Finite Group Databasebeta

← #6435233

Subgroups — #6435233

Order 512.

2056 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#29928C212yesmaximal, complemented
4#29927C212yesmaximal, complemented
5#29926C212yesmaximal, complemented
6#29925C212yesmaximal, complemented
7#29924C214yesmaximal, complemented
8#29923C211yesmaximal, characteristic, complemented
9#29922C211yesmaximal, characteristic, complemented
10#29921C211yesmaximal, characteristic, complemented
11#29920C211yesmaximal, characteristic, complemented
12#23730C212yesmaximal, complemented
13#23627C212yesmaximal, complemented
14#23479C214yesmaximal, complemented
15#21257C212yesmaximal, complemented
16#21169C212yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525C2212yes—
20C23×C42C2211yescharacteristic
21C2×#427C2214yes—
22C22×C4⋊C8C2212yes—
23C2×#416C2214yes—
24C2×#416C2214yes—
25C22×C22⋊C8C2212yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2856C2211yescharacteristic
29#2856C2211yescharacteristic
30#2854—21no—
31#2854—21no—
32#2850C2212yes—
33#2850C2212yes—
34#2847—21no—
35#2847—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121—21no—
40#2297C2212yes—
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2285C2211yescharacteristic
47#2285C2211yescharacteristic
48#2283—21no—
49#2283—21no—
50#2283—21no—
51#2283—21no—
52#2283C2212yes—
53#2283C2212yes—
54#2280—21no—
55#2280—21no—
56#2280C2212yes—
57C4×#117—21no—
58C4×#117—21no—
59C4×#117C2212yes—
60#2097C2214yescomplemented
61#2096C2212yescomplemented
62#2095C2212yescomplemented
63#2094C2212yescomplemented
64#2093C2212yescomplemented
65#2092C2214yescomplemented
66#2074C2214yescomplemented
67#2073C2214yescomplemented
68#2072C2212yescomplemented
69#2072C2212yescomplemented
70#2071C2212yescomplemented
71#2071C2212yescomplemented
72#2036C2214yes—
73#2036C2214yes—
74#2035C2214yes—
75#2035C2214yes—
76#2034C2214yes—
77#2034C2214yes—
78#2033C2214yes—
79#2033C2214yes—
80#1983C2214yescomplemented
81#1983C2214yescomplemented
82#1982C2212yescomplemented
83#1982C2212yescomplemented
84#1981C2212yescomplemented
85#1981C2212yescomplemented
86#1949C2214yescomplemented
87#1949C2214yescomplemented
88#1948C2212yescomplemented
89#1948C2212yescomplemented
90#1947C2212yescomplemented
91#1947C2212yescomplemented
92#1797C2211yescharacteristic
93#1797C2211yescharacteristic
94#1797C2212yes—
95#1797C2212yes—
96#1797C2212yes—
97#1735C2214yes—
98C2×#336C2212yes—
99C22×#41C2312yes—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C23×C8C2314yes—
104#532—28no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×#127C2311yescharacteristic
107C2×#124C2312yes—
108#525—48no—
109C2×#123—22no—
110C2×C22⋊Q8C2312yes—
111C2×C22⋊Q8C2312yes—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121C2312yes—
119C2×#121C2312yes—
120C2×#120—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117C2312yes—
130C2×#117C2312yes—
131C2×#117C2312yes—
132C22×C42—28no—
133C22×C42D411yescharacteristic
134C22×C42D411yescharacteristic
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145#427—48no—
146C2×#107C2314yes—
147C2×#107C2314yes—
148C2×#106C2314yes—
149C2×#106C2314yes—
150C2×C4⋊C8—28no—
151C2×C4⋊C8C2312yes—
152C2×C4⋊C8C2312yes—
153C2×C4⋊C8C2314yes—
154#416—48no—
155#416—48no—
156C2×#103C2314yes—
157C2×#103C2314yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×C22⋊C8—44no—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2312yes—
168#391C2312yes—
169#391C2312yes—
170#390—21no—
171#390—21no—
172#390—21no—
173#390—21no—
174#390C2312yes—
175#390C2312yes—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180#388—22no—
181#388—22no—
182#388—22no—
183#388—22no—
184#386—22no—
185#386—22no—
186#386—22no—
187#386—22no—
188#386—22no—
189#386—22no—
190#384C2311yescharacteristic
191#384C2311yescharacteristic
192#384C2311yescharacteristic
193#384C2311yescharacteristic
194#384C2311yescharacteristic
195#384C2311yescharacteristic
196#383—22no—
197#383—22no—
198#382—21no—
199#382—21no—
200#382—21no—
201#382—21no—
202#382C2312yes—
203#382C2312yes—
204#382C2312yes—
205#381—22no—
206#381—22no—
207#381—22no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380C2312yes—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#379—22no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C4⋊C4C2312yes—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249#376—22no—
250#376—22no—
251#376—22no—
252C43—22no—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#336C2312yes—
258#336C2312yes—
259#336C2314yes—
260C25C2×D411yescharacteristic
261C2×#41—28no—
262C2×#41—28no—
263C2×#41—24no—
264C2×#41—24no—
265C22×Q8C2412yes—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C2412yes—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C22×C8—28no—
302C22×C8—28no—
303C22×C8—28no—
304C22×C8C2414yes—
305C22×C8C2414yes—
306C4⋊Q8—24no—
307#127—24no—
308#124—28no—
309#123—48no—
310C22⋊Q8—44no—
311C22⋊Q8—44no—
312#121—44no—
313#121—44no—
314#121—44no—
315#121—44no—
316#121—44no—
317#121—44no—
318#121—44no—
319#121—44no—
320#120—48no—
321C4×D4—48no—
322C4×D4—48no—
323C4×D4—44no—
324C4×D4—44no—
325#117—28no—
326#117—24no—
327#117—24no—
328#117—24no—
329#117—24no—
330#117—44no—
331#117—44no—
332#117—44no—
333#117—44no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
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×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42#4118yes—
404C2×C42C2411yescharacteristic
405C2×C42C2411yescharacteristic
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408#107—44no—
409#107—44no—
410#106—44no—
411#106—44no—
412C4⋊C8—28no—
413C4⋊C8—24no—
414C4⋊C8—24no—
415#103—44no—
416#103—44no—
417#103—44no—
418#103—44no—
419#102—44no—
420#102—44no—
421#102—44no—
422#102—44no—
423C22⋊C8—42no—
424C22⋊C8—44no—
425C22⋊C8—42no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
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—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—41no—
451C24—41no—
452C24C22×D411yescharacteristic
453C24C22×D411yescharacteristic
454C24C22×D411yescharacteristic
455#41—416no—
456#41—416no—
457C2×Q8—24no—
458C2×Q8—22no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—24no—
464C2×D4—22no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C22×C4—22no—
481C22×C4—22no—
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—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—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
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—416no—
538C22×C4—416no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4#12314yes—
545C22×C4#12314yes—
546C22×C4#13514yes—
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C2×#4114yes—
559C22×C4H(5,𝔽2)14yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C42−1+412yes—
562C22×C4C2511yescharacteristic
563C2×C8—24no—
564C2×C8—24no—
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—416no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
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—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42#12314yes—
633C42#12314yes—
634C42C2×#4114yes—
635C42C2×#4114yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—28no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C2×#12312yes—
667C23#53512yes—
668C23#53712yes—
669C23C2×#13512yes—
670C23#57512yes—
671C23C23×D411yescharacteristic
672Q8—44no—
673Q8—44no—
674D4—44no—
675D4—44no—
676D4—84no—
677D4—88no—
678D4—88no—
679D4—88no—
680D4—84no—
681C2×C4—28no—
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—28no—
693C2×C4—28no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
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—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
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—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—88no—
744C2×C4C2×#12312yes—
745C2×C4C2×#12312yes—
746C2×C4C2×#12312yes—
747C2×C4C2×#12312yes—
748C2×C4C2×#12312yes—
749C2×C4#53512yes—
750C2×C4#53712yes—
751C2×C4#54018yes—
752C2×C4#54218yes—
753C2×C4C2×#13512yes—
754C2×C4C2×#13512yes—
755C2×C4#57512yes—
756C2×C4#57512yes—
757C2×C4C22×#4112yes—
758C2×C4C2×H(5,𝔽2)11yescharacteristic
759C2×C4C2×H(5,𝔽2)12yes—
760C2×C4C2×2−1+411yescharacteristic
761C8—44no—
762C8—44no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—416no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22#262414yes—
792C22C22×#12311yescharacteristic
793C22C2×#53511yescharacteristic
794C22C2×#53711yescharacteristic
795C22C22×#13511yescharacteristic
796C22C2×#57511yescharacteristic
797C22C2×#57511yescharacteristic
798C22C2×#57511yescharacteristic
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4#262414yes—
816C4#309114yes—
817C4C2×#54012yes—
818C4C2×#54212yes—
819C2—24no—
820C2—42no—
821C2—42no—
822C2—162no—
823C2C2×#262411yescharacteristic
824C2C2×#309111yescharacteristic
825C2#6051111yescharacteristic
826C2#6078211yescharacteristic
827C2#6079011yescharacteristic
828C2#6090011yescharacteristic
829C2#6090711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34012C2semidirect
3. #29928C2semidirect
4. #29927C2semidirect
5. #29926C2semidirect
6. #29925C2semidirect
7. #29924C2semidirect
8. #29923C2semidirect
9. #29922C2semidirect
10. #29921C2semidirect
11. #29920C2semidirect
12. #23730C2semidirect
13. #23627C2semidirect
14. #23479C2semidirect
15. #21257C2semidirect
16. #21169C2semidirect
17. C2×#1797C2semidirect
60. #2097C22semidirect
61. #2096C22semidirect
62. #2095C22semidirect
63. #2094C22semidirect
64. #2093C22semidirect
65. #2092C22semidirect
66. #2074C22semidirect
67. #2073C22semidirect
68. #2072C22semidirect
69. #2072C22semidirect
70. #2071C22semidirect
71. #2071C22semidirect
80. #1983C22semidirect
81. #1983C22semidirect
82. #1982C22semidirect
83. #1982C22semidirect
84. #1981C22semidirect
85. #1981C22semidirect
86. #1949C22semidirect
87. #1949C22semidirect
88. #1948C22semidirect
89. #1948C22semidirect
90. #1947C22semidirect
91. #1947C22semidirect

Maximal subgroups

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

subgroupindex
#366242
#340122
#299282
#299272
#299262
#299252
#299242
#299232
#299222
#299212
#299202
#237302
#236272
#234792
#212572
#211692
C2×#17972