Finite Group Databasebeta

← #10577084

Subgroups — #10577084

Order 512.

6740 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62984C212yesmaximal, complemented
2#61553C2112yesmaximal, complemented
3#61482C216yesmaximal, complemented
4#61475C216yesmaximal, complemented
5#61466C214yesmaximal, complemented
6#61435C212yesmaximal, complemented
7D8×#41C212yesmaximal, complemented
8#61393C211yesmaximal, characteristic, complemented
9C2×Q8×D8C211yesmaximal, characteristic, complemented
10#61317C212yesmaximal, complemented
11#61287C213yesmaximal, complemented
12#61199C216yesmaximal, complemented
13#61084C213yesmaximal, complemented
14#60718C213yesmaximal, complemented
15#60596C216yesmaximal, complemented
16#60218C211yesmaximal, characteristic, complemented
17C4×#576C213yesmaximal, complemented
18C2×#576C2213yes—
19#3520—26no—
20#3520C22112yescomplemented
21#3514—26no—
22#3514C22112yescomplemented
23#3511C2216yescomplemented
24#3511C2216yescomplemented
25#3505—212no—
26#3496C2216yescomplemented
27#3482—22no—
28#3482C2214yescomplemented
29#3480C2211yescharacteristic
30#3480C2212yescomplemented
31D4×#41—22no—
32D4×#41C2214yescomplemented
33C2×D4×Q8C2212yescomplemented
34C2×#548—24no—
35C4×H(5,𝔽2)C2216yescomplemented
36#3396C2213yescomplemented
37#3395C2211yescharacteristic, complemented
38#3394C2216yescomplemented
39#3393C2213yescomplemented
40#3392C2212yescomplemented
41#3391C2211yescharacteristic, complemented
42Q8×D8C2212yescomplemented
43Q8×D8C2216yescomplemented
44Q8×D8C2216yescomplemented
45Q8×D8C2212yescomplemented
46#3373C22112yescomplemented
47#3367C22112yescomplemented
48#3359C2214yescomplemented
49#3358C2214yescomplemented
50#3357C22112yescomplemented
51#3353C22112yescomplemented
52#3342C2216yescomplemented
53#3341C2216yescomplemented
54#3338C2216yescomplemented
55#3334C2216yescomplemented
56#3330C22112yescomplemented
57#3324C22112yescomplemented
58#3319C22124yescomplemented
59#3314C22124yescomplemented
60#3302C22112yescomplemented
61#3294C22112yescomplemented
62#3283C2216yescomplemented
63#3280C22112yescomplemented
64D4×D8C2216yescomplemented
65#3273C22112yescomplemented
66#3272C22112yescomplemented
67#3182C22112yescomplemented
68#3175C22112yescomplemented
69#3175C22112yescomplemented
70#3170C2216yescomplemented
71#3169C2216yescomplemented
72C2×#500C2213yescomplemented
73#3147C2213yescomplemented
74#3141C2216yescomplemented
75#3124C22124yescomplemented
76#3118C22124yescomplemented
77#3115C22112yescomplemented
78#3110C22112yescomplemented
79#3107C22112yescomplemented
80#3100C22112yescomplemented
81#3098C22112yescomplemented
82#3079C2216yescomplemented
83C2×#474C2216yescomplemented
84#3061C2216yescomplemented
85#3061C2216yescomplemented
86#3036C2216yescomplemented
87#3035C2216yescomplemented
88#3012C22112yescomplemented
89#2971C2212yescomplemented
90#2969C2216yescomplemented
91#2966C2216yescomplemented
92C8×#41C2212yescomplemented
93Q8×M16C2211yescharacteristic, complemented
94C2×C8×Q8C2211yescharacteristic, complemented
95#2951C2216yescomplemented
96#2951C2213yescomplemented
97#2951C2216yescomplemented
98#2948C2211yescharacteristic
99#2948C2216yescomplemented
100#2946C22112yescomplemented
101#2946C2216yescomplemented
102C4×AGL(1,ℤ/8)C2216yescomplemented
103C4×AGL(1,ℤ/8)C22112yescomplemented
104C4×#135C2216yescomplemented
105C4×#135C2213yescomplemented
106C2×C4×D8C2213yes—
107C2×C4×D8C2216yescomplemented
108#2935C2213yescomplemented
109#2931C2213yescomplemented
110#2925C2213yescomplemented
111#2913C2213yescomplemented
112#2897C2216yescomplemented
113C4×#131C2213yescomplemented
114C2×H(5,𝔽2)C2316yes—
115C22×#41—24no—
116C23×Q8—22no—
117#576—224no—
118C2×AGL(1,ℤ/8)C2316yes—
119C2×AGL(1,ℤ/8)C23112yes—
120C2×#135C2313yes—
121C2×#135C2316yes—
122C2×#135C2316yes—
123C22×D8C2316yes—
124C22×D8C2311yescharacteristic
125C2×#131C2313yes—
126C2×#131C2313yes—
127#559D413yes—
128#559C2316yes—
129#557D411yescharacteristic
130#557C2312yes—
131#556—26no—
132#556D413yes—
133#556C2316yes—
134#556C23112yes—
135#555—26no—
136#555C23112yes—
137#554—26no—
138#554C23112yes—
139#553—212no—
140#553—212no—
141#553—26no—
142#553D416yes—
143#552—212no—
144#552—212no—
145#551—224no—
146#551—224no—
147#550D411yescharacteristic
148#550C2312yes—
149D4×Q8—22no—
150D4×Q8—26no—
151D4×Q8C2314yes—
152D4×Q8C23112yes—
153#548—24no—
154#548—22no—
155#548—212no—
156#548—212no—
157#548—212no—
158#548—24no—
159#548—212no—
160#548D412yes—
161#547—26no—
162#547—26no—
163#547C23112yes—
164#547C23112yes—
165#546—212no—
166#546—212no—
167#546—212no—
168#546C23124yes—
169D42—26no—
170D42C23112yes—
171#542—212no—
172#542C23124yes—
173#539—224no—
174#538—224no—
175#537C23112yes—
176#534—212no—
177#533—26no—
178#533C23112yes—
179#532—26no—
180#532C2316yes—
181#532C23112yes—
182#532C2313yes—
183C2×C4⋊Q8C2316yes—
184#529—212no—
185#529—26no—
186#529—212no—
187#529C2316yes—
188C2×#124—212no—
189#525—212no—
190#525—212no—
191C2×C22⋊Q8—212no—
192C2×C22⋊Q8—26no—
193C2×#121—212no—
194#520—26no—
195#520C23112yes—
196#520C2316yes—
197#520C2316yes—
198#518—212no—
199#518—26no—
200#518C23112yes—
201#518C2312yes—
202C4×#41—26no—
203C4×#41—22no—
204C4×#41C2316yes—
205C4×#41C23112yes—
206C4×#41C2312yes—
207C4×#41C2313yes—
208C2×C4×Q8—24no—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×D4—212no—
211C2×C4×D4—26no—
212C2×C4×D4C23112yes—
213C2×C4×D4C2316yes—
214#500C2316yes—
215#500C2316yes—
216#500C2316yes—
217#500C2316yes—
218#495C2316yes—
219#495C2316yes—
220#494C2313yes—
221#493C2313yes—
222#492C2316yes—
223#489C23124yes—
224#487C23112yes—
225#486C23112yes—
226#485C23124yes—
227#484C23124yes—
228#482C23124yes—
229#480C23124yes—
230#477C23112yes—
231#476C23112yes—
232#475C23112yes—
233#474C23112yes—
234#474C23112yes—
235#474C23112yes—
236#474C23124yes—
237#468C23124yes—
238#468C23124yes—
239#467C23112yes—
240#467C23112yes—
241#466C23112yes—
242#466C23112yes—
243#464C23112yes—
244#463C23124yes—
245#463C23112yes—
246#462C2316yes—
247#461C2316yes—
248#461C23112yes—
249#460C2316yes—
250#459C2316yes—
251#459C23112yes—
252#452C23124yes—
253#450C23124yes—
254#449C23124yes—
255#447C23124yes—
256#446C2316yes—
257C8×Q8C2312yes—
258C8×Q8C2311yescharacteristic
259C8×Q8C2311yescharacteristic
260C8×Q8C2313yes—
261C8×Q8C2313yes—
262#442C23112yes—
263#442C23112yes—
264#442C2314yes—
265#440C23112yes—
266#440C23124yes—
267#440C23112yes—
268#440C23112yes—
269C4×Q16C2313yes—
270C4×Q16C2313yes—
271C4×Q16C23112yes—
272C4×Q16C2316yes—
273C4×SD16C2316yes—
274C4×SD16C2316yes—
275C4×SD16C23112yes—
276C4×SD16C23112yes—
277C4×D8C23112yes—
278C4×D8C2313yes—
279C4×D8C2313yes—
280C4×D8C23112yes—
281C4×D8C23112yes—
282C4×D8C2316yes—
283C4×D8C2316yes—
284C4×D8C2316yes—
285C4×D8C2316yes—
286C4×D8C2316yes—
287C4×D8C2312yes—
288C4×D8C2312yes—
289#436C2316yes—
290#436C2316yes—
291#436C2316yes—
292#435C23112yes—
293C8×D4C2316yes—
294C8×D4C2316yes—
295C8×D4C2316yes—
296#433C23112yes—
297#432C2316yes—
298#431C2316yes—
299#428C2316yes—
300#428C23112yes—
301#427C2316yes—
302#427C2311yescharacteristic
303C2×#107C2316yes—
304C2×#107C2316yes—
305C2×#107C2313yes—
306#423C2313yes—
307C2×C4⋊C8C2313yes—
308#418C2312yes—
309#418C23112yes—
310#417C23112yes—
311#417C23112yes—
312#417C2316yes—
313#416C2316yes—
314#416C23112yes—
315C2×#102C2316yes—
316C2×#102C23112yes—
317#408C2316yes—
318#405C2311yescharacteristic
319#405C2316yes—
320#405C2316yes—
321#405C2313yes—
322C4×M16C2313yes—
323C4×M16C2316yes—
324C2×C4×C8C2313yes—
325C2×C4×C8C2316yes—
326H(5,𝔽2)—224no—
327H(5,𝔽2)—412no—
328C2×#41—26no—
329C2×#41—22no—
330C2×#41—212no—
331C2×#41—212no—
332C2×#41—816no—
333C2×#41C2×D412yes—
334C2×#41C2416yes—
335C2×#41C24112yes—
336C2×#41C2413yes—
337C22×Q8—24no—
338C22×Q8—212no—
339C22×Q8—26no—
340C22×Q8—88no—
341C22×Q8C2×D411yescharacteristic
342C22×D4—212no—
343C22×D4—26no—
344C22×D4—212no—
345C22×D4C24112yes—
346C22×D4C2412yes—
347C23×C4—26no—
348C23×C4—212no—
349AGL(1,ℤ/8)—224no—
350AGL(1,ℤ/8)—248no—
351#135—224no—
352#135—212no—
353#135—412no—
354C2×Q16C2413yes—
355C2×Q16C2416yes—
356C2×SD16C24112yes—
357C2×SD16C2416yes—
358C2×SD16C24112yes—
359C2×D8—224no—
360C2×D8#4118yescomplemented
361C2×D8C2413yes—
362C2×D8C24112yes—
363C2×D8C2416yes—
364C2×D8C2412yes—
365C2×D8C2412yes—
366#131—212no—
367#131—46no—
368C2×M16C2411yescharacteristic
369C2×M16C2413yes—
370C2×M16C2416yes—
371C2×M16C2416yes—
372C22×C8C2416yes—
373C22×C8C2413yes—
374C22×C8C2416yes—
375C22×C8C2411yescharacteristic
376C4⋊Q8—26no—
377C4⋊Q8—26no—
378C4⋊Q8C2×D413yes—
379C4⋊Q8C2416yes—
380C4⋊Q8C24112yes—
381C4⋊Q8C24112yes—
382#127C2×D413yes—
383#127C2416yes—
384#126—224no—
385#126—212no—
386#126—224no—
387#126C2×D4112yes—
388#125—26no—
389#125—212no—
390#125—212no—
391#125C2×D416yes—
392#124—26no—
393#124—212no—
394#124—224no—
395#124—224no—
396#124—212no—
397#124C2×D416yes—
398#124C2×D416yes—
399#124C24112yes—
400#123—224no—
401#123—212no—
402#123—224no—
403#123—224no—
404#123—224no—
405#123C2×D4112yes—
406C22⋊Q8—26no—
407C22⋊Q8—212no—
408C22⋊Q8—212no—
409C22⋊Q8—212no—
410C22⋊Q8—212no—
411C22⋊Q8—212no—
412C22⋊Q8—224no—
413C22⋊Q8—224no—
414C22⋊Q8—224no—
415C22⋊Q8C2×D416yes—
416C22⋊Q8C24124yes—
417#121—212no—
418#121—224no—
419#121—212no—
420#121—212no—
421#121—26no—
422#121—26no—
423#121—212no—
424#121—212no—
425#121—26no—
426#121—224no—
427#121C2×D416yes—
428#121C2×D416yes—
429#121C2×D416yes—
430#121C24124yes—
431#120—224no—
432#120—224no—
433C4×Q8—22no—
434C4×Q8—26no—
435C4×Q8—212no—
436C4×Q8—212no—
437C4×Q8C2×D412yes—
438C4×Q8C2×D411yescharacteristic
439C4×Q8C2×D413yes—
440C4×Q8C2×D413yes—
441C4×Q8C2×D413yes—
442C4×Q8C2416yes—
443C4×Q8C24112yes—
444C4×Q8C2416yes—
445C4×Q8C2411yescharacteristic
446C4×Q8C2413yes—
447C4×D4—26no—
448C4×D4—212no—
449C4×D4—212no—
450C4×D4—212no—
451C4×D4—26no—
452C4×D4—212no—
453C4×D4—26no—
454C4×D4—22no—
455C4×D4—212no—
456C4×D4—22no—
457C4×D4—212no—
458C4×D4—26no—
459C4×D4—212no—
460C4×D4—212no—
461C4×D4—212no—
462C4×D4—26no—
463C4×D4—212no—
464C4×D4—212no—
465C4×D4—26no—
466C4×D4—26no—
467C4×D4—212no—
468C4×D4—26no—
469C4×D4C2×D413yes—
470C4×D4C2×D416yes—
471C4×D4C2×D416yes—
472C4×D4C2×D413yes—
473C4×D4C2×D416yes—
474C4×D4C2414yes—
475C4×D4C24112yes—
476C4×D4C2416yes—
477C4×D4C24112yes—
478C4×D4C24112yes—
479C4×D4C2414yes—
480C4×D4C2416yes—
481C4×D4C2416yes—
482C4×D4C2416yes—
483#117—212no—
484#117—212no—
485#117—26no—
486#117—26no—
487#117—212no—
488#117—26no—
489#117—212no—
490#117C2×D416yes—
491#117C2412yes—
492#117C24112yes—
493#117C2411yescharacteristic
494#117C2416yes—
495C2×C4⋊C4—26no—
496C2×C4⋊C4—212no—
497C2×C4⋊C4—26no—
498C2×C4⋊C4—212no—
499C2×C4⋊C4C2×D413yes—
500C2×C4⋊C4C2416yes—
501C2×C4⋊C4C24112yes—
502C2×C22⋊C4—26no—
503C2×C22⋊C4—212no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—212no—
506C2×C22⋊C4—212no—
507C2×C22⋊C4—224no—
508C2×C42—212no—
509C2×C42—26no—
510C2×C42C2413yes—
511C2×C42C2416yes—
512#107C2411yescharacteristic
513#107C2416yes—
514#107C2416yes—
515#107C24112yes—
516#107C24112yes—
517#107C24112yes—
518#107C2411yescharacteristic
519#106C2412yes—
520#106C24112yes—
521C4⋊C8C2413yes—
522C4⋊C8C2413yes—
523C4⋊C8C2416yes—
524C4⋊C8C2416yes—
525C4⋊C8C2416yes—
526#103C2416yes—
527#103C2416yes—
528#103C24112yes—
529#103C24124yes—
530#102C2414yes—
531#102C24112yes—
532#102C2416yes—
533#102C24112yes—
534#102C24112yes—
535#102C2414yes—
536#102C2416yes—
537#102C24124yes—
538C22⋊C8C24112yes—
539C22⋊C8C24112yes—
540#97C2412yes—
541#97C2416yes—
542#97C2416yes—
543C4×C8C2412yes—
544C4×C8C2413yes—
545C4×C8C2416yes—
546C4×C8C2413yes—
547C4×C8C2416yes—
548C4×C8C2413yes—
549C4×C8C2413yes—
550C24—22no—
551C24—212no—
552#41—28no—
553#41—26no—
554#41—26no—
555#41—224no—
556#41—212no—
557#41—212no—
558#41—412no—
559#41—424no—
560#41—48no—
561#41—824no—
562#41—824no—
563C2×Q8—24no—
564C2×Q8—212no—
565C2×Q8—212no—
566C2×Q8—416no—
567C2×Q8—812no—
568C2×Q8—824no—
569C2×Q8C22×D413yes—
570C2×Q8C22×D413yes—
571C2×Q8C22×D411yescharacteristic
572C2×Q8C2516yes—
573C2×D4—224no—
574C2×D4—212no—
575C2×D4—26no—
576C2×D4—224no—
577C2×D4—22no—
578C2×D4—212no—
579C2×D4—26no—
580C2×D4—26no—
581C2×D4—24no—
582C2×D4—412no—
583C2×D4—424no—
584C2×D4—448no—
585C2×D4—824no—
586C2×D4C22×D416yes—
587C2×D4C22×D413yes—
588C2×D4C22×D416yes—
589C2×D4C22×D416yes—
590C2×D4C2×#4118yescomplemented
591C2×D4C2516yes—
592C2×D4C2514yes—
593C22×C4—26no—
594C22×C4—212no—
595C22×C4—212no—
596C22×C4—26no—
597C22×C4—212no—
598C22×C4—26no—
599C22×C4—24no—
600C22×C4—26no—
601C22×C4—212no—
602C22×C4—24no—
603C22×C4—212no—
604C22×C4—812no—
605C22×C4—824no—
606C22×C4C22×D413yes—
607C22×C4C22×D416yes—
608C22×C4C22×D413yes—
609C22×C4C22×D416yes—
610C22×C4C2516yes—
611C22×C4C2511yescharacteristic
612Q16—26no—
613Q16—46no—
614SD16—224no—
615SD16—212no—
616SD16—412no—
617D8—224no—
618D8—26no—
619D8—46no—
620D8C2×#4118yescomplemented
621D8C2×#4118yescomplemented
622M16—26no—
623M16—22no—
624M16—212no—
625M16—46no—
626C2×C8—26no—
627C2×C8—212no—
628C2×C8—46no—
629C2×C8C2×#4114yescomplemented
630C2×C8C2512yes—
631C2×C8C2513yes—
632C2×C8C2513yes—
633C2×C8C2516yes—
634C2×C8C2511yescharacteristic
635C2×C8C2511yescharacteristic
636C4⋊C4—26no—
637C4⋊C4—212no—
638C4⋊C4—26no—
639C4⋊C4—26no—
640C4⋊C4—212no—
641C4⋊C4—212no—
642C4⋊C4—212no—
643C4⋊C4—224no—
644C4⋊C4—26no—
645C4⋊C4—26no—
646C4⋊C4C22×D411yescharacteristic
647C4⋊C4C22×D416yes—
648C4⋊C4C22×D416yes—
649C4⋊C4C22×D413yes—
650C4⋊C4C22×D413yes—
651C4⋊C4C22×D416yes—
652C4⋊C4C22×D411yescharacteristic
653C4⋊C4C22×D416yes—
654C4⋊C4C22×D416yes—
655C4⋊C4C2512yes—
656C4⋊C4C2512yes—
657C4⋊C4C25112yes—
658C22⋊C4—22no—
659C22⋊C4—212no—
660C22⋊C4—224no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—212no—
664C22⋊C4—212no—
665C22⋊C4—26no—
666C22⋊C4—212no—
667C22⋊C4—26no—
668C22⋊C4—212no—
669C22⋊C4—224no—
670C22⋊C4—212no—
671C22⋊C4C22×D412yes—
672C22⋊C4C22×D416yes—
673C22⋊C4C22×D416yes—
674C22⋊C4C22×D4112yes—
675C22⋊C4C22×D4112yes—
676C42—22no—
677C42—26no—
678C42—26no—
679C42—212no—
680C42—212no—
681C42C22×D413yes—
682C42C22×D416yes—
683C42C22×D416yes—
684C42C22×D413yes—
685C42C2512yes—
686C42C2513yes—
687C42C2513yes—
688C23—24no—
689C23—28no—
690C23—26no—
691C23—424no—
692C23—82no—
693C23—82no—
694C23—812no—
695C23—812no—
696C23C23×D416yes—
697C23C23×D411yescharacteristic
698Q8—26no—
699Q8—26no—
700Q8—26no—
701Q8—26no—
702Q8—424no—
703Q8—812no—
704Q8#57614yescomplemented
705D4—212no—
706D4—26no—
707D4—24no—
708D4—26no—
709D4—28no—
710D4—26no—
711D4—212no—
712D4—46no—
713D4—424no—
714D4—424no—
715D4—412no—
716D4—412no—
717D4—86no—
718D4—824no—
719D4C22×#4118yes—
720C2×C4—26no—
721C2×C4—26no—
722C2×C4—26no—
723C2×C4—212no—
724C2×C4—22no—
725C2×C4—26no—
726C2×C4—22no—
727C2×C4—212no—
728C2×C4—46no—
729C2×C4—43no—
730C2×C4—424no—
731C2×C4—412no—
732C2×C4—424no—
733C2×C4—412no—
734C2×C4—84no—
735C2×C4—86no—
736C2×C4—84no—
737C2×C4—812no—
738C2×C4—812no—
739C2×C4—86no—
740C2×C4—812no—
741C2×C4C23×D412yes—
742C2×C4C23×D416yes—
743C2×C4C23×D413yes—
744C2×C4C23×D413yes—
745C2×C4C23×D412yes—
746C2×C4C23×D413yes—
747C2×C4C23×D411yescharacteristic
748C2×C4C23×D413yes—
749C2×C4C22×#4112yes—
750C2×C4#58512yes—
751C2×C4C2611yescharacteristic
752C8—26no—
753C8—23no—
754C8—23no—
755C8—22no—
756C8C22×#4112yes—
757C8C22×#4112yes—
758C22—21no—
759C22—21no—
760C22—26no—
761C22—26no—
762C22—26no—
763C22—28no—
764C22—44no—
765C22—44no—
766C22—46no—
767C22—46no—
768C22—46no—
769C22—88no—
770C22—1624no—
771C22D4×#4112yes—
772C22C24×D411yescharacteristic
773C4—22no—
774C4—23no—
775C4—22no—
776C4—23no—
777C4—23no—
778C4—26no—
779C4—42no—
780C4—412no—
781C4—42no—
782C4—46no—
783C4D4×#4112yes—
784C4C2×#57616yes—
785C4C23×#4111yescharacteristic
786C4C2×#58511yescharacteristic
787C2—22no—
788C2—46no—
789C2—48no—
790C2—86no—
791C2C2×D4×#4111yescharacteristic
792C2C22×#57611yescharacteristic
793C2#6309311yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3480 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62984C2semidirect
2. #61553C2semidirect
3. #61482C2semidirect
4. #61475C2semidirect
5. #61466C2semidirect
6. #61435C2semidirect
7. D8×#41C2semidirect
8. #61393C2semidirect
9. C2×Q8×D8C2semidirect
10. #61317C2semidirect
11. #61287C2semidirect
12. #61199C2semidirect
13. #61084C2semidirect
14. #60718C2semidirect
15. #60596C2semidirect
16. #60218C2semidirect
17. C4×#576C2semidirect
20. #3520C22semidirect
22. #3514C22semidirect
23. #3511C22semidirect
24. #3511C22semidirect
26. #3496C22semidirect
28. #3482C22semidirect
30. #3480C22semidirect
32. D4×#41C22semidirect
33. C2×D4×Q8C22semidirect
35. C4×H(5,𝔽2)C22semidirect
36. #3396C22semidirect
37. #3395C22semidirect
38. #3394C22semidirect
39. #3393C22semidirect
40. #3392C22semidirect
41. #3391C22semidirect
42. Q8×D8C22semidirect
43. Q8×D8C22semidirect
44. Q8×D8C22semidirect
45. Q8×D8C22semidirect
46. #3373C22semidirect
47. #3367C22semidirect
48. #3359C22semidirect
49. #3358C22semidirect
50. #3357C22semidirect
51. #3353C22semidirect
52. #3342C22semidirect
53. #3341C22semidirect
54. #3338C22semidirect
55. #3334C22semidirect
56. #3330C22semidirect
57. #3324C22semidirect
58. #3319C22semidirect
59. #3314C22semidirect
60. #3302C22semidirect
61. #3294C22semidirect
62. #3283C22semidirect
63. #3280C22semidirect
64. D4×D8C22semidirect
65. #3273C22semidirect
66. #3272C22semidirect
67. #3182C22semidirect
68. #3175C22semidirect
69. #3175C22semidirect
70. #3170C22semidirect
71. #3169C22semidirect
72. C2×#500C22semidirect
73. #3147C22semidirect
74. #3141C22semidirect
75. #3124C22semidirect
76. #3118C22semidirect
77. #3115C22semidirect
78. #3110C22semidirect
79. #3107C22semidirect
80. #3100C22semidirect
81. #3098C22semidirect
82. #3079C22semidirect
83. C2×#474C22semidirect
84. #3061C22semidirect
85. #3061C22semidirect
86. #3036C22semidirect
87. #3035C22semidirect
88. #3012C22semidirect
89. #2971C22semidirect
90. #2969C22semidirect
91. #2966C22semidirect
92. C8×#41C22semidirect
93. Q8×M16C22semidirect
94. C2×C8×Q8C22semidirect
95. #2951C22semidirect
96. #2951C22semidirect
97. #2951C22semidirect
99. #2948C22semidirect
100. #2946C22semidirect
101. #2946C22semidirect
102. C4×AGL(1,ℤ/8)C22semidirect
103. C4×AGL(1,ℤ/8)C22semidirect
104. C4×#135C22semidirect
105. C4×#135C22semidirect
107. C2×C4×D8C22semidirect
108. #2935C22semidirect
109. #2931C22semidirect
110. #2925C22semidirect
111. #2913C22semidirect
112. #2897C22semidirect
113. C4×#131C22semidirect
360. C2×D8#41semidirect
590. C2×D4C2×#41semidirect
620. D8C2×#41semidirect
621. D8C2×#41semidirect
629. C2×C8C2×#41semidirect
704. Q8#576semidirect

Maximal subgroups

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

subgroupindex
#629842
#615532
#614822
#614752
#614662
#614352
D8×#412
#613932
C2×Q8×D82
#613172
#612872
#611992
#610842
#607182
#605962
#602182
C4×#5762