Finite Group Databasebeta

← #6493627

Subgroups — #6493627

Order 512.

1950 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#33114C212yesmaximal, complemented
4#33113C212yesmaximal, complemented
5#29926C212yesmaximal, complemented
6#29925C212yesmaximal, complemented
7#27979C212yesmaximal, complemented
8#27915C212yesmaximal, complemented
9#27895C212yesmaximal, complemented
10#27894C212yesmaximal, complemented
11#27590C214yesmaximal, complemented
12#24008C214yesmaximal, complemented
13#21988C211yesmaximal, characteristic, complemented
14#21988C211yesmaximal, characteristic, complemented
15#21809C211yesmaximal, characteristic, complemented
16#21809C211yesmaximal, characteristic, complemented
17#20715C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525C2212yes—
20C23×C42C2211yescharacteristic
21C2×#485C2214yes—
22C2×#482C2214yes—
23C2×#432C2211yescharacteristic
24C2×#432C2211yescharacteristic
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2856C2211yescharacteristic
28#2856C2211yescharacteristic
29#2854—21no—
30#2854—21no—
31#2850C2212yes—
32#2850C2212yes—
33#2847—21no—
34#2847—21no—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39#2297C2212yes—
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2285C2211yescharacteristic
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283—21no—
51#2283C2212yes—
52#2283C2212yes—
53#2280—21no—
54#2280—21no—
55#2280C2212yes—
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yes—
59#2097C2214yescomplemented
60#2092C2214yescomplemented
61#2074C2214yescomplemented
62#2073C2214yescomplemented
63#2036C2214yes—
64#2035C2214yes—
65#2034C2214yes—
66#2033C2214yes—
67#1982C2212yescomplemented
68#1982C2212yescomplemented
69#1981C2212yescomplemented
70#1981C2212yescomplemented
71#1959C2212yescomplemented
72#1959C2212yescomplemented
73#1959C2212yescomplemented
74#1959C2212yescomplemented
75#1948C2212yescomplemented
76#1948C2212yescomplemented
77#1947C2212yescomplemented
78#1947C2212yescomplemented
79#1928C2214yescomplemented
80#1927C2214yescomplemented
81#1926C2214yescomplemented
82#1925C2214yescomplemented
83#1875C2214yes—
84#1873C2214yes—
85#1854C2214yes—
86#1854C2214yes—
87#1847C2212yescomplemented
88#1847C2212yescomplemented
89#1836C2212yescomplemented
90#1836C2212yescomplemented
91#1817C2212yes—
92#1797C2212yes—
93#1797C2212yes—
94#1788C2214yes—
95#1788C2214yes—
96#1779C2212yes—
97#1749C2212yes—
98#1749C2212yes—
99C22×#41C2312yes—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103#532—24no—
104#532—24no—
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—24no—
133C22×C42—24no—
134C22×C42D411yescharacteristic
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146#485—48no—
147#482—48no—
148#432—24no—
149#432—24no—
150C2×#107C2314yes—
151C2×#107C2314yes—
152C2×#106C2314yes—
153C2×#106C2314yes—
154C2×C4⋊C8C2312yes—
155C2×C4⋊C8C2312yes—
156C2×#103C2314yes—
157C2×#103C2314yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×C22⋊C8C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2314yes—
168C2×#97C2312yes—
169C2×#97C2312yes—
170#391C2312yes—
171#391C2312yes—
172#390—21no—
173#390—21no—
174#390—21no—
175#390—21no—
176#390C2312yes—
177#390C2312yes—
178#389—21no—
179#389—21no—
180#389—21no—
181#389—21no—
182#388—22no—
183#388—22no—
184#388—22no—
185#388—22no—
186#386—22no—
187#386—22no—
188#386—22no—
189#386—22no—
190#386—22no—
191#386—22no—
192#384C2311yescharacteristic
193#384C2311yescharacteristic
194#384C2311yescharacteristic
195#384C2311yescharacteristic
196#384C2311yescharacteristic
197#384C2311yescharacteristic
198#383—22no—
199#383—22no—
200#382—21no—
201#382—21no—
202#382—21no—
203#382—21no—
204#382C2312yes—
205#382C2312yes—
206#382C2312yes—
207#381—22no—
208#381—22no—
209#381—22no—
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#380—21no—
223#380—21no—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228#379—22no—
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⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C2312yes—
240C4×C4⋊C4C2312yes—
241C4×C4⋊C4C2312yes—
242C4×C4⋊C4C2312yes—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251#376—22no—
252#376—22no—
253#376—22no—
254C43—22no—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2314yes—
260#336C2314yes—
261C25C2×D411yescharacteristic
262C2×#41—24no—
263C2×#41—24no—
264C2×#41—44no—
265C2×#41—44no—
266C22×Q8C2412yes—
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—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
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×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C22×C8C2414yes—
303C22×C8C2414yes—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#127—22no—
307#127—22no—
308#124—24no—
309#124—24no—
310#123—48no—
311C22⋊Q8—28no—
312C22⋊Q8—44no—
313#121—28no—
314#121—44no—
315#121—44no—
316#121—44no—
317#121—44no—
318#121—44no—
319#121—44no—
320#121—44no—
321#120—48no—
322C4×D4—48no—
323C4×D4—48no—
324C4×D4—44no—
325C4×D4—44no—
326#117—24no—
327#117—24no—
328#117—42no—
329#117—42no—
330#117—44no—
331#117—44no—
332#117—44no—
333#117—44no—
334#117—44no—
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—21no—
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⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
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×C42#4114yes—
410C2×C42#4114yes—
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415#107—44no—
416#107—44no—
417#106—44no—
418#106—44no—
419C4⋊C8—24no—
420C4⋊C8—24no—
421#103—44no—
422#103—44no—
423#103—44no—
424#103—44no—
425#102—44no—
426#102—44no—
427#102—44no—
428#102—44no—
429C22⋊C8—24no—
430C22⋊C8—24no—
431C22⋊C8—28no—
432C22⋊C8—44no—
433#97—24no—
434#97—24no—
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—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24C22×D411yescharacteristic
462C24C22×D411yescharacteristic
463C24C22×D411yescharacteristic
464#41—88no—
465#41—88no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—24no—
469C2×Q8—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
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—21no—
522C22×C4—21no—
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—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—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—416no—
551C22×C4—416no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4#12314yes—
556C22×C4#12314yes—
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×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)14yes—
571C22×C4C2511yescharacteristic
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C2×C8—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
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—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42#12314yes—
643C42#12314yes—
644C42C2×#4112yes—
645C42C2×#4112yes—
646C42C2×#4112yes—
647C42C2×#4112yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23C2×#12312yes—
681C23#53512yes—
682C23#57512yes—
683C23C23×D411yescharacteristic
684Q8—44no—
685Q8—44no—
686D4—44no—
687D4—44no—
688D4—84no—
689D4—88no—
690D4—88no—
691D4—88no—
692D4—84no—
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—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
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—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
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—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—88no—
760C2×C4C2×#12312yes—
761C2×C4C2×#12312yes—
762C2×C4C2×#12312yes—
763C2×C4C2×#12312yes—
764C2×C4C2×#12312yes—
765C2×C4#53512yes—
766C2×C4#57512yes—
767C2×C4#57512yes—
768C2×C4#57512yes—
769C2×C4C22×#4111yescharacteristic
770C2×C4C22×#4111yescharacteristic
771C2×C4C2×H(5,𝔽2)12yes—
772C2×C4#58512yes—
773C8—44no—
774C8—44no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—416no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22C22×#12311yescharacteristic
805C22C2×#53511yescharacteristic
806C22#344911yescharacteristic
807C22C2×#57511yescharacteristic
808C22C2×#57511yescharacteristic
809C22C2×#57511yescharacteristic
810C22C2×#57511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4#309314yes—
829C4#349412yes—
830C4#349412yes—
831C2—42no—
832C2—42no—
833C2—42no—
834C2—162no—
835C2#3526211yescharacteristic
836C2C2×#309311yescharacteristic
837C2#6051111yescharacteristic
838C2#6079011yescharacteristic
839C2#6080211yescharacteristic
840C2#6095311yescharacteristic
841C2#6096111yescharacteristic
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. #34012C2semidirect
3. #33114C2semidirect
4. #33113C2semidirect
5. #29926C2semidirect
6. #29925C2semidirect
7. #27979C2semidirect
8. #27915C2semidirect
9. #27895C2semidirect
10. #27894C2semidirect
11. #27590C2semidirect
12. #24008C2semidirect
13. #21988C2semidirect
14. #21988C2semidirect
15. #21809C2semidirect
16. #21809C2semidirect
17. #20715C2semidirect
59. #2097C22semidirect
60. #2092C22semidirect
61. #2074C22semidirect
62. #2073C22semidirect
67. #1982C22semidirect
68. #1982C22semidirect
69. #1981C22semidirect
70. #1981C22semidirect
71. #1959C22semidirect
72. #1959C22semidirect
73. #1959C22semidirect
74. #1959C22semidirect
75. #1948C22semidirect
76. #1948C22semidirect
77. #1947C22semidirect
78. #1947C22semidirect
79. #1928C22semidirect
80. #1927C22semidirect
81. #1926C22semidirect
82. #1925C22semidirect
87. #1847C22semidirect
88. #1847C22semidirect
89. #1836C22semidirect
90. #1836C22semidirect

Maximal subgroups

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

subgroupindex
#366242
#340122
#331142
#331132
#299262
#299252
#279792
#279152
#278952
#278942
#275902
#240082
#219882
#218092
#207152