Finite Group Databasebeta

← #664779

Subgroups — #664779

Order 512.

2810 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2497C211yesmaximal, characteristic
2C2×Q8×C22⋊C4C211yesmaximal, characteristic
3#15691C214yesmaximal, complemented
4#15488C214yesmaximal
5#15195C211yesmaximal, characteristic
6#15195C211yesmaximal, characteristic
7#15185C211yesmaximal, characteristic, complemented
8#15184C211yesmaximal, characteristic, complemented
9#14992C214yesmaximal, complemented
10#14703C211yesmaximal, characteristic, complemented
11#14114C214yesmaximal
12#14000C211yesmaximal, characteristic, complemented
13#13976C211yesmaximal, characteristic, complemented
14#13976C211yesmaximal, characteristic, complemented
15#13926C211yesmaximal, characteristic, complemented
16#13922C211yesmaximal, characteristic
17#13922C211yesmaximal, characteristic
18C4×#391C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23#2497—28no—
24C2×#400C2212yes—
25C2×#396C2212yes—
26Q8×C22⋊C4—28no—
27C2×#391C2212yes—
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2212yes—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#387C2212yes—
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C43C2211yescharacteristic
58#1446C2214yes—
59#1446C2214yes—
60#1445C2214yes—
61#1444C2214yes—
62#1444C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1437C2212yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2214yes—
76#1436C2212yes—
77#1436C2214yes—
78#1436C2214yes—
79C4⋊#95C2214yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86#1434C2214yes—
87#1434C2212yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C4×#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8—24no—
94C23×Q8—24no—
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8C2311yescharacteristic
101C23×Q8C2312yes—
102C23×Q8C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2312yes—
105C2×C4×Q8—24no—
106C2×C4×Q8—24no—
107C2×C4×Q8—24no—
108C2×C4×Q8—24no—
109C2×C4×Q8—42no—
110C2×C4×Q8—42no—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2312yes—
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2312yes—
142C22×C42C2312yes—
143C22×C42C2312yes—
144#400—28no—
145#396—28no—
146#391—24no—
147#391—24no—
148#391—24no—
149#391—24no—
150#391—24no—
151#391—24no—
152#391—24no—
153#391—24no—
154#391—28no—
155#391—28no—
156#391—42no—
157#391—42no—
158#389—24no—
159#389—24no—
160#388—28no—
161#388Q8116yescomplemented
162#387—28no—
163#384—24no—
164#384—42no—
165#384—42no—
166#380—24no—
167#380—24no—
168#380—24no—
169#380—28no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4—42no—
172C4×C22⋊C4—28no—
173C4×C22⋊C4—42no—
174C4×C22⋊C4—42no—
175C4×C22⋊C4D418yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C43—42no—
210C25C2411yescharacteristic
211C22×Q8—232no—
212C22×Q8—22no—
213C22×Q8—24no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—24no—
217C22×Q8—24no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—24no—
222C22×Q8—24no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—42no—
228C22×Q8—42no—
229C22×Q8—416no—
230C22×Q8—416no—
231C22×Q8—416no—
232C22×Q8—416no—
233C22×Q8—416no—
234C22×Q8—416no—
235C22×Q8#4114yes—
236C22×Q8#4114yes—
237C22×Q8#4114yes—
238C22×Q8#4114yes—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4C2×D414yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C4×Q8—416no—
272C4×Q8—416no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4C2×Q818yescomplemented
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4C2×D414yes—
326C2×C22⋊C4C2×D414yes—
327C2×C22⋊C4C2×Q818yes—
328C2×C22⋊C4C2×Q818yes—
329C2×C22⋊C4C2×Q818yes—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—44no—
359C2×C42C2×D414yes—
360C2×C42C2×D414yes—
361C2×C42C2×Q818yescomplemented
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—28no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—44no—
390#95—44no—
391#95C2×D414yes—
392#95C2×D414yes—
393#95C2×Q818yescomplemented
394#95C2×Q818yescomplemented
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24C22×D412yes—
405C24C22×Q814yes—
406C24C2511yescharacteristic
407C2×Q8—216no—
408C2×Q8—28no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—28no—
413C2×Q8—28no—
414C2×Q8—28no—
415C2×Q8—28no—
416C2×Q8—28no—
417C2×Q8—48no—
418C2×Q8—48no—
419C2×Q8—48no—
420C2×Q8—48no—
421C2×Q8—48no—
422C2×Q8—4128no—
423C2×Q8—48no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8#126116yes—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—216no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
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—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q814yes—
535C22×C4C22×Q814yes—
536C22×C4C22×Q814yes—
537C22×C4C22×Q814yes—
538C22×C4C22×Q814yes—
539C22×C4C2×#4114yes—
540C22×C4C2×#4114yes—
541C22×C4C2×#4114yes—
542C22×C4C2×#4114yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C4H(5,𝔽2)12yes—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—84no—
560C4⋊C4—84no—
561C4⋊C4—84no—
562C4⋊C4—88no—
563C4⋊C4—88no—
564C22⋊C4—44no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—84no—
569C22⋊C4—84no—
570C22⋊C4C4⋊Q8116yes—
571C42—28no—
572C42—28no—
573C42—48no—
574C42—48no—
575C42—48no—
576C42—48no—
577C42—44no—
578C42—44no—
579C42—44no—
580C42—44no—
581C42—84no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23C2×C4⋊Q814yes—
605C23C23×D411yescharacteristic
606C23C23×Q812yes—
607C23C22×#4111yescharacteristic
608C23C22×#4111yescharacteristic
609C23C22×#4111yescharacteristic
610C23C22×#4111yescharacteristic
611C23C2×H(5,𝔽2)11yescharacteristic
612C23C2×H(5,𝔽2)11yescharacteristic
613C23#58512yes—
614C23#58512yes—
615C23#58512yes—
616Q8—232no—
617Q8—432no—
618Q8—416no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—432no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—416no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4#52514yes—
718C2×C4C2×#12618yes—
719C2×C4C2×#12614yes—
720C2×C4C2×C4⋊Q814yes—
721C2×C4C2×C4⋊Q814yes—
722C2×C4#53814yes—
723C2×C4#54614yes—
724C2×C4#54614yes—
725C2×C4#55114yes—
726C2×C4#55114yes—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—44no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—44no—
735C22—42no—
736C22—44no—
737C22—44no—
738C22C2×#52511yescharacteristic
739C22C22×#12611yescharacteristic
740C22C22×C4⋊Q811yescharacteristic
741C22#344911yescharacteristic
742C22C2×#53811yescharacteristic
743C22C2×#54611yescharacteristic
744C22C2×#54611yescharacteristic
745C22C2×#55111yescharacteristic
746C22C2×#55111yescharacteristic
747C22Q8×#4112yes—
748C22Q8×#4112yes—
749C22Q8×#4112yes—
750C22Q8×#4112yes—
751C22#350011yescharacteristic
752C22#350011yescharacteristic
753C22#350112yes—
754C22#350112yes—
755C22#352412yes—
756C22#352412yes—
757C22#352412yes—
758C22#352412yes—
759C22#354012yes—
760C22#355112yes—
761C4—28no—
762C4—24no—
763C4—24no—
764C4—44no—
765C4—42no—
766C4—42no—
767C4—44no—
768C4—42no—
769C4—44no—
770C4—44no—
771C4—44no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4#248018yes—
779C2—44no—
780C2C2×#248011yescharacteristic
781C2#3495311yescharacteristic
782C2#3567811yescharacteristic
783C2#3627611yescharacteristic
784C2#3627611yescharacteristic
785C2Q8×#12612yes—
786C2#3809511yescharacteristic
787C2#3894811yescharacteristic
788C2#3966612yes—
789C2#5937612yes—
790C2#5993312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #15691C2semidirect
7. #15185C2semidirect
8. #15184C2semidirect
9. #14992C2semidirect
10. #14703C2semidirect
12. #14000C2semidirect
13. #13976C2semidirect
14. #13976C2semidirect
15. #13926C2semidirect
18. C4×#391C2semidirect
161. #388Q8semidirect
313. C2×C4⋊C4C2×Q8semidirect
361. C2×C42C2×Q8semidirect
393. #95C2×Q8semidirect
394. #95C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24972
C2×Q8×C22⋊C42
#156912
#154882
#151952
#151852
#151842
#149922
#147032
#141142
#140002
#139762
#139262
#139222
C4×#3912
C4×#3882