Finite Group Databasebeta

← #6458964

Subgroups — #6458964

Order 512.

1926 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Q8C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic
3#27682C212yesmaximal, complemented
4#27649C212yesmaximal, complemented
5#27629C212yesmaximal, complemented
6#27628C212yesmaximal, complemented
7#27616C212yesmaximal, complemented
8#27602C212yesmaximal
9#27589C212yesmaximal, complemented
10#24010C212yesmaximal
11#23765C214yesmaximal, complemented
12#21583C214yesmaximal, complemented
13#21365C211yesmaximal, characteristic, complemented
14#21365C211yesmaximal, characteristic, complemented
15#20740C211yesmaximal, characteristic, complemented
16#20740C211yesmaximal, characteristic, complemented
17#20715C211yesmaximal, characteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#485C2214yes—
22C2×#432C2211yescharacteristic
23C2×#432C2211yescharacteristic
24C4×C22⋊Q8—21no—
25C4×C22⋊Q8—21no—
26C4×C22⋊Q8—21no—
27C4×C22⋊Q8—21no—
28C4×C22⋊Q8C2212yes—
29C4×C22⋊Q8C2212yes—
30C4×C22⋊Q8C2212yes—
31C4×C22⋊Q8C2212yes—
32C2×#391C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#387—21no—
35C2×#385—21no—
36#2285C2211yescharacteristic
37#2285C2211yescharacteristic
38#2285C2211yescharacteristic
39#2285C2211yescharacteristic
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2283—21no—
43#2283—21no—
44#2283—21no—
45#2283—21no—
46#2283C2212yes—
47#2283C2212yes—
48#2280—21no—
49#2280—21no—
50#2280C2212yes—
51C2×#380C2211yescharacteristic
52C4×#117—21no—
53C4×#117—21no—
54C4×#117C2212yes—
55C2×C4×C4⋊C4—21no—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4—21no—
58#2101C2214yescomplemented
59#2097C2214yescomplemented
60#2085C2214yescomplemented
61#2077C2214yes—
62#2076C2214yes—
63#2074C2214yescomplemented
64#2036C2214yes—
65#2035C2214yes—
66#1948C2212yescomplemented
67#1948C2212yescomplemented
68#1947C2212yescomplemented
69#1947C2212yescomplemented
70#1928C2214yescomplemented
71#1927C2214yescomplemented
72#1921C2214yescomplemented
73#1920C2214yescomplemented
74#1873C2214yes—
75#1854C2214yes—
76#1853C2212yes—
77#1853C2212yes—
78#1852C2212yes—
79#1852C2212yes—
80#1825C2214yes—
81#1823C2212yes—
82#1823C2212yes—
83#1817C2212yes—
84#1803C2212yescomplemented
85#1803C2212yescomplemented
86#1803C2212yescomplemented
87#1803C2212yescomplemented
88#1797C2212yes—
89#1797C2212yes—
90#1787C2212yes—
91#1787C2212yes—
92#1779C2212yes—
93#1776C2214yescomplemented
94#1776C2214yescomplemented
95#1763C2214yescomplemented
96#1763C2214yescomplemented
97#1749C2212yes—
98#1749C2212yes—
99C23×Q8C2311yescharacteristic
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C2×C22⋊Q8—21no—
104C2×C22⋊Q8—21no—
105C2×C22⋊Q8—28no—
106C2×C22⋊Q8C2312yes—
107C2×C22⋊Q8C2312yes—
108C2×C4×Q8—21no—
109C2×C4×Q8—21no—
110C2×C4×Q8—24no—
111C2×C4×Q8—24no—
112C2×C4×Q8C2312yes—
113C2×C4×Q8C2312yes—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117C2312yes—
119C2×#117C2312yes—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C42—24no—
129C22×C42—24no—
130C22×C42—21no—
131C22×C42—21no—
132C22×C42D411yescharacteristic
133C22×C42D411yescharacteristic
134C22×C42D411yescharacteristic
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144#485—216no—
145#432—24no—
146#432—24no—
147C2×#107C2314yes—
148C2×#107C2314yes—
149C2×#106C2314yes—
150C2×#106C2314yes—
151C2×C4⋊C8C2312yes—
152C2×C4⋊C8C2312yes—
153C2×#103C2314yes—
154C2×#103C2314yes—
155C2×#103C2314yes—
156C2×#103C2314yes—
157C2×C22⋊C8C2314yes—
158C2×C22⋊C8C2312yes—
159C2×C22⋊C8C2312yes—
160C2×C22⋊C8C2314yes—
161C2×#97C2312yes—
162C2×#97C2312yes—
163#391—21no—
164#391—21no—
165#391C2312yes—
166#391C2312yes—
167#389—21no—
168#389—21no—
169#389C2312yes—
170#389C2312yes—
171#387—22no—
172#387—22no—
173#387—22no—
174#387—22no—
175#385—22no—
176#385—22no—
177#385—22no—
178#385—22no—
179#384C2311yescharacteristic
180#384C2311yescharacteristic
181#384C2311yescharacteristic
182#384C2311yescharacteristic
183#383—22no—
184#383—22no—
185#382—21no—
186#382—21no—
187#382—21no—
188#382—21no—
189#382C2312yes—
190#382C2312yes—
191#381—22no—
192#381—22no—
193#381—22no—
194#380—21no—
195#380—21no—
196#380—21no—
197#380—21no—
198#380—21no—
199#380—21no—
200#380—21no—
201#380—21no—
202#380—21no—
203#380—21no—
204#380C2312yes—
205#380C2312yes—
206#380C2312yes—
207#380C2312yes—
208#380C2312yes—
209#380C2312yes—
210#379—22no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—22no—
213C4×C4⋊C4—22no—
214C4×C4⋊C4—22no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
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×C4⋊C4C2312yes—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241#376—22no—
242#376—22no—
243#376—22no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C43—22no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2314yes—
259#336C2314yes—
260C25C2×D411yescharacteristic
261C22×Q8—24no—
262C22×Q8—21no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—42no—
266C22×Q8C2412yes—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C22×C8C2414yes—
300C22×C8C2414yes—
301C22⋊Q8—28no—
302C22⋊Q8—28no—
303C22⋊Q8—24no—
304C22⋊Q8—24no—
305C22⋊Q8—24no—
306C22⋊Q8#4118yes—
307C4×Q8—24no—
308C4×Q8—24no—
309C4×Q8—24no—
310C4×Q8—24no—
311C4×Q8—44no—
312C4×Q8—44no—
313#117—28no—
314#117—44no—
315#117—44no—
316#117—44no—
317#117—44no—
318#117—44no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
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—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4C2412yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
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—44no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—44no—
389C2×C42—44no—
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×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42#4114yes—
403C2×C42#4114yes—
404C2×C42C2411yescharacteristic
405C2×C42C2411yescharacteristic
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408#107—28no—
409#107—44no—
410#106—28no—
411#106—44no—
412C4⋊C8—24no—
413C4⋊C8—24no—
414#103—28no—
415#103—28no—
416#103—44no—
417#103—44no—
418C22⋊C8—24no—
419C22⋊C8—24no—
420C22⋊C8—28no—
421C22⋊C8—44no—
422#97—24no—
423#97—24no—
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—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—41no—
452C24—41no—
453C24C22×D411yescharacteristic
454C24C22×D411yescharacteristic
455C24C22×D411yescharacteristic
456C2×Q8—24no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8C2×#4114yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
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—21no—
505C22×C4—21no—
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—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
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—416no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—416no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4#12314yes—
543C22×C4#12314yes—
544C22×C4#13714yes—
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4114yes—
559C22×C4C2511yescharacteristic
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—24no—
565C2×C8—24no—
566C4⋊C4—24no—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4C2×#4114yes—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—44no—
618C42—44no—
619C42—44no—
620C42—44no—
621C42—44no—
622C42—44no—
623C42—44no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42#12314yes—
628C42#12314yes—
629C42C2×#4112yes—
630C42C2×#4112yes—
631C42C2×#4112yes—
632C42C2×#4112yes—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—28no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23C2×#12312yes—
657C23#52512yes—
658C23C2×#13712yes—
659C23#57512yes—
660C23#57512yes—
661C23C23×D411yescharacteristic
662Q8—24no—
663Q8—24no—
664Q8—48no—
665Q8—42no—
666Q8—42no—
667C2×C4—28no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—24no—
691C2×C4—24no—
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—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—48no—
711C2×C4—48no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
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—84no—
739C2×C4—84no—
740C2×C4C2×#12312yes—
741C2×C4C2×#12312yes—
742C2×C4C2×#12312yes—
743C2×C4C2×#12312yes—
744C2×C4C2×#12312yes—
745C2×C4#52512yes—
746C2×C4C2×#13712yes—
747C2×C4C2×#13712yes—
748C2×C4#57512yes—
749C2×C4C22×#4111yescharacteristic
750C2×C4C22×#4111yescharacteristic
751C2×C4C22×#4112yes—
752C2×C4#58512yes—
753C8—44no—
754C8—44no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—416no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22#309314yes—
777C22C22×#12311yescharacteristic
778C22C2×#52511yescharacteristic
779C22#344911yescharacteristic
780C22C22×#13711yescharacteristic
781C22C2×#57511yescharacteristic
782C22C2×#57511yescharacteristic
783C22C2×#57511yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—44no—
794C4—41no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4#309514yes—
803C4#347512yes—
804C4#347512yes—
805C2—24no—
806C2—42no—
807C2—42no—
808C2#3480911yescharacteristic
809C2C2×#309311yescharacteristic
810C2C2×#309511yescharacteristic
811C2#6054611yescharacteristic
812C2#6056011yescharacteristic
813C2#6096311yescharacteristic
814C2#6097011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
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
3. #27682C2semidirect
4. #27649C2semidirect
5. #27629C2semidirect
6. #27628C2semidirect
7. #27616C2semidirect
9. #27589C2semidirect
11. #23765C2semidirect
12. #21583C2semidirect
13. #21365C2semidirect
14. #21365C2semidirect
15. #20740C2semidirect
16. #20740C2semidirect
58. #2101C22semidirect
59. #2097C22semidirect
60. #2085C22semidirect
63. #2074C22semidirect
66. #1948C22semidirect
67. #1948C22semidirect
68. #1947C22semidirect
69. #1947C22semidirect
70. #1928C22semidirect
71. #1927C22semidirect
72. #1921C22semidirect
73. #1920C22semidirect
84. #1803C22semidirect
85. #1803C22semidirect
86. #1803C22semidirect
87. #1803C22semidirect
93. #1776C22semidirect
94. #1776C22semidirect
95. #1763C22semidirect
96. #1763C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Q82
#340122
#276822
#276492
#276292
#276282
#276162
#276022
#275892
#240102
#237652
#215832
#213652
#207402
#207152