Finite Group Databasebeta

← #6472786

Subgroups — #6472786

Order 512.

3328 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C22×#380C211yesmaximal, characteristic
3#32983C212yesmaximal, complemented
4#32982C212yesmaximal, complemented
5#29894C214yesmaximal, complemented
6#27601C212yesmaximal, complemented
7#27600C212yesmaximal, complemented
8#24559C214yesmaximal, complemented
9#24556C214yesmaximal, complemented
10#24006C212yesmaximal, complemented
11#24003C212yesmaximal, complemented
12#21942C212yesmaximal, complemented
13#21765C212yesmaximal, complemented
14#20579C211yesmaximal, characteristic
15C25×C4C2211yescharacteristic
16C22×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4—21no—
22C2×#484C2214yescomplemented
23C2×#483C2214yescomplemented
24C2×#407C2212yes—
25C2×#407C2212yes—
26C2×#407C2212yes—
27#2848—21no—
28#2848—21no—
29#2848—21no—
30#2848—21no—
31#2848C2212yes—
32#2848C2212yes—
33#2848C2212yes—
34#2848C2212yes—
35C2×#385—21no—
36C2×#385—21no—
37C2×#385—21no—
38C2×#380—21no—
39C2×#380—21no—
40C2×#380—21no—
41C2×#380—21no—
42C2×#380—21no—
43C2×#380—21no—
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#379—21no—
54C22×#95—21no—
55#2077C2218yescomplemented
56#2075C2218yescomplemented
57#2036C2218yescomplemented
58#2035C2218yescomplemented
59#1894C2218yescomplemented
60#1872C2214yescomplemented
61#1872C2214yescomplemented
62#1872C2214yescomplemented
63#1872C2214yescomplemented
64#1853C2214yescomplemented
65#1853C2214yescomplemented
66#1853C2214yescomplemented
67#1852C2214yescomplemented
68#1852C2214yescomplemented
69#1852C2214yescomplemented
70#1824C2214yescomplemented
71#1823C2214yescomplemented
72#1823C2214yescomplemented
73#1809C2218yescomplemented
74#1787C2214yescomplemented
75#1779C2212yes—
76#1779C2212yes—
77#1779C2212yes—
78#1779C2212yes—
79C26D411yescharacteristic
80C23×Q8C2311yescharacteristic
81C24×C4—28no—
82C24×C4—21no—
83C24×C4—21no—
84C24×C4—44no—
85C24×C4—44no—
86C24×C4D411yescharacteristic
87C24×C4D411yescharacteristic
88C24×C4D411yescharacteristic
89C24×C4D411yescharacteristic
90C24×C4D411yescharacteristic
91C24×C4D411yescharacteristic
92C24×C4D411yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C22×M16C2314yes—
101C2×C22⋊Q8—21no—
102C2×C22⋊Q8—21no—
103C2×C22⋊Q8—21no—
104C2×C22⋊Q8—21no—
105C2×C22⋊Q8—21no—
106C2×C22⋊Q8—21no—
107C2×C22⋊Q8—28no—
108C2×C22⋊Q8—44no—
109C2×C22⋊Q8—44no—
110C2×C22⋊Q8C2312yes—
111C2×C22⋊Q8C2312yes—
112C2×C22⋊Q8C2312yes—
113C2×C22⋊Q8C2312yes—
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—44no—
126C22×C4⋊C4—44no—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4—22no—
137C22×C22⋊C4—22no—
138C22×C22⋊C4—22no—
139C22×C22⋊C4—22no—
140C22×C22⋊C4—22no—
141C22×C22⋊C4—22no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—48no—
149#484—48no—
150#483—48no—
151C2×#107C2318yescomplemented
152C2×#106C2318yescomplemented
153C2×#103C2318yescomplemented
154C2×#103C2318yescomplemented
155#407—28no—
156#407—44no—
157#407—44no—
158C2×C22⋊C8C2314yes—
159C2×C22⋊C8C2314yes—
160C2×C22⋊C8C2314yes—
161C2×C22⋊C8C2314yes—
162C2×C22⋊C8C2314yes—
163C2×C22⋊C8C2314yes—
164#385—22no—
165#385—22no—
166#385—22no—
167#385—22no—
168#385—22no—
169#385—22no—
170#385—22no—
171#385—22no—
172#385—22no—
173#385—22no—
174#385—22no—
175#385—22no—
176#380—21no—
177#380—21no—
178#380—21no—
179#380—21no—
180#380—21no—
181#380—21no—
182#380—22no—
183#380—22no—
184#380—22no—
185#380—22no—
186#380—22no—
187#380—22no—
188#380—22no—
189#380—22no—
190#380—22no—
191#380—22no—
192#380—22no—
193#380—22no—
194#380C2312yes—
195#380C2314yes—
196#380C2312yes—
197#380C2314yes—
198#380C2312yes—
199#380C2314yes—
200#380C2312yes—
201#380C2314yes—
202#380C2312yes—
203#380C2312yes—
204#379—22no—
205#379—22no—
206#379—22no—
207#379—22no—
208C2×#95—22no—
209C2×#95—22no—
210C2×#95—22no—
211C2×#95—22no—
212C2×#95—22no—
213C2×#95—22no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217#340C2318yescomplemented
218#340C2318yescomplemented
219#340C2318yescomplemented
220#340C2318yescomplemented
221C25—24no—
222C25—24no—
223C25—24no—
224C25—24no—
225C25—42no—
226C25—42no—
227C25—42no—
228C25C2×D411yescharacteristic
229C25C2×D411yescharacteristic
230C25C2×D411yescharacteristic
231C25C2×D411yescharacteristic
232C25C2×D411yescharacteristic
233C25C2×D411yescharacteristic
234C25C2×D411yescharacteristic
235C22×Q8—21no—
236C22×Q8—24no—
237C22×Q8—42no—
238C22×Q8—42no—
239C22×Q8C2412yes—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—464no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4#4118yes—
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C2×M16—28no—
328C2×M16—44no—
329C2×M16—44no—
330C22×C8C2418yes—
331C22⋊Q8—28no—
332C22⋊Q8—28no—
333C22⋊Q8—28no—
334C22⋊Q8—28no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337C22⋊Q8—44no—
338C22⋊Q8—44no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342C22⋊Q8—44no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4C2414yes—
377C2×C4⋊C4C2414yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
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×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—48no—
399C2×C22⋊C4—48no—
400C2×C22⋊C4—48no—
401C2×C22⋊C4—48no—
402C2×C22⋊C4—48no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—48no—
408C2×C22⋊C4—44no—
409#107—48no—
410#106—48no—
411#103—48no—
412#103—48no—
413C22⋊C8—28no—
414C22⋊C8—28no—
415C22⋊C8—28no—
416C22⋊C8—28no—
417C22⋊C8—44no—
418C22⋊C8—44no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—232no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—41no—
464C24—41no—
465C24—41no—
466C24—41no—
467C24—41no—
468C24—41no—
469C24—41no—
470C24—41no—
471C24—41no—
472C24—41no—
473C24—41no—
474C24—41no—
475C24—416no—
476C24—416no—
477C24—416no—
478C24—416no—
479C24—416no—
480C24—416no—
481C24#12314yes—
482C24AGL(1,ℤ/8)14yes—
483C24#13714yes—
484C24#13714yes—
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487C24C22×D411yescharacteristic
488C24C22×D411yescharacteristic
489C24C22×D411yescharacteristic
490C24C22×D411yescharacteristic
491C24C22×D411yescharacteristic
492C2×Q8—24no—
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—88no—
499C22×C4—232no—
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—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—416no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—416no—
584C22×C4—416no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—416no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—416no—
593C22×C4—416no—
594C22×C4—416no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—816no—
626C22×C4—816no—
627C22×C4#12314yes—
628C22×C4#12314yes—
629C22×C4#12314yes—
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C2×#4114yes—
638C22×C4C2×#4114yes—
639C22×C4C2×#4114yes—
640C22×C4H(5,𝔽2)14yes—
641C22×C4H(5,𝔽2)14yes—
642C22×C4C2511yescharacteristic
643M16—88no—
644C2×C8—28no—
645C2×C8—28no—
646C2×C8—28no—
647C4⋊C4—24no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—28no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—28no—
697C23—28no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—28no—
722C23—28no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—4128no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23C2×#12312yes—
768C23C2×#12312yes—
769C23C2×#12312yes—
770C23#53412yes—
771C23#53412yes—
772C23C2×AGL(1,ℤ/8)12yes—
773C23C2×AGL(1,ℤ/8)12yes—
774C23C2×AGL(1,ℤ/8)12yes—
775C23C2×#13712yes—
776C23C2×#13712yes—
777C23C2×#13712yes—
778C23C2×#13712yes—
779C23C2×#13712yes—
780C23C2×#13712yes—
781C23#57512yes—
782C23C23×D411yescharacteristic
783Q8—48no—
784Q8—84no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—84no—
848C2×C4—84no—
849C2×C4—88no—
850C2×C4—88no—
851C2×C4—88no—
852C2×C4—88no—
853C2×C4—88no—
854C2×C4—84no—
855C2×C4—84no—
856C2×C4—88no—
857C2×C4C2×#12312yes—
858C2×C4C2×#12312yes—
859C2×C4C2×#12312yes—
860C2×C4#53412yes—
861C2×C4#53412yes—
862C2×C4C22×#4112yes—
863C2×C4C2×H(5,𝔽2)12yes—
864C2×C4C2×H(5,𝔽2)12yes—
865C8—48no—
866C22—232no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—416no—
901C22—416no—
902C22—416no—
903C22—416no—
904C22—416no—
905C22—416no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22#309214yes—
919C22#309514yes—
920C22#319314yes—
921C22#319514yes—
922C22C22×#12311yescharacteristic
923C22C2×#53411yescharacteristic
924C22C2×#53411yescharacteristic
925C22C22×AGL(1,ℤ/8)11yescharacteristic
926C22C22×#13711yescharacteristic
927C22C22×#13711yescharacteristic
928C22C2×#57511yescharacteristic
929C4—22no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—41no—
935C4—41no—
936C4—84no—
937C4—82no—
938C4—84no—
939C4—82no—
940C4—82no—
941C4—82no—
942C4#349014yes—
943C2—24no—
944C2—24no—
945C2—24no—
946C2—24no—
947C2—42no—
948C2—42no—
949C2—42no—
950C2#3499211yescharacteristic
951C2C2×#309211yescharacteristic
952C2C2×#309511yescharacteristic
953C2C2×#319311yescharacteristic
954C2C2×#319511yescharacteristic
955C2#6075011yescharacteristic
956C2#6075111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32983C2semidirect
4. #32982C2semidirect
5. #29894C2semidirect
6. #27601C2semidirect
7. #27600C2semidirect
8. #24559C2semidirect
9. #24556C2semidirect
10. #24006C2semidirect
11. #24003C2semidirect
12. #21942C2semidirect
13. #21765C2semidirect
22. C2×#484C22semidirect
23. C2×#483C22semidirect
55. #2077C22semidirect
56. #2075C22semidirect
57. #2036C22semidirect
58. #2035C22semidirect
59. #1894C22semidirect
60. #1872C22semidirect
61. #1872C22semidirect
62. #1872C22semidirect
63. #1872C22semidirect
64. #1853C22semidirect
65. #1853C22semidirect
66. #1853C22semidirect
67. #1852C22semidirect
68. #1852C22semidirect
69. #1852C22semidirect
70. #1824C22semidirect
71. #1823C22semidirect
72. #1823C22semidirect
73. #1809C22semidirect
74. #1787C22semidirect
151. C2×#107C23semidirect
152. C2×#106C23semidirect
153. C2×#103C23semidirect
154. C2×#103C23semidirect
217. #340C23semidirect
218. #340C23semidirect
219. #340C23semidirect
220. #340C23semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C22×#3802
#329832
#329822
#298942
#276012
#276002
#245592
#245562
#240062
#240032
#219422
#217652
#205792