Finite Group Databasebeta

← #6493722

Subgroups — #6493722

Order 512.

1972 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×#2283C211yesmaximal, characteristic, complemented
3#33147C211yesmaximal, characteristic, complemented
4#33146C211yesmaximal, characteristic, complemented
5#33107C211yesmaximal, characteristic, complemented
6#33106C211yesmaximal, characteristic, complemented
7#29941C212yesmaximal, complemented
8#29925C212yesmaximal, complemented
9#27865C214yesmaximal, complemented
10#27684C212yesmaximal, complemented
11#27651C212yesmaximal, complemented
12#27632C214yesmaximal, complemented
13#24558C212yesmaximal, complemented
14#24557C212yesmaximal, complemented
15#21963C212yesmaximal, complemented
16#21891C212yesmaximal, complemented
17#20626C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C23×C42C2211yescharacteristic
21C2×#481C2212yes—
22C2×#480C2212yes—
23C2×#423C2212yes—
24C2×#407C2212yes—
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2856C2211yescharacteristic
28#2856C2211yescharacteristic
29#2854—21no—
30#2854C2212yes—
31#2850—21no—
32#2850—21no—
33#2847—21no—
34#2847C2212yes—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121C2212yes—
38C4×#121C2212yes—
39#2297—21no—
40#2285C2211yescharacteristic
41#2283—21no—
42#2283—21no—
43#2283—21no—
44#2283—21no—
45#2283C2212yes—
46#2283C2212yes—
47#2283C2212yes—
48#2283C2212yes—
49C2×#383—21no—
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#381—21no—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4—21no—
58C2×#376—21no—
59#2101C2214yescomplemented
60#2092C2214yescomplemented
61#2085C2214yescomplemented
62#2077C2214yes—
63#2076C2214yes—
64#2073C2214yescomplemented
65#2034C2214yes—
66#2033C2214yes—
67#1988C2212yescomplemented
68#1988C2212yescomplemented
69#1982C2212yescomplemented
70#1982C2212yescomplemented
71#1949C2214yescomplemented
72#1949C2214yescomplemented
73#1948C2212yescomplemented
74#1948C2212yescomplemented
75#1947C2212yescomplemented
76#1947C2212yescomplemented
77#1926C2214yescomplemented
78#1925C2214yescomplemented
79#1919C2214yescomplemented
80#1918C2214yescomplemented
81#1895C2214yes—
82#1895C2214yes—
83#1874C2212yes—
84#1874C2212yes—
85#1853C2212yes—
86#1852C2212yes—
87#1824C2212yes—
88#1823C2212yes—
89#1809C2214yes—
90#1809C2214yes—
91#1804C2214yescomplemented
92#1804C2214yescomplemented
93#1797C2212yes—
94#1797C2211yescharacteristic
95#1797C2211yescharacteristic
96#1797C2212yes—
97#1797C2212yes—
98#1728C2212yes—
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×M16C2314yes—
104#532—28no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×#127C2311yescharacteristic
107C2×#124—21no—
108#525—48no—
109C2×#123—22no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121C2312yes—
118C2×#121C2312yes—
119C2×#121C2312yes—
120C2×#120—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—21no—
124C2×C4×D4C2312yes—
125C2×#117—21no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C42—28no—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#481—44no—
148#480—44no—
149C2×#107C2314yes—
150C2×#107C2314yes—
151C2×#106C2314yes—
152C2×#106C2314yes—
153#423—28no—
154C2×C4⋊C8C2314yes—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2312yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161#407—44no—
162C2×C22⋊C8C2312yes—
163C2×C22⋊C8C2312yes—
164C2×C22⋊C8C2314yes—
165#391—21no—
166#391—21no—
167#390—21no—
168#390—21no—
169#390—21no—
170#390—21no—
171#390C2312yes—
172#390C2312yes—
173#389—21no—
174#389—21no—
175#389C2312yes—
176#389C2312yes—
177#388—22no—
178#388—22no—
179#388—22no—
180#388—22no—
181#386—22no—
182#386—22no—
183#386—22no—
184#386—22no—
185#386—22no—
186#386—22no—
187#384C2311yescharacteristic
188#384C2311yescharacteristic
189#383—22no—
190#383—22no—
191#383—22no—
192#383—22no—
193#382—21no—
194#382—21no—
195#382—21no—
196#382—21no—
197#382—21no—
198#382C2312yes—
199#382C2312yes—
200#382C2312yes—
201#382C2312yes—
202#381—22no—
203#381—22no—
204#381—22no—
205#381—22no—
206#380—21no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380C2312yes—
214#380C2312yes—
215#380C2312yes—
216#380C2312yes—
217#380C2312yes—
218#380C2312yes—
219#380C2312yes—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4C2312yes—
226C4×C4⋊C4C2312yes—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2312yes—
229C4×C4⋊C4C2312yes—
230C4×C22⋊C4—22no—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236#376—22no—
237#376—22no—
238#376—22no—
239#376—22no—
240C2×#95—21no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2314yes—
257#336C2312yes—
258#336C2312yes—
259C25C2×D411yescharacteristic
260C2×#41—44no—
261C2×#41—44no—
262C2×#41—44no—
263C22×Q8—21no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4C2412yes—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—22no—
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×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×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C2×M16—28no—
304C2×M16—44no—
305C2×M16—44no—
306C22×C8C2414yes—
307C22×C8C2414yes—
308C4⋊Q8—24no—
309#127—24no—
310#124—44no—
311#123—48no—
312C22⋊Q8—44no—
313C22⋊Q8—44no—
314#121—28no—
315#121—24no—
316#121—24no—
317#121—44no—
318#121—44no—
319#121—44no—
320#121—44no—
321#121—44no—
322#121—44no—
323#120—48no—
324C4×D4—28no—
325C4×D4—48no—
326C4×D4—48no—
327C4×D4—44no—
328#117—44no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
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—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
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—44no—
369C2×C22⋊C4—44no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
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—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—44no—
387C2×C42—44no—
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
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×C42#4118yes—
401C2×C42C2411yescharacteristic
402C2×C42C2411yescharacteristic
403C2×C42C2411yescharacteristic
404C2×C42C2411yescharacteristic
405#107—44no—
406#107—44no—
407#106—44no—
408#106—44no—
409C4⋊C8—28no—
410C4⋊C8—24no—
411C4⋊C8—24no—
412#102—44no—
413#102—44no—
414#102—44no—
415#102—44no—
416C22⋊C8—24no—
417C22⋊C8—24no—
418C22⋊C8—44no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
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—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—41no—
448C24—41no—
449C24C22×D411yescharacteristic
450C24C22×D411yescharacteristic
451C24C22×D411yescharacteristic
452#41—816no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—24no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
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—21no—
510C22×C4—21no—
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—41no—
520C22×C4—41no—
521C22×C4—41no—
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—416no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—416no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—44no—
552C22×C4#12314yes—
553C22×C4#12314yes—
554C22×C4AGL(1,ℤ/8)14yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C42−1+412yes—
569C22×C4C2511yescharacteristic
570M16—88no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—44no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊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—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
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#53712yes—
668C23C2×AGL(1,ℤ/8)12yes—
669C23#57512yes—
670C23#57512yes—
671C23C23×D411yescharacteristic
672Q8—84no—
673D4—44no—
674D4—44no—
675D4—84no—
676D4—88no—
677D4—88no—
678D4—88no—
679D4—84no—
680C2×C4—21no—
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—28no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
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—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—88no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4C2×#12312yes—
752C2×C4C2×#12312yes—
753C2×C4C2×#12312yes—
754C2×C4C2×#12312yes—
755C2×C4C2×#12312yes—
756C2×C4#53712yes—
757C2×C4C2×AGL(1,ℤ/8)12yes—
758C2×C4C2×AGL(1,ℤ/8)12yes—
759C2×C4#57512yes—
760C2×C4C22×#4112yes—
761C2×C4C2×H(5,𝔽2)11yescharacteristic
762C2×C4C2×2−1+411yescharacteristic
763C2×C4#58512yes—
764C8—44no—
765C8—44no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—416no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22#325114yes—
795C22C22×#12311yescharacteristic
796C22C2×#53711yescharacteristic
797C22#344911yescharacteristic
798C22C22×AGL(1,ℤ/8)11yescharacteristic
799C22C2×#57511yescharacteristic
800C22C2×#57511yescharacteristic
801C22C2×#57511yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4#309414yes—
820C4#349412yes—
821C4#349512yes—
822C2—24no—
823C2—42no—
824C2—42no—
825C2—162no—
826C2#3526311yescharacteristic
827C2C2×#309411yescharacteristic
828C2#6051111yescharacteristic
829C2C2×#325111yescharacteristic
830C2#6091711yescharacteristic
831C2#6094911yescharacteristic
832C2#6097011yescharacteristic
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×#2283C2semidirect
3. #33147C2semidirect
4. #33146C2semidirect
5. #33107C2semidirect
6. #33106C2semidirect
7. #29941C2semidirect
8. #29925C2semidirect
9. #27865C2semidirect
10. #27684C2semidirect
11. #27651C2semidirect
12. #27632C2semidirect
13. #24558C2semidirect
14. #24557C2semidirect
15. #21963C2semidirect
16. #21891C2semidirect
17. #20626C2semidirect
59. #2101C22semidirect
60. #2092C22semidirect
61. #2085C22semidirect
64. #2073C22semidirect
67. #1988C22semidirect
68. #1988C22semidirect
69. #1982C22semidirect
70. #1982C22semidirect
71. #1949C22semidirect
72. #1949C22semidirect
73. #1948C22semidirect
74. #1948C22semidirect
75. #1947C22semidirect
76. #1947C22semidirect
77. #1926C22semidirect
78. #1925C22semidirect
79. #1919C22semidirect
80. #1918C22semidirect
91. #1804C22semidirect
92. #1804C22semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×#22832
#331472
#331462
#331072
#331062
#299412
#299252
#278652
#276842
#276512
#276322
#245582
#245572
#219632
#218912
#206262