Finite Group Databasebeta

← #4307964

Subgroups — #4307964

Order 512.

4564 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C212yesmaximal, complemented
2C2×#2617C211yesmaximal, characteristic
3C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
4#14838C214yesmaximal, complemented
5#14837C214yesmaximal, complemented
6#14761C214yesmaximal, complemented
7#14760C214yesmaximal, complemented
8#14698C211yesmaximal, characteristic, complemented
9#14697C211yesmaximal, characteristic, complemented
10#14696C212yesmaximal, complemented
11#14338C211yesmaximal, characteristic, complemented
12#14275C211yesmaximal, characteristic, complemented
13#14271C211yesmaximal, characteristic, complemented
14#14259C212yesmaximal, complemented
15#14255C212yesmaximal, complemented
16C25×C4C2211yescharacteristic
17C22×#123C2214yes—
18C22×#121C2211yescharacteristic
19C22×#120C2212yes—
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2849—216no—
25#2617—28no—
26C2×#397C2212yes—
27C2×#394C2212yes—
28C2×#394C2212yes—
29C2×#392C2212yes—
30C2×#390C2212yescomplemented
31C2×#389C2212yescomplemented
32C2×#388C2214yescomplemented
33C2×#386C2212yes—
34C2×#386C2214yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#385C2212yes—
40C2×#385C2214yes—
41C2×#385C2212yes—
42C2×#381C2214yes—
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#379C2212yes—
47C2×C4×C22⋊C4—28no—
48C2×C4×C22⋊C4C2214yes—
49C2×C4×C22⋊C4C2214yes—
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52#1445C2212yescomplemented
53#1444C2212yescomplemented
54#1443C2214yescomplemented
55#1442C2214yescomplemented
56#1442C2212yescomplemented
57#1441C2214yescomplemented
58#1440C2214yes—
59#1440C2214yes—
60#1440C2214yescomplemented
61#1439C2214yes—
62#1439C2214yes—
63#1439C2214yescomplemented
64#1439C2214yescomplemented
65#1438C2214yes—
66#1438C2214yes—
67#1438C2212yescomplemented
68#1437C2214yescomplemented
69#1437C2214yescomplemented
70#1436C2214yescomplemented
71#1436C2214yescomplemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74#1434C2214yescomplemented
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C26C2311yescharacteristic
79C23×D4C2312yes—
80C23×D4C2311yescharacteristic
81C23×D4C2312yes—
82C23×D4C2312yes—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—44no—
86C24×C4—44no—
87C24×C4D418yescomplemented
88C24×C4C2311yescharacteristic
89C24×C4C2314yes—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C2×#123—216no—
96C2×#123—48no—
97C2×#123—48no—
98C2×#121—24no—
99C2×#121—24no—
100C2×#121—24no—
101C2×#120—28no—
102C2×#120—28no—
103C2×#120—28no—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4D418yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C42—24no—
135C22×C42—24no—
136C22×C42—44no—
137C22×C42—44no—
138C22×C42C2314yes—
139C22×C42C2312yes—
140C22×C42C2312yes—
141#397—28no—
142#394—28no—
143#394—28no—
144#392—28no—
145#390—44no—
146#389—44no—
147#388—48no—
148#386—28no—
149#386—216no—
150#386—28no—
151#386—28no—
152#386—28no—
153#386—28no—
154#385—28no—
155#385—216no—
156#385—28no—
157#381—216no—
158#380—24no—
159#380—24no—
160#380—24no—
161#379—28no—
162C4×C22⋊C4—216no—
163C4×C22⋊C4—216no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C25—22no—
187C25—22no—
188C25—22no—
189C25—22no—
190C25—42no—
191C25—42no—
192C25—42no—
193C25—42no—
194C25C2×D414yes—
195C25C2×D414yes—
196C25#4114yes—
197C25C2412yes—
198C25C2412yes—
199C25C2411yescharacteristic
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
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—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4—42no—
219C22×D4—44no—
220C22×D4—44no—
221C22×D4—42no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—232no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—28no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—28no—
236C23×C4—22no—
237C23×C4—28no—
238C23×C4—28no—
239C23×C4—432no—
240C23×C4—44no—
241C23×C4—44no—
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—416no—
253C23×C4—416no—
254C23×C4—432no—
255C23×C4C2×D414yes—
256C23×C4C2×D4116yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4#4114yes—
261C23×C4#4114yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4C2414yes—
265C23×C4C2414yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276#123—464no—
277#121—416no—
278#120—432no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C22⋊C4—232no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—232no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
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⋊C4C2×D418yes—
348C2×C22⋊C4C2×D418yes—
349C2×C42—28no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—28no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—44no—
358C2×C42—416no—
359C2×C42—416no—
360#95—28no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—28no—
373#95—28no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—28no—
385C24—28no—
386C24—28no—
387C24—28no—
388C24—28no—
389C24—28no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—48no—
410C24—44no—
411C24—44no—
412C24—48no—
413C24—48no—
414C24—44no—
415C24—44no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—48no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24#121116yes—
426C24C22×D414yes—
427C24C22×D414yes—
428C24C22×D412yes—
429C24C22×D412yes—
430C24C2×#4114yes—
431C24C2×#4112yes—
432C24C2×#4112yes—
433C24C2×#4112yes—
434C24C2×#4112yes—
435C24C2×#4112yes—
436C24C2511yescharacteristic
437C2×D4—48no—
438C2×D4—416no—
439C2×D4—416no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—44no—
450C2×D4—82no—
451C2×D4—82no—
452C2×D4—84no—
453C2×D4—84no—
454C2×D4—84no—
455C2×D4—84no—
456C2×D4—84no—
457C2×D4—88no—
458C2×D4—88no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—216no—
462C22×C4—28no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—216no—
472C22×C4—232no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—232no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
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—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—416no—
530C22×C4—48no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—416no—
538C22×C4—416no—
539C22×C4—416no—
540C22×C4—416no—
541C22×C4—4128no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4#123116yescomplemented
554C22×C4C22×D414yes—
555C22×C4C22×D414yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D414yes—
559C22×C4C2×#4114yes—
560C22×C4C2×#4114yes—
561C22×C4C2×#4112yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4H(5,𝔽2)14yes—
566C22×C4H(5,𝔽2)14yes—
567C4⋊C4—48no—
568C4⋊C4—416no—
569C4⋊C4—44no—
570C4⋊C4—416no—
571C4⋊C4—82no—
572C4⋊C4—82no—
573C4⋊C4—84no—
574C22⋊C4—232no—
575C22⋊C4—216no—
576C22⋊C4—216no—
577C22⋊C4—416no—
578C22⋊C4—416no—
579C22⋊C4—416no—
580C22⋊C4—416no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—416no—
588C22⋊C4—84no—
589C22⋊C4—84no—
590C22⋊C4—88no—
591C42—48no—
592C42—48no—
593C42—416no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—232no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—28no—
618C23—28no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—28no—
624C23—28no—
625C23—416no—
626C23—416no—
627C23—432no—
628C23—416no—
629C23—416no—
630C23—416no—
631C23—416no—
632C23—432no—
633C23—432no—
634C23—432no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23C2×#12118yes—
667C23C2×#12114yes—
668C23C2×#12314yes—
669C23#52514yes—
670C23#52914yes—
671C23#52914yes—
672C23#53214yes—
673C23#53214yes—
674C23C23×D411yescharacteristic
675C23C23×D411yescharacteristic
676C23C22×#4111yescharacteristic
677C23C22×#4111yescharacteristic
678C23C22×#4111yescharacteristic
679C23C22×#4111yescharacteristic
680C23C22×#4111yescharacteristic
681C23C2×H(5,𝔽2)12yes—
682C23C2×H(5,𝔽2)12yes—
683C23#58512yes—
684C23#58512yes—
685D4—88no—
686D4—816no—
687D4—816no—
688D4—816no—
689C2×C4—232no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—416no—
715C2×C4—464no—
716C2×C4—416no—
717C2×C4—416no—
718C2×C4—416no—
719C2×C4—416no—
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—42no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
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—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4C2×#12314yes—
764C2×C4C2×#12314yes—
765C2×C4#53418yes—
766C22—28no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—28no—
774C22—28no—
775C22—28no—
776C22—28no—
777C22—28no—
778C22—28no—
779C22—464no—
780C22—48no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—48no—
786C22—48no—
787C22—48no—
788C22—82no—
789C22—84no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—84no—
797C22—84no—
798C22—84no—
799C22#285418yes—
800C22C22×#12111yescharacteristic
801C22C22×#12311yescharacteristic
802C22C2×#52511yescharacteristic
803C22C2×#52911yescharacteristic
804C22C2×#52911yescharacteristic
805C22C2×#53211yescharacteristic
806C22C2×#53211yescharacteristic
807C22C2×#53412yes—
808C22#344912yes—
809C22#345912yes—
810C22#345912yes—
811C22#346012yes—
812C22#346012yes—
813C22#348411yescharacteristic
814C22#348411yescharacteristic
815C22#348511yescharacteristic
816C22#348511yescharacteristic
817C22#349012yes—
818C22#349112yes—
819C22#350512yes—
820C22#350512yes—
821C22#350612yes—
822C22#350612yes—
823C4—28no—
824C4—24no—
825C4—24no—
826C4—44no—
827C4—44no—
828C4—44no—
829C4—44no—
830C4—82no—
831C4—84no—
832C4—82no—
833C4—82no—
834C4—84no—
835C2—28no—
836C2—48no—
837C2—162no—
838C2#3457512yes—
839C2#3498111yescharacteristic
840C2#3498311yescharacteristic
841C2#3498611yescharacteristic
842C2#3502212yes—
843C2#3503212yes—
844C2#3504312yes—
845C2#3508911yescharacteristic
846C2#3509111yescharacteristic
847C2#3515211yescharacteristic
848C2C2×#285411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2617C2
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×#2849C2semidirect
3. C22×C4×C22⋊C4C2semidirect
4. #14838C2semidirect
5. #14837C2semidirect
6. #14761C2semidirect
7. #14760C2semidirect
8. #14698C2semidirect
9. #14697C2semidirect
10. #14696C2semidirect
11. #14338C2semidirect
12. #14275C2semidirect
13. #14271C2semidirect
14. #14259C2semidirect
15. #14255C2semidirect
30. C2×#390C22semidirect
31. C2×#389C22semidirect
32. C2×#388C22semidirect
52. #1445C22semidirect
53. #1444C22semidirect
54. #1443C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1441C22semidirect
60. #1440C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
67. #1438C22semidirect
68. #1437C22semidirect
69. #1437C22semidirect
70. #1436C22semidirect
71. #1436C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. #1434C22semidirect
87. C24×C4D4semidirect
553. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#26172
C22×C4×C22⋊C42
#148382
#148372
#147612
#147602
#146982
#146972
#146962
#143382
#142752
#142712
#142592
#142552