C2314yes—
422#480C2314yes—
423#480C2318yes—
424#480C2314yes—
425#480C2318yes—
426#479C2318yes—
427#477C2314yes—
428#477C2318yes—
429#476C2314yes—
430#476C2314yes—
431#475C2314yes—
432#474C2314yes—
433#474C2314yes—
434#474C2318yes—
435#474C2314yes—
436#474C2314yes—
437#474C2318yes—
438#469C23116yes—
439#469C2318yes—
440#468C23116yes—
441#468C23116yes—
442#468C23116yes—
443#468C2318yes—
444#468C23116yes—
445#467C23116yes—
446#467C2318yes—
447#466C23116yes—
448#466C23116yes—
449#466C2318yes—
450#466C2318yes—
451#465C23116yes—
452#465C2318yes—
453#464C2318yes—
454#462C2314yes—
455#461C2314yes—
456#461C2314yes—
457#461C2318yes—
458#460C2314yes—
459#460C2318yes—
460#459C2314yes—
461#459C2318yes—
462#459C2314yes—
463#459C2314yes—
464#459C2314yes—
465#452C23116yes—
466#452C23116yes—
467#452C2318yes—
468#451C2314yes—
469#450C2314yes—
470#450C2318yes—
471#450C23116yes—
472#449C23116yes—
473#449C23116yes—
474#449C23116yes—
475#449C2318yes—
476#449C23116yes—
477#448C2314yes—
478#448C2318yes—
479#447C2314yes—
480#447C2314yes—
481#447C2314yes—
482#447C2318yes—
483#447C23116yes—
484#440C23116yes—
485C4×Q16C2318yes—
486C4×SD16C2318yes—
487C4×SD16C2318yes—
488C4×D8C2318yes—
489C4×D8C2318yes—
490C4×D8C2318yes—
491#436C2318yes—
492#436C2318yes—
493#436C2318yes—
494#435C23116yes—
495C8×D4C2318yes—
496C8×D4C2318yes—
497C8×D4C2318yes—
498#432C2312yes—
499#432C2312yes—
500#431C2311yescharacteristic
501#431C2311yescharacteristic
502#431C2312yes—
503#431C2312yes—
504#431C2312yes—
505#431C2312yes—
506#431C2312yes—
507#428C23116yes—
508C2×#107C23116yes—
509#423C2312yes—
510C2×C4⋊C8C2312yes—
511#417C23116yes—
512#417C23116yes—
513#416C23116yes—
514C2×#102C23116yes—
515#408C23116yes—
516#408C2318yes—
517#407C2318yes—
518#407C2312yes—
519C2×C22⋊C8C2318yes—
520C2×C22⋊C8C2312yes—
521C4×M16C2312yes—
522C2×C4×C8C2312yes—
523H(5,𝔽2)—88no—
524H(5,𝔽2)—88no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—21no—
531C2×#41—22no—
532C2×#41—21no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—28no—
541C2×#41—84no—
542C2×#41—84no—
543C2×#41—84no—
544C2×#41—88no—
545C2×#41—88no—
546C2×#41C2×D414yes—
547C2×#41C2×D414yes—
548C2×#41C2412yes—
549C2×#41C2418yes—
550C2×#41C24116yes—
551C2×#41C2414yes—
552C2×#41C2414yes—
553C22×Q8—21no—
554C22×Q8—21no—
555C22×Q8—21no—
556C22×Q8C2×D412yes—
557C22×Q8C2412yes—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—24no—
561C22×D4—22no—
562C22×D4—28no—
563C22×D4—24no—
564C22×D4—28no—
565C22×D4—24no—
566C22×D4—24no—
567C22×D4—24no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4C2×D412yes—
573C22×D4C2×D412yes—
574C22×D4C2×D414yes—
575C22×D4C2×D412yes—
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2418yes—
579C23×C4—24no—
580C23×C4—22no—
581C23×C4—24no—
582C23×C4—22no—
583C23×C4C2×D411yescharacteristic
584C23×C4C2×D411yescharacteristic
585C23×C4C2414yes—
586C23×C4C2411yescharacteristic
587AGL(1,ℤ/8)—816no—
588#135—816no—
589C2×Q16C2418yes—
590C2×SD16C2418yes—
591C2×SD16C24116yes—
592C2×SD16C2418yes—
593C2×D8C2418yes—
594C2×D8C2418yes—
595C2×D8C2418yes—
596#131—88no—
597C2×M16C2414yes—
598C2×M16C24116yes—
599C22×C8C2414yes—
600C22×C8C24116yes—
601C4⋊Q8—21no—
602C4⋊Q8—21no—
603C4⋊Q8—21no—
604C4⋊Q8—21no—
605C4⋊Q8—21no—
606C4⋊Q8—21no—
607C4⋊Q8—21no—
608C4⋊Q8—21no—
609C4⋊Q8C2×D412yes—
610C4⋊Q8C2×D412yes—
611C4⋊Q8C2×D412yes—
612C4⋊Q8C2×D412yes—
613C4⋊Q8C2412yes—
614C4⋊Q8C2412yes—
615C4⋊Q8C2411yescharacteristic
616C4⋊Q8C2412yes—
617C4⋊Q8C2412yes—
618C4⋊Q8C2412yes—
619C4⋊Q8C2412yes—
620C4⋊Q8C2412yes—
621C4⋊Q8C2412yes—
622C4⋊Q8C2411yescharacteristic
623C4⋊Q8C2411yescharacteristic
624#127—24no—
625#127—24no—
626#127—24no—
627#127—28no—
628#127—28no—
629#127—28no—
630#127—21no—
631#127—21no—
632#127—21no—
633#127—21no—
634#127C2×D412yes—
635#127C2×D412yes—
636#127C2×D412yes—
637#127C2×D412yes—
638#127C2412yes—
639#127C2412yes—
640#127C2412yes—
641#127C2412yes—
642#127C2411yescharacteristic
643#126—28no—
644#126—28no—
645#126—22no—
646#126—22no—
647#125—28no—
648#125—28no—
649#125—24no—
650#125—22no—
651#125—22no—
652#125—22no—
653#125—22no—
654#125—21no—
655#125—21no—
656#125C2412yes—
657#124—24no—
658#124—28no—
659#124—24no—
660#124—28no—
661#124—28no—
662#124—22no—
663#124—22no—
664#124—22no—
665#124—22no—
666#124—22no—
667#124—22no—
668#124—22no—
669#124—22no—
670#124—21no—
671#124—21no—
672#124C2×D414yes—
673#124C2×D414yes—
674#124C2×D414yes—
675#124C2×D414yes—
676#124C2412yes—
677#123—22no—
678#123—22no—
679#123—22no—
680#123—28no—
681#123—28no—
682#123—216no—
683#123—216no—
684#123—216no—
685#123—216no—
686#123—28no—
687#123—28no—
688#123—28no—
689#123—28no—
690C22⋊Q8—216no—
691C22⋊Q8—216no—
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—28no—
701C22⋊Q8—21no—
702C22⋊Q8—21no—
703C22⋊Q8—21no—
704C22⋊Q8—21no—
705C22⋊Q8—28no—
706C22⋊Q8—28no—
707C22⋊Q8—24no—
708C22⋊Q8—24no—
709C22⋊Q8—216no—
710C22⋊Q8—216no—
711C22⋊Q8—28no—
712C22⋊Q8C2414yes—
713C22⋊Q8C2414yes—
714C22⋊Q8C24116yes—
715C22⋊Q8C2412yes—
716C22⋊Q8C2412yes—
717C22⋊Q8C2418yes—
718#121—28no—
719#121—24no—
720#121—216no—
721#121—216no—
722#121—216no—
723#121—216no—
724#121—28no—
725#121—28no—
726#121—216no—
727#121—216no—
728#121—24no—
729#121—24no—
730#121—24no—
731#121—28no—
732#121—28no—
733#121—28no—
734#121—28no—
735#121—21no—
736#121—22no—
737#121—22no—
738#121—22no—
739#121—22no—
740#121—22no—
741#121—22no—
742#121—22no—
743#121—22no—
744#121—22no—
745#121—22no—
746#121—22no—
747#121—22no—
748#121—28no—
749#121—28no—
750#121—28no—
751#121—21no—
752#121—21no—
753#121—21no—
754#121—24no—
755#121—24no—
756#121—24no—
757#121—216no—
758#121—216no—
759#121—28no—
760#121—28no—
761#121—28no—
762#121C2×D414yes—
763#121C2×D414yes—
764#121C2×D414yes—
765#121C2×D414yes—
766#121C2×D414yes—
767#121C2×D414yes—
768#121C2×D414yes—
769#121C2×D414yes—
770#121C2412yes—
771#121C2414yes—
772#121C2414yes—
773#121C2414yes—
774#121C2414yes—
775#121C2418yes—
776#121C2418yes—
777#121C24116yes—
778#121C2412yes—
779#121C2418yes—
780#120—22no—
781#120—28no—
782#120—28no—
783#120—28no—
784#120—28no—
785#120—28no—
786#120—28no—
787#120—28no—
788#120—28no—
789C4×Q8—24no—
790C4×Q8—24no—
791C4×Q8—22no—
792C4×Q8—22no—
793C4×Q8—22no—
794C4×Q8—22no—
795C4×Q8—22no—
796C4×Q8—22no—
797C4×Q8—21no—
798C4×Q8—21no—
799C4×Q8—21no—
800C4×Q8—21no—
801C4×Q8C2414yes—
802C4×Q8C2414yes—
803C4×Q8C2412yes—
804C4×Q8C2412yes—
805C4×D4—28no—
806C4×D4—28no—
807C4×D4—24no—
808C4×D4—28no—
809C4×D4—24no—
810C4×D4—22no—
811C4×D4—22no—
812C4×D4—22no—
813C4×D4—22no—
814C4×D4—22no—
815C4×D4—22no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—28no—
819C4×D4—28no—
820C4×D4—24no—
821C4×D4—24no—
822C4×D4—28no—
823C4×D4—22no—
824C4×D4—22no—
825C4×D4—22no—
826C4×D4—22no—
827C4×D4—22no—
828C4×D4—22no—
829C4×D4—22no—
830C4×D4—22no—
831C4×D4—22no—
832C4×D4—22no—
833C4×D4—22no—
834C4×D4—22no—
835C4×D4—21no—
836C4×D4—21no—
837C4×D4—21no—
838C4×D4—21no—
839C4×D4C2×D414yes—
840C4×D4C2×D414yes—
841C4×D4C2×D414yes—
842C4×D4C2×D414yes—
843C4×D4C2414yes—
844C4×D4C2414yes—
845C4×D4C2414yes—
846C4×D4C2414yes—
847C4×D4C2412yes—
848C4×D4C2412yes—
849C4×D4C2414yes—
850C4×D4C2414yes—
851C4×D4C2414yes—
852C4×D4C2414yes—
853#117—22no—
854#117—22no—
855#117—22no—
856#117—22no—
857#117—21no—
858#117—21no—
859#117—24no—
860#117—24no—
861#117—22no—
862#117—22no—
863#117—22no—
864#117C2412yes—
865#117C2418yes—
866C2×C4⋊C4—21no—
867C2×C4⋊C4—24no—
868C2×C4⋊C4—24no—
869C2×C4⋊C4—28no—
870C2×C4⋊C4—21no—
871C2×C4⋊C4—21no—
872C2×C4⋊C4—21no—
873C2×C4⋊C4—21no—
874C2×C4⋊C4—22no—
875C2×C4⋊C4—22no—
876C2×C4⋊C4—28no—
877C2×C4⋊C4—28no—
878C2×C4⋊C4—24no—
879C2×C4⋊C4C2×D412yes—
880C2×C4⋊C4C2×D412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C24116yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2418yes—
886C2×C22⋊C4—22no—
887C2×C22⋊C4—24no—
888C2×C22⋊C4—24no—
889C2×C22⋊C4—22no—
890C2×C22⋊C4—22no—
891C2×C22⋊C4—22no—
892C2×C22⋊C4—22no—
893C2×C22⋊C4—28no—
894C2×C22⋊C4—28no—
895C2×C22⋊C4C2×D414yes—
896C2×C22⋊C4C2×D414yes—
897C2×C42—22no—
898C2×C42—22no—
899C2×C42C2×D411yescharacteristic
900C2×C42C2×D411yescharacteristic
901C2×C42C2×D411yescharacteristic
902C2×C42C2×D411yescharacteristic
903C2×C42C2×D411yescharacteristic
904C2×C42C2×D411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911#107C2418yes—
912#107C2418yes—
913#107C2418yes—
914#107C24116yes—
915#107C2418yes—
916#106C2418yes—
917#106C2418yes—
918C4⋊C8C2412yes—
919C4⋊C8C2414yes—
920C4⋊C8C2412yes—
921C4⋊C8C2414yes—
922C4⋊C8C2414yes—
923#103C2418yes—
924#103C24116yes—
925#103C2418yes—
926#103C2418yes—
927#103C2418yes—
928#102C2418yes—
929#102C2418yes—
930#102C2418yes—
931#102C24116yes—
932#102C2418yes—
933#102C2418yes—
934#102C2418yes—
935#102C2418yes—
936#102C2418yes—
937C22⋊C8C2412yes—
938C22⋊C8C2414yes—
939C22⋊C8C2412yes—
940C22⋊C8C2414yes—
941C22⋊C8C24116yes—
942C22⋊C8C2414yes—
943C22⋊C8C24116yes—
944#97C2414yes—
945C4×C8C2412yes—
946C4×C8C2414yes—
947C4×C8C2412yes—
948C4×C8C2414yes—
949C24—22no—
950C24—22no—
951C24—28no—
952C24C22×D411yescharacteristic
953C24C22×D414yes—
954#41—48no—
955#41—48no—
956#41—44no—
957#41—416no—
958#41—416no—
959#41—416no—
960#41—48no—
961#41—44no—
962#41—82no—
963#41—84no—
964#41—84no—
965#41—84no—
966#41—84no—
967#41—84no—
968#41—84no—
969#41—84no—
970#41—84no—
971#41—84no—
972#41—816no—
973#41—816no—
974#41—88no—
975#41—88no—
976#41—816no—
977#41—88no—
978C2×Q8—21no—
979C2×Q8—22no—
980C2×Q8—22no—
981C2×Q8—22no—
982C2×Q8—22no—
983C2×Q8—21no—
984C2×Q8—22no—
985C2×Q8—22no—
986C2×Q8—22no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8—82no—
990C2×Q8—82no—
991C2×Q8—82no—
992C2×Q8C22×D414yes—
993C2×Q8C22×D414yes—
994C2×Q8C2512yes—
995C2×Q8C2514yes—
996C2×D4—24no—
997C2×D4—22no—
998C2×D4—22no—
999C2×D4—22no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—216no—
1008C2×D4—216no—
1009C2×D4—28no—
1010C2×D4—22no—
1011C2×D4—22no—
1012C2×D4—22no—
1013C2×D4—21no—
1014C2×D4—22no—
1015C2×D4—22no—
1016C2×D4—22no—
1017C2×D4—21no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C2×D4—28no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—416no—
1027C2×D4—44no—
1028C2×D4—82no—
1029C2×D4—82no—
1030C2×D4—82no—
1031C2×D4—88no—
1032C2×D4—88no—
1033C2×D4—88no—
1034C2×D4—84no—
1035C2×D4—82no—
1036C2×D4—88no—
1037C2×D4—84no—
1038C2×D4—88no—
1039C2×D4—88no—
1040C2×D4—84no—
1041C2×D4—816no—
1042C2×D4—816no—
1043C2×D4C22×D414yes—
1044C2×D4C22×D414yes—
1045C2×D4C22×D414yes—
1046C2×D4C22×D414yes—
1047C2×D4C22×D418yes—
1048C2×D4C22×D414yes—
1049C2×D4C22×D414yes—
1050C2×D4C22×D418yes—
1051C2×D4C2512yes—
1052C2×D4C2514yes—
1053C2×D4C2514yes—
1054C22×C4—24no—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—28no—
1060C22×C4—216no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—28no—
1069C22×C4—216no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—48no—
1073C22×C4—48no—
1074C22×C4—84no—
1075C22×C4—88no—
1076C22×C4—88no—
1077C22×C4C22×D411yescharacteristic
1078C22×C4C22×D411yescharacteristic
1079C22×C4C22×D411yescharacteristic
1080C22×C4C22×D411yescharacteristic
1081C22×C4C22×D411yescharacteristic
1082C22×C4C22×D411yescharacteristic
1083C22×C4C22×D411yescharacteristic
1084C22×C4C22×D411yescharacteristic
1085C22×C4C22×D411yescharacteristic
1086C22×C4C22×D411yescharacteristic
1087C22×C4C22×D411yescharacteristic
1088C22×C4C22×D411yescharacteristic
1089C22×C4C22×D411yescharacteristic
1090C22×C4C22×D411yescharacteristic
1091C22×C4C22×D414yes—
1092C22×C4C22×D418yes—
1093C22×C4C22×D411yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2518yes—
1097C22×C4C2511yescharacteristic
1098Q16—48no—
1099SD16—48no—
1100SD16—416no—
1101SD16—48no—
1102D8—48no—
1103D8—48no—
1104D8—48no—
1105M16—44no—
1106M16—416no—
1107C2×C8—44no—
1108C2×C8—416no—
1109C2×C8C2514yes—
1110C2×C8C2514yes—
1111C2×C8C2518yes—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—21no—
1117C4⋊C4—216no—
1118C4⋊C4—216no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—28no—
1134C4⋊C4—21no—
1135C4⋊C4—22no—
1136C4⋊C4—22no—
1137C4⋊C4—22no—
1138C4⋊C4—22no—
1139C4⋊C4—21no—
1140C4⋊C4—21no—
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4C22×D414yes—
1144C4⋊C4C22×D414yes—
1145C4⋊C4C22×D414yes—
1146C4⋊C4C22×D414yes—
1147C4⋊C4C2514yes—
1148C4⋊C4C2514yes—
1149C4⋊C4C2512yes—
1150C4⋊C4C2512yes—
1151C4⋊C4C2514yes—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—28no—
1155C22⋊C4—216no—
1156C22⋊C4—22no—
1157C22⋊C4—22no—
1158C22⋊C4—22no—
1159C22⋊C4—28no—
1160C22⋊C4—22no—
1161C22⋊C4—22no—
1162C22⋊C4—24no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—216no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—22no—
1174C22⋊C4—22no—
1175C22⋊C4—28no—
1176C22⋊C4—22no—
1177C22⋊C4—22no—
1178C22⋊C4C22×D418yes—
1179C22⋊C4C22×D418yes—
1180C22⋊C4C22×D418yes—
1181C22⋊C4C22×D418yes—
1182C42—22no—
1183C42—22no—
1184C42—24no—
1185C42—24no—
1186C42—22no—
1187C42—28no—
1188C42C22×D411yescharacteristic
1189C42C22×D411yescharacteristic
1190C42C22×D411yescharacteristic
1191C42C22×D411yescharacteristic
1192C42C22×D411yescharacteristic
1193C42C22×D411yescharacteristic
1194C42C22×D411yescharacteristic
1195C42C22×D411yescharacteristic
1196C42C22×D411yescharacteristic
1197C42C22×D411yescharacteristic
1198C42C22×D411yescharacteristic
1199C42C22×D411yescharacteristic
1200C42C2511yescharacteristic
1201C42C2511yescharacteristic
1202C42C2511yescharacteristic
1203C42C2511yescharacteristic
1204C23—22no—
1205C23—28no—
1206C23—22no—
1207C23—24no—
1208C23—24no—
1209C23—41no—
1210C23—44no—
1211C23—41no—
1212C23—44no—
1213C23—44no—
1214C23—44no—
1215C23—44no—
1216C23—44no—
1217C23—82no—
1218C23—82no—
1219C23—88no—
1220C23—88no—
1221C23—88no—
1222C23C23×D411yescharacteristic
1223C23C23×D411yescharacteristic
1224C23C23×D418yes—
1225C23C23×D411yescharacteristic
1226Q8—28no—
1227Q8—24no—
1228Q8—44no—
1229Q8—44no—
1230Q8—44no—
1231Q8—44no—
1232Q8—44no—
1233Q8—44no—
1234Q8—42no—
1235Q8—82no—
1236Q8—82no—
1237Q8—82no—
1238Q8—81no—
1239D4—28no—
1240D4—24no—
1241D4—24no—
1242D4—28no—
1243D4—24no—
1244D4—28no—
1245D4—28no—
1246D4—44no—
1247D4—44no—
1248D4—48no—
1249D4—48no—
1250D4—44no—
1251D4—44no—
1252D4—44no—
1253D4—44no—
1254D4—44no—
1255D4—44no—
1256D4—48no—
1257D4—44no—
1258D4—44no—
1259D4—42no—
1260D4—44no—
1261D4—88no—
1262D4—82no—
1263D4—82no—
1264D4—82no—
1265D4—82no—
1266D4—81no—
1267D4—88no—
1268D4—88no—
1269D4—88no—
1270D4—88no—
1271D4—816no—
1272D4—84no—
1273D4—84no—
1274D4—84no—
1275D4—816no—
1276D4—82no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—216no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—44no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—48no—
1303C2×C4—41no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—44no—
1307C2×C4—44no—
1308C2×C4—44no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—44no—
1313C2×C4—816no—
1314C2×C4—84no—
1315C2×C4—88no—
1316C2×C4—82no—
1317C2×C4—816no—
1318C2×C4—88no—
1319C2×C4#57614yes—
1320C2×C4C23×D411yescharacteristic
1321C2×C4C23×D411yescharacteristic
1322C2×C4C23×D418yes—
1323C2×C4C23×D411yescharacteristic
1324C2×C4C23×D411yescharacteristic
1325C2×C4C23×D411yescharacteristic
1326C2×C4C23×D411yescharacteristic
1327C2×C4C23×D411yescharacteristic
1328C2×C4C23×D411yescharacteristic
1329C2×C4C23×D411yescharacteristic
1330C2×C4C23×D411yescharacteristic
1331C2×C4C23×D411yescharacteristic
1332C2×C4C2611yescharacteristic
1333C8—24no—
1334C8—28no—
1335C8—24no—
1336C22—21no—
1337C22—21no—
1338C22—21no—
1339C22—21no—
1340C22—28no—
1341C22—21no—
1342C22—21no—
1343C22—28no—
1344C22—21no—
1345C22—21no—
1346C22—28no—
1347C22—44no—
1348C22—44no—
1349C22—42no—
1350C22—42no—
1351C22—44no—
1352C22—44no—
1353C22—42no—
1354C22—44no—
1355C22—44no—
1356C22—82no—
1357C22—88no—
1358C22—88no—
1359C22—164no—
1360C22—328no—
1361C22C2×#57612yes—
1362C22C24×D411yescharacteristic
1363C4—21no—
1364C4—21no—
1365C4—21no—
1366C4—21no—
1367C4—21no—
1368C4—21no—
1369C4—21no—
1370C4—28no—
1371C4—21no—
1372C4—44no—
1373C4—42no—
1374C4—44no—
1375C4—44no—
1376C4—42no—
1377C4—42no—
1378C4—44no—
1379C4C2×#57612yes—
1380C4C2×#57612yes—
1381C4#358612yes—
1382C4H(7,𝔽2)12yes—
1383C2—22no—
1384C2—41no—
1385C2—41no—
1386C2—48no—
1387C2—84no—
1388C2—84no—
1389C2—82no—
1390C2#6284211yescharacteristic
1391C2C22×#57611yescharacteristic
1392C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62834C2semidirect
2. C2×#3548C2semidirect
3. #62353C2semidirect
4. #62342C2semidirect
5. #62332C2semidirect
6. #61807C2semidirect
7. #61791C2semidirect
8. #61726C2semidirect
9. #61717C2semidirect
10. #61694C2semidirect
11. #61684C2semidirect
12. #61668C2semidirect
13. #61605C2semidirect
14. #61585C2semidirect
15. #61565C2semidirect
16. #60969C2semidirect
17. #60951C2semidirect
18. #60947C2semidirect
19. #60940C2semidirect
20. #60762C2semidirect
21. #60236C2semidirect
24. #3549C22semidirect
29. #3548C22semidirect
30. #3548C22semidirect
31. #3548C22semidirect
32. #3548C22semidirect
33. #3548C22semidirect
35. #3546C22semidirect
41. #3511C22semidirect
44. #3506C22semidirect
46. #3498C22semidirect
48. #3496C22semidirect
52. C2×#554C22semidirect
54. C2×#550C22semidirect
55. C2×#547C22semidirect
56. C2×#547C22semidirect
59. C2×#537C22semidirect
61. C2×#533C22semidirect
64. C2×#532C22semidirect
65. #3357C22semidirect
66. #3354C22semidirect
67. #3353C22semidirect
68. #3346C22semidirect
69. #3338C22semidirect
70. #3334C22semidirect
71. #3334C22semidirect
72. #3333C22semidirect
73. #3333C22semidirect
74. #3332C22semidirect
75. #3330C22semidirect
76. #3330C22semidirect
77. #3330C22semidirect
78. #3314C22semidirect
79. #3309C22semidirect
80. #3305C22semidirect
81. #3303C22semidirect
82. #3302C22semidirect
83. #3295C22semidirect
84. #3294C22semidirect
85. #3294C22semidirect
86. #3287C22semidirect
87. #3284C22semidirect
88. #3283C22semidirect
89. #3274C22semidirect
90. #3272C22semidirect
91. #3272C22semidirect
92. #3268C22semidirect
93. #3254C22semidirect
94. #3254C22semidirect
95. #3253C22semidirect
96. #3248C22semidirect
97. #3245C22semidirect
98. #3238C22semidirect
99. #3235C22semidirect
100. #3231C22semidirect
101. #3230C22semidirect
102. #3229C22semidirect
103. #3226C22semidirect
104. #3226C22semidirect
105. #3226C22semidirect
106. #3226C22semidirect
107. #3217C22semidirect
108. #3214C22semidirect
109. #3210C22semidirect
110. #3209C22semidirect
111. #3208C22semidirect
112. #3206C22semidirect
113. #3206C22semidirect
114. #3205C22semidirect
115. #3205C22semidirect
116. #3203C22semidirect
117. #3203C22semidirect
118. #3198C22semidirect
119. #3198C22semidirect
120. #3194C22semidirect
121. #3194C22semidirect
122. #3193C22semidirect
123. #3193C22semidirect
124. #3190C22semidirect
125. #3190C22semidirect
126. #3186C22semidirect
127. #3186C22semidirect
128. #3182C22semidirect
129. #3171C22semidirect
130. #3170C22semidirect
131. #3169C22semidirect
132. #3167C22semidirect
133. #3112C22semidirect
134. #3110C22semidirect
135. #3108C22semidirect
136. #3107C22semidirect
137. #3106C22semidirect
138. #3101C22semidirect
139. #3100C22semidirect
140. #3100C22semidirect
141. #3100C22semidirect
142. #3100C22semidirect
143. #3098C22semidirect
144. #3092C22semidirect
145. C2×#480C22semidirect
146. #3062C22semidirect
147. #3061C22semidirect
148. #3012C22semidirect
149. #3006C22semidirect
150. #3002C22semidirect
151. #2981C22semidirect
152. #2979C22semidirect
153. #2975C22semidirect
154. #2974C22semidirect
155. #2972C22semidirect
156. #2935C22semidirect
157. #2931C22semidirect
158. #2920C22semidirect
159. C2×#431C22semidirect
160. #2880C22semidirect

Maximal subgroups

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

subgroupindex
#628342
C2×#35482
#623532
#623422
#623322
#618072
#617912
#617262
#617172
#616942
#616842
#616682
#616052
#615852
#615652
#609692
#609512
#609472
#609402
#607622
#602362