Finite Group Databasebeta

← #10575373

Subgroups — #10575373

Order 512.

6789 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62810C212yesmaximal, complemented
2#60724C216yesmaximal, complemented
3#60717C213yesmaximal, complemented
4#60713C213yesmaximal, complemented
5#60708C213yesmaximal, complemented
6#60707C213yesmaximal, complemented
7#60706C216yesmaximal, complemented
8#60702C216yesmaximal, complemented
9#60696C213yesmaximal, complemented
10#60695C213yesmaximal, complemented
11#60694C216yesmaximal, complemented
12#60673C213yesmaximal, complemented
13C2×#3168C213yesmaximal, complemented
14#60666C211yesmaximal, characteristic, complemented
15#60649C211yesmaximal, characteristic, complemented
16#60624C212yesmaximal, complemented
17#60459C211yesmaximal, characteristic, complemented
18#60458C211yesmaximal, characteristic, complemented
19#60457C212yesmaximal, complemented
20C4×#578C211yesmaximal, characteristic, complemented
21C4×#577C212yesmaximal, complemented
22C4×#576C211yesmaximal, characteristic, complemented
23C2×C4×#131C211yesmaximal, characteristic, complemented
24C2×#578C2211yescharacteristic
25C2×#577C2212yes—
26C2×#576C2211yescharacteristic
27C22×#131C2211yescharacteristic
28C22×#131C2211yescharacteristic
29#3524—22no—
30#3521—26no—
31#3516—22no—
32#3513—26no—
33#3512C2216yescomplemented
34#3510C2216yescomplemented
35#3504C2212yes—
36#3500C2212yes—
37#3495C2216yescomplemented
38#3494C2216yescomplemented
39#3489C2212yes—
40#3488C2212yes—
41#3482—22no—
42#3481—26no—
43#3480—22no—
44#3475—26no—
45#3461C2216yescomplemented
46#3460C2216yescomplemented
47#3444C2216yescomplemented
48C2×#529C2216yescomplemented
49C4×2−1+4C2212yes—
50C4×H(5,𝔽2)C2212yes—
51C2×C4×#41C2211yescharacteristic
52#3183C22112yescomplemented
53#3183C22112yescomplemented
54#3181C22112yescomplemented
55#3180C22112yescomplemented
56#3179C22112yescomplemented
57#3179C22112yescomplemented
58#3178C22112yescomplemented
59#3178C22112yescomplemented
60#3177C2216yescomplemented
61#3176C2216yescomplemented
62#3175C2216yescomplemented
63#3175C2216yescomplemented
64#3174C22112yescomplemented
65#3173C22112yescomplemented
66#3172C22112yescomplemented
67#3171C22112yescomplemented
68#3170C2213yescomplemented
69#3170C2213yescomplemented
70#3169C2213yescomplemented
71#3169C2213yescomplemented
72#3168C2211yescharacteristic, complemented
73#3168C2216yescomplemented
74#3168C2213yescomplemented
75#3168C2213yescomplemented
76#3168C2216yescomplemented
77#3168C2213yescomplemented
78#3168C2216yescomplemented
79#3168C2216yescomplemented
80#3168C2216yescomplemented
81#3168C2216yescomplemented
82#3168C2216yescomplemented
83#3168C2216yescomplemented
84#3168C2216yescomplemented
85#3167C2216yescomplemented
86#3167C2216yescomplemented
87#3166C2216yescomplemented
88#3164C2213yescomplemented
89#3164C2213yescomplemented
90#3163C2216yescomplemented
91#3160C2213yescomplemented
92C2×#499C2213yescomplemented
93#3156C2213yescomplemented
94#3155C2213yescomplemented
95#3154C2216yescomplemented
96#3153C2216yescomplemented
97#3147C2213yescomplemented
98C2×#495C2213yescomplemented
99#3142C2216yescomplemented
100#3140C2216yescomplemented
101#3137C2216yescomplemented
102#3137C2216yescomplemented
103#3136C2216yescomplemented
104#3136C2216yescomplemented
105#3131C2216yescomplemented
106C2×#488C2216yescomplemented
107#3063C2216yescomplemented
108#3063C2216yescomplemented
109#3062C2216yes—
110#3062C2216yescomplemented
111#3061C2213yes—
112#3061C2213yescomplemented
113#3060C2216yescomplemented
114#3059C2213yescomplemented
115#3058C2213yes—
116#3057C2216yescomplemented
117#3056C2216yescomplemented
118#3056C2216yescomplemented
119#3055C2216yes—
120#3055C2216yescomplemented
121#3050C2213yes—
122#3050C2216yescomplemented
123#3050C2213yescomplemented
124C2×#467C2213yescomplemented
125C2×#466C2213yes—
126C2×#465C2216yescomplemented
127#2952C2216yescomplemented
128#2951C2213yescomplemented
129#2951C2213yescomplemented
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
141C4×#135C2213yescomplemented
142C4×#135C2216yescomplemented
143C4×#135C2213yescomplemented
144C2×C4×Q16C2213yescomplemented
145C2×C4×SD16C2216yescomplemented
146C2×C4×D8C2213yescomplemented
147#2913C2211yescharacteristic
148#2913C2211yescharacteristic
149#2912C2212yes—
150#2898C2212yes—
151#2898C2212yes—
152#2897C2212yes—
153#2897C2212yes—
154C4×#131C2211yescharacteristic
155C4×#131C2211yescharacteristic
156C4×#131C2211yescharacteristic
157C4×#131C2211yescharacteristic
158C4×#131C2213yescomplemented
159C4×#131C2213yescomplemented
160C4×#131C2213yescomplemented
161C4×#131C2213yescomplemented
162C2×#405C2213yescomplemented
163C2×#405C2213yescomplemented
164C2×C4×M16C2213yescomplemented
165C22×C4×C8C2213yescomplemented
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—
182C2×#131—28no—
183C2×#131—28no—
184C2×#131C2311yescharacteristic
185C2×#131C2311yescharacteristic
186C2×#131C2313yes—
187C2×#131C2313yes—
188C2×#131C2313yes—
189C2×#131C2313yes—
190C2×#131C2311yescharacteristic
191C2×#131C2311yescharacteristic
192C22×M16C2313yes—
193C22×M16C2313yes—
194C23×C8C2313yes—
195C23×C8C2313yes—
196#559—26no—
197#559—26no—
198#557—22no—
199#557—22no—
200#556—26no—
201#556—26no—
202#556—26no—
203#555—26no—
204#554—26no—
205#554—26no—
206#554—26no—
207#553—212no—
208#553—26no—
209#553—212no—
210#553—26no—
211#553—26no—
212#553—26no—
213#552—26no—
214#552—26no—
215#552—212no—
216#552—26no—
217#552—26no—
218#551—212no—
219#551—212no—
220#551—212no—
221#551—212no—
222#550—22no—
223D4×Q8—22no—
224#548—22no—
225#548—22no—
226#548—22no—
227#548—22no—
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#542C23112yes—
241#542C23112yes—
242#541—26no—
243#541C23112yes—
244#540—26no—
245#540C23112yes—
246#539—212no—
247#538—212no—
248#537C2316yes—
249#537C2316yes—
250#536C2316yes—
251#536C2316yes—
252#535C2316yes—
253#535C2316yes—
254#533—26no—
255#533C2316yes—
256#533C2316yes—
257#533C2316yes—
258#532—26no—
259#532C2316yes—
260#532C2316yes—
261#532C2316yes—
262#529—26no—
263#529—212no—
264#529—26no—
265#529—26no—
266#529—26no—
267#529—26no—
268#529—26no—
269#529—26no—
270#529—26no—
271#529—26no—
272#529—26no—
273#529C2316yes—
274#529C2312yes—
275#529C23112yes—
276#529C23112yes—
277#529C23112yes—
278#529C2316yes—
279#529C2316yes—
280C2×#126—26no—
281C2×#125C2316yes—
282C2×#124C2316yes—
283#525—26no—
284#525—26no—
285#525—212no—
286#525C2316yes—
287#525C2316yes—
288C2×#123—26no—
289C2×C22⋊Q8C2316yes—
290C2×#121C2316yes—
291#520—22no—
292#520—26no—
293#520C2316yes—
294#520C2316yes—
295#520C2312yes—
296#520C2312yes—
297#519—22no—
298#519C2316yes—
299#518—26no—
300#518C2316yes—
301C4×#41—22no—
302C4×#41—26no—
303C4×#41—26no—
304C4×#41—26no—
305C4×#41D413yes—
306C4×#41D411yescharacteristic
307C4×#41D413yes—
308C4×#41D411yescharacteristic
309C4×#41C2316yes—
310C4×#41C2316yes—
311C4×#41C2311yescharacteristic
312C4×#41C2311yescharacteristic
313C4×#41C2313yes—
314C4×#41C2313yes—
315C2×C4×Q8—22no—
316C2×C4×Q8D411yescharacteristic
317C2×C4×Q8D411yescharacteristic
318C2×C4×Q8C2316yes—
319C2×C4×D4—26no—
320C2×C4×D4—26no—
321C2×C4×D4D413yes—
322C2×C4×D4D413yes—
323C2×C4×D4C2316yes—
324C2×#117—26no—
325C2×#117C2313yes—
326C22×C42C2313yes—
327#501C23112yes—
328#501C23112yes—
329#500C2313yes—
330#500C2313yes—
331#499C2313yes—
332#499C2316yes—
333#499C2316yes—
334#499C2316yes—
335#499C2311yescharacteristic
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#491C23112yes—
350#490C23112yes—
351#489C23112yes—
352#489C23112yes—
353#488C2316yes—
354#488C23112yes—
355#488C23112yes—
356#488C23112yes—
357#488C2312yes—
358#488C2316yes—
359#488C2316yes—
360#487C2316yes—
361#487C2316yes—
362#486C2316yes—
363#486C2316yes—
364#470C23112yes—
365#470C23112yes—
366#469C23112yes—
367#469C23112yes—
368#468C23112yes—
369#468C23112yes—
370#468C23112yes—
371#468C23112yes—
372#467C2313yes—
373#467C2316yes—
374#467C2316yes—
375#467C2316yes—
376#467C2311yescharacteristic
377#467C2313yes—
378#467C2313yes—
379#467C2316yes—
380#467C2316yes—
381#466C2313yes—
382#466C2316yes—
383#466C2316yes—
384#466C2316yes—
385#466C2311yescharacteristic
386#466C2313yes—
387#466C2313yes—
388#466C2316yes—
389#466C2316yes—
390#465C2312yes—
391#465C2316yes—
392#465C2316yes—
393#465C2316yes—
394#465C2316yes—
395#465C2316yes—
396#465C2316yes—
397#465C2316yes—
398#465C23112yes—
399#465C23112yes—
400#465C23112yes—
401#442C23112yes—
402#442C23112yes—
403#441C23112yes—
404#441C23112yes—
405#440C23112yes—
406#440C23112yes—
407#440C23112yes—
408#440C23112yes—
409C4×Q16C2313yes—
410C4×Q16C2316yes—
411C4×Q16C2316yes—
412C4×Q16C2316yes—
413C4×Q16C2311yescharacteristic
414C4×Q16C2316yes—
415C4×Q16C2313yes—
416C4×Q16C2313yes—
417C4×Q16C2316yes—
418C4×SD16C2312yes—
419C4×SD16C2316yes—
420C4×SD16C2316yes—
421C4×SD16C2316yes—
422C4×SD16C2316yes—
423C4×SD16C2316yes—
424C4×SD16C2316yes—
425C4×SD16C2316yes—
426C4×SD16C23112yes—
427C4×SD16C23112yes—
428C4×SD16C23112yes—
429C4×D8C2313yes—
430C4×D8C2316yes—
431C4×D8C2316yes—
432C4×D8C2316yes—
433C4×D8C2311yescharacteristic
434C4×D8C2316yes—
435C4×D8C2313yes—
436C4×D8C2313yes—
437C4×D8C2316yes—
438#428C2316yes—
439#428C2316yes—
440#428C2316yes—
441#428C2316yes—
442#427C2316yes—
443#427C2313yes—
444#427C2313yes—
445C2×#107C2313yes—
446C2×#107C2313yes—
447C2×#106C2316yes—
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#405C2313yes—
465#405C2313yes—
466#405C2313yes—
467#405C2313yes—
468#405C2313yes—
469#405C2313yes—
470#405C2313yes—
471#405C2313yes—
472#405C2316yes—
473#405C2316yes—
474#405C2316yes—
475#405C2316yes—
476C4×M16C2313yes—
477C4×M16C2313yes—
478C4×M16C2313yes—
479C4×M16C2313yes—
480C4×M16C2316yes—
481C4×M16C2316yes—
482C2×#97C2316yes—
483C2×C4×C8C2311yescharacteristic
484C2×C4×C8C2313yes—
485C2×C4×C8C2313yes—
486C2×C4×C8C2313yes—
487C2×C4×C8C2313yes—
488C2×C4×C8C2313yes—
489C2×C4×C8C2313yes—
490C2×C4×C8C2313yes—
491C2×C4×C8C2313yes—
492C2×C4×C8C2313yes—
493C2×C4×C8C2313yes—
494C2×C4×C8C2313yes—
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—26no—
504C2×#41—26no—
505C2×#41C2×D413yes—
506C2×#41C2×D411yescharacteristic
507C2×#41C2416yes—
508C2×#41C2416yes—
509C2×#41C2413yes—
510C2×#41C2411yescharacteristic
511C22×Q8—22no—
512C22×Q8C2×D411yescharacteristic
513C22×Q8C2416yes—
514C22×D4—26no—
515C22×D4—26no—
516C22×D4C2×D413yes—
517C22×D4C2416yes—
518C23×C4—26no—
519C23×C4C2×D413yes—
520C23×C4C2×D413yes—
521C23×C4C2413yes—
522#137—224no—
523#137—224no—
524AGL(1,ℤ/8)—224no—
525AGL(1,ℤ/8)—224no—
526#135—212no—
527#135—224no—
528#135—212no—
529C2×Q16—212no—
530C2×Q16C2413yes—
531C2×Q16C2416yes—
532C2×Q16C2411yescharacteristic
533C2×Q16C2416yes—
534C2×SD16—224no—
535C2×SD16C2416yes—
536C2×SD16C24112yes—
537C2×SD16C2412yes—
538C2×SD16C2416yes—
539C2×SD16C2416yes—
540C2×D8—212no—
541C2×D8C2413yes—
542C2×D8C2416yes—
543C2×D8C2411yescharacteristic
544C2×D8C2416yes—
545#131—24no—
546#131—24no—
547#131—212no—
548#131—212no—
549#131—212no—
550#131—212no—
551#131#4118yescomplemented
552#131#4118yescomplemented
553C2×M16—212no—
554C2×M16—212no—
555C2×M16C2413yes—
556C2×M16C2413yes—
557C2×M16C2416yes—
558C2×M16C2416yes—
559C2×M16C2413yes—
560C2×M16C2413yes—
561C22×C8—212no—
562C22×C8—212no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2413yes—
566C22×C8C2413yes—
567C22×C8C2413yes—
568C22×C8C2413yes—
569C22×C8C2413yes—
570C22×C8C2413yes—
571C22×C8C2413yes—
572C22×C8C2413yes—
573C22×C8C2413yes—
574C22×C8C2413yes—
575C4⋊Q8—26no—
576C4⋊Q8—26no—
577C4⋊Q8—26no—
578C4⋊Q8C2416yes—
579C4⋊Q8C2416yes—
580C4⋊Q8C2416yes—
581#127—26no—
582#127C2416yes—
583#126—212no—
584#126—212no—
585#126—212no—
586#126—212no—
587#126—26no—
588#126—212no—
589#126—212no—
590#126—212no—
591#126—22no—
592#126—26no—
593#126—26no—
594#125—26no—
595#125—212no—
596#125—26no—
597#125—212no—
598#125—26no—
599#125—26no—
600#125—26no—
601#125—26no—
602#125C2416yes—
603#125C24112yes—
604#125C2412yes—
605#124—26no—
606#124—26no—
607#124—212no—
608#124—212no—
609#124—26no—
610#124—26no—
611#124—26no—
612#124—26no—
613#124C2416yes—
614#124C24112yes—
615#124C2412yes—
616#123—212no—
617#123—26no—
618#123—212no—
619#123—212no—
620#123—212no—
621#123—22no—
622#123—26no—
623#123—26no—
624#123—26no—
625#123—26no—
626#123—212no—
627#123—212no—
628#123—212no—
629#123—212no—
630#123—212no—
631C22⋊Q8—26no—
632C22⋊Q8—26no—
633C22⋊Q8—26no—
634C22⋊Q8—26no—
635C22⋊Q8—26no—
636C22⋊Q8—26no—
637C22⋊Q8—26no—
638C22⋊Q8—26no—
639C22⋊Q8—212no—
640C22⋊Q8—26no—
641C22⋊Q8—26no—
642C22⋊Q8—212no—
643C22⋊Q8—212no—
644C22⋊Q8—212no—
645C22⋊Q8C2416yes—
646C22⋊Q8C24112yes—
647C22⋊Q8C2412yes—
648C22⋊Q8C2416yes—
649C22⋊Q8C2416yes—
650#121—212no—
651#121—212no—
652#121—26no—
653#121—26no—
654#121—26no—
655#121—26no—
656#121—26no—
657#121—26no—
658#121—26no—
659#121—26no—
660#121—26no—
661#121—26no—
662#121—212no—
663#121—212no—
664#121C2416yes—
665#121C24112yes—
666#121C2412yes—
667#121C2416yes—
668#121C2416yes—
669#120—26no—
670#120—26no—
671#120—212no—
672#120—212no—
673C4×Q8—22no—
674C4×Q8—22no—
675C4×Q8—26no—
676C4×Q8—26no—
677C4×Q8—26no—
678C4×Q8—26no—
679C4×Q8—26no—
680C4×Q8—26no—
681C4×Q8—26no—
682C4×Q8—26no—
683C4×Q8C2×D411yescharacteristic
684C4×Q8C2×D411yescharacteristic
685C4×Q8C2×D413yes—
686C4×Q8C2×D413yes—
687C4×Q8C2×D411yescharacteristic
688C4×Q8C2×D411yescharacteristic
689C4×Q8C2×D413yes—
690C4×Q8C2×D413yes—
691C4×Q8C2416yes—
692C4×Q8C24112yes—
693C4×Q8C2412yes—
694C4×Q8C2416yes—
695C4×Q8C2416yes—
696C4×D4—26no—
697C4×D4—26no—
698C4×D4—26no—
699C4×D4—26no—
700C4×D4—212no—
701C4×D4—212no—
702C4×D4—212no—
703C4×D4—22no—
704C4×D4—26no—
705C4×D4—26no—
706C4×D4—26no—
707C4×D4—26no—
708C4×D4—26no—
709C4×D4—26no—
710C4×D4—26no—
711C4×D4—26no—
712C4×D4—26no—
713C4×D4—26no—
714C4×D4—26no—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—26no—
718C4×D4—26no—
719C4×D4—26no—
720C4×D4—26no—
721C4×D4—26no—
722C4×D4—26no—
723C4×D4C2×D413yes—
724C4×D4C2×D413yes—
725C4×D4C2×D416yes—
726C4×D4C2×D413yes—
727C4×D4C2×D416yes—
728C4×D4C2×D413yes—
729C4×D4C2×D413yes—
730C4×D4C2×D413yes—
731C4×D4C2×D416yes—
732C4×D4C2×D416yes—
733C4×D4C2×D413yes—
734C4×D4C2×D413yes—
735C4×D4C2416yes—
736C4×D4C24112yes—
737C4×D4C2412yes—
738C4×D4C2416yes—
739C4×D4C2416yes—
740#117—26no—
741#117—26no—
742#117—26no—
743#117—26no—
744#117—212no—
745#117—26no—
746#117—212no—
747#117—212no—
748#117—212no—
749#117—22no—
750#117—26no—
751#117—26no—
752#117—26no—
753#117—26no—
754#117C2×D416yes—
755#117C2×D413yes—
756#117C2×D413yes—
757#117C2416yes—
758#117C2416yes—
759#117C2413yes—
760#117C2413yes—
761#117C2416yes—
762C2×C4⋊C4—26no—
763C2×C4⋊C4—26no—
764C2×C4⋊C4—26no—
765C2×C4⋊C4—26no—
766C2×C4⋊C4—26no—
767C2×C4⋊C4—26no—
768C2×C4⋊C4C2×D413yes—
769C2×C4⋊C4C2×D413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C22⋊C4—26no—
773C2×C22⋊C4—26no—
774C2×C22⋊C4—26no—
775C2×C22⋊C4—26no—
776C2×C22⋊C4—26no—
777C2×C22⋊C4—212no—
778C2×C22⋊C4C2×D416yes—
779C2×C42—26no—
780C2×C42—26no—
781C2×C42—26no—
782C2×C42C2×D413yes—
783C2×C42C2×D413yes—
784C2×C42C2×D413yes—
785C2×C42C2×D413yes—
786C2×C42C2×D413yes—
787C2×C42C2×D413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2411yescharacteristic
794#107C2413yes—
795#107C2413yes—
796#107C2416yes—
797#107C2416yes—
798#107C2411yescharacteristic
799#107C2411yescharacteristic
800#107C2416yes—
801#107C2416yes—
802#106C2416yes—
803#106C24112yes—
804#106C2412yes—
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#97C2416yes—
828#97C2416yes—
829#97C2416yes—
830#97C2416yes—
831C4×C8C2411yescharacteristic
832C4×C8C2411yescharacteristic
833C4×C8C2411yescharacteristic
834C4×C8C2411yescharacteristic
835C4×C8C2413yes—
836C4×C8C2413yes—
837C4×C8C2413yes—
838C4×C8C2413yes—
839C4×C8C2413yes—
840C4×C8C2413yes—
841C4×C8C2413yes—
842C4×C8C2413yes—
843C4×C8C2413yes—
844C4×C8C2413yes—
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—812no—
860#41—812no—
861#41C2×#4114yes—
862#41C2×#4114yes—
863C2×Q8—24no—
864C2×Q8—26no—
865C2×Q8—26no—
866C2×Q8—26no—
867C2×Q8—212no—
868C2×Q8—212no—
869C2×Q8—48no—
870C2×Q8C22×D413yes—
871C2×Q8C22×D411yescharacteristic
872C2×Q8C2516yes—
873C2×Q8C2512yes—
874C2×D4—212no—
875C2×D4—26no—
876C2×D4—22no—
877C2×D4—26no—
878C2×D4—26no—
879C2×D4—26no—
880C2×D4—26no—
881C2×D4—212no—
882C2×D4—26no—
883C2×D4—26no—
884C2×D4—26no—
885C2×D4—212no—
886C2×D4—212no—
887C2×D4—424no—
888C2×D4—812no—
889C2×D4C22×D416yes—
890C2×D4C22×D413yes—
891C2×D4C22×D413yes—
892C2×D4C2516yes—
893C2×D4C2512yes—
894C22×C4—26no—
895C22×C4—26no—
896C22×C4—26no—
897C22×C4—26no—
898C22×C4—26no—
899C22×C4—26no—
900C22×C4—26no—
901C22×C4—22no—
902C22×C4—26no—
903C22×C4—26no—
904C22×C4—26no—
905C22×C4—212no—
906C22×C4—46no—
907C22×C4—46no—
908C22×C4—812no—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D413yes—
911C22×C4C22×D413yes—
912C22×C4C22×D413yes—
913C22×C4C22×D413yes—
914C22×C4C22×D413yes—
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D413yes—
917C22×C4C22×D413yes—
918C22×C4C22×D413yes—
919C22×C4C22×D413yes—
920C22×C4C22×D413yes—
921C22×C4C22×D413yes—
922C22×C4C22×D413yes—
923C22×C4C22×D413yes—
924C22×C4C2511yescharacteristic
925C22×C4C2513yes—
926C22×C4C2513yes—
927Q16—26no—
928Q16—212no—
929Q16—22no—
930Q16—212no—
931SD16—212no—
932SD16—224no—
933SD16—24no—
934SD16—212no—
935SD16—212no—
936D8—26no—
937D8—212no—
938D8—22no—
939D8—212no—
940M16—26no—
941M16—26no—
942M16—212no—
943M16—212no—
944M16C2×#41112yes—
945M16C2×#41112yes—
946C2×C8—26no—
947C2×C8—26no—
948C2×C8—22no—
949C2×C8—22no—
950C2×C8—26no—
951C2×C8—26no—
952C2×C8—26no—
953C2×C8—26no—
954C2×C8—26no—
955C2×C8—26no—
956C2×C8C2×#41112yes—
957C2×C8C2×#41112yes—
958C2×C8C2511yescharacteristic
959C2×C8C2511yescharacteristic
960C2×C8C2513yes—
961C2×C8C2513yes—
962C2×C8C2511yescharacteristic
963C2×C8C2511yescharacteristic
964C2×C8C2513yes—
965C2×C8C2513yes—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—212no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—212no—
975C4⋊C4—212no—
976C4⋊C4—212no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—26no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4C22×D413yes—
989C4⋊C4C22×D413yes—
990C4⋊C4C22×D413yes—
991C4⋊C4C22×D413yes—
992C4⋊C4C22×D416yes—
993C4⋊C4C22×D416yes—
994C4⋊C4C2516yes—
995C4⋊C4C2516yes—
996C4⋊C4C2512yes—
997C4⋊C4C2512yes—
998C22⋊C4—26no—
999C22⋊C4—26no—
1000C22⋊C4—212no—
1001C22⋊C4—22no—
1002C22⋊C4—26no—
1003C22⋊C4—26no—
1004C22⋊C4—26no—
1005C22⋊C4—26no—
1006C22⋊C4—26no—
1007C22⋊C4—26no—
1008C22⋊C4—212no—
1009C22⋊C4—26no—
1010C22⋊C4—26no—
1011C22⋊C4—212no—
1012C22⋊C4—212no—
1013C22⋊C4—212no—
1014C22⋊C4—22no—
1015C22⋊C4—26no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—26no—
1020C22⋊C4—26no—
1021C22⋊C4C22×D416yes—
1022C22⋊C4C22×D416yes—
1023C22⋊C4C22×D416yes—
1024C22⋊C4C22×D416yes—
1025C42—26no—
1026C42—212no—
1027C42—26no—
1028C42—26no—
1029C42—26no—
1030C42—26no—
1031C42—22no—
1032C42C22×D411yescharacteristic
1033C42C22×D413yes—
1034C42C22×D413yes—
1035C42C22×D413yes—
1036C42C22×D413yes—
1037C42C22×D413yes—
1038C42C22×D413yes—
1039C42C22×D413yes—
1040C42C22×D413yes—
1041C42C22×D413yes—
1042C42C22×D411yescharacteristic
1043C42C22×D413yes—
1044C42C2511yescharacteristic
1045C42C2513yes—
1046C42C2513yes—
1047C42C2511yescharacteristic
1048C23—26no—
1049C23—26no—
1050C23—26no—
1051C23—22no—
1052C23—43no—
1053C23—412no—
1054C23—86no—
1055C23—86no—
1056C23C23×D413yes—
1057C23C23×D411yescharacteristic
1058C23C23×D413yes—
1059Q8—26no—
1060Q8—26no—
1061Q8—22no—
1062Q8—26no—
1063Q8—22no—
1064Q8—412no—
1065Q8—86no—
1066Q8—86no—
1067Q8#53214yes—
1068D4—212no—
1069D4—26no—
1070D4—22no—
1071D4—26no—
1072D4—22no—
1073D4—26no—
1074D4—412no—
1075D4—44no—
1076D4—412no—
1077D4—412no—
1078D4—412no—
1079D4—86no—
1080D4—86no—
1081D4—812no—
1082D4—86no—
1083D4—86no—
1084D4#532112yes—
1085C2×C4—22no—
1086C2×C4—26no—
1087C2×C4—26no—
1088C2×C4—22no—
1089C2×C4—26no—
1090C2×C4—26no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—26no—
1096C2×C4—26no—
1097C2×C4—22no—
1098C2×C4—26no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—26no—
1102C2×C4—26no—
1103C2×C4—43no—
1104C2×C4—43no—
1105C2×C4—43no—
1106C2×C4—43no—
1107C2×C4—43no—
1108C2×C4—43no—
1109C2×C4—43no—
1110C2×C4—412no—
1111C2×C4—412no—
1112C2×C4—44no—
1113C2×C4—412no—
1114C2×C4—412no—
1115C2×C4—812no—
1116C2×C4—86no—
1117C2×C4—86no—
1118C2×C4—86no—
1119C2×C4—86no—
1120C2×C4C23×D413yes—
1121C2×C4C23×D413yes—
1122C2×C4C23×D411yescharacteristic
1123C2×C4C23×D411yescharacteristic
1124C2×C4C23×D411yescharacteristic
1125C2×C4C23×D411yescharacteristic
1126C2×C4C23×D413yes—
1127C2×C4C23×D413yes—
1128C2×C4C23×D413yes—
1129C2×C4C23×D413yes—
1130C2×C4C23×D411yescharacteristic
1131C2×C4C22×#4116yes—
1132C2×C4C22×#4116yes—
1133C2×C4C2611yescharacteristic
1134C8—21no—
1135C8—21no—
1136C8—23no—
1137C8—23no—
1138C8C22×#4112yes—
1139C8C22×#4112yes—
1140C8C22×#4116yes—
1141C8C22×#4116yes—
1142C22—21no—
1143C22—23no—
1144C22—23no—
1145C22—21no—
1146C22—23no—
1147C22—23no—
1148C22—23no—
1149C22—412no—
1150C22—46no—
1151C22—42no—
1152C22—42no—
1153C22—46no—
1154C22—42no—
1155C22—46no—
1156C22—1612no—
1157C22C2×#53216yes—
1158C22#358412yes—
1159C22C24×D411yescharacteristic
1160C4—21no—
1161C4—21no—
1162C4—21no—
1163C4—23no—
1164C4—23no—
1165C4—23no—
1166C4—23no—
1167C4—21no—
1168C4—23no—
1169C4—46no—
1170C4—42no—
1171C4—46no—
1172C4—42no—
1173C4—42no—
1174C4—46no—
1175C4C2×#53216yes—
1176C4#358412yes—
1177C4C23×#4111yescharacteristic
1178C4C23×#4111yescharacteristic
1179C2—22no—
1180C2—26no—
1181C2—43no—
1182C2—82no—
1183C2—86no—
1184C2C22×#53211yescharacteristic
1185C2C2×#358411yescharacteristic
1186C2C2×#358411yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62810C2semidirect
2. #60724C2semidirect
3. #60717C2semidirect
4. #60713C2semidirect
5. #60708C2semidirect
6. #60707C2semidirect
7. #60706C2semidirect
8. #60702C2semidirect
9. #60696C2semidirect
10. #60695C2semidirect
11. #60694C2semidirect
12. #60673C2semidirect
13. C2×#3168C2semidirect
14. #60666C2semidirect
15. #60649C2semidirect
16. #60624C2semidirect
17. #60459C2semidirect
18. #60458C2semidirect
19. #60457C2semidirect
20. C4×#578C2semidirect
21. C4×#577C2semidirect
22. C4×#576C2semidirect
23. C2×C4×#131C2semidirect
33. #3512C22semidirect
34. #3510C22semidirect
37. #3495C22semidirect
38. #3494C22semidirect
45. #3461C22semidirect
46. #3460C22semidirect
47. #3444C22semidirect
48. C2×#529C22semidirect
52. #3183C22semidirect
53. #3183C22semidirect
54. #3181C22semidirect
55. #3180C22semidirect
56. #3179C22semidirect
57. #3179C22semidirect
58. #3178C22semidirect
59. #3178C22semidirect
60. #3177C22semidirect
61. #3176C22semidirect
62. #3175C22semidirect
63. #3175C22semidirect
64. #3174C22semidirect
65. #3173C22semidirect
66. #3172C22semidirect
67. #3171C22semidirect
68. #3170C22semidirect
69. #3170C22semidirect
70. #3169C22semidirect
71. #3169C22semidirect
72. #3168C22semidirect
73. #3168C22semidirect
74. #3168C22semidirect
75. #3168C22semidirect
76. #3168C22semidirect
77. #3168C22semidirect
78. #3168C22semidirect
79. #3168C22semidirect
80. #3168C22semidirect
81. #3168C22semidirect
82. #3168C22semidirect
83. #3168C22semidirect
84. #3168C22semidirect
85. #3167C22semidirect
86. #3167C22semidirect
87. #3166C22semidirect
88. #3164C22semidirect
89. #3164C22semidirect
90. #3163C22semidirect
91. #3160C22semidirect
92. C2×#499C22semidirect
93. #3156C22semidirect
94. #3155C22semidirect
95. #3154C22semidirect
96. #3153C22semidirect
97. #3147C22semidirect
98. C2×#495C22semidirect
99. #3142C22semidirect
100. #3140C22semidirect
101. #3137C22semidirect
102. #3137C22semidirect
103. #3136C22semidirect
104. #3136C22semidirect
105. #3131C22semidirect
106. C2×#488C22semidirect
107. #3063C22semidirect
108. #3063C22semidirect
110. #3062C22semidirect
112. #3061C22semidirect
113. #3060C22semidirect
114. #3059C22semidirect
116. #3057C22semidirect
117. #3056C22semidirect
118. #3056C22semidirect
120. #3055C22semidirect
122. #3050C22semidirect
123. #3050C22semidirect
124. C2×#467C22semidirect
126. C2×#465C22semidirect
127. #2952C22semidirect
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. C4×#135C22semidirect
142. C4×#135C22semidirect
143. C4×#135C22semidirect
144. C2×C4×Q16C22semidirect
145. C2×C4×SD16C22semidirect
146. C2×C4×D8C22semidirect
158. C4×#131C22semidirect
159. C4×#131C22semidirect
160. C4×#131C22semidirect
161. C4×#131C22semidirect
162. C2×#405C22semidirect
163. C2×#405C22semidirect
164. C2×C4×M16C22semidirect
165. C22×C4×C8C22semidirect
551. #131#41semidirect
552. #131#41semidirect

Maximal subgroups

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

subgroupindex
#628102
#607242
#607172
#607132
#607082
#607072
#607062
#607022
#606962
#606952
#606942
#606732
C2×#31682
#606662
#606492
#606242
#604592
#604582
#604572
C4×#5782
C4×#5772
C4×#5762
C2×C4×#1312