Finite Group Databasebeta

← #722629

Subgroups — #722629

Order 512.

3248 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2396C211yesmaximal, characteristic, complemented
3C2×#2349C211yesmaximal, characteristic, complemented
4C2×#2324C211yesmaximal, characteristic
5#16400C212yesmaximal, complemented
6#16265C212yesmaximal, complemented
7#15436C214yesmaximal, complemented
8#15309C214yesmaximal, complemented
9#15194C212yesmaximal, complemented
10#15131C212yesmaximal, complemented
11#14836C212yesmaximal, complemented
12#14758C212yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#13970C212yesmaximal
15#13925C211yesmaximal, characteristic, complemented
16#13910C211yesmaximal, characteristic, complemented
17#13906C212yesmaximal, complemented
18C22×C22⋊Q8C2212yes—
19C22×#121C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24#2538—28no—
25#2396—28no—
26C2×#400C2211yescharacteristic
27C2×#399C2211yescharacteristic
28C2×#398C2212yes—
29C2×#396C2214yes—
30C2×#396C2212yes—
31C2×#396C2214yes—
32C2×#395C2211yescharacteristic
33C2×#393C2211yescharacteristic
34#2349—28no—
35#2324—28no—
36C2×#390C2211yescharacteristic
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#389C2211yescharacteristic
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2214yes—
43C2×#388C2212yes—
44C2×#386C2212yes—
45C2×#386C2214yes—
46C2×#385C2212yes—
47C2×#385C2214yes—
48C2×#384C2211yescharacteristic
49C2×#384C2212yes—
50C2×#382C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2214yes—
56C2×#380C2214yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61C22×#95C2212yes—
62#1446C2212yes—
63#1445C2212yes—
64#1445C2214yes—
65#1444C2212yes—
66#1444C2212yes—
67#1444C2214yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1440C2214yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1436C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C22⋊#95C2214yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2314yes—
92C24×C4C2312yes—
93C2×C22⋊Q8—28no—
94C2×C22⋊Q8—48no—
95C2×#121—24no—
96C2×#121—24no—
97C2×#121Q818yescomplemented
98C2×C4×Q8—24no—
99C2×C4×Q8—24no—
100C2×C4×Q8—24no—
101C2×C4×D4—28no—
102C2×C4×D4—24no—
103C2×C4×D4—28no—
104C2×C4×D4—24no—
105C2×C4×D4—44no—
106C2×C4×D4D418yes—
107C2×#117—24no—
108C2×#117—24no—
109C2×#117—24no—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C42C2311yescharacteristic
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2312yes—
146C22×C42C2311yescharacteristic
147#400—24no—
148#399—24no—
149#398—28no—
150#396—28no—
151#396—216no—
152#396—48no—
153#395—24no—
154#393—24no—
155#390—24no—
156#390—28no—
157#390—28no—
158#389—24no—
159#389—28no—
160#389—28no—
161#389—48no—
162#388—28no—
163#386—28no—
164#386—48no—
165#385—28no—
166#385—216no—
167#384—24no—
168#384—44no—
169#382—24no—
170#380—28no—
171#380—24no—
172#380—28no—
173#380—48no—
174#380—44no—
175#380—48no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4—28no—
178C4×C4⋊C4D418yescomplemented
179C4×C22⋊C4—28no—
180C2×#95—28no—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C25C2411yescharacteristic
204C25C2412yes—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8—24no—
209C22×Q8—42no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4C2×D414yes—
219C22×D4C2×Q814yes—
220C22×D4C2×Q818yes—
221C22×D4#4114yes—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—28no—
231C23×C4—28no—
232C23×C4—28no—
233C23×C4—28no—
234C23×C4—44no—
235C23×C4—44no—
236C23×C4—44no—
237C23×C4—44no—
238C23×C4—44no—
239C23×C4C2×D418yes—
240C23×C4C2×Q814yes—
241C23×C4C2414yes—
242C23×C4C2412yes—
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2412yes—
246C23×C4C2414yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C22⋊Q8—432no—
257#121—232no—
258C4×Q8—416no—
259C4×D4—232no—
260C4×D4—432no—
261#117—416no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
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×D414yes—
314C2×C4⋊C4C2×D418yes—
315C2×C4⋊C4C2×Q814yes—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4C2×D418yes—
351C2×C22⋊C4C2×Q818yes—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—44no—
362C2×C42C2×D418yes—
363C2×C42C2×D414yes—
364C2×C42C2×D414yes—
365C2×C42#4114yes—
366#95—24no—
367#95—28no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—24no—
376#95—24no—
377#95—28no—
378#95—28no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95C2×D414yes—
387#95C2×D414yes—
388C24—22no—
389C24—22no—
390C24—24no—
391C24—24no—
392C24—22no—
393C24—24no—
394C24—22no—
395C24—24no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—21no—
403C24—22no—
404C24—21no—
405C24—22no—
406C24C22×D414yes—
407C24C22×Q812yes—
408C24C22×Q814yes—
409C24C2×#4114yes—
410C24C2511yescharacteristic
411C2×Q8—28no—
412C2×Q8—48no—
413C2×Q8—48no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×D4—216no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—416no—
424C2×D4—84no—
425C2×D4—84no—
426C2×D4—88no—
427C2×D4C22⋊Q8116yes—
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—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—216no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—416no—
505C22×C4—416no—
506C22×C4—416no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—416no—
512C22×C4—88no—
513C22×C4—88no—
514C22×C4—88no—
515C22×C4—88no—
516C22×C4—88no—
517C22×C4C22×D414yes—
518C22×C4C22×D414yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D414yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×Q812yes—
527C22×C4C22×Q814yes—
528C22×C4C22×Q812yes—
529C22×C4C2×#4112yes—
530C22×C4C2×#4112yes—
531C22×C4C2×#4112yes—
532C22×C4C2×#4112yes—
533C22×C4H(5,𝔽2)14yes—
534C22×C4H(5,𝔽2)14yes—
535C22×C4H(5,𝔽2)12yes—
536C22×C42−1+414yes—
537C22×C42−1+412yes—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—216no—
541C4⋊C4—48no—
542C4⋊C4—416no—
543C4⋊C4—48no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—48no—
547C4⋊C4—44no—
548C4⋊C4—48no—
549C4⋊C4—44no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—84no—
553C4⋊C4—88no—
554C4⋊C4—84no—
555C4⋊C4—88no—
556C4⋊C4—88no—
557C22⋊C4—216no—
558C22⋊C4—216no—
559C22⋊C4—48no—
560C22⋊C4—416no—
561C22⋊C4—416no—
562C22⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4—48no—
565C22⋊C4—84no—
566C22⋊C4—84no—
567C22⋊C4—84no—
568C22⋊C4—88no—
569C22⋊C4—88no—
570C42—216no—
571C42—44no—
572C42—48no—
573C42—84no—
574C42#121116yes—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—28no—
586C23—28no—
587C23—28no—
588C23—28no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23C2×C22⋊Q818yes—
621C23C23×D411yescharacteristic
622C23C23×D411yescharacteristic
623C23C23×Q811yescharacteristic
624C23C22×#4111yescharacteristic
625C23C22×#4111yescharacteristic
626C23C2×H(5,𝔽2)11yescharacteristic
627C23C2×H(5,𝔽2)12yes—
628C23C2×H(5,𝔽2)12yes—
629C23C2×2−1+411yescharacteristic
630C23C2×2−1+412yes—
631C23#58512yes—
632Q8—416no—
633D4—232no—
634D4—816no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—28no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—416no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
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—816no—
718C2×C4—832no—
719C2×C4C2×#12114yes—
720C2×C4C2×#12114yes—
721C2×C4C2×#12114yes—
722C2×C4C2×C22⋊Q814yes—
723C2×C4#53718yes—
724C2×C4#53714yes—
725C2×C4#54614yes—
726C2×C4D4×Q814yes—
727C2×C4#55214yes—
728C2×C4#55414yes—
729C22—28no—
730C22—28no—
731C22—28no—
732C22—48no—
733C22—48no—
734C22—44no—
735C22—48no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—48no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—44no—
744C22—42no—
745C22—82no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—82no—
751C22C22×#12111yescharacteristic
752C22C22×C22⋊Q811yescharacteristic
753C22C2×#53711yescharacteristic
754C22C2×#53712yes—
755C22C2×#54611yescharacteristic
756C22C2×D4×Q811yescharacteristic
757C22C2×#55211yescharacteristic
758C22C2×#55411yescharacteristic
759C22#348411yescharacteristic
760C22#348511yescharacteristic
761C22#348812yes—
762C22#349412yes—
763C22#349811yescharacteristic
764C22#349911yescharacteristic
765C22#350112yes—
766C22#350312yes—
767C22#351112yes—
768C22#351312yes—
769C22#352012yes—
770C22#354312yes—
771C22#354812yes—
772C22#355512yes—
773C22#356112yes—
774C4—28no—
775C4—24no—
776C4—24no—
777C4—42no—
778C4—44no—
779C4—44no—
780C4—44no—
781C4—44no—
782C4—84no—
783C4—84no—
784C4—82no—
785C4—81no—
786C4—81no—
787C4—82no—
788C4#241718yes—
789C2—48no—
790C2—82no—
791C2C2×#241711yescharacteristic
792C2#3527311yescharacteristic
793C2#3551411yescharacteristic
794C2#3573911yescharacteristic
795C2#3583611yescharacteristic
796C2#3802412yes—
797C2#3959812yes—
798C2#4242511yescharacteristic
799C2#4264911yescharacteristic
800C2#4494012yes—
801C2#4505012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2538C2semidirect
2. C2×#2396C2semidirect
3. C2×#2349C2semidirect
5. #16400C2semidirect
6. #16265C2semidirect
7. #15436C2semidirect
8. #15309C2semidirect
9. #15194C2semidirect
10. #15131C2semidirect
11. #14836C2semidirect
12. #14758C2semidirect
13. #14340C2semidirect
15. #13925C2semidirect
16. #13910C2semidirect
17. #13906C2semidirect
97. C2×#121Q8semidirect
178. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#23962
C2×#23492
C2×#23242
#164002
#162652
#154362
#153092
#151942
#151312
#148362
#147582
#143402
#139702
#139252
#139102
#139062