Finite Group Databasebeta

← #763547

Subgroups — #763547

Order 512.

4426 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×#2483C211yesmaximal, characteristic, complemented
2C22×#394C211yesmaximal, characteristic
3C2×#2308C211yesmaximal, characteristic
4C2×#2308C211yesmaximal, characteristic
5#15538C214yesmaximal, complemented
6#15494C214yesmaximal, complemented
7#15390C214yesmaximal, complemented
8#15383C214yesmaximal, complemented
9#15073C212yesmaximal, complemented
10#14919C212yesmaximal, complemented
11#14127C211yesmaximal, characteristic, complemented
12#13877C212yesmaximal, complemented
13#13869C211yesmaximal, characteristic, complemented
14#13869C212yesmaximal, complemented
15#13869C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C22⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2212yes—
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25#2483—28no—
26C2×#397C2214yescomplemented
27C2×#394—28no—
28C2×#394C2214yes—
29C2×#394C2214yes—
30#2308—28no—
31#2308—28no—
32C2×#386C2212yes—
33C2×#386C2214yes—
34C2×#386C2212yes—
35C2×#386C2214yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yescomplemented
41C2×#385C2212yescomplemented
42C2×#381C2212yes—
43C2×#381C2212yes—
44C2×#381C2212yes—
45C2×#381C2212yes—
46C2×#381C2212yescomplemented
47C2×#381C2212yescomplemented
48C2×#380C2214yescomplemented
49C2×#379C2211yescharacteristic
50C2×#379C2212yes—
51C2×#379C2211yescharacteristic
52C22×#95C2211yescharacteristic
53#1445C2214yescomplemented
54#1443C2214yescomplemented
55#1443C2214yescomplemented
56#1442C2214yescomplemented
57#1442C2214yescomplemented
58#1442C2214yescomplemented
59#1441C2214yescomplemented
60#1441C2214yescomplemented
61#1440C2214yescomplemented
62#1440C2214yescomplemented
63#1440C2214yescomplemented
64#1440C2214yescomplemented
65#1439C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68C22⋊#95C2212yes—
69C22⋊#95C2212yes—
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2214yescomplemented
73C22⋊#95C2212yescomplemented
74C22⋊#95C2214yescomplemented
75C22⋊#95C2212yescomplemented
76C22⋊#95C2212yescomplemented
77C22⋊#95C2212yescomplemented
78C22⋊#95C2214yescomplemented
79C26C2311yescharacteristic
80C26C2311yescharacteristic
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—28no—
84C23×D4—44no—
85C23×D4D418yes—
86C23×D4C2312yes—
87C23×D4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C22×C4⋊C4—24no—
99C22×C4⋊C4—44no—
100C22×C4⋊C4C2314yes—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2314yes—
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—28no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—28no—
115C22×C22⋊C4—28no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4—44no—
118C22×C22⋊C4—44no—
119C22×C22⋊C4—44no—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141#397—216no—
142#394—216no—
143#394—216no—
144#386—28no—
145#386—28no—
146#386—28no—
147#386—28no—
148#386—216no—
149#386—216no—
150#385—28no—
151#385—28no—
152#385—44no—
153#385—44no—
154#381—28no—
155#381—28no—
156#381—28no—
157#381—28no—
158#381—44no—
159#381—44no—
160#380—48no—
161#379—24no—
162#379—28no—
163#379D418yes—
164C2×#95—24no—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C25—22no—
187C25—22no—
188C25—24no—
189C25—24no—
190C25—24no—
191C25—42no—
192C25—42no—
193C25—42no—
194C25—42no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25—42no—
199C25C2×D414yes—
200C25C2×D414yes—
201C25C2×D414yes—
202C25#4114yes—
203C25#4118yes—
204C25C2411yescharacteristic
205C25C2411yescharacteristic
206C25C2412yes—
207C25C2411yescharacteristic
208C22×D4—232no—
209C22×D4—232no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—416no—
219C22×D4—42no—
220C22×D4—42no—
221C22×D4—42no—
222C22×D4—42no—
223C22×D4—432no—
224C22×D4—432no—
225C22×D4C2×D418yes—
226C22×D4C2×D418yes—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—28no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—28no—
254C23×C4—42no—
255C23×C4—44no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—44no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4C2×D414yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2414yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—416no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—432no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—416no—
346C2×C22⋊C4—416no—
347C2×C22⋊C4—416no—
348C2×C22⋊C4—416no—
349C2×C22⋊C4—416no—
350C2×C22⋊C4—416no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4C2×D418yes—
360C2×C22⋊C4C2×D418yes—
361C2×C22⋊C4C2×D418yes—
362#95—28no—
363#95—28no—
364#95—28no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—28no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—22no—
407C24—28no—
408C24—28no—
409C24—28no—
410C24—28no—
411C24—216no—
412C24—216no—
413C24—216no—
414C24—216no—
415C24—44no—
416C24—44no—
417C24—44no—
418C24—44no—
419C24—44no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—48no—
424C24—48no—
425C24—48no—
426C24—416no—
427C24—48no—
428C24—416no—
429C24—84no—
430C24—88no—
431C24—84no—
432C24—84no—
433C24—88no—
434C24—84no—
435C24—88no—
436C24—88no—
437C24—88no—
438C24—88no—
439C24#121116yes—
440C24#123116yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C22×D412yes—
444C24C22×D412yes—
445C24C22×D414yes—
446C24C22×D412yes—
447C24C22×D412yes—
448C24C2×#4112yes—
449C24C2×#4112yes—
450C24C2×#4114yes—
451C24C2×#4114yes—
452C24C2×#4112yes—
453C24C2×#4114yes—
454C24H(5,𝔽2)14yes—
455C24C2511yescharacteristic
456C2×D4—216no—
457C2×D4—216no—
458C2×D4—216no—
459C2×D4—216no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—4128no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
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—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—416no—
534C22×C4—416no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—416no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4—88no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4—88no—
572C22×C4—84no—
573C22×C4—88no—
574C22×C4—88no—
575C22×C4—88no—
576C22×C4—88no—
577C22×C4C22×D414yes—
578C22×C4C22×D418yes—
579C22×C4H(5,𝔽2)14yes—
580C4⋊C4—416no—
581C4⋊C4—88no—
582C4⋊C4—88no—
583C22⋊C4—216no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—416no—
587C22⋊C4—416no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—416no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—84no—
599C22⋊C4—84no—
600C22⋊C4—84no—
601C22⋊C4—84no—
602C22⋊C4—84no—
603C22⋊C4—84no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—28no—
610C23—24no—
611C23—24no—
612C23—28no—
613C23—24no—
614C23—28no—
615C23—28no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
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—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—28no—
646C23—24no—
647C23—28no—
648C23—24no—
649C23—24no—
650C23—28no—
651C23—24no—
652C23—28no—
653C23—24no—
654C23—232no—
655C23—232no—
656C23—416no—
657C23—416no—
658C23—416no—
659C23—416no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—832no—
677C23—832no—
678C23—88no—
679C23—88no—
680C23—832no—
681C23—832no—
682C23—88no—
683C23—88no—
684C23—88no—
685C23—88no—
686C23—88no—
687C23—88no—
688C23C2×#12114yes—
689C23C2×#12114yes—
690C23C2×#12114yes—
691C23C2×#12318yes—
692C23C2×#12314yes—
693C23#53414yes—
694C23#54618yes—
695C23#55118yes—
696C23C23×D411yescharacteristic
697C23C23×D411yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4112yes—
700C23C2×H(5,𝔽2)12yes—
701C23C2×H(5,𝔽2)12yes—
702C23#58512yes—
703C23#58512yes—
704C23#58512yes—
705D4—432no—
706D4—432no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—28no—
711C2×C4—24no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—416no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
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—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—832no—
771C2×C4—88no—
772C2×C4—88no—
773C2×C4—88no—
774C2×C4—88no—
775C2×C4—88no—
776C2×C4—88no—
777C2×C4—88no—
778C22—216no—
779C22—24no—
780C22—24no—
781C22—216no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—28no—
792C22—24no—
793C22—24no—
794C22—28no—
795C22—48no—
796C22—48no—
797C22—48no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—48no—
803C22—48no—
804C22—48no—
805C22—48no—
806C22—44no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—44no—
815C22—832no—
816C22—832no—
817C22#241218yes—
818C22C22×#12111yescharacteristic
819C22C22×#12311yescharacteristic
820C22C2×#53411yescharacteristic
821C22C2×#54612yes—
822C22C2×#55112yes—
823C22#348411yescharacteristic
824C22#348512yes—
825C22#348511yescharacteristic
826C22#348511yescharacteristic
827C22#348511yescharacteristic
828C22#349114yes—
829C22#349112yes—
830C22#349612yes—
831C22#350514yes—
832C22#350512yes—
833C22#353414yes—
834C22#354514yes—
835C4—48no—
836C4—44no—
837C4—44no—
838C4—84no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C2—28no—
847C2—48no—
848C2—44no—
849C2—44no—
850C2C2×#241211yescharacteristic
851C2#3535111yescharacteristic
852C2#3535811yescharacteristic
853C2#3544711yescharacteristic
854C2#3544811yescharacteristic
855C2#3711711yescharacteristic
856C2#3711911yescharacteristic
857C2#4301614yes—
858C2#4304614yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2483C2semidirect
5. #15538C2semidirect
6. #15494C2semidirect
7. #15390C2semidirect
8. #15383C2semidirect
9. #15073C2semidirect
10. #14919C2semidirect
11. #14127C2semidirect
12. #13877C2semidirect
13. #13869C2semidirect
14. #13869C2semidirect
15. #13869C2semidirect
26. C2×#397C22semidirect
40. C2×#385C22semidirect
41. C2×#385C22semidirect
46. C2×#381C22semidirect
47. C2×#381C22semidirect
48. C2×#380C22semidirect
53. #1445C22semidirect
54. #1443C22semidirect
55. #1443C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
61. #1440C22semidirect
62. #1440C22semidirect
63. #1440C22semidirect
64. #1440C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
72. C22⋊#95C22semidirect
73. C22⋊#95C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
78. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24832
C22×#3942
C2×#23082
#155382
#154942
#153902
#153832
#150732
#149192
#141272
#138772
#138692