Finite Group Databasebeta

← #6396559

Subgroups — #6396559

Order 512.

1858 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60790C211yesmaximal, characteristic
2#60268C211yesmaximal, characteristic, complemented
3#60236C211yesmaximal, characteristic, complemented
4#23115C214yesmaximal, complemented
5#23017C214yesmaximal, complemented
6#22888C214yesmaximal, complemented
7#22886C214yesmaximal, complemented
8#22281C211yesmaximal, characteristic, complemented
9#22281C211yesmaximal, characteristic, complemented
10#22235C211yesmaximal, characteristic, complemented
11#22235C211yesmaximal, characteristic, complemented
12#21994C211yesmaximal, characteristic, complemented
13#21709C211yesmaximal, characteristic, complemented
14#21708C211yesmaximal, characteristic, complemented
15#21663C211yesmaximal, characteristic, complemented
16#21661C211yesmaximal, characteristic, complemented
17#21417C211yesmaximal, characteristic, complemented
18C2×#1963C211yesmaximal, characteristic, complemented
19#20469C211yesmaximal, characteristic, complemented
20#3444C2211yescharacteristic
21C2×#532C2211yescharacteristic
22#3219C412yescomplemented
23#3219C412yescomplemented
24#3218C412yescomplemented
25#3217C412yescomplemented
26#3216C412yescomplemented
27#3215C412yescomplemented
28#3214C412yescomplemented
29#3213C412yescomplemented
30#3150C2211yescharacteristic
31#3150C2211yescharacteristic
32#3135C2211yescharacteristic
33#3135C2211yescharacteristic
34#3035C2214yes—
35#3002C2214yes—
36#2994—21no—
37#2994—21no—
38#2993—21no—
39#2993—21no—
40#2991—21no—
41#2990—21no—
42#2989—21no—
43#2988—21no—
44#2981—21no—
45#2981—21no—
46#2979—21no—
47#2979—21no—
48#2975—21no—
49#2974—21no—
50#2974—21no—
51#2972—21no—
52#2960C2211yescharacteristic, complemented
53#2960C2211yescharacteristic, complemented
54C2×#444C2214yescomplemented
55C2×#443C2214yescomplemented
56#2935C2212yes—
57#2935C2212yes—
58#2933C2212yes—
59#2933C2212yes—
60#2931C2211yescharacteristic
61#2931C2211yescharacteristic
62#2931C2211yescharacteristic
63#2931C2211yescharacteristic
64#2931C2211yescharacteristic, complemented
65#2931C2211yescharacteristic, complemented
66#2925C2212yescomplemented
67#2920C2211yescharacteristic
68C2×#432C2211yescharacteristic
69C2×#431C2211yescharacteristic
70#2906C2212yescomplemented
71C2×#423C2211yescharacteristic
72C22×#104C2214yes—
73#2880C2212yes—
74#2880C2212yes—
75C2×#376C2211yescharacteristic
76#1995C2211yescharacteristic, complemented
77#1995C2211yescharacteristic, complemented
78#1975C2214yescomplemented
79#1974C2214yescomplemented
80#1963C2211yescharacteristic
81#1963C2211yescharacteristic
82#1963C2214yes—
83#1963C2211yescharacteristic
84#1963C2211yescharacteristic
85#1963C2211yescharacteristic, complemented
86#1963C2211yescharacteristic, complemented
87#1950C2214yescomplemented
88#1938C2214yescomplemented
89#1937C2214yescomplemented
90#1929C2214yescomplemented
91#1929C2214yescomplemented
92#1896C2214yes—
93#1876C2214yescomplemented
94#1876C2214yescomplemented
95#1876C2214yescomplemented
96#1876C2214yescomplemented
97#1866C2214yescomplemented
98#1866C2214yescomplemented
99#1855C2214yes—
100#1849C2211yescharacteristic, complemented
101#1849C2211yescharacteristic, complemented
102#1838C2211yescharacteristic, complemented
103#1838C2211yescharacteristic, complemented
104#1768C2212yescomplemented
105#1768C2212yescomplemented
106#1765C2214yescomplemented
107#1764C2214yescomplemented
108#1759C2214yescomplemented
109#1749C2212yes—
110C4×C22⋊C8C2212yes—
111#1746C2211yescharacteristic, complemented
112#1746C2211yescharacteristic, complemented
113#1726C2211yescharacteristic, complemented
114#1726C2211yescharacteristic, complemented
115C22×#41C2312yes—
116C2×#135C2314yes—
117C2×#135C2314yes—
118C2×#131C2312yes—
119C2×#131C2312yes—
120C2×#131C2312yes—
121C2×#131C2312yes—
122C2×#131C2312yes—
123C2×#131C2312yes—
124C22×M16C2312yes—
125#533C2×C411yescharacteristic
126#533C2×C411yescharacteristic
127#533C2311yescharacteristic
128#532—21no—
129#532—21no—
130#532—21no—
131#532—21no—
132#532C2×C412yes—
133#532C2×C411yescharacteristic
134#532C2×C411yescharacteristic
135#532C2×C411yescharacteristic
136#532C2×C411yescharacteristic
137#532C2311yescharacteristic
138#532C2311yescharacteristic
139#532C2311yescharacteristic
140#532C2312yes—
141C2×C4⋊Q8C2×C411yescharacteristic
142C2×#127C2×C411yescharacteristic
143#529—21no—
144#529—21no—
145#529—21no—
146#529—21no—
147#529C2×C412yes—
148#529C2×C412yes—
149C2×#124C2×C412yes—
150#525—21no—
151#525—21no—
152#525C2312yes—
153C2×#121—21no—
154C2×#121—21no—
155C4×#41—21no—
156C4×#41—21no—
157C4×#41C2312yes—
158C2×C4×D4—21no—
159C2×C4×D4—21no—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162#497C2×C412yescomplemented
163#497C2×C412yescomplemented
164#497C2×C412yescomplemented
165#497C2×C412yescomplemented
166#496C2×C412yescomplemented
167#496C2×C412yescomplemented
168#496C2×C412yescomplemented
169#496C2×C412yescomplemented
170#491C2×C412yescomplemented
171#491C2×C412yescomplemented
172#490C2×C412yescomplemented
173#490C2×C412yescomplemented
174#489C2×C412yescomplemented
175#489C2×C412yescomplemented
176#489C2×C412yescomplemented
177#489C2×C412yescomplemented
178#464C2×C414yescomplemented
179#464C2×C414yescomplemented
180#463C2×C414yescomplemented
181#463C2×C414yescomplemented
182#462C2×C414yescomplemented
183#461C2×C414yescomplemented
184#460C2×C414yescomplemented
185#459C2×C414yescomplemented
186#452C2×C414yes—
187#452C2×C414yes—
188#451C2×C414yes—
189#450C2×C414yes—
190#449C2×C414yes—
191#449C2×C414yes—
192#448C2×C414yes—
193#447C2×C414yes—
194#446—21no—
195#446—21no—
196#446—21no—
197#446—21no—
198C8×Q8—21no—
199C8×Q8—21no—
200C8×Q8—21no—
201C8×Q8—21no—
202#444—48no—
203#443—48no—
204#436—22no—
205#436—22no—
206#436—22no—
207#436—22no—
208#436—21no—
209#436—21no—
210#436—21no—
211#436—21no—
212#436—21no—
213#436—21no—
214#436—21no—
215#436—21no—
216#436—21no—
217#436—21no—
218#436—21no—
219#436—21no—
220#435—22no—
221#435—22no—
222#435—22no—
223#435—22no—
224#435—22no—
225#435—22no—
226#435—22no—
227#435—22no—
228C8×D4—22no—
229C8×D4—22no—
230C8×D4—22no—
231C8×D4—22no—
232C8×D4—21no—
233C8×D4—21no—
234C8×D4—21no—
235C8×D4—21no—
236C8×D4—21no—
237C8×D4—21no—
238C8×D4—21no—
239C8×D4—21no—
240C8×D4—21no—
241C8×D4—21no—
242C8×D4—21no—
243C8×D4—21no—
244#433—22no—
245#433—22no—
246#432—21no—
247#432—21no—
248#432—22no—
249#432C2×C412yes—
250#432C2×C412yes—
251#432C2×C412yes—
252#432C2×C412yes—
253#431—21no—
254#431—21no—
255#431—22no—
256#431D411yescharacteristic
257#431D411yescharacteristic
258#431D411yescharacteristic
259#431D411yescharacteristic
260#431D411yescharacteristic
261#431D411yescharacteristic
262#431D411yescharacteristic
263#431D411yescharacteristic
264C2×#108C2314yes—
265C2×#108C2314yes—
266#424—22no—
267#424—22no—
268#424C2312yes—
269#424C2312yes—
270#423—21no—
271#423—21no—
272#423—22no—
273#423C2311yescharacteristic
274#423C2311yescharacteristic
275#423C2311yescharacteristic
276#423C2311yescharacteristic
277#423C2312yes—
278C2×C4⋊C8—21no—
279C2×C4⋊C8—21no—
280C2×C4⋊C8—22no—
281C2×C4⋊C8C2312yes—
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#104—48no—
285C2×#104C2314yes—
286C2×#104C2314yes—
287C2×#104C2314yes—
288C2×#104C2314yes—
289C2×#104C2314yes—
290C2×#104C2314yes—
291#416C2314yes—
292#416C2314yes—
293#408—22no—
294#408—22no—
295#408—22no—
296#408—22no—
297#408C2312yes—
298#408C2312yes—
299#408C2312yes—
300#408C2312yes—
301#408C2312yes—
302#408C2312yes—
303#407—22no—
304#407—22no—
305#407C2312yes—
306C2×C22⋊C8—22no—
307C2×C22⋊C8—22no—
308C2×C22⋊C8C2312yes—
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311#405C2312yes—
312#405C2312yes—
313C4×M16C2312yes—
314C2×#97C2312yes—
315C2×#97C2312yes—
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2312yes—
319C2×C4×C8C2312yes—
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#376—21no—
323#376—21no—
324#376C2311yescharacteristic
325#376C2311yescharacteristic
326#376C2312yes—
327C2×#95—21no—
328C2×#95—21no—
329#341C2314yes—
330#341C2314yes—
331#339C2314yes—
332#339C2314yes—
333#336C2312yes—
334#336C2312yes—
335#336C2312yes—
336#336C2312yes—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—44no—
342C2×#41—44no—
343C2×#41C22×C412yes—
344C2×#41C22×C412yes—
345C2×#41C2412yes—
346C2×#41C2412yes—
347C2×#41C2412yes—
348C22×Q8C22×C412yes—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4C22×C412yes—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4#4111yescharacteristic
356C23×C4#4111yescharacteristic
357C23×C4C2411yescharacteristic
358#135—44no—
359#135—44no—
360#135—44no—
361#135—44no—
362C2×Q16C22×C414yes—
363C2×Q16C22×C414yes—
364C2×SD16C22×C414yes—
365C2×SD16C22×C414yes—
366C2×SD16C22×C414yes—
367C2×SD16C22×C414yes—
368C2×D8C22×C414yes—
369C2×D8C22×C414yes—
370#131—44no—
371#131—44no—
372#131—44no—
373#131—44no—
374#131—44no—
375#131—44no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—44no—
384C2×M16C2412yes—
385C2×M16C2412yes—
386C2×M16C2412yes—
387C2×M16C2412yes—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—22no—
394C22×C8—22no—
395C22×C8C2412yes—
396C22×C8C2412yes—
397C22×C8C2411yescharacteristic
398C22×C8C2411yescharacteristic
399C22×C8C2411yescharacteristic
400C22×C8C2411yescharacteristic
401C4⋊Q8—21no—
402C4⋊Q8—21no—
403C4⋊Q8C22×C412yes—
404C4⋊Q8C22×C411yescharacteristic
405C4⋊Q8C22×C411yescharacteristic
406C4⋊Q8C22×C411yescharacteristic
407C4⋊Q8C22×C411yescharacteristic
408C4⋊Q8C22×C411yescharacteristic
409#127—21no—
410#127—21no—
411#127C22×C412yes—
412#127C22×C411yescharacteristic
413#127C22×C411yescharacteristic
414#127C22×C411yescharacteristic
415#126—22no—
416#126—22no—
417#125—21no—
418#125—21no—
419#125C22×C412yes—
420#124—22no—
421#124—22no—
422#124—21no—
423#124—21no—
424#124C22×C412yes—
425#124C22×C412yes—
426#124C22×C412yes—
427#124C22×C412yes—
428#124C22×C412yes—
429#123—22no—
430#123—22no—
431#123—22no—
432C22⋊Q8—21no—
433C22⋊Q8—21no—
434C22⋊Q8—21no—
435C22⋊Q8—21no—
436C22⋊Q8C22×C412yes—
437C22⋊Q8C22×C412yes—
438#121—22no—
439#121—21no—
440#121—21no—
441#121—22no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121—22no—
447#121—22no—
448#121—21no—
449#121—21no—
450#121—21no—
451#121—21no—
452#121—21no—
453#121—21no—
454#121C22×C412yes—
455#121C22×C412yes—
456#120—22no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×Q8—21no—
461C4×Q8C22×C412yes—
462C4×Q8C22×C412yes—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—21no—
470C4×D4—21no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—22no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—22no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4C22×C412yes—
486C4×D4C22×C412yes—
487#117—21no—
488#117—21no—
489#117—22no—
490#117—22no—
491#117—22no—
492#117C2412yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C42—22no—
498C2×C42—24no—
499C2×C42—22no—
500C2×C42—42no—
501C2×C42C22×C411yescharacteristic
502C2×C42C22×C411yescharacteristic
503C2×C42C22×C411yescharacteristic
504C2×C42C22×C411yescharacteristic
505C2×C42C2×D411yescharacteristic
506C2×C42C2×D411yescharacteristic
507C2×C42C2×D411yescharacteristic
508C2×C42C2×D411yescharacteristic
509C2×C42#4111yescharacteristic
510C2×C42#4111yescharacteristic
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2411yescharacteristic
514C2×C42C2411yescharacteristic
515#108—44no—
516#108—44no—
517C4⋊C8—22no—
518C4⋊C8—22no—
519C4⋊C8—22no—
520C4⋊C8—22no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523C4⋊C8—21no—
524C4⋊C8—21no—
525C4⋊C8—21no—
526C4⋊C8—21no—
527C4⋊C8—21no—
528C4⋊C8—21no—
529C4⋊C8—21no—
530C4⋊C8—21no—
531C4⋊C8C22×C414yes—
532C4⋊C8C22×C414yes—
533C4⋊C8C2×D411yescharacteristic
534C4⋊C8C2×D411yescharacteristic
535C4⋊C8C2×D411yescharacteristic
536C4⋊C8C2×D411yescharacteristic
537C4⋊C8C2×D411yescharacteristic
538C4⋊C8C2×D411yescharacteristic
539C4⋊C8C2×D411yescharacteristic
540C4⋊C8C2×D411yescharacteristic
541#104—28no—
542#104—28no—
543#104—28no—
544#104—44no—
545#104—44no—
546#104—44no—
547#103C22×C414yes—
548#103C22×C414yes—
549#103C22×C414yes—
550#103C22×C414yes—
551#102C22×C414yes—
552#102C22×C414yes—
553#102C22×C414yes—
554#102C22×C414yes—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—22no—
559C22⋊C8—22no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—22no—
565C22⋊C8—22no—
566C22⋊C8—22no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8C22×C414yes—
570C22⋊C8C22×C414yes—
571C22⋊C8C2×D411yescharacteristic
572C22⋊C8C2×D411yescharacteristic
573C22⋊C8C2×D411yescharacteristic
574C22⋊C8C2×D411yescharacteristic
575C22⋊C8C2×D411yescharacteristic
576C22⋊C8C2×D411yescharacteristic
577C22⋊C8C2×D411yescharacteristic
578C22⋊C8C2×D411yescharacteristic
579#97—22no—
580#97—22no—
581#97—22no—
582#97—24no—
583#97—42no—
584#97C22×C412yes—
585#97C22×C412yes—
586#97C22×C412yes—
587#97C22×C412yes—
588C4×C8—22no—
589C4×C8—22no—
590C4×C8—22no—
591C4×C8—24no—
592C4×C8—42no—
593C4×C8C2×D411yescharacteristic
594C4×C8C2×D411yescharacteristic
595C4×C8C2×D411yescharacteristic
596C4×C8C2×D411yescharacteristic
597C4×C8C2×D411yescharacteristic
598C4×C8C2×D411yescharacteristic
599C4×C8C2×D411yescharacteristic
600C4×C8C2×D411yescharacteristic
601#95—21no—
602#95—21no—
603#95—22no—
604#95—22no—
605#95—21no—
606#95—21no—
607C24—22no—
608C24C2×#4111yescharacteristic
609#41—24no—
610#41—24no—
611#41—24no—
612#41—24no—
613#41—24no—
614#41—24no—
615#41—44no—
616#41—44no—
617#41—44no—
618#41—82no—
619#41—82no—
620#41—84no—
621#41—82no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—44no—
626C2×Q8C23×C412yes—
627C2×Q8C23×C412yes—
628C2×Q8C23×C412yes—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—84no—
649C2×D4C23×C412yes—
650C2×D4C23×C412yes—
651C2×D4C23×C412yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—42no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—82no—
668C22×C4—82no—
669C22×C4—81no—
670C22×C4—82no—
671C22×C4C4×D411yescharacteristic
672C22×C4C4×D411yescharacteristic
673C22×C4C4×D411yescharacteristic
674C22×C4C4×D411yescharacteristic
675C22×C4C4×D411yescharacteristic
676C22×C4C4×D411yescharacteristic
677C22×C4C4×D411yescharacteristic
678C22×C4C4×D411yescharacteristic
679C22×C4C23×C411yescharacteristic
680C22×C4C23×C411yescharacteristic
681C22×C4C22×D411yescharacteristic
682C22×C4C22×D411yescharacteristic
683C22×C4C2×#4111yescharacteristic
684C22×C4C2×#4111yescharacteristic
685C22×C4C2×#4111yescharacteristic
686C22×C4C2×#4111yescharacteristic
687C22×C4C2×#4111yescharacteristic
688C22×C4C2511yescharacteristic
689Q16—44no—
690Q16—44no—
691SD16—44no—
692SD16—44no—
693SD16—44no—
694SD16—44no—
695D8—44no—
696D8—44no—
697M16—24no—
698M16—24no—
699M16—24no—
700M16—24no—
701M16—82no—
702M16—82no—
703M16—82no—
704M16—82no—
705M16—82no—
706M16—82no—
707M16—82no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—22no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—82no—
721C2×C8—82no—
722C2×C8—82no—
723C2×C8—82no—
724C2×C8—82no—
725C2×C8—82no—
726C2×C8—82no—
727C2×C8C23×C414yes—
728C2×C8C23×C414yes—
729C2×C8C22×D411yescharacteristic
730C2×C8C22×D411yescharacteristic
731C2×C8C22×D411yescharacteristic
732C2×C8C22×D411yescharacteristic
733C2×C8C22×D411yescharacteristic
734C2×C8C22×D411yescharacteristic
735C2×C8C22×D411yescharacteristic
736C2×C8C22×D411yescharacteristic
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—22no—
748C4⋊C4—22no—
749C4⋊C4—22no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—22no—
753C4⋊C4C23×C412yes—
754C4⋊C4C23×C412yes—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—22no—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C42—22no—
773C42—22no—
774C42—22no—
775C42—22no—
776C42—22no—
777C42—22no—
778C42—44no—
779C42C4×D411yescharacteristic
780C42C4×D411yescharacteristic
781C42C4×D411yescharacteristic
782C42C4×D411yescharacteristic
783C42C4×D411yescharacteristic
784C42C4×D411yescharacteristic
785C42C4×D411yescharacteristic
786C42C4×D411yescharacteristic
787C42C23×C411yescharacteristic
788C42C23×C411yescharacteristic
789C42C23×C411yescharacteristic
790C42C23×C411yescharacteristic
791C42C22×D411yescharacteristic
792C42C22×D411yescharacteristic
793C42C22×D411yescharacteristic
794C42C22×D411yescharacteristic
795C42H(5,𝔽2)14yes—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—41no—
802C23—44no—
803C23—82no—
804C23—82no—
805C23C2×C4×D411yescharacteristic
806C23C2×C4×D411yescharacteristic
807C23C22×#4111yescharacteristic
808Q8—24no—
809Q8—24no—
810Q8—24no—
811Q8—42no—
812Q8—42no—
813Q8—82no—
814D4—24no—
815D4—24no—
816D4—24no—
817D4—44no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—42no—
823D4—42no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—44no—
828D4—82no—
829D4—82no—
830D4—82no—
831D4—82no—
832D4—82no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—82no—
871C2×C4—82no—
872C2×C4—82no—
873C2×C4—82no—
874C2×C4—88no—
875C2×C4C2×C4×D411yescharacteristic
876C2×C4C2×C4×D411yescharacteristic
877C2×C4C2×C4×D411yescharacteristic
878C2×C4C2×C4×D411yescharacteristic
879C2×C4C2×C4×D411yescharacteristic
880C2×C4C2×C4×D411yescharacteristic
881C2×C4C2×C4×D411yescharacteristic
882C2×C4C2×C4×D411yescharacteristic
883C2×C4C2×C4×D411yescharacteristic
884C2×C4C2×C4×D411yescharacteristic
885C2×C4C24×C411yescharacteristic
886C2×C4C23×D411yescharacteristic
887C2×C4C2×H(5,𝔽2)12yes—
888C2×C4#58512yes—
889C8—24no—
890C8—24no—
891C8—21no—
892C8—21no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—21no—
898C8—21no—
899C8—42no—
900C8—42no—
901C8—42no—
902C8—42no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—44no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—164no—
921C22#295512yes—
922C22C22×C4×D411yescharacteristic
923C22#349412yes—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—44no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—82no—
941C4C4×H(5,𝔽2)12yes—
942C4#349811yescharacteristic
943C4#350011yescharacteristic
944C2—22no—
945C2—22no—
946C2—41no—
947C2—82no—
948C2—82no—
949C2—82no—
950C2#3427511yescharacteristic
951C2C2×#295511yescharacteristic
952C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×C4×D4
prime radical#60790C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#431 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60268C2semidirect
3. #60236C2semidirect
4. #23115C2semidirect
5. #23017C2semidirect
6. #22888C2semidirect
7. #22886C2semidirect
8. #22281C2semidirect
9. #22281C2semidirect
10. #22235C2semidirect
11. #22235C2semidirect
12. #21994C2semidirect
13. #21709C2semidirect
14. #21708C2semidirect
15. #21663C2semidirect
16. #21661C2semidirect
17. #21417C2semidirect
18. C2×#1963C2semidirect
19. #20469C2semidirect
22. #3219C4semidirect
23. #3219C4semidirect
24. #3218C4semidirect
25. #3217C4semidirect
26. #3216C4semidirect
27. #3215C4semidirect
28. #3214C4semidirect
29. #3213C4semidirect
52. #2960C22semidirect
53. #2960C22semidirect
54. C2×#444C22semidirect
55. C2×#443C22semidirect
64. #2931C22semidirect
65. #2931C22semidirect
66. #2925C22semidirect
70. #2906C22semidirect
76. #1995C22semidirect
77. #1995C22semidirect
78. #1975C22semidirect
79. #1974C22semidirect
85. #1963C22semidirect
86. #1963C22semidirect
87. #1950C22semidirect
88. #1938C22semidirect
89. #1937C22semidirect
90. #1929C22semidirect
91. #1929C22semidirect
93. #1876C22semidirect
94. #1876C22semidirect
95. #1876C22semidirect
96. #1876C22semidirect
97. #1866C22semidirect
98. #1866C22semidirect
100. #1849C22semidirect
101. #1849C22semidirect
102. #1838C22semidirect
103. #1838C22semidirect
104. #1768C22semidirect
105. #1768C22semidirect
106. #1765C22semidirect
107. #1764C22semidirect
108. #1759C22semidirect
111. #1746C22semidirect
112. #1746C22semidirect
113. #1726C22semidirect
114. #1726C22semidirect
162. #497C2×C4semidirect
163. #497C2×C4semidirect
164. #497C2×C4semidirect
165. #497C2×C4semidirect
166. #496C2×C4semidirect
167. #496C2×C4semidirect
168. #496C2×C4semidirect
169. #496C2×C4semidirect
170. #491C2×C4semidirect
171. #491C2×C4semidirect
172. #490C2×C4semidirect
173. #490C2×C4semidirect
174. #489C2×C4semidirect
175. #489C2×C4semidirect
176. #489C2×C4semidirect
177. #489C2×C4semidirect
178. #464C2×C4semidirect
179. #464C2×C4semidirect
180. #463C2×C4semidirect
181. #463C2×C4semidirect
182. #462C2×C4semidirect
183. #461C2×C4semidirect
184. #460C2×C4semidirect
185. #459C2×C4semidirect

Maximal subgroups

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

subgroupindex
#607902
#602682
#602362
#231152
#230172
#228882
#228862
#222812
#222352
#219942
#217092
#217082
#216632
#216612
#214172
C2×#19632
#204692