Finite Group Databasebeta

← #10584764

Subgroups — #10584764

Order 512.

6160 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63015C212yesmaximal, complemented
2#62520C216yesmaximal, complemented
3#62481C213yesmaximal, complemented
4#62476C211yesmaximal, characteristic, complemented
5#62397C212yesmaximal, complemented
6#62384C213yesmaximal, complemented
7#62187C216yesmaximal, complemented
8#62180C216yesmaximal, complemented
9#62151C212yesmaximal, complemented
10#62143C216yesmaximal, complemented
11#61863C216yesmaximal, complemented
12#61823C212yesmaximal, complemented
13#61817C212yesmaximal, complemented
14#61539C216yesmaximal, complemented
15#61444C213yesmaximal, complemented
16D8×#41C211yesmaximal, characteristic, complemented
17#61370C213yesmaximal, complemented
18Q8×AGL(1,ℤ/8)C212yesmaximal, complemented
19#60345C211yesmaximal, characteristic, complemented
20#3561—26no—
21#3554C2216yescomplemented
22#3552C2216yescomplemented
23#3547C2216yescomplemented
24#3541—26no—
25#3536—26no—
26#3522C2212yescomplemented
27#3520—26no—
28#3519C2216yescomplemented
29#3518C2212yescomplemented
30#3516—22no—
31#3514C2216yescomplemented
32#3511C2216yescomplemented
33#3501C2216yescomplemented
34#3497C2212yescomplemented
35#3489—22no—
36#3486—22no—
37#3482C2211yescharacteristic
38#3481C2216yescomplemented
39Q8×#41C2212yescomplemented
40D4×#41C2212yescomplemented
41C2×D4×Q8C2212yescomplemented
42C2×#548—22no—
43#3403C2213yescomplemented
44#3399C2216yescomplemented
45#3391C2211yescharacteristic, complemented
46#3389C2213yes—
47#3389C2216yescomplemented
48#3389C2216yescomplemented
49#3386C2216yescomplemented
50#3386C2216yescomplemented
51#3384C2216yes—
52#3384C2216yescomplemented
53#3384C2216yescomplemented
54Q8×Q16C2211yescharacteristic, complemented
55#3381C2216yescomplemented
56#3380C2216yescomplemented
57#3380C22112yescomplemented
58Q8×SD16C2212yescomplemented
59Q8×SD16C2212yescomplemented
60Q8×D8C2211yescharacteristic
61Q8×D8C2211yescharacteristic, complemented
62Q8×D8C2216yescomplemented
63Q8×D8C2212yescomplemented
64Q8×D8C2216yescomplemented
65#3373C2216yescomplemented
66#3370C2216yescomplemented
67#3366C2216yescomplemented
68#3365C2216yescomplemented
69#3362C2212yescomplemented
70#3361C2216yescomplemented
71#3361C22112yescomplemented
72#3358C2216yescomplemented
73#3358C2212yescomplemented
74#3358C2216yescomplemented
75#3358C2212yescomplemented
76#3357C22112yescomplemented
77#3355C2213yescomplemented
78#3355C2216yescomplemented
79#3355C22112yescomplemented
80#3354C2216yescomplemented
81#3353C2216yescomplemented
82#3347C22112yescomplemented
83#3347C22112yescomplemented
84#3346C2216yescomplemented
85#3342C2213yescomplemented
86#3341C2213yescomplemented
87#3340C2216yescomplemented
88#3334C2213yescomplemented
89#3325C22112yescomplemented
90#3325C2216yescomplemented
91#3324C2216yescomplemented
92#3322C2216yescomplemented
93#3322C22112yescomplemented
94#3318C2216yescomplemented
95#3314C2216yescomplemented
96#3294C2216yescomplemented
97D4×D8C2213yes—
98#3273C2211yescharacteristic
99#3264C2216yes—
100#3262C2216yescomplemented
101#3259C2216yescomplemented
102#3253C2216yescomplemented
103#3251C2216yescomplemented
104#3251C2216yescomplemented
105#3243C22112yescomplemented
106#3241C22112yescomplemented
107#3233C2216yescomplemented
108#3233C2216yescomplemented
109#3228C2216yescomplemented
110#3228C2216yescomplemented
111#3226C2216yescomplemented
112#3226C2216yescomplemented
113#3184C2216yescomplemented
114#3179C22112yescomplemented
115#3171C2216yescomplemented
116#3169C2213yescomplemented
117#3168C2213yescomplemented
118#3165C2216yescomplemented
119#3164C2216yescomplemented
120#3160C2213yescomplemented
121#3122C22112yescomplemented
122#3118C22112yescomplemented
123#3106C2216yescomplemented
124#3105C2216yescomplemented
125#3102C2216yescomplemented
126#3100C2216yescomplemented
127#3100C2216yescomplemented
128#3100C2216yescomplemented
129#3081C22112yescomplemented
130#3079C2216yescomplemented
131#3077C2216yescomplemented
132#3077C2216yescomplemented
133#2993C2216yescomplemented
134#2991C2213yescomplemented
135#2991C2211yescharacteristic, complemented
136#2986C2213yescomplemented
137#2982C2212yescomplemented
138#2969C2216yescomplemented
139#2965C2213yescomplemented
140C8×#41C2211yescharacteristic, complemented
141Q8×M16C2212yescomplemented
142#2960C2213yescomplemented
143#2948C2216yes—
144C4×AGL(1,ℤ/8)C2216yes—
145C2×C4×D8C2213yes—
146C2×2−1+4—22no—
147C22×#41—22no—
148C23×Q8—22no—
149C2×AGL(1,ℤ/8)C2312yes—
150C22×D8C2313yes—
151#563—212no—
152#562—212no—
153#562—212no—
154#559C2316yes—
155#559C2316yes—
156Q82C2312yes—
157#557D411yescharacteristic
158#557C2316yes—
159#556—26no—
160#556—26no—
161#556D413yes—
162#556C2316yes—
163#555C2316yes—
164#555C23112yes—
165#554—26no—
166#554—212no—
167#554—26no—
168#554C2316yes—
169#554C23112yes—
170#554C2316yes—
171#554C2316yes—
172#554C2316yes—
173#553—26no—
174#553—26no—
175#553C2316yes—
176#553C23112yes—
177#553C2316yes—
178#552—26no—
179#552D416yes—
180#551—212no—
181#551—26no—
182#551—26no—
183#550C2312yes—
184#550C2316yes—
185D4×Q8—22no—
186D4×Q8—26no—
187D4×Q8—26no—
188D4×Q8—22no—
189D4×Q8—26no—
190D4×Q8D411yescharacteristic
191D4×Q8C2312yes—
192D4×Q8C2312yes—
193D4×Q8C2316yes—
194D4×Q8C2316yes—
195D4×Q8C2316yes—
196#548—22no—
197#548—22no—
198#548—26no—
199#548—26no—
200#548—26no—
201#548—26no—
202#548—22no—
203#548—22no—
204#548—26no—
205#548—26no—
206#548—26no—
207#548D412yes—
208#547—26no—
209#547—26no—
210#547—26no—
211#547D413yes—
212#547C2316yes—
213#546—26no—
214#546—26no—
215#546—212no—
216#546—26no—
217#546—26no—
218#546C2312yes—
219#546C2316yes—
220D42C2316yes—
221D42C2316yes—
222#544C23112yes—
223#543—212no—
224#542—26no—
225#542—212no—
226#542—26no—
227#542—26no—
228#542—26no—
229#542—26no—
230#542C23112yes—
231#541—26no—
232#540C23112yes—
233#539—212no—
234#539—212no—
235#538—212no—
236#538—212no—
237#537—26no—
238#537—26no—
239#537—26no—
240#536—26no—
241#536—26no—
242#536—26no—
243#533—26no—
244#533C2316yes—
245#533C2316yes—
246#533C2313yes—
247#532C2316yes—
248#532C2316yes—
249#532C2316yes—
250#532C2316yes—
251C2×C4⋊Q8C2316yes—
252#529—26no—
253#529—26no—
254#529C2316yes—
255#529C2316yes—
256#529C2316yes—
257C2×#124—26no—
258#525—26no—
259#525—26no—
260#525—26no—
261#525—26no—
262C2×C22⋊Q8—26no—
263C2×C22⋊Q8—26no—
264C2×C22⋊Q8—26no—
265C2×#121—26no—
266#520—22no—
267#520—26no—
268#519—22no—
269#518C23112yes—
270C4×#41C2316yes—
271C4×#41C2311yescharacteristic
272C4×#41C2313yes—
273C2×C4×Q8—22no—
274C2×C4×Q8C2312yes—
275C2×C4×D4—26no—
276C2×C4×D4C2316yes—
277C2×C4×D4C2316yes—
278#501C2316yes—
279#501C23112yes—
280#501C23112yes—
281#500C2313yes—
282#500C2313yes—
283#500C2313yes—
284#500C2316yes—
285#500C23112yes—
286#499C23112yes—
287#499C2316yes—
288#499C2313yes—
289#498C2316yes—
290#498C2316yes—
291#496C2316yes—
292#495C2311yescharacteristic
293#493C2313yes—
294#490C2316yes—
295#489C2316yes—
296#488C23112yes—
297#488C2316yes—
298#486C23112yes—
299#486C2316yes—
300#486C2316yes—
301#486C2316yes—
302#485C23112yes—
303#485C2316yes—
304#484C2316yes—
305#482C23112yes—
306#482C23112yes—
307#482C23112yes—
308#482C2316yes—
309#482C23112yes—
310#481C2316yes—
311#480C23112yes—
312#480C2316yes—
313#480C2316yes—
314#480C23112yes—
315#479C2316yes—
316#478C2316yes—
317#478C23112yes—
318#478C23112yes—
319#478C23112yes—
320#478C2316yes—
321#478C23112yes—
322#478C23112yes—
323#478C23112yes—
324#478C2316yes—
325#477C23112yes—
326#477C2316yes—
327#476C2316yes—
328#476C2316yes—
329#476C2316yes—
330#476C23112yes—
331#476C23112yes—
332#475C2316yes—
333#475C2316yes—
334#474C2316yes—
335#474C2316yes—
336#474C2316yes—
337#474C2316yes—
338#474C2316yes—
339#474C2316yes—
340#474C23112yes—
341#474C2316yes—
342#474C2316yes—
343#474C23112yes—
344#469C2316yes—
345#469C23112yes—
346#469C23112yes—
347#469C2316yes—
348#468C2312yes—
349#468C23112yes—
350#468C2316yes—
351#467C2313yes—
352#466C2316yes—
353#466C2313yes—
354#466C2316yes—
355#465C2316yes—
356#464C2316yes—
357#463C2316yes—
358#463C2312yes—
359#463C2316yes—
360#463C23112yes—
361#460C2316yes—
362#459C2316yes—
363#459C2316yes—
364#459C2316yes—
365#459C2316yes—
366#459C2316yes—
367#459C23112yes—
368#452C2312yes—
369#450C2316yes—
370#449C2316yes—
371#447C2316yes—
372#447C2312yes—
373#447C23112yes—
374#447C2316yes—
375#446C2316yes—
376#446C2313yes—
377#446C2316yes—
378#446C2313yes—
379C8×Q8C2311yescharacteristic
380C8×Q8C2316yes—
381C8×Q8C2312yes—
382C8×Q8C2316yes—
383C8×Q8C2316yes—
384C8×Q8C2311yescharacteristic
385#442C23112yes—
386#442C23112yes—
387#442C2316yes—
388#442C2316yes—
389#440C2316yes—
390#440C2316yes—
391C4×Q16C2313yes—
392C4×SD16C2316yes—
393C4×SD16C2316yes—
394C4×SD16C23112yes—
395C4×SD16C2316yes—
396C4×D8C2313yes—
397C4×D8C2313yes—
398C4×D8C2316yes—
399C4×D8C2316yes—
400C4×D8C23112yes—
401C4×D8C2313yes—
402C4×D8C2316yes—
403C4×D8C2316yes—
404C4×D8C2316yes—
405C4×D8C23112yes—
406C4×D8C23112yes—
407C4×D8C2313yes—
408C4×D8C2311yescharacteristic
409#436C2316yes—
410#436C2311yescharacteristic
411#436C2313yes—
412#436C23112yes—
413#435C2316yes—
414#435C2316yes—
415C8×D4C2313yes—
416C8×D4C2313yes—
417#433C23112yes—
418#431C2313yes—
419#431C2316yes—
420#431C2316yes—
421#431C2313yes—
422#428C23112yes—
423#428C23112yes—
424#428C2316yes—
425#427C2316yes—
426#427C2316yes—
427C2×#107C2313yes—
428#424C2316yes—
429#423C2313yes—
430#423C2316yes—
431#418C2316yes—
432#418C23112yes—
433#417C2316yes—
434C2×#102C2316yes—
435#405C2316yes—
436C4×M16C2316yes—
437C2×C4×C8C2313yes—
4382−1+4—88no—
439C2×#41—22no—
440C2×#41—26no—
441C2×#41—26no—
442C2×#41—26no—
443C2×#41—26no—
444C2×#41—26no—
445C2×#41—26no—
446C2×#41—88no—
447C2×#41C2×D411yescharacteristic
448C2×#41C2×D413yes—
449C2×#41C2412yes—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—26no—
453C22×Q8—26no—
454C22×Q8—26no—
455C22×Q8—26no—
456C22×Q8—88no—
457C22×Q8C2×D412yes—
458C22×D4—26no—
459C22×D4—26no—
460C22×D4C2412yes—
461C22×D4C2416yes—
462C23×C4—26no—
463C23×C4—26no—
464AGL(1,ℤ/8)—28no—
465C2×Q16C2411yescharacteristic
466C2×SD16C2412yes—
467C2×SD16C2412yes—
468C2×SD16C2416yes—
469C2×D8—212no—
470C2×D8C2416yes—
471C2×D8C2413yes—
472C2×D8C2412yes—
473C2×D8C2411yescharacteristic
474C2×D8C2416yes—
475C2×D8C2416yes—
476C2×D8C2411yescharacteristic
477C2×M16C2412yes—
478C2×M16C2416yes—
479C2×M16C2416yes—
480C22×C8C2413yes—
481C22×C8C2413yes—
482C4⋊Q8—26no—
483C4⋊Q8—26no—
484C4⋊Q8—212no—
485C4⋊Q8—26no—
486C4⋊Q8—26no—
487C4⋊Q8C2×D413yes—
488C4⋊Q8C2×D413yes—
489C4⋊Q8C2416yes—
490C4⋊Q8C2416yes—
491C4⋊Q8C24112yes—
492C4⋊Q8C2416yes—
493C4⋊Q8C2416yes—
494#127C2416yes—
495#127C2416yes—
496#126—212no—
497#126—26no—
498#126—26no—
499#126—212no—
500#126—212no—
501#126—26no—
502#126—26no—
503#126C2×D4112yes—
504#125—26no—
505#125—212no—
506#125—212no—
507#125C2×D416yes—
508#125C2×D416yes—
509#125C2416yes—
510#125C2416yes—
511#125C24112yes—
512#124—26no—
513#124—26no—
514#124—26no—
515#124—212no—
516#124—212no—
517#124—212no—
518#124—212no—
519#124—26no—
520#124—26no—
521#124—26no—
522#124—26no—
523#124C2×D416yes—
524#124C2412yes—
525#124C2416yes—
526#123—26no—
527#123—26no—
528#123—212no—
529#123—26no—
530#123—26no—
531#123—26no—
532#123—22no—
533#123—212no—
534#123—212no—
535#123—26no—
536#123—212no—
537#123—26no—
538#123—212no—
539#123—212no—
540#123C2×D4112yes—
541C22⋊Q8—26no—
542C22⋊Q8—26no—
543C22⋊Q8—26no—
544C22⋊Q8—212no—
545C22⋊Q8—26no—
546C22⋊Q8—26no—
547C22⋊Q8—26no—
548C22⋊Q8—26no—
549C22⋊Q8—26no—
550C22⋊Q8—26no—
551C22⋊Q8—26no—
552C22⋊Q8—26no—
553C22⋊Q8—26no—
554C22⋊Q8—26no—
555C22⋊Q8—212no—
556C22⋊Q8—212no—
557C22⋊Q8—212no—
558C22⋊Q8—26no—
559C22⋊Q8—26no—
560C22⋊Q8—212no—
561C22⋊Q8—212no—
562C22⋊Q8—212no—
563C22⋊Q8—212no—
564C22⋊Q8—212no—
565C22⋊Q8—212no—
566C22⋊Q8—212no—
567C22⋊Q8—26no—
568C22⋊Q8—26no—
569C22⋊Q8C2×D416yes—
570C22⋊Q8C2×D416yes—
571C22⋊Q8C2×D416yes—
572C22⋊Q8C2412yes—
573C22⋊Q8C2416yes—
574#121—212no—
575#121—26no—
576#121—26no—
577#121—26no—
578#121—212no—
579#121—26no—
580#121—26no—
581#121—26no—
582#121—26no—
583#121—26no—
584#121—26no—
585#121—26no—
586#121—26no—
587#121—212no—
588#121—212no—
589#121—22no—
590#121—26no—
591#121—212no—
592#121C2×D416yes—
593#121C2416yes—
594#121C2416yes—
595#121C2412yes—
596#121C2416yes—
597#121C24112yes—
598#120—22no—
599#120—26no—
600#120—26no—
601#120—212no—
602#120—26no—
603C4×Q8—22no—
604C4×Q8—26no—
605C4×Q8—26no—
606C4×Q8—26no—
607C4×Q8—26no—
608C4×Q8—26no—
609C4×Q8—26no—
610C4×Q8C2×D412yes—
611C4×Q8C2×D416yes—
612C4×Q8C2×D411yescharacteristic
613C4×Q8C2×D413yes—
614C4×Q8C2416yes—
615C4×Q8C2416yes—
616C4×Q8C2411yescharacteristic
617C4×Q8C2416yes—
618C4×Q8C2413yes—
619C4×D4—26no—
620C4×D4—26no—
621C4×D4—26no—
622C4×D4—26no—
623C4×D4—26no—
624C4×D4—26no—
625C4×D4—212no—
626C4×D4—212no—
627C4×D4—26no—
628C4×D4—26no—
629C4×D4—26no—
630C4×D4—212no—
631C4×D4—26no—
632C4×D4—26no—
633C4×D4—26no—
634C4×D4—26no—
635C4×D4—26no—
636C4×D4—26no—
637C4×D4—26no—
638C4×D4—26no—
639C4×D4C2×D416yes—
640C4×D4C2×D413yes—
641C4×D4C2×D413yes—
642C4×D4C2412yes—
643C4×D4C2416yes—
644C4×D4C2416yes—
645C4×D4C2416yes—
646C4×D4C2416yes—
647C4×D4C2416yes—
648C4×D4C2416yes—
649C4×D4C2416yes—
650C4×D4C24112yes—
651C4×D4C24112yes—
652C4×D4C2411yescharacteristic
653C4×D4C2413yes—
654C4×D4C2416yes—
655#117—26no—
656#117—212no—
657#117—26no—
658#117—26no—
659#117—26no—
660#117C2×D416yes—
661#117C2×D413yes—
662#117C2×D413yes—
663#117C2416yes—
664#117C24112yes—
665#117C2416yes—
666C2×C4⋊C4—26no—
667C2×C4⋊C4—26no—
668C2×C4⋊C4—26no—
669C2×C4⋊C4—26no—
670C2×C4⋊C4—212no—
671C2×C4⋊C4C2×D416yes—
672C2×C4⋊C4C2416yes—
673C2×C4⋊C4C2416yes—
674C2×C22⋊C4—26no—
675C2×C22⋊C4—26no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—26no—
678C2×C22⋊C4—212no—
679C2×C22⋊C4—212no—
680C2×C42—26no—
681C2×C42C2413yes—
682C2×C42C2416yes—
683#107C2411yescharacteristic
684#107C2413yes—
685#107C2416yes—
686#107C2413yes—
687#107C2413yes—
688#107C2416yes—
689#107C2416yes—
690#107C2416yes—
691#107C24112yes—
692#107C2416yes—
693#107C2416yes—
694#106C2416yes—
695#106C24112yes—
696#106C24112yes—
697#106C2416yes—
698#106C2416yes—
699C4⋊C8C2413yes—
700C4⋊C8C2416yes—
701C4⋊C8C2413yes—
702C4⋊C8C24112yes—
703C4⋊C8C2416yes—
704C4⋊C8C2413yes—
705C4⋊C8C2411yescharacteristic
706C4⋊C8C2416yes—
707#103C2416yes—
708#103C2416yes—
709#103C2412yes—
710#103C2416yes—
711#102C2412yes—
712#102C2416yes—
713#102C2416yes—
714#102C2416yes—
715#102C2416yes—
716#102C2416yes—
717#102C2416yes—
718#102C24112yes—
719#102C24112yes—
720#102C2416yes—
721#102C2416yes—
722#102C2412yes—
723#102C24112yes—
724#102C2416yes—
725#102C2416yes—
726C22⋊C8C2412yes—
727C22⋊C8C2416yes—
728C22⋊C8C2416yes—
729C22⋊C8C2416yes—
730#97C2416yes—
731#97C2416yes—
732C4×C8C2411yescharacteristic
733C4×C8C2413yes—
734C4×C8C2413yes—
735C4×C8C2413yes—
736C4×C8C2416yes—
737C4×C8C24112yes—
738C24—22no—
739C24—26no—
740#41—24no—
741#41—24no—
742#41—42no—
743#41—48no—
744#41—812no—
745#41—812no—
746#41—812no—
747#41—83no—
748#41—812no—
749#41—812no—
750#41—812no—
751C2×Q8—28no—
752C2×Q8—26no—
753C2×Q8—26no—
754C2×Q8—26no—
755C2×Q8—26no—
756C2×Q8—212no—
757C2×Q8—48no—
758C2×Q8—48no—
759C2×Q8—812no—
760C2×Q8—812no—
761C2×Q8—812no—
762C2×Q8—812no—
763C2×Q8C22×D416yes—
764C2×Q8C22×D413yes—
765C2×Q8C22×D411yescharacteristic
766C2×Q8C2512yes—
767C2×D4—212no—
768C2×D4—24no—
769C2×D4—22no—
770C2×D4—26no—
771C2×D4—26no—
772C2×D4—22no—
773C2×D4—26no—
774C2×D4—212no—
775C2×D4—26no—
776C2×D4—22no—
777C2×D4—26no—
778C2×D4—26no—
779C2×D4—26no—
780C2×D4—26no—
781C2×D4—46no—
782C2×D4—42no—
783C2×D4—812no—
784C2×D4—812no—
785C2×D4C22×D413yes—
786C2×D4C22×D416yes—
787C2×D4C22×D411yescharacteristic
788C2×D4C2516yes—
789C2×D4C2512yes—
790C2×D4C2512yes—
791C22×C4—26no—
792C22×C4—26no—
793C22×C4—22no—
794C22×C4—26no—
795C22×C4—26no—
796C22×C4—26no—
797C22×C4—26no—
798C22×C4—26no—
799C22×C4—22no—
800C22×C4—212no—
801C22×C4—212no—
802C22×C4—26no—
803C22×C4—26no—
804C22×C4—812no—
805C22×C4—812no—
806C22×C4C22×D416yes—
807C22×C4C22×D413yes—
808C22×C4C22×D413yes—
809C22×C4C22×D416yes—
810C22×C4C2512yes—
811C22×C4C2513yes—
812Q16—41no—
813SD16—24no—
814SD16—24no—
815SD16—46no—
816D8—212no—
817D8—24no—
818D8—26no—
819D8—41no—
820D8—46no—
821D8—46no—
822D82−1+414yescomplemented
823M16—24no—
824M16—46no—
825M16—46no—
826C2×C8—26no—
827C2×C8—43no—
828C2×C8C2513yes—
829C2×C8C2511yescharacteristic
830C2×C8C2512yes—
831C2×C8C2516yes—
832C2×C8C2513yes—
833C2×C8C2511yescharacteristic
834C4⋊C4—26no—
835C4⋊C4—26no—
836C4⋊C4—26no—
837C4⋊C4—212no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—212no—
843C4⋊C4—212no—
844C4⋊C4—26no—
845C4⋊C4—26no—
846C4⋊C4—22no—
847C4⋊C4—26no—
848C4⋊C4—26no—
849C4⋊C4—26no—
850C4⋊C4—26no—
851C4⋊C4C22×D416yes—
852C4⋊C4C22×D416yes—
853C4⋊C4C22×D413yes—
854C4⋊C4C22×D4112yes—
855C4⋊C4C22×D413yes—
856C4⋊C4C22×D416yes—
857C4⋊C4C22×D411yescharacteristic
858C4⋊C4C22×D413yes—
859C4⋊C4C22×D416yes—
860C4⋊C4C22×D416yes—
861C4⋊C4C2516yes—
862C4⋊C4C2512yes—
863C4⋊C4C2516yes—
864C4⋊C4C2516yes—
865C22⋊C4—212no—
866C22⋊C4—22no—
867C22⋊C4—26no—
868C22⋊C4—26no—
869C22⋊C4—26no—
870C22⋊C4—22no—
871C22⋊C4—26no—
872C22⋊C4—26no—
873C22⋊C4—26no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—26no—
877C22⋊C4—212no—
878C22⋊C4—26no—
879C22⋊C4—26no—
880C22⋊C4—26no—
881C22⋊C4—26no—
882C22⋊C4—212no—
883C22⋊C4—26no—
884C22⋊C4—22no—
885C22⋊C4—212no—
886C22⋊C4—26no—
887C22⋊C4—26no—
888C22⋊C4C22×D4112yes—
889C22⋊C4C22×D412yes—
890C22⋊C4C22×D416yes—
891C22⋊C4C22×D416yes—
892C22⋊C4C22×D416yes—
893C42—26no—
894C42—26no—
895C42—26no—
896C42—212no—
897C42C22×D416yes—
898C42C22×D413yes—
899C42C22×D416yes—
900C42C22×D413yes—
901C42C2511yescharacteristic
902C42C2513yes—
903C42C2516yes—
904C23—22no—
905C23—22no—
906C23—26no—
907C23—44no—
908C23—412no—
909C23—44no—
910C23—82no—
911C23—86no—
912C23—86no—
913C23C23×D413yes—
914C23C23×D412yes—
915Q8—212no—
916Q8—22no—
917Q8—22no—
918Q8—43no—
919Q8—412no—
920Q8—412no—
921Q8—812no—
922Q8—86no—
923Q8—86no—
924Q8#57614yes—
925D4—26no—
926D4—22no—
927D4—22no—
928D4—22no—
929D4—26no—
930D4—26no—
931D4—46no—
932D4—41no—
933D4—44no—
934D4—412no—
935D4—44no—
936D4—412no—
937D4—412no—
938D4—86no—
939D4—86no—
940D4—86no—
941D4—86no—
942D4—812no—
943D4—82no—
944D4—86no—
945D4C2×2−1+414yes—
946C2×C4—23no—
947C2×C4—22no—
948C2×C4—23no—
949C2×C4—22no—
950C2×C4—26no—
951C2×C4—212no—
952C2×C4—22no—
953C2×C4—26no—
954C2×C4—26no—
955C2×C4—26no—
956C2×C4—22no—
957C2×C4—43no—
958C2×C4—46no—
959C2×C4—44no—
960C2×C4—412no—
961C2×C4—412no—
962C2×C4—412no—
963C2×C4—82no—
964C2×C4—86no—
965C2×C4—86no—
966C2×C4—86no—
967C2×C4—86no—
968C2×C4—812no—
969C2×C4—812no—
970C2×C4—86no—
971C2×C4—86no—
972C2×C4C23×D413yes—
973C2×C4C23×D412yes—
974C2×C4C23×D416yes—
975C2×C4C23×D411yescharacteristic
976C2×C4C23×D413yes—
977C2×C4C23×D411yescharacteristic
978C2×C4C23×D416yes—
979C2×C4C23×D413yes—
980C2×C4C2611yescharacteristic
981C8—23no—
982C8—22no—
983C8—21no—
984C8—23no—
985C8—26no—
986C8C2×2−1+412yes—
987C22—22no—
988C22—23no—
989C22—24no—
990C22—22no—
991C22—23no—
992C22—22no—
993C22—23no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—46no—
998C22—42no—
999C22—46no—
1000C22—46no—
1001C22—42no—
1002C22—88no—
1003C22—1612no—
1004C22C24×D411yescharacteristic
1005C4—22no—
1006C4—23no—
1007C4—21no—
1008C4—26no—
1009C4—21no—
1010C4—23no—
1011C4—26no—
1012C4—42no—
1013C4—42no—
1014C4—46no—
1015C4—46no—
1016C4—46no—
1017C4C2×#57616yes—
1018C4C22×2−1+411yescharacteristic
1019C42−1+611yescharacteristic
1020C2—42no—
1021C2—43no—
1022C2—44no—
1023C2—82no—
1024C2—86no—
1025C2D4×2−1+411yescharacteristic
1026C2C22×#57611yescharacteristic
1027C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3482 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63015C2semidirect
2. #62520C2semidirect
3. #62481C2semidirect
4. #62476C2semidirect
5. #62397C2semidirect
6. #62384C2semidirect
7. #62187C2semidirect
8. #62180C2semidirect
9. #62151C2semidirect
10. #62143C2semidirect
11. #61863C2semidirect
12. #61823C2semidirect
13. #61817C2semidirect
14. #61539C2semidirect
15. #61444C2semidirect
16. D8×#41C2semidirect
17. #61370C2semidirect
18. Q8×AGL(1,ℤ/8)C2semidirect
19. #60345C2semidirect
21. #3554C22semidirect
22. #3552C22semidirect
23. #3547C22semidirect
26. #3522C22semidirect
28. #3519C22semidirect
29. #3518C22semidirect
31. #3514C22semidirect
32. #3511C22semidirect
33. #3501C22semidirect
34. #3497C22semidirect
38. #3481C22semidirect
39. Q8×#41C22semidirect
40. D4×#41C22semidirect
41. C2×D4×Q8C22semidirect
43. #3403C22semidirect
44. #3399C22semidirect
45. #3391C22semidirect
47. #3389C22semidirect
48. #3389C22semidirect
49. #3386C22semidirect
50. #3386C22semidirect
52. #3384C22semidirect
53. #3384C22semidirect
54. Q8×Q16C22semidirect
55. #3381C22semidirect
56. #3380C22semidirect
57. #3380C22semidirect
58. Q8×SD16C22semidirect
59. Q8×SD16C22semidirect
61. Q8×D8C22semidirect
62. Q8×D8C22semidirect
63. Q8×D8C22semidirect
64. Q8×D8C22semidirect
65. #3373C22semidirect
66. #3370C22semidirect
67. #3366C22semidirect
68. #3365C22semidirect
69. #3362C22semidirect
70. #3361C22semidirect
71. #3361C22semidirect
72. #3358C22semidirect
73. #3358C22semidirect
74. #3358C22semidirect
75. #3358C22semidirect
76. #3357C22semidirect
77. #3355C22semidirect
78. #3355C22semidirect
79. #3355C22semidirect
80. #3354C22semidirect
81. #3353C22semidirect
82. #3347C22semidirect
83. #3347C22semidirect
84. #3346C22semidirect
85. #3342C22semidirect
86. #3341C22semidirect
87. #3340C22semidirect
88. #3334C22semidirect
89. #3325C22semidirect
90. #3325C22semidirect
91. #3324C22semidirect
92. #3322C22semidirect
93. #3322C22semidirect
94. #3318C22semidirect
95. #3314C22semidirect
96. #3294C22semidirect
100. #3262C22semidirect
101. #3259C22semidirect
102. #3253C22semidirect
103. #3251C22semidirect
104. #3251C22semidirect
105. #3243C22semidirect
106. #3241C22semidirect
107. #3233C22semidirect
108. #3233C22semidirect
109. #3228C22semidirect
110. #3228C22semidirect
111. #3226C22semidirect
112. #3226C22semidirect
113. #3184C22semidirect
114. #3179C22semidirect
115. #3171C22semidirect
116. #3169C22semidirect
117. #3168C22semidirect
118. #3165C22semidirect
119. #3164C22semidirect
120. #3160C22semidirect
121. #3122C22semidirect
122. #3118C22semidirect
123. #3106C22semidirect
124. #3105C22semidirect
125. #3102C22semidirect
126. #3100C22semidirect
127. #3100C22semidirect
128. #3100C22semidirect
129. #3081C22semidirect
130. #3079C22semidirect
131. #3077C22semidirect
132. #3077C22semidirect
133. #2993C22semidirect
134. #2991C22semidirect
135. #2991C22semidirect
136. #2986C22semidirect
137. #2982C22semidirect
138. #2969C22semidirect
139. #2965C22semidirect
140. C8×#41C22semidirect
141. Q8×M16C22semidirect
142. #2960C22semidirect
822. D82−1+4semidirect

Maximal subgroups

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

subgroupindex
#630152
#625202
#624812
#624762
#623972
#623842
#621872
#621802
#621512
#621432
#618632
#618232
#618172
#615392
#614442
D8×#412
#613702
Q8×AGL(1,ℤ/8)2
#603452