Finite Group Databasebeta

← #6434021

Subgroups — #6434021

Order 512.

2032 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#30366C212yesmaximal, complemented
4#30364C212yesmaximal, complemented
5#30327C212yesmaximal, complemented
6#30325C212yesmaximal, complemented
7#30291C211yesmaximal, characteristic, complemented
8#30240C211yesmaximal, characteristic, complemented
9#30187C211yesmaximal, characteristic, complemented
10#30185C211yesmaximal, characteristic, complemented
11#29735C214yesmaximal, complemented
12#23763C212yesmaximal, complemented
13#23760C212yesmaximal, complemented
14#23576C212yesmaximal, complemented
15#23574C212yesmaximal, complemented
16#21528C214yesmaximal, complemented
17C2×#1749C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×#465C2214yes—
23C2×#440C2214yescomplemented
24C22×C22⋊C8C2212yes—
25C22×#97C2212yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2855—21no—
35#2855C2212yes—
36#2854—21no—
37#2854C2212yes—
38#2851—21no—
39#2851—21no—
40#2850—21no—
41#2850—21no—
42#2848—21no—
43#2848C2212yes—
44#2847—21no—
45#2847C2212yes—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8C2212yes—
49C4×C22⋊Q8C2212yes—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121C2212yes—
53C4×#121C2212yes—
54#2297—21no—
55#2296—21no—
56#2285C2211yescharacteristic
57#2285C2211yescharacteristic
58#2280—21no—
59#2100C2212yescomplemented
60#2099C2212yescomplemented
61#2096C2212yescomplemented
62#2094C2212yescomplemented
63#2083C2212yescomplemented
64#2083C2212yescomplemented
65#2077C2214yes—
66#2077C2214yes—
67#2072C2212yescomplemented
68#2071C2212yescomplemented
69#2057C2212yescomplemented
70#2057C2212yescomplemented
71#2043C2212yescomplemented
72#2041C2212yescomplemented
73#2036C2214yes—
74#2036C2214yes—
75#2033C2214yes—
76#2033C2214yes—
77#2024C2212yescomplemented
78#2023C2212yescomplemented
79#2014C2212yescomplemented
80#2013C2212yescomplemented
81#2000C2214yes—
82#2000C2214yes—
83#1973C2214yescomplemented
84#1944C2214yescomplemented
85#1936C2214yescomplemented
86#1935C2214yescomplemented
87#1893C2214yes—
88#1892C2214yes—
89#1808C2214yes—
90#1776C2214yescomplemented
91#1763C2214yescomplemented
92#1762C2214yescomplemented
93#1749C2212yes—
94#1749C2212yes—
95#1749C2212yes—
96#1749C2212yes—
97C2×#336C2211yescharacteristic
98C2×#336C2211yescharacteristic
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×SD16C2314yes—
104C23×C8C2312yes—
105C23×C8C2312yes—
106#533—44no—
107#532—44no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×C4⋊Q8C2311yescharacteristic
111C2×#127C2311yescharacteristic
112C2×#125—21no—
113C2×#124—21no—
114#525—48no—
115C2×#123—22no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×C22⋊Q8C2312yes—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×#121C2312yes—
130C2×#121C2312yes—
131C2×#121C2312yes—
132C2×#120—22no—
133C2×C4×Q8—21no—
134C2×C4×Q8C2312yes—
135C2×C4×D4—22no—
136C2×C4×D4—22no—
137C2×C4×D4—21no—
138C2×C4×D4C2312yes—
139C2×#117—21no—
140C2×#117—21no—
141C2×#117—21no—
142C22×C42—44no—
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#465—216no—
156#440—48no—
157C2×#107C2314yes—
158C2×#107C2314yes—
159C2×#106C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×C22⋊C8—28no—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C2×#97—44no—
170C2×#97C2314yes—
171C2×#97C2314yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#391C2312yes—
177#391C2312yes—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#384C2311yescharacteristic
219#384C2311yescharacteristic
220#382—21no—
221#382—21no—
222#381—22no—
223#380—21no—
224#380—21no—
225#380—21no—
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#379—22no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2312yes—
257#336C2312yes—
258#336C2312yes—
259#336C2312yes—
260C25C2×D411yescharacteristic
261C2×#41—44no—
262C2×#41—44no—
263C2×#41—44no—
264C22×Q8—21no—
265C22×Q8—21no—
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—24no—
276C23×C4—22no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—41no—
280C23×C4—41no—
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
302C2×SD16—28no—
303C2×SD16—44no—
304C2×SD16—44no—
305C22×C8—24no—
306C22×C8—42no—
307C22×C8—42no—
308C22×C8—42no—
309C22×C8—42no—
310C22×C8#4118yescomplemented
311C22×C8C2414yes—
312C22×C8C2414yes—
313C4⋊Q8—42no—
314C4⋊Q8—42no—
315C4⋊Q8—42no—
316#127—42no—
317#125—44no—
318#124—44no—
319#123—48no—
320C22⋊Q8—28no—
321C22⋊Q8—42no—
322C22⋊Q8—42no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329#121—28no—
330#121—42no—
331#121—42no—
332#121—44no—
333#121—44no—
334#121—44no—
335#121—44no—
336#121—44no—
337#121—44no—
338#120—48no—
339C4×Q8—28no—
340C4×Q8—44no—
341C4×D4—28no—
342C4×D4—44no—
343C4×D4—48no—
344C4×D4—48no—
345#117—44no—
346#117—44no—
347#117—44no—
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—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
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—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
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×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422#107—44no—
423#107—44no—
424#106—28no—
425#103—28no—
426#103—44no—
427#103—44no—
428#102—28no—
429#102—44no—
430#102—44no—
431C22⋊C8—28no—
432C22⋊C8—28no—
433#97—28no—
434#97—44no—
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—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—41no—
458C24—41no—
459C24C22×D411yescharacteristic
460C24C22×D411yescharacteristic
461C24C22×D411yescharacteristic
462#41—816no—
463C2×Q8—24no—
464C2×Q8—24no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—42no—
491C2×D4—42no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
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—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
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—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—416no—
554C22×C4—416no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4AGL(1,ℤ/8)14yes—
561C22×C4#13714yes—
562C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
574C22×C4C2511yescharacteristic
575SD16—416no—
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—48no—
582C2×C8—48no—
583C2×C8C2×#4118yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—42no—
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—
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—
645C42—44no—
646C42—44no—
647C42H(5,𝔽2)14yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—28no—
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—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23#53212yes—
679C23C2×AGL(1,ℤ/8)12yes—
680C23C2×#13712yes—
681C23#57512yes—
682C23#57512yes—
683C23C23×D411yescharacteristic
684Q8—44no—
685Q8—44no—
686Q8—84no—
687Q8—84no—
688D4—44no—
689D4—44no—
690D4—84no—
691D4—84no—
692D4—88no—
693D4—88no—
694D4—88no—
695C2×C4—28no—
696C2×C4—28no—
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—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—24no—
712C2×C4—24no—
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—21no—
724C2×C4—21no—
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—44no—
737C2×C4—44no—
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—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—88no—
764C2×C4#53212yes—
765C2×C4#53412yes—
766C2×C4#53412yes—
767C2×C4C2×AGL(1,ℤ/8)12yes—
768C2×C4C2×AGL(1,ℤ/8)12yes—
769C2×C4C2×#13712yes—
770C2×C4C2×#13712yes—
771C2×C4C22×#4112yes—
772C2×C4C2×H(5,𝔽2)12yes—
773C2×C4#58511yescharacteristic
774C2×C4#58511yescharacteristic
775C8—28no—
776C8—44no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—416no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22#318214yes—
806C22C2×#53211yescharacteristic
807C22C2×#53411yescharacteristic
808C22#344911yescharacteristic
809C22C22×AGL(1,ℤ/8)11yescharacteristic
810C22C22×#13711yescharacteristic
811C22C2×#57511yescharacteristic
812C22C2×#57511yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#345912yes—
832C4#346012yes—
833C2—24no—
834C2—42no—
835C2—42no—
836C2—162no—
837C2#3457511yescharacteristic
838C2#6068811yescharacteristic
839C2C2×#318211yescharacteristic
840C2#6075011yescharacteristic
841C2#6075111yescharacteristic
842C2#6096211yescharacteristic
843C2#6096311yescharacteristic
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
1. #36625C2semidirect
3. #30366C2semidirect
4. #30364C2semidirect
5. #30327C2semidirect
6. #30325C2semidirect
7. #30291C2semidirect
8. #30240C2semidirect
9. #30187C2semidirect
10. #30185C2semidirect
11. #29735C2semidirect
12. #23763C2semidirect
13. #23760C2semidirect
14. #23576C2semidirect
15. #23574C2semidirect
16. #21528C2semidirect
17. C2×#1749C2semidirect
23. C2×#440C22semidirect
59. #2100C22semidirect
60. #2099C22semidirect
61. #2096C22semidirect
62. #2094C22semidirect
63. #2083C22semidirect
64. #2083C22semidirect
67. #2072C22semidirect
68. #2071C22semidirect
69. #2057C22semidirect
70. #2057C22semidirect
71. #2043C22semidirect
72. #2041C22semidirect
77. #2024C22semidirect
78. #2023C22semidirect
79. #2014C22semidirect
80. #2013C22semidirect
83. #1973C22semidirect
84. #1944C22semidirect
85. #1936C22semidirect
86. #1935C22semidirect
90. #1776C22semidirect
91. #1763C22semidirect
92. #1762C22semidirect
310. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#303662
#303642
#303272
#303252
#302912
#302402
#301872
#301852
#297352
#237632
#237602
#235762
#235742
#215282
C2×#17492