Finite Group Databasebeta

← #6394581

Subgroups — #6394581

Order 512.

2568 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3192C211yesmaximal, characteristic
2#34205C211yesmaximal, characteristic, complemented
3C2×#2363C211yesmaximal, characteristic, complemented
4#23140C214yesmaximal, complemented
5#23039C214yesmaximal, complemented
6#22943C214yesmaximal, complemented
7#22868C214yesmaximal, complemented
8#22082C212yesmaximal, complemented
9#22040C212yesmaximal, complemented
10#21764C211yesmaximal, characteristic, complemented
11C4×#481C212yesmaximal, complemented
12#21452C212yesmaximal, complemented
13#20912C211yesmaximal, characteristic, complemented
14#20846C211yesmaximal, characteristic, complemented
15#20524C211yesmaximal, characteristic, complemented
16C22×#121C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C2×#518—21no—
19C22×C4×D4C2211yescharacteristic, complemented
20C22×#117C2211yescharacteristic
21#3192C4116yescomplemented
22C2×#481C2212yes—
23C2×#481C2212yes—
24C2×#469C2214yes—
25C2×#447C2212yes—
26C2×#447C2212yes—
27C2×#442C2214yescomplemented
28C2×#428C2212yescomplemented
29C2×#418C2212yescomplemented
30C2×#407C2211yescharacteristic
31C2×#407C2211yescharacteristic
32#2364—22no—
33#2363—22no—
34#2363—22no—
35#2363C2214yes—
36#2363C2214yescomplemented
37#2361C2212yescomplemented
38#2361C2212yescomplemented
39#2344C2212yescomplemented
40#2342—22no—
41D4×C22⋊C4C2212yescomplemented
42#2325—21no—
43#2325—21no—
44#2308—21no—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C2×#390—21no—
48C2×#390C2211yescharacteristic, complemented
49C2×#389C2211yescharacteristic, complemented
50C2×#388—21no—
51C2×#386—21no—
52C2×#380C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic, complemented
54C2×C4×C22⋊C4—21no—
55C2×C4×C22⋊C4C2211yescharacteristic
56#1970C2214yescomplemented
57#1944C2214yescomplemented
58#1936C2214yescomplemented
59#1934C2214yescomplemented
60#1926C2214yescomplemented
61#1925C2214yescomplemented
62#1919C2214yescomplemented
63#1919C2214yescomplemented
64#1895C2214yes—
65#1879C2214yescomplemented
66#1879C2214yescomplemented
67#1875C2214yescomplemented
68#1874C2212yes—
69#1874C2212yes—
70#1874C2212yescomplemented
71#1874C2212yescomplemented
72#1864C2214yescomplemented
73#1862C2214yescomplemented
74#1854C2214yescomplemented
75#1853C2212yescomplemented
76#1852C2212yescomplemented
77#1824C2212yescomplemented
78#1786C2212yescomplemented
79C4×#106C2214yescomplemented
80#1762C2214yescomplemented
81C4×#102C2214yescomplemented
82#1753C2214yescomplemented
83#1753C2214yescomplemented
84#1749C2212yescomplemented
85C4×C22⋊C8C2212yescomplemented
86#1736C2212yescomplemented
87#1736C2212yescomplemented
88C23×D4—21no—
89C23×D4—21no—
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C22×D8C2314yes—
95C22×M16C2312yes—
96C22×M16C2312yes—
97C2×#121—21no—
98C2×#121—21no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—24no—
102C2×#121—24no—
103C2×#121C2×C418yescomplemented
104C2×#121C2×C418yescomplemented
105C2×#121C2312yes—
106C2×#121C2312yes—
107C2×#121C2312yes—
108C2×#121C2312yes—
109#518—48no—
110C2×C4×D4—22no—
111C2×C4×D4—22no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4—22no—
115C2×C4×D4—44no—
116C2×C4×D4C2314yes—
117C2×C4×D4C2312yes—
118C2×C4×D4C2312yes—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—22no—
122C2×#117—44no—
123C2×#117C2312yes—
124C2×#117C2312yes—
125C22×C4⋊C4—21no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—22no—
140C22×C22⋊C4D411yescharacteristic
141C22×C22⋊C4D411yescharacteristic
142C22×C42—21no—
143C22×C42—21no—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146#481C2×C4116yescomplemented
147#481C2×C4116yescomplemented
148#469C2×C4132yescomplemented
149#447C2×C4116yescomplemented
150#447C2×C4116yescomplemented
151#442—48no—
152#428—44no—
153C2×#107C2314yes—
154C2×#106C2314yes—
155C2×#106C2314yes—
156#418—44no—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163#407—24no—
164#407C2×C418yescomplemented
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×#97C2314yes—
170C2×C4×C8C2314yes—
171#390—24no—
172#390—24no—
173#390—22no—
174#390C2312yes—
175#390C2312yes—
176#390C2314yes—
177#389—22no—
178#389C2312yes—
179#389C2312yes—
180#389C2314yes—
181#388—22no—
182#388—22no—
183#388—22no—
184#388—22no—
185#388—24no—
186#388—24no—
187#387—22no—
188#387—22no—
189#386—22no—
190#386—22no—
191#386—22no—
192#386—22no—
193#386—24no—
194#386—24no—
195#386—22no—
196#386—22no—
197#385—22no—
198#385—22no—
199#381—22no—
200#380—21no—
201#380—21no—
202#380C2312yes—
203#380C2312yes—
204#379—22no—
205C4×C4⋊C4—22no—
206C4×C4⋊C4C2312yes—
207C4×C4⋊C4C2312yes—
208C4×C4⋊C4C2314yes—
209C4×C22⋊C4—22no—
210C4×C22⋊C4—22no—
211C4×C22⋊C4—24no—
212C4×C22⋊C4—24no—
213C4×C22⋊C4D412yes—
214C4×C22⋊C4D412yes—
215C4×C22⋊C4C2312yes—
216C4×C22⋊C4C2312yes—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95D411yescharacteristic
221C2×#95D411yescharacteristic
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#340C2314yes—
226#340C2314yes—
227#340C2314yes—
228#336C2314yes—
229#336C2314yes—
230C25—21no—
231C25—21no—
232C25C2×D411yescharacteristic
233C22×D4—28no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—28no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—82no—
250C22×D4—82no—
251C22×D4C22×C414yes—
252C22×D4C22×C414yescomplemented
253C22×D4C2412yes—
254C22×D4C2412yes—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—82no—
269C23×C4C22×C414yes—
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4#4114yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C2×D8—44no—
282C2×D8—44no—
283C2×D8C22×C4116yes—
284C2×M16—24no—
285C2×M16—42no—
286C2×M16—42no—
287C2×M16—42no—
288C2×M16—42no—
289C2×M16C22×C418yescomplemented
290C22×C8C2414yes—
291C22×C8C2414yes—
292#121—28no—
293#121—28no—
294#121—28no—
295#121—28no—
296#121—24no—
297#121—24no—
298#121—24no—
299#121—24no—
300#121C22×C418yes—
301#121C22×C418yes—
302#121C22×C418yes—
303#121C22×C418yescomplemented
304C4×D4—28no—
305C4×D4—44no—
306C4×D4—44no—
307C4×D4—44no—
308C4×D4—48no—
309C4×D4—48no—
310C4×D4—48no—
311C4×D4—48no—
312C4×D4—48no—
313#117—24no—
314#117—24no—
315#117—48no—
316#117—42no—
317#117—42no—
318#117—44no—
319#117—44no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—82no—
336C2×C4⋊C4C22×C414yes—
337C2×C4⋊C4C22×C414yescomplemented
338C2×C4⋊C4C2412yes—
339C2×C4⋊C4C2412yes—
340C2×C4⋊C4C2412yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—48no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—82no—
371C2×C22⋊C4C2×D412yes—
372C2×C22⋊C4C2×D412yes—
373C2×C22⋊C4C2×D412yes—
374C2×C22⋊C4C2×D412yes—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—24no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—44no—
383C2×C42—82no—
384C2×C42C2×D412yes—
385C2×C42C2×D412yes—
386C2×C42C2412yes—
387C2×C42C2412yes—
388#107—44no—
389#106—28no—
390#106C22×C4116yescomplemented
391#102—28no—
392#102—44no—
393#102—44no—
394#102—44no—
395#102C22×C4116yes—
396#102C22×C4116yescomplemented
397C22⋊C8—24no—
398C22⋊C8—24no—
399C22⋊C8C22×C418yes—
400C22⋊C8C22×C418yescomplemented
401#97—44no—
402C4×C8—44no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95C2×D412yes—
412#95C2×D412yes—
413#95C2×D412yes—
414#95C2×D412yes—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—41no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—81no—
434C24—81no—
435C24—81no—
436C24—81no—
437C24C4×D414yes—
438C24C22×D411yescharacteristic
439C24C22×D411yescharacteristic
440C24C22×D411yescharacteristic
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—432no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—84no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4—82no—
467C2×D4—82no—
468C2×D4—82no—
469C2×D4—82no—
470C2×D4—816no—
471C2×D4C23×C414yes—
472C2×D4C23×C414yes—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—44no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—44no—
522C22×C4—84no—
523C22×C4—82no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4—82no—
527C22×C4—816no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C4×D414yes—
533C22×C4C4×D414yes—
534C22×C4C4×D414yes—
535C22×C4AGL(1,ℤ/8)14yes—
536C22×C4C23×C412yes—
537C22×C4C23×C412yes—
538C22×C4C23×C412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D412yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4C2511yescharacteristic
550D8—416no—
551M16—48no—
552M16—84no—
553C2×C8—24no—
554C2×C8—24no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8C23×C418yes—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—24no—
569C4⋊C4—42no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—81no—
573C4⋊C4—81no—
574C4⋊C4—84no—
575C4⋊C4C23×C414yes—
576C4⋊C4C23×C414yes—
577C4⋊C4H(5,𝔽2)14yes—
578C22⋊C4—28no—
579C22⋊C4—28no—
580C22⋊C4—28no—
581C22⋊C4—28no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—48no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—48no—
593C22⋊C4—44no—
594C22⋊C4—82no—
595C22⋊C4—82no—
596C22⋊C4—84no—
597C22⋊C4—82no—
598C22⋊C4—82no—
599C42—24no—
600C42—24no—
601C42—42no—
602C42—42no—
603C42—44no—
604C42—44no—
605C42—44no—
606C42—44no—
607C42—84no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—28no—
625C23—24no—
626C23—24no—
627C23—44no—
628C23—44no—
629C23—48no—
630C23—48no—
631C23—48no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—48no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—82no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—162no—
656C23—162no—
657C23—162no—
658C23—162no—
659C23C2×C4×D412yes—
660C23C2×C4×D412yes—
661C23C2×C4×D412yes—
662C23C2×AGL(1,ℤ/8)12yes—
663C23#57512yes—
664C23C23×D411yescharacteristic
665D4—28no—
666D4—28no—
667D4—48no—
668D4—416no—
669D4—416no—
670D4—44no—
671D4—44no—
672D4—84no—
673D4—88no—
674D4—88no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—48no—
706C2×C4—44no—
707C2×C4—48no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—816no—
727C2×C4—84no—
728C2×C4—164no—
729C2×C4—164no—
730C2×C4—162no—
731C2×C4—162no—
732C2×C4C2×C4×D412yes—
733C2×C4C2×C4×D412yes—
734C2×C4C2×C4×D412yes—
735C2×C4C2×AGL(1,ℤ/8)14yes—
736C2×C4C24×C411yescharacteristic
737C2×C4C22×#4111yescharacteristic
738C2×C4C2×H(5,𝔽2)12yes—
739C2×C4#58512yes—
740C8—28no—
741C8—44no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—88no—
769C22—816no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—168no—
779C22C4×AGL(1,ℤ/8)14yes—
780C22C22×C4×D411yescharacteristic
781C22#348411yescharacteristic
782C22#348511yescharacteristic
783C22C22×AGL(1,ℤ/8)11yescharacteristic
784C22C2×#57511yescharacteristic
785C22#358511yescharacteristic
786C22#358511yescharacteristic
787C4—24no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—44no—
792C4—42no—
793C4—42no—
794C4—44no—
795C4—42no—
796C4—44no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4C4×H(5,𝔽2)12yes—
801C4#350512yes—
802C2—24no—
803C2—42no—
804C2—42no—
805C2—84no—
806C2—84no—
807C2#3426411yescharacteristic
808C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
809C2#6016811yescharacteristic
810C2#6158111yescharacteristic
811C2#6158711yescharacteristic
812C2#6170711yescharacteristic
813C2#6171011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3192C2
LCSG ▷ C2×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
2. #34205C2semidirect
3. C2×#2363C2semidirect
4. #23140C2semidirect
5. #23039C2semidirect
6. #22943C2semidirect
7. #22868C2semidirect
8. #22082C2semidirect
9. #22040C2semidirect
10. #21764C2semidirect
11. C4×#481C2semidirect
12. #21452C2semidirect
13. #20912C2semidirect
14. #20846C2semidirect
15. #20524C2semidirect
19. C22×C4×D4C22semidirect
21. #3192C4semidirect
27. C2×#442C22semidirect
28. C2×#428C22semidirect
29. C2×#418C22semidirect
36. #2363C22semidirect
37. #2361C22semidirect
38. #2361C22semidirect
39. #2344C22semidirect
41. D4×C22⋊C4C22semidirect
48. C2×#390C22semidirect
49. C2×#389C22semidirect
53. C2×C4×C4⋊C4C22semidirect
56. #1970C22semidirect
57. #1944C22semidirect
58. #1936C22semidirect
59. #1934C22semidirect
60. #1926C22semidirect
61. #1925C22semidirect
62. #1919C22semidirect
63. #1919C22semidirect
65. #1879C22semidirect
66. #1879C22semidirect
67. #1875C22semidirect
70. #1874C22semidirect
71. #1874C22semidirect
72. #1864C22semidirect
73. #1862C22semidirect
74. #1854C22semidirect
75. #1853C22semidirect
76. #1852C22semidirect
77. #1824C22semidirect
78. #1786C22semidirect
79. C4×#106C22semidirect
80. #1762C22semidirect
81. C4×#102C22semidirect
82. #1753C22semidirect
83. #1753C22semidirect
84. #1749C22semidirect
85. C4×C22⋊C8C22semidirect
86. #1736C22semidirect
87. #1736C22semidirect
103. C2×#121C2×C4semidirect
104. C2×#121C2×C4semidirect
146. #481C2×C4semidirect
147. #481C2×C4semidirect
148. #469C2×C4semidirect
149. #447C2×C4semidirect
150. #447C2×C4semidirect
164. #407C2×C4semidirect
252. C22×D4C22×C4semidirect
289. C2×M16C22×C4semidirect
303. #121C22×C4semidirect
337. C2×C4⋊C4C22×C4semidirect
390. #106C22×C4semidirect
396. #102C22×C4semidirect
400. C22⋊C8C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#31922
#342052
C2×#23632
#231402
#230392
#229432
#228682
#220822
#220402
#217642
C4×#4812
#214522
#209122
#208462
#205242