Finite Group Databasebeta

← #1394319

Subgroups — #1394319

Order 512.

3254 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2C2×#2417C212yesmaximal, complemented
3C2×#2344C211yesmaximal, characteristic, complemented
4#17061C212yesmaximal, complemented
5#16519C212yesmaximal, complemented
6#16463C214yesmaximal, complemented
7#16392C214yesmaximal, complemented
8#15188C211yesmaximal, characteristic, complemented
9#15179C212yesmaximal, complemented
10#15178C211yesmaximal, characteristic, complemented
11#15177C212yesmaximal, complemented
12#15129C211yesmaximal, characteristic, complemented
13#14886C212yesmaximal
14#14340C212yesmaximal, complemented
15#13997C212yesmaximal, complemented
16#13918C211yesmaximal, characteristic, complemented
17C4×#392C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×#117C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26#2542—28no—
27#2417—216no—
28C2×#399C2214yes—
29C2×#398C2214yes—
30C2×#396C2214yes—
31C2×#394C2212yes—
32C2×#392C2211yescharacteristic
33#2344—28no—
34C2×#391C2212yes—
35C2×#391C2212yes—
36C2×#391C2212yes—
37C2×#390C2212yes—
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2212yes—
41C2×#387C2212yes—
42C2×#387C2212yes—
43C2×#386C2214yes—
44C2×#384C2212yes—
45C2×#382C2212yes—
46C2×#381C2212yes—
47C2×#380C2214yes—
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2212yes—
55#1445C2214yes—
56#1444C2211yescharacteristic
57#1444C2214yes—
58#1444C2212yes—
59#1444C2212yes—
60#1442C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1441C2212yes—
64#1441C2214yes—
65#1441C2212yes—
66#1441C2212yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2211yescharacteristic
70#1439C2214yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2214yes—
74#1439C2212yes—
75#1439C2214yes—
76#1439C2214yes—
77#1438C2212yes—
78#1438C2214yes—
79#1438C2211yescharacteristic
80#1437C2214yes—
81C4⋊#95C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2212yes—
84#1434C2212yes—
85C4×#95C2211yescharacteristic
86C23×Q8C2312yes—
87C23×D4C2311yescharacteristic
88C23×D4C2312yes—
89C24×C4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8—44no—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—44no—
100C2×C22⋊Q8—44no—
101C2×C22⋊Q8—44no—
102C2×C22⋊Q8—44no—
103C2×C4×D4—28no—
104C2×C4×D4—24no—
105C2×C4×D4—44no—
106C2×C4×D4—44no—
107C2×C4×D4—44no—
108C2×#117—28no—
109C2×#117—28no—
110C2×#117—44no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4D418yescomplemented
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C42C2312yes—
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148#399—216no—
149#398—216no—
150#396—216no—
151#394—44no—
152#392—24no—
153#391—28no—
154#391—44no—
155#391—44no—
156#390—28no—
157#389—24no—
158#389—28no—
159#389—24no—
160#387—28no—
161#387—28no—
162#386—216no—
163#384—28no—
164#382—44no—
165#381—28no—
166#380—216no—
167#380—24no—
168#380—28no—
169#380—44no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4D418yescomplemented
172C4×C22⋊C4—24no—
173C4×C22⋊C4—44no—
174C2×#95C2311yescharacteristic
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2311yescharacteristic
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2311yescharacteristic
184C2×#95C2311yescharacteristic
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C25C2412yes—
200C25C2411yescharacteristic
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—24no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—24no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4—42no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4C2×D414yes—
238C23×C4C2×D418yes—
239C23×C4C2414yes—
240C23×C4C2414yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2411yescharacteristic
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2411yescharacteristic
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C4⋊Q8—416no—
255C22⋊Q8—432no—
256C22⋊Q8—432no—
257C22⋊Q8—432no—
258C4×D4—416no—
259C4×D4—432no—
260#117—432no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—232no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4C2×D418yes—
301C2×C4⋊C4C2×D414yes—
302C2×C4⋊C4C2×D414yes—
303C2×C4⋊C4C2×D414yes—
304C2×C4⋊C4#4114yes—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—41no—
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—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4#4114yes—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—42no—
355C2×C42C2×D418yes—
356C2×C42C2×D414yes—
357#95—22no—
358#95—22no—
359#95—24no—
360#95—28no—
361#95—24no—
362#95—28no—
363#95—24no—
364#95—24no—
365#95—28no—
366#95—28no—
367#95—22no—
368#95—22no—
369#95—24no—
370#95—24no—
371#95—28no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95C2×D418yes—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24C22×D412yes—
405C24C2×#4112yes—
406C242−1+414yes—
407C242−1+412yes—
408C24C2511yescharacteristic
409C2×Q8—48no—
410C2×Q8—48no—
411C2×Q8—48no—
412C2×Q8—48no—
413C2×Q8—48no—
414C2×Q8—48no—
415C2×Q8—48no—
416C2×D4—28no—
417C2×D4—216no—
418C2×D4—48no—
419C2×D4—48no—
420C2×D4—48no—
421C2×D4—48no—
422C2×D4—44no—
423C2×D4—48no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—44no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—216no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—216no—
464C22×C4—28no—
465C22×C4—216no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4C22×D414yes—
520C22×C4C22×D412yes—
521C22×C4C22×D414yes—
522C22×C4C22×D412yes—
523C22×C4C22×D414yes—
524C22×C4C22×D414yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4114yes—
530C22×C4C2×#4112yes—
531C22×C4C2×#4112yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4H(5,𝔽2)14yes—
534C22×C4H(5,𝔽2)14yes—
535C22×C42−1+414yes—
536C4⋊C4—216no—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—48no—
540C4⋊C4—44no—
541C4⋊C4—48no—
542C4⋊C4—416no—
543C4⋊C4—416no—
544C4⋊C4—48no—
545C4⋊C4—48no—
546C4⋊C4—416no—
547C4⋊C4—44no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—88no—
551C4⋊C4#121116yes—
552C22⋊C4—28no—
553C22⋊C4—48no—
554C22⋊C4—44no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—416no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—416no—
562C22⋊C4—416no—
563C22⋊C4—88no—
564C22⋊C4—88no—
565C42—28no—
566C42—216no—
567C42—48no—
568C42—44no—
569C42—48no—
570C23—22no—
571C23—24no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—22no—
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—41no—
590C23—41no—
591C23—42no—
592C23—41no—
593C23—41no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23#54714yes—
628C23C23×D411yescharacteristic
629C23C23×D411yescharacteristic
630C23C22×#4111yescharacteristic
631C23C22×#4111yescharacteristic
632C23C2×H(5,𝔽2)12yes—
633C23C2×H(5,𝔽2)12yes—
634C23C2×H(5,𝔽2)11yescharacteristic
635C23C2×2−1+411yescharacteristic
636C23C2×2−1+412yes—
637C23C2×2−1+412yes—
638C23#58511yescharacteristic
639Q8—816no—
640D4—416no—
641D4—432no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—432no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—416no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—816no—
727C2×C4C2×#12118yes—
728C2×C4C2×#12114yes—
729C2×C4#53514yes—
730C2×C4#53514yes—
731C2×C4#53518yes—
732C2×C4#54018yes—
733C2×C4#54614yes—
734C22—28no—
735C22—24no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—42no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22C22×#12111yescharacteristic
761C22C2×#53512yes—
762C22C2×#53511yescharacteristic
763C22C2×#53511yescharacteristic
764C22C2×#54012yes—
765C22C2×#54611yescharacteristic
766C22C2×#54711yescharacteristic
767C22#347511yescharacteristic
768C22#348612yes—
769C22#348611yescharacteristic
770C22#348911yescharacteristic
771C22#349611yescharacteristic
772C22#349911yescharacteristic
773C22#352012yes—
774C22#352012yes—
775C22#352011yescharacteristic
776C22#352312yes—
777C22#353612yes—
778C22#353812yes—
779C22#353812yes—
780C22#354112yes—
781C22#354712yes—
782C22#354812yes—
783C4—28no—
784C4—24no—
785C4—44no—
786C4—44no—
787C4—42no—
788C4—42no—
789C4—44no—
790C4—42no—
791C4—82no—
792C4—84no—
793C4—81no—
794C4—82no—
795C4—84no—
796C4—82no—
797C4#261918yes—
798C2—44no—
799C2—84no—
800C2C2×#261911yescharacteristic
801C2#3570011yescharacteristic
802C2#3615311yescharacteristic
803C2#3890511yescharacteristic
804C2#3891712yes—
805C2#3895111yescharacteristic
806C2#3902812yes—
807C2#4243412yes—
808C2#4263312yes—
809C2#4280811yescharacteristic
810C2#4299411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
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×#2542C2semidirect
2. C2×#2417C2semidirect
3. C2×#2344C2semidirect
4. #17061C2semidirect
5. #16519C2semidirect
6. #16463C2semidirect
7. #16392C2semidirect
8. #15188C2semidirect
9. #15179C2semidirect
10. #15178C2semidirect
11. #15177C2semidirect
12. #15129C2semidirect
14. #14340C2semidirect
15. #13997C2semidirect
16. #13918C2semidirect
113. C22×C4⋊C4D4semidirect
171. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#24172
C2×#23442
#170612
#165192
#164632
#163922
#151882
#151792
#151782
#151772
#151292
#148862
#143402
#139972
#139182
C4×#3922