Finite Group Databasebeta

← #846796

Subgroups — #846796

Order 512.

4148 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2415C212yesmaximal, complemented
2C2×#2409C212yesmaximal, complemented
3C2×#2409C211yesmaximal, characteristic, complemented
4C2×C4×#127C211yesmaximal, characteristic
5#16374C214yesmaximal, complemented
6#15662C212yesmaximal, complemented
7#15625C212yesmaximal, complemented
8#15342C212yesmaximal, complemented
9#15313C212yesmaximal
10#15177C212yesmaximal, complemented
11#15177C212yesmaximal, complemented
12#15129C212yesmaximal, complemented
13#14703C212yesmaximal, complemented
14#14518C214yesmaximal, complemented
15#13871C211yesmaximal, characteristic, complemented
16C24×Q8C2211yescharacteristic
17C22×#127C2211yescharacteristic
18C22×C22⋊Q8C2212yes—
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2415—216no—
27#2409—216no—
28#2409—28no—
29C2×#397C2214yes—
30C2×#395C2212yes—
31C2×#395C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#393C2214yes—
35C2×#393C2212yes—
36C4×#127—28no—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#390C2211yescharacteristic
41C2×#390C2212yes—
42C2×#390C2211yescharacteristic
43C2×#390C2212yes—
44C2×#389C2214yes—
45C2×#389C2212yes—
46C2×#388C2214yes—
47C2×#386C2214yes—
48C2×#386C2212yes—
49C2×#385C2212yes—
50C2×#385C2214yes—
51C2×#384C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×C43C2211yescharacteristic
58#1444C2214yes—
59#1444C2214yes—
60#1441C2214yes—
61#1440C2214yes—
62#1440C2214yes—
63#1440C2212yes—
64#1439C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1438C2214yes—
69#1438C2212yes—
70#1438C2214yes—
71#1437C2212yes—
72#1436C2212yes—
73#1436C2214yes—
74#1436C2214yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77#1434C2214yes—
78#1434C2214yes—
79C23×Q8—28no—
80C23×Q8—24no—
81C23×Q8—44no—
82C23×Q8—42no—
83C23×Q8—42no—
84C23×Q8C2312yes—
85C23×Q8C2312yes—
86C23×D4C2312yes—
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C2×#127—24no—
95C2×#127—28no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—44no—
102C2×C22⋊Q8—44no—
103C2×C22⋊Q8—44no—
104C2×C22⋊Q8—44no—
105C2×C4×D4—28no—
106C2×C4×D4—28no—
107C2×C4×D4—24no—
108C2×C4×D4—28no—
109C2×C4×D4—28no—
110C2×C4×D4—42no—
111C2×C4×D4—42no—
112C2×C4×D4—44no—
113C2×C4×D4—44no—
114C2×C4×D4—42no—
115C2×C4×D4—42no—
116C2×C4×D4D418yes—
117C2×#117—28no—
118C2×#117—42no—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152#397—216no—
153#395—28no—
154#395—216no—
155#394—216no—
156#394—216no—
157#393—28no—
158#393—216no—
159#391—28no—
160#391—28no—
161#391D4116yescomplemented
162#390—24no—
163#390—24no—
164#390—28no—
165#390—28no—
166#389—28no—
167#389—216no—
168#388—216no—
169#386—28no—
170#386—216no—
171#385—28no—
172#385—216no—
173#384—24no—
174#380—24no—
175#380—28no—
176#380—28no—
177#380—42no—
178#380—44no—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C43—24no—
196C25C2411yescharacteristic
197C25C2412yes—
198C25C2411yescharacteristic
199C22×Q8—24no—
200C22×Q8—24no—
201C22×Q8—24no—
202C22×Q8—28no—
203C22×Q8—24no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—42no—
208C22×Q8—44no—
209C22×Q8—42no—
210C22×Q8—432no—
211C22×Q8—416no—
212C22×Q8—416no—
213C22×Q8—432no—
214C22×Q8—416no—
215C22×Q8C2×D418yes—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—22no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—41no—
231C22×D4—41no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—41no—
235C22×D4—41no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4C2×D414yes—
239C22×D4#4118yes—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—28no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—42no—
258C23×C4—44no—
259C23×C4—42no—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4C2414yes—
263C23×C4C2414yes—
264C23×C4C2412yes—
265C23×C4C2414yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2414yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274#127—232no—
275C22⋊Q8—432no—
276C22⋊Q8—432no—
277C22⋊Q8—432no—
278C4×D4—416no—
279C4×D4—432no—
280C4×D4—432no—
281C4×D4—416no—
282#117—416no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4C2×D418yes—
315C2×C4⋊C4C2×D414yes—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4C2×D414yes—
360C2×C22⋊C4C2×D414yes—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—28no—
368C2×C42—24no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42C2×D418yes—
375C2×C42C2×D414yes—
376#95—28no—
377#95—28no—
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#95C2×D4116yes—
391#95C2×D4116yes—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24C22×D412yes—
422C24C22×D412yes—
423C24C2×#4114yes—
424C24C2×#4114yes—
425C24C2511yescharacteristic
426C2×Q8—216no—
427C2×Q8—216no—
428C2×Q8—216no—
429C2×Q8—416no—
430C2×Q8—48no—
431C2×Q8—48no—
432C2×Q8—416no—
433C2×Q8—4128no—
434C2×Q8—48no—
435C2×Q8—48no—
436C2×Q8—48no—
437C2×Q8—48no—
438C2×Q8—48no—
439C2×D4—28no—
440C2×D4—216no—
441C2×D4—28no—
442C2×D4—216no—
443C2×D4—28no—
444C2×D4—216no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—44no—
460C2×D4—48no—
461C2×D4—44no—
462C2×D4—48no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—48no—
526C22×C4—416no—
527C22×C4—416no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4C22×D414yes—
544C22×C4C22×D412yes—
545C22×C4C22×D418yes—
546C22×C4C22×D412yes—
547C22×C4C22×D418yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D414yes—
551C22×C4C22×D412yes—
552C22×C4C22×D414yes—
553C22×C4C2×#4114yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4H(5,𝔽2)14yes—
557C22×C42−1+414yes—
558C22×C42−1+414yes—
559C4⋊C4—216no—
560C4⋊C4—44no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—416no—
564C4⋊C4—416no—
565C4⋊C4—44no—
566C4⋊C4—416no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—416no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—416no—
576C22⋊C4—416no—
577C22⋊C4—416no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—416no—
581C22⋊C4—48no—
582C22⋊C4—416no—
583C22⋊C4—48no—
584C22⋊C4—88no—
585C22⋊C4—84no—
586C42—28no—
587C42—28no—
588C42—216no—
589C42—48no—
590C42—48no—
591C42—44no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23#52514yes—
669C23C23×D411yescharacteristic
670C23C23×D412yes—
671C23C22×#4112yes—
672C23C2×H(5,𝔽2)11yescharacteristic
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×H(5,𝔽2)12yes—
675C23C2×2−1+412yes—
676C23C2×2−1+412yes—
677C23#58512yes—
678Q8—432no—
679Q8—432no—
680D4—432no—
681D4—416no—
682D4—432no—
683D4—416no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—24no—
709C2×C4—432no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—816no—
755C2×C4#53414yes—
756C2×C4#53518yes—
757C2×C4#53614yes—
758C2×C4D4218yes—
759C2×C4D4214yes—
760C2×C4#54818yes—
761C2×C4#56014yes—
762C22—28no—
763C22—24no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22C2×#52511yescharacteristic
796C22C2×#53411yescharacteristic
797C22C2×#53512yes—
798C22C2×#53611yescharacteristic
799C22C2×D4212yes—
800C22C2×D4211yescharacteristic
801C22C2×#54812yes—
802C22D4×#4112yes—
803C22#348912yes—
804C22#349712yes—
805C22#349912yes—
806C22#350512yes—
807C22#352012yes—
808C22#352012yes—
809C22#352012yes—
810C22C2×#56011yescharacteristic
811C22#354712yes—
812C22#354712yes—
813C22#355011yescharacteristic
814C22#355012yes—
815C22#355111yescharacteristic
816C4—28no—
817C4—24no—
818C4—42no—
819C4—48no—
820C4—42no—
821C4—42no—
822C4—48no—
823C4—44no—
824C4—84no—
825C4—84no—
826C4—82no—
827C4#266918yes—
828C2—44no—
829C2—82no—
830C2—84no—
831C2#3508411yescharacteristic
832C2#3609712yes—
833C2#3737611yescharacteristic
834C2#3916712yes—
835C2#3934312yes—
836C2#3995012yes—
837C2#4634212yes—
838C2C2×#266911yescharacteristic
839C2#5965412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#127C22
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×#2415C2semidirect
2. C2×#2409C2semidirect
3. C2×#2409C2semidirect
5. #16374C2semidirect
6. #15662C2semidirect
7. #15625C2semidirect
8. #15342C2semidirect
10. #15177C2semidirect
11. #15177C2semidirect
12. #15129C2semidirect
13. #14703C2semidirect
14. #14518C2semidirect
15. #13871C2semidirect
161. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24152
C2×#24092
C2×C4×#1272
#163742
#156622
#156252
#153422
#153132
#151772
#151292
#147032
#145182
#138712