Finite Group Databasebeta

← #636504

Subgroups — #636504

Order 512.

3682 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2442C211yesmaximal, characteristic, complemented
2C22×#380C211yesmaximal, characteristic
3#16569C214yesmaximal, complemented
4#16568C214yesmaximal, complemented
5#15223C212yesmaximal, complemented
6#15220C212yesmaximal, complemented
7#15220C212yesmaximal, complemented
8#15216C212yesmaximal, complemented
9#15015C212yesmaximal, complemented
10#14920C212yesmaximal, complemented
11#14680C211yesmaximal, characteristic
12#14338C212yesmaximal
13#14262C212yesmaximal
14#14130C211yesmaximal, characteristic, complemented
15#13907C211yesmaximal, characteristic, complemented
16#13881C211yesmaximal, characteristic, complemented
17C4×#379C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×#125C2211yescharacteristic, complemented
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23#2442—28no—
24C2×#400C2212yescomplemented
25C2×#398C2212yescomplemented
26C2×#389C2211yescharacteristic, complemented
27C2×#389C2211yescharacteristic, complemented
28C2×#389C2212yescomplemented
29C2×#389C2212yescomplemented
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#382C2211yescharacteristic, complemented
33C2×#382C2212yescomplemented
34C2×#380—28no—
35C2×#380C2212yes—
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2214yes—
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×#380C2212yes—
44C2×#379C2211yescharacteristic
45C2×#379C2212yes—
46C2×#379C2211yescharacteristic
47C2×C4×C22⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2212yes—
50C2×C4×C22⋊C4C2212yes—
51C22×#95C2212yes—
52#1445C2214yescomplemented
53#1445C2214yescomplemented
54#1444C2212yescomplemented
55#1443C2214yescomplemented
56#1443C2214yescomplemented
57#1442C2212yescomplemented
58#1442C2214yescomplemented
59#1442C2214yescomplemented
60#1442C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1439C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C22⋊#95C2211yescharacteristic
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2214yes—
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C26C2311yescharacteristic
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4Q818yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C2×#125—24no—
98C2×#125—44no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4—44no—
102C22×C4⋊C4D418yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C22⋊C4—28no—
118C22×C22⋊C4—28no—
119C22×C22⋊C4—44no—
120C22×C22⋊C4C2311yescharacteristic
121C22×C22⋊C4C2311yescharacteristic
122C22×C22⋊C4C2311yescharacteristic
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C42C2311yescharacteristic
135C22×C42C2312yes—
136C22×C42C2311yescharacteristic
137#400—28no—
138#398—28no—
139#389—24no—
140#389—24no—
141#389—44no—
142#389—44no—
143#385—28no—
144#385—44no—
145#382—24no—
146#382—44no—
147#380—28no—
148#380—24no—
149#380—24no—
150#380—28no—
151#380—28no—
152#380—216no—
153#380—44no—
154#380—44no—
155#380—44no—
156#379—24no—
157#379—24no—
158#379—28no—
159C4×C22⋊C4—24no—
160C4×C22⋊C4—24no—
161C4×C22⋊C4—44no—
162C4×C22⋊C4—44no—
163C2×#95—28no—
164C2×#95C2311yescharacteristic
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2311yescharacteristic
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25—42no—
199C25C2×Q814yes—
200C25#4114yes—
201C25#4114yes—
202C25C2412yes—
203C25C2411yescharacteristic
204C23×C4—24no—
205C23×C4—24no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—232no—
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—432no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—44no—
230C23×C4—44no—
231C23×C4—44no—
232C23×C4—44no—
233C23×C4—416no—
234C23×C4—416no—
235C23×C4—432no—
236C23×C4C2×D414yes—
237C23×C4C2×D418yes—
238C23×C4C2×Q818yes—
239C23×C4C2×Q814yes—
240C23×C4C2×Q814yes—
241C23×C4C2×Q818yes—
242C23×C4#4114yes—
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2414yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2414yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258#125—416no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
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—416no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—44no—
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⋊C4C2×D414yes—
291C2×C4⋊C4C2×D414yes—
292C2×C4⋊C4C2×D418yes—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—432no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—24no—
343#95—28no—
344#95—28no—
345#95—22no—
346#95—22no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—44no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—44no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—28no—
375C24—28no—
376C24—28no—
377C24—28no—
378C24—28no—
379C24—28no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—48no—
393C24—48no—
394C24—48no—
395C24—48no—
396C24—48no—
397C24—48no—
398C24—44no—
399C24—44no—
400C24—48no—
401C24—44no—
402C24—44no—
403C24—48no—
404C24—48no—
405C24—48no—
406C24—48no—
407C24—48no—
408C24#125116yescomplemented
409C24C22×D412yes—
410C24C22×Q814yes—
411C24C22×Q812yes—
412C24C2×#4114yes—
413C24C2×#4114yes—
414C24C2×#4112yes—
415C24C2×#4112yes—
416C24C2×#4112yes—
417C24H(5,𝔽2)12yes—
418C242−1+412yes—
419C24C2511yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—216no—
425C22×C4—216no—
426C22×C4—28no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—216no—
442C22×C4—216no—
443C22×C4—216no—
444C22×C4—216no—
445C22×C4—216no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—48no—
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—4128no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—88no—
525C22×C4—88no—
526C22×C4—88no—
527C22×C4—88no—
528C22×C4C22⋊Q8116yes—
529C22×C4C22×D414yes—
530C22×C4C22×D414yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q812yes—
535C22×C4C22×Q812yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4H(5,𝔽2)14yes—
539C22×C4H(5,𝔽2)14yes—
540C4⋊C4—28no—
541C4⋊C4—28no—
542C4⋊C4—48no—
543C4⋊C4—48no—
544C4⋊C4—48no—
545C4⋊C4—48no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—84no—
551C4⋊C4—84no—
552C4⋊C4—88no—
553C4⋊C4—88no—
554C22⋊C4—416no—
555C22⋊C4—416no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—44no—
561C22⋊C4—44no—
562C22⋊C4—48no—
563C22⋊C4—44no—
564C22⋊C4—44no—
565C22⋊C4—48no—
566C22⋊C4—88no—
567C22⋊C4—88no—
568C42—44no—
569C42—44no—
570C42—48no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—232no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—432no—
607C23—416no—
608C23—416no—
609C23—416no—
610C23—416no—
611C23—416no—
612C23—432no—
613C23—432no—
614C23—416no—
615C23—432no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23C2×C22⋊Q814yes—
633C23C2×#12518yes—
634C23C2×#12514yes—
635C23#54414yes—
636C23#54614yes—
637C23#54814yes—
638C23#55214yes—
639C23#55314yes—
640C23C23×D411yescharacteristic
641C23C23×Q811yescharacteristic
642C23C22×#4111yescharacteristic
643C23C22×#4111yescharacteristic
644C23C22×#4111yescharacteristic
645C23C2×H(5,𝔽2)12yes—
646C23C2×H(5,𝔽2)12yes—
647C23C2×H(5,𝔽2)11yescharacteristic
648C23C2×2−1+411yescharacteristic
649C23#58512yes—
650C23#58512yes—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—232no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—432no—
666C2×C4—416no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—432no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—816no—
735C2×C4—816no—
736C2×C4C2×C22⋊Q814yes—
737C2×C4C2×C22⋊Q814yes—
738C2×C4#53414yes—
739C2×C4#53514yes—
740C2×C4#53818yes—
741C2×C4#54318yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—28no—
747C22—28no—
748C22—24no—
749C22—28no—
750C22—28no—
751C22—24no—
752C22—28no—
753C22—28no—
754C22—28no—
755C22—464no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22#244218yes—
769C22C22×C22⋊Q811yescharacteristic
770C22C22×#12511yescharacteristic
771C22C2×#53411yescharacteristic
772C22C2×#53511yescharacteristic
773C22C2×#53812yes—
774C22C2×#54312yes—
775C22C2×#54411yescharacteristic
776C22#345812yes—
777C22C2×#54611yescharacteristic
778C22C2×#54811yescharacteristic
779C22C2×#55211yescharacteristic
780C22C2×#55311yescharacteristic
781C22#348511yescharacteristic
782C22#348711yescharacteristic
783C22#349312yes—
784C22#350512yes—
785C22#350512yes—
786C22#350512yes—
787C22#350512yes—
788C22#354112yes—
789C22#354112yes—
790C22#354212yes—
791C22#354212yes—
792C4—24no—
793C4—44no—
794C4—44no—
795C4—44no—
796C4—81no—
797C4—81no—
798C4—82no—
799C4—81no—
800C4—84no—
801C4—81no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—84no—
806C4#262618yes—
807C2—28no—
808C2—48no—
809C2C2×#262611yescharacteristic
810C2C2×#244211yescharacteristic
811C2#3502012yes—
812C2#3515111yescharacteristic
813C2#3747612yes—
814C2#3946611yescharacteristic
815C2#3946711yescharacteristic
816C2#3947712yes—
817C2#3972211yescharacteristic
818C2#3972311yescharacteristic
819C2#3973312yes—
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×#2442C2semidirect
3. #16569C2semidirect
4. #16568C2semidirect
5. #15223C2semidirect
6. #15220C2semidirect
7. #15220C2semidirect
8. #15216C2semidirect
9. #15015C2semidirect
10. #14920C2semidirect
14. #14130C2semidirect
15. #13907C2semidirect
16. #13881C2semidirect
19. C22×#125C22semidirect
24. C2×#400C22semidirect
25. C2×#398C22semidirect
26. C2×#389C22semidirect
27. C2×#389C22semidirect
28. C2×#389C22semidirect
29. C2×#389C22semidirect
32. C2×#382C22semidirect
33. C2×#382C22semidirect
52. #1445C22semidirect
53. #1445C22semidirect
54. #1444C22semidirect
55. #1443C22semidirect
56. #1443C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
408. C24#125semidirect

Maximal subgroups

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

subgroupindex
C2×#24422
C22×#3802
#165692
#165682
#152232
#152202
#152162
#150152
#149202
#146802
#143382
#142622
#141302
#139072
#138812
C4×#3792