Finite Group Databasebeta

← #627239

Subgroups — #627239

Order 512.

4794 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2315C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3#15961C214yesmaximal, complemented
4#15958C214yesmaximal, complemented
5#15328C214yesmaximal, complemented
6#15324C214yesmaximal, complemented
7#14920C212yesmaximal, complemented
8#14726C212yesmaximal, complemented
9#14693C212yesmaximal, complemented
10#14338C211yesmaximal, characteristic, complemented
11#14265C212yesmaximal, complemented
12#14127C211yesmaximal, characteristic, complemented
13#14127C211yesmaximal, characteristic, complemented
14#13867C211yesmaximal, characteristic
15#13867C211yesmaximal, characteristic
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C23×C22⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C2×#396C2214yescomplemented
24#2315—28no—
25C2×#386—28no—
26C2×#386C2214yes—
27C2×#386C2214yes—
28C2×#386C2212yes—
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#385C2212yes—
33C2×#385C2212yes—
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yescomplemented
37C2×#385C2212yescomplemented
38C2×#385C2212yescomplemented
39C2×#385C2212yescomplemented
40C2×#385C2214yescomplemented
41C2×#385C2214yescomplemented
42C2×#380C2212yes—
43C2×#380C2212yescomplemented
44C2×#380C2212yescomplemented
45C2×#379C2211yescharacteristic
46C2×#379C2211yescharacteristic
47C2×#379C2212yes—
48C2×#379C2212yes—
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51#1445C2214yescomplemented
52#1445C2214yescomplemented
53#1443C2214yescomplemented
54#1442C2214yescomplemented
55#1442C2214yescomplemented
56#1441C2214yescomplemented
57#1441C2214yescomplemented
58#1441C2214yescomplemented
59#1439C2214yescomplemented
60#1439C2214yescomplemented
61#1439C2214yescomplemented
62#1439C2214yescomplemented
63#1439C2214yescomplemented
64#1439C2214yescomplemented
65#1439C2214yescomplemented
66#1438C2214yes—
67#1438C2214yes—
68C22⋊#95C2212yes—
69C22⋊#95C2212yes—
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yescomplemented
74C22⋊#95C2212yescomplemented
75C22⋊#95C2214yescomplemented
76C22⋊#95C2214yescomplemented
77C26C2311yescharacteristic
78C26C2311yescharacteristic
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—44no—
82C23×D4—44no—
83C23×D4Q818yes—
84C23×D4C2312yes—
85C23×D4C2312yes—
86C24×C4—24no—
87C24×C4—44no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4C2311yescharacteristic
91C24×C4C2314yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2314yes—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—28no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—44no—
113C22×C22⋊C4—44no—
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⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136#396—48no—
137#386—216no—
138#386—216no—
139#386—44no—
140#386—44no—
141#386—44no—
142#386—44no—
143#385—28no—
144#385—28no—
145#385—28no—
146#385—28no—
147#385—28no—
148#385—44no—
149#385—48no—
150#385—44no—
151#385—48no—
152#385—44no—
153#380—28no—
154#380—28no—
155#380—44no—
156#379—24no—
157#379—24no—
158#379—28no—
159#379—44no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95C2314yes—
163C2×#95C2312yes—
164C2×#95C2312yes—
165C2×#95C2314yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C25—22no—
182C25—22no—
183C25—24no—
184C25—24no—
185C25—24no—
186C25—24no—
187C25—24no—
188C25—24no—
189C25—42no—
190C25—42no—
191C25—42no—
192C25—42no—
193C25—42no—
194C25—42no—
195C25C2×D414yes—
196C25C2×Q814yes—
197C25C2×Q814yes—
198C25#4114yes—
199C25C2411yescharacteristic
200C25C2411yescharacteristic
201C25C2412yes—
202C25C2411yescharacteristic
203C22×D4—232no—
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—42no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4—42no—
216C22×D4—432no—
217C22×D4—416no—
218C22×D4—416no—
219C22×D4—432no—
220C22×D4C2×Q818yes—
221C22×D4C2×Q818yes—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—28no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—416no—
264C23×C4—416no—
265C23×C4—416no—
266C23×C4—464no—
267C23×C4C2×D414yes—
268C23×C4C2×D414yes—
269C23×C4C2×Q814yes—
270C23×C4C2414yes—
271C23×C4C2414yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
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×C22⋊C4—232no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
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—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
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—416no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—416no—
347C2×C22⋊C4—416no—
348C2×C22⋊C4—416no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4C2×D418yes—
358C2×C22⋊C4C2×D418yes—
359C2×C22⋊C4#4118yes—
360#95—28no—
361#95—28no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—28no—
367#95—28no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—28no—
384C24—28no—
385C24—216no—
386C24—28no—
387C24—216no—
388C24—22no—
389C24—22no—
390C24—24no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—24no—
397C24—22no—
398C24—24no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—22no—
407C24—22no—
408C24—28no—
409C24—28no—
410C24—216no—
411C24—216no—
412C24—216no—
413C24—48no—
414C24—44no—
415C24—44no—
416C24—44no—
417C24—48no—
418C24—48no—
419C24—44no—
420C24—48no—
421C24—48no—
422C24—416no—
423C24—416no—
424C24—416no—
425C24—416no—
426C24—44no—
427C24—48no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—48no—
432C24—88no—
433C24—88no—
434C24—88no—
435C24—88no—
436C24C22⋊Q8116yes—
437C24C22×D412yes—
438C24C22×D412yes—
439C24C22×D412yes—
440C24C22×Q812yes—
441C24C22×Q812yes—
442C24C22×Q814yes—
443C24C22×Q812yes—
444C24C2×#4112yes—
445C24C2×#4112yes—
446C24C2×#4112yes—
447C24C2×#4114yes—
448C24H(5,𝔽2)14yes—
449C24H(5,𝔽2)14yes—
450C24H(5,𝔽2)14yes—
451C24C2511yescharacteristic
452C2×D4—216no—
453C2×D4—216no—
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—4128no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
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—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—48no—
531C22×C4—416no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—416no—
535C22×C4—416no—
536C22×C4—416no—
537C22×C4—416no—
538C22×C4—416no—
539C22×C4—44no—
540C22×C4—416no—
541C22×C4—416no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—4128no—
546C22×C4—416no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—88no—
554C22×C4—88no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—88no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—88no—
565C22×C4—88no—
566C22×C4—88no—
567C22×C4C22×D414yes—
568C22×C4C22×D414yes—
569C22×C4C22×Q814yes—
570C22×C4C2×#4114yes—
571C22×C4C2×#4114yes—
572C22×C4H(5,𝔽2)14yes—
573C4⋊C4—84no—
574C4⋊C4—84no—
575C4⋊C4—84no—
576C4⋊C4—84no—
577C4⋊C4—88no—
578C4⋊C4—88no—
579C4⋊C4—88no—
580C22⋊C4—216no—
581C22⋊C4—216no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—416no—
585C22⋊C4—416no—
586C22⋊C4—416no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C22⋊C4—88no—
598C22⋊C4—88no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—28no—
611C23—232no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—28no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—232no—
649C23—416no—
650C23—416no—
651C23—464no—
652C23—416no—
653C23—416no—
654C23—416no—
655C23—464no—
656C23—416no—
657C23—416no—
658C23—416no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—44no—
663C23—42no—
664C23—42no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—88no—
678C23—88no—
679C23—88no—
680C23—832no—
681C23—832no—
682C23—88no—
683C23C2×C22⋊Q814yes—
684C23C2×C22⋊Q814yes—
685C23C2×C22⋊Q814yes—
686C23#52514yes—
687C23#53414yes—
688C23#54318yes—
689C23#55318yes—
690C23#55418yes—
691C23C23×D411yescharacteristic
692C23C23×Q811yescharacteristic
693C23C22×#4111yescharacteristic
694C23C22×#4112yes—
695C23C2×H(5,𝔽2)12yes—
696C23C2×H(5,𝔽2)12yes—
697C23C2×H(5,𝔽2)12yes—
698C23C2×H(5,𝔽2)12yes—
699C23#58512yes—
700D4—432no—
701D4—432no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—416no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—464no—
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—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—88no—
768C2×C4—88no—
769C2×C4—88no—
770C2×C4—88no—
771C2×C4—88no—
772C2×C4—88no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—216no—
777C22—24no—
778C22—24no—
779C22—216no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—216no—
789C22—464no—
790C22—44no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—48no—
801C22—48no—
802C22—48no—
803C22—48no—
804C22—44no—
805C22—48no—
806C22—48no—
807C22—48no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—832no—
812C22#257918yes—
813C22C22×C22⋊Q811yescharacteristic
814C22C2×#52511yescharacteristic
815C22C2×#53411yescharacteristic
816C22C2×#54312yes—
817C22#345912yes—
818C22C2×#55312yes—
819C22C2×#55412yes—
820C22#348411yescharacteristic
821C22#348411yescharacteristic
822C22#348411yescharacteristic
823C22#348511yescharacteristic
824C22#349012yes—
825C22#350112yes—
826C22#351314yes—
827C22#351914yes—
828C22#353214yes—
829C22#353414yes—
830C4—44no—
831C4—44no—
832C4—44no—
833C4—44no—
834C4—44no—
835C4—44no—
836C4—82no—
837C4—82no—
838C4—84no—
839C4—84no—
840C4—82no—
841C2—28no—
842C2—48no—
843C2—44no—
844C2—44no—
845C2C2×#257911yescharacteristic
846C2#3498211yescharacteristic
847C2#3498511yescharacteristic
848C2#3535411yescharacteristic
849C2#3535511yescharacteristic
850C2#3671411yescharacteristic
851C2#3711711yescharacteristic
852C2#3809614yes—
853C2#3904814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2315C2semidirect
3. #15961C2semidirect
4. #15958C2semidirect
5. #15328C2semidirect
6. #15324C2semidirect
7. #14920C2semidirect
8. #14726C2semidirect
9. #14693C2semidirect
10. #14338C2semidirect
11. #14265C2semidirect
12. #14127C2semidirect
13. #14127C2semidirect
23. C2×#396C22semidirect
36. C2×#385C22semidirect
37. C2×#385C22semidirect
38. C2×#385C22semidirect
39. C2×#385C22semidirect
40. C2×#385C22semidirect
41. C2×#385C22semidirect
43. C2×#380C22semidirect
44. C2×#380C22semidirect
51. #1445C22semidirect
52. #1445C22semidirect
53. #1443C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1441C22semidirect
57. #1441C22semidirect
58. #1441C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
73. C22⋊#95C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#23152
C22×#3862
#159612
#159582
#153282
#153242
#149202
#147262
#146932
#143382
#142652
#141272
#138672