Finite Group Databasebeta

← #10575380

Subgroups — #10575380

Order 512.

6720 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62857C212yesmaximal, complemented
2#60727C216yesmaximal, complemented
3#60718C213yesmaximal, complemented
4#60713C213yesmaximal, complemented
5#60709C216yesmaximal, complemented
6#60708C213yesmaximal, complemented
7#60707C213yesmaximal, complemented
8#60703C216yesmaximal, complemented
9#60697C216yesmaximal, complemented
10#60696C213yesmaximal, complemented
11#60695C213yesmaximal, complemented
12#60682C213yesmaximal, complemented
13C2×#3175C213yesmaximal, complemented
14#60667C211yesmaximal, characteristic, complemented
15#60649C211yesmaximal, characteristic, complemented
16#60625C212yesmaximal, complemented
17#60460C212yesmaximal, complemented
18#60459C211yesmaximal, characteristic, complemented
19#60458C211yesmaximal, characteristic, complemented
20#60174C212yesmaximal, complemented
21C4×#578C211yesmaximal, characteristic, complemented
22C4×#576C211yesmaximal, characteristic, complemented
23#60058C211yesmaximal, characteristic, complemented
24C2×#578C2211yescharacteristic
25C2×#577C2212yes—
26C2×#576C2211yescharacteristic
27C2×#568C2211yescharacteristic
28C22×#131C2211yescharacteristic
29#3524—22no—
30#3522—22no—
31#3521—26no—
32#3520—26no—
33#3518—22no—
34#3516—22no—
35#3514—26no—
36#3513—26no—
37#3511C2216yescomplemented
38#3510C2216yescomplemented
39#3503C2212yes—
40#3500C2212yes—
41#3495C2216yescomplemented
42#3494C2216yescomplemented
43#3489C2212yes—
44#3488C2212yes—
45#3461C2216yescomplemented
46#3460C2216yescomplemented
47#3455C2216yescomplemented
48C2×#542C2216yescomplemented
49C4×2−1+4C2212yes—
50C4×H(5,𝔽2)C2212yes—
51#3428C2211yescharacteristic
52#3183C22112yescomplemented
53#3182C22112yescomplemented
54#3181C22112yescomplemented
55#3180C22112yescomplemented
56#3179C22112yescomplemented
57#3179C22112yescomplemented
58#3178C22112yescomplemented
59#3178C22112yescomplemented
60#3177C2213yescomplemented
61#3177C2213yescomplemented
62#3176C2213yescomplemented
63#3176C2213yescomplemented
64#3175C2213yescomplemented
65#3175C2216yescomplemented
66#3175C2216yescomplemented
67#3175C2216yescomplemented
68#3175C2216yescomplemented
69#3175C2216yescomplemented
70#3175C2216yescomplemented
71#3175C2216yescomplemented
72#3175C2211yescharacteristic, complemented
73#3175C2213yescomplemented
74#3175C2213yescomplemented
75#3175C22112yescomplemented
76#3174C2216yescomplemented
77#3174C2216yescomplemented
78#3173C2216yescomplemented
79#3173C2216yescomplemented
80#3173C22112yescomplemented
81#3172C22112yescomplemented
82#3171C22112yescomplemented
83#3170C2216yescomplemented
84#3169C2216yescomplemented
85#3168C2216yescomplemented
86#3168C2216yescomplemented
87#3165C2216yescomplemented
88#3164C2213yescomplemented
89#3164C2213yescomplemented
90#3164C2216yescomplemented
91#3160C2213yescomplemented
92C2×#500C2213yescomplemented
93#3156C2213yescomplemented
94#3155C2213yescomplemented
95#3154C2216yescomplemented
96#3153C2216yescomplemented
97#3147C2213yescomplemented
98C2×#495C2213yescomplemented
99#3141C2216yescomplemented
100#3140C2216yescomplemented
101#3137C2216yescomplemented
102#3137C2216yescomplemented
103#3136C2216yescomplemented
104#3136C2216yescomplemented
105#3135C2216yescomplemented
106C2×#489C2216yescomplemented
107#3063C2216yescomplemented
108#3063C2216yescomplemented
109#3062C2216yes—
110#3062C2216yescomplemented
111#3061C2213yes—
112#3061C2213yescomplemented
113#3061C2216yescomplemented
114#3059C2213yescomplemented
115#3058C2213yes—
116#3057C2216yescomplemented
117#3056C2216yescomplemented
118#3056C2216yescomplemented
119#3055C2216yes—
120#3055C2216yescomplemented
121#3054C2216yescomplemented
122C2×#468C2216yescomplemented
123#3050C2213yes—
124#3050C2213yescomplemented
125C2×#467C2213yescomplemented
126C2×#466C2213yes—
127#2951C2213yescomplemented
128#2951C2213yescomplemented
129#2951C2216yescomplemented
130#2950C2213yescomplemented
131#2949C2216yescomplemented
132#2948C2213yescomplemented
133#2947C2216yescomplemented
134#2947C2216yescomplemented
135#2946C2216yescomplemented
136#2946C2216yescomplemented
137C4×#137C2216yescomplemented
138C4×#137C2216yescomplemented
139C4×AGL(1,ℤ/8)C2216yescomplemented
140C4×AGL(1,ℤ/8)C2216yescomplemented
141#2943C2216yescomplemented
142C2×#440C2216yescomplemented
143C4×#135C2213yescomplemented
144C4×#135C2213yescomplemented
145C2×C4×Q16C2213yescomplemented
146C2×C4×D8C2213yescomplemented
147#2913C2211yescharacteristic
148#2913C2211yescharacteristic
149#2913C2212yes—
150#2898C2212yes—
151#2898C2212yes—
152#2897C2212yes—
153#2897C2212yes—
154#2875C2211yescharacteristic
155#2875C2211yescharacteristic
156#2875C2213yescomplemented
157#2875C2213yescomplemented
158C4×#131C2211yescharacteristic
159C4×#131C2211yescharacteristic
160C4×#131C2213yescomplemented
161C4×#131C2213yescomplemented
162#2873C2213yescomplemented
163#2873C2213yescomplemented
164C2×#405C2213yescomplemented
165C2×#405C2213yescomplemented
166C2×2−1+4C2312yes—
167C2×H(5,𝔽2)C2312yes—
168C22×#41C2311yescharacteristic
169#578—28no—
170#577—216no—
171#576—28no—
172C2×#137C2316yes—
173C2×#137C2316yes—
174C2×AGL(1,ℤ/8)C2316yes—
175C2×AGL(1,ℤ/8)C2316yes—
176C2×#135C2316yes—
177C2×#135C2313yes—
178C2×#135C2313yes—
179C22×Q16C2313yes—
180C22×SD16C2316yes—
181C22×D8C2313yes—
182#568—28no—
183C2×#131—28no—
184C2×#131C2311yescharacteristic
185C2×#131C2313yes—
186C2×#131C2313yes—
187C2×#131C2313yes—
188C2×#131C2311yescharacteristic
189C2×#131C2313yes—
190C2×#131C2311yescharacteristic
191C2×#131C2311yescharacteristic
192C22×M16C2313yes—
193C22×M16C2313yes—
194C22×M16C2313yes—
195C23×C8C2313yes—
196#559—26no—
197#559—26no—
198Q82—22no—
199#557—22no—
200#556—26no—
201#556—26no—
202#556—26no—
203#556—26no—
204#555—26no—
205#555—26no—
206#554—26no—
207#554—26no—
208#554—26no—
209#553—212no—
210#553—26no—
211#553—26no—
212#552—26no—
213#552—212no—
214#552—26no—
215#551—212no—
216#551—212no—
217#551—212no—
218#551—212no—
219#550—22no—
220D4×Q8—22no—
221D4×Q8—26no—
222#548—22no—
223#548—22no—
224#548—22no—
225#548—22no—
226#548—212no—
227#547—26no—
228#547—26no—
229#547—26no—
230#546—26no—
231#546—26no—
232#546—26no—
233#546—26no—
234#546—212no—
235D42—26no—
236#544C2316yes—
237#544C2316yes—
238#542—26no—
239#542—26no—
240#542—26no—
241#542—26no—
242#542—26no—
243#542—26no—
244#542C2312yes—
245#542C2316yes—
246#542C2316yes—
247#542C23112yes—
248#542C2316yes—
249#542C23112yes—
250#542C23112yes—
251#541—26no—
252#541C2316yes—
253#541C2316yes—
254#540—26no—
255#540C2316yes—
256#540C2316yes—
257#539—212no—
258#539—26no—
259#539—26no—
260#538—212no—
261#538—26no—
262#538—26no—
263#537C2316yes—
264#537C2316yes—
265#536C2316yes—
266#536C2316yes—
267#535C2316yes—
268#535C2316yes—
269#533—26no—
270#533C23112yes—
271#533C2316yes—
272#532—26no—
273#532C2316yes—
274#532C23112yes—
275C2×C4⋊Q8C2316yes—
276#529—26no—
277#529—26no—
278#529—212no—
279#529—26no—
280#529—26no—
281#529—26no—
282#529—26no—
283#529C23112yes—
284#529C23112yes—
285C2×#126—26no—
286C2×#124—26no—
287C2×#124C2316yes—
288#525—212no—
289#525C2316yes—
290#525C2316yes—
291C2×#123—26no—
292C2×C22⋊Q8—26no—
293C2×C22⋊Q8C2316yes—
294C2×#121C2316yes—
295#520—22no—
296#520—26no—
297#520D413yes—
298#520D413yes—
299#520D411yescharacteristic
300#520D411yescharacteristic
301#520C2316yes—
302#520C2316yes—
303#520C2312yes—
304#520C2312yes—
305#519—22no—
306#519D411yescharacteristic
307#519D411yescharacteristic
308#519C2316yes—
309#518—26no—
310#518D413yes—
311#518D413yes—
312#518C2316yes—
313C4×#41—22no—
314C4×#41—26no—
315C4×#41C2316yes—
316C4×#41C2316yes—
317C4×#41C2311yescharacteristic
318C4×#41C2311yescharacteristic
319C4×#41C2313yes—
320C4×#41C2313yes—
321C2×C4×Q8—22no—
322C2×C4×Q8C2316yes—
323C2×C4×D4—26no—
324C2×C4×D4C2316yes—
325C2×#117C2313yes—
326C2×#117C2313yes—
327#501C23112yes—
328#501C23112yes—
329#500C2313yes—
330#500C2316yes—
331#500C2316yes—
332#500C2316yes—
333#500C2311yescharacteristic
334#499C2313yes—
335#499C2313yes—
336#499C2316yes—
337#498C2316yes—
338#497C23112yes—
339#496C23112yes—
340#495C2313yes—
341#495C2316yes—
342#495C2316yes—
343#495C2316yes—
344#495C2311yescharacteristic
345#495C2316yes—
346#494C2313yes—
347#493C2313yes—
348#492C2316yes—
349#491C2316yes—
350#491C2316yes—
351#490C2316yes—
352#490C2316yes—
353#489C2316yes—
354#489C23112yes—
355#489C23112yes—
356#489C23112yes—
357#489C2312yes—
358#489C2316yes—
359#489C2316yes—
360#488C23112yes—
361#488C23112yes—
362#487C23112yes—
363#486C23112yes—
364#470C2316yes—
365#470C23112yes—
366#470C2316yes—
367#469C2316yes—
368#469C23112yes—
369#469C2316yes—
370#468C23112yes—
371#468C23112yes—
372#468C23112yes—
373#468C2312yes—
374#468C2316yes—
375#468C2316yes—
376#468C2316yes—
377#468C23112yes—
378#468C23112yes—
379#467C2313yes—
380#467C2316yes—
381#467C2313yes—
382#467C23112yes—
383#467C2313yes—
384#467C2316yes—
385#467C2316yes—
386#467C2311yescharacteristic
387#466C2313yes—
388#466C2316yes—
389#466C2313yes—
390#466C23112yes—
391#466C2313yes—
392#466C2316yes—
393#466C2316yes—
394#466C2311yescharacteristic
395#465C23112yes—
396#465C23112yes—
397#465C2316yes—
398#465C2316yes—
399#465C2316yes—
400#465C2316yes—
401#442C2316yes—
402#442C2316yes—
403#442C23112yes—
404#441C2316yes—
405#441C2316yes—
406#441C23112yes—
407#440C2312yes—
408#440C2316yes—
409#440C2316yes—
410#440C2316yes—
411#440C23112yes—
412#440C23112yes—
413#440C23112yes—
414#440C23112yes—
415#440C23112yes—
416C4×Q16C2313yes—
417C4×Q16C2316yes—
418C4×Q16C2313yes—
419C4×Q16C23112yes—
420C4×Q16C2316yes—
421C4×Q16C2313yes—
422C4×Q16C2316yes—
423C4×Q16C2311yescharacteristic
424C4×SD16C23112yes—
425C4×SD16C23112yes—
426C4×SD16C2316yes—
427C4×SD16C2316yes—
428C4×SD16C2316yes—
429C4×SD16C2316yes—
430C4×D8C2313yes—
431C4×D8C2316yes—
432C4×D8C2313yes—
433C4×D8C23112yes—
434C4×D8C2316yes—
435C4×D8C2313yes—
436C4×D8C2316yes—
437C4×D8C2311yescharacteristic
438#428C2316yes—
439#428C2316yes—
440#428C2316yes—
441#428C2316yes—
442#427C2313yes—
443#427C2313yes—
444#427C2316yes—
445C2×#107C2313yes—
446C2×#107C2313yes—
447C2×#107C2316yes—
448#419C2316yes—
449#419C2316yes—
450#418C2316yes—
451#418C2316yes—
452#417C2316yes—
453#417C2316yes—
454#417C2316yes—
455#417C2316yes—
456#416C2316yes—
457#416C2316yes—
458#416C2316yes—
459#416C2316yes—
460C2×#103C2316yes—
461C2×#103C2316yes—
462C2×#102C2316yes—
463C2×#102C2316yes—
464#405C2311yescharacteristic
465#405C2313yes—
466#405C2313yes—
467#405C2313yes—
468#405C2316yes—
469#405C2313yes—
470#405C2313yes—
471#405C2313yes—
472#405C2313yes—
473#405C2313yes—
474#405C2313yes—
475#405C2313yes—
476#405C2313yes—
477#405C2313yes—
478#405C2313yes—
479#405C2313yes—
480#405C2313yes—
481#405C2316yes—
482#405C2316yes—
483C4×M16C2313yes—
484C4×M16C2313yes—
485C4×M16C2313yes—
486C4×M16C2313yes—
487C4×M16C2316yes—
488C4×M16C2316yes—
489C2×#97C2313yes—
490C2×#97C2313yes—
491C2×#97C2316yes—
492C2×C4×C8C2313yes—
493C2×C4×C8C2313yes—
494C2×C4×C8C2316yes—
4952−1+4—28no—
4962−1+4—28no—
497H(5,𝔽2)—28no—
498H(5,𝔽2)—28no—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—22no—
502C2×#41—26no—
503C2×#41—212no—
504C2×#41C2×D413yes—
505C2×#41C2×D411yescharacteristic
506C2×#41C2416yes—
507C2×#41C2416yes—
508C2×#41C2413yes—
509C2×#41C2411yescharacteristic
510C22×Q8—22no—
511C22×Q8—26no—
512C22×Q8C2×D411yescharacteristic
513C22×Q8C2416yes—
514C22×D4—26no—
515C22×D4—26no—
516C22×D4C2×D413yes—
517C22×D4C2416yes—
518C23×C4—26no—
519C23×C4C2413yes—
520#137—224no—
521#137—224no—
522AGL(1,ℤ/8)—224no—
523AGL(1,ℤ/8)—224no—
524#135—212no—
525#135—224no—
526#135—212no—
527C2×Q16—212no—
528C2×Q16C2413yes—
529C2×Q16C2416yes—
530C2×Q16C2411yescharacteristic
531C2×Q16C2416yes—
532C2×SD16—224no—
533C2×SD16C2416yes—
534C2×SD16C24112yes—
535C2×SD16C2412yes—
536C2×SD16C2416yes—
537C2×SD16C2416yes—
538C2×D8—212no—
539C2×D8C2413yes—
540C2×D8C2416yes—
541C2×D8C2411yescharacteristic
542C2×D8C2416yes—
543#131—24no—
544#131—24no—
545#131—212no—
546#131—212no—
547#131—212no—
548#131—212no—
549#131#4118yescomplemented
550#131#4118yescomplemented
551C2×M16—212no—
552C2×M16—212no—
553C2×M16—212no—
554C2×M16C2411yescharacteristic
555C2×M16C2413yes—
556C2×M16C2413yes—
557C2×M16C2413yes—
558C2×M16C2413yes—
559C2×M16C2413yes—
560C2×M16C2416yes—
561C2×M16C2413yes—
562C2×M16C2413yes—
563C22×C8—212no—
564C22×C8C2411yescharacteristic
565C22×C8C2413yes—
566C22×C8C2413yes—
567C22×C8C2413yes—
568C22×C8C2413yes—
569C22×C8C2413yes—
570C22×C8C2416yes—
571C22×C8C2413yes—
572C22×C8C2413yes—
573C4⋊Q8—26no—
574C4⋊Q8—26no—
575C4⋊Q8—26no—
576C4⋊Q8—26no—
577C4⋊Q8—26no—
578C4⋊Q8C2416yes—
579C4⋊Q8C2416yes—
580C4⋊Q8C24112yes—
581C4⋊Q8C2412yes—
582#127—26no—
583#127C2416yes—
584#126—26no—
585#126—212no—
586#126—212no—
587#126—212no—
588#126—22no—
589#126—26no—
590#126—26no—
591#126—26no—
592#126—26no—
593#126—26no—
594#126—26no—
595#126—212no—
596#126—212no—
597#125—26no—
598#125—26no—
599#125—26no—
600#125—26no—
601#125—26no—
602#125—26no—
603#125—212no—
604#125C2416yes—
605#125C2416yes—
606#124—26no—
607#124—26no—
608#124—26no—
609#124—212no—
610#124—212no—
611#124—212no—
612#124—22no—
613#124—26no—
614#124—26no—
615#124—26no—
616#124—26no—
617#124—212no—
618#124C2416yes—
619#124C24112yes—
620#124C2412yes—
621#123—212no—
622#123—26no—
623#123—26no—
624#123—212no—
625#123—212no—
626#123—26no—
627#123—26no—
628#123—26no—
629#123—26no—
630#123—26no—
631#123—212no—
632#123—212no—
633#123—212no—
634#123—22no—
635#123—212no—
636#123—26no—
637#123—26no—
638C22⋊Q8—26no—
639C22⋊Q8—26no—
640C22⋊Q8—26no—
641C22⋊Q8—26no—
642C22⋊Q8—26no—
643C22⋊Q8—26no—
644C22⋊Q8—212no—
645C22⋊Q8—26no—
646C22⋊Q8—212no—
647C22⋊Q8—212no—
648C22⋊Q8—212no—
649C22⋊Q8—22no—
650C22⋊Q8—26no—
651C22⋊Q8—26no—
652C22⋊Q8—26no—
653C22⋊Q8—26no—
654C22⋊Q8—212no—
655C22⋊Q8—212no—
656C22⋊Q8C2416yes—
657C22⋊Q8C24112yes—
658C22⋊Q8C2412yes—
659C22⋊Q8C2416yes—
660C22⋊Q8C2416yes—
661#121—212no—
662#121—212no—
663#121—26no—
664#121—26no—
665#121—26no—
666#121—26no—
667#121—26no—
668#121—26no—
669#121—212no—
670#121—26no—
671#121—26no—
672#121—26no—
673#121—26no—
674#121—26no—
675#121—26no—
676#121C2416yes—
677#121C24112yes—
678#121C2412yes—
679#121C2416yes—
680#121C2416yes—
681#120—26no—
682#120—26no—
683#120—212no—
684#120—212no—
685C4×Q8—22no—
686C4×Q8—22no—
687C4×Q8—26no—
688C4×Q8—26no—
689C4×Q8—26no—
690C4×Q8—26no—
691C4×Q8—26no—
692C4×Q8—26no—
693C4×Q8—212no—
694C4×Q8C2×D411yescharacteristic
695C4×Q8C2×D411yescharacteristic
696C4×Q8C2×D413yes—
697C4×Q8C2×D413yes—
698C4×Q8C2×D411yescharacteristic
699C4×Q8C2×D411yescharacteristic
700C4×Q8C2×D413yes—
701C4×Q8C2×D413yes—
702C4×Q8C2416yes—
703C4×Q8C24112yes—
704C4×Q8C2412yes—
705C4×Q8C2416yes—
706C4×Q8C2416yes—
707C4×D4—26no—
708C4×D4—26no—
709C4×D4—26no—
710C4×D4—26no—
711C4×D4—26no—
712C4×D4—26no—
713C4×D4—212no—
714C4×D4—26no—
715C4×D4—26no—
716C4×D4—26no—
717C4×D4—26no—
718C4×D4—212no—
719C4×D4—26no—
720C4×D4—26no—
721C4×D4—212no—
722C4×D4—212no—
723C4×D4—26no—
724C4×D4—26no—
725C4×D4—212no—
726C4×D4—26no—
727C4×D4—26no—
728C4×D4C2×D413yes—
729C4×D4C2×D413yes—
730C4×D4C2×D416yes—
731C4×D4C2×D416yes—
732C4×D4C2×D413yes—
733C4×D4C2×D413yes—
734C4×D4C2×D413yes—
735C4×D4C2×D413yes—
736C4×D4C2×D413yes—
737C4×D4C2×D416yes—
738C4×D4C2×D416yes—
739C4×D4C2×D413yes—
740C4×D4C2416yes—
741C4×D4C24112yes—
742C4×D4C2412yes—
743C4×D4C2416yes—
744C4×D4C2416yes—
745#117—212no—
746#117—26no—
747#117—26no—
748#117—212no—
749#117—26no—
750#117—26no—
751#117—212no—
752#117—212no—
753#117C2×D413yes—
754#117C2×D413yes—
755#117C2×D413yes—
756#117C2×D413yes—
757#117C2×D413yes—
758#117C2×D413yes—
759#117C2×D416yes—
760#117C2416yes—
761#117C2416yes—
762#117C2413yes—
763#117C2411yescharacteristic
764#117C2413yes—
765#117C2413yes—
766#117C2413yes—
767#117C2413yes—
768C2×C4⋊C4—26no—
769C2×C4⋊C4—26no—
770C2×C4⋊C4—26no—
771C2×C4⋊C4—26no—
772C2×C4⋊C4—26no—
773C2×C4⋊C4C2×D413yes—
774C2×C4⋊C4C2×D413yes—
775C2×C4⋊C4C2×D413yes—
776C2×C4⋊C4C2×D413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2416yes—
779C2×C22⋊C4—26no—
780C2×C22⋊C4—26no—
781C2×C22⋊C4—26no—
782C2×C22⋊C4—26no—
783C2×C22⋊C4—26no—
784C2×C22⋊C4—212no—
785C2×C22⋊C4C2×D413yes—
786C2×C22⋊C4C2×D413yes—
787C2×C22⋊C4C2×D416yes—
788C2×C42—26no—
789C2×C42—26no—
790C2×C42—26no—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2416yes—
794#107C2413yes—
795#107C2413yes—
796#107C2416yes—
797#107C2416yes—
798#107C24112yes—
799#107C2416yes—
800#107C2411yescharacteristic
801#107C2411yescharacteristic
802#107C2412yes—
803#106C2416yes—
804#106C2416yes—
805#106C2416yes—
806#106C2416yes—
807#103C2416yes—
808#103C2416yes—
809#103C24112yes—
810#103C24112yes—
811#103C2412yes—
812#103C2412yes—
813#103C2416yes—
814#103C2416yes—
815#103C2416yes—
816#103C2416yes—
817#102C2416yes—
818#102C2416yes—
819#102C24112yes—
820#102C24112yes—
821#102C2412yes—
822#102C2412yes—
823#102C2416yes—
824#102C2416yes—
825#102C2416yes—
826#102C2416yes—
827#97C2411yescharacteristic
828#97C2413yes—
829#97C2411yescharacteristic
830#97C2413yes—
831#97C2413yes—
832#97C2413yes—
833#97C2416yes—
834#97C2413yes—
835#97C2413yes—
836#97C2416yes—
837C4×C8C2411yescharacteristic
838C4×C8C2413yes—
839C4×C8C2413yes—
840C4×C8C2411yescharacteristic
841C4×C8C2413yes—
842C4×C8C2413yes—
843C4×C8C2416yes—
844C4×C8C2416yes—
845C4×C8C2413yes—
846C4×C8C2413yes—
847C24—26no—
848C24C22×D413yes—
849#41—24no—
850#41—212no—
851#41—26no—
852#41—26no—
853#41—212no—
854#41—212no—
855#41—212no—
856#41—212no—
857#41—48no—
858#41—424no—
859#41—1612no—
860#41C2×#4114yes—
861#41C2×#4114yes—
862C2×Q8—24no—
863C2×Q8—26no—
864C2×Q8—22no—
865C2×Q8—26no—
866C2×Q8—212no—
867C2×Q8—212no—
868C2×Q8—212no—
869C2×Q8—48no—
870C2×Q8—166no—
871C2×Q8C22×D413yes—
872C2×Q8C22×D411yescharacteristic
873C2×Q8C2516yes—
874C2×Q8C2512yes—
875C2×D4—212no—
876C2×D4—26no—
877C2×D4—26no—
878C2×D4—22no—
879C2×D4—26no—
880C2×D4—26no—
881C2×D4—26no—
882C2×D4—212no—
883C2×D4—26no—
884C2×D4—26no—
885C2×D4—26no—
886C2×D4—212no—
887C2×D4—212no—
888C2×D4—424no—
889C2×D4—166no—
890C2×D4C22×D416yes—
891C2×D4C22×D413yes—
892C2×D4C22×D413yes—
893C2×D4C2516yes—
894C2×D4C2512yes—
895C22×C4—26no—
896C22×C4—26no—
897C22×C4—26no—
898C22×C4—26no—
899C22×C4—26no—
900C22×C4—26no—
901C22×C4—26no—
902C22×C4—22no—
903C22×C4—26no—
904C22×C4—26no—
905C22×C4—26no—
906C22×C4—212no—
907C22×C4—166no—
908C22×C4C22×D413yes—
909C22×C4C22×D413yes—
910C22×C4C22×D413yes—
911C22×C4C22×D413yes—
912C22×C4C22×D413yes—
913C22×C4C22×D413yes—
914C22×C4C22×D413yes—
915C22×C4C22×D416yes—
916C22×C4C22×D416yes—
917C22×C4C2513yes—
918C22×C4C2511yescharacteristic
919C22×C4C2513yes—
920Q16—26no—
921Q16—212no—
922Q16—22no—
923Q16—212no—
924SD16—212no—
925SD16—224no—
926SD16—24no—
927SD16—212no—
928SD16—212no—
929D8—26no—
930D8—212no—
931D8—22no—
932D8—212no—
933M16—26no—
934M16—26no—
935M16—26no—
936M16—22no—
937M16—212no—
938M16—26no—
939M16—26no—
940M16C2×#41112yes—
941M16C2×#41112yes—
942C2×C8—26no—
943C2×C8—26no—
944C2×C8—22no—
945C2×C8—26no—
946C2×C8—26no—
947C2×C8—26no—
948C2×C8—212no—
949C2×C8C2×#41112yes—
950C2×C8C2×#41112yes—
951C2×C8C2511yescharacteristic
952C2×C8C2513yes—
953C2×C8C2513yes—
954C2×C8C2511yescharacteristic
955C2×C8C2511yescharacteristic
956C2×C8C2513yes—
957C2×C8C2513yes—
958C2×C8C2511yescharacteristic
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—212no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—212no—
967C4⋊C4—212no—
968C4⋊C4—22no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—22no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—22no—
980C4⋊C4C22×D413yes—
981C4⋊C4C22×D411yescharacteristic
982C4⋊C4C22×D413yes—
983C4⋊C4C22×D411yescharacteristic
984C4⋊C4C22×D413yes—
985C4⋊C4C22×D413yes—
986C4⋊C4C22×D413yes—
987C4⋊C4C22×D413yes—
988C4⋊C4C22×D413yes—
989C4⋊C4C22×D413yes—
990C4⋊C4C22×D413yes—
991C4⋊C4C22×D413yes—
992C4⋊C4C2512yes—
993C4⋊C4C2512yes—
994C4⋊C4C2516yes—
995C4⋊C4C2516yes—
996C22⋊C4—26no—
997C22⋊C4—26no—
998C22⋊C4—212no—
999C22⋊C4—26no—
1000C22⋊C4—26no—
1001C22⋊C4—22no—
1002C22⋊C4—26no—
1003C22⋊C4—26no—
1004C22⋊C4—26no—
1005C22⋊C4—212no—
1006C22⋊C4—26no—
1007C22⋊C4—26no—
1008C22⋊C4—26no—
1009C22⋊C4—212no—
1010C22⋊C4—212no—
1011C22⋊C4—212no—
1012C22⋊C4—22no—
1013C22⋊C4—26no—
1014C22⋊C4—26no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—26no—
1018C22⋊C4—22no—
1019C22⋊C4C22×D416yes—
1020C22⋊C4C22×D413yes—
1021C22⋊C4C22×D413yes—
1022C22⋊C4C22×D411yescharacteristic
1023C22⋊C4C22×D411yescharacteristic
1024C22⋊C4C22×D416yes—
1025C22⋊C4C22×D413yes—
1026C22⋊C4C22×D413yes—
1027C22⋊C4C22×D413yes—
1028C22⋊C4C22×D413yes—
1029C42—22no—
1030C42—26no—
1031C42—26no—
1032C42—26no—
1033C42—212no—
1034C42—26no—
1035C42—26no—
1036C42C22×D413yes—
1037C42C22×D413yes—
1038C42C22×D416yes—
1039C42C22×D416yes—
1040C42C22×D413yes—
1041C42C22×D413yes—
1042C42C2511yescharacteristic
1043C42C2513yes—
1044C42C2511yescharacteristic
1045C42C2513yes—
1046C23—26no—
1047C23—26no—
1048C23—22no—
1049C23—43no—
1050C23—43no—
1051C23—412no—
1052C23—86no—
1053C23—86no—
1054C23C23×D411yescharacteristic
1055C23C23×D413yes—
1056C23C23×D413yes—
1057Q8—26no—
1058Q8—26no—
1059Q8—22no—
1060Q8—26no—
1061Q8—22no—
1062Q8—412no—
1063Q8—82no—
1064Q8—86no—
1065Q8—812no—
1066Q8#53214yes—
1067D4—212no—
1068D4—26no—
1069D4—22no—
1070D4—26no—
1071D4—22no—
1072D4—26no—
1073D4—412no—
1074D4—412no—
1075D4—412no—
1076D4—86no—
1077D4—86no—
1078D4—82no—
1079D4—86no—
1080D4—86no—
1081D4—812no—
1082D4—86no—
1083D4#532112yes—
1084C2×C4—26no—
1085C2×C4—21no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—21no—
1089C2×C4—26no—
1090C2×C4—26no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—26no—
1094C2×C4—22no—
1095C2×C4—26no—
1096C2×C4—26no—
1097C2×C4—43no—
1098C2×C4—43no—
1099C2×C4—46no—
1100C2×C4—43no—
1101C2×C4—43no—
1102C2×C4—46no—
1103C2×C4—412no—
1104C2×C4—412no—
1105C2×C4—412no—
1106C2×C4—86no—
1107C2×C4—82no—
1108C2×C4—86no—
1109C2×C4—812no—
1110C2×C4—86no—
1111C2×C4—86no—
1112C2×C4—86no—
1113C2×C4C23×D411yescharacteristic
1114C2×C4C23×D413yes—
1115C2×C4C23×D411yescharacteristic
1116C2×C4C23×D413yes—
1117C2×C4C23×D413yes—
1118C2×C4C23×D411yescharacteristic
1119C2×C4C23×D411yescharacteristic
1120C2×C4C23×D413yes—
1121C2×C4C23×D413yes—
1122C2×C4C23×D411yescharacteristic
1123C2×C4C23×D413yes—
1124C2×C4C22×#4116yes—
1125C2×C4C22×#4116yes—
1126C2×C4C2611yescharacteristic
1127C8—21no—
1128C8—23no—
1129C8—21no—
1130C8—23no—
1131C8C22×#4112yes—
1132C8C22×#4116yes—
1133C8C22×#4116yes—
1134C8C22×#4112yes—
1135C22—23no—
1136C22—23no—
1137C22—23no—
1138C22—21no—
1139C22—23no—
1140C22—21no—
1141C22—21no—
1142C22—23no—
1143C22—42no—
1144C22—46no—
1145C22—42no—
1146C22—46no—
1147C22—42no—
1148C22—46no—
1149C22—86no—
1150C22—1612no—
1151C22C2×#53216yes—
1152C22C24×D411yescharacteristic
1153C4—21no—
1154C4—23no—
1155C4—23no—
1156C4—21no—
1157C4—21no—
1158C4—23no—
1159C4—23no—
1160C4—21no—
1161C4—21no—
1162C4—23no—
1163C4—46no—
1164C4—46no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—46no—
1169C4C2×#53216yes—
1170C4C23×#4111yescharacteristic
1171C4C23×#4111yescharacteristic
1172C2—26no—
1173C2—43no—
1174C2—41no—
1175C2—82no—
1176C2—86no—
1177C2C22×#53211yescharacteristic
1178C2#6309111yescharacteristic
1179C2#6309311yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3428 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62857C2semidirect
2. #60727C2semidirect
3. #60718C2semidirect
4. #60713C2semidirect
5. #60709C2semidirect
6. #60708C2semidirect
7. #60707C2semidirect
8. #60703C2semidirect
9. #60697C2semidirect
10. #60696C2semidirect
11. #60695C2semidirect
12. #60682C2semidirect
13. C2×#3175C2semidirect
14. #60667C2semidirect
15. #60649C2semidirect
16. #60625C2semidirect
17. #60460C2semidirect
18. #60459C2semidirect
19. #60458C2semidirect
20. #60174C2semidirect
21. C4×#578C2semidirect
22. C4×#576C2semidirect
23. #60058C2semidirect
37. #3511C22semidirect
38. #3510C22semidirect
41. #3495C22semidirect
42. #3494C22semidirect
45. #3461C22semidirect
46. #3460C22semidirect
47. #3455C22semidirect
48. C2×#542C22semidirect
52. #3183C22semidirect
53. #3182C22semidirect
54. #3181C22semidirect
55. #3180C22semidirect
56. #3179C22semidirect
57. #3179C22semidirect
58. #3178C22semidirect
59. #3178C22semidirect
60. #3177C22semidirect
61. #3177C22semidirect
62. #3176C22semidirect
63. #3176C22semidirect
64. #3175C22semidirect
65. #3175C22semidirect
66. #3175C22semidirect
67. #3175C22semidirect
68. #3175C22semidirect
69. #3175C22semidirect
70. #3175C22semidirect
71. #3175C22semidirect
72. #3175C22semidirect
73. #3175C22semidirect
74. #3175C22semidirect
75. #3175C22semidirect
76. #3174C22semidirect
77. #3174C22semidirect
78. #3173C22semidirect
79. #3173C22semidirect
80. #3173C22semidirect
81. #3172C22semidirect
82. #3171C22semidirect
83. #3170C22semidirect
84. #3169C22semidirect
85. #3168C22semidirect
86. #3168C22semidirect
87. #3165C22semidirect
88. #3164C22semidirect
89. #3164C22semidirect
90. #3164C22semidirect
91. #3160C22semidirect
92. C2×#500C22semidirect
93. #3156C22semidirect
94. #3155C22semidirect
95. #3154C22semidirect
96. #3153C22semidirect
97. #3147C22semidirect
98. C2×#495C22semidirect
99. #3141C22semidirect
100. #3140C22semidirect
101. #3137C22semidirect
102. #3137C22semidirect
103. #3136C22semidirect
104. #3136C22semidirect
105. #3135C22semidirect
106. C2×#489C22semidirect
107. #3063C22semidirect
108. #3063C22semidirect
110. #3062C22semidirect
112. #3061C22semidirect
113. #3061C22semidirect
114. #3059C22semidirect
116. #3057C22semidirect
117. #3056C22semidirect
118. #3056C22semidirect
120. #3055C22semidirect
121. #3054C22semidirect
122. C2×#468C22semidirect
124. #3050C22semidirect
125. C2×#467C22semidirect
127. #2951C22semidirect
128. #2951C22semidirect
129. #2951C22semidirect
130. #2950C22semidirect
131. #2949C22semidirect
132. #2948C22semidirect
133. #2947C22semidirect
134. #2947C22semidirect
135. #2946C22semidirect
136. #2946C22semidirect
137. C4×#137C22semidirect
138. C4×#137C22semidirect
139. C4×AGL(1,ℤ/8)C22semidirect
140. C4×AGL(1,ℤ/8)C22semidirect
141. #2943C22semidirect
142. C2×#440C22semidirect
143. C4×#135C22semidirect
144. C4×#135C22semidirect
145. C2×C4×Q16C22semidirect
146. C2×C4×D8C22semidirect
156. #2875C22semidirect
157. #2875C22semidirect
160. C4×#131C22semidirect
161. C4×#131C22semidirect
162. #2873C22semidirect
163. #2873C22semidirect
164. C2×#405C22semidirect
165. C2×#405C22semidirect
549. #131#41semidirect
550. #131#41semidirect

Maximal subgroups

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

subgroupindex
#628572
#607272
#607182
#607132
#607092
#607082
#607072
#607032
#606972
#606962
#606952
#606822
C2×#31752
#606672
#606492
#606252
#604602
#604592
#604582
#601742
C4×#5782
C4×#5762
#600582