Finite Group Databasebeta

← #6661059

Subgroups — #6661059

Order 512.

1952 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×#2851C211yesmaximal, characteristic, complemented
3#32746C214yesmaximal, complemented
4#30295C212yesmaximal, complemented
5#30201C212yesmaximal, complemented
6#29967C211yesmaximal, characteristic, complemented
7#29966C211yesmaximal, characteristic, complemented
8#29943C212yesmaximal, complemented
9#29755C211yesmaximal, characteristic, complemented
10#29754C211yesmaximal, characteristic, complemented
11#29694C212yesmaximal, complemented
12#27651C212yesmaximal, complemented
13#24841C214yesmaximal, complemented
14#24558C212yesmaximal, complemented
15#24557C212yesmaximal, complemented
16#24305C212yesmaximal, complemented
17#20626C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C22×#125C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×#481C2212yes—
23C2×#480C2212yes—
24C2×#478C2214yescomplemented
25C2×#423C2212yes—
26C2×#407C2212yes—
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2856C2211yescharacteristic
30#2856C2211yescharacteristic
31#2854—21no—
32#2854C2212yes—
33#2851—21no—
34#2851—21no—
35#2851—21no—
36#2851—21no—
37#2851C2212yes—
38#2851C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2850—21no—
42#2850—21no—
43#2847—21no—
44#2847C2212yes—
45C4×#121—21no—
46C4×#121—21no—
47C4×#121C2212yes—
48C4×#121C2212yes—
49#2297—21no—
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#387—21no—
53C2×#387—21no—
54C2×#385—21no—
55C2×#385—21no—
56#2285C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60#2099C2212yescomplemented
61#2099C2212yescomplemented
62#2088C2214yescomplemented
63#2086C2214yescomplemented
64#2085C2214yescomplemented
65#2084C2212yescomplemented
66#2083C2212yescomplemented
67#2077C2214yes—
68#2076C2214yes—
69#2073C2214yescomplemented
70#2067C2214yescomplemented
71#2065C2214yescomplemented
72#2059C2214yescomplemented
73#2058C2212yescomplemented
74#2057C2212yescomplemented
75#2041C2212yescomplemented
76#2041C2212yescomplemented
77#2034C2214yes—
78#2033C2214yes—
79#2025C2214yescomplemented
80#1989C2214yescomplemented
81#1949C2214yescomplemented
82#1895C2214yes—
83#1895C2214yes—
84#1874C2212yes—
85#1874C2212yes—
86#1853C2212yes—
87#1852C2212yes—
88#1824C2212yes—
89#1823C2212yes—
90#1809C2214yes—
91#1809C2214yes—
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—44no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×#127C2311yescharacteristic
107C2×#125—21no—
108C2×#125—21no—
109C2×#125—44no—
110C2×#125C2312yes—
111C2×#125C2312yes—
112C2×#124—21no—
113#525—48no—
114C2×#123—22no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121C2312yes—
123C2×#121C2312yes—
124C2×#121C2312yes—
125C2×#120—22no—
126C2×C4×D4—22no—
127C2×C4×D4—22no—
128C2×C4×D4—21no—
129C2×C4×D4C2312yes—
130C2×#117—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C42—44no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#481—44no—
155#480—44no—
156#478—48no—
157C2×#107C2314yes—
158C2×#107C2314yes—
159C2×#106C2314yes—
160C2×#106C2314yes—
161#423—44no—
162C2×C4⋊C8C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169#407—44no—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2314yes—
173#391—21no—
174#391—21no—
175#390—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390C2312yes—
180#390C2312yes—
181#389—21no—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389C2312yes—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#388—22no—
194#388—22no—
195#388—22no—
196#388—22no—
197#387—22no—
198#387—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#387—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#382—21no—
222#382—21no—
223#382—21no—
224#382C2312yes—
225#382C2312yes—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240C4×C4⋊C4—21no—
241C4×C4⋊C4C2312yes—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2314yes—
261C25C2×D411yescharacteristic
262C2×#41—44no—
263C2×#41—44no—
264C2×#41—44no—
265C22×Q8—21no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C2412yes—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—24no—
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×C4—42no—
286C23×C4—42no—
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×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C2×M16—28no—
306C2×M16—44no—
307C2×M16—44no—
308C22×C8C2414yes—
309C22×C8C2414yes—
310C4⋊Q8—42no—
311#127—42no—
312#125—28no—
313#125—44no—
314#125—44no—
315#125—44no—
316#124—44no—
317#123—48no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320#121—24no—
321#121—28no—
322#121—24no—
323#121—44no—
324#121—44no—
325#121—44no—
326#121—44no—
327#121—44no—
328#121—44no—
329#120—48no—
330C4×D4—28no—
331C4×D4—44no—
332C4×D4—48no—
333C4×D4—48no—
334#117—44no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
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⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
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—44no—
387C2×C22⋊C4—44no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
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×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417#107—44no—
418#107—44no—
419#106—44no—
420#106—44no—
421C4⋊C8—28no—
422C4⋊C8—42no—
423C4⋊C8—42no—
424#102—44no—
425#102—44no—
426#102—44no—
427#102—44no—
428C22⋊C8—24no—
429C22⋊C8—24no—
430C22⋊C8—44no—
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—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—41no—
456C24—41no—
457C24C22×D411yescharacteristic
458C24C22×D411yescharacteristic
459C24C22×D411yescharacteristic
460#41—816no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×D4—22no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—22no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
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—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
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—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—48no—
544C22×C4—48no—
545C22×C4—416no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—416no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—44no—
562C22×C4AGL(1,ℤ/8)14yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4H(5,𝔽2)12yes—
575C22×C42−1+414yes—
576C22×C42−1+412yes—
577C22×C4C2511yescharacteristic
578M16—88no—
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—44no—
645C42H(5,𝔽2)14yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—28no—
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—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23#53612yes—
677C23#53712yes—
678C23C2×AGL(1,ℤ/8)12yes—
679C23#57512yes—
680C23#57512yes—
681C23C23×D411yescharacteristic
682Q8—84no—
683D4—44no—
684D4—44no—
685D4—84no—
686D4—84no—
687D4—88no—
688D4—88no—
689D4—88no—
690C2×C4—28no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
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—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—21no—
710C2×C4—21no—
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—44no—
722C2×C4—44no—
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—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—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—88no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4#53412yes—
764C2×C4#53412yes—
765C2×C4#53612yes—
766C2×C4#53712yes—
767C2×C4C2×AGL(1,ℤ/8)12yes—
768C2×C4C2×AGL(1,ℤ/8)12yes—
769C2×C4#57512yes—
770C2×C4C2×H(5,𝔽2)11yescharacteristic
771C2×C4C2×H(5,𝔽2)12yes—
772C2×C4C2×2−1+412yes—
773C2×C4C2×2−1+411yescharacteristic
774C8—44no—
775C8—44no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—416no—
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—
804C22#325114yes—
805C22C2×#53411yescharacteristic
806C22C2×#53611yescharacteristic
807C22C2×#53711yescharacteristic
808C22C22×AGL(1,ℤ/8)11yescharacteristic
809C22C2×#57511yescharacteristic
810C22C2×#57511yescharacteristic
811C22C2×#57511yescharacteristic
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4#353612yes—
831C4#353812yes—
832C2—24no—
833C2—42no—
834C2—42no—
835C2—162no—
836C2#3744211yescharacteristic
837C2#6074111yescharacteristic
838C2#6075011yescharacteristic
839C2#6086111yescharacteristic
840C2#6086411yescharacteristic
841C2C2×#325111yescharacteristic
842C2#6091711yescharacteristic
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×#2851C2semidirect
3. #32746C2semidirect
4. #30295C2semidirect
5. #30201C2semidirect
6. #29967C2semidirect
7. #29966C2semidirect
8. #29943C2semidirect
9. #29755C2semidirect
10. #29754C2semidirect
11. #29694C2semidirect
12. #27651C2semidirect
13. #24841C2semidirect
14. #24558C2semidirect
15. #24557C2semidirect
16. #24305C2semidirect
17. #20626C2semidirect
24. C2×#478C22semidirect
60. #2099C22semidirect
61. #2099C22semidirect
62. #2088C22semidirect
63. #2086C22semidirect
64. #2085C22semidirect
65. #2084C22semidirect
66. #2083C22semidirect
69. #2073C22semidirect
70. #2067C22semidirect
71. #2065C22semidirect
72. #2059C22semidirect
73. #2058C22semidirect
74. #2057C22semidirect
75. #2041C22semidirect
76. #2041C22semidirect
79. #2025C22semidirect
80. #1989C22semidirect
81. #1949C22semidirect
92. #1804C22semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×#28512
#327462
#302952
#302012
#299672
#299662
#299432
#297552
#297542
#296942
#276512
#248412
#245582
#245572
#243052
#206262