Finite Group Databasebeta

← #6343169

Subgroups — #6343169

Order 512.

2840 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C211yesmaximal, characteristic
2#60281C211yesmaximal, characteristic, complemented
3#60269C211yesmaximal, characteristic, complemented
4#17523C214yesmaximal, complemented
5#17521C214yesmaximal, complemented
6#17513C214yesmaximal, complemented
7#17512C214yesmaximal, complemented
8#17506C214yesmaximal, complemented
9#17498C211yesmaximal, characteristic, complemented
10#17494C211yesmaximal, characteristic, complemented
11#17453C214yesmaximal, complemented
12#17452C211yesmaximal, characteristic, complemented
13#17451C211yesmaximal, characteristic, complemented
14#3521—22no—
15#3521C414yes—
16#3515—21no—
17#3515C412yes—
18#3514—21no—
19#3514C412yes—
20#3507C411yescharacteristic
21#3507C411yescharacteristic
22#3505—22no—
23#3501C411yescharacteristic
24#3496C411yescharacteristic
25#3493C412yes—
26#3491—22no—
27#3485C412yes—
28#3482—21no—
29#3482C2212yes—
30#3481—21no—
31#3481C2212yes—
32#3475—22no—
33#3475C2214yes—
34#3461C2212yes—
35#3459—22no—
36#3444C2211yescharacteristic
37#3444C2211yescharacteristic
38C2×#529—22no—
39C4×H(5,𝔽2)C2212yes—
40C2×C4×#41C2211yescharacteristic
41#2995—22no—
42#2995—22no—
43#2995—22no—
44#2992—22no—
45#2990C2214yescomplemented
46#2989C2214yescomplemented
47#2987—21no—
48#2980—21no—
49#2978—22no—
50#2965C2214yescomplemented
51#2965C2214yescomplemented
52#2961—21no—
53#2933—22no—
54#2932—21no—
55#2925C2212yescomplemented
56#2922C2214yescomplemented
57#2920C2211yescharacteristic, complemented
58#2920C2211yescharacteristic, complemented
59C2×#432C2211yescharacteristic, complemented
60#2906C2212yescomplemented
61C2×#423C2211yescharacteristic, complemented
62#1497C2212yescomplemented
63#1497C2214yescomplemented
64#1496C2212yescomplemented
65#1495C2214yescomplemented
66#1495C2214yescomplemented
67#1494C2214yescomplemented
68#1493C2214yescomplemented
69#1491C2212yescomplemented
70#1490C2212yes—
71#1490C2214yescomplemented
72#1489C2214yescomplemented
73#1489C2214yescomplemented
74#1489C2214yescomplemented
75#1488C2214yescomplemented
76#1488C2214yescomplemented
77#1488C2214yescomplemented
78#1487C2212yescomplemented
79#1486C2212yes—
80#1486C2214yescomplemented
81#1485C2214yescomplemented
82#1483C2212yescomplemented
83#1483C2212yescomplemented
84#1483C2214yescomplemented
85#1482C2214yescomplemented
86#1481C2212yescomplemented
87#1481C2214yescomplemented
88#1480C2212yescomplemented
89#1478C2214yescomplemented
90#1477C2214yescomplemented
91#1477C2212yescomplemented
92#1477C2212yescomplemented
93#1477C2214yescomplemented
94#1476C2214yescomplemented
95C2×D4⋊C8C2214yescomplemented
96C2×H(5,𝔽2)C2×C412yes—
97C22×#41C2×C411yescharacteristic
98C2×#131—22no—
99C22×M16—21no—
100#559—21no—
101#559C2×C412yes—
102#557—21no—
103#557C2×C412yes—
104#556—21no—
105#556—22no—
106#556—22no—
107#556C2×C414yes—
108#556C2×C414yes—
109#556C2×C412yes—
110#555—22no—
111#555C2×C414yes—
112#554—21no—
113#554—21no—
114#554—22no—
115#554C2×C414yes—
116#554C2×C412yes—
117#554C2×C412yes—
118#553—24no—
119#553—22no—
120#553—22no—
121#553—24no—
122#553—22no—
123#553C2×C414yes—
124#552—24no—
125#552—22no—
126#552—24no—
127#552—22no—
128#552—22no—
129#552—24no—
130#552—24no—
131#552—22no—
132#552C2×C414yes—
133#552C2×C414yes—
134#551—24no—
135#551—24no—
136#551—24no—
137#551—24no—
138#551—24no—
139#551—24no—
140D4×Q8—21no—
141D4×Q8C2×C412yes—
142#548—22no—
143#548—22no—
144#547—21no—
145#547—22no—
146#547—22no—
147#547C2×C414yes—
148#547C2×C414yes—
149#547C2×C412yes—
150#546—22no—
151#546—22no—
152#546—22no—
153#546—22no—
154#546—22no—
155#546C2×C414yes—
156#546C2×C414yes—
157#546C2×C414yes—
158D42—21no—
159D42C2×C412yes—
160#544C2×C412yes—
161#543—22no—
162#542—22no—
163#542C2×C414yes—
164#541—22no—
165#541C2×C414yes—
166#539—24no—
167#539—22no—
168#539—24no—
169#539—22no—
170#539—24no—
171#538—24no—
172#538—24no—
173#538—24no—
174#537C2×C412yes—
175#536C2×C412yes—
176#536C2×C412yes—
177#534—22no—
178#534—24no—
179#533—22no—
180#533C2×C411yescharacteristic
181#533C2×C411yescharacteristic
182#533C2×C411yescharacteristic
183#533D411yescharacteristic
184#533D411yescharacteristic
185#533C2311yescharacteristic
186#533C2314yes—
187#532C2×C411yescharacteristic
188#532C2×C411yescharacteristic
189#532C2×C411yescharacteristic
190#532D411yescharacteristic
191#532D411yescharacteristic
192#532C2311yescharacteristic
193#529—24no—
194#529—22no—
195#529—22no—
196#529—24no—
197#529—22no—
198#529—22no—
199#529—22no—
200#529—24no—
201#529—22no—
202#529—24no—
203#529—22no—
204#529—24no—
205#529—24no—
206#529—21no—
207#529—21no—
208#529—21no—
209#529—21no—
210#529C2×C412yes—
211#529C2×C412yes—
212#529C2×C412yes—
213#529D412yes—
214#529D412yes—
215#529D412yes—
216#529D412yes—
217#529C2312yes—
218#529C2314yes—
219C2×#126—24no—
220C2×#125—22no—
221C2×#124—22no—
222#525—24no—
223#525—21no—
224#525—21no—
225#525—24no—
226#525C2×C412yes—
227#525C2×C412yes—
228#525D412yes—
229#525D412yes—
230C2×#123—24no—
231C2×C22⋊Q8—22no—
232C2×#121—22no—
233#520—22no—
234#520C2×C412yes—
235#520C2×C414yes—
236#520C2×C412yes—
237#518—24no—
238#518—22no—
239#518C2×C412yes—
240#518C2×C414yes—
241C4×#41—22no—
242C4×#41—21no—
243C4×#41—21no—
244C4×#41—21no—
245C4×#41—21no—
246C4×#41—21no—
247C4×#41—21no—
248C4×#41C2×C412yes—
249C4×#41C2×C412yes—
250C4×#41C2312yes—
251C4×#41C2312yes—
252C4×#41C2312yes—
253C4×#41C2314yes—
254C4×#41C2312yes—
255C4×#41C2312yes—
256C4×#41C2312yes—
257C2×C4×Q8—22no—
258C2×C4×Q8C2×C411yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4—21no—
262C2×C4×D4—24no—
263C2×C4×D4—22no—
264C2×C4×D4—22no—
265C2×C4×D4C2×C411yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2314yes—
268C2×#117—24no—
269C2×#117—21no—
270C2×#117C2×C411yescharacteristic
271C22×C42—21no—
272C22×C42C2311yescharacteristic
273#446—24no—
274#446—24no—
275#446—24no—
276#446—24no—
277#436—24no—
278#436—24no—
279#436—24no—
280#435—24no—
281#435—24no—
282#435—24no—
283#435—24no—
284#435—24no—
285#435—24no—
286#435—24no—
287#435—24no—
288C8×D4—24no—
289#433—24no—
290#433—24no—
291#433—24no—
292#432—21no—
293#432—21no—
294#432—21no—
295#432—21no—
296#432—21no—
297#432—21no—
298#432C2312yes—
299#432C2312yes—
300#432C2314yes—
301#431C2314yes—
302#431C2312yes—
303#431C2312yes—
304#431C2312yes—
305#431C2312yes—
306#431C2314yes—
307#431C2314yes—
308#424—22no—
309#424—24no—
310#424—24no—
311#423—21no—
312#423—21no—
313#423—21no—
314#423—21no—
315#423C2312yes—
316#423C2312yes—
317#423C2314yes—
318C2×C4⋊C8—21no—
319C2×C4⋊C8C2312yes—
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2314yes—
322C2×C4⋊C8C2311yescharacteristic
323#408—24no—
324#408—22no—
325#407—21no—
326#407—21no—
327C2×C22⋊C8—21no—
328#405—22no—
329C4×M16C2312yes—
330C4×M16C2312yes—
331C4×M16C2314yes—
332C2×#97—21no—
333C2×C4×C8C2314yes—
334Q8⋊C8C2314yes—
335Q8⋊C8C2314yes—
336Q8⋊C8C2314yes—
337Q8⋊C8C2314yes—
338Q8⋊C8C2314yes—
339Q8⋊C8C2314yes—
340Q8⋊C8C2314yes—
341Q8⋊C8C2314yes—
342D4⋊C8C2314yes—
343D4⋊C8C2314yes—
344D4⋊C8C2314yes—
345D4⋊C8C2314yes—
346D4⋊C8C2314yes—
347D4⋊C8C2314yes—
348D4⋊C8C2314yes—
349D4⋊C8C2314yes—
350H(5,𝔽2)—48no—
351C2×#41—22no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—44no—
357C2×#41C22×C412yes—
358C2×#41C22×C412yes—
359C2×#41C22×C414yes—
360C2×#41C22×C412yes—
361C2×#41C22×C412yes—
362C2×#41C2×D412yes—
363C2×#41C2×D412yes—
364C22×Q8—22no—
365C22×Q8C22×C411yescharacteristic
366C22×D4—21no—
367C22×D4—24no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4C22×C411yescharacteristic
371C22×D4C22×C414yes—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—24no—
375C23×C4—21no—
376C23×C4C22×C411yescharacteristic
377C23×C4C2×D411yescharacteristic
378C23×C4C2×D411yescharacteristic
379#131—84no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—24no—
383C2×M16—22no—
384C2×M16—22no—
385C2×M16—24no—
386C2×M16—82no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—22no—
390C22×C8—24no—
391C22×C8—24no—
392C4⋊Q8—22no—
393C4⋊Q8—22no—
394C4⋊Q8C22⋊C411yescharacteristic
395C4⋊Q8C22⋊C411yescharacteristic
396C4⋊Q8C22⋊C411yescharacteristic
397C4⋊Q8C22×C411yescharacteristic
398C4⋊Q8C22×C414yes—
399C4⋊Q8C22×C411yescharacteristic
400C4⋊Q8C22×C411yescharacteristic
401C4⋊Q8C22×C414yes—
402#127C22⋊C411yescharacteristic
403#127C22×C411yescharacteristic
404#126—24no—
405#126—24no—
406#126—24no—
407#126—24no—
408#126—24no—
409#126—24no—
410#126—24no—
411#126—24no—
412#126—24no—
413#126—24no—
414#126—24no—
415#126—22no—
416#126—22no—
417#126—24no—
418#126C22⋊C414yes—
419#126C22⋊C414yes—
420#125—24no—
421#125—24no—
422#125—22no—
423#125—22no—
424#125—24no—
425#125—24no—
426#125—22no—
427#125—24no—
428#125—21no—
429#125—21no—
430#125—24no—
431#125C22⋊C412yes—
432#125C22⋊C412yes—
433#125C22⋊C412yes—
434#125C22×C412yes—
435#125C22×C414yes—
436#124—22no—
437#124—22no—
438#124—22no—
439#124—24no—
440#124—24no—
441#124—24no—
442#124—24no—
443#124—21no—
444#124—21no—
445#124C22⋊C412yes—
446#124C22⋊C412yes—
447#124C22⋊C412yes—
448#124C22×C412yes—
449#124C22×C414yes—
450#123—24no—
451#123—24no—
452#123—24no—
453#123—22no—
454#123—22no—
455#123—22no—
456#123—24no—
457#123—24no—
458#123—24no—
459#123—24no—
460#123—24no—
461#123—24no—
462#123—24no—
463#123—24no—
464#123—24no—
465#123—24no—
466#123—24no—
467#123—24no—
468#123—24no—
469#123C22⋊C414yes—
470#123C22⋊C414yes—
471#123C22⋊C414yes—
472C22⋊Q8—22no—
473C22⋊Q8—24no—
474C22⋊Q8—24no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—24no—
481C22⋊Q8—22no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484C22⋊Q8—22no—
485C22⋊Q8—24no—
486C22⋊Q8—24no—
487C22⋊Q8—22no—
488C22⋊Q8—24no—
489C22⋊Q8—24no—
490C22⋊Q8—24no—
491C22⋊Q8C22⋊C412yes—
492C22⋊Q8C22⋊C412yes—
493C22⋊Q8C22⋊C412yes—
494C22⋊Q8C22⋊C412yes—
495C22⋊Q8C22⋊C412yes—
496C22⋊Q8C22⋊C412yes—
497C22⋊Q8C22×C412yes—
498C22⋊Q8C22×C412yes—
499C22⋊Q8C22×C414yes—
500C22⋊Q8C22×C414yes—
501C22⋊Q8C22×C414yes—
502#121—24no—
503#121—22no—
504#121—24no—
505#121—24no—
506#121—24no—
507#121—24no—
508#121—22no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—22no—
514#121—24no—
515#121—24no—
516#121—24no—
517#121C22⋊C412yes—
518#121C22⋊C412yes—
519#121C22⋊C412yes—
520#121C22⋊C412yes—
521#121C22⋊C412yes—
522#121C22⋊C412yes—
523#121C22×C412yes—
524#121C22×C412yes—
525#121C22×C414yes—
526#120—22no—
527#120—24no—
528#120—24no—
529#120—24no—
530#120—24no—
531#120C22⋊C414yes—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—24no—
536C4×Q8—21no—
537C4×Q8—21no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—24no—
543C4×Q8—21no—
544C4×Q8—21no—
545C4×Q8C22×C412yes—
546C4×Q8C22×C412yes—
547C4×Q8C22×C412yes—
548C4×Q8C22×C412yes—
549C4×Q8C22×C414yes—
550C4×Q8C22×C412yes—
551C4×Q8C22×C412yes—
552C4×Q8C2×D412yes—
553C4×Q8C2×D412yes—
554C4×Q8C2×D412yes—
555C4×Q8C2×D412yes—
556C4×Q8C2412yes—
557C4×Q8C2412yes—
558C4×D4—24no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—24no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—24no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—24no—
595C4×D4—21no—
596C4×D4—24no—
597C4×D4C22×C412yes—
598C4×D4C22×C412yes—
599C4×D4C22×C412yes—
600C4×D4C22×C414yes—
601C4×D4C22×C414yes—
602C4×D4C22×C412yes—
603C4×D4C22×C414yes—
604C4×D4C22×C414yes—
605C4×D4C22×C414yes—
606C4×D4C22×C412yes—
607C4×D4C22×C412yes—
608C4×D4C2×D414yes—
609C4×D4C2×D412yes—
610C4×D4C2×D412yes—
611C4×D4C2×D414yes—
612C4×D4C2×D412yes—
613C4×D4C2×D414yes—
614C4×D4C2×D414yes—
615C4×D4C2×D412yes—
616C4×D4C2412yes—
617C4×D4C2412yes—
618#117—21no—
619#117—21no—
620#117—21no—
621#117—24no—
622#117—21no—
623#117—24no—
624#117—24no—
625#117—24no—
626#117—22no—
627#117—24no—
628#117—24no—
629#117—22no—
630#117—22no—
631#117—22no—
632#117—22no—
633#117—22no—
634#117—22no—
635#117—24no—
636#117—22no—
637#117—24no—
638#117C22×C412yes—
639#117C22×C412yes—
640#117C22×C412yes—
641#117C22×C414yes—
642#117C22×C412yes—
643#117C22×C414yes—
644#117C2×D414yes—
645#117C2×D412yes—
646#117C2×D412yes—
647#117C2×D414yes—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—24no—
651C2×C4⋊C4—24no—
652C2×C4⋊C4—24no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—24no—
657C2×C4⋊C4C22×C411yescharacteristic
658C2×C4⋊C4C22×C411yescharacteristic
659C2×C4⋊C4C22×C414yes—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—24no—
666C2×C22⋊C4—24no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—24no—
669C2×C22⋊C4—24no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—22no—
674C2×C42—22no—
675C2×C42—22no—
676C2×C42—24no—
677C2×C42—22no—
678C2×C42—22no—
679C2×C42C22×C411yescharacteristic
680C2×C42C22×C411yescharacteristic
681C2×C42C22×C411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2414yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C4⋊C8—22no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—21no—
696C4⋊C8—24no—
697C4⋊C8—21no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—24no—
703C4⋊C8—24no—
704C4⋊C8—24no—
705C4⋊C8C2412yes—
706C4⋊C8C2414yes—
707C4⋊C8C2412yes—
708C22⋊C8—22no—
709C22⋊C8—22no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—22no—
713C22⋊C8—22no—
714C22⋊C8—24no—
715C22⋊C8—24no—
716C22⋊C8—24no—
717C22⋊C8—24no—
718#97—22no—
719#97—22no—
720#97—22no—
721#97—22no—
722#97—24no—
723#97—24no—
724C4×C8—24no—
725C4×C8—24no—
726C4×C8C2414yes—
727C4×C8C2414yes—
728C24—21no—
729C24—24no—
730C24C2×C22⋊C411yescharacteristic
731#41—24no—
732#41—24no—
733#41—28no—
734#41—42no—
735#41—44no—
736#41—42no—
737#41—42no—
738#41—42no—
739#41—44no—
740#41—44no—
741#41—44no—
742#41—44no—
743#41—48no—
744#41—81no—
745#41—81no—
746#41—82no—
747#41—82no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—24no—
752C2×Q8—42no—
753C2×Q8—84no—
754C2×Q8C2×C22⋊C412yes—
755C2×Q8C2×C22⋊C412yes—
756C2×Q8C2×C22⋊C412yes—
757C2×Q8C23×C412yes—
758C2×Q8C23×C412yes—
759C2×D4—24no—
760C2×D4—28no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—22no—
766C2×D4—22no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—24no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—44no—
773C2×D4—48no—
774C2×D4—44no—
775C2×D4—416no—
776C2×D4—84no—
777C2×D4C2×C22⋊C412yes—
778C2×D4C2×C22⋊C414yes—
779C2×D4C2×C22⋊C412yes—
780C2×D4C2×C22⋊C412yes—
781C2×D4C2×C22⋊C414yes—
782C2×D4C2×C22⋊C414yes—
783C2×D4C23×C412yes—
784C2×D4C23×C412yes—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—41no—
803C22×C4—42no—
804C22×C4—41no—
805C22×C4—44no—
806C22×C4—84no—
807C22×C4—81no—
808C22×C4—81no—
809C22×C4—84no—
810C22×C4—81no—
811C22×C4—82no—
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×D411yescharacteristic
832C22×C4C22×D414yes—
833M16—44no—
834M16—82no—
835M16—84no—
836M16—84no—
837M16—82no—
838M16—82no—
839C2×C8—24no—
840C2×C8—24no—
841C2×C8—22no—
842C2×C8—24no—
843C2×C8—22no—
844C2×C8—42no—
845C2×C8—42no—
846C2×C8—82no—
847C2×C8—84no—
848C2×C8—84no—
849C4⋊C4—21no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—21no—
853C4⋊C4—24no—
854C4⋊C4—22no—
855C4⋊C4—21no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4C2×C22⋊C414yes—
876C4⋊C4C2×C22⋊C414yes—
877C4⋊C4C2×C22⋊C412yes—
878C4⋊C4C2×C22⋊C414yes—
879C4⋊C4C2×C22⋊C412yes—
880C4⋊C4C2×C22⋊C412yes—
881C4⋊C4C2×C22⋊C414yes—
882C4⋊C4C2×C22⋊C412yes—
883C4⋊C4C2×C22⋊C414yes—
884C4⋊C4C2×C22⋊C412yes—
885C4⋊C4C2×C22⋊C412yes—
886C4⋊C4C2×C22⋊C414yes—
887C4⋊C4C23×C412yes—
888C4⋊C4C23×C412yes—
889C4⋊C4C23×C412yes—
890C4⋊C4C23×C412yes—
891C22⋊C4—22no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—24no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—22no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—22no—
914C22⋊C4—22no—
915C22⋊C4—22no—
916C22⋊C4C2×C22⋊C414yes—
917C22⋊C4C2×C22⋊C414yes—
918C22⋊C4C2×C22⋊C414yes—
919C22⋊C4C2×C22⋊C414yes—
920C22⋊C4C2×C22⋊C414yes—
921C22⋊C4C2×C22⋊C414yes—
922C22⋊C4C2×C22⋊C414yes—
923C22⋊C4C2×C22⋊C414yes—
924C22⋊C4C2×C22⋊C414yes—
925C42—22no—
926C42—22no—
927C42—22no—
928C42—22no—
929C42—22no—
930C42—22no—
931C42—24no—
932C42—24no—
933C42—22no—
934C42—22no—
935C42—22no—
936C42C2×C22⋊C411yescharacteristic
937C42C2×C22⋊C411yescharacteristic
938C42C2×C22⋊C411yescharacteristic
939C42C2×C22⋊C411yescharacteristic
940C42C2×C22⋊C411yescharacteristic
941C42C2×C22⋊C411yescharacteristic
942C42C23×C411yescharacteristic
943C42C23×C411yescharacteristic
944C42C23×C411yescharacteristic
945C42C23×C414yes—
946C42C22×D414yes—
947C42C22×D411yescharacteristic
948C42C22×D411yescharacteristic
949C42C22×D411yescharacteristic
950C42C22×D414yes—
951C42C22×D411yescharacteristic
952C42C22×D411yescharacteristic
953C42C22×D411yescharacteristic
954C42C2511yescharacteristic
955C23—24no—
956C23—22no—
957C23—22no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—48no—
962C23—81no—
963C23—81no—
964C23—84no—
965C23—84no—
966C23C22×C22⋊C414yes—
967C23C22×C22⋊C411yescharacteristic
968C23C22×C22⋊C411yescharacteristic
969C23C22×C22⋊C411yescharacteristic
970Q8—22no—
971Q8—22no—
972Q8—24no—
973Q8—42no—
974Q8—42no—
975Q8—42no—
976Q8—42no—
977Q8—42no—
978Q8—84no—
979Q8—81no—
980D4—24no—
981D4—22no—
982D4—24no—
983D4—42no—
984D4—44no—
985D4—42no—
986D4—42no—
987D4—44no—
988D4—44no—
989D4—48no—
990D4—42no—
991D4—48no—
992D4—44no—
993D4—44no—
994D4—44no—
995D4—81no—
996D4—84no—
997D4—82no—
998D4—82no—
999D4#56814yes—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—24no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—44no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—44no—
1033C2×C4—44no—
1034C2×C4—48no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—82no—
1043C2×C4—84no—
1044C2×C4—84no—
1045C2×C4—82no—
1046C2×C4—84no—
1047C2×C4—82no—
1048C2×C4—81no—
1049C2×C4—84no—
1050C2×C4—81no—
1051C2×C4C22×C22⋊C411yescharacteristic
1052C2×C4C22×C22⋊C411yescharacteristic
1053C2×C4C22×C22⋊C411yescharacteristic
1054C2×C4C22×C22⋊C411yescharacteristic
1055C2×C4C22×C22⋊C411yescharacteristic
1056C2×C4C22×C22⋊C411yescharacteristic
1057C2×C4C22×C22⋊C411yescharacteristic
1058C2×C4C22×C22⋊C414yes—
1059C2×C4C22×C22⋊C414yes—
1060C2×C4C22×C22⋊C411yescharacteristic
1061C2×C4C22×C22⋊C411yescharacteristic
1062C2×C4C22×C22⋊C414yes—
1063C2×C4C24×C411yescharacteristic
1064C2×C4C23×D411yescharacteristic
1065C2×C4C23×D411yescharacteristic
1066C8—44no—
1067C8—44no—
1068C8—42no—
1069C8—44no—
1070C8—42no—
1071C22—21no—
1072C22—21no—
1073C22—21no—
1074C22—24no—
1075C22—24no—
1076C22—21no—
1077C22—21no—
1078C22—21no—
1079C22—24no—
1080C22—21no—
1081C22—21no—
1082C22—21no—
1083C22—24no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—84no—
1090C22—82no—
1091C22—168no—
1092C22C23×C22⋊C411yescharacteristic
1093C4—21no—
1094C4—21no—
1095C4—21no—
1096C4—24no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—24no—
1101C4—21no—
1102C4—21no—
1103C4—21no—
1104C4—21no—
1105C4—24no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4C2×#56812yes—
1113C4#358511yescharacteristic
1114C4#358611yescharacteristic
1115C2—41no—
1116C2—41no—
1117C2—41no—
1118C2—44no—
1119C2—44no—
1120C2—82no—
1121C2#6006411yescharacteristic
1122C2#6008911yescharacteristic
1123C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62781C2
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. #60281C2semidirect
3. #60269C2semidirect
4. #17523C2semidirect
5. #17521C2semidirect
6. #17513C2semidirect
7. #17512C2semidirect
8. #17506C2semidirect
9. #17498C2semidirect
10. #17494C2semidirect
11. #17453C2semidirect
12. #17452C2semidirect
13. #17451C2semidirect
45. #2990C22semidirect
46. #2989C22semidirect
50. #2965C22semidirect
51. #2965C22semidirect
55. #2925C22semidirect
56. #2922C22semidirect
57. #2920C22semidirect
58. #2920C22semidirect
59. C2×#432C22semidirect
60. #2906C22semidirect
61. C2×#423C22semidirect
62. #1497C22semidirect
63. #1497C22semidirect
64. #1496C22semidirect
65. #1495C22semidirect
66. #1495C22semidirect
67. #1494C22semidirect
68. #1493C22semidirect
69. #1491C22semidirect
71. #1490C22semidirect
72. #1489C22semidirect
73. #1489C22semidirect
74. #1489C22semidirect
75. #1488C22semidirect
76. #1488C22semidirect
77. #1488C22semidirect
78. #1487C22semidirect
80. #1486C22semidirect
81. #1485C22semidirect
82. #1483C22semidirect
83. #1483C22semidirect
84. #1483C22semidirect
85. #1482C22semidirect
86. #1481C22semidirect
87. #1481C22semidirect
88. #1480C22semidirect
89. #1478C22semidirect
90. #1477C22semidirect
91. #1477C22semidirect
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
#627812
#602812
#602692
#175232
#175212
#175132
#175122
#175062
#174982
#174942
#174532
#174522
#174512