Finite Group Databasebeta

← #6343273

Subgroups — #6343273

Order 512.

2875 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62748C211yesmaximal, characteristic
2#60280C211yesmaximal, characteristic, complemented
3#60266C211yesmaximal, characteristic, complemented
4#17522C214yesmaximal, complemented
5#17521C214yesmaximal, complemented
6#17515C212yesmaximal, complemented
7#17511C212yesmaximal, complemented
8#17510C212yesmaximal, complemented
9#17507C212yesmaximal, complemented
10#17505C214yesmaximal, complemented
11#17487C211yesmaximal, characteristic, complemented
12#17485C211yesmaximal, characteristic, complemented
13#17483C214yesmaximal, complemented
14#17478C211yesmaximal, characteristic, complemented
15C2×#1495C211yesmaximal, characteristic, complemented
16#3562—22no—
17#3561—21no—
18#3560—22no—
19#3559C412yes—
20#3558—21no—
21#3558C412yes—
22#3554C412yes—
23#3552C412yes—
24#3546C412yes—
25#3543C412yes—
26#3537C412yes—
27#3536C412yes—
28#3534—22no—
29#3529—22no—
30#3481C2214yes—
31#3480C2212yes—
32D4×#41—22no—
33D4×#41C2212yes—
34#3460C2214yes—
35#3459—22no—
36#3455—21no—
37#3449—21no—
38#3444C2211yescharacteristic
39C2×#532C2211yescharacteristic
40C2×#529C2211yescharacteristic
41#2995—22no—
42#2994—22no—
43#2994—22no—
44#2993—22no—
45#2991C2212yescomplemented
46#2990C2212yescomplemented
47#2989C2214yescomplemented
48#2986—21no—
49#2979—21no—
50#2977—22no—
51#2965C2212yescomplemented
52#2965C2212yescomplemented
53C8×#41C2212yescomplemented
54C8×#41C2212yescomplemented
55#2962—21no—
56#2935—21no—
57#2930—22no—
58#2925C2212yescomplemented
59#2922C2214yescomplemented
60#2920C2211yescharacteristic, complemented
61C2×#431C2211yescharacteristic, complemented
62C2×#431C2211yescharacteristic, complemented
63#2906C2212yescomplemented
64C2×#423C2211yescharacteristic, complemented
65#1496C2212yescomplemented
66#1496C2212yescomplemented
67#1496C2214yescomplemented
68#1495C2212yescomplemented
69#1495C2212yescomplemented
70#1495C2212yescomplemented
71#1495C2212yescomplemented
72#1495C2214yescomplemented
73#1494C2214yescomplemented
74#1494C2214yescomplemented
75#1492C2212yescomplemented
76#1492C2212yescomplemented
77#1492C2214yescomplemented
78#1492C2214yescomplemented
79#1490C2214yescomplemented
80#1489C2214yescomplemented
81#1488C2214yescomplemented
82#1487C2211yescharacteristic, complemented
83#1487C2211yescharacteristic, complemented
84#1486C2212yescomplemented
85#1486C2212yescomplemented
86#1486C2211yescharacteristic, complemented
87#1486C2211yescharacteristic, complemented
88#1486C2214yescomplemented
89#1484C2214yescomplemented
90#1483C2214yescomplemented
91#1482C2214yescomplemented
92#1482C2214yescomplemented
93#1480C2212yescomplemented
94#1480C2212yescomplemented
95#1480C2214yescomplemented
96#1478C2214yescomplemented
97#1478C2214yescomplemented
98#1477C2214yescomplemented
99#1476C2214yescomplemented
100C2×Q8⋊C8C2212yescomplemented
101C2×D4⋊C8C2212yescomplemented
102C2×D4⋊C8C2214yescomplemented
103C22×#41—22no—
104C22×#41—21no—
105C2×#131—22no—
106C22×M16—21no—
107#563—24no—
108#563—22no—
109#562—22no—
110#562—22no—
111#562—24no—
112#562—24no—
113H(3,𝔽4)—22no—
114#560—24no—
115#560—24no—
116#560—24no—
117#559—22no—
118#559C2×C412yes—
119#559C2×C414yes—
120#557C2×C412yes—
121#556—22no—
122#556C2×C412yes—
123#554C2×C414yes—
124#554C2×C414yes—
125#553—24no—
126#553—24no—
127#553C2×C414yes—
128#553C2×C414yes—
129#553C2×C414yes—
130#551—24no—
131#551—24no—
132#550—22no—
133#550C2×C412yes—
134#550C2×C412yes—
135D4×Q8—22no—
136D4×Q8C2×C412yes—
137#548—22no—
138#548—22no—
139#548—22no—
140#548C2×C414yes—
141#547—24no—
142#547—22no—
143#547C2×C414yes—
144#547C2×C412yes—
145#546—24no—
146#546—24no—
147#546—22no—
148#546—22no—
149#546—24no—
150#546—24no—
151#546—22no—
152#546C2×C414yes—
153#546C2×C414yes—
154D42—22no—
155D42—24no—
156D42C2×C414yes—
157D42C2×C412yes—
158D42C2×C414yes—
159#544C2×C414yes—
160#543—22no—
161#542—22no—
162#542—22no—
163#542—24no—
164#542C2×C414yes—
165#542C2×C414yes—
166#541—22no—
167#540—22no—
168#540—24no—
169#540C2×C414yes—
170#540C2×C414yes—
171#539—24no—
172#539—24no—
173#539—24no—
174#539—22no—
175#539—22no—
176#538—24no—
177#538—24no—
178#538—22no—
179#538—22no—
180#538—22no—
181#538—22no—
182#538—24no—
183#538—24no—
184#537—22no—
185#537—22no—
186#537C2×C414yes—
187#536—22no—
188#536—22no—
189#535—22no—
190#535—22no—
191#535C2×C414yes—
192#535C2×C414yes—
193#534—24no—
194#534—22no—
195#534—22no—
196#534—22no—
197#533C2×C411yescharacteristic
198#533D411yescharacteristic
199#533D411yescharacteristic
200#532—22no—
201#532—24no—
202#532—21no—
203#532—21no—
204#532—21no—
205#532—21no—
206#532C2×C412yes—
207#532C2×C412yes—
208#532C2×C411yescharacteristic
209#532D411yescharacteristic
210#532D411yescharacteristic
211#532C2312yes—
212#532C2312yes—
213#532C2314yes—
214C2×C4⋊Q8C2×C411yescharacteristic
215C2×#127C2×C411yescharacteristic
216#529—24no—
217#529—24no—
218#529—24no—
219#529—21no—
220#529—21no—
221#529—21no—
222#529—21no—
223#529C2×C412yes—
224#529C2×C412yes—
225#529C2×C412yes—
226#529C2×C412yes—
227#529D412yes—
228#529D412yes—
229#529D412yes—
230#529D412yes—
231#529C2312yes—
232#529C2312yes—
233#529C2314yes—
234C2×#126—21no—
235C2×#125C2×C411yescharacteristic
236C2×#124—21no—
237C2×#124C2×C411yescharacteristic
238#525—24no—
239#525—24no—
240#525—24no—
241#525—24no—
242#525—22no—
243#525—24no—
244#525C2×C412yes—
245#525D412yes—
246#525D412yes—
247C2×#123—21no—
248C2×C22⋊Q8C2×C411yescharacteristic
249C2×#121—21no—
250C2×#121C2×C411yescharacteristic
251C2×#121C2×C412yes—
252C4×#41—22no—
253C4×#41C2314yes—
254C4×#41C2312yes—
255C4×#41C2312yes—
256C4×#41C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4—24no—
260C2×C4×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×#117—21no—
265C22×C42C2311yescharacteristic
266#446—24no—
267#446—22no—
268#446—22no—
269#446—22no—
270C8×Q8—22no—
271C8×Q8—22no—
272C8×Q8—22no—
273#436—24no—
274#436—24no—
275#436—22no—
276#436—22no—
277#436—22no—
278#435—24no—
279#435—24no—
280#435—24no—
281#435—24no—
282#435—24no—
283C8×D4—22no—
284C8×D4—24no—
285C8×D4—24no—
286C8×D4—22no—
287C8×D4—22no—
288#433—24no—
289#433—24no—
290#433—24no—
291#432—21no—
292#432C2312yes—
293#432C2314yes—
294#431—21no—
295#431—21no—
296#431—21no—
297#431—21no—
298#431—21no—
299#431C2312yes—
300#431C2314yes—
301#431C2312yes—
302#431C2312yes—
303#431C2311yescharacteristic
304#431C2311yescharacteristic
305#431C2311yescharacteristic
306#431C2311yescharacteristic
307#431C2314yes—
308#431C2314yes—
309#424—22no—
310#424—24no—
311#424—24no—
312#423—21no—
313#423—21no—
314#423C2312yes—
315#423C2311yescharacteristic
316#423C2311yescharacteristic
317#423C2311yescharacteristic
318#423C2314yes—
319#423C2311yescharacteristic
320C2×C4⋊C8—21no—
321C2×C4⋊C8—21no—
322C2×C4⋊C8—21no—
323C2×C4⋊C8C2312yes—
324C2×C4⋊C8C2314yes—
325#408—24no—
326#408—22no—
327#407—21no—
328C2×C22⋊C8—21no—
329C2×C22⋊C8—21no—
330#405—22no—
331C4×M16—21no—
332C4×M16C2314yes—
333C2×C4×C8C2312yes—
334C2×C4×C8C2312yes—
335C2×C4×C8C2314yes—
336Q8⋊C8C2312yes—
337Q8⋊C8C2312yes—
338Q8⋊C8C2312yes—
339Q8⋊C8C2312yes—
340Q8⋊C8C2314yes—
341Q8⋊C8C2314yes—
342D4⋊C8C2312yes—
343D4⋊C8C2314yes—
344D4⋊C8C2312yes—
345D4⋊C8C2314yes—
346D4⋊C8C2312yes—
347D4⋊C8C2314yes—
348D4⋊C8C2312yes—
349D4⋊C8C2314yes—
350D4⋊C8C2314yes—
351D4⋊C8C2314yes—
352D4⋊C8C2314yes—
353D4⋊C8C2314yes—
354D4⋊C8C2314yes—
355D4⋊C8C2314yes—
356C2×#41—22no—
357C2×#41—22no—
358C2×#41—24no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—24no—
363C2×#41—22no—
364C2×#41—82no—
365C2×#41—82no—
366C2×#41—84no—
367C2×#41—84no—
368C2×#41C22×C414yes—
369C2×#41C22×C412yes—
370C2×#41C2×D412yes—
371C2×#41C2×D412yes—
372C22×Q8—22no—
373C22×Q8—21no—
374C22×Q8C22×C411yescharacteristic
375C22×D4—21no—
376C22×D4—22no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—22no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4C22×C411yescharacteristic
383C22×D4C22×C412yes—
384C22×D4C22×C414yes—
385C23×C4—21no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4C22×C411yescharacteristic
389C23×C4C2×D411yescharacteristic
390C23×C4C2×D411yescharacteristic
391#131—84no—
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—22no—
396C2×M16—21no—
397C2×M16—24no—
398C2×M16—24no—
399C2×M16—82no—
400C22×C8—22no—
401C22×C8—24no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—24no—
405C4⋊Q8—22no—
406C4⋊Q8—24no—
407C4⋊Q8—21no—
408C4⋊Q8—21no—
409C4⋊Q8C22⋊C411yescharacteristic
410C4⋊Q8C22⋊C411yescharacteristic
411C4⋊Q8C22⋊C411yescharacteristic
412C4⋊Q8C22×C412yes—
413C4⋊Q8C22×C412yes—
414C4⋊Q8C22×C414yes—
415#127—22no—
416#127—24no—
417#127—21no—
418#127—21no—
419#127C22⋊C411yescharacteristic
420#127C22×C412yes—
421#127C22×C412yes—
422#127C22×C414yes—
423#126—24no—
424#126—24no—
425#126—24no—
426#126—24no—
427#126—24no—
428#126—24no—
429#126—22no—
430#126—22no—
431#126—22no—
432#126—22no—
433#126—24no—
434#126C22⋊C414yes—
435#126C22⋊C414yes—
436#125—24no—
437#125—24no—
438#125—24no—
439#125—21no—
440#125—21no—
441#125C22⋊C412yes—
442#125C22⋊C412yes—
443#125C22⋊C412yes—
444#125C22×C412yes—
445#125C22×C412yes—
446#125C22×C414yes—
447#124—24no—
448#124—24no—
449#124—22no—
450#124—22no—
451#124—24no—
452#124—24no—
453#124—24no—
454#124—22no—
455#124—22no—
456#124—21no—
457#124—21no—
458#124—22no—
459#124—22no—
460#124—24no—
461#124C22⋊C412yes—
462#124C22⋊C412yes—
463#124C22⋊C412yes—
464#124C22×C412yes—
465#124C22×C412yes—
466#124C22×C414yes—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
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#123—24no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123C22⋊C414yes—
490#123C22⋊C414yes—
491#123C22⋊C414yes—
492C22⋊Q8—24no—
493C22⋊Q8—24no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—24no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8C22⋊C412yes—
510C22⋊Q8C22⋊C412yes—
511C22⋊Q8C22⋊C412yes—
512C22⋊Q8C22⋊C412yes—
513C22⋊Q8C22⋊C412yes—
514C22⋊Q8C22⋊C412yes—
515C22⋊Q8C22×C412yes—
516C22⋊Q8C22×C412yes—
517C22⋊Q8C22×C414yes—
518#121—24no—
519#121—24no—
520#121—24no—
521#121—24no—
522#121—24no—
523#121—24no—
524#121—24no—
525#121—22no—
526#121—22no—
527#121—21no—
528#121—21no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—24no—
534#121—24no—
535#121—24no—
536#121—22no—
537#121—22no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121—24no—
547#121—24no—
548#121C22⋊C412yes—
549#121C22⋊C412yes—
550#121C22⋊C412yes—
551#121C22⋊C412yes—
552#121C22⋊C412yes—
553#121C22⋊C412yes—
554#121C22×C412yes—
555#121C22×C412yes—
556#121C22×C414yes—
557#121C22×C414yes—
558#121C22×C414yes—
559#121C22×C414yes—
560#121C22×C414yes—
561#120—24no—
562#120—24no—
563#120—24no—
564#120—24no—
565#120—24no—
566#120—24no—
567#120—24no—
568#120—24no—
569#120—24no—
570#120—24no—
571#120—24no—
572#120C22⋊C414yes—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—21no—
576C4×Q8—21no—
577C4×Q8C22×C412yes—
578C4×Q8C22×C414yes—
579C4×Q8C22×C412yes—
580C4×Q8C22×C412yes—
581C4×Q8C2×D412yes—
582C4×Q8C2×D412yes—
583C4×Q8C2×D412yes—
584C4×Q8C2×D412yes—
585C4×Q8C2412yes—
586C4×D4—24no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—24no—
591C4×D4—22no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—24no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—21no—
607C4×D4—24no—
608C4×D4—22no—
609C4×D4—21no—
610C4×D4—22no—
611C4×D4—24no—
612C4×D4C22×C412yes—
613C4×D4C22×C414yes—
614C4×D4C22×C414yes—
615C4×D4C22×C414yes—
616C4×D4C22×C414yes—
617C4×D4C22×C414yes—
618C4×D4C22×C414yes—
619C4×D4C22×C412yes—
620C4×D4C22×C412yes—
621C4×D4C2×D414yes—
622C4×D4C2×D412yes—
623C4×D4C2×D412yes—
624C4×D4C2×D414yes—
625C4×D4C2×D414yes—
626C4×D4C2×D414yes—
627C4×D4C2×D412yes—
628C4×D4C2×D412yes—
629C4×D4C2412yes—
630C4×D4C2414yes—
631#117—22no—
632#117—22no—
633#117—22no—
634#117—22no—
635#117—24no—
636#117—24no—
637#117C22×C414yes—
638#117C22×C412yes—
639#117C22×C414yes—
640#117C2×D412yes—
641#117C2×D414yes—
642#117C2×D412yes—
643#117C2×D414yes—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4C22×C412yes—
651C2×C4⋊C4C22×C411yescharacteristic
652C2×C4⋊C4C22×C414yes—
653C2×C4⋊C4C22×C411yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C42—21no—
665C2×C42—24no—
666C2×C42C22×C411yescharacteristic
667C2×C42C22×C411yescharacteristic
668C2×C42C22×C411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2414yes—
678C2×C42C2411yescharacteristic
679C4⋊C8—21no—
680C4⋊C8—22no—
681C4⋊C8—21no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—21no—
685C4⋊C8—21no—
686C4⋊C8—21no—
687C4⋊C8—21no—
688C4⋊C8—22no—
689C4⋊C8—24no—
690C4⋊C8—21no—
691C4⋊C8—24no—
692C4⋊C8—21no—
693C4⋊C8—24no—
694C4⋊C8—24no—
695C4⋊C8C2412yes—
696C4⋊C8C2412yes—
697C4⋊C8C2412yes—
698C4⋊C8C2412yes—
699C22⋊C8—22no—
700C22⋊C8—22no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704C22⋊C8—21no—
705C22⋊C8—22no—
706C22⋊C8—22no—
707C22⋊C8—24no—
708C22⋊C8—24no—
709C22⋊C8—24no—
710C22⋊C8—24no—
711#97—22no—
712#97—24no—
713#97—24no—
714C4×C8—22no—
715C4×C8—22no—
716C4×C8—24no—
717C4×C8—22no—
718C4×C8—24no—
719C4×C8C2412yes—
720C4×C8C2412yes—
721C4×C8C2412yes—
722C4×C8C2412yes—
723C24—21no—
724C24—22no—
725C24—24no—
726C24C2×C22⋊C411yescharacteristic
727#41—24no—
728#41—24no—
729#41—44no—
730#41—48no—
731#41—44no—
732#41—44no—
733#41—84no—
734#41—82no—
735#41—82no—
736#41—84no—
737#41—84no—
738#41—84no—
739#41—82no—
740#41—88no—
741#41—84no—
742#41—84no—
743C2×Q8—22no—
744C2×Q8—21no—
745C2×Q8—24no—
746C2×Q8—22no—
747C2×Q8—42no—
748C2×Q8—82no—
749C2×Q8—84no—
750C2×Q8C2×C22⋊C412yes—
751C2×Q8C2×C22⋊C412yes—
752C2×Q8C2×C22⋊C412yes—
753C2×Q8C23×C412yes—
754C2×D4—22no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—22no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—22no—
763C2×D4—21no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—24no—
770C2×D4—22no—
771C2×D4—44no—
772C2×D4—42no—
773C2×D4—48no—
774C2×D4—82no—
775C2×D4—84no—
776C2×D4—82no—
777C2×D4—88no—
778C2×D4—84no—
779C2×D4—88no—
780C2×D4—82no—
781C2×D4C2×C22⋊C414yes—
782C2×D4C2×C22⋊C412yes—
783C2×D4C2×C22⋊C414yes—
784C2×D4C2×C22⋊C412yes—
785C2×D4C2×C22⋊C412yes—
786C2×D4C2×C22⋊C414yes—
787C2×D4C23×C412yes—
788C2×D4C23×C414yes—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—24no—
796C22×C4—22no—
797C22×C4—24no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—84no—
808C22×C4—82no—
809C22×C4—82no—
810C22×C4—84no—
811C22×C4—81no—
812C22×C4C2×C22⋊C411yescharacteristic
813C22×C4C2×C22⋊C411yescharacteristic
814C22×C4C2×C22⋊C411yescharacteristic
815C22×C4C2×C22⋊C411yescharacteristic
816C22×C4C2×C22⋊C411yescharacteristic
817C22×C4C2×C22⋊C411yescharacteristic
818C22×C4C2×C22⋊C411yescharacteristic
819C22×C4C2×C22⋊C411yescharacteristic
820C22×C4C2×C22⋊C411yescharacteristic
821C22×C4C23×C411yescharacteristic
822C22×C4C23×C411yescharacteristic
823C22×C4C23×C411yescharacteristic
824C22×C4C23×C414yes—
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D414yes—
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D414yes—
832C22×C4C22×D411yescharacteristic
833M16—42no—
834M16—42no—
835M16—81no—
836M16—82no—
837M16—81no—
838M16—84no—
839M16—84no—
840C2×C8—22no—
841C2×C8—22no—
842C2×C8—22no—
843C2×C8—22no—
844C2×C8—22no—
845C2×C8—22no—
846C2×C8—22no—
847C2×C8—22no—
848C2×C8—44no—
849C2×C8—84no—
850C2×C8—84no—
851C2×C8—82no—
852C2×C8—82no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4C2×C22⋊C414yes—
873C4⋊C4C2×C22⋊C414yes—
874C4⋊C4C2×C22⋊C414yes—
875C4⋊C4C2×C22⋊C412yes—
876C4⋊C4C2×C22⋊C412yes—
877C4⋊C4C2×C22⋊C412yes—
878C4⋊C4C2×C22⋊C412yes—
879C4⋊C4C2×C22⋊C414yes—
880C4⋊C4C2×C22⋊C414yes—
881C4⋊C4C2×C22⋊C412yes—
882C4⋊C4C2×C22⋊C414yes—
883C4⋊C4C2×C22⋊C412yes—
884C4⋊C4C23×C412yes—
885C4⋊C4C23×C414yes—
886C4⋊C4C23×C412yes—
887C22⋊C4—22no—
888C22⋊C4—24no—
889C22⋊C4—22no—
890C22⋊C4—24no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—22no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—22no—
910C22⋊C4—24no—
911C22⋊C4C2×C22⋊C414yes—
912C22⋊C4C2×C22⋊C414yes—
913C22⋊C4C2×C22⋊C414yes—
914C22⋊C4C2×C22⋊C414yes—
915C22⋊C4C2×C22⋊C414yes—
916C22⋊C4C2×C22⋊C414yes—
917C22⋊C4C2×C22⋊C414yes—
918C22⋊C4C2×C22⋊C414yes—
919C22⋊C4C2×C22⋊C414yes—
920C42—22no—
921C42—24no—
922C42—24no—
923C42—22no—
924C42C2×C22⋊C411yescharacteristic
925C42C2×C22⋊C411yescharacteristic
926C42C2×C22⋊C411yescharacteristic
927C42C2×C22⋊C411yescharacteristic
928C42C2×C22⋊C411yescharacteristic
929C42C2×C22⋊C411yescharacteristic
930C42C23×C411yescharacteristic
931C42C23×C411yescharacteristic
932C42C23×C411yescharacteristic
933C42C23×C414yes—
934C42C22×D411yescharacteristic
935C42C22×D411yescharacteristic
936C42C22×D414yes—
937C42C22×D411yescharacteristic
938C42C22×D411yescharacteristic
939C42C22×D414yes—
940C42C22×D411yescharacteristic
941C42C22×D411yescharacteristic
942C42C2511yescharacteristic
943C23—22no—
944C23—22no—
945C23—24no—
946C23—41no—
947C23—41no—
948C23—44no—
949C23—42no—
950C23—82no—
951C23—84no—
952C23—81no—
953C23—82no—
954C23—84no—
955C23—81no—
956C23—84no—
957C23C22×C22⋊C414yes—
958C23C22×C22⋊C411yescharacteristic
959C23C22×C22⋊C411yescharacteristic
960C23C22×C22⋊C411yescharacteristic
961Q8—24no—
962Q8—24no—
963Q8—42no—
964Q8—42no—
965Q8—44no—
966Q8—81no—
967Q8—82no—
968Q8—84no—
969D4—28no—
970D4—24no—
971D4—24no—
972D4—28no—
973D4—44no—
974D4—42no—
975D4—44no—
976D4—42no—
977D4—44no—
978D4—48no—
979D4—44no—
980D4—82no—
981D4—81no—
982D4—84no—
983D4—82no—
984D4—82no—
985D4—84no—
986D4—82no—
987D4—84no—
988D4—82no—
989D4—84no—
990D4—84no—
991D4—84no—
992D4—84no—
993D4—84no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—28no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—44no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—42no—
1022C2×C4—44no—
1023C2×C4—42no—
1024C2×C4—44no—
1025C2×C4—42no—
1026C2×C4—44no—
1027C2×C4—84no—
1028C2×C4—84no—
1029C2×C4—84no—
1030C2×C4—84no—
1031C2×C4—84no—
1032C2×C4—82no—
1033C2×C4—84no—
1034C2×C4—81no—
1035C2×C4—81no—
1036C2×C4C22×C22⋊C414yes—
1037C2×C4C22×C22⋊C414yes—
1038C2×C4C22×C22⋊C411yescharacteristic
1039C2×C4C22×C22⋊C411yescharacteristic
1040C2×C4C22×C22⋊C411yescharacteristic
1041C2×C4C22×C22⋊C411yescharacteristic
1042C2×C4C22×C22⋊C411yescharacteristic
1043C2×C4C22×C22⋊C411yescharacteristic
1044C2×C4C22×C22⋊C411yescharacteristic
1045C2×C4C22×C22⋊C411yescharacteristic
1046C2×C4C22×C22⋊C414yes—
1047C2×C4C22×C22⋊C411yescharacteristic
1048C2×C4#57612yes—
1049C2×C4#57712yes—
1050C2×C4C24×C411yescharacteristic
1051C2×C4C23×D411yescharacteristic
1052C2×C4C23×D411yescharacteristic
1053C8—42no—
1054C8—42no—
1055C8—42no—
1056C8—42no—
1057C8—42no—
1058C8—42no—
1059C8—42no—
1060C8—42no—
1061C22—21no—
1062C22—21no—
1063C22—21no—
1064C22—21no—
1065C22—24no—
1066C22—21no—
1067C22—21no—
1068C22—24no—
1069C22—21no—
1070C22—21no—
1071C22—24no—
1072C22—44no—
1073C22—42no—
1074C22—42no—
1075C22—44no—
1076C22—44no—
1077C22—42no—
1078C22—82no—
1079C22—162no—
1080C22—164no—
1081C22—168no—
1082C22#289712yes—
1083C22C23×C22⋊C411yescharacteristic
1084C4—21no—
1085C4—21no—
1086C4—21no—
1087C4—24no—
1088C4—21no—
1089C4—21no—
1090C4—24no—
1091C4—21no—
1092C4—21no—
1093C4—21no—
1094C4—21no—
1095C4—24no—
1096C4—42no—
1097C4—42no—
1098C4—44no—
1099C4—42no—
1100C4#289712yes—
1101C4#357312yes—
1102C4C2×#57611yescharacteristic
1103C4C2×#57711yescharacteristic
1104C2—22no—
1105C2—41no—
1106C2—41no—
1107C2—44no—
1108C2—84no—
1109C2—82no—
1110C2#6006511yescharacteristic
1111C2C2×#289711yescharacteristic
1112C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62748C2
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. #60280C2semidirect
3. #60266C2semidirect
4. #17522C2semidirect
5. #17521C2semidirect
6. #17515C2semidirect
7. #17511C2semidirect
8. #17510C2semidirect
9. #17507C2semidirect
10. #17505C2semidirect
11. #17487C2semidirect
12. #17485C2semidirect
13. #17483C2semidirect
14. #17478C2semidirect
15. C2×#1495C2semidirect
45. #2991C22semidirect
46. #2990C22semidirect
47. #2989C22semidirect
51. #2965C22semidirect
52. #2965C22semidirect
53. C8×#41C22semidirect
54. C8×#41C22semidirect
58. #2925C22semidirect
59. #2922C22semidirect
60. #2920C22semidirect
61. C2×#431C22semidirect
62. C2×#431C22semidirect
63. #2906C22semidirect
64. C2×#423C22semidirect
65. #1496C22semidirect
66. #1496C22semidirect
67. #1496C22semidirect
68. #1495C22semidirect
69. #1495C22semidirect
70. #1495C22semidirect
71. #1495C22semidirect
72. #1495C22semidirect
73. #1494C22semidirect
74. #1494C22semidirect
75. #1492C22semidirect
76. #1492C22semidirect
77. #1492C22semidirect
78. #1492C22semidirect
79. #1490C22semidirect
80. #1489C22semidirect
81. #1488C22semidirect
82. #1487C22semidirect
83. #1487C22semidirect
84. #1486C22semidirect
85. #1486C22semidirect
86. #1486C22semidirect
87. #1486C22semidirect
88. #1486C22semidirect
89. #1484C22semidirect
90. #1483C22semidirect
91. #1482C22semidirect
92. #1482C22semidirect
93. #1480C22semidirect
94. #1480C22semidirect
95. #1480C22semidirect
96. #1478C22semidirect
97. #1478C22semidirect
98. #1477C22semidirect
99. #1476C22semidirect
100. C2×Q8⋊C8C22semidirect
101. C2×D4⋊C8C22semidirect
102. C2×D4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627482
#602802
#602662
#175222
#175212
#175152
#175112
#175102
#175072
#175052
#174872
#174852
#174832
#174782
C2×#14952