Finite Group Databasebeta

← #10577764

Subgroups — #10577764

Order 512.

6830 conjugacy classes of subgroups.

The subgroup lattice has 1007 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62834C212yesmaximal, complemented
2#62342C214yesmaximal, complemented
3#62334C218yesmaximal, complemented
4#62331C212yesmaximal, complemented
5#62328C212yesmaximal, complemented
6#62304C218yesmaximal, complemented
7#62299C218yesmaximal, complemented
8#61279C214yesmaximal, complemented
9#61205C214yesmaximal, complemented
10#61200C214yesmaximal, complemented
11#61093C214yesmaximal, complemented
12#60907C211yesmaximal, characteristic, complemented
13C2×#3253C211yesmaximal, characteristic, complemented
14#60771C214yesmaximal, complemented
15#60700C212yesmaximal, complemented
16#60461C214yesmaximal, complemented
17#60144C211yesmaximal, characteristic, complemented
18C2×#576C2214yescomplemented
19C2×#568C2212yescomplemented
20#3558—24no—
21#3558—24no—
22#3549C2214yescomplemented
23#3548C2214yescomplemented
24#3546—24no—
25#3546C2218yescomplemented
26#3537—24no—
27#3519—24no—
28#3519C2218yescomplemented
29#3511—22no—
30#3511C2214yescomplemented
31#3508—24no—
32#3506C2214yescomplemented
33#3506C2214yescomplemented
34#3498—22no—
35#3498C2214yescomplemented
36#3496C2214yescomplemented
37#3496C2214yescomplemented
38#3488—24no—
39#3488C2218yescomplemented
40#3444C2212yescomplemented
41C2×#532C2211yescharacteristic
42C2×#532C2212yescomplemented
43#3357C2218yescomplemented
44#3354C2218yescomplemented
45#3350C22116yescomplemented
46#3345C22116yescomplemented
47#3341C2218yescomplemented
48#3335C2218yescomplemented
49#3332C2218yescomplemented
50#3331C2218yescomplemented
51#3325C2218yescomplemented
52#3325C2218yescomplemented
53#3318C22116yescomplemented
54#3311C22116yescomplemented
55#3309C22116yescomplemented
56#3306C22116yescomplemented
57#3305C2218yescomplemented
58#3303C2218yescomplemented
59#3295C2218yescomplemented
60#3294C2218yescomplemented
61#3284C2218yescomplemented
62D4×D8C2218yescomplemented
63#3274C2218yescomplemented
64#3272C2218yescomplemented
65#3268C22116yescomplemented
66#3264C22116yescomplemented
67#3256C2214yescomplemented
68#3255C2211yescharacteristic, complemented
69#3254C2212yescomplemented
70#3253C2218yescomplemented
71#3253C2211yescharacteristic, complemented
72#3253C2212yescomplemented
73#3253C2214yescomplemented
74#3253C2212yescomplemented
75#3252C2214yescomplemented
76#3251C2214yescomplemented
77#3204C2218yescomplemented
78#3199C2218yescomplemented
79#3198C22116yescomplemented
80#3197C2218yescomplemented
81#3194C22116yescomplemented
82#3192C2218yescomplemented
83#3184C2214yescomplemented
84#3182C2214yescomplemented
85#3180C2218yescomplemented
86#3171C2218yescomplemented
87#3169C2214yescomplemented
88#3167C2214yescomplemented
89#3165C2212yescomplemented
90#3151C2212yescomplemented
91#3141C2212yescomplemented
92#3138C2212yescomplemented
93#3099C2218yescomplemented
94#3096C2218yescomplemented
95#3076C2214yescomplemented
96C2×#476C2214yescomplemented
97#3062C2218yescomplemented
98#3062C22116yescomplemented
99#3060C2214yescomplemented
100#3060C2218yescomplemented
101#3058C2214yescomplemented
102#3058C2218yescomplemented
103#3055C2214yescomplemented
104#3055C2214yescomplemented
105#3055C22116yescomplemented
106#3054C2218yescomplemented
107#3054C2214yescomplemented
108C2×#469C2218yescomplemented
109C2×#469C2214yescomplemented
110#3035C2214yescomplemented
111C2×#459C2214yescomplemented
112#3012C2218yescomplemented
113#3008C2218yescomplemented
114C4×AGL(1,ℤ/8)C2214yescomplemented
115C4×AGL(1,ℤ/8)C2214yescomplemented
116#2935C2214yescomplemented
117#2935C2214yescomplemented
118D4×M16C2218yescomplemented
119#2932C2214yescomplemented
120#2931C2212yescomplemented
121#2931C2212yescomplemented
122#2912C2214yescomplemented
123C2×#423C2211yescharacteristic, complemented
124#2897C2218yescomplemented
125#2879C2212yescomplemented
126C2×C4×M16C2211yescharacteristic, complemented
127C2×H(5,𝔽2)—24no—
128C2×H(5,𝔽2)C2318yes—
129C22×#41—22no—
130C22×#41C2312yes—
131#576—416no—
132C2×AGL(1,ℤ/8)C2314yes—
133C2×AGL(1,ℤ/8)C2314yes—
134C2×AGL(1,ℤ/8)C23116yes—
135C2×#135C2314yes—
136C2×#135C2318yes—
137C22×D8C2314yes—
138C22×D8C2318yes—
139#568—48no—
140C2×#131C2314yes—
141C2×#131C2314yes—
142C2×#131C2314yes—
143C2×#131C2314yes—
144C22×M16C2311yescharacteristic
145C22×M16C2311yescharacteristic
146C22×M16C2312yes—
147C22×M16C2318yes—
148#562—28no—
149H(3,𝔽4)—28no—
150#560—216no—
151#559—28no—
152#559—28no—
153#556—24no—
154#556C2318yes—
155#555—24no—
156#555C2318yes—
157#555C2318yes—
158#554—24no—
159#554C2318yes—
160#553—28no—
161#553—28no—
162#553—28no—
163#553C23116yes—
164#550—28no—
165#550—24no—
166#550—24no—
167#550—28no—
168#550C2318yes—
169#550C2318yes—
170#548—28no—
171#548—28no—
172#547—24no—
173#547C2318yes—
174#547C2318yes—
175#547C2318yes—
176#546—28no—
177#546—216no—
178#546—28no—
179#546—28no—
180#546—28no—
181#546—28no—
182#546—216no—
183#546C23116yes—
184D42—216no—
185D42—28no—
186D42—28no—
187D42—24no—
188D42—24no—
189D42—28no—
190D42—28no—
191D42C2318yes—
192D42C2318yes—
193D42C2318yes—
194#542—28no—
195#542—28no—
196#540—28no—
197#540—28no—
198#538—216no—
199#538—28no—
200#538—216no—
201#538—28no—
202#537—28no—
203#537—24no—
204#537C2318yes—
205#537C23116yes—
206#535—24no—
207#535—28no—
208#535—28no—
209#535—28no—
210#535—28no—
211#535C2318yes—
212#535C23116yes—
213#534—28no—
214#534—28no—
215#533—24no—
216#533C2312yes—
217#533C2312yes—
218#533C2312yes—
219#532—24no—
220#532—24no—
221#532—22no—
222#532—22no—
223#532—22no—
224#532—22no—
225#532D414yes—
226#532D412yes—
227#532D412yes—
228#532C2312yes—
229#532C2314yes—
230#532C2312yes—
231#532C2314yes—
232#532C2314yes—
233#532C2314yes—
234#532C2312yes—
235#532C2312yes—
236#532C2312yes—
237#532C2314yes—
238C2×C4⋊Q8D411yescharacteristic
239C2×C4⋊Q8C2312yes—
240C2×#127—24no—
241C2×#127D411yescharacteristic
242C2×#127C2312yes—
243#529—22no—
244#529—22no—
245#529—22no—
246#529—22no—
247#529C2314yes—
248#529C2314yes—
249C2×#124—22no—
250C2×#124D412yes—
251#525—22no—
252#525—22no—
253#525—28no—
254#525C2314yes—
255#525C23116yes—
256C2×#121—22no—
257C2×#121—28no—
258C2×#121D414yes—
259C2×#121C2314yes—
260C2×#121C23116yes—
261#520—24no—
262#520C2318yes—
263#518—28no—
264C4×#41—22no—
265C4×#41—22no—
266C4×#41C2314yes—
267C2×C4×D4—22no—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C22×C42C2311yescharacteristic
271#501C2318yes—
272#500C2314yes—
273#498C2314yes—
274#496C2318yes—
275#493C2314yes—
276#492C2314yes—
277#490C2318yes—
278#489C2318yes—
279#487C2314yes—
280#486C2314yes—
281#486C2314yes—
282#486C2314yes—
283#485C23116yes—
284#483C23116yes—
285#482C23116yes—
286#482C23116yes—
287#482C23116yes—
288#481C23116yes—
289#481C23116yes—
290#480C23116yes—
291#479C2318yes—
292#478C2318yes—
293#477C2314yes—
294#476C2318yes—
295#476C2314yes—
296#476C23116yes—
297#476C2318yes—
298#475C2314yes—
299#474C2314yes—
300#470C2318yes—
301#470C2314yes—
302#470C2314yes—
303#469C2318yes—
304#469C23116yes—
305#469C2318yes—
306#469C2318yes—
307#469C2314yes—
308#469C2318yes—
309#469C2318yes—
310#469C2318yes—
311#469C2314yes—
312#469C2318yes—
313#469C2318yes—
314#469C2318yes—
315#468C23116yes—
316#468C2318yes—
317#468C2318yes—
318#468C2318yes—
319#468C2318yes—
320#466C23116yes—
321#466C2318yes—
322#466C2318yes—
323#466C23116yes—
324#465C23116yes—
325#465C2318yes—
326#465C2318yes—
327#465C23116yes—
328#464C2318yes—
329#463C2318yes—
330#462C2314yes—
331#461C2314yes—
332#460C2314yes—
333#459C2318yes—
334#459C2314yes—
335#459C23116yes—
336#459C2318yes—
337#452C23116yes—
338#450C23116yes—
339#449C23116yes—
340#449C23116yes—
341#449C23116yes—
342#447C23116yes—
343#447C23116yes—
344#447C23116yes—
345#442C2318yes—
346#442C2318yes—
347#440C2318yes—
348#440C2318yes—
349C4×SD16C2318yes—
350C4×SD16C2318yes—
351C4×D8C2318yes—
352C4×D8C2318yes—
353#436C2318yes—
354#436C2318yes—
355#435C23116yes—
356#435C23116yes—
357C8×D4C2318yes—
358C8×D4C2318yes—
359#428C23116yes—
360#428C2314yes—
361#428C2314yes—
362#427C2314yes—
363#427C2318yes—
364C2×#106C2318yes—
365C2×#106C2314yes—
366#423C2311yescharacteristic
367#423C2311yescharacteristic
368#423C2312yes—
369#423C2314yes—
370C2×C4⋊C8C2314yes—
371#418C2314yes—
372#418C2314yes—
373#418C23116yes—
374#417C23116yes—
375#417C2314yes—
376#417C2314yes—
377#416C2318yes—
378#416C23116yes—
379C2×#102C2318yes—
380C2×#102C23116yes—
381#408C2318yes—
382#408C2314yes—
383#408C2314yes—
384#407C2318yes—
385C4×M16C2312yes—
386C4×M16C2312yes—
387C4×M16C2314yes—
388C2×#97C2312yes—
389C2×C4×C8C2312yes—
390H(5,𝔽2)—416no—
391H(5,𝔽2)—416no—
392H(5,𝔽2)—816no—
393C2×#41—28no—
394C2×#41—28no—
395C2×#41—28no—
396C2×#41—22no—
397C2×#41—24no—
398C2×#41—22no—
399C2×#41—24no—
400C2×#41—24no—
401C2×#41—24no—
402C2×#41—44no—
403C2×#41—44no—
404C2×#41—88no—
405C2×#41C2×D414yes—
406C2×#41C2×D414yes—
407C2×#41C2414yes—
408C2×#41C24116yes—
409C2×#41C2414yes—
410C2×#41C2414yes—
411C22×Q8—22no—
412C22×Q8C2×D412yes—
413C22×D4—24no—
414C22×D4—216no—
415C22×D4—28no—
416C22×D4—216no—
417C22×D4—28no—
418C22×D4—28no—
419C22×D4—28no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4C2×D414yes—
423C22×D4C2×D414yes—
424C22×D4C2×D412yes—
425C22×D4C2414yes—
426C22×D4C24116yes—
427C23×C4—24no—
428C23×C4C2×D412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2414yes—
431AGL(1,ℤ/8)—216no—
432AGL(1,ℤ/8)—432no—
433AGL(1,ℤ/8)—48no—
434#135—416no—
435#135—48no—
436C2×Q16C2414yes—
437C2×SD16C2418yes—
438C2×SD16C2418yes—
439C2×SD16C2418yes—
440C2×D8—416no—
441C2×D8—48no—
442C2×D8C2418yes—
443C2×D8C2414yes—
444C2×D8C2418yes—
445C2×D8C2418yes—
446C2×D8C2418yes—
447#131—216no—
448#131—48no—
449#131—48no—
450#131—48no—
451C2×M16—24no—
452C2×M16—44no—
453C2×M16—416no—
454C2×M16—42no—
455C2×M16C2412yes—
456C2×M16C2411yescharacteristic
457C2×M16C2418yes—
458C2×M16C2412yes—
459C2×M16C2414yes—
460C2×M16C2412yes—
461C2×M16C2412yes—
462C2×M16C2418yes—
463C2×M16C2412yes—
464C2×M16C2411yescharacteristic
465C22×C8C2412yes—
466C22×C8C2414yes—
467C22×C8C2418yes—
468C22×C8C2418yes—
469C22×C8C2412yes—
470C4⋊Q8—22no—
471C4⋊Q8—22no—
472C4⋊Q8C2×D414yes—
473C4⋊Q8C2×D412yes—
474C4⋊Q8C2×D412yes—
475C4⋊Q8C2412yes—
476C4⋊Q8C2414yes—
477C4⋊Q8C2414yes—
478C4⋊Q8C2412yes—
479C4⋊Q8C2412yes—
480#127—28no—
481#127—28no—
482#127—28no—
483#127—216no—
484#127—22no—
485#127—22no—
486#127C2×D414yes—
487#127C2×D412yes—
488#127C2×D412yes—
489#127C2414yes—
490#127C2414yes—
491#127C2412yes—
492#126—216no—
493#126—216no—
494#126—24no—
495#126—24no—
496#125—28no—
497#125—22no—
498#125—22no—
499#125C2414yes—
500#124—28no—
501#124—216no—
502#124—28no—
503#124—216no—
504#124—216no—
505#124—24no—
506#124—24no—
507#124—24no—
508#124—24no—
509#124—22no—
510#124—22no—
511#124C2×D418yes—
512#124C2×D414yes—
513#124C2×D414yes—
514#124C2414yes—
515#123—24no—
516#123—24no—
517#123—24no—
518#123—216no—
519#123—216no—
520#123—216no—
521#123—216no—
522#123—216no—
523#123—216no—
524C22⋊Q8—28no—
525C22⋊Q8—216no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—28no—
531C22⋊Q8—28no—
532C22⋊Q8—216no—
533C22⋊Q8C2414yes—
534C22⋊Q8C2414yes—
535C22⋊Q8C24116yes—
536#121—216no—
537#121—28no—
538#121—28no—
539#121—28no—
540#121—28no—
541#121—216no—
542#121—216no—
543#121—216no—
544#121—216no—
545#121—22no—
546#121—24no—
547#121—24no—
548#121—24no—
549#121—24no—
550#121—24no—
551#121—24no—
552#121—216no—
553#121—216no—
554#121—22no—
555#121—22no—
556#121—22no—
557#121—28no—
558#121—28no—
559#121—28no—
560#121—216no—
561#121—216no—
562#121—216no—
563#121C2×D418yes—
564#121C2×D418yes—
565#121C2×D418yes—
566#121C2×D418yes—
567#121C2414yes—
568#121C2418yes—
569#121C2418yes—
570#121C24116yes—
571#121C24116yes—
572#121C2414yes—
573#121C24116yes—
574#120—24no—
575#120—216no—
576#120—216no—
577#120—216no—
578#120—216no—
579#120—216no—
580#120—216no—
581#120—216no—
582#120—216no—
583C4×Q8—28no—
584C4×Q8—28no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8C2414yes—
590C4×Q8C2414yes—
591C4×D4—28no—
592C4×D4—216no—
593C4×D4—28no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—216no—
601C4×D4—216no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4—216no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—24no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4C2×D418yes—
616C4×D4C2×D418yes—
617C4×D4C2418yes—
618C4×D4C2418yes—
619C4×D4C2414yes—
620C4×D4C2414yes—
621C4×D4C2418yes—
622C4×D4C2418yes—
623#117—22no—
624#117—22no—
625#117—28no—
626#117—28no—
627#117—24no—
628#117—24no—
629#117—24no—
630#117C2414yes—
631#117C24116yes—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—28no—
634C2×C4⋊C4C2×D414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C24116yes—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—216no—
640C2×C22⋊C4—216no—
641C2×C22⋊C4C2×D418yes—
642C2×C42—24no—
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D412yes—
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107C2418yes—
653#107C2418yes—
654#107C2418yes—
655#106C2414yes—
656#106C2418yes—
657#106C2418yes—
658#106C2418yes—
659#106C2414yes—
660#106C2418yes—
661C4⋊C8C2414yes—
662C4⋊C8C2414yes—
663C4⋊C8C2418yes—
664#103C2418yes—
665#103C2418yes—
666#103C2418yes—
667#103C2418yes—
668#102C2418yes—
669#102C24116yes—
670#102C2418yes—
671#102C2418yes—
672#102C24116yes—
673#102C2418yes—
674#102C2418yes—
675#102C2418yes—
676#102C2418yes—
677#102C2418yes—
678C22⋊C8C24116yes—
679C22⋊C8C24116yes—
680#97C2414yes—
681#97C2414yes—
682C4×C8C2414yes—
683C4×C8C2414yes—
684C24—24no—
685C24—216no—
686C24C22×D411yescharacteristic
687C24C22×D414yes—
688#41—28no—
689#41—28no—
690#41—28no—
691#41—28no—
692#41—44no—
693#41—44no—
694#41—48no—
695#41—48no—
696#41—416no—
697#41—48no—
698#41—416no—
699#41—416no—
700#41—84no—
701#41—88no—
702#41—816no—
703#41—88no—
704#41—816no—
705#41—88no—
706#41—816no—
707C2×Q8—22no—
708C2×Q8—24no—
709C2×Q8—22no—
710C2×Q8—24no—
711C2×Q8—44no—
712C2×Q8—84no—
713C2×Q8C22×D414yes—
714C2×Q8C22×D414yes—
715C2×Q8C2514yes—
716C2×D4—28no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—216no—
725C2×D4—24no—
726C2×D4—22no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—22no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—216no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—416no—
738C2×D4—416no—
739C2×D4—48no—
740C2×D4—84no—
741C2×D4—816no—
742C2×D4—816no—
743C2×D4—816no—
744C2×D4—84no—
745C2×D4—816no—
746C2×D4—832no—
747C2×D4—88no—
748C2×D4—832no—
749C2×D4C22×D418yes—
750C2×D4C22×D414yes—
751C2×D4C22×D418yes—
752C2×D4C22×D418yes—
753C2×D4C22×D414yes—
754C2×D4C22×D418yes—
755C2×D4C2514yes—
756C2×D4C2518yes—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—216no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—216no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—88no—
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D412yes—
775C22×C4C22×D412yes—
776C22×C4C22×D412yes—
777C22×C4C22×D412yes—
778C22×C4C22×D412yes—
779C22×C4C22×D412yes—
780C22×C4C22×D418yes—
781C22×C4C22×D414yes—
782C22×C4C2518yes—
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786Q16—44no—
787SD16—216no—
788SD16—48no—
789SD16—48no—
790D8—216no—
791D8—44no—
792D8—48no—
793D8—48no—
794D8—48no—
795M16—22no—
796M16—24no—
797M16—24no—
798M16—216no—
799M16—44no—
800M16—42no—
801M16—42no—
802M16—48no—
803M16—42no—
804M16H(5,𝔽2)14yescomplemented
805C2×C8—28no—
806C2×C8—24no—
807C2×C8—216no—
808C2×C8—42no—
809C2×C8—48no—
810C2×C8C2514yes—
811C2×C8C2512yes—
812C2×C8C2514yes—
813C2×C8C2514yes—
814C2×C8C2512yes—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—216no—
819C4⋊C4—24no—
820C4⋊C4—216no—
821C4⋊C4—22no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4C22×D418yes—
831C4⋊C4C22×D418yes—
832C4⋊C4C2514yes—
833C4⋊C4C2518yes—
834C4⋊C4C2514yes—
835C22⋊C4—216no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—216no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—28no—
843C22⋊C4—216no—
844C22⋊C4—216no—
845C22⋊C4—28no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—216no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4C22×D4116yes—
854C22⋊C4C22×D4116yes—
855C42—24no—
856C42—24no—
857C42—24no—
858C42—216no—
859C42C22×D412yes—
860C42C22×D411yescharacteristic
861C42C22×D412yes—
862C42C22×D412yes—
863C42C22×D411yescharacteristic
864C42C22×D411yescharacteristic
865C42C22×D412yes—
866C42C22×D411yescharacteristic
867C42C2512yes—
868C42C2512yes—
869C23—22no—
870C23—24no—
871C23—28no—
872C23—42no—
873C23—44no—
874C23—48no—
875C23—48no—
876C23—84no—
877C23—84no—
878C23—816no—
879C23—816no—
880C23—816no—
881C23C23×D418yes—
882C23C23×D411yescharacteristic
883C23C23×D411yescharacteristic
884C23C23×D411yescharacteristic
885Q8—28no—
886Q8—24no—
887Q8—24no—
888Q8—44no—
889Q8—48no—
890Q8—44no—
891Q8—84no—
892Q8—82no—
893D4—216no—
894D4—216no—
895D4—24no—
896D4—28no—
897D4—24no—
898D4—28no—
899D4—28no—
900D4—48no—
901D4—44no—
902D4—48no—
903D4—48no—
904D4—48no—
905D4—416no—
906D4—48no—
907D4—48no—
908D4—44no—
909D4—48no—
910D4—816no—
911D4—84no—
912D4—84no—
913D4—82no—
914D4—816no—
915D4—816no—
916D4—816no—
917D4—816no—
918D4—88no—
919D4—84no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—21no—
925C2×C4—28no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—28no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—28no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—44no—
937C2×C4—42no—
938C2×C4—48no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—48no—
942C2×C4—416no—
943C2×C4—48no—
944C2×C4—48no—
945C2×C4—88no—
946C2×C4—816no—
947C2×C4—84no—
948C2×C4—816no—
949C2×C4C23×D412yes—
950C2×C4C23×D418yes—
951C2×C4C23×D411yescharacteristic
952C2×C4C23×D411yescharacteristic
953C2×C4C23×D412yes—
954C2×C4C23×D412yes—
955C2×C4C23×D412yes—
956C2×C4C23×D411yescharacteristic
957C2×C4C2×H(5,𝔽2)12yes—
958C2×C4#58512yes—
959C2×C4C2611yescharacteristic
960C8—24no—
961C8—22no—
962C8—24no—
963C8—24no—
964C8C2×H(5,𝔽2)14yes—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—28no—
969C22—22no—
970C22—22no—
971C22—216no—
972C22—44no—
973C22—48no—
974C22—48no—
975C22—44no—
976C22—44no—
977C22—48no—
978C22—82no—
979C22—168no—
980C22—164no—
981C22—3216no—
982C22#349612yes—
983C22C24×D411yescharacteristic
984C4—21no—
985C4—21no—
986C4—28no—
987C4—22no—
988C4—22no—
989C4—22no—
990C4—44no—
991C4—44no—
992C4—48no—
993C4—44no—
994C4#349612yes—
995C4#358514yes—
996C4C22×H(5,𝔽2)11yescharacteristic
997C4C2×#58511yescharacteristic
998C2—22no—
999C2—41no—
1000C2—41no—
1001C2—48no—
1002C2—88no—
1003C2—84no—
1004C2C2×#349611yescharacteristic
1005C2C2×#358512yes—
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. #62342C2semidirect
3. #62334C2semidirect
4. #62331C2semidirect
5. #62328C2semidirect
6. #62304C2semidirect
7. #62299C2semidirect
8. #61279C2semidirect
9. #61205C2semidirect
10. #61200C2semidirect
11. #61093C2semidirect
12. #60907C2semidirect
13. C2×#3253C2semidirect
14. #60771C2semidirect
15. #60700C2semidirect
16. #60461C2semidirect
17. #60144C2semidirect
18. C2×#576C22semidirect
19. C2×#568C22semidirect
22. #3549C22semidirect
23. #3548C22semidirect
25. #3546C22semidirect
28. #3519C22semidirect
30. #3511C22semidirect
32. #3506C22semidirect
33. #3506C22semidirect
35. #3498C22semidirect
36. #3496C22semidirect
37. #3496C22semidirect
39. #3488C22semidirect
40. #3444C22semidirect
42. C2×#532C22semidirect
43. #3357C22semidirect
44. #3354C22semidirect
45. #3350C22semidirect
46. #3345C22semidirect
47. #3341C22semidirect
48. #3335C22semidirect
49. #3332C22semidirect
50. #3331C22semidirect
51. #3325C22semidirect
52. #3325C22semidirect
53. #3318C22semidirect
54. #3311C22semidirect
55. #3309C22semidirect
56. #3306C22semidirect
57. #3305C22semidirect
58. #3303C22semidirect
59. #3295C22semidirect
60. #3294C22semidirect
61. #3284C22semidirect
62. D4×D8C22semidirect
63. #3274C22semidirect
64. #3272C22semidirect
65. #3268C22semidirect
66. #3264C22semidirect
67. #3256C22semidirect
68. #3255C22semidirect
69. #3254C22semidirect
70. #3253C22semidirect
71. #3253C22semidirect
72. #3253C22semidirect
73. #3253C22semidirect
74. #3253C22semidirect
75. #3252C22semidirect
76. #3251C22semidirect
77. #3204C22semidirect
78. #3199C22semidirect
79. #3198C22semidirect
80. #3197C22semidirect
81. #3194C22semidirect
82. #3192C22semidirect
83. #3184C22semidirect
84. #3182C22semidirect
85. #3180C22semidirect
86. #3171C22semidirect
87. #3169C22semidirect
88. #3167C22semidirect
89. #3165C22semidirect
90. #3151C22semidirect
91. #3141C22semidirect
92. #3138C22semidirect
93. #3099C22semidirect
94. #3096C22semidirect
95. #3076C22semidirect
96. C2×#476C22semidirect
97. #3062C22semidirect
98. #3062C22semidirect
99. #3060C22semidirect
100. #3060C22semidirect
101. #3058C22semidirect
102. #3058C22semidirect
103. #3055C22semidirect
104. #3055C22semidirect
105. #3055C22semidirect
106. #3054C22semidirect
107. #3054C22semidirect
108. C2×#469C22semidirect
109. C2×#469C22semidirect
110. #3035C22semidirect
111. C2×#459C22semidirect
112. #3012C22semidirect
113. #3008C22semidirect
114. C4×AGL(1,ℤ/8)C22semidirect
115. C4×AGL(1,ℤ/8)C22semidirect
116. #2935C22semidirect
117. #2935C22semidirect
118. D4×M16C22semidirect
119. #2932C22semidirect
120. #2931C22semidirect
121. #2931C22semidirect
122. #2912C22semidirect
123. C2×#423C22semidirect
124. #2897C22semidirect
125. #2879C22semidirect
126. C2×C4×M16C22semidirect
804. M16H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
#628342
#623422
#623342
#623312
#623282
#623042
#622992
#612792
#612052
#612002
#610932
#609072
C2×#32532
#607712
#607002
#604612
#601442