Finite Group Databasebeta

← #4308831

Subgroups — #4308831

Order 512.

3584 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2639C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C2×#2617C211yesmaximal, characteristic
4C22×#388C211yesmaximal, characteristic, complemented
5#16467C214yesmaximal, complemented
6#16466C214yesmaximal, complemented
7#16294C214yesmaximal, complemented
8#16290C214yesmaximal, complemented
9#14921C212yesmaximal, complemented
10#14729C212yesmaximal, complemented
11#14725C212yesmaximal, complemented
12#14725C212yesmaximal, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14698C211yesmaximal, characteristic, complemented
15#14353C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C22×#120C2212yes—
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2639—28no—
25#2626—28no—
26#2617—28no—
27C2×#400C2212yescomplemented
28C2×#399C2212yes—
29C2×#397C2212yes—
30C2×#397C2212yescomplemented
31C2×#396C2214yes—
32C2×#396C2214yescomplemented
33C2×#394C2214yes—
34C2×#394C2214yes—
35C2×#394C2214yes—
36C2×#394C2212yescomplemented
37C2×#393C2212yes—
38C2×#393C2212yescomplemented
39C2×#392C2212yes—
40C2×#391C2212yescomplemented
41C2×#390C2212yescomplemented
42C2×#388—28no—
43C2×#388C2214yes—
44C2×#388C2214yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#385C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#379C2212yes—
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58#1444C2214yescomplemented
59#1444C2214yescomplemented
60#1443C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1440C2214yes—
65#1440C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1438C2214yes—
72#1438C2214yes—
73#1437C2214yescomplemented
74#1436C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C26C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4C2312yes—
82C23×D4C2311yescharacteristic
83C23×D4C2314yes—
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C2×C22⋊Q8—24no—
91C2×C22⋊Q8—24no—
92C2×C22⋊Q8—24no—
93C2×#121—24no—
94C2×#121—24no—
95C2×#121—24no—
96C2×#120—28no—
97C2×#120—44no—
98C2×#120—44no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—44no—
115C22×C22⋊C4—44no—
116C22×C22⋊C4D418yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C42—24no—
136C22×C42—44no—
137C22×C42C2312yes—
138C22×C42C2312yes—
139#400—28no—
140#399—28no—
141#397—28no—
142#397—28no—
143#396—216no—
144#396—48no—
145#394—216no—
146#394—28no—
147#394—48no—
148#394—48no—
149#393—28no—
150#393—28no—
151#392—28no—
152#391—44no—
153#390—44no—
154#388—216no—
155#388—216no—
156#386—28no—
157#386—28no—
158#386—28no—
159#386—44no—
160#386—44no—
161#385—28no—
162#380—24no—
163#380—24no—
164#380—44no—
165#380—44no—
166#379—28no—
167C2×#95—24no—
168C2×#95D418yescomplemented
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C25—22no—
189C25—22no—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—42no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25C2×D414yes—
199C25C2412yes—
200C25C2412yes—
201C25C2411yescharacteristic
202C22×Q8—22no—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—42no—
206C22×Q8—42no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—28no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4—42no—
221C22×D4—42no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4—44no—
225C22×D4—44no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
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×C4C2×D414yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4C2×D414yes—
255C23×C4#4114yes—
256C23×C4C2412yes—
257C23×C4C2414yes—
258C23×C4C2412yes—
259C23×C4C2414yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C22⋊Q8—416no—
269#121—416no—
270#120—432no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—416no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C22⋊C4—232no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—28no—
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—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—416no—
335C2×C22⋊C4—416no—
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⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4C2×D418yes—
351C2×C22⋊C4C2×D418yes—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—416no—
359#95—28no—
360#95—24no—
361#95—24no—
362#95—28no—
363#95—24no—
364#95—24no—
365#95—28no—
366#95—24no—
367#95—24no—
368#95—28no—
369#95—28no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95C2×D418yes—
377#95C2×D418yes—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—28no—
383C24—22no—
384C24—22no—
385C24—24no—
386C24—24no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—24no—
393C24—28no—
394C24—28no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—24no—
405C24—24no—
406C24—48no—
407C24—48no—
408C24—44no—
409C24—44no—
410C24—48no—
411C24—48no—
412C24—44no—
413C24—44no—
414C24—44no—
415C24—44no—
416C24—44no—
417C24—44no—
418C24—84no—
419C24—84no—
420C24—84no—
421C24—84no—
422C24—84no—
423C24—84no—
424C24—84no—
425C24—84no—
426C24C22×D414yes—
427C24C22×D412yes—
428C24C22×D412yes—
429C24C2×#4112yes—
430C24H(5,𝔽2)12yes—
431C24H(5,𝔽2)12yes—
432C242−1+412yes—
433C242−1+412yes—
434C24C2511yescharacteristic
435C2×Q8—48no—
436C2×Q8—44no—
437C2×Q8—82no—
438C2×Q8—82no—
439C2×Q8—84no—
440C2×D4—48no—
441C2×D4—416no—
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—88no—
454C2×D4—88no—
455C2×D4—88no—
456C2×D4—88no—
457C2×D4—88no—
458C2×D4—88no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—22no—
467C22×C4—22no—
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—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—48no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—84no—
546C22×C4—84no—
547C22×C4#121116yes—
548C22×C4C22×D414yes—
549C22×C4C22×D414yes—
550C22×C4C22×D414yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4112yes—
557C22×C4H(5,𝔽2)14yes—
558C22×C4H(5,𝔽2)14yes—
559C4⋊C4—416no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—48no—
563C4⋊C4—84no—
564C4⋊C4—84no—
565C4⋊C4—88no—
566C4⋊C4—88no—
567C4⋊C4—88no—
568C22⋊C4—216no—
569C22⋊C4—216no—
570C22⋊C4—416no—
571C22⋊C4—416no—
572C22⋊C4—416no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—84no—
578C22⋊C4—84no—
579C22⋊C4—84no—
580C22⋊C4—84no—
581C22⋊C4—88no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C22⋊C4—88no—
585C22⋊C4—88no—
586C42—48no—
587C42—48no—
588C23—24no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—28no—
608C23—28no—
609C23—416no—
610C23—416no—
611C23—416no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—44no—
617C23—44no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—44no—
638C23—44no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—816no—
654C23—816no—
655C23—816no—
656C23—816no—
657C23—88no—
658C23—88no—
659C23—88no—
660C23—88no—
661C23C2×#12114yes—
662C23#53514yes—
663C23#53614yes—
664C23#53714yes—
665C23#53714yes—
666C23#54214yes—
667C23#54214yes—
668C23C23×D411yescharacteristic
669C23C23×D411yescharacteristic
670C23C22×#4111yescharacteristic
671C23C2×H(5,𝔽2)11yescharacteristic
672C23C2×H(5,𝔽2)11yescharacteristic
673C23C2×H(5,𝔽2)12yes—
674C23C2×H(5,𝔽2)12yes—
675C23C2×2−1+411yescharacteristic
676C23C2×2−1+411yescharacteristic
677C23#58512yes—
678C23#58512yes—
679Q8—88no—
680D4—88no—
681D4—832no—
682D4—816no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—416no—
706C2×C4—416no—
707C2×C4—416no—
708C2×C4—416no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
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—44no—
754C2×C4—44no—
755C2×C4—88no—
756C2×C4—88no—
757C2×C4C2×#12114yes—
758C2×C4C2×#12114yes—
759C22—28no—
760C22—28no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—24no—
769C22—44no—
770C22—44no—
771C22—48no—
772C22—48no—
773C22—44no—
774C22—832no—
775C22—84no—
776C22—84no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—84no—
783C22—84no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—84no—
790C22—84no—
791C22—82no—
792C22#262018yes—
793C22C22×#12111yescharacteristic
794C22C2×#53511yescharacteristic
795C22C2×#53611yescharacteristic
796C22C2×#53711yescharacteristic
797C22C2×#53711yescharacteristic
798C22C2×#54211yescharacteristic
799C22C2×#54211yescharacteristic
800C22#345912yes—
801C22#346012yes—
802C22#348411yescharacteristic
803C22#348411yescharacteristic
804C22#348511yescharacteristic
805C22#348711yescharacteristic
806C22#349612yes—
807C22#349612yes—
808C22#353412yes—
809C22#353512yes—
810C22#353612yes—
811C22#353712yes—
812C22#355812yes—
813C22#356012yes—
814C22#356112yes—
815C22#356412yes—
816C4—24no—
817C4—24no—
818C4—44no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—44no—
823C4—82no—
824C4—82no—
825C4—84no—
826C4—84no—
827C4—82no—
828C2—28no—
829C2—84no—
830C2—162no—
831C2C2×#262011yescharacteristic
832C2#3498411yescharacteristic
833C2#3516811yescharacteristic
834C2#3670611yescharacteristic
835C2#3672211yescharacteristic
836C2#3673912yes—
837C2#3674012yes—
838C2#3695711yescharacteristic
839C2#3697111yescharacteristic
840C2#3746112yes—
841C2#3746212yes—
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×#2639C2semidirect
2. C2×#2626C2semidirect
4. C22×#388C2semidirect
5. #16467C2semidirect
6. #16466C2semidirect
7. #16294C2semidirect
8. #16290C2semidirect
9. #14921C2semidirect
10. #14729C2semidirect
11. #14725C2semidirect
12. #14725C2semidirect
13. #14702C2semidirect
14. #14698C2semidirect
15. #14353C2semidirect
27. C2×#400C22semidirect
30. C2×#397C22semidirect
32. C2×#396C22semidirect
36. C2×#394C22semidirect
38. C2×#393C22semidirect
40. C2×#391C22semidirect
41. C2×#390C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1443C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
73. #1437C22semidirect
74. #1436C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
168. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26392
C2×#26262
C2×#26172
C22×#3882
#164672
#164662
#162942
#162902
#149212
#147292
#147252
#147022
#146982
#143532