Finite Group Databasebeta

← #656737

Subgroups — #656737

Order 512.

3814 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2345C211yesmaximal, characteristic, complemented
2C22×#380C211yesmaximal, characteristic
3#16071C214yesmaximal, complemented
4#15432C214yesmaximal, complemented
5#15183C212yesmaximal, complemented
6#15135C212yesmaximal, complemented
7#15014C212yesmaximal, complemented
8#14734C212yesmaximal
9#14680C211yesmaximal, characteristic
10#14130C211yesmaximal, characteristic, complemented
11#14040C212yesmaximal, complemented
12#13991C212yesmaximal
13#13973C212yesmaximal, complemented
14#13924C211yesmaximal, characteristic, complemented
15#13880C211yesmaximal, characteristic, complemented
16#13876C212yesmaximal, complemented
17C4×#379C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2212yes—
22C2×#399C2214yes—
23#2345—28no—
24C2×#389C2211yescharacteristic, complemented
25C2×#389C2211yescharacteristic, complemented
26C2×#389C2212yescomplemented
27C2×#388C2214yes—
28C2×#387C2212yescomplemented
29C2×#387C2212yescomplemented
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#385C2212yes—
33C2×#384C2212yescomplemented
34C2×#380—28no—
35C2×#380C2212yes—
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2212yes—
40C2×#380C2214yes—
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×#379C2211yescharacteristic
44C2×#379C2212yes—
45C2×#379C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic, complemented
47C2×C4×C4⋊C4C2211yescharacteristic, complemented
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2212yes—
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C22×#95C2212yes—
54#1445C2214yescomplemented
55#1445C2214yescomplemented
56#1445C2214yescomplemented
57#1444C2214yescomplemented
58#1444C2212yescomplemented
59#1444C2214yescomplemented
60#1443C2214yescomplemented
61#1442C2212yescomplemented
62#1442C2214yescomplemented
63#1442C2214yescomplemented
64#1440C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1437C2214yes—
70#1436C2214yescomplemented
71C4⋊#95C2212yescomplemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75#1434C2214yescomplemented
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C22⋊#95C2214yes—
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2211yescharacteristic
85C26C2311yescharacteristic
86C24×C4—24no—
87C24×C4—28no—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—44no—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2312yes—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4D418yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C22⋊C4—28no—
116C22×C22⋊C4—48no—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2311yescharacteristic
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2311yescharacteristic
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C42C2312yes—
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2312yes—
135C22×C42C2312yes—
136#399—48no—
137#389—24no—
138#389—24no—
139#389—44no—
140#388—48no—
141#387—28no—
142#387—28no—
143#385—28no—
144#385—44no—
145#385—44no—
146#384—44no—
147#380—28no—
148#380—24no—
149#380—24no—
150#380—28no—
151#380—28no—
152#380—216no—
153#380—28no—
154#380—44no—
155#379—24no—
156#379—44no—
157#379Q818yes—
158C4×C4⋊C4—24no—
159C4×C4⋊C4—24no—
160C4×C22⋊C4—24no—
161C4×C22⋊C4—28no—
162C4×C22⋊C4—24no—
163C4×C22⋊C4—28no—
164C4×C22⋊C4—44no—
165C2×#95—28no—
166C2×#95C2314yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2311yescharacteristic
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2311yescharacteristic
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C25—22no—
193C25—24no—
194C25—24no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—42no—
201C25—42no—
202C25C2×Q814yes—
203C25C2412yes—
204C25C2411yescharacteristic
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—232no—
208C23×C4—22no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—432no—
232C23×C4—432no—
233C23×C4—44no—
234C23×C4—44no—
235C23×C4—44no—
236C23×C4—44no—
237C23×C4—416no—
238C23×C4—416no—
239C23×C4C2×D414yes—
240C23×C4C2×D418yes—
241C23×C4#4118yes—
242C23×C4#4114yes—
243C23×C4#4114yes—
244C23×C4C2411yescharacteristic
245C23×C4C2412yes—
246C23×C4C2414yes—
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2414yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C2×C4⋊C4—232no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—416no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4C2×D414yes—
293C2×C4⋊C4C2×D418yes—
294C2×C4⋊C4C2×D414yes—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—432no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4C2×Q814yes—
334C2×C22⋊C4C2×Q818yes—
335C2×C22⋊C4C2×Q814yes—
336C2×C22⋊C4C2×Q818yes—
337C2×C22⋊C4#4114yes—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—44no—
348C2×C42—44no—
349#95—28no—
350#95—28no—
351#95—22no—
352#95—22no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—28no—
362#95—24no—
363#95—28no—
364#95—44no—
365#95—44no—
366#95—42no—
367#95—42no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—28no—
380C24—28no—
381C24—216no—
382C24—28no—
383C24—216no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—28no—
397C24—28no—
398C24—48no—
399C24—48no—
400C24—48no—
401C24—48no—
402C24—48no—
403C24—48no—
404C24—48no—
405C24—48no—
406C24—48no—
407C24—44no—
408C24—44no—
409C24—48no—
410C24—44no—
411C24—44no—
412C24—44no—
413C24—44no—
414C24C22×D412yes—
415C24C22×Q814yes—
416C24C22×Q812yes—
417C24C2×#4114yes—
418C24C2×#4112yes—
419C24C2×#4112yes—
420C24C2×#4112yes—
421C24H(5,𝔽2)14yes—
422C24H(5,𝔽2)12yes—
423C242−1+412yes—
424C24C2511yescharacteristic
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—216no—
432C22×C4—28no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—216no—
468C22×C4—216no—
469C22×C4—216no—
470C22×C4—216no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—4128no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—88no—
526C22×C4—88no—
527C22×C4—88no—
528C22×C4—88no—
529C22×C4#123116yes—
530C22×C4C22×D414yes—
531C22×C4C22×D414yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×Q812yes—
535C22×C4C22×Q812yes—
536C22×C4C22×Q814yes—
537C22×C4C2×#4114yes—
538C22×C4C2×#4114yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4114yes—
544C22×C4H(5,𝔽2)14yes—
545C4⋊C4—216no—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—48no—
549C4⋊C4—44no—
550C4⋊C4—44no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C4⋊C4—88no—
556C4⋊C4—88no—
557C4⋊C4—88no—
558C22⋊C4—28no—
559C22⋊C4—28no—
560C22⋊C4—216no—
561C22⋊C4—28no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—416no—
566C22⋊C4—416no—
567C22⋊C4—48no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—88no—
571C22⋊C4—88no—
572C42—44no—
573C42—44no—
574C42—48no—
575C42—84no—
576C42—84no—
577C23—22no—
578C23—22no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—22no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—232no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—432no—
613C23—432no—
614C23—416no—
615C23—432no—
616C23—416no—
617C23—416no—
618C23—416no—
619C23—432no—
620C23—416no—
621C23—42no—
622C23—42no—
623C23—416no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C2×#12314yes—
639C23#53314yes—
640C23#54214yes—
641C23D4×Q814yes—
642C23#55014yes—
643C23#55214yes—
644C23#55418yes—
645C23#55414yes—
646C23C23×D411yescharacteristic
647C23C23×Q811yescharacteristic
648C23C22×#4111yescharacteristic
649C23C22×#4111yescharacteristic
650C23C22×#4112yes—
651C23C22×#4111yescharacteristic
652C23C2×H(5,𝔽2)12yes—
653C23C2×H(5,𝔽2)11yescharacteristic
654C23C2×H(5,𝔽2)12yes—
655C23C2×2−1+411yescharacteristic
656C23#58512yes—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—232no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—432no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—432no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—816no—
741C2×C4—816no—
742C2×C4C2×#12314yes—
743C2×C4C2×#12314yes—
744C2×C4#52514yes—
745C2×C4#53514yes—
746C2×C4#55118yes—
747C2×C4#55118yes—
748C22—28no—
749C22—28no—
750C22—28no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—28no—
756C22—24no—
757C22—24no—
758C22—28no—
759C22—28no—
760C22—28no—
761C22—464no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22#242318yes—
775C22C22×#12311yescharacteristic
776C22C2×#52511yescharacteristic
777C22C2×#53311yescharacteristic
778C22C2×#53511yescharacteristic
779C22C2×#54211yescharacteristic
780C22C2×D4×Q811yescharacteristic
781C22C2×#55011yescharacteristic
782C22C2×#55112yes—
783C22C2×#55112yes—
784C22C2×#55211yescharacteristic
785C22C2×#55411yescharacteristic
786C22C2×#55412yes—
787C22#347512yes—
788C22#348411yescharacteristic
789C22#348511yescharacteristic
790C22#349212yes—
791C22#349412yes—
792C22#349412yes—
793C22#349412yes—
794C22#350112yes—
795C22#351912yes—
796C22#353712yes—
797C22#354112yes—
798C4—24no—
799C4—44no—
800C4—44no—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—44no—
805C4—44no—
806C4—81no—
807C4—82no—
808C4—84no—
809C4—81no—
810C4—82no—
811C4—84no—
812C4#248218yes—
813C2—28no—
814C2—48no—
815C2C2×#242311yescharacteristic
816C2C2×#248211yescharacteristic
817C2#3554011yescharacteristic
818C2#3619012yes—
819C2#3651711yescharacteristic
820C2#3654611yescharacteristic
821C2#3785212yes—
822C2#3913211yescharacteristic
823C2#3959411yescharacteristic
824C2#5919912yes—
825C2#5920512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
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×#2345C2semidirect
3. #16071C2semidirect
4. #15432C2semidirect
5. #15183C2semidirect
6. #15135C2semidirect
7. #15014C2semidirect
10. #14130C2semidirect
11. #14040C2semidirect
13. #13973C2semidirect
14. #13924C2semidirect
15. #13880C2semidirect
16. #13876C2semidirect
24. C2×#389C22semidirect
25. C2×#389C22semidirect
26. C2×#389C22semidirect
28. C2×#387C22semidirect
29. C2×#387C22semidirect
33. C2×#384C22semidirect
46. C2×C4×C4⋊C4C22semidirect
47. C2×C4×C4⋊C4C22semidirect
54. #1445C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1443C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
70. #1436C22semidirect
71. C4⋊#95C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#23452
C22×#3802
#160712
#154322
#151832
#151352
#150142
#147342
#146802
#141302
#140402
#139912
#139732
#139242
#138802
#138762
C4×#3792