Finite Group Databasebeta

← #554237

Subgroups — #554237

Order 512.

4310 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C2×#2308C211yesmaximal, characteristic
3C22×#388C211yesmaximal, characteristic, complemented
4#14706C212yesmaximal, complemented
5#14540C214yesmaximal, complemented
6#14528C214yesmaximal, complemented
7#14384C214yesmaximal, complemented
8#14366C214yesmaximal, complemented
9#14259C212yesmaximal, complemented
10#14127C211yesmaximal, characteristic, complemented
11#14019C212yesmaximal, complemented
12#13996C212yesmaximal, complemented
13#13869C211yesmaximal, characteristic, complemented
14#13867C211yesmaximal, characteristic
15#13775C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C22×#123C2212yes—
18C23×C4⋊C4C2211yescharacteristic, complemented
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic, complemented
24#2405C4116yescomplemented
25C2×#394C2214yes—
26#2308—28no—
27C2×#388—28no—
28C2×#388C2214yes—
29C2×#388C2214yescomplemented
30C2×#388C2214yescomplemented
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#386C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yescomplemented
40C2×#385C2212yescomplemented
41C2×#381C2212yes—
42C2×#381C2212yescomplemented
43C2×#379C2212yes—
44C2×#379C2211yescharacteristic
45C2×#379C2212yes—
46C2×#379C2211yescharacteristic
47C2×#379C2212yes—
48C2×C4×C22⋊C4C2212yescomplemented
49C22×#95C2211yescharacteristic, complemented
50C22×#95C2211yescharacteristic, complemented
51#1445C2214yescomplemented
52#1443C2214yescomplemented
53#1442C2214yescomplemented
54#1442C2214yescomplemented
55#1440C2214yes—
56#1440C2214yescomplemented
57#1439C2214yes—
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1439C2214yescomplemented
61#1438C2214yes—
62#1437C2214yes—
63#1437C2214yescomplemented
64#1437C2214yescomplemented
65#1437C2214yescomplemented
66#1437C2214yescomplemented
67#1436C2214yescomplemented
68#1436C2214yescomplemented
69#1436C2214yescomplemented
70C4⋊#95C2214yescomplemented
71C22⋊#95C2212yes—
72C22⋊#95C2212yescomplemented
73C22⋊#95C2212yescomplemented
74C22⋊#95C2212yescomplemented
75C22⋊#95C2212yescomplemented
76C22⋊#95C2212yescomplemented
77C22⋊#95C2212yescomplemented
78C26C2311yescharacteristic
79C26C2311yescharacteristic
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—44no—
83C23×D4—44no—
84C23×D4C2×C418yes—
85C23×D4C2312yes—
86C23×D4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C2×#123—44no—
97C2×#123—44no—
98C2×#123C2×C4116yescomplemented
99C22×C4⋊C4—24no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2314yes—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—44no—
109C22×C22⋊C4—44no—
110C22×C22⋊C4—44no—
111C22×C22⋊C4C2×C418yes—
112C22×C22⋊C4D418yes—
113C22×C22⋊C4C2312yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C42—24no—
136C22×C42—44no—
137C22×C42C2314yes—
138C22×C42C2314yes—
139#394C2×C4132yescomplemented
140#388—216no—
141#388—216no—
142#388—48no—
143#386—28no—
144#386—28no—
145#386—28no—
146#386—28no—
147#386—44no—
148#386—44no—
149#386C2×C4116yescomplemented
150#385—44no—
151#385—44no—
152#385C2×C4116yescomplemented
153#381—28no—
154#381—44no—
155#379—24no—
156#379—28no—
157#379—44no—
158#379C2×C418yes—
159#379C2×C4116yescomplemented
160C4×C22⋊C4—44no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2314yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C25—24no—
183C25—24no—
184C25—22no—
185C25—22no—
186C25—42no—
187C25—42no—
188C25—42no—
189C25—42no—
190C25—42no—
191C25—42no—
192C25—42no—
193C25—42no—
194C25—42no—
195C25—42no—
196C25C22×C414yes—
197C25C22×C414yes—
198C25C2×D414yes—
199C25#4114yes—
200C25C2412yes—
201C25C2411yescharacteristic
202C25C2411yescharacteristic
203C25C2411yescharacteristic
204C22×D4—232no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4—42no—
216C22×D4—42no—
217C22×D4—432no—
218C22×D4—416no—
219C22×D4—416no—
220C22×D4—432no—
221C22×D4C22×C418yes—
222C22×D4C22×C418yes—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4C22×C414yes—
258C23×C4C22×C414yes—
259C23×C4C22×C414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2414yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273#123—432no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—44no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—416no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4C22×C4116yes—
284C2×C22⋊C4—232no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
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—24no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—416no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—416no—
327C2×C22⋊C4—416no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4C22×C418yes—
342C2×C22⋊C4C22×C418yes—
343C2×C22⋊C4C22×C418yes—
344C2×C22⋊C4C22×C4116yes—
345C2×C22⋊C4C22×C418yes—
346C2×C22⋊C4C22×C418yes—
347C2×C22⋊C4C22×C4116yes—
348C2×C22⋊C4C2×D418yes—
349C2×C22⋊C4C2×D418yes—
350C2×C42—28no—
351C2×C42—44no—
352C2×C42—44no—
353C2×C42—416no—
354C2×C42—44no—
355C2×C42—44no—
356C2×C42—44no—
357#95—28no—
358#95—28no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—28no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95C22×C4116yes—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
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—216no—
393C24—28no—
394C24—28no—
395C24—216no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—28no—
407C24—44no—
408C24—48no—
409C24—48no—
410C24—48no—
411C24—44no—
412C24—44no—
413C24—44no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—48no—
418C24—44no—
419C24—44no—
420C24—48no—
421C24—88no—
422C24—88no—
423C24—88no—
424C24—88no—
425C24—82no—
426C24—82no—
427C24—82no—
428C24—82no—
429C24—84no—
430C24—84no—
431C24—88no—
432C24—88no—
433C24—88no—
434C24—88no—
435C24C4×D4116yes—
436C24C23×C414yes—
437C24C23×C412yes—
438C24C23×C412yes—
439C24C23×C412yes—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C2×#4112yes—
444C24C2×#4112yes—
445C24C2×#4112yes—
446C24H(5,𝔽2)14yes—
447C24H(5,𝔽2)14yes—
448C24C2511yescharacteristic
449C2×D4—216no—
450C2×D4—216no—
451C2×D4—216no—
452C2×D4—216no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—4128no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—216no—
469C22×C4—28no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—28no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—416no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—416no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—88no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—88no—
555C22×C4—88no—
556C22×C4—88no—
557C22×C4C23×C414yes—
558C22×C4C23×C414yes—
559C22×C4C23×C418yes—
560C22×C4C23×C414yes—
561C22×C4C22×D414yes—
562C22×C4C22×D414yes—
563C22×C4H(5,𝔽2)14yes—
564C4⋊C4—416no—
565C4⋊C4—416no—
566C4⋊C4—88no—
567C22⋊C4—216no—
568C22⋊C4—216no—
569C22⋊C4—216no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—416no—
575C22⋊C4—416no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—84no—
582C22⋊C4—84no—
583C22⋊C4—84no—
584C22⋊C4—84no—
585C22⋊C4—88no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C22⋊C4—88no—
589C42—416no—
590C42—88no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—28no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—232no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—28no—
632C23—28no—
633C23—416no—
634C23—416no—
635C23—416no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—88no—
663C23—88no—
664C23—88no—
665C23—832no—
666C23—832no—
667C23—88no—
668C23—88no—
669C23—88no—
670C23—832no—
671C23—88no—
672C23—88no—
673C23—88no—
674C23—832no—
675C23—88no—
676C23C2×C4×D414yes—
677C23C2×C4×D414yes—
678C23C2×C4×D414yes—
679C23#51818yes—
680C23#53414yes—
681C23#53514yes—
682C23#53818yes—
683C23C24×C411yescharacteristic
684C23C23×D411yescharacteristic
685C23C22×#4111yescharacteristic
686C23C2×H(5,𝔽2)12yes—
687C23C2×H(5,𝔽2)12yes—
688C23C2×H(5,𝔽2)12yes—
689C23#58512yes—
690C23#58512yes—
691C23#58512yes—
692D4—432no—
693D4—432no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—416no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—416no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—88no—
761C2×C4—88no—
762C2×C4—88no—
763C2×C4—88no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—216no—
768C22—24no—
769C22—216no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—48no—
785C22—48no—
786C22—48no—
787C22—48no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—48no—
793C22—48no—
794C22—44no—
795C22—832no—
796C22—832no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—84no—
801C22—84no—
802C22—82no—
803C22#232118yes—
804C22C22×C4×D411yescharacteristic
805C22C2×#51812yes—
806C22#342812yes—
807C22C4×H(5,𝔽2)12yes—
808C22C2×#53411yescharacteristic
809C22C2×#53511yescharacteristic
810C22C2×#53812yes—
811C22#348411yescharacteristic
812C22#348511yescharacteristic
813C22#348511yescharacteristic
814C22#348511yescharacteristic
815C22#349112yes—
816C22#350512yes—
817C22#353314yes—
818C22#353414yes—
819C22#355814yes—
820C22#356014yes—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—48no—
825C4—44no—
826C4—44no—
827C4—44no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—84no—
832C2—28no—
833C2—44no—
834C2—44no—
835C2—84no—
836C2C2×#232111yescharacteristic
837C2#3419911yescharacteristic
838C2#3426411yescharacteristic
839C2#3447014yes—
840C2#3696511yescharacteristic
841C2#3696711yescharacteristic
842C2#3696911yescharacteristic
843C2#3698614yes—
844C2#3711711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#388C2semidirect
4. #14706C2semidirect
5. #14540C2semidirect
6. #14528C2semidirect
7. #14384C2semidirect
8. #14366C2semidirect
9. #14259C2semidirect
10. #14127C2semidirect
11. #14019C2semidirect
12. #13996C2semidirect
13. #13869C2semidirect
15. #13775C2semidirect
18. C23×C4⋊C4C22semidirect
23. C23×C42C22semidirect
24. #2405C4semidirect
29. C2×#388C22semidirect
30. C2×#388C22semidirect
39. C2×#385C22semidirect
40. C2×#385C22semidirect
42. C2×#381C22semidirect
48. C2×C4×C22⋊C4C22semidirect
49. C22×#95C22semidirect
50. C22×#95C22semidirect
51. #1445C22semidirect
52. #1443C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
56. #1440C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
63. #1437C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1437C22semidirect
67. #1436C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. C4⋊#95C22semidirect
72. C22⋊#95C22semidirect
73. C22⋊#95C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
98. C2×#123C2×C4semidirect
139. #394C2×C4semidirect
149. #386C2×C4semidirect
152. #385C2×C4semidirect
159. #379C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C2×#23082
C22×#3882
#147062
#145402
#145282
#143842
#143662
#142592
#141272
#140192
#139962
#138692
#138672
#137752