Finite Group Databasebeta

← #6660596

Subgroups — #6660596

Order 512.

1878 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#32789C212yesmaximal, complemented
4#32776C212yesmaximal, complemented
5#30362C214yesmaximal, complemented
6#29938C211yesmaximal, characteristic, complemented
7#29936C211yesmaximal, characteristic, complemented
8#29896C214yesmaximal, complemented
9#29690C211yesmaximal, characteristic, complemented
10#29687C211yesmaximal, characteristic, complemented
11#29337C212yesmaximal, complemented
12#29304C212yesmaximal, complemented
13#27679C212yesmaximal, complemented
14#24709C212yesmaximal, complemented
15#24708C212yesmaximal, complemented
16#24300C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22C2×#476C2212yescomplemented
23C2×#474C2212yescomplemented
24C2×#432C2212yes—
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2856C2211yescharacteristic
32#2856C2211yescharacteristic
33#2855—21no—
34#2855—21no—
35#2854—21no—
36#2854C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2850—21no—
40#2850—21no—
41#2848—21no—
42#2848—21no—
43#2847—21no—
44#2847C2212yes—
45C4×C22⋊Q8—21no—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8—21no—
49C4×#121—21no—
50C4×#121—21no—
51C4×#121C2212yes—
52C4×#121C2212yes—
53#2297—21no—
54#2296C2212yes—
55#2285C2211yescharacteristic
56#2285C2211yescharacteristic
57#2280C2212yes—
58#2101C2214yescomplemented
59#2099C2212yescomplemented
60#2099C2212yescomplemented
61#2092C2214yescomplemented
62#2084C2212yescomplemented
63#2083C2212yescomplemented
64#2077C2214yes—
65#2077C2214yes—
66#2076C2214yes—
67#2075C2214yes—
68#2059C2214yescomplemented
69#2058C2212yescomplemented
70#2057C2212yescomplemented
71#2041C2212yescomplemented
72#2041C2212yescomplemented
73#2034C2214yes—
74#2034C2214yes—
75#2033C2214yes—
76#2033C2214yes—
77#2025C2214yescomplemented
78#1988C2212yescomplemented
79#1987C2212yescomplemented
80#1948C2212yescomplemented
81#1947C2212yescomplemented
82#1944C2214yescomplemented
83#1943C2214yescomplemented
84#1936C2214yescomplemented
85#1936C2214yescomplemented
86#1875C2214yes—
87#1875C2214yes—
88#1854C2214yes—
89#1854C2214yes—
90#1817C2212yes—
91#1802C2212yescomplemented
92#1802C2212yescomplemented
93#1797C2212yes—
94#1797C2211yescharacteristic
95#1797C2211yescharacteristic
96#1779C2212yes—
97#1749C2212yes—
98#1749C2212yes—
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103#533—44no—
104#532—44no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#125C2312yes—
110C2×#124—21no—
111#525—48no—
112C2×#123—22no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#120—22no—
130C2×C4×Q8—21no—
131C2×C4×Q8—21no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—21no—
135C2×C4×D4C2312yes—
136C2×#117—21no—
137C2×#117C2312yes—
138C2×#117C2312yes—
139C22×C42—44no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#476—44no—
153#474—44no—
154#432—44no—
155C2×#107C2314yes—
156C2×#107C2314yes—
157C2×#106C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2314yes—
169C2×#97C2314yes—
170#391—21no—
171#391—21no—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#390—21no—
177#390—21no—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#387—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#386—22no—
203#386—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#384C2311yescharacteristic
215#384C2311yescharacteristic
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#382—21no—
219#382C2312yes—
220#381—22no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#379—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4C2312yes—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2312yes—
257#336C2312yes—
258#336C2314yes—
259C25C2×D411yescharacteristic
260C2×#41—44no—
261C2×#41—44no—
262C2×#41—44no—
263C22×Q8—21no—
264C22×Q8—21no—
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—24no—
274C23×C4—22no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—41no—
280C23×C4—41no—
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×C8C2414yes—
302C22×C8C2414yes—
303C4⋊Q8—24no—
304C4⋊Q8—24no—
305C4⋊Q8—42no—
306#127—42no—
307#125—44no—
308#124—44no—
309#123—48no—
310C22⋊Q8—44no—
311C22⋊Q8—44no—
312C22⋊Q8—44no—
313C22⋊Q8—44no—
314C22⋊Q8—44no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318#121—24no—
319#121—24no—
320#121—42no—
321#121—42no—
322#121—42no—
323#121—42no—
324#121—44no—
325#121—44no—
326#121—44no—
327#121—44no—
328#121—44no—
329#120—48no—
330C4×Q8—44no—
331C4×Q8—44no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—44no—
335C4×D4—48no—
336C4×D4—48no—
337#117—42no—
338#117—42no—
339#117—44no—
340#117—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
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—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
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×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×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
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×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
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#102—44no—
422#102—44no—
423#102—44no—
424#102—44no—
425C22⋊C8—28no—
426C22⋊C8—42no—
427C22⋊C8—42no—
428C22⋊C8—44no—
429#97—44no—
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—
444#95—22no—
445#95—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24C22×D411yescharacteristic
455C24C22×D411yescharacteristic
456C24C22×D411yescharacteristic
457#41—816no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
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—44no—
486C2×D4—42no—
487C2×D4—42no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
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—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
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—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—416no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—416no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×D411yescharacteristic
569C22×C42−1+414yes—
570C22×C4C2511yescharacteristic
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
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—22no—
588C4⋊C4—22no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
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—42no—
603C4⋊C4—42no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊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—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—44no—
641C42—44no—
642C42—44no—
643C42H(5,𝔽2)14yes—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
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—44no—
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—
677C23C2×AGL(1,ℤ/8)12yes—
678C23#57512yes—
679C23C23×D411yescharacteristic
680Q8—84no—
681Q8—84no—
682Q8—84no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—42no—
687D4—84no—
688D4—84no—
689D4—88no—
690D4—88no—
691D4—88no—
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—28no—
701C2×C4—24no—
702C2×C4—24no—
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—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—42no—
759C2×C4—42no—
760C2×C4—88no—
761C2×C4#53412yes—
762C2×C4#53412yes—
763C2×C4#53612yes—
764C2×C4C2×AGL(1,ℤ/8)12yes—
765C2×C4C2×AGL(1,ℤ/8)12yes—
766C2×C4#57512yes—
767C2×C4#57512yes—
768C2×C4C2×H(5,𝔽2)12yes—
769C2×C4C2×2−1+412yes—
770C2×C4#58511yescharacteristic
771C2×C4#58511yescharacteristic
772C8—44no—
773C8—44no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—416no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22C2×#53411yescharacteristic
804C22C2×#53611yescharacteristic
805C22#344911yescharacteristic
806C22C22×AGL(1,ℤ/8)11yescharacteristic
807C22C2×#57511yescharacteristic
808C22C2×#57511yescharacteristic
809C22C2×#57511yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—22no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4#319414yes—
828C4#354112yes—
829C4#354112yes—
830C2—42no—
831C2—42no—
832C2—42no—
833C2—162no—
834C2#3743811yescharacteristic
835C2C2×#319411yescharacteristic
836C2#6075211yescharacteristic
837C2#6085411yescharacteristic
838C2#6086411yescharacteristic
839C2#6096211yescharacteristic
840C2#6096711yescharacteristic
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. #32789C2semidirect
4. #32776C2semidirect
5. #30362C2semidirect
6. #29938C2semidirect
7. #29936C2semidirect
8. #29896C2semidirect
9. #29690C2semidirect
10. #29687C2semidirect
11. #29337C2semidirect
12. #29304C2semidirect
13. #27679C2semidirect
14. #24709C2semidirect
15. #24708C2semidirect
16. #24300C2semidirect
17. #20715C2semidirect
22. C2×#476C22semidirect
23. C2×#474C22semidirect
58. #2101C22semidirect
59. #2099C22semidirect
60. #2099C22semidirect
61. #2092C22semidirect
62. #2084C22semidirect
63. #2083C22semidirect
68. #2059C22semidirect
69. #2058C22semidirect
70. #2057C22semidirect
71. #2041C22semidirect
72. #2041C22semidirect
77. #2025C22semidirect
78. #1988C22semidirect
79. #1987C22semidirect
80. #1948C22semidirect
81. #1947C22semidirect
82. #1944C22semidirect
83. #1943C22semidirect
84. #1936C22semidirect
85. #1936C22semidirect
91. #1802C22semidirect
92. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#327892
#327762
#303622
#299382
#299362
#298962
#296902
#296872
#293372
#293042
#276792
#247092
#247082
#243002
#207152