Finite Group Databasebeta

← #6500329

Subgroups — #6500329

Order 512.

2808 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3195C211yesmaximal, characteristic, complemented
2C2×#3007C211yesmaximal, characteristic
3C2×#2432C211yesmaximal, characteristic
4#34212C211yesmaximal, characteristic, complemented
5#28124C212yesmaximal, complemented
6#28120C212yesmaximal, complemented
7#25100C214yesmaximal, complemented
8#25098C214yesmaximal, complemented
9#24491C214yesmaximal, complemented
10#24369C214yesmaximal, complemented
11#24217C212yesmaximal, complemented
12#24212C212yesmaximal, complemented
13#21934C211yesmaximal, characteristic, complemented
14#21765C211yesmaximal, characteristic, complemented
15#20601C211yesmaximal, characteristic
16C23×#41C2211yescharacteristic
17C22×#137C2212yes—
18C22×C4⋊Q8C2211yescharacteristic
19C22×#124C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22#3195—28no—
23C2×#483C2212yes—
24C2×#483C2212yescomplemented
25C2×#470C2214yescomplemented
26C2×#464C2214yescomplemented
27C2×#462C2214yescomplemented
28#3007—28no—
29C2×#452C2214yes—
30C2×#451C2212yes—
31C2×#451C2212yes—
32C2×#451C2212yescomplemented
33C2×#450C2212yes—
34C2×#417C2212yes—
35C2×#417C2212yes—
36C2×#417C2212yes—
37C2×#407C2211yescharacteristic
38C2×#407C2211yescharacteristic
39#2432—22no—
40#2432—22no—
41#2432C2214yes—
42#2432C2214yes—
43C2×#394—21no—
44C2×#394—21no—
45#2368—22no—
46#2360C2212yescomplemented
47#2360C2212yescomplemented
48#2345—22no—
49#2345C2212yescomplemented
50Q8×C22⋊C4C2212yescomplemented
51#2329—21no—
52#2329—21no—
53#2315—21no—
54C4×C22⋊Q8C2212yes—
55C4×C22⋊Q8C2212yes—
56C2×#391C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#385—21no—
59C2×#385—21no—
60C2×#380C2211yescharacteristic
61#2273—21no—
62C2×C4×C22⋊C4C2211yescharacteristic
63#2066C2214yescomplemented
64#2065C2214yescomplemented
65#2056C2214yescomplemented
66#2055C2214yescomplemented
67#2043C2214yescomplemented
68#2042C2214yescomplemented
69#2016C2214yescomplemented
70#2015C2214yescomplemented
71#1983C2214yescomplemented
72#1981C2214yescomplemented
73#1927C2214yescomplemented
74#1926C2214yescomplemented
75#1894C2214yescomplemented
76#1880C2214yescomplemented
77#1878C2214yescomplemented
78#1872C2212yescomplemented
79#1872C2212yescomplemented
80#1851C2214yescomplemented
81#1851C2214yescomplemented
82#1823C2212yes—
83#1797C2212yes—
84#1797C2212yes—
85#1788C2214yes—
86#1787C2212yes—
87#1787C2212yes—
88#1786C2212yes—
89C22×#41—21no—
90C22×#41—21no—
91C22×#41—24no—
92C22×#41—24no—
93C22×#41—44no—
94C22×#41—44no—
95C22×#41C2312yes—
96C22×#41C2312yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4C2311yescharacteristic
104C2×#137—28no—
105C2×#137—44no—
106C2×#137—44no—
107C22×Q16C2314yes—
108C22×Q16C2314yes—
109C22×SD16C2314yes—
110C22×M16C2312yes—
111C22×M16C2312yes—
112C2×C4⋊Q8—22no—
113C2×C4⋊Q8—44no—
114C2×C4⋊Q8C2314yes—
115C2×#124—22no—
116C2×#124—44no—
117C2×#124C2314yes—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8D418yes—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×C4×Q8C2312yes—
131C2×C4×Q8C2312yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#483—28no—
152#483—28no—
153#470—216no—
154#464—48no—
155#462—48no—
156#452—216no—
157#451—28no—
158#451—28no—
159#451—28no—
160#450—28no—
161C2×#106C2314yes—
162C2×C4⋊C8C2314yes—
163C2×C4⋊C8C2314yes—
164#417—28no—
165#417—44no—
166#417—44no—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177#407—24no—
178#407—24no—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183#394—24no—
184#394—24no—
185#394—24no—
186#394—24no—
187#391—22no—
188#391—22no—
189#391—22no—
190#391C2312yes—
191#391C2312yes—
192#391C2314yes—
193#390—22no—
194#390C2314yes—
195#389—22no—
196#389—22no—
197#389C2312yes—
198#389C2312yes—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#387—22no—
205#385—22no—
206#385—22no—
207#385—22no—
208#385—22no—
209#385—24no—
210#385—24no—
211#385—24no—
212#385—24no—
213#380—21no—
214#380—21no—
215#380—22no—
216#380—22no—
217#380C2312yes—
218#380C2312yes—
219C4×C4⋊C4—22no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4C2312yes—
222C4×C4⋊C4C2312yes—
223C4×C22⋊C4—22no—
224C4×C22⋊C4—22no—
225C4×C22⋊C4—22no—
226C4×C22⋊C4—22no—
227C4×C22⋊C4—22no—
228C4×C22⋊C4—22no—
229C4×C22⋊C4D412yes—
230C4×C22⋊C4D412yes—
231C4×C22⋊C4C2312yes—
232C4×C22⋊C4C2312yes—
233C2×#95—21no—
234C2×#95—21no—
235C2×#95—21no—
236C2×#95D411yescharacteristic
237C2×#95D411yescharacteristic
238#340C2314yes—
239#340C2314yes—
240#336C2314yes—
241#336C2314yes—
242C25—21no—
243C25C2×D411yescharacteristic
244C2×#41—24no—
245C2×#41—24no—
246C2×#41—24no—
247C2×#41—24no—
248C2×#41—24no—
249C2×#41—24no—
250C2×#41—24no—
251C2×#41—24no—
252C2×#41—42no—
253C2×#41—42no—
254C2×#41—42no—
255C2×#41—42no—
256C2×#41—44no—
257C2×#41—44no—
258C2×#41—44no—
259C2×#41—44no—
260C2×#41—432no—
261C2×#41—432no—
262C2×#41—44no—
263C2×#41—44no—
264C22×Q8—24no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—42no—
274C22×Q8—42no—
275C22×Q8—42no—
276C22×Q8—42no—
277C22×Q8—42no—
278C22×Q8C2×D414yes—
279C22×Q8C2412yes—
280C22×Q8C2412yes—
281C22×Q8C2412yes—
282C22×D4—24no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—42no—
289C22×D4—44no—
290C22×D4—44no—
291C22×D4—44no—
292C22×D4C2412yes—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—44no—
305C23×C4—44no—
306C23×C4—44no—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D414yes—
314C23×C4C2×D411yescharacteristic
315C23×C4#4114yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319#137—432no—
320C2×Q16—28no—
321C2×Q16—28no—
322C2×Q16—28no—
323C2×Q16—44no—
324C2×Q16—44no—
325C2×Q16—44no—
326C2×SD16—28no—
327C2×SD16—28no—
328C2×SD16—44no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—42no—
332C2×M16—42no—
333C2×M16—42no—
334C2×M16—42no—
335C22×C8C2414yes—
336C22×C8C2414yes—
337C4⋊Q8—28no—
338C4⋊Q8—44no—
339C4⋊Q8—48no—
340#124—28no—
341#124—44no—
342#124—48no—
343C22⋊Q8—28no—
344C22⋊Q8—28no—
345C22⋊Q8—24no—
346C22⋊Q8—24no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—24no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8C2×D418yes—
354C22⋊Q8C2×D418yes—
355C4×Q8—44no—
356C4×Q8—44no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4C2×D414yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4C2×D412yes—
405C2×C22⋊C4C2×D412yes—
406C2×C22⋊C4C2×D412yes—
407C2×C22⋊C4C2×D412yes—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42C2×D412yes—
415C2×C42C2×D412yes—
416C2×C42C2412yes—
417C2×C42C2412yes—
418#106—28no—
419C4⋊C8—44no—
420C4⋊C8—44no—
421#103—28no—
422#103—28no—
423#103—28no—
424#103—28no—
425#103—44no—
426#103—44no—
427#103—44no—
428#102—28no—
429#102—28no—
430#102—44no—
431C22⋊C8—24no—
432C22⋊C8—24no—
433C22⋊C8—24no—
434C22⋊C8—24no—
435#95—22no—
436#95—22no—
437#95—24no—
438#95—24no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95C2×D412yes—
448#95C2×D412yes—
449#95C2×D412yes—
450#95C2×D412yes—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—22no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24#12114yes—
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468C24C22×D411yescharacteristic
469#41—216no—
470#41—216no—
471#41—48no—
472#41—48no—
473#41—48no—
474#41—48no—
475#41—48no—
476#41—48no—
477#41—432no—
478#41—432no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—22no—
491C2×Q8—24no—
492C2×Q8—24no—
493C2×Q8—48no—
494C2×Q8—48no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—48no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—81no—
502C2×Q8—81no—
503C2×Q8—84no—
504C2×Q8—84no—
505C2×Q8—84no—
506C2×Q8C22×D414yes—
507C2×Q8H(5,𝔽2)14yes—
508C2×D4—24no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—42no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—432no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—42no—
525C2×D4H(5,𝔽2)14yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—42no—
566C22×C4—432no—
567C22×C4—42no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4#12114yes—
587C22×C4#12114yes—
588C22×C4#12114yes—
589C22×C4#13714yescomplemented
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2511yescharacteristic
604Q16—416no—
605Q16—88no—
606SD16—416no—
607M16—48no—
608M16—84no—
609C2×C8—24no—
610C2×C8—24no—
611C2×C8—24no—
612C2×C8—24no—
613C2×C8—24no—
614C2×C8—24no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—82no—
629C4⋊C4—82no—
630C4⋊C4—81no—
631C4⋊C4—81no—
632C4⋊C4—82no—
633C4⋊C4—82no—
634C4⋊C4C22×D414yes—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—48no—
649C42—24no—
650C42—24no—
651C42—42no—
652C42—42no—
653C42—82no—
654C42—82no—
655C42—82no—
656C42—82no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—28no—
674C23—24no—
675C23—44no—
676C23—44no—
677C23—48no—
678C23—48no—
679C23—48no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—82no—
687C23—82no—
688C23—82no—
689C23—82no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23C2×#12112yes—
695C23C2×#12112yes—
696C23C2×#12112yes—
697C23C2×#13712yes—
698C23#57512yes—
699C23C23×D411yescharacteristic
700Q8—28no—
701Q8—24no—
702Q8—24no—
703Q8—48no—
704Q8—42no—
705Q8—42no—
706Q8—44no—
707Q8—44no—
708Q8—44no—
709Q8—84no—
710Q8—84no—
711D4—24no—
712D4—24no—
713D4—48no—
714D4—416no—
715D4—416no—
716D4—42no—
717D4—42no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—416no—
749C2×C4—416no—
750C2×C4—44no—
751C2×C4—48no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—82no—
771C2×C4—82no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—162no—
777C2×C4—162no—
778C2×C4C2×#12112yes—
779C2×C4C2×#12112yes—
780C2×C4C2×#12112yes—
781C2×C4C2×#13714yes—
782C2×C4C23×D411yescharacteristic
783C2×C4C22×#4111yescharacteristic
784C2×C4C2×H(5,𝔽2)12yes—
785C2×C4C2×H(5,𝔽2)12yes—
786C8—44no—
787C8—44no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—88no—
812C22—816no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22#303714yes—
818C22C22×#12111yescharacteristic
819C22#348411yescharacteristic
820C22#348411yescharacteristic
821C22C22×#13711yescharacteristic
822C22C2×#57511yescharacteristic
823C22#358611yescharacteristic
824C22#358611yescharacteristic
825C4—22no—
826C4—22no—
827C4—22no—
828C4—24no—
829C4—44no—
830C4—44no—
831C4—44no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4#348412yes—
840C4#349012yes—
841C2—24no—
842C2—42no—
843C2—42no—
844C2—84no—
845C2#3534811yescharacteristic
846C2C2×#303711yescharacteristic
847C2#6042711yescharacteristic
848C2#6157311yescharacteristic
849C2#6157511yescharacteristic
850C2#6158311yescharacteristic
851C2#6158611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3195C2semidirect
4. #34212C2semidirect
5. #28124C2semidirect
6. #28120C2semidirect
7. #25100C2semidirect
8. #25098C2semidirect
9. #24491C2semidirect
10. #24369C2semidirect
11. #24217C2semidirect
12. #24212C2semidirect
13. #21934C2semidirect
14. #21765C2semidirect
24. C2×#483C22semidirect
25. C2×#470C22semidirect
26. C2×#464C22semidirect
27. C2×#462C22semidirect
32. C2×#451C22semidirect
46. #2360C22semidirect
47. #2360C22semidirect
49. #2345C22semidirect
50. Q8×C22⋊C4C22semidirect
63. #2066C22semidirect
64. #2065C22semidirect
65. #2056C22semidirect
66. #2055C22semidirect
67. #2043C22semidirect
68. #2042C22semidirect
69. #2016C22semidirect
70. #2015C22semidirect
71. #1983C22semidirect
72. #1981C22semidirect
73. #1927C22semidirect
74. #1926C22semidirect
75. #1894C22semidirect
76. #1880C22semidirect
77. #1878C22semidirect
78. #1872C22semidirect
79. #1872C22semidirect
80. #1851C22semidirect
81. #1851C22semidirect
589. C22×C4#137semidirect

Maximal subgroups

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

subgroupindex
C2×#31952
C2×#30072
C2×#24322
#342122
#281242
#281202
#251002
#250982
#244912
#243692
#242172
#242122
#219342
#217652
#206012