Finite Group Databasebeta

← #774419

Subgroups — #774419

Order 512.

4822 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#547C211yesmaximal, characteristic
2C2×#2489C212yesmaximal, complemented
3C2×#2454C211yesmaximal, characteristic, complemented
4#16362C212yesmaximal, complemented
5#15669C214yesmaximal, complemented
6#15667C214yesmaximal, complemented
7#15188C211yesmaximal, characteristic, complemented
8#15181C211yesmaximal, characteristic, complemented
9#15180C211yesmaximal, characteristic, complemented
10#14843C212yesmaximal, complemented
11#14764C212yesmaximal, complemented
12#13997C212yesmaximal, complemented
13#13937C212yesmaximal, complemented
14#13937C212yesmaximal, complemented
15#13881C212yesmaximal, complemented
16C4×#394C211yesmaximal, characteristic, complemented
17#13820C211yesmaximal, characteristic, complemented
18C23×#41C2212yes—
19C2×#547—216no—
20C2×#547—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#125C2211yescharacteristic
23C22×#123C2214yes—
24C22×C22⋊Q8C2212yes—
25C22×#121C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C23×C4⋊C4C2212yes—
29#2489—216no—
30#2454—28no—
31C2×#400C2214yes—
32C2×#399C2212yes—
33C2×#397C2214yes—
34C2×#396C2212yes—
35C2×#394C2211yescharacteristic
36C2×#391C2212yes—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2212yes—
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#388C2214yes—
46C2×#385C2212yes—
47C2×#382C2214yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56#1445C2214yes—
57#1442C2211yescharacteristic
58#1442C2212yes—
59#1442C2212yes—
60#1442C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1441C2211yescharacteristic
64#1441C2214yes—
65#1441C2212yes—
66#1441C2212yes—
67#1440C2212yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1438C2211yescharacteristic
72#1438C2214yes—
73#1438C2214yes—
74#1438C2214yes—
75#1438C2214yes—
76#1438C2212yes—
77#1437C2214yes—
78#1437C2214yes—
79C4⋊#95C2214yes—
80C4⋊#95C2211yescharacteristic
81C22⋊#95C2214yes—
82C22⋊#95C2214yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C4×#95C2211yescharacteristic
87C22×#41—28no—
88C22×#41—28no—
89C22×#41—28no—
90C22×#41—28no—
91C22×#41—28no—
92C22×#41—44no—
93C22×#41—44no—
94C23×Q8C2312yes—
95C23×D4C2314yes—
96C23×D4C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2314yes—
100C24×C4C2312yes—
101#547—2128no—
102C2×C4⋊Q8—28no—
103C2×C4⋊Q8—24no—
104C2×#125—24no—
105C2×#125—28no—
106C2×#123—216no—
107C2×#123—216no—
108C2×#123—216no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8D4116yes—
112C2×#121—28no—
113C2×#121—216no—
114C2×C4×D4—28no—
115C2×C4×D4—28no—
116C2×C4×D4—24no—
117C2×C4×D4D418yes—
118C22×C4⋊C4—28no—
119C22×C4⋊C4—216no—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2314yes—
153C22×C42C2311yescharacteristic
154#400—216no—
155#399—28no—
156#397—216no—
157#396—28no—
158#394—24no—
159#391—28no—
160#391—28no—
161#391—44no—
162#391—44no—
163#390—24no—
164#390—24no—
165#390—28no—
166#389—24no—
167#389—24no—
168#388—216no—
169#385—28no—
170#382—216no—
171#380—28no—
172#380—28no—
173#380—44no—
174C4×C4⋊C4—28no—
175C4×C4⋊C4—24no—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—28no—
178C4×C22⋊C4—44no—
179C2×#95C2311yescharacteristic
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2311yescharacteristic
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C25C2412yes—
204C25C2412yes—
205C2×#41—264no—
206C2×#41—432no—
207C2×#41—432no—
208C2×#41—432no—
209C2×#41—432no—
210C2×#41—432no—
211C2×#41—432no—
212C22×Q8—24no—
213C22×Q8—24no—
214C22×Q8—24no—
215C22×Q8—24no—
216C22×Q8—24no—
217C22×Q8—24no—
218C22×Q8C2×D418yes—
219C22×D4—24no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—24no—
225C22×D4—22no—
226C22×D4—28no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—42no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4C2×D414yes—
235C22×D4#4118yes—
236C23×C4—28no—
237C23×C4—28no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—28no—
249C23×C4—28no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4C2×D418yes—
254C23×C4C2×D418yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C4⋊Q8—232no—
271#125—416no—
272#123—2128no—
273C22⋊Q8—264no—
274#121—264no—
275C4×D4—232no—
276C4×D4—232no—
277C2×C4⋊C4—264no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C2×D4116yes—
309C2×C4⋊C4C2×D418yes—
310C2×C4⋊C4C2×D414yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
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×D4116yes—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—28no—
357C2×C42—22no—
358C2×C42—28no—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—44no—
364C2×C42C2×D414yes—
365#95—24no—
366#95—24no—
367#95—22no—
368#95—22no—
369#95—28no—
370#95—28no—
371#95—24no—
372#95—28no—
373#95—28no—
374#95—24no—
375#95—28no—
376#95—28no—
377#95—24no—
378#95—22no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95#4114yescomplemented
389C24—24no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—24no—
396C24—22no—
397C24—24no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24C22×D414yes—
413C24C22×D414yes—
414C24C2×#4118yes—
415C24C2511yescharacteristic
416#41—4256no—
417C2×Q8—216no—
418C2×Q8—216no—
419C2×Q8—216no—
420C2×Q8—48no—
421C2×Q8—48no—
422C2×Q8—48no—
423C2×Q8—48no—
424C2×D4—28no—
425C2×D4—232no—
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—216no—
429C2×D4—216no—
430C2×D4—48no—
431C2×D4—48no—
432C2×D4—416no—
433C2×D4—416no—
434C2×D4—44no—
435C2×D4—416no—
436C2×D4—416no—
437C2×D4—416no—
438C2×D4—416no—
439C2×D4—44no—
440C2×D4#124116yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—232no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—216no—
476C22×C4—216no—
477C22×C4—216no—
478C22×C4—216no—
479C22×C4—216no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—48no—
520C22×C4—416no—
521C22×C4—416no—
522C22×C4—416no—
523C22×C4—416no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—416no—
527C22×C4—416no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4C22×D414yes—
533C22×C4C22×D418yes—
534C22×C4C22×D412yes—
535C22×C4C22×D418yes—
536C22×C4C22×D414yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D414yes—
540C22×C4C2×#4114yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4114yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C42−1+412yes—
546C22×C42−1+412yes—
547C4⋊C4—28no—
548C4⋊C4—216no—
549C4⋊C4—216no—
550C4⋊C4—232no—
551C4⋊C4—44no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C4⋊C4—44no—
558C4⋊C4—84no—
559C4⋊C4—84no—
560C4⋊C4#120116yes—
561C22⋊C4—216no—
562C22⋊C4—216no—
563C22⋊C4—232no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—416no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—416no—
570C22⋊C4—48no—
571C22⋊C4—84no—
572C22⋊C4—84no—
573C22⋊C4—84no—
574C22⋊C4—88no—
575C22⋊C4—88no—
576C42—28no—
577C42—416no—
578C42—44no—
579C42—44no—
580C42—48no—
581C23—24no—
582C23—24no—
583C23—28no—
584C23—28no—
585C23—24no—
586C23—28no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—28no—
591C23—28no—
592C23—28no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—42no—
608C23—42no—
609C23—44no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C2×#12418yes—
639C23C23×D411yescharacteristic
640C23C23×D412yes—
641C23C22×#4112yes—
642C23C22×#4111yescharacteristic
643C23C2×H(5,𝔽2)11yescharacteristic
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×2−1+411yescharacteristic
646C23C2×2−1+411yescharacteristic
647C23#58512yes—
648C23#58512yes—
649C23#58511yescharacteristic
650Q8—432no—
651D4—232no—
652D4—416no—
653D4—464no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—28no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—28no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—432no—
678C2×C4—464no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—432no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4C2×#12018yes—
738C2×C4C2×#12014yes—
739C2×C4C2×#12414yes—
740C2×C4#53514yes—
741C2×C4#54618yes—
742C2×C4#54618yes—
743C2×C4#54714yes—
744C22—28no—
745C22—28no—
746C22—28no—
747C22—44no—
748C22—48no—
749C22—44no—
750C22—48no—
751C22—44no—
752C22—48no—
753C22—44no—
754C22—48no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22C22×#12011yescharacteristic
771C22C22×#12411yescharacteristic
772C22C2×#53511yescharacteristic
773C22C2×#54612yes—
774C22C2×#54612yes—
775C22C2×#54711yescharacteristic
776C22D4×#4112yes—
777C22#347512yes—
778C22#348511yescharacteristic
779C22#348712yes—
780C22#348911yescharacteristic
781C22#348912yes—
782C22#349712yes—
783C22#350011yescharacteristic
784C22#351512yes—
785C22#351512yes—
786C22#351711yescharacteristic
787C22#352011yescharacteristic
788C22#352112yes—
789C22#353912yes—
790C22#354711yescharacteristic
791C22#355211yescharacteristic
792C22#356212yes—
793C4—24no—
794C4—28no—
795C4—42no—
796C4—44no—
797C4—48no—
798C4—44no—
799C4—42no—
800C4—82no—
801C4—81no—
802C4—81no—
803C4—82no—
804C4—81no—
805C4—82no—
806C4—84no—
807C4#243518yes—
808C2—48no—
809C2—84no—
810C2C2×#243511yescharacteristic
811C2#3575711yescharacteristic
812C2#3604211yescharacteristic
813C2#3616411yescharacteristic
814C2#3621311yescharacteristic
815C2#3892011yescharacteristic
816C2#4265211yescharacteristic
817C2#4517512yes—
818C2#4541212yes—
819C2#5910212yes—
820C2#5955012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#547C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2489C2semidirect
3. C2×#2454C2semidirect
4. #16362C2semidirect
5. #15669C2semidirect
6. #15667C2semidirect
7. #15188C2semidirect
8. #15181C2semidirect
9. #15180C2semidirect
10. #14843C2semidirect
11. #14764C2semidirect
12. #13997C2semidirect
13. #13937C2semidirect
14. #13937C2semidirect
15. #13881C2semidirect
16. C4×#394C2semidirect
17. #13820C2semidirect
388. #95#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5472
C2×#24892
C2×#24542
#163622
#156692
#156672
#151882
#151812
#151802
#148432
#147642
#139972
#139372
#138812
C4×#3942
#138202