Finite Group Databasebeta

← #6473131

Subgroups — #6473131

Order 512.

2318 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3200C212yesmaximal, complemented
2#35272C211yesmaximal, characteristic
3C4×#536C211yesmaximal, characteristic, complemented
4#33113C212yesmaximal, complemented
5#32903C212yesmaximal, complemented
6#29765C212yesmaximal, complemented
7#29722C212yesmaximal, complemented
8#28587C214yesmaximal, complemented
9#28130C214yesmaximal, complemented
10#27649C212yesmaximal, complemented
11#24761C212yesmaximal, complemented
12#24753C212yesmaximal, complemented
13#24211C212yesmaximal, complemented
14#21770C212yesmaximal, complemented
15#20629C211yesmaximal, characteristic, complemented
16C2×#536C2211yescharacteristic
17C2×#535C2212yes—
18C22×#127C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic, complemented
21#3200—216no—
22C2×#485C2214yes—
23C2×#482C2214yescomplemented
24C2×#468C2214yescomplemented
25C2×#465C2214yescomplemented
26C2×#460C2212yes—
27C2×#460C2212yes—
28C2×#448C2214yescomplemented
29C2×#450C2214yes—
30C2×#423C2211yescharacteristic, complemented
31C22×C4⋊C8C2211yescharacteristic, complemented
32C2×#408C2212yes—
33#2856C2212yes—
34#2856C2212yes—
35#2619C2212yes—
36#2619C2212yes—
37#2548—21no—
38#2548—21no—
39#2541—21no—
40#2541—21no—
41#2408—21no—
42#2408—21no—
43#2408—21no—
44#2408—21no—
45#2327—21no—
46#2326—21no—
47#2323C2212yes—
48#2323C2212yescomplemented
49#2322—21no—
50#2322—21no—
51#2317C2211yescharacteristic, complemented
52#2311C2211yescharacteristic
53#2310C2211yescharacteristic, complemented
54#2309C2212yes—
55C4×C4⋊Q8—21no—
56C4×#124—21no—
57C4×C22⋊Q8C2212yes—
58C4×C22⋊Q8C2212yescomplemented
59C4×#123—21no—
60C4×#123—21no—
61#2285C2211yescharacteristic
62C4×#117C2211yescharacteristic, complemented
63#2085C2214yescomplemented
64#2074C2214yescomplemented
65#2067C2214yescomplemented
66#2065C2214yescomplemented
67#2055C2214yescomplemented
68#2055C2214yescomplemented
69#2041C2214yes—
70#2014C2214yes—
71#1982C2212yes—
72#1982C2212yes—
73#1948C2212yescomplemented
74#1947C2212yescomplemented
75#1926C2214yescomplemented
76#1925C2214yescomplemented
77#1895C2214yescomplemented
78#1893C2214yescomplemented
79#1880C2214yescomplemented
80#1880C2214yescomplemented
81#1875C2214yescomplemented
82#1874C2214yescomplemented
83#1825C2214yes—
84#1803C2212yescomplemented
85#1803C2212yescomplemented
86#1798C2212yes—
87#1798C2212yescomplemented
88#1797C2212yes—
89#1797C2212yescomplemented
90#1786C2214yes—
91#1729C2212yescomplemented
92C22×#41C2311yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4—21no—
95C23×D4—21no—
96C23×D4C2312yes—
97C22×SD16C2314yes—
98C22×SD16C2314yes—
99C22×M16C2312yes—
100C23×C8C2312yes—
101#536—24no—
102#536D418yescomplemented
103#535—28no—
104#535—28no—
105C2×C4⋊Q8—21no—
106C2×#127—22no—
107C2×#127—21no—
108C2×#127—21no—
109C2×#127—42no—
110C2×#127—42no—
111C2×#127C2312yes—
112C2×#127C2312yes—
113C2×#124—21no—
114C2×#124—22no—
115C2×#123—21no—
116C2×#123—21no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121—22no—
120C2×#121—22no—
121C2×#121—22no—
122C2×#121—22no—
123C2×#121C2314yes—
124C2×#121C2314yes—
125C2×#120—22no—
126C2×#120—22no—
127C4×#41—42no—
128C4×#41—42no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—42no—
132C2×C4×Q8—42no—
133C2×C4×Q8D411yescharacteristic
134C2×C4×Q8D411yescharacteristic
135C2×C4×Q8C2312yes—
136C2×C4×Q8C2312yes—
137C2×C4×D4D411yescharacteristic
138C2×C4×D4D411yescharacteristic
139C2×C4×D4D411yescharacteristic
140C2×C4×D4D411yescharacteristic
141C2×C4×D4D411yescharacteristic
142C2×C4×D4D411yescharacteristic
143C2×#117C2312yes—
144C2×#117C2311yescharacteristic
145C2×#117C2311yescharacteristic
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C2×#117C2311yescharacteristic
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2311yescharacteristic
151C22×C42—21no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#485—216no—
156#482—216no—
157#468—216no—
158#465—216no—
159#460—44no—
160#460—44no—
161#450—216no—
162#448—216no—
163C2×#107C2314yes—
164C2×#106C2314yes—
165#423—42no—
166C2×C4⋊C8—42no—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179#408—28no—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182#394—22no—
183#394—22no—
184#394—22no—
185#394—22no—
186#392—22no—
187#392—22no—
188#392—22no—
189#392—22no—
190#391—21no—
191#391—21no—
192#391—21no—
193#391C2312yes—
194#391C2312yes—
195#390—21no—
196#390—22no—
197#390—22no—
198#390—22no—
199#390—22no—
200#390—22no—
201#390—22no—
202#390C2314yes—
203#390C2314yes—
204#389—22no—
205#389—22no—
206#389C2312yes—
207#389C2312yes—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#387—22no—
213#387—22no—
214#387—22no—
215#387—22no—
216#386—21no—
217#386—21no—
218#385—22no—
219#385—22no—
220#385—21no—
221#385—21no—
222#384—21no—
223#384C2312yes—
224#382—21no—
225#382C2312yes—
226#381—21no—
227#381—21no—
228#380—21no—
229#380—21no—
230#380C2312yes—
231#380C2312yes—
232#379—22no—
233#379—22no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C22⋊C4—21no—
241C4×C22⋊C4—21no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244#376—21no—
245C43—21no—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#336C2314yes—
251#336C2314yes—
252C25—22no—
253C2×#41—41no—
254C2×#41—41no—
255C2×#41—41no—
256C2×#41—41no—
257C2×#41C2×D414yes—
258C2×#41#4114yes—
259C22×Q8—21no—
260C22×Q8—22no—
261C22×Q8—41no—
262C22×Q8—41no—
263C22×Q8—41no—
264C22×Q8—41no—
265C22×Q8C2×D411yescharacteristic
266C22×Q8C2×D414yescomplemented
267C22×Q8C2412yes—
268C22×D4—24no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—24no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—42no—
280C22×D4—42no—
281C22×D4—44no—
282C22×D4—44no—
283C22×D4—84no—
284C22×D4—84no—
285C22×D4C2×D411yescharacteristic
286C22×D4C2×D411yescharacteristic
287C22×D4C2×D411yescharacteristic
288C22×D4C2414yes—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×SD16—28no—
301C2×SD16—28no—
302C2×SD16—44no—
303C2×SD16—44no—
304C2×SD16—44no—
305C2×SD16—44no—
306C2×M16—24no—
307C2×M16—42no—
308C2×M16—42no—
309C22×C8—24no—
310C22×C8—42no—
311C22×C8—42no—
312C22×C8C2414yes—
313C22×C8C2414yes—
314C4⋊Q8—28no—
315#127—24no—
316#127—24no—
317#127—42no—
318#127—42no—
319#127—44no—
320#127—44no—
321#127—48no—
322#124—28no—
323#124—48no—
324#123—28no—
325#123—28no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8C2×D418yes—
329C22⋊Q8C2×D418yescomplemented
330#121—28no—
331#121—28no—
332#121—28no—
333#121—28no—
334#121—84no—
335#121—84no—
336#121—84no—
337#121—84no—
338#120—48no—
339#120—48no—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—42no—
343C4×Q8—42no—
344C4×Q8—42no—
345C4×Q8—42no—
346C4×Q8—44no—
347C4×Q8—44no—
348C4×D4—42no—
349C4×D4—42no—
350C4×D4—42no—
351C4×D4—42no—
352C4×D4—42no—
353C4×D4—42no—
354#117—22no—
355#117—24no—
356#117—24no—
357#117—41no—
358#117—41no—
359#117—41no—
360#117—41no—
361#117—41no—
362#117—41no—
363#117—41no—
364#117—41no—
365#117C2×D414yescomplemented
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2414yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C42—21no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—21no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—44no—
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431#107—28no—
432#106—28no—
433C4⋊C8—24no—
434C4⋊C8—24no—
435C4⋊C8—42no—
436C4⋊C8—42no—
437#103—28no—
438#103—28no—
439#102—28no—
440#102—28no—
441#102—44no—
442#102—44no—
443#102—44no—
444#102—44no—
445C22⋊C8—28no—
446C22⋊C8—28no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459C24—24no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—84no—
464C24—84no—
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468#41—44no—
469#41—44no—
470#41—44no—
471#41—44no—
472C2×Q8—24no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—41no—
479C2×Q8—41no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8#12114yes—
487C2×Q8C22×D414yes—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—84no—
514C2×D4—84no—
515C2×D4—84no—
516C2×D4—84no—
517C2×D4—84no—
518C2×D4—84no—
519C2×D4—816no—
520C2×D4—816no—
521C2×D4—84no—
522C2×D4—84no—
523C2×D4—84no—
524C2×D4—84no—
525C2×D4#12114yes—
526C2×D4#12114yes—
527C2×D4#12114yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—82no—
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C2×#4112yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4112yes—
579C22×C4C2511yescharacteristic
580SD16—88no—
581SD16—88no—
582M16—84no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—84no—
590C4⋊C4—28no—
591C4⋊C4—28no—
592C4⋊C4—22no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—42no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—82no—
611C4⋊C4—82no—
612C4⋊C4C22×D414yes—
613C22⋊C4—24no—
614C22⋊C4—28no—
615C22⋊C4—28no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C42—24no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—44no—
646C42—42no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—82no—
651C42H(5,𝔽2)12yes—
652C42H(5,𝔽2)12yes—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—88no—
673C23—88no—
674C23—88no—
675C23—168no—
676C23—168no—
677C23C2×#12112yes—
678C23C2×#12112yes—
679C23C2×#12112yes—
680C23C23×D411yescharacteristic
681Q8—24no—
682Q8—24no—
683Q8—44no—
684Q8—48no—
685Q8—42no—
686Q8—42no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—88no—
695D4—88no—
696D4—88no—
697D4—88no—
698D4—88no—
699D4—168no—
700D4—168no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—48no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—84no—
755C2×C4C2×#12112yes—
756C2×C4C2×#12112yes—
757C2×C4C2×#12112yes—
758C2×C4#53412yes—
759C2×C4#53412yes—
760C2×C4#57714yes—
761C2×C4C23×D411yescharacteristic
762C2×C4C22×#4111yescharacteristic
763C2×C4C2×H(5,𝔽2)11yescharacteristic
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C2×C4#58511yescharacteristic
766C2×C4#58511yescharacteristic
767C8—44no—
768C8—44no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—84no—
785C22—84no—
786C22—84no—
787C22—84no—
788C22—84no—
789C22—84no—
790C22—84no—
791C22—1616no—
792C22C22×#12111yescharacteristic
793C22C2×#53411yescharacteristic
794C22#344911yescharacteristic
795C22C2×#57712yes—
796C22#358512yes—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—44no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—44no—
809C4—84no—
810C4—82no—
811C4—82no—
812C4#320014yescomplemented
813C4#349611yescharacteristic
814C4#349611yescharacteristic
815C4#350511yescharacteristic
816C4#350511yescharacteristic
817C2—42no—
818C2—42no—
819C2—42no—
820C2—164no—
821C2#3500011yescharacteristic
822C2#6043112yes—
823C2C2×#320011yescharacteristic
824C2#6075311yescharacteristic
825C2#6099412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35272C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3200C2semidirect
3. C4×#536C2semidirect
4. #33113C2semidirect
5. #32903C2semidirect
6. #29765C2semidirect
7. #29722C2semidirect
8. #28587C2semidirect
9. #28130C2semidirect
10. #27649C2semidirect
11. #24761C2semidirect
12. #24753C2semidirect
13. #24211C2semidirect
14. #21770C2semidirect
15. #20629C2semidirect
20. C22×C4×Q8C22semidirect
23. C2×#482C22semidirect
24. C2×#468C22semidirect
25. C2×#465C22semidirect
28. C2×#448C22semidirect
30. C2×#423C22semidirect
31. C22×C4⋊C8C22semidirect
48. #2323C22semidirect
51. #2317C22semidirect
53. #2310C22semidirect
58. C4×C22⋊Q8C22semidirect
62. C4×#117C22semidirect
63. #2085C22semidirect
64. #2074C22semidirect
65. #2067C22semidirect
66. #2065C22semidirect
67. #2055C22semidirect
68. #2055C22semidirect
73. #1948C22semidirect
74. #1947C22semidirect
75. #1926C22semidirect
76. #1925C22semidirect
77. #1895C22semidirect
78. #1893C22semidirect
79. #1880C22semidirect
80. #1880C22semidirect
81. #1875C22semidirect
82. #1874C22semidirect
84. #1803C22semidirect
85. #1803C22semidirect
87. #1798C22semidirect
89. #1797C22semidirect
91. #1729C22semidirect
102. #536D4semidirect
266. C22×Q8C2×D4semidirect
329. C22⋊Q8C2×D4semidirect
365. #117C2×D4semidirect
812. C4#3200semidirect

Maximal subgroups

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

subgroupindex
C2×#32002
#352722
C4×#5362
#331132
#329032
#297652
#297222
#285872
#281302
#276492
#247612
#247532
#242112
#217702
#206292