Finite Group Databasebeta

← #6489118

Subgroups — #6489118

Order 512.

2156 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36639C211yesmaximal, characteristic, complemented
2C2×C4×#124C211yesmaximal, characteristic, complemented
3#32909C212yesmaximal, complemented
4#32908C212yesmaximal, complemented
5#30046C212yesmaximal, complemented
6#30045C212yesmaximal, complemented
7#29142C212yesmaximal, complemented
8#28442C212yesmaximal, complemented
9#28163C214yesmaximal, complemented
10#27977C212yesmaximal, complemented
11#25724C212yesmaximal, complemented
12#23934C211yesmaximal, characteristic, complemented
13#23933C211yesmaximal, characteristic, complemented
14#23931C211yesmaximal, characteristic, complemented
15#23930C211yesmaximal, characteristic
16#22271C214yesmaximal, complemented
17#20777C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C22×#124C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C2×#495C2214yes—
24C2×#464C2214yescomplemented
25C2×#463C2214yes—
26C2×#451C2212yes—
27C2×#448C2212yes—
28C2×#450C2212yes—
29C2×#447C2212yes—
30#2862C2211yescharacteristic, complemented
31#2862C2211yescharacteristic, complemented
32#2861—21no—
33#2861—21no—
34#2858C2211yescharacteristic, complemented
35#2858C2211yescharacteristic, complemented
36#2850—21no—
37#2850—21no—
38#2850C2212yes—
39#2850C2212yes—
40C4×#124—21no—
41C4×#124—21no—
42C4×#124—21no—
43C4×#124—21no—
44C4×#124—21no—
45C4×#124—21no—
46C4×#124C2212yes—
47C4×#124C2212yes—
48C4×#124C2212yes—
49C4×#124C2212yes—
50C4×#124C2212yescomplemented
51C4×#124C2212yescomplemented
52#2297—21no—
53#2297—21no—
54C2×#391C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#388—21no—
57C2×#388—21no—
58C2×#382C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60C2×C4×C22⋊C4—21no—
61C2×C43C2211yescharacteristic
62#2074C2214yescomplemented
63#2073C2214yescomplemented
64#2024C2212yescomplemented
65#2024C2212yescomplemented
66#2023C2212yes—
67#2023C2212yes—
68#2016C2212yescomplemented
69#2015C2214yes—
70#2014C2212yescomplemented
71#2013C2212yes—
72#2012C2214yes—
73#2011C2212yes—
74#1958C2214yes—
75#1958C2214yescomplemented
76#1880C2214yes—
77#1880C2214yescomplemented
78#1879C2214yes—
79#1879C2214yes—
80#1878C2214yescomplemented
81#1878C2214yescomplemented
82#1877C2214yes—
83#1877C2214yescomplemented
84#1874C2212yes—
85#1874C2212yes—
86#1872C2212yes—
87#1872C2212yes—
88#1839C2212yescomplemented
89#1835C2214yescomplemented
90#1831C2212yescomplemented
91#1817C2211yescharacteristic
92#1817C2211yescharacteristic
93#1805C2214yescomplemented
94#1804C2214yes—
95#1797C2212yes—
96C4×C4⋊C8C2212yescomplemented
97C4×C22⋊C8C2212yes—
98#1744C2212yescomplemented
99C22×#41—21no—
100C23×Q8C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C22×Q16C2314yes—
104C22×SD16C2314yes—
105C22×SD16C2314yes—
106C22×D8C2314yes—
107#533—44no—
108#532—44no—
109C2×C4⋊Q8C2311yescharacteristic
110C2×C4⋊Q8C2311yescharacteristic
111C2×C4⋊Q8C2311yescharacteristic
112C2×#127C2311yescharacteristic
113C2×#125—21no—
114C2×#124—28no—
115C2×#124—21no—
116C2×#124—21no—
117C2×#124—21no—
118C2×#124—21no—
119C2×#124—21no—
120C2×#124C2312yes—
121C2×#124C2312yes—
122C2×#124C2312yes—
123C2×#124C2312yes—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8C2312yes—
126C2×#121—21no—
127C2×#121C2312yes—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—44no—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×Q8C2312yes—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—44no—
139C2×C4×D4C2312yes—
140C2×C4×D4C2312yes—
141C2×C4×D4C2312yes—
142C2×#117—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C42—21no—
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#495—216no—
160#464—48no—
161#463—48no—
162#451—44no—
163#450—44no—
164#448—44no—
165#447—44no—
166C2×C4⋊C8C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C4×C8C2314yes—
178#391—21no—
179#391—21no—
180#391—21no—
181#391—21no—
182#391—21no—
183#391—21no—
184#391—21no—
185#391—21no—
186#391C2312yes—
187#391C2312yes—
188#391C2312yes—
189#391C2312yes—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#390C2312yes—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#386—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#382—21no—
223#382—21no—
224#382—21no—
225#382—21no—
226#382C2312yes—
227#382C2312yes—
228#382C2312yes—
229#382C2312yes—
230C4×C22⋊C4—22no—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C43D411yescharacteristic
247C43D411yescharacteristic
248C43D411yescharacteristic
249C43D411yescharacteristic
250C43C2311yescharacteristic
251C43C2311yescharacteristic
252C43C2311yescharacteristic
253C43C2311yescharacteristic
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2314yes—
259#336C2312yes—
260#336C2312yes—
261#336C2312yes—
262#336C2312yes—
263#336C2314yes—
264C25—21no—
265C2×#41—44no—
266C2×#41—44no—
267C2×#41—44no—
268C22×Q8—24no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—21no—
272C22×Q8—24no—
273C22×Q8—42no—
274C22×Q8C2412yes—
275C22×Q8C2412yes—
276C22×D4—24no—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—24no—
282C22×D4—42no—
283C22×D4C2412yes—
284C22×D4C2412yes—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2411yescharacteristic
301C2×Q16—28no—
302C2×Q16—44no—
303C2×Q16—44no—
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—44no—
307C2×SD16—44no—
308C2×SD16—44no—
309C2×SD16—44no—
310C2×D8—28no—
311C2×D8—44no—
312C2×D8—44no—
313C22×C8C2414yes—
314C22×C8C2414yes—
315C4⋊Q8—42no—
316C4⋊Q8—42no—
317C4⋊Q8—42no—
318#127—42no—
319#125—44no—
320#124—28no—
321#124—28no—
322#124—24no—
323#124—24no—
324#124—24no—
325#124—28no—
326#124—28no—
327#124—44no—
328#124—44no—
329#124—44no—
330#124#4118yescomplemented
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8—44no—
334#121—24no—
335#121—24no—
336#121—44no—
337C4×Q8—28no—
338C4×Q8—44no—
339C4×Q8—42no—
340C4×Q8—42no—
341C4×Q8—44no—
342C4×Q8—44no—
343C4×Q8—44no—
344C4×D4—28no—
345C4×D4—44no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4—44no—
349C4×D4—44no—
350C4×D4—44no—
351#117—44no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
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—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—44no—
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C4⋊C8—28no—
435#103—44no—
436#103—44no—
437#103—44no—
438#103—44no—
439#102—44no—
440#102—44no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445C4×C8—28no—
446#95—22no—
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—
459#95—22no—
460#95—22no—
461#95—22no—
462C24—24no—
463C24—22no—
464C24—22no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24C22×D411yescharacteristic
472#41—816no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—416no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8C2×#4114yes—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—416no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4C2×#4114yes—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—816no—
556C22×C4#13514yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
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×C4H(5,𝔽2)14yes—
571C22×C4C2511yescharacteristic
572Q16—88no—
573SD16—88no—
574SD16—88no—
575D8—88no—
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—24no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊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—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42C2×#4114yes—
649C42H(5,𝔽2)14yes—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—24no—
655C23—48no—
656C23—48no—
657C23—48no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23#53512yes—
676C23C2×#13512yes—
677C23#57512yes—
678C23C23×D411yescharacteristic
679Q8—28no—
680Q8—48no—
681Q8—44no—
682Q8—44no—
683Q8—44no—
684Q8—84no—
685Q8—84no—
686D4—28no—
687D4—48no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—84no—
692D4—84no—
693D4—88no—
694C2×C4—28no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—28no—
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—28no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—24no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—48no—
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—88no—
751C2×C4—88no—
752C2×C4—88no—
753C2×C4—84no—
754C2×C4—84no—
755C2×C4#52512yes—
756C2×C4#52512yes—
757C2×C4#53512yes—
758C2×C4#53512yes—
759C2×C4#53512yes—
760C2×C4C2×#13512yes—
761C2×C4C2×#13512yes—
762C2×C4#57512yes—
763C2×C4#57512yes—
764C2×C4C22×#4112yes—
765C2×C4C2×H(5,𝔽2)12yes—
766C2×C4C2×H(5,𝔽2)12yes—
767C8—44no—
768C8—44no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—816no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22#321114yes—
791C22C2×#52511yescharacteristic
792C22C2×#53511yescharacteristic
793C22C2×#53511yescharacteristic
794C22C22×#13511yescharacteristic
795C22C2×#57511yescharacteristic
796C22C2×#57511yescharacteristic
797C22C2×#57511yescharacteristic
798C4—22no—
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—44no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4#351914yes—
818C2—24no—
819C2—84no—
820C2—162no—
821C2#3523711yescharacteristic
822C2#6053611yescharacteristic
823C2#6054611yescharacteristic
824C2C2×#321111yescharacteristic
825C2#6078211yescharacteristic
826C2#6079911yescharacteristic
827C2#6080511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23930C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36639C2semidirect
2. C2×C4×#124C2semidirect
3. #32909C2semidirect
4. #32908C2semidirect
5. #30046C2semidirect
6. #30045C2semidirect
7. #29142C2semidirect
8. #28442C2semidirect
9. #28163C2semidirect
10. #27977C2semidirect
11. #25724C2semidirect
12. #23934C2semidirect
13. #23933C2semidirect
14. #23931C2semidirect
16. #22271C2semidirect
17. #20777C2semidirect
24. C2×#464C22semidirect
30. #2862C22semidirect
31. #2862C22semidirect
34. #2858C22semidirect
35. #2858C22semidirect
50. C4×#124C22semidirect
51. C4×#124C22semidirect
62. #2074C22semidirect
63. #2073C22semidirect
64. #2024C22semidirect
65. #2024C22semidirect
68. #2016C22semidirect
70. #2014C22semidirect
75. #1958C22semidirect
77. #1880C22semidirect
80. #1878C22semidirect
81. #1878C22semidirect
83. #1877C22semidirect
88. #1839C22semidirect
89. #1835C22semidirect
90. #1831C22semidirect
93. #1805C22semidirect
96. C4×C4⋊C8C22semidirect
98. #1744C22semidirect
330. #124#41semidirect

Maximal subgroups

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

subgroupindex
#366392
C2×C4×#1242
#329092
#329082
#300462
#300452
#291422
#284422
#281632
#279772
#257242
#239342
#239332
#239312
#239302
#222712
#207772