Finite Group Databasebeta

← #6671588

Subgroups — #6671588

Order 512.

3009 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3217C211yesmaximal, characteristic, complemented
2C22×#459C211yesmaximal, characteristic, complemented
3D4×#127C211yesmaximal, characteristic, complemented
4#34700C211yesmaximal, characteristic, complemented
5#32902C211yesmaximal, characteristic, complemented
6#31000C212yesmaximal, complemented
7#30890C212yesmaximal, complemented
8#30749C212yesmaximal, complemented
9#30460C212yesmaximal, complemented
10#29794C211yesmaximal, characteristic, complemented
11#29662C211yesmaximal, characteristic, complemented
12#28448C211yesmaximal, characteristic, complemented
13#28158C211yesmaximal, characteristic, complemented
14#27264C212yesmaximal, complemented
15#25788C212yesmaximal, complemented
16#24753C211yesmaximal, characteristic, complemented
17#24658C211yesmaximal, characteristic, complemented
18#24432C212yesmaximal, complemented
19#24211C211yesmaximal, characteristic, complemented
20#24208C211yesmaximal, characteristic, complemented
21#23848C212yesmaximal, complemented
22#22750C211yesmaximal, characteristic, complemented
23#22151C211yesmaximal, characteristic, complemented
24C23×D8C2212yescomplemented
25C2×D42—21no—
26C2×D42—21no—
27C2×D42C2212yes—
28C22×#127C2211yescharacteristic
29C22×#127C2211yescharacteristic, complemented
30C2×#529C2211yescharacteristic, complemented
31C22×C4×D4C2211yescharacteristic, complemented
32#3217—28no—
33C2×#496C2212yescomplemented
34C2×#496C2212yescomplemented
35C2×#490C2212yescomplemented
36C2×#465C2212yescomplemented
37C2×#460C2211yescharacteristic, complemented
38C2×#460C2211yescharacteristic, complemented
39C2×#460C2211yescharacteristic, complemented
40C2×#459—28no—
41C2×#459C2211yescharacteristic
42C2×#459C2211yescharacteristic
43C2×#459C2212yescomplemented
44C2×#459C2211yescharacteristic, complemented
45C2×#459C2211yescharacteristic, complemented
46C2×#459C2211yescharacteristic, complemented
47C2×#459C2212yescomplemented
48C2×#459C2211yescharacteristic, complemented
49C2×#450C2212yescomplemented
50C2×#450C2212yescomplemented
51C2×#447C2212yescomplemented
52C2×#447C2212yescomplemented
53C2×#447C2212yescomplemented
54C2×#432C2211yescharacteristic, complemented
55C22×C4⋊C8C2211yescharacteristic, complemented
56C22×#102C2212yescomplemented
57#2867C2211yescharacteristic, complemented
58#2856C2211yescharacteristic
59#2856C2211yescharacteristic, complemented
60#2541—21no—
61#2541—21no—
62#2541C2212yescomplemented
63#2480—21no—
64#2468—21no—
65#2457—21no—
66#2454C2211yescharacteristic, complemented
67#2447C2211yescharacteristic, complemented
68#2442C2211yescharacteristic, complemented
69#2435C2211yescharacteristic, complemented
70#2433—21no—
71#2433—21no—
72#2433—21no—
73#2433—21no—
74#2433C2212yes—
75#2433C2212yescomplemented
76#2427C2211yescharacteristic, complemented
77#2420C2211yescharacteristic, complemented
78#2418—21no—
79#2417C2211yescharacteristic
80#2408C2211yescharacteristic
81#2395—21no—
82#2392—21no—
83C4×#127C2211yescharacteristic, complemented
84C4×#124C2211yescharacteristic, complemented
85C4×C22⋊Q8C2211yescharacteristic, complemented
86C4×#121C2211yescharacteristic, complemented
87C4×#120—21no—
88#2293C2211yescharacteristic, complemented
89#2280—21no—
90C42×D4C2211yescharacteristic
91#2073C2212yescomplemented
92#2065C2212yescomplemented
93#2055C2212yescomplemented
94#2041C2212yescomplemented
95#2041C2212yescomplemented
96#2041C2212yescomplemented
97#2041C2212yescomplemented
98#2034C2212yescomplemented
99#2025C2212yescomplemented
100#2014C2212yescomplemented
101#2014C2212yescomplemented
102#2012C2212yescomplemented
103#2012C2212yescomplemented
104#2011C2212yescomplemented
105#2011C2212yescomplemented
106#2011C2212yescomplemented
107#2011C2212yescomplemented
108#2000C2212yescomplemented
109#1999C2212yescomplemented
110#1999C2212yescomplemented
111#1982C2211yescharacteristic, complemented
112#1982C2211yescharacteristic, complemented
113#1982C2211yescharacteristic, complemented
114#1972C2212yescomplemented
115#1972C2212yescomplemented
116#1961C2212yescomplemented
117#1948C2211yescharacteristic, complemented
118#1936C2212yescomplemented
119#1936C2212yescomplemented
120#1924C2212yescomplemented
121#1917C2212yescomplemented
122#1893C2212yescomplemented
123#1879C2212yescomplemented
124#1879C2212yescomplemented
125#1879C2212yescomplemented
126#1879C2212yescomplemented
127#1877C2212yescomplemented
128#1874C2212yescomplemented
129#1869C2212yes—
130#1864C2212yescomplemented
131#1831C2211yescharacteristic, complemented
132#1803C2211yescharacteristic, complemented
133#1802C2211yescharacteristic, complemented
134#1802C2211yescharacteristic, complemented
135#1797C2211yescharacteristic, complemented
136#1797C2211yescharacteristic, complemented
137#1786C2212yescomplemented
138#1786C2212yescomplemented
139#1767C2211yescharacteristic, complemented
140#1752C2212yescomplemented
141C23×D4—22no—
142C23×D4—21no—
143C23×D4—21no—
144C23×D4—21no—
145C23×D4—21no—
146C23×D4C2311yescharacteristic
147C23×D4C2312yes—
148C23×D4C2312yes—
149C24×C4—21no—
150C22×SD16C2312yes—
151C22×SD16C2312yes—
152C22×SD16C2312yes—
153C22×D8—28no—
154C22×D8—44no—
155C22×D8—44no—
156C22×D8C2312yes—
157C22×D8C2312yes—
158C22×D8C2312yes—
159C22×D8C2312yes—
160C22×D8C2312yes—
161C22×D8C2312yes—
162C23×C8C2312yes—
163D42—44no—
164D42—44no—
165D42—48no—
166D42—48no—
167C2×#127—24no—
168C2×#127—24no—
169C2×#127—21no—
170C2×#127—21no—
171C2×#127—21no—
172C2×#127—21no—
173C2×#127—21no—
174C2×#127—21no—
175C2×#127—21no—
176C2×#127—21no—
177C2×#127—42no—
178C2×#127—42no—
179C2×#127C2311yescharacteristic
180C2×#127C2311yescharacteristic
181C2×#127C2312yes—
182C2×#127C2312yes—
183C2×#127C2311yescharacteristic
184C2×#127C2312yes—
185C2×#127C2312yes—
186#529—24no—
187#529—42no—
188C2×#126—21no—
189C2×#125C2311yescharacteristic
190C2×#124C2311yescharacteristic
191C2×#124C2311yescharacteristic
192C2×#123—21no—
193C2×C22⋊Q8C2311yescharacteristic
194C2×C22⋊Q8C2311yescharacteristic
195C2×#121—21no—
196C2×#121—21no—
197C2×#121—21no—
198C2×#121—21no—
199C2×#121—22no—
200C2×#121—22no—
201C2×#121—22no—
202C2×#121C2312yes—
203C2×#121C2311yescharacteristic
204C2×#121C2311yescharacteristic
205C2×#121C2312yes—
206C2×#120—21no—
207C2×#120—22no—
208C2×#120—22no—
209C2×#120—22no—
210C2×#120—22no—
211C2×#120—22no—
212C2×#120—22no—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4—21no—
215C2×C4×D4—21no—
216C2×C4×D4—24no—
217C2×C4×D4—21no—
218C2×C4×D4—21no—
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4—42no—
222C2×C4×D4D411yescharacteristic
223C2×C4×D4D411yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2312yes—
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117—21no—
232C22×C4⋊C4C2311yescharacteristic
233C22×C22⋊C4—21no—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236#496—28no—
237#496—44no—
238#490—28no—
239#465—44no—
240#460—24no—
241#460—24no—
242#460—42no—
243#459—28no—
244#459—24no—
245#459—24no—
246#459—24no—
247#459—24no—
248#459—28no—
249#459—42no—
250#459D418yescomplemented
251#450—28no—
252#450—44no—
253#447—28no—
254#447—44no—
255#447—44no—
256#432—24no—
257C2×#106C2312yes—
258C2×C4⋊C8—24no—
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2312yes—
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2312yes—
265C2×#102—28no—
266C2×#102C2312yes—
267C2×#102C2312yes—
268C2×#102C2312yes—
269C2×#102C2312yes—
270C2×#102C2312yes—
271C2×#102C2312yes—
272C2×#102C2312yes—
273C2×#102C2312yes—
274C2×#102C2312yes—
275C2×#102C2312yes—
276C2×#102C2312yes—
277C2×#102C2312yes—
278C2×#102C2312yes—
279C2×#102C2312yes—
280C2×#102C2312yes—
281C2×#102C2312yes—
282C2×#102C2312yes—
283C2×C22⋊C8C2312yes—
284C2×C22⋊C8C2312yes—
285C2×C22⋊C8C2312yes—
286C2×#97C2312yes—
287C2×#97C2312yes—
288#400—21no—
289#399—21no—
290#398—21no—
291#398—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#396—21no—
297#396—21no—
298#394—21no—
299#394—21no—
300#394—21no—
301#394—21no—
302#394—21no—
303#392—21no—
304#392—22no—
305#392—22no—
306#392—22no—
307#392—22no—
308#392—22no—
309#392—22no—
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#390—21no—
313#390—21no—
314#390—21no—
315#390—21no—
316#390—21no—
317#390—21no—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#388—21no—
330#388—21no—
331#388—21no—
332#388—21no—
333#388—21no—
334#387—21no—
335#386—21no—
336#386—21no—
337#386—21no—
338#386—21no—
339#385—21no—
340#385—21no—
341#385—21no—
342#385—21no—
343#384C2311yescharacteristic
344#382C2311yescharacteristic
345#381—21no—
346#381—21no—
347#380—21no—
348#380—21no—
349#380—21no—
350#380—21no—
351#380C2311yescharacteristic
352#380C2311yescharacteristic
353#379—21no—
354#379—21no—
355#379—21no—
356C4×C4⋊C4—21no—
357C4×C4⋊C4D411yescharacteristic
358C4×C4⋊C4D411yescharacteristic
359C4×C4⋊C4C2311yescharacteristic
360C4×C4⋊C4C2311yescharacteristic
361C4×C22⋊C4—21no—
362C4×C22⋊C4—21no—
363C4×C22⋊C4—21no—
364C4×C22⋊C4—21no—
365C4×C22⋊C4—21no—
366C4×C22⋊C4D411yescharacteristic
367C4×C22⋊C4D411yescharacteristic
368C4×C22⋊C4D411yescharacteristic
369C4×C22⋊C4D411yescharacteristic
370C4×C22⋊C4C2311yescharacteristic
371C4×C22⋊C4C2311yescharacteristic
372C43C2311yescharacteristic
373#340C2312yes—
374#340C2312yes—
375#340C2312yes—
376#340C2312yes—
377#336C2312yes—
378#336C2312yes—
379#336C2312yes—
380#336C2312yes—
381#336C2312yes—
382C25—21no—
383C25—22no—
384C25—22no—
385C22×Q8C2411yescharacteristic
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—24no—
389C22×D4—24no—
390C22×D4—22no—
391C22×D4—22no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—22no—
398C22×D4—21no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4—21no—
402C22×D4—22no—
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4—22no—
410C22×D4—22no—
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—42no—
418C22×D4—42no—
419C22×D4—42no—
420C22×D4—42no—
421C22×D4—42no—
422C22×D4—42no—
423C22×D4—42no—
424C22×D4—42no—
425C22×D4—44no—
426C22×D4—44no—
427C22×D4—44no—
428C22×D4—44no—
429C22×D4—44no—
430C22×D4—44no—
431C22×D4—44no—
432C22×D4—48no—
433C22×D4—48no—
434C22×D4—48no—
435C22×D4—44no—
436C22×D4—82no—
437C22×D4—82no—
438C22×D4—82no—
439C22×D4—82no—
440C22×D4C2×D411yescharacteristic
441C22×D4C2412yes—
442C22×D4C2412yes—
443C22×D4C2411yescharacteristic
444C22×D4C2412yes—
445C22×D4C2411yescharacteristic
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—22no—
449C23×C4—21no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—44no—
453C23×C4—44no—
454C23×C4—82no—
455C23×C4C2×D411yescharacteristic
456C23×C4C2×D411yescharacteristic
457C23×C4C2×D411yescharacteristic
458C23×C4C2×D411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C2×SD16—24no—
462C2×SD16—24no—
463C2×SD16—42no—
464C2×SD16—42no—
465C2×SD16—42no—
466C2×SD16—42no—
467C2×SD16—42no—
468C2×SD16—42no—
469C2×SD16—42no—
470C2×D8—24no—
471C2×D8—24no—
472C2×D8—24no—
473C2×D8—24no—
474C2×D8—24no—
475C2×D8—24no—
476C2×D8—24no—
477C2×D8—42no—
478C2×D8—42no—
479C2×D8—42no—
480C2×D8—42no—
481C2×D8—42no—
482C2×D8—42no—
483C2×D8—42no—
484C2×D8—42no—
485C2×D8—42no—
486C2×D8—42no—
487C2×D8—432no—
488C2×D8C2×D418yescomplemented
489C22×C8—24no—
490C22×C8—24no—
491C22×C8—42no—
492C22×C8C2412yes—
493C22×C8C2412yes—
494C22×C8C2412yes—
495C22×C8C2412yes—
496#127—24no—
497#127—24no—
498#127—22no—
499#127—22no—
500#127—22no—
501#127—22no—
502#127—22no—
503#127—42no—
504#127—42no—
505#127—42no—
506#127—42no—
507#127—42no—
508#127—42no—
509#127—44no—
510#127—44no—
511#127—44no—
512#127—44no—
513#127—44no—
514#127—44no—
515#127—82no—
516#127—82no—
517#127C2×D414yes—
518#126—44no—
519#125—22no—
520#125—41no—
521#124—22no—
522#124—22no—
523#124—41no—
524#124—41no—
525#123—44no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—22no—
532#121—24no—
533#121—24no—
534#121—41no—
535#121—41no—
536#121—42no—
537#121—42no—
538#121—48no—
539#121—48no—
540#121—48no—
541#121—44no—
542#121—44no—
543#121—44no—
544#121—44no—
545#120—48no—
546#120—48no—
547#120—48no—
548#120—48no—
549#120—48no—
550#120—48no—
551#120—44no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—44no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—42no—
567C4×D4—42no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571C4×D4—44no—
572C4×D4—82no—
573C4×D4C2×D414yescomplemented
574#117—44no—
575#117—82no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—44no—
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656#106—42no—
657C4⋊C8—24no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8C2×D414yescomplemented
662#103—42no—
663#102—24no—
664#102—24no—
665#102—24no—
666#102—24no—
667#102—24no—
668#102—24no—
669#102—42no—
670#102—42no—
671#102—42no—
672#102—42no—
673#102—42no—
674#102—42no—
675#102—42no—
676#102—42no—
677#102—42no—
678#102—42no—
679#102C2×D418yescomplemented
680C22⋊C8—24no—
681C22⋊C8—24no—
682C22⋊C8—42no—
683#97—24no—
684#97—42no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95C2×D411yescharacteristic
699#95C2×D411yescharacteristic
700#95C2×D411yescharacteristic
701#95C2×D411yescharacteristic
702#95C2×D411yescharacteristic
703#95C2×D411yescharacteristic
704C24—21no—
705C24—21no—
706C24—22no—
707C24—22no—
708C24—22no—
709C24—42no—
710C24—42no—
711C24—44no—
712C24—44no—
713C24—44no—
714C24—44no—
715C24—42no—
716C24—42no—
717C24—42no—
718C24—44no—
719C24—44no—
720C24—44no—
721C24—44no—
722C24—81no—
723C24—81no—
724C24—82no—
725C24—82no—
726C24—82no—
727C24—82no—
728C24—82no—
729C24—82no—
730C24C22×D411yescharacteristic
731C24C22×D411yescharacteristic
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—28no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—21no—
751C2×D4—22no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—22no—
767C2×D4—21no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—44no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—44no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—84no—
823C2×D4—84no—
824C2×D4—816no—
825C2×D4—82no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—82no—
831C2×D4—82no—
832C2×D4—82no—
833C2×D4—82no—
834C2×D4—82no—
835C2×D4—82no—
836C2×D4—82no—
837C2×D4—84no—
838C2×D4—84no—
839C2×D4—84no—
840C2×D4—84no—
841C2×D4—816no—
842C2×D4—816no—
843C2×D4—816no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—832no—
847C2×D4AGL(1,ℤ/8)14yes—
848C2×D4C22×D414yes—
849C2×D4C22×D412yes—
850C2×D4H(5,𝔽2)12yes—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—24no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—44no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—816no—
897C22×C4—81no—
898C22×C4AGL(1,ℤ/8)14yes—
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4H(5,𝔽2)12yes—
912C22×C4H(5,𝔽2)12yes—
913C22×C4C2511yescharacteristic
914SD16—84no—
915SD16—84no—
916SD16—84no—
917D8—48no—
918D8—48no—
919D8—48no—
920D8—48no—
921D8—84no—
922D8—84no—
923C2×C8—22no—
924C2×C8—22no—
925C2×C8—22no—
926C2×C8—22no—
927C2×C8—22no—
928C2×C8—22no—
929C2×C8—22no—
930C2×C8—22no—
931C2×C8—22no—
932C2×C8—22no—
933C2×C8—22no—
934C2×C8—48no—
935C2×C8C22×D414yes—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—22no—
947C4⋊C4—21no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4C22×D412yes—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—24no—
969C22⋊C4—22no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—44no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—44no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C42—22no—
1001C42—22no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—41no—
1016C42—42no—
1017C42—42no—
1018C42C22×D412yes—
1019C42H(5,𝔽2)12yes—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—22no—
1031C23—24no—
1032C23—22no—
1033C23—48no—
1034C23—41no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—84no—
1067C23—84no—
1068C23—84no—
1069C23—84no—
1070C23—88no—
1071C23—88no—
1072C23—88no—
1073C23—88no—
1074C23—84no—
1075C23—88no—
1076C23—88no—
1077C23—88no—
1078C23—84no—
1079C23—88no—
1080C23—164no—
1081C23—164no—
1082C23—164no—
1083C23—164no—
1084C23—164no—
1085C23—164no—
1086C23#53512yes—
1087C23C2×AGL(1,ℤ/8)12yes—
1088C23C2×AGL(1,ℤ/8)12yes—
1089C23C2×AGL(1,ℤ/8)12yes—
1090C23C23×D411yescharacteristic
1091Q8—41no—
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095D4—28no—
1096D4—22no—
1097D4—22no—
1098D4—24no—
1099D4—22no—
1100D4—24no—
1101D4—22no—
1102D4—48no—
1103D4—48no—
1104D4—42no—
1105D4—42no—
1106D4—41no—
1107D4—42no—
1108D4—42no—
1109D4—48no—
1110D4—41no—
1111D4—42no—
1112D4—42no—
1113D4—42no—
1114D4—41no—
1115D4—41no—
1116D4—42no—
1117D4—42no—
1118D4—42no—
1119D4—88no—
1120D4—88no—
1121D4—88no—
1122D4—84no—
1123D4—84no—
1124D4—88no—
1125D4—88no—
1126D4—88no—
1127D4—88no—
1128D4—84no—
1129D4—84no—
1130D4—88no—
1131D4—88no—
1132D4—84no—
1133D4—84no—
1134D4—164no—
1135D4—164no—
1136D4—164no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—28no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—44no—
1179C2×C4—48no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—88no—
1203C2×C4—84no—
1204C2×C4—84no—
1205C2×C4#53512yes—
1206C2×C4D4212yes—
1207C2×C4D4212yes—
1208C2×C4C2×AGL(1,ℤ/8)12yes—
1209C2×C4C2×AGL(1,ℤ/8)12yes—
1210C2×C4C2×AGL(1,ℤ/8)12yes—
1211C2×C4#57612yes—
1212C2×C4C23×D411yescharacteristic
1213C2×C4C2×H(5,𝔽2)11yescharacteristic
1214C2×C4C2×H(5,𝔽2)11yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C8—24no—
1219C8—42no—
1220C8—42no—
1221C8—42no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—44no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—44no—
1243C22—42no—
1244C22—816no—
1245C22—81no—
1246C22—82no—
1247C22—81no—
1248C22—82no—
1249C22—81no—
1250C22—82no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—1616no—
1272C22—1616no—
1273C22#321714yescomplemented
1274C22C2×#53511yescharacteristic
1275C22C2×D4211yescharacteristic
1276C22#348811yescharacteristic
1277C22C22×AGL(1,ℤ/8)11yescharacteristic
1278C22C22×AGL(1,ℤ/8)11yescharacteristic
1279C22C2×#57611yescharacteristic
1280C22#358511yescharacteristic
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—42no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—82no—
1297C4—81no—
1298C4—81no—
1299C4#326414yes—
1300C4#348411yescharacteristic
1301C4#348811yescharacteristic
1302C4#353711yescharacteristic
1303C4#354211yescharacteristic
1304C2—24no—
1305C2—42no—
1306C2—82no—
1307C2—82no—
1308C2—84no—
1309C2—162no—
1310C2—162no—
1311C2#3765011yescharacteristic
1312C2C2×#321711yescharacteristic
1313C2#6083211yescharacteristic
1314C2C2×#326411yescharacteristic
1315C2D4×AGL(1,ℤ/8)11yescharacteristic
1316C2#6195911yescharacteristic
1317C2#6197911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3217C2semidirect
2. C22×#459C2semidirect
3. D4×#127C2semidirect
4. #34700C2semidirect
5. #32902C2semidirect
6. #31000C2semidirect
7. #30890C2semidirect
8. #30749C2semidirect
9. #30460C2semidirect
10. #29794C2semidirect
11. #29662C2semidirect
12. #28448C2semidirect
13. #28158C2semidirect
14. #27264C2semidirect
15. #25788C2semidirect
16. #24753C2semidirect
17. #24658C2semidirect
18. #24432C2semidirect
19. #24211C2semidirect
20. #24208C2semidirect
21. #23848C2semidirect
22. #22750C2semidirect
23. #22151C2semidirect
24. C23×D8C22semidirect
29. C22×#127C22semidirect
30. C2×#529C22semidirect
31. C22×C4×D4C22semidirect
33. C2×#496C22semidirect
34. C2×#496C22semidirect
35. C2×#490C22semidirect
36. C2×#465C22semidirect
37. C2×#460C22semidirect
38. C2×#460C22semidirect
39. C2×#460C22semidirect
43. C2×#459C22semidirect
44. C2×#459C22semidirect
45. C2×#459C22semidirect
46. C2×#459C22semidirect
47. C2×#459C22semidirect
48. C2×#459C22semidirect
49. C2×#450C22semidirect
50. C2×#450C22semidirect
51. C2×#447C22semidirect
52. C2×#447C22semidirect
53. C2×#447C22semidirect
54. C2×#432C22semidirect
55. C22×C4⋊C8C22semidirect
56. C22×#102C22semidirect
57. #2867C22semidirect
59. #2856C22semidirect
62. #2541C22semidirect
66. #2454C22semidirect
67. #2447C22semidirect
68. #2442C22semidirect
69. #2435C22semidirect
75. #2433C22semidirect
76. #2427C22semidirect
77. #2420C22semidirect
83. C4×#127C22semidirect
84. C4×#124C22semidirect
85. C4×C22⋊Q8C22semidirect
86. C4×#121C22semidirect
88. #2293C22semidirect
91. #2073C22semidirect
92. #2065C22semidirect
93. #2055C22semidirect
94. #2041C22semidirect
95. #2041C22semidirect
96. #2041C22semidirect
97. #2041C22semidirect
98. #2034C22semidirect
99. #2025C22semidirect
100. #2014C22semidirect
101. #2014C22semidirect
102. #2012C22semidirect
103. #2012C22semidirect
104. #2011C22semidirect
105. #2011C22semidirect
106. #2011C22semidirect
107. #2011C22semidirect
108. #2000C22semidirect
109. #1999C22semidirect
110. #1999C22semidirect
111. #1982C22semidirect
112. #1982C22semidirect
113. #1982C22semidirect
114. #1972C22semidirect
115. #1972C22semidirect
116. #1961C22semidirect
117. #1948C22semidirect
118. #1936C22semidirect
119. #1936C22semidirect
120. #1924C22semidirect
121. #1917C22semidirect
122. #1893C22semidirect
123. #1879C22semidirect
124. #1879C22semidirect
125. #1879C22semidirect
126. #1879C22semidirect
127. #1877C22semidirect
128. #1874C22semidirect
130. #1864C22semidirect
131. #1831C22semidirect
132. #1803C22semidirect
133. #1802C22semidirect
134. #1802C22semidirect
135. #1797C22semidirect
136. #1797C22semidirect
137. #1786C22semidirect
138. #1786C22semidirect
139. #1767C22semidirect
140. #1752C22semidirect
250. #459D4semidirect
488. C2×D8C2×D4semidirect
573. C4×D4C2×D4semidirect
661. C4⋊C8C2×D4semidirect
679. #102C2×D4semidirect
1273. C22#3217semidirect

Maximal subgroups

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

subgroupindex
C2×#32172
C22×#4592
D4×#1272
#347002
#329022
#310002
#308902
#307492
#304602
#297942
#296622
#284482
#281582
#272642
#257882
#247532
#246582
#244322
#242112
#242082
#238482
#227502
#221512