Finite Group Databasebeta

← #628051

Subgroups — #628051

Order 512.

3652 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2618C211yesmaximal, characteristic, complemented
2C2×#2617C211yesmaximal, characteristic
3C2×#2313C211yesmaximal, characteristic, complemented
4C22×#388C211yesmaximal, characteristic, complemented
5#15607C214yesmaximal, complemented
6#15583C214yesmaximal, complemented
7#15458C214yesmaximal, complemented
8#15428C214yesmaximal, complemented
9#14912C212yesmaximal, complemented
10#14911C212yesmaximal, complemented
11#14698C211yesmaximal, characteristic, complemented
12#14697C211yesmaximal, characteristic, complemented
13#14338C211yesmaximal, characteristic, complemented
14#14020C212yesmaximal, complemented
15#13995C212yesmaximal, complemented
16C22×#123C2212yes—
17C22×#121C2211yescharacteristic
18C22×#120C2212yes—
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2618—28no—
25#2617—28no—
26C2×#398C2212yescomplemented
27C2×#397C2212yes—
28C2×#396C2212yescomplemented
29C2×#396C2212yescomplemented
30C2×#394C2214yes—
31C2×#394C2212yescomplemented
32C2×#392C2212yes—
33#2313—28no—
34C2×#390C2214yes—
35C2×#390C2212yescomplemented
36C2×#389C2212yescomplemented
37C2×#388—28no—
38C2×#388C2214yes—
39C2×#388C2214yes—
40C2×#387C2214yescomplemented
41C2×#387C2214yescomplemented
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#385C2212yes—
47C2×#381C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#379C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55#1443C2214yescomplemented
56#1442C2214yescomplemented
57#1441C2214yescomplemented
58#1440C2214yescomplemented
59#1440C2214yescomplemented
60#1439C2214yes—
61#1439C2212yes—
62#1439C2212yes—
63#1439C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1439C2214yescomplemented
67#1438C2214yes—
68#1438C2214yes—
69#1438C2214yes—
70#1437C2214yes—
71#1437C2214yescomplemented
72#1437C2214yescomplemented
73#1436C2214yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76#1434C2214yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C26C2311yescharacteristic
80C23×D4C2312yes—
81C23×D4C2311yescharacteristic
82C23×D4C2314yes—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C2×#123—28no—
90C2×#123—44no—
91C2×#123—44no—
92C2×#121—24no—
93C2×#121—24no—
94C2×#121—24no—
95C2×#120—28no—
96C2×#120—28no—
97C2×#120—44no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4D418yescomplemented
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2314yes—
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⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—44no—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C42—24no—
138C22×C42—44no—
139C22×C42C2312yes—
140C22×C42C2312yes—
141C22×C42C2314yes—
142#398—28no—
143#397—28no—
144#396—28no—
145#396—28no—
146#394—216no—
147#394—28no—
148#392—28no—
149#390—44no—
150#390—48no—
151#389—44no—
152#388—216no—
153#388—216no—
154#387—216no—
155#387—216no—
156#386—28no—
157#386—28no—
158#386—28no—
159#386—44no—
160#385—44no—
161#381—28no—
162#380—24no—
163#380—24no—
164#380D418yes—
165#379—44no—
166C4×C22⋊C4—28no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C25—22no—
188C25—22no—
189C25—22no—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—42no—
194C25—42no—
195C25—42no—
196C25—42no—
197C25#4114yes—
198C25C2412yes—
199C25C2412yes—
200C25C2411yescharacteristic
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—28no—
209C22×D4—28no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—44no—
214C22×D4—42no—
215C22×D4—44no—
216C22×D4—42no—
217C22×D4—44no—
218C22×D4—44no—
219C22×D4—44no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2×D414yes—
249C23×C4C2×D414yes—
250C23×C4#4114yes—
251C23×C4#4114yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2414yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2414yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264#123—432no—
265#121—416no—
266#120—432no—
267C2×C4⋊C4—232no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4C2×D418yes—
294C2×C4⋊C4C2×D418yes—
295C2×C4⋊C4C2×D418yes—
296C2×C22⋊C4—232no—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
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—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
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×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—28no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—416no—
359C2×C42—44no—
360C2×C42—44no—
361#95—28no—
362#95—28no—
363#95—28no—
364#95—24no—
365#95—24no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—24no—
370#95—24no—
371#95—28no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95C2×D418yes—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—28no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—24no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—24no—
393C24—24no—
394C24—28no—
395C24—28no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—24no—
402C24—22no—
403C24—22no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24—48no—
408C24—48no—
409C24—44no—
410C24—48no—
411C24—44no—
412C24—44no—
413C24—44no—
414C24—48no—
415C24—44no—
416C24—44no—
417C24—44no—
418C24—44no—
419C24—84no—
420C24—84no—
421C24—84no—
422C24—84no—
423C24—84no—
424C24—84no—
425C24—84no—
426C24—84no—
427C24C22×D412yes—
428C24C22×D412yes—
429C24C2×#4114yes—
430C24C2×#4112yes—
431C24C2×#4112yes—
432C24C2×#4112yes—
433C24H(5,𝔽2)12yes—
434C24H(5,𝔽2)12yes—
435C24C2511yescharacteristic
436C2×D4—416no—
437C2×D4—48no—
438C2×D4—416no—
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—44no—
447C2×D4—82no—
448C2×D4—82no—
449C2×D4—84no—
450C2×D4—88no—
451C2×D4—88no—
452C2×D4—88no—
453C2×D4—88no—
454C2×D4—88no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
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—22no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
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×D418yes—
549C22×C4C22×D414yes—
550C22×C4C22×D414yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C2×#4114yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4H(5,𝔽2)14yes—
559C4⋊C4—216no—
560C4⋊C4—216no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—44no—
565C4⋊C4—82no—
566C4⋊C4—82no—
567C4⋊C4—84no—
568C4⋊C4—88no—
569C22⋊C4—232no—
570C22⋊C4—216no—
571C22⋊C4—416no—
572C22⋊C4—416no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—84no—
581C22⋊C4—84no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C22⋊C4—88no—
585C22⋊C4—88no—
586C22⋊C4—88no—
587C42—48no—
588C42—48no—
589C42—88no—
590C23—24no—
591C23—24no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
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—24no—
609C23—24no—
610C23—28no—
611C23—416no—
612C23—416no—
613C23—42no—
614C23—416no—
615C23—42no—
616C23—44no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—44no—
636C23—44no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—816no—
656C23—816no—
657C23—88no—
658C23—816no—
659C23—88no—
660C23—88no—
661C23—88no—
662C23—816no—
663C23C2×#12114yes—
664C23#52514yes—
665C23#53514yes—
666C23#54614yes—
667C23#55014yes—
668C23#55314yes—
669C23#55514yes—
670C23C23×D411yescharacteristic
671C23C23×D411yescharacteristic
672C23C22×#4111yescharacteristic
673C23C22×#4111yescharacteristic
674C23C22×#4111yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×H(5,𝔽2)11yescharacteristic
677C23C2×H(5,𝔽2)12yes—
678C23#58512yes—
679C23#58512yes—
680C23#58512yes—
681D4—88no—
682D4—832no—
683D4—816no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
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—28no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—416no—
708C2×C4—416no—
709C2×C4—416no—
710C2×C4—416no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
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—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—88no—
759C2×C4—88no—
760C2×C4C2×#12114yes—
761C2×C4C2×#12114yes—
762C22—24no—
763C22—24no—
764C22—28no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—28no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—44no—
773C22—48no—
774C22—44no—
775C22—44no—
776C22—48no—
777C22—832no—
778C22—82no—
779C22—84no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—84no—
784C22—82no—
785C22—82no—
786C22—84no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—84no—
791C22—82no—
792C22—82no—
793C22—84no—
794C22—84no—
795C22#241418yes—
796C22C22×#12111yescharacteristic
797C22C2×#52511yescharacteristic
798C22C2×#53511yescharacteristic
799C22#345512yes—
800C22#345912yes—
801C22C2×#54611yescharacteristic
802C22C2×#55011yescharacteristic
803C22C2×#55311yescharacteristic
804C22C2×#55511yescharacteristic
805C22#348411yescharacteristic
806C22#348511yescharacteristic
807C22#348711yescharacteristic
808C22#348711yescharacteristic
809C22#349112yes—
810C22#349612yes—
811C22#350012yes—
812C22#350512yes—
813C22#350512yes—
814C22#351012yes—
815C22#353412yes—
816C22#353412yes—
817C22#356012yes—
818C22#356012yes—
819C4—24no—
820C4—24no—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—44no—
825C4—48no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—84no—
831C2—28no—
832C2—84no—
833C2—162no—
834C2C2×#241411yescharacteristic
835C2#3498711yescharacteristic
836C2#3509411yescharacteristic
837C2#3535811yescharacteristic
838C2#3567711yescharacteristic
839C2#3671011yescharacteristic
840C2#3696111yescharacteristic
841C2#3938012yes—
842C2#3941412yes—
843C2#3949912yes—
844C2#3955012yes—
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×#2618C2semidirect
3. C2×#2313C2semidirect
4. C22×#388C2semidirect
5. #15607C2semidirect
6. #15583C2semidirect
7. #15458C2semidirect
8. #15428C2semidirect
9. #14912C2semidirect
10. #14911C2semidirect
11. #14698C2semidirect
12. #14697C2semidirect
13. #14338C2semidirect
14. #14020C2semidirect
15. #13995C2semidirect
26. C2×#398C22semidirect
28. C2×#396C22semidirect
29. C2×#396C22semidirect
31. C2×#394C22semidirect
35. C2×#390C22semidirect
36. C2×#389C22semidirect
40. C2×#387C22semidirect
41. C2×#387C22semidirect
55. #1443C22semidirect
56. #1442C22semidirect
57. #1441C22semidirect
58. #1440C22semidirect
59. #1440C22semidirect
66. #1439C22semidirect
71. #1437C22semidirect
72. #1437C22semidirect
73. #1436C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. #1434C22semidirect
100. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26182
C2×#26172
C2×#23132
C22×#3882
#156072
#155832
#154582
#154282
#149122
#149112
#146982
#146972
#143382
#140202
#139952