Finite Group Databasebeta

← #642420

Subgroups — #642420

Order 512.

3730 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×#2848C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic
3#16892C212yesmaximal, complemented
4#16815C212yesmaximal, complemented
5#16698C212yesmaximal, complemented
6#16364C212yesmaximal, complemented
7#15114C212yesmaximal, complemented
8#15061C212yesmaximal, complemented
9#15001C212yesmaximal, complemented
10#14892C212yesmaximal, complemented
11#14820C214yesmaximal
12#14353C211yesmaximal, characteristic, complemented
13#14347C211yesmaximal, characteristic, complemented
14#14281C211yesmaximal, characteristic, complemented
15#14281C211yesmaximal, characteristic, complemented
16#14047C214yesmaximal, complemented
17C2×C22⋊#95C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C22⋊C4C2212yes—
25#2848—28no—
26C2×#397C2214yes—
27C2×#397C2214yes—
28C2×#387C2214yescomplemented
29C2×#385C2212yes—
30C2×#385C2212yes—
31C2×#385C2212yes—
32#2280—28no—
33C2×#381C2212yes—
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2214yes—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#379C2212yes—
43C2×#379C2212yes—
44C2×C4×C22⋊C4C2212yes—
45C2×C4×C22⋊C4C2212yes—
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2212yes—
49#1446C2212yescomplemented
50#1446C2212yescomplemented
51#1445C2212yescomplemented
52#1445C2212yescomplemented
53#1445C2214yescomplemented
54#1444C2212yescomplemented
55#1444C2212yescomplemented
56#1444C2212yescomplemented
57#1444C2212yescomplemented
58#1443C2214yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1442C2212yescomplemented
62#1442C2212yescomplemented
63#1442C2214yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2214yescomplemented
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1436C2214yescomplemented
76#1436C2214yescomplemented
77#1434C2214yescomplemented
78C22⋊#95C2212yes—
79C22⋊#95C2214yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C26C2311yescharacteristic
86C23×Q8C2311yescharacteristic
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4D418yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×#117—24no—
108C2×#117—24no—
109C2×#117—44no—
110C2×#117—44no—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2314yes—
123C22×C22⋊C4—28no—
124C22×C22⋊C4—44no—
125C22×C22⋊C4—44no—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C42C2312yes—
141C22×C42C2312yes—
142#397—48no—
143#397—48no—
144#387—48no—
145#385—28no—
146#385—28no—
147#385—28no—
148#381—28no—
149#380—24no—
150#380—24no—
151#380—24no—
152#380—24no—
153#380—24no—
154#380—24no—
155#380—24no—
156#380—216no—
157#379—28no—
158#379—28no—
159C4×C22⋊C4—28no—
160C4×C22⋊C4—28no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—44no—
164C2×#95C2314yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C25—24no—
192C25—22no—
193C25—24no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—24no—
198C25—42no—
199C25—41no—
200C25—41no—
201C25C2×D414yes—
202C25C2411yescharacteristic
203C25C2411yescharacteristic
204C25C2411yescharacteristic
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8—42no—
209C22×Q8—42no—
210C23×C4—24no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—24no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—232no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—416no—
232C23×C4—416no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
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×C4—42no—
247C23×C4—42no—
248C23×C4—432no—
249C23×C4—432no—
250C23×C4C2×D414yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4C2×D414yes—
255C23×C4C2×D414yes—
256C23×C4#4118yes—
257C23×C4#4114yes—
258C23×C4#4114yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2414yes—
268C23×C4C2411yescharacteristic
269C23×C4C2414yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C22⋊Q8—416no—
274C22⋊Q8—416no—
275C22⋊Q8—416no—
276#117—416no—
277#117—416no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
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—24no—
315C2×C22⋊C4—24no—
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—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—432no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—28no—
345C2×C42—44no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—44no—
361#95—44no—
362#95—44no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373C24—22no—
374C24—22no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—216no—
380C24—216no—
381C24—28no—
382C24—28no—
383C24—28no—
384C24—22no—
385C24—22no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—28no—
402C24—28no—
403C24—44no—
404C24—44no—
405C24—48no—
406C24—48no—
407C24—44no—
408C24—44no—
409C24—44no—
410C24—44no—
411C24—48no—
412C24—48no—
413C24—48no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24C22×D412yes—
420C24C22×D412yes—
421C24C22×D412yes—
422C24C2×#4112yes—
423C24C2×#4112yes—
424C24C2×#4114yes—
425C24H(5,𝔽2)14yes—
426C24H(5,𝔽2)12yes—
427C242−1+412yes—
428C242−1+414yes—
429C24C2511yescharacteristic
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—84no—
434C2×Q8—84no—
435C22×C4—216no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—216no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—4128no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4—84no—
540C22×C4—84no—
541C22×C4—84no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4#123116yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C2×#4118yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)14yes—
556C4⋊C4—416no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—48no—
564C4⋊C4—44no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—88no—
568C22⋊C4—416no—
569C22⋊C4—416no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C42—48no—
583C42—48no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—232no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—416no—
630C23—416no—
631C23—416no—
632C23—416no—
633C23—416no—
634C23—432no—
635C23—432no—
636C23—432no—
637C23—432no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—416no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C2×#12314yes—
658C23#53214yes—
659C23#53414yes—
660C23#53614yes—
661C23#53714yes—
662C23#55218yes—
663C23#55618yes—
664C23C23×D411yescharacteristic
665C23C22×#4111yescharacteristic
666C23C22×#4111yescharacteristic
667C23C22×#4112yes—
668C23C2×H(5,𝔽2)12yes—
669C23C2×H(5,𝔽2)12yes—
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×2−1+412yes—
672C23C2×2−1+411yescharacteristic
673C23#58511yescharacteristic
674C23#58511yescharacteristic
675Q8—88no—
676C2×C4—232no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—416no—
696C2×C4—416no—
697C2×C4—416no—
698C2×C4—416no—
699C2×C4—416no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—816no—
756C2×C4—816no—
757C2×C4C2×#12314yes—
758C2×C4C2×#12314yes—
759C2×C4#53414yes—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—464no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22#249918yes—
794C22C22×#12311yescharacteristic
795C22C2×#53211yescharacteristic
796C22C2×#53411yescharacteristic
797C22C2×#53411yescharacteristic
798C22C2×#53611yescharacteristic
799C22C2×#53711yescharacteristic
800C22#344911yescharacteristic
801C22#345912yes—
802C22#346012yes—
803C22C2×#55212yes—
804C22C2×#55612yes—
805C22#349012yes—
806C22#349012yes—
807C22#349012yes—
808C22#349212yes—
809C22#349411yescharacteristic
810C22#349411yescharacteristic
811C22#349511yescharacteristic
812C22#349511yescharacteristic
813C22#353512yes—
814C22#353512yes—
815C22#353612yes—
816C22#353812yes—
817C4—24no—
818C4—24no—
819C4—24no—
820C4—48no—
821C4—42no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—84no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C2—28no—
832C2—44no—
833C2—44no—
834C2#3457511yescharacteristic
835C2C2×#249911yescharacteristic
836C2#3499211yescharacteristic
837C2#3505111yescharacteristic
838C2#3526311yescharacteristic
839C2#3744211yescharacteristic
840C2#3744711yescharacteristic
841C2#3793212yes—
842C2#3793312yes—
843C2#3795612yes—
844C2#3795712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #16892C2semidirect
4. #16815C2semidirect
5. #16698C2semidirect
6. #16364C2semidirect
7. #15114C2semidirect
8. #15061C2semidirect
9. #15001C2semidirect
10. #14892C2semidirect
12. #14353C2semidirect
13. #14347C2semidirect
14. #14281C2semidirect
15. #14281C2semidirect
16. #14047C2semidirect
28. C2×#387C22semidirect
49. #1446C22semidirect
50. #1446C22semidirect
51. #1445C22semidirect
52. #1445C22semidirect
53. #1445C22semidirect
54. #1444C22semidirect
55. #1444C22semidirect
56. #1444C22semidirect
57. #1444C22semidirect
58. #1443C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
75. #1436C22semidirect
76. #1436C22semidirect
77. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#22802
#168922
#168152
#166982
#163642
#151142
#150612
#150012
#148922
#148202
#143532
#143472
#142812
#140472
C2×C22⋊#952