Finite Group Databasebeta

← #10581113

Subgroups — #10581113

Order 512.

6307 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62834C211yesmaximal, characteristic, complemented
2#62829C211yesmaximal, characteristic, complemented
3#62584C214yesmaximal, complemented
4#62576C214yesmaximal, complemented
5#62506C214yesmaximal, complemented
6#62447C214yesmaximal, complemented
7#62387C214yesmaximal, complemented
8#62336C214yesmaximal, complemented
9#62280C214yesmaximal, complemented
10#62270C212yesmaximal, complemented
11#62268C212yesmaximal, complemented
12#61521C218yesmaximal, complemented
13#61519C218yesmaximal, complemented
14#61019C212yesmaximal, complemented
15#61017C212yesmaximal, complemented
16#60949C212yesmaximal, complemented
17#60725C212yesmaximal, complemented
18#60719C212yesmaximal, complemented
19C2×#3180C212yesmaximal, complemented
20#60207C211yesmaximal, characteristic, complemented
21#3566—24no—
22#3564—22no—
23#3560—22no—
24#3558—22no—
25#3558—22no—
26#3557C2212yescomplemented
27#3551C2212yescomplemented
28#3549C2212yescomplemented
29#3548C2212yescomplemented
30#3546—24no—
31#3538C2211yescharacteristic, complemented
32#3537C2212yes—
33#3537C2211yescharacteristic, complemented
34#3537C2212yescomplemented
35#3536C2212yescomplemented
36#3519C2218yescomplemented
37#3516C2214yescomplemented
38#3515C2214yescomplemented
39#3514C2214yescomplemented
40#3513—24no—
41#3513C2214yescomplemented
42#3512C2212yescomplemented
43#3511C2214yescomplemented
44#3510C2212yescomplemented
45#3508C2212yescomplemented
46#3508C2212yescomplemented
47#3506—22no—
48#3498C2214yescomplemented
49#3496—22no—
50#3493—22no—
51#3491—22no—
52#3488—24no—
53#3444C2211yescharacteristic
54C2×#532C2212yescomplemented
55C2×#529C2212yescomplemented
56#3399C2218yescomplemented
57#3397C2218yescomplemented
58#3389C2218yescomplemented
59#3388C2218yescomplemented
60#3376C2218yescomplemented
61#3370C2218yescomplemented
62#3368C2218yescomplemented
63#3366C2218yescomplemented
64#3348C2218yescomplemented
65#3347C2218yescomplemented
66#3346C2218yescomplemented
67#3345C2218yescomplemented
68#3339C2218yescomplemented
69#3337C2218yescomplemented
70#3321C2218yescomplemented
71#3320C2218yescomplemented
72#3319C2218yescomplemented
73#3318C2218yescomplemented
74#3318C2218yescomplemented
75#3318C2218yescomplemented
76#3310C2218yescomplemented
77#3310C2218yescomplemented
78#3301C2218yescomplemented
79#3297C2218yescomplemented
80#3295C2218yescomplemented
81#3294C2218yescomplemented
82D4×SD16C2218yescomplemented
83D4×D8C2218yescomplemented
84#3265C2218yescomplemented
85#3265C2218yescomplemented
86#3264C2218yescomplemented
87#3264C2218yescomplemented
88#3260C2214yescomplemented
89#3259C2214yescomplemented
90#3257C2218yescomplemented
91#3251C2218yescomplemented
92#3240C2214yescomplemented
93#3240C2214yescomplemented
94#3239C2214yescomplemented
95#3235C2214yescomplemented
96#3234C2214yescomplemented
97#3234C2214yescomplemented
98#3217C2214yescomplemented
99#3217C2214yescomplemented
100#3217C2214yescomplemented
101#3214C2214yescomplemented
102#3213C2214yescomplemented
103#3213C2214yescomplemented
104#3200C2214yescomplemented
105#3199C2214yescomplemented
106#3198C2218yescomplemented
107#3193C2214yescomplemented
108#3192C2214yescomplemented
109#3180C2214yescomplemented
110#3180C2214yescomplemented
111#3180C2218yescomplemented
112#3180C2214yescomplemented
113#3180C2214yescomplemented
114#3180C2218yescomplemented
115#3180C2214yescomplemented
116#3180C2214yescomplemented
117#3179C2218yescomplemented
118#3179C2218yescomplemented
119#3176C2214yescomplemented
120#3176C2214yescomplemented
121#3174C2214yescomplemented
122#3174C2214yescomplemented
123#3171C2214yescomplemented
124#3171C2214yescomplemented
125#3171C2214yescomplemented
126#3171C2214yescomplemented
127#3166C2212yescomplemented
128#3162C2212yescomplemented
129C2×#501C2212yescomplemented
130#3151C2212yescomplemented
131C2×#496C2212yescomplemented
132C2×#496C2212yescomplemented
133#3140C2212yescomplemented
134#3138C2212yescomplemented
135#3135C2212yescomplemented
136C2×#490C2212yescomplemented
137C2×#490C2212yescomplemented
138C2×#489C2212yescomplemented
139#3126C2214yescomplemented
140#3123C2214yescomplemented
141#3122C2214yescomplemented
142#3122C2214yescomplemented
143#3119C2218yescomplemented
144#3118C2218yescomplemented
145#3105C2218yescomplemented
146#3103C2214yescomplemented
147#3100C2214yescomplemented
148#3062C2218yescomplemented
149#3058C2214yescomplemented
150#3057C2214yescomplemented
151C2×#466C2214yescomplemented
152C2×#465C2214yescomplemented
153#2970C2214yescomplemented
154#2970C2214yescomplemented
155#2968C2218yescomplemented
156#2961C2212yescomplemented
157#2949C2214yescomplemented
158#2948C2214yescomplemented
159#2946C2218yescomplemented
160C2×#442C2214yescomplemented
161C2×#440C2214yescomplemented
162#2932C2212yescomplemented
163#2929C2212yescomplemented
164#2929C2212yescomplemented
165#2923C2211yescharacteristic, complemented
166#2923C2211yescharacteristic, complemented
167#2920C2211yescharacteristic, complemented
168#2875C2211yescharacteristic, complemented
169#2875C2211yescharacteristic, complemented
170C22×#97C2211yescharacteristic, complemented
171C2×H(5,𝔽2)—24no—
172C22×#41—22no—
173C2×AGL(1,ℤ/8)C2318yes—
174C22×SD16C2314yes—
175C22×SD16C2314yes—
176C22×D8C2314yes—
177C22×D8C2314yes—
178C2×#131C2312yes—
179C2×#131C2312yes—
180C23×C8C2312yes—
181#563—22no—
182#563—24no—
183#563—22no—
184#562—24no—
185#562—24no—
186H(3,𝔽4)—22no—
187H(3,𝔽4)—22no—
188#560—22no—
189#560—24no—
190#560—24no—
191#560—22no—
192#559—24no—
193#559—24no—
194#559—24no—
195#559C2314yes—
196#557C2314yes—
197#556—24no—
198#556—24no—
199#556—24no—
200#556C2314yes—
201#555—22no—
202#555—22no—
203#555—24no—
204#555C2318yes—
205#554—24no—
206#554C2314yes—
207#554C2318yes—
208#554C2314yes—
209#553—24no—
210#553—28no—
211#553—24no—
212#553—24no—
213#553—24no—
214#553—24no—
215#553C2318yes—
216#553C2314yes—
217#553C2318yes—
218#553C2314yes—
219#552—24no—
220#552—24no—
221#552—24no—
222#552—24no—
223#552—24no—
224#552—24no—
225#552C2314yes—
226#552C2314yes—
227#551—24no—
228#551—22no—
229#551—24no—
230#551—22no—
231#551—24no—
232#551—24no—
233#551—24no—
234#551—24no—
235#550—24no—
236#550—24no—
237#550—24no—
238#550C2318yes—
239D4×Q8C2314yes—
240#548—24no—
241#548—24no—
242#548C2314yes—
243#548C2314yes—
244#547—24no—
245#547—24no—
246#547—24no—
247#547C2314yes—
248#546—24no—
249#546—28no—
250#546—28no—
251#546—28no—
252#546—24no—
253#546—24no—
254#546—24no—
255#546—24no—
256#546—24no—
257#546—24no—
258#546C2314yes—
259#546C2314yes—
260D42—22no—
261D42—24no—
262D42—24no—
263D42—22no—
264D42—24no—
265D42—24no—
266D42—24no—
267D42C2318yes—
268D42C2318yes—
269D42C2318yes—
270D42C2314yes—
271#544—22no—
272#543—22no—
273#542—24no—
274#542—24no—
275#542—24no—
276#542—24no—
277#542—24no—
278#542C2314yes—
279#542C2314yes—
280#541—24no—
281#541—24no—
282#541C2312yes—
283#541C2312yes—
284#540—24no—
285#540C2314yes—
286#540C2312yes—
287#540C2314yes—
288#540C2314yes—
289#540C2312yes—
290#540C2314yes—
291#539—24no—
292#539—22no—
293#539—24no—
294#539—22no—
295#539—24no—
296#539—24no—
297#538—28no—
298#538—28no—
299#538—24no—
300#538—22no—
301#538—24no—
302#538—24no—
303#538—22no—
304#538—24no—
305#538—24no—
306#538—24no—
307#537—24no—
308#537—28no—
309#537—22no—
310#537C2314yes—
311#536C2312yes—
312#535—28no—
313#535—24no—
314#535—24no—
315#535—24no—
316#535C2314yes—
317#535C2312yes—
318#535C2314yes—
319#534—22no—
320#534—24no—
321#534—24no—
322#533D412yes—
323#533C2312yes—
324#533C2312yes—
325#533C2312yes—
326#533C2311yescharacteristic
327#532—22no—
328#532—22no—
329#532—22no—
330#532—22no—
331#532D412yes—
332#532C2312yes—
333#532C2314yes—
334#532C2314yes—
335#532C2314yes—
336#532C2314yes—
337#532C2314yes—
338#532C2314yes—
339#532C2311yescharacteristic
340C2×C4⋊Q8C2312yes—
341C2×#127C2312yes—
342C2×#127C2312yes—
343C2×#127C2312yes—
344#529—24no—
345#529—24no—
346#529—22no—
347#529—22no—
348#529—22no—
349#529—22no—
350#529D412yes—
351#529D412yes—
352#529D414yes—
353#529C2314yes—
354#529C2314yes—
355#529C2314yes—
356#529C2314yes—
357#529C2314yes—
358#529C2314yes—
359#529C2314yes—
360C2×#126—22no—
361C2×#125C2312yes—
362C2×#125C2312yes—
363C2×#124—22no—
364C2×#124C2312yes—
365C2×#124C2312yes—
366#525—24no—
367#525—28no—
368#525D414yes—
369#525C2311yescharacteristic
370#525C2311yescharacteristic
371C2×#123—22no—
372C2×#123—24no—
373C2×C22⋊Q8C2312yes—
374C2×#121—22no—
375C2×#121—28no—
376C2×#121C2312yes—
377C2×#121C2314yes—
378#520—24no—
379#520—24no—
380#520C2314yes—
381#519C2312yes—
382#518—24no—
383#518C2314yes—
384#518C2312yes—
385#518C2314yes—
386C4×#41C2314yes—
387C4×#41C2311yescharacteristic
388C4×#41C2311yescharacteristic
389C2×C4×Q8C2312yes—
390C2×C4×D4—22no—
391C2×C4×D4—22no—
392C2×C4×D4C2312yes—
393C2×C4×D4C2314yes—
394C2×#117—22no—
395C22×C42C2311yescharacteristic
396#501C2318yes—
397#501C2318yes—
398#501C2314yes—
399#501C2314yes—
400#501C2314yes—
401#501C2314yes—
402#499C2314yes—
403#499C2314yes—
404#496C2318yes—
405#496C2318yes—
406#496C2314yes—
407#496C2314yes—
408#496C2314yes—
409#496C2314yes—
410#493C2314yes—
411#492C2314yes—
412#491C2314yes—
413#490C2314yes—
414#490C2318yes—
415#490C2314yes—
416#490C2314yes—
417#490C2314yes—
418#490C2314yes—
419#490C2314yes—
420#490C2314yes—
421#489C2318yes—
422#489C2314yes—
423#489C2314yes—
424#489C2314yes—
425#489C2314yes—
426#488C2318yes—
427#486C2318yes—
428#485C2318yes—
429#485C2318yes—
430#484C2318yes—
431#482C2318yes—
432#482C2318yes—
433#482C2318yes—
434#482C2318yes—
435#481C2318yes—
436#481C2318yes—
437#481C2318yes—
438#480C2318yes—
439#480C2318yes—
440#479C2318yes—
441#479C2318yes—
442#478C2318yes—
443#478C2318yes—
444#478C2318yes—
445#478C2318yes—
446#478C2318yes—
447#478C2318yes—
448#476C2318yes—
449#475C2318yes—
450#474C2318yes—
451#474C2318yes—
452#469C2318yes—
453#469C2318yes—
454#469C2318yes—
455#469C2318yes—
456#468C2318yes—
457#468C2318yes—
458#468C2318yes—
459#468C2318yes—
460#466C2318yes—
461#466C2318yes—
462#466C2318yes—
463#466C2318yes—
464#466C2318yes—
465#466C2318yes—
466#465C2318yes—
467#465C2318yes—
468#465C2318yes—
469#465C2318yes—
470#465C2318yes—
471#465C2318yes—
472#463C2318yes—
473#463C2318yes—
474#463C2318yes—
475#463C2318yes—
476#461C2318yes—
477#460C2318yes—
478#460C2318yes—
479#460C2318yes—
480#459C2318yes—
481#459C2318yes—
482#459C2318yes—
483#459C2318yes—
484#450C2318yes—
485#450C2318yes—
486#450C2318yes—
487#449C2318yes—
488#449C2318yes—
489#448C2318yes—
490#448C2318yes—
491#447C2318yes—
492#447C2318yes—
493#447C2318yes—
494#447C2318yes—
495#447C2318yes—
496#446C2318yes—
497#446C2318yes—
498#442C2318yes—
499#442C2318yes—
500#442C2318yes—
501#442C2318yes—
502#442C2318yes—
503#442C2318yes—
504#440C2318yes—
505#440C2318yes—
506#440C2318yes—
507#440C2318yes—
508#440C2318yes—
509#440C2318yes—
510C4×SD16C2318yes—
511C4×SD16C2318yes—
512C4×SD16C2318yes—
513C4×SD16C2318yes—
514C4×D8C2318yes—
515C4×D8C2318yes—
516C4×D8C2318yes—
517C4×D8C2318yes—
518#435C2318yes—
519#435C2318yes—
520#435C2318yes—
521#435C2318yes—
522C8×D4C2318yes—
523C8×D4C2318yes—
524#433C2314yes—
525#433C2314yes—
526#432C2314yes—
527#432C2314yes—
528#432C2314yes—
529#431C2314yes—
530#428C2318yes—
531#427C2314yes—
532#427C2314yes—
533C2×#107C2314yes—
534C2×#106C2314yes—
535#424C2312yes—
536#424C2312yes—
537#423C2312yes—
538#419C2314yes—
539#418C2314yes—
540#418C2314yes—
541#418C2314yes—
542#416C2318yes—
543C2×#103C2314yes—
544C2×#102C2314yes—
545C2×#102C2314yes—
546C2×#102C2314yes—
547C2×#102C2318yes—
548#408C2312yes—
549#408C2312yes—
550#407C2312yes—
551#405C2312yes—
552#405C2314yes—
553#405C2312yes—
554#405C2314yes—
555C4×M16C2312yes—
556C4×M16C2312yes—
557C4×M16C2311yescharacteristic
558C4×M16C2311yescharacteristic
559C2×#97C2311yescharacteristic
560C2×#97C2312yes—
561C2×#97C2312yes—
562C2×#97C2311yescharacteristic
563C2×#97C2312yes—
564C2×#97C2314yes—
565C2×#97C2312yes—
566C2×#97C2312yes—
567H(5,𝔽2)—816no—
568C2×#41—28no—
569C2×#41—24no—
570C2×#41—24no—
571C2×#41—24no—
572C2×#41—24no—
573C2×#41—24no—
574C2×#41—24no—
575C2×#41—24no—
576C2×#41—88no—
577C2×#41C2×D414yes—
578C2×#41C2414yes—
579C2×#41C2411yescharacteristic
580C2×#41C2411yescharacteristic
581C22×Q8—22no—
582C22×Q8C2412yes—
583C22×Q8C2412yes—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—28no—
588C22×D4—28no—
589C22×D4—28no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—24no—
593C22×D4—24no—
594C22×D4C2412yes—
595C22×D4C2414yes—
596C22×D4C2412yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C23×C4—22no—
600C23×C4—24no—
601C23×C4C2×D412yes—
602C23×C4C2411yescharacteristic
603AGL(1,ℤ/8)—416no—
604C2×SD16—48no—
605C2×SD16—48no—
606C2×SD16C2418yes—
607C2×SD16C2418yes—
608C2×SD16C2418yes—
609C2×SD16C2418yes—
610C2×D8—48no—
611C2×D8—48no—
612C2×D8C2418yes—
613C2×D8C2418yes—
614C2×D8C2418yes—
615C2×D8C2418yes—
616#131—44no—
617#131—44no—
618C2×M16C2414yes—
619C2×M16C2412yes—
620C2×M16C2412yes—
621C2×M16C2414yes—
622C22×C8—44no—
623C22×C8C2412yes—
624C22×C8C2414yes—
625C22×C8C2414yes—
626C22×C8C2412yes—
627C22×C8C2414yes—
628C22×C8C2414yes—
629C4⋊Q8—22no—
630C4⋊Q8—24no—
631C4⋊Q8—24no—
632C4⋊Q8—22no—
633C4⋊Q8—22no—
634C4⋊Q8C2×D412yes—
635C4⋊Q8C2×D411yescharacteristic
636C4⋊Q8C2412yes—
637C4⋊Q8C2414yes—
638C4⋊Q8C2414yes—
639C4⋊Q8C2414yes—
640#127—24no—
641#127—24no—
642#127—22no—
643#127—22no—
644#127—22no—
645#127—24no—
646#127—24no—
647#127C2×D411yescharacteristic
648#127C2414yes—
649#127C2414yes—
650#127C2414yes—
651#127C2414yes—
652#127C2412yes—
653#126—24no—
654#126—24no—
655#126—28no—
656#126—28no—
657#126—24no—
658#126—24no—
659#126—24no—
660#126—24no—
661#126—24no—
662#126—24no—
663#126—24no—
664#126—24no—
665#126—24no—
666#126—24no—
667#126—24no—
668#126—24no—
669#126—24no—
670#126—24no—
671#126C2×D414yes—
672#126C2×D414yes—
673#125—24no—
674#125—24no—
675#125—24no—
676#125—24no—
677#125—24no—
678#125—24no—
679#125—24no—
680#125—22no—
681#125—22no—
682#125—24no—
683#125C2×D412yes—
684#125C2×D414yes—
685#125C2414yes—
686#125C2414yes—
687#125C2412yes—
688#125C2412yes—
689#125C2414yes—
690#125C2414yes—
691#124—22no—
692#124—24no—
693#124—24no—
694#124—24no—
695#124—22no—
696#124—24no—
697#124—24no—
698#124—28no—
699#124—28no—
700#124—24no—
701#124—24no—
702#124—24no—
703#124—24no—
704#124—24no—
705#124—24no—
706#124—22no—
707#124—22no—
708#124—24no—
709#124—24no—
710#124—24no—
711#124C2×D411yescharacteristic
712#124C2×D411yescharacteristic
713#124C2×D414yes—
714#124C2414yes—
715#124C2414yes—
716#124C2414yes—
717#123—24no—
718#123—22no—
719#123—22no—
720#123—24no—
721#123—24no—
722#123—24no—
723#123—24no—
724#123—24no—
725#123—24no—
726#123—24no—
727#123—24no—
728#123—24no—
729#123—28no—
730#123—28no—
731#123—28no—
732#123—28no—
733#123—24no—
734#123—24no—
735#123—24no—
736#123—24no—
737#123—24no—
738#123—24no—
739#123—24no—
740#123—28no—
741#123—28no—
742#123—24no—
743#123—24no—
744#123—24no—
745#123C2×D414yes—
746#123C2×D414yes—
747#123C2×D412yes—
748#123C2×D412yes—
749C22⋊Q8—28no—
750C22⋊Q8—24no—
751C22⋊Q8—24no—
752C22⋊Q8—24no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—24no—
756C22⋊Q8—24no—
757C22⋊Q8—24no—
758C22⋊Q8—24no—
759C22⋊Q8—24no—
760C22⋊Q8—28no—
761C22⋊Q8—28no—
762C22⋊Q8—24no—
763C22⋊Q8—24no—
764C22⋊Q8—24no—
765C22⋊Q8—24no—
766C22⋊Q8—24no—
767C22⋊Q8—24no—
768C22⋊Q8—24no—
769C22⋊Q8—24no—
770C22⋊Q8—24no—
771C22⋊Q8C2×D414yes—
772C22⋊Q8C2×D414yes—
773C22⋊Q8C2×D412yes—
774C22⋊Q8C2×D412yes—
775C22⋊Q8C2414yes—
776C22⋊Q8C2414yes—
777C22⋊Q8C2414yes—
778C22⋊Q8C2414yes—
779#121—28no—
780#121—28no—
781#121—28no—
782#121—24no—
783#121—24no—
784#121—24no—
785#121—24no—
786#121—24no—
787#121—24no—
788#121—24no—
789#121—24no—
790#121—24no—
791#121—24no—
792#121—24no—
793#121—22no—
794#121—22no—
795#121—24no—
796#121—24no—
797#121—24no—
798#121—24no—
799#121—24no—
800#121—28no—
801#121—28no—
802#121—28no—
803#121—28no—
804#121—28no—
805#121—28no—
806#121—24no—
807#121—28no—
808#121—28no—
809#121—24no—
810#121—24no—
811#121—28no—
812#121—28no—
813#121—24no—
814#121—24no—
815#121C2×D414yes—
816#121C2×D414yes—
817#121C2×D412yes—
818#121C2×D412yes—
819#121C2414yes—
820#121C2414yes—
821#121C2418yes—
822#121C2418yes—
823#121C2414yes—
824#121C2414yes—
825#121C2418yes—
826#121C2418yes—
827#120—24no—
828#120—24no—
829#120—24no—
830#120—22no—
831#120—24no—
832#120—24no—
833#120—22no—
834#120—24no—
835#120—28no—
836#120—28no—
837#120—24no—
838#120—28no—
839#120—28no—
840#120—24no—
841#120—28no—
842#120—28no—
843#120C2×D412yes—
844#120C2×D412yes—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8—22no—
848C4×Q8—22no—
849C4×Q8—24no—
850C4×Q8—24no—
851C4×Q8—24no—
852C4×Q8C2×D414yes—
853C4×Q8C2×D412yes—
854C4×Q8C2×D412yes—
855C4×Q8C2414yes—
856C4×Q8C2414yes—
857C4×Q8C2414yes—
858C4×Q8C2414yes—
859C4×Q8C2414yes—
860C4×D4—24no—
861C4×D4—24no—
862C4×D4—24no—
863C4×D4—24no—
864C4×D4—24no—
865C4×D4—24no—
866C4×D4—24no—
867C4×D4—24no—
868C4×D4—24no—
869C4×D4—28no—
870C4×D4—28no—
871C4×D4—24no—
872C4×D4—24no—
873C4×D4—24no—
874C4×D4—28no—
875C4×D4—28no—
876C4×D4—24no—
877C4×D4—24no—
878C4×D4—24no—
879C4×D4—24no—
880C4×D4—24no—
881C4×D4—24no—
882C4×D4—24no—
883C4×D4—24no—
884C4×D4—22no—
885C4×D4—22no—
886C4×D4—24no—
887C4×D4—24no—
888C4×D4—24no—
889C4×D4—24no—
890C4×D4—24no—
891C4×D4C2×D414yes—
892C4×D4C2×D414yes—
893C4×D4C2×D414yes—
894C4×D4C2×D414yes—
895C4×D4C2×D414yes—
896C4×D4C2×D412yes—
897C4×D4C2×D412yes—
898C4×D4C2418yes—
899C4×D4C2414yes—
900C4×D4C2414yes—
901C4×D4C2418yes—
902C4×D4C2414yes—
903C4×D4C2418yes—
904C4×D4C2418yes—
905C4×D4C2414yes—
906C4×D4C2414yes—
907C4×D4C2414yes—
908C4×D4C2414yes—
909#117—24no—
910#117—28no—
911#117—24no—
912#117—24no—
913#117—24no—
914#117—24no—
915#117—24no—
916#117—24no—
917#117—24no—
918#117—24no—
919#117—24no—
920#117—24no—
921#117C2×D414yes—
922#117C2×D414yes—
923#117C2×D414yes—
924#117C2414yes—
925#117C2414yes—
926#117C2412yes—
927#117C2412yes—
928#117C2412yes—
929#117C2412yes—
930#117C2411yescharacteristic
931#117C2411yescharacteristic
932C2×C4⋊C4—22no—
933C2×C4⋊C4—22no—
934C2×C4⋊C4—22no—
935C2×C4⋊C4—22no—
936C2×C4⋊C4—22no—
937C2×C4⋊C4—24no—
938C2×C4⋊C4—28no—
939C2×C4⋊C4—24no—
940C2×C4⋊C4—24no—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2414yes—
945C2×C22⋊C4—22no—
946C2×C22⋊C4—22no—
947C2×C22⋊C4—22no—
948C2×C22⋊C4—24no—
949C2×C22⋊C4—22no—
950C2×C22⋊C4—24no—
951C2×C22⋊C4—22no—
952C2×C22⋊C4—24no—
953C2×C22⋊C4—24no—
954C2×C22⋊C4—24no—
955C2×C22⋊C4—28no—
956C2×C22⋊C4—28no—
957C2×C22⋊C4—24no—
958C2×C42—22no—
959C2×C42C2×D412yes—
960C2×C42C2×D412yes—
961C2×C42C2×D412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968#107C2418yes—
969#107C2418yes—
970#107C2418yes—
971#107C2418yes—
972#106C2418yes—
973#106C2418yes—
974#106C2418yes—
975#106C2418yes—
976C4⋊C8C2418yes—
977C4⋊C8C2418yes—
978C4⋊C8C2418yes—
979#103C2418yes—
980#103C2418yes—
981#103C2418yes—
982#103C2418yes—
983#102C2418yes—
984#102C2418yes—
985#102C2418yes—
986#102C2418yes—
987#102C2418yes—
988#102C2418yes—
989#102C2418yes—
990#102C2418yes—
991#102C2418yes—
992#102C2418yes—
993#102C2418yes—
994#102C2418yes—
995C22⋊C8C2418yes—
996C22⋊C8C2418yes—
997C22⋊C8C2418yes—
998#97C2411yescharacteristic
999#97C2411yescharacteristic
1000#97C2412yes—
1001#97C2412yes—
1002#97C2412yes—
1003#97C2414yes—
1004#97C2414yes—
1005#97C2412yes—
1006#97C2412yes—
1007#97C2414yes—
1008#97C2414yes—
1009C4×C8C2412yes—
1010C4×C8C2412yes—
1011C4×C8C2414yes—
1012C4×C8C2414yes—
1013C24—22no—
1014C24—24no—
1015C24—22no—
1016C24—24no—
1017C24—24no—
1018C24C22×D411yescharacteristic
1019#41—42no—
1020#41—42no—
1021#41—48no—
1022#41—416no—
1023#41—48no—
1024#41—88no—
1025#41—88no—
1026#41—88no—
1027#41—88no—
1028#41—88no—
1029#41—88no—
1030#41—816no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—22no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—84no—
1039C2×Q8C22×D411yescharacteristic
1040C2×Q8C22×D411yescharacteristic
1041C2×Q8C22×D414yes—
1042C2×Q8C2514yes—
1043C2×D4—24no—
1044C2×D4—28no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—28no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—24no—
1062C2×D4—28no—
1063C2×D4—28no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—48no—
1071C2×D4—48no—
1072C2×D4—84no—
1073C2×D4—88no—
1074C2×D4—88no—
1075C2×D4—816no—
1076C2×D4—88no—
1077C2×D4—816no—
1078C2×D4—816no—
1079C2×D4—84no—
1080C2×D4—88no—
1081C2×D4C22×D414yes—
1082C2×D4C22×D414yes—
1083C2×D4C22×D411yescharacteristic
1084C2×D4C22×D411yescharacteristic
1085C2×D4C22×D412yes—
1086C2×D4C22×D412yes—
1087C2×D4C22×D414yes—
1088C2×D4C2514yes—
1089C2×D4C2518yes—
1090C22×C4—22no—
1091C22×C4—22no—
1092C22×C4—22no—
1093C22×C4—24no—
1094C22×C4—22no—
1095C22×C4—24no—
1096C22×C4—28no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—28no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—28no—
1103C22×C4—28no—
1104C22×C4—24no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—84no—
1108C22×C4—88no—
1109C22×C4C22×D412yes—
1110C22×C4C22×D412yes—
1111C22×C4C22×D412yes—
1112C22×C4C22×D411yescharacteristic
1113C22×C4C22×D412yes—
1114C22×C4C22×D412yes—
1115C22×C4C22×D412yes—
1116C22×C4C22×D412yes—
1117C22×C4C22×D414yes—
1118C22×C4C22×D414yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123SD16—216no—
1124SD16—48no—
1125SD16—48no—
1126SD16—48no—
1127D8—216no—
1128D8—48no—
1129D8—48no—
1130D8—48no—
1131M16—28no—
1132M16—44no—
1133M16—42no—
1134M16—42no—
1135C2×C8—24no—
1136C2×C8—28no—
1137C2×C8—28no—
1138C2×C8—44no—
1139C2×C8—42no—
1140C2×C8—44no—
1141C2×C8C2512yes—
1142C2×C8C2514yes—
1143C2×C8C2514yes—
1144C2×C8C2514yes—
1145C2×C8C2512yes—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—28no—
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4C22×D414yes—
1171C4⋊C4C22×D414yes—
1172C4⋊C4C22×D414yes—
1173C4⋊C4C22×D414yes—
1174C4⋊C4C22×D414yes—
1175C4⋊C4C22×D414yes—
1176C4⋊C4C22×D414yes—
1177C4⋊C4C22×D414yes—
1178C4⋊C4C22×D412yes—
1179C4⋊C4C22×D412yes—
1180C4⋊C4C2514yes—
1181C4⋊C4C2514yes—
1182C4⋊C4C2518yes—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—22no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—22no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4C22×D414yes—
1214C22⋊C4C22×D414yes—
1215C22⋊C4C22×D414yes—
1216C22⋊C4C22×D414yes—
1217C22⋊C4C22×D414yes—
1218C22⋊C4C22×D414yes—
1219C22⋊C4C22×D414yes—
1220C22⋊C4C22×D414yes—
1221C22⋊C4C22×D412yes—
1222C22⋊C4C22×D412yes—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—22no—
1230C42—22no—
1231C42C22×D411yescharacteristic
1232C42C22×D412yes—
1233C42C22×D412yes—
1234C42C22×D412yes—
1235C42C22×D412yes—
1236C42C22×D411yescharacteristic
1237C42C22×D412yes—
1238C42C22×D414yes—
1239C42C22×D414yes—
1240C42C2511yescharacteristic
1241C42C2512yes—
1242C42C2512yes—
1243C42C2511yescharacteristic
1244C42C2512yes—
1245C23—24no—
1246C23—24no—
1247C23—28no—
1248C23—41no—
1249C23—44no—
1250C23—48no—
1251C23—84no—
1252C23—82no—
1253C23—84no—
1254C23—82no—
1255C23—82no—
1256C23—84no—
1257C23—84no—
1258C23—88no—
1259C23—88no—
1260C23—84no—
1261C23C23×D412yes—
1262C23C23×D412yes—
1263C23C23×D411yescharacteristic
1264C23C23×D412yes—
1265Q8—28no—
1266Q8—41no—
1267Q8—41no—
1268Q8—44no—
1269Q8—48no—
1270Q8—82no—
1271Q8—82no—
1272Q8—84no—
1273Q8—84no—
1274D4—28no—
1275D4—28no—
1276D4—28no—
1277D4—28no—
1278D4—28no—
1279D4—44no—
1280D4—41no—
1281D4—41no—
1282D4—42no—
1283D4—42no—
1284D4—48no—
1285D4—48no—
1286D4—48no—
1287D4—416no—
1288D4—48no—
1289D4—82no—
1290D4—84no—
1291D4—84no—
1292D4—82no—
1293D4—84no—
1294D4—84no—
1295D4—88no—
1296D4—88no—
1297D4—84no—
1298D4—84no—
1299D4—84no—
1300D4—88no—
1301D4—88no—
1302D4—88no—
1303D4—84no—
1304D4—84no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—28no—
1314C2×C4—24no—
1315C2×C4—42no—
1316C2×C4—42no—
1317C2×C4—41no—
1318C2×C4—42no—
1319C2×C4—42no—
1320C2×C4—42no—
1321C2×C4—44no—
1322C2×C4—44no—
1323C2×C4—416no—
1324C2×C4—44no—
1325C2×C4—84no—
1326C2×C4—84no—
1327C2×C4—88no—
1328C2×C4—84no—
1329C2×C4—88no—
1330C2×C4—88no—
1331C2×C4—84no—
1332C2×C4—84no—
1333C2×C4—84no—
1334C2×C4—82no—
1335C2×C4—82no—
1336C2×C4—82no—
1337C2×C4—84no—
1338C2×C4C23×D412yes—
1339C2×C4C23×D412yes—
1340C2×C4C23×D412yes—
1341C2×C4C23×D412yes—
1342C2×C4C23×D414yes—
1343C2×C4C23×D414yes—
1344C2×C4C23×D412yes—
1345C2×C4C23×D411yescharacteristic
1346C2×C4C23×D412yes—
1347C2×C4C23×D412yes—
1348C2×C4C2611yescharacteristic
1349C8—22no—
1350C8—24no—
1351C8—24no—
1352C8—24no—
1353C8#58514yes—
1354C22—22no—
1355C22—22no—
1356C22—21no—
1357C22—22no—
1358C22—22no—
1359C22—22no—
1360C22—24no—
1361C22—24no—
1362C22—44no—
1363C22—44no—
1364C22—48no—
1365C22—48no—
1366C22—44no—
1367C22—48no—
1368C22—44no—
1369C22—164no—
1370C22—168no—
1371C22—324no—
1372C22—322no—
1373C22—324no—
1374C22#358514yes—
1375C22C24×D411yescharacteristic
1376C4—21no—
1377C4—22no—
1378C4—22no—
1379C4—22no—
1380C4—22no—
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—24no—
1385C4—24no—
1386C4—44no—
1387C4—48no—
1388C4—44no—
1389C4—44no—
1390C4C2×#58512yes—
1391C2—24no—
1392C2—41no—
1393C2—42no—
1394C2—42no—
1395C2—84no—
1396C2—88no—
1397C2#6281211yescharacteristic
1398C2C2×#358512yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3444 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62834C2semidirect
2. #62829C2semidirect
3. #62584C2semidirect
4. #62576C2semidirect
5. #62506C2semidirect
6. #62447C2semidirect
7. #62387C2semidirect
8. #62336C2semidirect
9. #62280C2semidirect
10. #62270C2semidirect
11. #62268C2semidirect
12. #61521C2semidirect
13. #61519C2semidirect
14. #61019C2semidirect
15. #61017C2semidirect
16. #60949C2semidirect
17. #60725C2semidirect
18. #60719C2semidirect
19. C2×#3180C2semidirect
20. #60207C2semidirect
26. #3557C22semidirect
27. #3551C22semidirect
28. #3549C22semidirect
29. #3548C22semidirect
31. #3538C22semidirect
33. #3537C22semidirect
34. #3537C22semidirect
35. #3536C22semidirect
36. #3519C22semidirect
37. #3516C22semidirect
38. #3515C22semidirect
39. #3514C22semidirect
41. #3513C22semidirect
42. #3512C22semidirect
43. #3511C22semidirect
44. #3510C22semidirect
45. #3508C22semidirect
46. #3508C22semidirect
48. #3498C22semidirect
54. C2×#532C22semidirect
55. C2×#529C22semidirect
56. #3399C22semidirect
57. #3397C22semidirect
58. #3389C22semidirect
59. #3388C22semidirect
60. #3376C22semidirect
61. #3370C22semidirect
62. #3368C22semidirect
63. #3366C22semidirect
64. #3348C22semidirect
65. #3347C22semidirect
66. #3346C22semidirect
67. #3345C22semidirect
68. #3339C22semidirect
69. #3337C22semidirect
70. #3321C22semidirect
71. #3320C22semidirect
72. #3319C22semidirect
73. #3318C22semidirect
74. #3318C22semidirect
75. #3318C22semidirect
76. #3310C22semidirect
77. #3310C22semidirect
78. #3301C22semidirect
79. #3297C22semidirect
80. #3295C22semidirect
81. #3294C22semidirect
82. D4×SD16C22semidirect
83. D4×D8C22semidirect
84. #3265C22semidirect
85. #3265C22semidirect
86. #3264C22semidirect
87. #3264C22semidirect
88. #3260C22semidirect
89. #3259C22semidirect
90. #3257C22semidirect
91. #3251C22semidirect
92. #3240C22semidirect
93. #3240C22semidirect
94. #3239C22semidirect
95. #3235C22semidirect
96. #3234C22semidirect
97. #3234C22semidirect
98. #3217C22semidirect
99. #3217C22semidirect
100. #3217C22semidirect
101. #3214C22semidirect
102. #3213C22semidirect
103. #3213C22semidirect
104. #3200C22semidirect
105. #3199C22semidirect
106. #3198C22semidirect
107. #3193C22semidirect
108. #3192C22semidirect
109. #3180C22semidirect
110. #3180C22semidirect
111. #3180C22semidirect
112. #3180C22semidirect
113. #3180C22semidirect
114. #3180C22semidirect
115. #3180C22semidirect
116. #3180C22semidirect
117. #3179C22semidirect
118. #3179C22semidirect
119. #3176C22semidirect
120. #3176C22semidirect
121. #3174C22semidirect
122. #3174C22semidirect
123. #3171C22semidirect
124. #3171C22semidirect
125. #3171C22semidirect
126. #3171C22semidirect
127. #3166C22semidirect
128. #3162C22semidirect
129. C2×#501C22semidirect
130. #3151C22semidirect
131. C2×#496C22semidirect
132. C2×#496C22semidirect
133. #3140C22semidirect
134. #3138C22semidirect
135. #3135C22semidirect
136. C2×#490C22semidirect
137. C2×#490C22semidirect
138. C2×#489C22semidirect
139. #3126C22semidirect
140. #3123C22semidirect
141. #3122C22semidirect
142. #3122C22semidirect
143. #3119C22semidirect
144. #3118C22semidirect
145. #3105C22semidirect
146. #3103C22semidirect
147. #3100C22semidirect
148. #3062C22semidirect
149. #3058C22semidirect
150. #3057C22semidirect
151. C2×#466C22semidirect
152. C2×#465C22semidirect
153. #2970C22semidirect
154. #2970C22semidirect
155. #2968C22semidirect
156. #2961C22semidirect
157. #2949C22semidirect
158. #2948C22semidirect
159. #2946C22semidirect
160. C2×#442C22semidirect
161. C2×#440C22semidirect
162. #2932C22semidirect
163. #2929C22semidirect
164. #2929C22semidirect
165. #2923C22semidirect
166. #2923C22semidirect
167. #2920C22semidirect
168. #2875C22semidirect
169. #2875C22semidirect
170. C22×#97C22semidirect

Maximal subgroups

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

subgroupindex
#628342
#628292
#625842
#625762
#625062
#624472
#623872
#623362
#622802
#622702
#622682
#615212
#615192
#610192
#610172
#609492
#607252
#607192
C2×#31802
#602072