Finite Group Databasebeta

← #6436655

Subgroups — #6436655

Order 512.

2232 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3105C212yesmaximal, complemented
2#36631C211yesmaximal, characteristic, complemented
3C2×#2293C211yesmaximal, characteristic, complemented
4#29870C212yesmaximal, complemented
5#29832C214yesmaximal, complemented
6#29800C212yesmaximal, complemented
7#29761C212yesmaximal, complemented
8#29757C211yesmaximal, characteristic, complemented
9#29755C211yesmaximal, characteristic, complemented
10#29718C212yesmaximal, complemented
11#29714C211yesmaximal, characteristic, complemented
12#29712C211yesmaximal, characteristic
13#23680C214yesmaximal, complemented
14#23677C212yesmaximal, complemented
15#23676C212yesmaximal, complemented
16#21388C212yesmaximal, complemented
17#20808C211yesmaximal, characteristic, complemented
18C2×#529C2212yes—
19C22×C4×D4C2211yescharacteristic
20C22×#117—21no—
21#3105—216no—
22C2×#484C2212yes—
23C2×#481C2212yes—
24C2×#478C2214yes—
25C2×#463C2214yes—
26C2×#450C2212yes—
27C2×#447C2212yes—
28C2×C4×SD16C2214yes—
29C2×C4×D8C2214yes—
30C2×#431C2212yes—
31#2861C2212yescomplemented
32#2860—21no—
33#2860—21no—
34#2859C2211yescharacteristic, complemented
35#2858C2211yescharacteristic, complemented
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2854—21no—
39#2854—21no—
40#2850C2212yes—
41C4×C4⋊Q8C2211yescharacteristic, complemented
42C4×#127C2211yescharacteristic, complemented
43C4×#124C2212yescomplemented
44C4×#121—21no—
45C4×#121—21no—
46#2293—21no—
47#2293—21no—
48#2293—21no—
49#2293—21no—
50#2293—21no—
51#2293—21no—
52#2293C2212yes—
53#2293C2212yes—
54#2293C2212yes—
55#2293C2212yes—
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#388—21no—
61C2×#388—21no—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4—21no—
64C2×C43C2211yescharacteristic
65#2085C2214yescomplemented
66#2084C2212yescomplemented
67#2083C2212yescomplemented
68#2073C2214yes—
69#2071C2212yes—
70#2071C2212yes—
71#2068C2214yescomplemented
72#2067C2214yescomplemented
73#2066C2214yescomplemented
74#2065C2214yescomplemented
75#2055C2214yes—
76#2055C2214yes—
77#2054C2214yes—
78#2054C2214yes—
79#2043C2212yescomplemented
80#2042C2214yescomplemented
81#2041C2212yescomplemented
82#2013C2212yes—
83#2012C2214yes—
84#2011C2212yes—
85#1989C2214yescomplemented
86#1983C2214yescomplemented
87#1874C2212yes—
88#1874C2212yes—
89#1872C2212yes—
90#1872C2212yes—
91#1842C2212yescomplemented
92#1831C2212yescomplemented
93#1797C2211yescharacteristic
94#1797C2211yescharacteristic
95#1797C2212yes—
96C4×C4⋊C8C2212yescomplemented
97C4×C4⋊C8C2212yescomplemented
98C4×#103C2214yescomplemented
99C4×#102C2214yescomplemented
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C22×SD16C2314yes—
103C22×D8C2314yes—
104C2×C4⋊Q8C2311yescharacteristic
105C2×#127C2311yescharacteristic
106#529—28no—
107#529—28no—
108C2×#126—22no—
109C2×#125C2312yes—
110C2×#124C2312yes—
111C2×#124C2312yes—
112C2×#123—22no—
113C2×C22⋊Q8C2312yes—
114C2×#121—21no—
115C2×#121—21no—
116C2×#121C2312yes—
117C2×C4×Q8C2312yes—
118C2×C4×D4—22no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—21no—
122C2×C4×D4—21no—
123C2×C4×D4—24no—
124C2×C4×D4D418yescomplemented
125C2×C4×D4C2312yes—
126C2×C4×D4C2312yes—
127C2×C4×D4C2312yes—
128C2×#117—22no—
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—22no—
133C2×#117—48no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C42—21no—
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#484—28no—
153#481—28no—
154#478—216no—
155#463—216no—
156#450—28no—
157#447—28no—
158C4×SD16—216no—
159C4×D8—216no—
160#431—28no—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8C2314yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2312yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C4×C8C2314yes—
178#391C2312yes—
179#391C2312yes—
180#390—21no—
181#390—21no—
182#390—21no—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390C2312yes—
193#390C2312yes—
194#390C2312yes—
195#390C2312yes—
196#390C2312yes—
197#390C2312yes—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#386—22no—
231#386—22no—
232#384C2311yescharacteristic
233#384C2311yescharacteristic
234#382C2312yes—
235#380—21no—
236#380—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
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—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C43D411yescharacteristic
253C43D411yescharacteristic
254C43D411yescharacteristic
255C43D411yescharacteristic
256C43C2311yescharacteristic
257C43C2311yescharacteristic
258C43C2311yescharacteristic
259C43C2311yescharacteristic
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#336C2312yes—
265#336C2312yes—
266#336C2314yes—
267C25—21no—
268C22×Q8C2412yes—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—22no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4C2×D414yes—
277C22×D4C2412yes—
278C22×D4C2412yes—
279C23×C4—21no—
280C23×C4—28no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2411yescharacteristic
295C2×SD16—28no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×D8—28no—
299C2×D8—44no—
300C2×D8—44no—
301C22×C8C2414yes—
302C22×C8C2414yes—
303C4⋊Q8—42no—
304#127—42no—
305#126—48no—
306#125—24no—
307#125—24no—
308#124—24no—
309#124—24no—
310#124—44no—
311#123—48no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314#121—24no—
315#121—24no—
316#121—44no—
317#121—44no—
318C4×Q8—24no—
319C4×Q8—24no—
320C4×D4—28no—
321C4×D4—28no—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—44no—
327C4×D4—48no—
328C4×D4—44no—
329C4×D4C2×D418yes—
330C4×D4C2×D418yes—
331#117—48no—
332#117—48no—
333#117—48no—
334#117—48no—
335#117—48no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C22⋊C4—28no—
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×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×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—44no—
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×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D414yes—
422C2×C42C2×D411yescharacteristic
423C2×C42#4114yes—
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—28no—
431#106—28no—
432C4⋊C8—28no—
433C4⋊C8—44no—
434C4⋊C8—42no—
435C4⋊C8—42no—
436#103—28no—
437#103—44no—
438#103—44no—
439#102—28no—
440#102—28no—
441#102—28no—
442#102—44no—
443#102—44no—
444C22⋊C8—24no—
445C22⋊C8—24no—
446C4×C8—28no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24C22×D411yescharacteristic
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8—24no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—48no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—48no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4C22×D414yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—432no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4#12114yes—
538C22×C4#12114yes—
539C22×C4#13514yes—
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2×#4112yes—
555C22×C4C2511yescharacteristic
556SD16—416no—
557D8—416no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4C22×D414yes—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42#12114yes—
637C42#12114yes—
638C42AGL(1,ℤ/8)14yes—
639C42C22×D412yes—
640C42C22×D412yes—
641C42C2×#4112yes—
642C42C2×#4112yes—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—24no—
648C23—48no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—48no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—84no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23C2×#12112yes—
669C23C2×#13512yes—
670C23#57512yes—
671C23C23×D411yescharacteristic
672Q8—44no—
673Q8—44no—
674D4—28no—
675D4—48no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—84no—
680D4—84no—
681D4—88no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—28no—
689C2×C4—21no—
690C2×C4—21no—
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—24no—
700C2×C4—24no—
701C2×C4—28no—
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—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—416no—
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—42no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—88no—
742C2×C4C2×#12112yes—
743C2×C4C2×#12112yes—
744C2×C4C2×#12112yes—
745C2×C4C2×#12112yes—
746C2×C4C2×#12112yes—
747C2×C4C2×#13512yes—
748C2×C4C2×#13512yes—
749C2×C4C2×AGL(1,ℤ/8)12yes—
750C2×C4C2×AGL(1,ℤ/8)12yes—
751C2×C4C2×AGL(1,ℤ/8)12yes—
752C2×C4#57512yes—
753C2×C4C23×D411yescharacteristic
754C2×C4C22×#4111yescharacteristic
755C2×C4#58512yes—
756C2×C4#58512yes—
757C8—44no—
758C8—44no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—816no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22#303514yes—
781C22C22×#12111yescharacteristic
782C22#344911yescharacteristic
783C22#344911yescharacteristic
784C22C22×#13511yescharacteristic
785C22C22×AGL(1,ℤ/8)11yescharacteristic
786C22C2×#57511yescharacteristic
787C22C2×#57511yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—44no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4#303614yes—
807C4#344912yes—
808C4#345512yes—
809C2—24no—
810C2—84no—
811C2—162no—
812C2#3463311yescharacteristic
813C2C2×#303511yescharacteristic
814C2C2×#303611yescharacteristic
815C2#6094511yescharacteristic
816C2#6094611yescharacteristic
817C2#6094911yescharacteristic
818C2#6095411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#29712C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3105C2semidirect
2. #36631C2semidirect
3. C2×#2293C2semidirect
4. #29870C2semidirect
5. #29832C2semidirect
6. #29800C2semidirect
7. #29761C2semidirect
8. #29757C2semidirect
9. #29755C2semidirect
10. #29718C2semidirect
11. #29714C2semidirect
13. #23680C2semidirect
14. #23677C2semidirect
15. #23676C2semidirect
16. #21388C2semidirect
17. #20808C2semidirect
31. #2861C22semidirect
34. #2859C22semidirect
35. #2858C22semidirect
41. C4×C4⋊Q8C22semidirect
42. C4×#127C22semidirect
43. C4×#124C22semidirect
65. #2085C22semidirect
66. #2084C22semidirect
67. #2083C22semidirect
71. #2068C22semidirect
72. #2067C22semidirect
73. #2066C22semidirect
74. #2065C22semidirect
79. #2043C22semidirect
80. #2042C22semidirect
81. #2041C22semidirect
85. #1989C22semidirect
86. #1983C22semidirect
91. #1842C22semidirect
92. #1831C22semidirect
96. C4×C4⋊C8C22semidirect
97. C4×C4⋊C8C22semidirect
98. C4×#103C22semidirect
99. C4×#102C22semidirect
124. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31052
#366312
C2×#22932
#298702
#298322
#298002
#297612
#297572
#297552
#297182
#297142
#297122
#236802
#236772
#236762
#213882
#208082