Finite Group Databasebeta

← #6495609

Subgroups — #6495609

Order 512.

2056 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C2×#2293C211yesmaximal, characteristic, complemented
3#33109C211yesmaximal, characteristic, complemented
4#33107C211yesmaximal, characteristic, complemented
5#32905C211yesmaximal, characteristic, complemented
6#32902C211yesmaximal, characteristic
7#29986C212yesmaximal, complemented
8#29795C212yesmaximal, complemented
9#29556C214yesmaximal, complemented
10#29372C214yesmaximal, complemented
11#29330C212yesmaximal, complemented
12#28303C212yesmaximal, complemented
13#24067C212yesmaximal, complemented
14#23936C212yesmaximal, complemented
15#22146C212yesmaximal, complemented
16#22145C212yesmaximal, complemented
17#20777C211yesmaximal, characteristic, complemented
18C2×#529C2212yes—
19C22×C4×D4C2211yescharacteristic
20C22×#117—21no—
21C2×#484C2212yes—
22C2×#481C2212yes—
23C2×#461C2212yes—
24C2×#459C2212yes—
25C2×#450C2212yes—
26C2×#447C2212yes—
27#2861C2212yescomplemented
28#2860—21no—
29#2860—21no—
30#2859C2211yescharacteristic, complemented
31#2858C2211yescharacteristic, complemented
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2854—21no—
35#2854—21no—
36#2850C2212yes—
37C4×C4⋊Q8C2211yescharacteristic, complemented
38C4×#127C2211yescharacteristic, complemented
39C4×#124C2212yescomplemented
40C4×#121—21no—
41C4×#121—21no—
42#2293—21no—
43#2293—21no—
44#2293—21no—
45#2293—21no—
46#2293—21no—
47#2293—21no—
48#2293C2212yes—
49#2293C2212yes—
50#2293C2212yes—
51#2293C2212yes—
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388—21no—
57C2×#388—21no—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60C2×C43C2211yescharacteristic
61#2101C2214yescomplemented
62#2092C2214yes—
63#2059C2214yescomplemented
64#2042C2214yescomplemented
65#2042C2214yescomplemented
66#2025C2214yes—
67#2012C2214yes—
68#2012C2214yes—
69#1982C2212yescomplemented
70#1981C2212yescomplemented
71#1970C2214yes—
72#1968C2214yes—
73#1948C2212yescomplemented
74#1947C2212yescomplemented
75#1934C2214yescomplemented
76#1933C2214yescomplemented
77#1928C2214yescomplemented
78#1926C2214yescomplemented
79#1880C2214yes—
80#1879C2214yes—
81#1879C2214yes—
82#1877C2214yes—
83#1874C2212yes—
84#1874C2212yes—
85#1872C2212yes—
86#1872C2212yes—
87#1865C2214yescomplemented
88#1862C2214yescomplemented
89#1839C2212yescomplemented
90#1831C2212yescomplemented
91#1817C2212yes—
92#1802C2212yes—
93#1802C2212yes—
94#1797C2211yescharacteristic
95#1797C2211yescharacteristic
96C4×C4⋊C8C2212yescomplemented
97C4×C22⋊C8C2212yes—
98#1744C2212yescomplemented
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C22×SD16C2314yes—
102C22×D8C2314yes—
103C2×C4⋊Q8C2311yescharacteristic
104C2×#127C2311yescharacteristic
105#529—44no—
106#529—44no—
107C2×#126—22no—
108C2×#125C2312yes—
109C2×#124C2312yes—
110C2×#124C2312yes—
111C2×#123—22no—
112C2×C22⋊Q8C2312yes—
113C2×#121—21no—
114C2×#121—21no—
115C2×#121C2312yes—
116C2×C4×Q8C2312yes—
117C2×C4×D4—28no—
118C2×C4×D4—22no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—21no—
122C2×C4×D4—21no—
123C2×C4×D4C2312yes—
124C2×C4×D4C2312yes—
125C2×C4×D4C2312yes—
126C2×#117—22no—
127C2×#117—22no—
128C2×#117—22no—
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—48no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C42—21no—
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#484—44no—
151#481—44no—
152#461—28no—
153#459—28no—
154#450—44no—
155#447—44no—
156C2×#107C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2312yes—
159C2×C4⋊C8C2312yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C2×C4×C8C2314yes—
171#391C2312yes—
172#391C2312yes—
173#390—21no—
174#390—21no—
175#390—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390—21no—
183#390—21no—
184#390—21no—
185#390C2312yes—
186#390C2312yes—
187#390C2312yes—
188#390C2312yes—
189#390C2312yes—
190#390C2312yes—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389C2312yes—
204#389C2312yes—
205#389C2312yes—
206#389C2312yes—
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#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#386—22no—
224#386—22no—
225#384C2311yescharacteristic
226#384C2311yescharacteristic
227#382C2312yes—
228#380—21no—
229#380—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
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—
245C43D411yescharacteristic
246C43D411yescharacteristic
247C43D411yescharacteristic
248C43D411yescharacteristic
249C43C2311yescharacteristic
250C43C2311yescharacteristic
251C43C2311yescharacteristic
252C43C2311yescharacteristic
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#336C2312yes—
258#336C2312yes—
259#336C2314yes—
260#336C2314yes—
261#336C2314yes—
262C25—21no—
263C22×Q8C2412yes—
264C22×D4—24no—
265C22×D4—22no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—42no—
272C22×D4C2412yes—
273C22×D4C2412yes—
274C23×C4—28no—
275C23×C4—21no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2411yescharacteristic
290C2×SD16—28no—
291C2×SD16—44no—
292C2×SD16—44no—
293C2×D8—28no—
294C2×D8—44no—
295C2×D8—44no—
296C22×C8C2414yes—
297C22×C8C2414yes—
298C4⋊Q8—24no—
299#127—24no—
300#126—48no—
301#125—42no—
302#125—42no—
303#124—44no—
304#124—42no—
305#124—42no—
306#123—48no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309#121—24no—
310#121—24no—
311#121—44no—
312#121—44no—
313C4×Q8—42no—
314C4×Q8—42no—
315C4×D4—28no—
316C4×D4—28no—
317C4×D4—24no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—42no—
321C4×D4—42no—
322C4×D4—44no—
323C4×D4—48no—
324C4×D4—44no—
325C4×D4#4118yes—
326#117—48no—
327#117—48no—
328#117—48no—
329#117—48no—
330#117—48no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
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—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—44no—
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425#107—44no—
426#106—44no—
427C4⋊C8—24no—
428C4⋊C8—24no—
429#103—28no—
430#103—44no—
431#103—44no—
432#102—28no—
433#102—44no—
434#102—44no—
435#102—44no—
436#102—44no—
437C22⋊C8—24no—
438C22⋊C8—24no—
439C4×C8—44no—
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—
449#95—22no—
450#95—22no—
451#95—22no—
452C24—24no—
453C24—22no—
454C24—22no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24C22×D411yescharacteristic
462C2×Q8—24no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—24no—
466C2×D4—24no—
467C2×D4—22no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—24no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4C2×#4114yes—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—28no—
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—28no—
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—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—44no—
519C22×C4—432no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—44no—
534C22×C4#13514yes—
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4H(5,𝔽2)12yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C4C2511yescharacteristic
551SD16—88no—
552D8—88no—
553C2×C8—24no—
554C2×C8—24no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—42no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—42no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4C2×#4114yes—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—22no—
626C42—22no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42AGL(1,ℤ/8)14yes—
639C42C2×#4114yes—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—24no—
645C23—48no—
646C23—48no—
647C23—48no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—84no—
662C23—84no—
663C23—84no—
664C23—84no—
665C23#53512yes—
666C23C2×#13512yes—
667C23#57512yes—
668C23C23×D411yescharacteristic
669Q8—44no—
670Q8—44no—
671D4—24no—
672D4—24no—
673D4—48no—
674D4—42no—
675D4—42no—
676D4—44no—
677D4—44no—
678D4—84no—
679D4—88no—
680D4—84no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—21no—
697C2×C4—24no—
698C2×C4—21no—
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—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—416no—
720C2×C4—48no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—416no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
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—88no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#52512yes—
744C2×C4#52512yes—
745C2×C4#53512yes—
746C2×C4C2×#13512yes—
747C2×C4C2×#13512yes—
748C2×C4C2×AGL(1,ℤ/8)12yes—
749C2×C4C2×AGL(1,ℤ/8)12yes—
750C2×C4C2×AGL(1,ℤ/8)12yes—
751C2×C4#57512yes—
752C2×C4C22×#4112yes—
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4#58512yes—
756C8—44no—
757C8—44no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22#321214yes—
780C22C2×#52511yescharacteristic
781C22C2×#53511yescharacteristic
782C22#344911yescharacteristic
783C22C22×#13511yescharacteristic
784C22C22×AGL(1,ℤ/8)11yescharacteristic
785C22C2×#57511yescharacteristic
786C22C2×#57511yescharacteristic
787C4—22no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—44no—
798C4—41no—
799C4—41no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#310514yes—
806C4#349412yes—
807C4#349412yes—
808C2—24no—
809C2—84no—
810C2—162no—
811C2#3530111yescharacteristic
812C2C2×#310511yescharacteristic
813C2#6056311yescharacteristic
814C2C2×#321211yescharacteristic
815C2#6080311yescharacteristic
816C2#6094211yescharacteristic
817C2#6096211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32902C2
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. #36631C2semidirect
2. C2×#2293C2semidirect
3. #33109C2semidirect
4. #33107C2semidirect
5. #32905C2semidirect
7. #29986C2semidirect
8. #29795C2semidirect
9. #29556C2semidirect
10. #29372C2semidirect
11. #29330C2semidirect
12. #28303C2semidirect
13. #24067C2semidirect
14. #23936C2semidirect
15. #22146C2semidirect
16. #22145C2semidirect
17. #20777C2semidirect
27. #2861C22semidirect
30. #2859C22semidirect
31. #2858C22semidirect
37. C4×C4⋊Q8C22semidirect
38. C4×#127C22semidirect
39. C4×#124C22semidirect
61. #2101C22semidirect
63. #2059C22semidirect
64. #2042C22semidirect
65. #2042C22semidirect
69. #1982C22semidirect
70. #1981C22semidirect
73. #1948C22semidirect
74. #1947C22semidirect
75. #1934C22semidirect
76. #1933C22semidirect
77. #1928C22semidirect
78. #1926C22semidirect
87. #1865C22semidirect
88. #1862C22semidirect
89. #1839C22semidirect
90. #1831C22semidirect
96. C4×C4⋊C8C22semidirect
98. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#366312
C2×#22932
#331092
#331072
#329052
#329022
#299862
#297952
#295562
#293722
#293302
#283032
#240672
#239362
#221462
#221452
#207772