Finite Group Databasebeta

← #6477241

Subgroups — #6477241

Order 512.

2018 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×#2851C211yesmaximal, characteristic, complemented
3#33217C212yesmaximal, complemented
4#33052C212yesmaximal, complemented
5#30362C214yesmaximal, complemented
6#29161C214yesmaximal, complemented
7#27969C211yesmaximal, characteristic, complemented
8#27918C211yesmaximal, characteristic, complemented
9#27880C212yesmaximal, complemented
10#25913C211yesmaximal, characteristic, complemented
11#25819C211yesmaximal, characteristic, complemented
12#25676C212yesmaximal, complemented
13#24553C212yesmaximal, complemented
14#24550C212yesmaximal, complemented
15#22082C212yesmaximal, complemented
16#22081C212yesmaximal, complemented
17C2×#1749C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C22×#125C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×#501C2212yescomplemented
23C2×#490C2212yescomplemented
24C2×#481C2212yes—
25C2×#480C2212yes—
26C22×C22⋊C8C2212yes—
27C22×#97C2212yes—
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2856C2211yescharacteristic
31#2856C2211yescharacteristic
32#2854—21no—
33#2854C2212yes—
34#2851—21no—
35#2851—21no—
36#2851—21no—
37#2851—21no—
38#2851C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2851C2212yes—
42#2850—21no—
43#2850—21no—
44#2847—21no—
45#2847C2212yes—
46C4×#121—21no—
47C4×#121—21no—
48C4×#121C2212yes—
49C4×#121C2212yes—
50#2297—21no—
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#387—21no—
54C2×#387—21no—
55C2×#385—21no—
56C2×#385—21no—
57#2285C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61#2101C2214yescomplemented
62#2092C2214yescomplemented
63#2077C2214yes—
64#2075C2214yes—
65#2059C2214yescomplemented
66#2034C2214yes—
67#2033C2214yes—
68#2025C2214yescomplemented
69#1993C2212yescomplemented
70#1992C2212yescomplemented
71#1992C2212yescomplemented
72#1961C2212yescomplemented
73#1944C2214yescomplemented
74#1943C2214yescomplemented
75#1936C2214yescomplemented
76#1936C2214yescomplemented
77#1921C2214yescomplemented
78#1919C2214yescomplemented
79#1893C2214yes—
80#1893C2214yes—
81#1874C2212yes—
82#1874C2212yes—
83#1864C2214yescomplemented
84#1862C2214yescomplemented
85#1853C2212yes—
86#1852C2212yes—
87#1847C2212yescomplemented
88#1836C2212yescomplemented
89#1824C2212yes—
90#1823C2212yes—
91#1808C2214yes—
92#1807C2214yes—
93#1749C2211yescharacteristic
94#1749C2211yescharacteristic
95#1749C2212yes—
96#1749C2212yes—
97#1749C2212yes—
98C2×#336C2212yes—
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C23×C8C2314yes—
104#532—44no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×#127C2311yescharacteristic
107C2×#125—21no—
108C2×#125—21no—
109C2×#125—44no—
110C2×#125C2312yes—
111C2×#125C2312yes—
112C2×#124—21no—
113#525—48no—
114C2×#123—22no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121C2312yes—
123C2×#121C2312yes—
124C2×#121C2312yes—
125C2×#120—22no—
126C2×C4×D4—22no—
127C2×C4×D4—22no—
128C2×C4×D4—21no—
129C2×C4×D4C2312yes—
130C2×#117—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C42—44no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#501—44no—
155#490—44no—
156#481—28no—
157#480—28no—
158C2×#107C2314yes—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×#106C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×C22⋊C8—28no—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C2×#97—44no—
171C2×#97C2312yes—
172C2×#97C2312yes—
173C2×#97C2314yes—
174#391—21no—
175#391—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#387—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#387—22no—
205#387—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#384C2311yescharacteristic
221#384C2311yescharacteristic
222#382—21no—
223#382—21no—
224#382—21no—
225#382C2312yes—
226#382C2312yes—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240#380C2312yes—
241C4×C4⋊C4—21no—
242C4×C4⋊C4C2312yes—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2312yes—
260#336C2312yes—
261#336C2314yes—
262C25C2×D411yescharacteristic
263C2×#41—44no—
264C2×#41—44no—
265C2×#41—44no—
266C22×Q8—21no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4C2412yes—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C22×C8—28no—
306C22×C8—28no—
307C22×C8—44no—
308C22×C8C2414yes—
309C22×C8C2414yes—
310C4⋊Q8—24no—
311#127—24no—
312#125—24no—
313#125—24no—
314#125—42no—
315#125—42no—
316#125—44no—
317#125—44no—
318#124—44no—
319#123—48no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322#121—24no—
323#121—24no—
324#121—28no—
325#121—44no—
326#121—44no—
327#121—44no—
328#121—44no—
329#121—44no—
330#121—44no—
331#120—48no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—48no—
335C4×D4—48no—
336#117—44no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417#107—28no—
418#107—44no—
419#106—28no—
420#106—44no—
421#102—28no—
422#102—28no—
423#102—44no—
424#102—44no—
425C22⋊C8—24no—
426C22⋊C8—28no—
427C22⋊C8#4118yescomplemented
428#97—24no—
429#97—24no—
430#97—44no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
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#95—22no—
448#95—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—41no—
455C24—41no—
456C24AGL(1,ℤ/8)14yes—
457C24C22×D411yescharacteristic
458C24C22×D411yescharacteristic
459C24C22×D411yescharacteristic
460#41—816no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—42no—
482C2×D4—42no—
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—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—416no—
543C22×C4—416no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—416no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—44no—
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
572C22×C42−1+414yes—
573C22×C4C2511yescharacteristic
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—416no—
580C2×C8C2×#4118yes—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—24no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—42no—
609C4⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—44no—
641C42H(5,𝔽2)14yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—28no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—28no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23#53212yes—
671C23#53612yes—
672C23C2×AGL(1,ℤ/8)12yes—
673C23C2×AGL(1,ℤ/8)12yes—
674C23C2×AGL(1,ℤ/8)12yes—
675C23#57512yes—
676C23#57512yes—
677C23C23×D411yescharacteristic
678Q8—84no—
679D4—44no—
680D4—44no—
681D4—84no—
682D4—84no—
683D4—88no—
684D4—88no—
685D4—88no—
686C2×C4—28no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—88no—
754C2×C4—84no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4#53212yes—
759C2×C4#53412yes—
760C2×C4#53412yes—
761C2×C4#53612yes—
762C2×C4#57512yes—
763C2×C4C22×#4112yes—
764C2×C4C2×H(5,𝔽2)12yes—
765C2×C4C2×2−1+412yes—
766C8—28no—
767C8—44no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—416no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22#318014yes—
796C22#323414yes—
797C22C2×#53211yescharacteristic
798C22C2×#53411yescharacteristic
799C22C2×#53611yescharacteristic
800C22C22×AGL(1,ℤ/8)11yescharacteristic
801C22C2×#57511yescharacteristic
802C22C2×#57511yescharacteristic
803C22C2×#57511yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4#352014yes—
823C2—24no—
824C2—24no—
825C2—42no—
826C2—162no—
827C2#3508511yescharacteristic
828C2C2×#318011yescharacteristic
829C2#6070211yescharacteristic
830C2#6075011yescharacteristic
831C2#6075211yescharacteristic
832C2C2×#323411yescharacteristic
833C2#6085411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2851C2semidirect
3. #33217C2semidirect
4. #33052C2semidirect
5. #30362C2semidirect
6. #29161C2semidirect
7. #27969C2semidirect
8. #27918C2semidirect
9. #27880C2semidirect
10. #25913C2semidirect
11. #25819C2semidirect
12. #25676C2semidirect
13. #24553C2semidirect
14. #24550C2semidirect
15. #22082C2semidirect
16. #22081C2semidirect
17. C2×#1749C2semidirect
22. C2×#501C22semidirect
23. C2×#490C22semidirect
61. #2101C22semidirect
62. #2092C22semidirect
65. #2059C22semidirect
68. #2025C22semidirect
69. #1993C22semidirect
70. #1992C22semidirect
71. #1992C22semidirect
72. #1961C22semidirect
73. #1944C22semidirect
74. #1943C22semidirect
75. #1936C22semidirect
76. #1936C22semidirect
77. #1921C22semidirect
78. #1919C22semidirect
83. #1864C22semidirect
84. #1862C22semidirect
87. #1847C22semidirect
88. #1836C22semidirect
427. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×#28512
#332172
#330522
#303622
#291612
#279692
#279182
#278802
#259132
#258192
#256762
#245532
#245502
#220822
#220812
C2×#17492