Finite Group Databasebeta

← #846067

Subgroups — #846067

Order 512.

4504 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C212yesmaximal, complemented
2C2×#2542C211yesmaximal, characteristic, complemented
3C2×#2415C212yesmaximal, complemented
4C2×C4×#120C211yesmaximal, characteristic
5#16269C214yesmaximal, complemented
6#15406C212yesmaximal, complemented
7#15342C212yesmaximal, complemented
8#15284C212yesmaximal, complemented
9#15281C212yesmaximal
10#15179C212yesmaximal, complemented
11#15178C212yesmaximal, complemented
12#15177C212yesmaximal, complemented
13#14405C214yesmaximal, complemented
14#13994C212yesmaximal, complemented
15#13871C211yesmaximal, characteristic, complemented
16C25×C4C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic, complemented
18C22×C22⋊Q8C2212yes—
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yescomplemented
22C22×#120C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic, complemented
26#2848—216no—
27#2542—28no—
28#2415—216no—
29C2×#399C2212yes—
30C2×#399C2212yescomplemented
31C2×#397C2214yescomplemented
32C2×#394C2214yes—
33C4×#120—28no—
34C2×#391C2212yescomplemented
35C2×#391C2212yescomplemented
36C2×#390C2212yes—
37C2×#389C2214yescomplemented
38C2×#389C2212yescomplemented
39C2×#388C2214yes—
40C2×#388C2214yes—
41C2×#386C2212yes—
42C2×#386C2211yescharacteristic
43C2×#385C2214yes—
44C2×#385C2214yes—
45C2×#385C2214yes—
46C2×#385C2211yescharacteristic
47C2×#385C2212yes—
48C2×#384C2212yescomplemented
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic, complemented
53C2×#379C2214yes—
54C2×#379C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic, complemented
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58#1444C2214yescomplemented
59#1444C2214yescomplemented
60#1444C2214yescomplemented
61#1442C2214yescomplemented
62#1442C2214yescomplemented
63#1441C2214yescomplemented
64#1440C2214yes—
65#1440C2214yes—
66#1440C2212yescomplemented
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yescomplemented
72#1438C2212yes—
73#1438C2214yes—
74#1437C2212yes—
75#1436C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78#1434C2214yescomplemented
79C26C2311yescharacteristic
80C23×Q8C2312yes—
81C23×D4C2312yes—
82C23×D4C2311yescharacteristic
83C24×C4—28no—
84C24×C4—24no—
85C24×C4—42no—
86C24×C4—44no—
87C24×C4—42no—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C2×C4⋊Q8—24no—
94C2×C4⋊Q8—42no—
95C2×C4⋊Q8—42no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—44no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×C22⋊Q8—44no—
108C2×#120—24no—
109C2×#120—28no—
110C2×C4×D4—28no—
111C2×C4×D4—28no—
112C2×C4×D4—42no—
113C2×C4×D4—42no—
114C2×C4×D4—44no—
115C2×C4×D4D418yes—
116C2×#117—28no—
117C2×#117—42no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151#399—28no—
152#399—28no—
153#397—216no—
154#394—216no—
155#391—28no—
156#391—44no—
157#390—28no—
158#389—28no—
159#389—216no—
160#388—216no—
161#388—216no—
162#386—24no—
163#386—28no—
164#385—28no—
165#385—216no—
166#385—24no—
167#385—216no—
168#385—216no—
169#384—28no—
170#380—28no—
171#380—28no—
172#380—42no—
173#380D4116yescomplemented
174#379—216no—
175#379—24no—
176C4×C4⋊C4—24no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—28no—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C25—22no—
197C25—24no—
198C25—24no—
199C25—24no—
200C25—24no—
201C25—42no—
202C25—41no—
203C25—41no—
204C25—42no—
205C25C2411yescharacteristic
206C25C2412yes—
207C25C2411yescharacteristic
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8—24no—
211C22×Q8—24no—
212C22×Q8—24no—
213C22×Q8—24no—
214C22×Q8—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—41no—
223C22×D4—41no—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4C2×D414yes—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—41no—
251C23×C4—42no—
252C23×C4—41no—
253C23×C4—432no—
254C23×C4—416no—
255C23×C4—416no—
256C23×C4—432no—
257C23×C4—416no—
258C23×C4C2×D414yes—
259C23×C4C2×D418yes—
260C23×C4C2×D414yes—
261C23×C4C2414yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2414yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C4⋊Q8—416no—
274C22⋊Q8—432no—
275C22⋊Q8—432no—
276C22⋊Q8—432no—
277C22⋊Q8—432no—
278#120—232no—
279C4×D4—416no—
280C4×D4—432no—
281#117—416no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4C2×D418yes—
316C2×C4⋊C4C2×D418yes—
317C2×C4⋊C4C2×D414yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4C2×D4116yes—
362C2×C22⋊C4C2×D414yes—
363C2×C22⋊C4C2×D414yes—
364C2×C22⋊C4#4118yes—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—28no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—28no—
372C2×C42—24no—
373C2×C42—42no—
374C2×C42C2×D414yes—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—44no—
387#95—44no—
388#95—42no—
389#95—44no—
390#95—44no—
391#95C2×D4116yes—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—21no—
402C24—21no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—28no—
412C24—216no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—44no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24—48no—
426C24—48no—
427C24—48no—
428C24—48no—
429C24—44no—
430C24—48no—
431C24—44no—
432C24—48no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—48no—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C22×D414yes—
443C24C2×#4114yes—
444C242−1+414yes—
445C242−1+414yes—
446C24C2511yescharacteristic
447C2×Q8—48no—
448C2×Q8—48no—
449C2×Q8—48no—
450C2×Q8—48no—
451C2×Q8—48no—
452C2×Q8—48no—
453C2×Q8—48no—
454C2×D4—216no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—44no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—216no—
508C22×C4—216no—
509C22×C4—216no—
510C22×C4—216no—
511C22×C4—216no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—48no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—4128no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—48no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4C22×D412yes—
557C22×C4C22×D418yes—
558C22×C4C22×D418yes—
559C22×C4C22×D412yes—
560C22×C4C22×D414yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D414yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4114yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C4H(5,𝔽2)14yes—
570C4⋊C4—216no—
571C4⋊C4—216no—
572C4⋊C4—44no—
573C4⋊C4—416no—
574C4⋊C4—48no—
575C4⋊C4—416no—
576C4⋊C4—416no—
577C4⋊C4—416no—
578C4⋊C4—416no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C22⋊C4—28no—
583C22⋊C4—232no—
584C22⋊C4—216no—
585C22⋊C4—44no—
586C22⋊C4—44no—
587C22⋊C4—48no—
588C22⋊C4—416no—
589C22⋊C4—416no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—416no—
594C22⋊C4—416no—
595C22⋊C4—416no—
596C22⋊C4—416no—
597C22⋊C4—44no—
598C22⋊C4—84no—
599C42—28no—
600C42—48no—
601C42—48no—
602C42—48no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—432no—
637C23—432no—
638C23—416no—
639C23—432no—
640C23—432no—
641C23—416no—
642C23—432no—
643C23—432no—
644C23—416no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23#53614yes—
688C23#54718yes—
689C23C23×D411yescharacteristic
690C23C23×D412yes—
691C23C22×#4112yes—
692C23C2×H(5,𝔽2)11yescharacteristic
693C23C2×H(5,𝔽2)11yescharacteristic
694C23C2×H(5,𝔽2)12yes—
695C23C2×2−1+412yes—
696C23C2×2−1+412yes—
697C23#58512yes—
698Q8—816no—
699D4—416no—
700D4—432no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—432no—
724C2×C4—416no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—416no—
751C2×C4—416no—
752C2×C4—432no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4#52514yes—
775C2×C4#53414yes—
776C2×C4#53518yes—
777C2×C4D4218yes—
778C2×C4D4214yes—
779C2×C4#56014yes—
780C22—28no—
781C22—28no—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—464no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—42no—
804C22—44no—
805C22—44no—
806C22—42no—
807C22—44no—
808C22—42no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22C2×#52511yescharacteristic
815C22C2×#53411yescharacteristic
816C22C2×#53512yes—
817C22C2×#53611yescharacteristic
818C22C2×D4212yes—
819C22C2×D4211yescharacteristic
820C22C2×#54712yes—
821C22D4×#4112yes—
822C22#348612yes—
823C22#348912yes—
824C22#348912yes—
825C22#350612yes—
826C22#352012yes—
827C22#352012yes—
828C22#352012yes—
829C22C2×#56011yescharacteristic
830C22#353811yescharacteristic
831C22#353812yes—
832C22#354011yescharacteristic
833C22#354112yes—
834C22#354112yes—
835C4—24no—
836C4—48no—
837C4—44no—
838C4—42no—
839C4—42no—
840C4—44no—
841C4—48no—
842C4—42no—
843C4—82no—
844C4—84no—
845C4—84no—
846C4#266918yes—
847C2—48no—
848C2—44no—
849C2—82no—
850C2#3508411yescharacteristic
851C2#3610012yes—
852C2#3737411yescharacteristic
853C2#3765112yes—
854C2#3891712yes—
855C2#3986312yes—
856C2#4562412yes—
857C2C2×#266911yescharacteristic
858C2#5900212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2848C2semidirect
2. C2×#2542C2semidirect
3. C2×#2415C2semidirect
5. #16269C2semidirect
6. #15406C2semidirect
7. #15342C2semidirect
8. #15284C2semidirect
10. #15179C2semidirect
11. #15178C2semidirect
12. #15177C2semidirect
13. #14405C2semidirect
14. #13994C2semidirect
15. #13871C2semidirect
17. C22×C4⋊Q8C22semidirect
21. C22×C22⋊Q8C22semidirect
25. C22×#117C22semidirect
30. C2×#399C22semidirect
31. C2×#397C22semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
37. C2×#389C22semidirect
38. C2×#389C22semidirect
48. C2×#384C22semidirect
52. C2×#380C22semidirect
55. C2×C4×C4⋊C4C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
66. #1440C22semidirect
71. #1439C22semidirect
75. #1436C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
78. #1434C22semidirect
173. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#25422
C2×#24152
C2×C4×#1202
#162692
#154062
#153422
#152842
#152812
#151792
#151782
#151772
#144052
#139942
#138712