Finite Group Databasebeta

← #6343264

Subgroups — #6343264

Order 512.

2836 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62759C211yesmaximal, characteristic
2#60293C211yesmaximal, characteristic, complemented
3#60279C211yesmaximal, characteristic, complemented
4#17526C214yesmaximal, complemented
5#17521C214yesmaximal, complemented
6#17513C214yesmaximal, complemented
7#17511C214yesmaximal, complemented
8#17505C214yesmaximal, complemented
9#17495C211yesmaximal, characteristic, complemented
10#17493C211yesmaximal, characteristic, complemented
11#17483C214yesmaximal, complemented
12#17482C211yesmaximal, characteristic, complemented
13#17478C211yesmaximal, characteristic, complemented
14#3551—22no—
15#3550C411yescharacteristic
16#3549C411yescharacteristic
17#3548C411yescharacteristic
18#3548C411yescharacteristic
19#3547—21no—
20#3547C412yes—
21#3546—21no—
22#3546C412yes—
23#3545—22no—
24#3544C412yes—
25#3543C412yes—
26#3542—22no—
27#3542C414yes—
28#3529—22no—
29#3483C2212yes—
30#3481C2212yes—
31#3475—21no—
32#3475C2212yes—
33D4×#41—21no—
34D4×#41C2212yes—
35#3460—22no—
36#3460C2214yes—
37#3449—22no—
38#3444C2211yescharacteristic
39#3444C2211yescharacteristic
40C2×#532C2211yescharacteristic
41#2993—22no—
42#2992—22no—
43#2990C2214yescomplemented
44#2989C2214yescomplemented
45#2987—21no—
46#2985—21no—
47#2981—21no—
48#2980—21no—
49#2976—22no—
50#2976—22no—
51#2968—22no—
52#2967—22no—
53#2965C2212yescomplemented
54#2965C2214yescomplemented
55C8×#41C2212yescomplemented
56#2925C2214yescomplemented
57#2922C2214yescomplemented
58#2920C2211yescharacteristic, complemented
59#2920C2211yescharacteristic, complemented
60C2×#432C2211yescharacteristic, complemented
61C2×#431C2211yescharacteristic, complemented
62#1497C2212yescomplemented
63#1496C2212yes—
64#1496C2212yes—
65#1496C2212yescomplemented
66#1496C2214yescomplemented
67#1496C2214yescomplemented
68#1495C2214yescomplemented
69#1495C2214yescomplemented
70#1494C2212yescomplemented
71#1494C2212yescomplemented
72#1494C2214yescomplemented
73#1492C2212yescomplemented
74#1492C2212yescomplemented
75#1492C2214yescomplemented
76#1490C2214yescomplemented
77#1490C2214yescomplemented
78#1489C2214yescomplemented
79#1488C2214yescomplemented
80#1488C2214yescomplemented
81#1486C2214yescomplemented
82#1485C2212yescomplemented
83#1484C2212yes—
84#1484C2214yescomplemented
85#1483C2214yescomplemented
86#1482C2214yescomplemented
87#1480C2212yes—
88#1480C2212yescomplemented
89#1480C2214yescomplemented
90#1478C2214yescomplemented
91#1478C2214yescomplemented
92#1477C2214yescomplemented
93#1477C2214yescomplemented
94#1476C2214yescomplemented
95C2×D4⋊C8C2214yescomplemented
96C22×#41—22no—
97C22×#41—21no—
98#563—24no—
99#563—22no—
100#562—22no—
101#562—22no—
102#562—24no—
103#562—24no—
104H(3,𝔽4)—22no—
105#560—24no—
106#560—24no—
107#560—24no—
108#559C2×C412yes—
109Q82C2×C412yes—
110#556—21no—
111#556C2×C412yes—
112#555—21no—
113#555—22no—
114#555—24no—
115#555C2×C412yes—
116#555C2×C414yes—
117#555C2×C412yes—
118#554—21no—
119#554C2×C412yes—
120#554C2×C412yes—
121#554C2×C412yes—
122#553—22no—
123#553—22no—
124#553—22no—
125#553C2×C414yes—
126#552—22no—
127#552—22no—
128#552—22no—
129#552C2×C414yes—
130#551—24no—
131#551—24no—
132#551—24no—
133#550—22no—
134#550—21no—
135#550C2×C414yes—
136#550C2×C412yes—
137#550C2×C412yes—
138#550C2×C412yes—
139D4×Q8—21no—
140D4×Q8C2×C412yes—
141#548—22no—
142#548—22no—
143#547—21no—
144#547—21no—
145#547—22no—
146#547C2×C412yes—
147#547C2×C414yes—
148#547C2×C412yes—
149#546—22no—
150#546—22no—
151#546—22no—
152#546—24no—
153#546—24no—
154#546—22no—
155#546C2×C414yes—
156#546C2×C414yes—
157D42—21no—
158D42—22no—
159D42C2×C414yes—
160D42C2×C412yes—
161D42C2×C412yes—
162#544—22no—
163#544C2×C414yes—
164#542—24no—
165#542—22no—
166#542—22no—
167#542—24no—
168#542C2×C414yes—
169#542C2×C414yes—
170#540—22no—
171#540—24no—
172#540—22no—
173#540—24no—
174#540C2×C414yes—
175#540C2×C414yes—
176#538—24no—
177#538—24no—
178#538—24no—
179#538—24no—
180#537—22no—
181#537—22no—
182#537—22no—
183#537—22no—
184#537—22no—
185#537C2×C414yes—
186#536—24no—
187#536—22no—
188#536—22no—
189#535—22no—
190#535—22no—
191#535—22no—
192#535—22no—
193#535—24no—
194#535C2×C414yes—
195#535C2×C414yes—
196#534—24no—
197#534—24no—
198#533C2×C411yescharacteristic
199#533C2×C411yescharacteristic
200#533C2×C411yescharacteristic
201#533D411yescharacteristic
202#533D411yescharacteristic
203#533C2311yescharacteristic
204#532—24no—
205#532—24no—
206#532—22no—
207#532—21no—
208#532—21no—
209#532—21no—
210#532—21no—
211#532C2×C411yescharacteristic
212#532C2×C412yes—
213#532C2×C411yescharacteristic
214#532C2×C411yescharacteristic
215#532C2×C411yescharacteristic
216#532C2×C411yescharacteristic
217#532D411yescharacteristic
218#532D411yescharacteristic
219#532C2312yes—
220#532C2311yescharacteristic
221#532C2311yescharacteristic
222#532C2311yescharacteristic
223#532C2314yes—
224C2×C4⋊Q8C2×C411yescharacteristic
225C2×#127C2×C411yescharacteristic
226#529—22no—
227#529—24no—
228#529—24no—
229#529—21no—
230#529—21no—
231#529—21no—
232#529—21no—
233#529C2×C412yes—
234#529C2×C412yes—
235#529C2×C412yes—
236#529D412yes—
237#529D412yes—
238#529D412yes—
239#529D412yes—
240#529C2312yes—
241#529C2314yes—
242C2×#124—21no—
243#525—22no—
244#525—21no—
245#525—21no—
246#525—24no—
247#525—24no—
248#525—24no—
249#525—22no—
250#525—24no—
251#525C2×C412yes—
252#525C2×C412yes—
253#525D412yes—
254#525D412yes—
255C2×#121—21no—
256C2×#121C2×C412yes—
257C4×#41—22no—
258C4×#41—21no—
259C4×#41—21no—
260C4×#41C2312yes—
261C4×#41C2314yes—
262C4×#41C2312yes—
263C4×#41C2312yes—
264C4×#41C2312yes—
265C2×C4×D4—22no—
266C2×C4×D4—21no—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×#117—22no—
270C22×C42C2311yescharacteristic
271#446—24no—
272#446—22no—
273#446—24no—
274#446—24no—
275C8×Q8—22no—
276#436—24no—
277#436—22no—
278#436—24no—
279#435—24no—
280#435—24no—
281#435—24no—
282#435—24no—
283#435—24no—
284#435—24no—
285#435—24no—
286C8×D4—24no—
287C8×D4—22no—
288C8×D4—24no—
289#433—24no—
290#433—24no—
291#433—24no—
292#433—24no—
293#432—21no—
294#432—21no—
295#432—21no—
296#432—21no—
297#432—21no—
298#432C2312yes—
299#432C2312yes—
300#432C2312yes—
301#432C2314yes—
302#431—21no—
303#431—21no—
304#431—21no—
305#431C2312yes—
306#431C2314yes—
307#431C2312yes—
308#431C2312yes—
309#431C2312yes—
310#431C2312yes—
311#431C2314yes—
312#431C2314yes—
313#424—24no—
314#423—21no—
315#423C2312yes—
316#423C2314yes—
317C2×C4⋊C8—21no—
318C2×C4⋊C8C2312yes—
319C2×C4⋊C8C2314yes—
320#408—24no—
321#408—24no—
322#407—21no—
323#407—21no—
324C2×C22⋊C8—21no—
325C2×C22⋊C8—21no—
326#405—24no—
327C4×M16—21no—
328C4×M16C2312yes—
329C4×M16C2314yes—
330C2×#97—21no—
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2314yes—
334Q8⋊C8C2314yes—
335Q8⋊C8C2314yes—
336Q8⋊C8C2314yes—
337Q8⋊C8C2314yes—
338D4⋊C8C2314yes—
339D4⋊C8C2314yes—
340D4⋊C8C2314yes—
341D4⋊C8C2314yes—
342D4⋊C8C2314yes—
343D4⋊C8C2314yes—
344D4⋊C8C2314yes—
345D4⋊C8C2314yes—
346D4⋊C8C2314yes—
347D4⋊C8C2314yes—
348D4⋊C8C2314yes—
349D4⋊C8C2314yes—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—24no—
353C2×#41—22no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—22no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—24no—
361C2×#41—22no—
362C2×#41—21no—
363C2×#41—84no—
364C2×#41—84no—
365C2×#41—84no—
366C2×#41C22×C412yes—
367C2×#41C22×C414yes—
368C2×#41C22×C412yes—
369C2×#41C2×D412yes—
370C2×#41C2×D412yes—
371C22×Q8—22no—
372C22×Q8—21no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—24no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4C22×C412yes—
380C22×D4C22×C414yes—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4C22×C411yescharacteristic
384C23×C4C2×D411yescharacteristic
385C23×C4C2×D411yescharacteristic
386C2×M16—22no—
387C2×M16—22no—
388C2×M16—24no—
389C2×M16—24no—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—24no—
393C22×C8—22no—
394C22×C8—24no—
395C4⋊Q8—24no—
396C4⋊Q8—24no—
397C4⋊Q8—22no—
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400C4⋊Q8C22⋊C411yescharacteristic
401C4⋊Q8C22⋊C411yescharacteristic
402C4⋊Q8C22⋊C411yescharacteristic
403C4⋊Q8C22×C411yescharacteristic
404C4⋊Q8C22×C412yes—
405C4⋊Q8C22×C411yescharacteristic
406C4⋊Q8C22×C411yescharacteristic
407C4⋊Q8C22×C411yescharacteristic
408C4⋊Q8C22×C411yescharacteristic
409C4⋊Q8C22×C414yes—
410#127—24no—
411#127—24no—
412#127—22no—
413#127—21no—
414#127—21no—
415#127C22⋊C411yescharacteristic
416#127C22×C412yes—
417#127C22×C411yescharacteristic
418#127C22×C411yescharacteristic
419#127C22×C411yescharacteristic
420#127C22×C414yes—
421#126—24no—
422#126—24no—
423#126—24no—
424#126—24no—
425#126—24no—
426#126—22no—
427#126—22no—
428#126—24no—
429#126C22⋊C414yes—
430#126C22⋊C414yes—
431#125—24no—
432#125—22no—
433#125—24no—
434#125—21no—
435#125—21no—
436#125C22⋊C412yes—
437#125C22⋊C412yes—
438#125C22⋊C412yes—
439#125C22×C412yes—
440#125C22×C414yes—
441#124—22no—
442#124—24no—
443#124—24no—
444#124—24no—
445#124—24no—
446#124—24no—
447#124—24no—
448#124—24no—
449#124—22no—
450#124—21no—
451#124—21no—
452#124—21no—
453#124—22no—
454#124—21no—
455#124—21no—
456#124—21no—
457#124—24no—
458#124C22⋊C412yes—
459#124C22⋊C412yes—
460#124C22⋊C412yes—
461#124C22×C412yes—
462#124C22×C414yes—
463#123—24no—
464#123—22no—
465#123—22no—
466#123—22no—
467#123—24no—
468#123—24no—
469#123—24no—
470#123—24no—
471#123—24no—
472#123—24no—
473#123—24no—
474#123—24no—
475#123—24no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123C22⋊C414yes—
483#123C22⋊C414yes—
484#123C22⋊C414yes—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—24no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—24no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—24no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8C22⋊C412yes—
505C22⋊Q8C22⋊C412yes—
506C22⋊Q8C22⋊C412yes—
507C22⋊Q8C22⋊C412yes—
508C22⋊Q8C22⋊C412yes—
509C22⋊Q8C22⋊C412yes—
510C22⋊Q8C22×C412yes—
511C22⋊Q8C22×C412yes—
512C22⋊Q8C22×C414yes—
513#121—24no—
514#121—22no—
515#121—22no—
516#121—24no—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—22no—
521#121—21no—
522#121—21no—
523#121—22no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—22no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121—24no—
534#121—22no—
535#121—22no—
536#121—24no—
537#121—24no—
538#121—22no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—22no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121—24no—
547#121—24no—
548#121—24no—
549#121—24no—
550#121—24no—
551#121—24no—
552#121C22⋊C412yes—
553#121C22⋊C412yes—
554#121C22⋊C412yes—
555#121C22⋊C412yes—
556#121C22⋊C412yes—
557#121C22⋊C412yes—
558#121C22×C412yes—
559#121C22×C412yes—
560#121C22×C412yes—
561#121C22×C412yes—
562#121C22×C412yes—
563#121C22×C412yes—
564#121C22×C414yes—
565#121C22×C414yes—
566#121C22×C414yes—
567#120—22no—
568#120—24no—
569#120—24no—
570#120—24no—
571#120—24no—
572#120—24no—
573#120—24no—
574#120—24no—
575#120—24no—
576#120—24no—
577#120—24no—
578#120C22⋊C414yes—
579C4×Q8—22no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8—21no—
584C4×Q8C22×C412yes—
585C4×Q8C22×C414yes—
586C4×Q8C22×C412yes—
587C4×Q8C22×C412yes—
588C4×Q8C2×D412yes—
589C4×Q8C2×D412yes—
590C4×Q8C2×D412yes—
591C4×Q8C2×D412yes—
592C4×Q8C2412yes—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—24no—
598C4×D4—22no—
599C4×D4—24no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—24no—
603C4×D4—22no—
604C4×D4—24no—
605C4×D4—22no—
606C4×D4—24no—
607C4×D4—21no—
608C4×D4—22no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—22no—
616C4×D4—24no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—24no—
620C4×D4—21no—
621C4×D4—24no—
622C4×D4C22×C412yes—
623C4×D4C22×C412yes—
624C4×D4C22×C414yes—
625C4×D4C22×C414yes—
626C4×D4C22×C412yes—
627C4×D4C22×C414yes—
628C4×D4C22×C414yes—
629C4×D4C22×C414yes—
630C4×D4C22×C412yes—
631C4×D4C22×C412yes—
632C4×D4C2×D412yes—
633C4×D4C2×D412yes—
634C4×D4C2×D414yes—
635C4×D4C2×D414yes—
636C4×D4C2×D414yes—
637C4×D4C2×D414yes—
638C4×D4C2×D412yes—
639C4×D4C2×D412yes—
640C4×D4C2412yes—
641C4×D4C2412yes—
642C4×D4C2412yes—
643#117—21no—
644#117—21no—
645#117—22no—
646#117—22no—
647#117—22no—
648#117—24no—
649#117—24no—
650#117—22no—
651#117—24no—
652#117—22no—
653#117—22no—
654#117—24no—
655#117C22×C412yes—
656#117C22×C414yes—
657#117C22×C412yes—
658#117C22×C414yes—
659#117C2×D412yes—
660#117C2×D414yes—
661#117C2×D412yes—
662#117C2×D414yes—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4C22×C412yes—
668C2×C4⋊C4C22×C414yes—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—24no—
672C2×C22⋊C4—24no—
673C2×C22⋊C4—24no—
674C2×C42—24no—
675C2×C42—22no—
676C2×C42C22×C411yescharacteristic
677C2×C42C22×C411yescharacteristic
678C2×C42C22×C411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C4⋊C8—22no—
690C4⋊C8—22no—
691C4⋊C8—22no—
692C4⋊C8—24no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—22no—
696C4⋊C8—24no—
697C4⋊C8—24no—
698C4⋊C8—24no—
699C4⋊C8C2414yes—
700C4⋊C8C2414yes—
701C22⋊C8—22no—
702C22⋊C8—22no—
703C22⋊C8—22no—
704C22⋊C8—22no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708C22⋊C8—22no—
709C22⋊C8—24no—
710C22⋊C8—24no—
711C22⋊C8—24no—
712C22⋊C8—24no—
713#97—22no—
714#97—22no—
715#97—22no—
716#97—22no—
717#97—24no—
718#97—24no—
719C4×C8—21no—
720C4×C8—21no—
721C4×C8—24no—
722C4×C8—22no—
723C4×C8—24no—
724C4×C8C2412yes—
725C4×C8C2414yes—
726C4×C8C2412yes—
727C24—22no—
728C24—24no—
729C24C2×C22⋊C411yescharacteristic
730#41—42no—
731#41—42no—
732#41—44no—
733#41—44no—
734#41—44no—
735#41—48no—
736#41—82no—
737#41—82no—
738#41—84no—
739#41—82no—
740#41—82no—
741#41—84no—
742#41—82no—
743#41—82no—
744#41—82no—
745#41—84no—
746#41—82no—
747#41—88no—
748#41—84no—
749#41—84no—
750#41—84no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—21no—
757C2×Q8—82no—
758C2×Q8—84no—
759C2×Q8C2×C22⋊C412yes—
760C2×Q8C2×C22⋊C412yes—
761C2×Q8C2×C22⋊C412yes—
762C2×Q8C23×C412yes—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—21no—
783C2×D4—22no—
784C2×D4—24no—
785C2×D4—21no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—82no—
789C2×D4—84no—
790C2×D4—84no—
791C2×D4—82no—
792C2×D4—84no—
793C2×D4—88no—
794C2×D4C2×C22⋊C412yes—
795C2×D4C2×C22⋊C414yes—
796C2×D4C2×C22⋊C414yes—
797C2×D4C2×C22⋊C412yes—
798C2×D4C2×C22⋊C412yes—
799C2×D4C2×C22⋊C414yes—
800C2×D4C23×C412yes—
801C2×D4C23×C412yes—
802C2×D4C23×C412yes—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—84no—
821C22×C4—84no—
822C22×C4—81no—
823C22×C4C2×C22⋊C411yescharacteristic
824C22×C4C2×C22⋊C411yescharacteristic
825C22×C4C2×C22⋊C411yescharacteristic
826C22×C4C2×C22⋊C411yescharacteristic
827C22×C4C2×C22⋊C411yescharacteristic
828C22×C4C2×C22⋊C411yescharacteristic
829C22×C4C2×C22⋊C411yescharacteristic
830C22×C4C2×C22⋊C411yescharacteristic
831C22×C4C2×C22⋊C411yescharacteristic
832C22×C4C23×C411yescharacteristic
833C22×C4C23×C411yescharacteristic
834C22×C4C23×C411yescharacteristic
835C22×C4C23×C414yes—
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D414yes—
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D414yes—
844M16—84no—
845M16—82no—
846M16—84no—
847M16—82no—
848C2×C8—22no—
849C2×C8—22no—
850C2×C8—24no—
851C2×C8—24no—
852C2×C8—24no—
853C2×C8—82no—
854C2×C8—84no—
855C2×C8—81no—
856C2×C8—84no—
857C2×C8—81no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4C2×C22⋊C412yes—
879C4⋊C4C2×C22⋊C412yes—
880C4⋊C4C2×C22⋊C412yes—
881C4⋊C4C2×C22⋊C412yes—
882C4⋊C4C2×C22⋊C414yes—
883C4⋊C4C2×C22⋊C414yes—
884C4⋊C4C2×C22⋊C414yes—
885C4⋊C4C2×C22⋊C412yes—
886C4⋊C4C2×C22⋊C412yes—
887C4⋊C4C2×C22⋊C414yes—
888C4⋊C4C2×C22⋊C414yes—
889C4⋊C4C2×C22⋊C414yes—
890C4⋊C4C23×C412yes—
891C4⋊C4C23×C412yes—
892C4⋊C4C23×C412yes—
893C4⋊C4C23×C412yes—
894C22⋊C4—22no—
895C22⋊C4—24no—
896C22⋊C4—22no—
897C22⋊C4—24no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—22no—
905C22⋊C4—22no—
906C22⋊C4—24no—
907C22⋊C4—22no—
908C22⋊C4—24no—
909C22⋊C4—22no—
910C22⋊C4—22no—
911C22⋊C4—22no—
912C22⋊C4—22no—
913C22⋊C4—24no—
914C22⋊C4—22no—
915C22⋊C4—24no—
916C22⋊C4—22no—
917C22⋊C4—24no—
918C22⋊C4—22no—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4C2×C22⋊C414yes—
922C22⋊C4C2×C22⋊C414yes—
923C22⋊C4C2×C22⋊C414yes—
924C22⋊C4C2×C22⋊C414yes—
925C22⋊C4C2×C22⋊C414yes—
926C22⋊C4C2×C22⋊C414yes—
927C22⋊C4C2×C22⋊C414yes—
928C22⋊C4C2×C22⋊C414yes—
929C22⋊C4C2×C22⋊C414yes—
930C42—24no—
931C42—22no—
932C42—22no—
933C42—24no—
934C42—22no—
935C42C2×C22⋊C411yescharacteristic
936C42C2×C22⋊C411yescharacteristic
937C42C2×C22⋊C411yescharacteristic
938C42C2×C22⋊C411yescharacteristic
939C42C2×C22⋊C411yescharacteristic
940C42C2×C22⋊C411yescharacteristic
941C42C23×C411yescharacteristic
942C42C23×C411yescharacteristic
943C42C23×C411yescharacteristic
944C42C23×C414yes—
945C42C22×D411yescharacteristic
946C42C22×D414yes—
947C42C22×D411yescharacteristic
948C42C22×D411yescharacteristic
949C42C22×D411yescharacteristic
950C42C22×D414yes—
951C42C22×D411yescharacteristic
952C42C22×D411yescharacteristic
953C42C2511yescharacteristic
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—44no—
961C23—84no—
962C23—82no—
963C23—84no—
964C23—82no—
965C23—84no—
966C23C22×C22⋊C414yes—
967C23C22×C22⋊C411yescharacteristic
968C23C22×C22⋊C411yescharacteristic
969C23C22×C22⋊C411yescharacteristic
970Q8—24no—
971Q8—42no—
972Q8—42no—
973Q8—42no—
974Q8—42no—
975Q8—81no—
976Q8—82no—
977Q8—81no—
978Q8—84no—
979Q8—81no—
980D4—24no—
981D4—24no—
982D4—24no—
983D4—42no—
984D4—44no—
985D4—42no—
986D4—42no—
987D4—44no—
988D4—44no—
989D4—42no—
990D4—42no—
991D4—42no—
992D4—44no—
993D4—82no—
994D4—84no—
995D4—82no—
996D4—81no—
997D4—82no—
998D4—81no—
999D4—84no—
1000D4—81no—
1001D4—84no—
1002D4—84no—
1003D4—82no—
1004D4—82no—
1005D4—82no—
1006D4—82no—
1007D4—84no—
1008D4—84no—
1009D4—82no—
1010D4—84no—
1011D4—82no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—28no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—41no—
1027C2×C4—44no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—44no—
1048C2×C4—84no—
1049C2×C4—84no—
1050C2×C4—82no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4—84no—
1054C2×C4C22×C22⋊C411yescharacteristic
1055C2×C4C22×C22⋊C411yescharacteristic
1056C2×C4C22×C22⋊C414yes—
1057C2×C4C22×C22⋊C414yes—
1058C2×C4C22×C22⋊C411yescharacteristic
1059C2×C4C22×C22⋊C411yescharacteristic
1060C2×C4C22×C22⋊C411yescharacteristic
1061C2×C4C22×C22⋊C411yescharacteristic
1062C2×C4C22×C22⋊C411yescharacteristic
1063C2×C4C22×C22⋊C411yescharacteristic
1064C2×C4C22×C22⋊C411yescharacteristic
1065C2×C4C22×C22⋊C414yes—
1066C2×C4C24×C411yescharacteristic
1067C2×C4C23×D411yescharacteristic
1068C2×C4C23×D411yescharacteristic
1069C8—42no—
1070C8—42no—
1071C8—44no—
1072C8—44no—
1073C8—44no—
1074C22—21no—
1075C22—21no—
1076C22—21no—
1077C22—24no—
1078C22—21no—
1079C22—21no—
1080C22—21no—
1081C22—24no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—24no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—82no—
1096C22—164no—
1097C22—168no—
1098C22C23×C22⋊C411yescharacteristic
1099C4—21no—
1100C4—21no—
1101C4—21no—
1102C4—24no—
1103C4—21no—
1104C4—21no—
1105C4—21no—
1106C4—24no—
1107C4—21no—
1108C4—21no—
1109C4—21no—
1110C4—21no—
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4#357312yes—
1118C4#358512yes—
1119C2—41no—
1120C2—41no—
1121C2—41no—
1122C2—44no—
1123C2—82no—
1124C2—82no—
1125C2—82no—
1126C2#6006511yescharacteristic
1127C2#6008711yescharacteristic
1128C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62759C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60293C2semidirect
3. #60279C2semidirect
4. #17526C2semidirect
5. #17521C2semidirect
6. #17513C2semidirect
7. #17511C2semidirect
8. #17505C2semidirect
9. #17495C2semidirect
10. #17493C2semidirect
11. #17483C2semidirect
12. #17482C2semidirect
13. #17478C2semidirect
43. #2990C22semidirect
44. #2989C22semidirect
53. #2965C22semidirect
54. #2965C22semidirect
55. C8×#41C22semidirect
56. #2925C22semidirect
57. #2922C22semidirect
58. #2920C22semidirect
59. #2920C22semidirect
60. C2×#432C22semidirect
61. C2×#431C22semidirect
62. #1497C22semidirect
65. #1496C22semidirect
66. #1496C22semidirect
67. #1496C22semidirect
68. #1495C22semidirect
69. #1495C22semidirect
70. #1494C22semidirect
71. #1494C22semidirect
72. #1494C22semidirect
73. #1492C22semidirect
74. #1492C22semidirect
75. #1492C22semidirect
76. #1490C22semidirect
77. #1490C22semidirect
78. #1489C22semidirect
79. #1488C22semidirect
80. #1488C22semidirect
81. #1486C22semidirect
82. #1485C22semidirect
84. #1484C22semidirect
85. #1483C22semidirect
86. #1482C22semidirect
88. #1480C22semidirect
89. #1480C22semidirect
90. #1478C22semidirect
91. #1478C22semidirect
92. #1477C22semidirect
93. #1477C22semidirect
94. #1476C22semidirect
95. C2×D4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627592
#602932
#602792
#175262
#175212
#175132
#175112
#175052
#174952
#174932
#174832
#174822
#174782