Finite Group Databasebeta

← #769970

Subgroups — #769970

Order 512.

2738 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2566C211yesmaximal, characteristic
3C2×#2330C211yesmaximal, characteristic, complemented
4C2×#2326C211yesmaximal, characteristic
5#15866C214yesmaximal, complemented
6#15441C214yesmaximal, complemented
7#15361C214yesmaximal, complemented
8#15305C214yesmaximal, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15222C211yesmaximal, characteristic
11#15184C211yesmaximal, characteristic, complemented
12#15134C211yesmaximal, characteristic
13#14153C211yesmaximal, characteristic
14#14153C211yesmaximal, characteristic
15#13926C211yesmaximal, characteristic, complemented
16#13911C211yesmaximal, characteristic, complemented
17#13910C211yesmaximal, characteristic, complemented
18#13906C211yesmaximal, characteristic
19#13856C211yesmaximal, characteristic, complemented
20C22×#125C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24#2566—28no—
25#2565—28no—
26C2×#398C2214yes—
27C2×#396C2214yes—
28C2×#396C2214yes—
29#2330—28no—
30#2326—28no—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#389C2212yes—
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#389C2214yes—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#387C2214yes—
49C2×#387C2212yes—
50C2×#387C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#385C2214yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2214yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×#376C2211yescharacteristic
70#1444C2212yes—
71#1444C2212yes—
72#1444C2212yes—
73#1444C2212yes—
74#1444C2214yes—
75#1443C2214yes—
76#1442C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1437C2214yes—
88#1437C2214yes—
89C4⋊#95C2214yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2312yes—
98C2×#125—24no—
99C2×#125—24no—
100C2×#125D418yes—
101C2×#124—24no—
102C2×#124—24no—
103C2×#124Q818yes—
104C2×C4×Q8—24no—
105C2×C4×Q8—24no—
106C2×C4×Q8—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C42C2312yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#398—216no—
153#396—216no—
154#396—48no—
155#391—24no—
156#391—24no—
157#391—24no—
158#391—42no—
159#391—42no—
160#390—24no—
161#390—24no—
162#390—24no—
163#390—42no—
164#390—42no—
165#389—24no—
166#389—24no—
167#389—28no—
168#389—28no—
169#389—48no—
170#388—28no—
171#388—28no—
172#387—216no—
173#387—28no—
174#387—28no—
175#385—216no—
176#385—28no—
177#385—28no—
178#384—24no—
179#384—24no—
180#384—24no—
181#384—24no—
182#382—24no—
183#382—24no—
184#380—48no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—24no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—42no—
192C4×C4⋊C4—42no—
193#376D418yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C25C2412yes—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8C2×Q814yes—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4C2×Q814yes—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—44no—
239C23×C4—44no—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258#125—232no—
259#124—232no—
260C4×Q8—416no—
261C4×D4—416no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D418yes—
324C2×C4⋊C4C2×D418yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
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⋊C4C2×Q818yes—
349C2×C22⋊C4C2×Q818yes—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—44no—
370C2×C42—44no—
371C2×C42C2×D414yes—
372C2×C42C2×D414yes—
373C2×C42C2×D414yes—
374C2×C42C2×D414yes—
375C2×C42C2×Q814yes—
376C2×C42#4114yes—
377C2×C42#4114yes—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—28no—
390#95—24no—
391#95—24no—
392#95—28no—
393#95—42no—
394#95—42no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95C2×D414yes—
401#95C2×D414yes—
402#95C2×D414yes—
403#95C2×D414yes—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—24no—
409C24—22no—
410C24—24no—
411C24—22no—
412C24—24no—
413C24—24no—
414C24C22×Q814yes—
415C24C2511yescharacteristic
416C2×Q8—28no—
417C2×Q8—28no—
418C2×Q8—28no—
419C2×Q8—44no—
420C2×Q8—44no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
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—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—416no—
507C22×C4—48no—
508C22×C4—88no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4C22×D412yes—
512C22×C4C22×D414yes—
513C22×C4C22×D412yes—
514C22×C4C22×D414yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×Q814yes—
524C22×C4C22×Q812yes—
525C22×C4C22×Q812yes—
526C22×C4C22×Q812yes—
527C22×C4C2×#4112yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4C2×#4112yes—
531C22×C4C2×#4112yes—
532C22×C4C2×#4112yes—
533C22×C4H(5,𝔽2)14yes—
534C22×C4H(5,𝔽2)12yes—
535C22×C42−1+414yes—
536C22×C42−1+412yes—
537C4⋊C4—216no—
538C4⋊C4—216no—
539C4⋊C4—216no—
540C4⋊C4—28no—
541C4⋊C4—28no—
542C4⋊C4—48no—
543C4⋊C4—48no—
544C4⋊C4—416no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—44no—
549C4⋊C4—48no—
550C4⋊C4—44no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C4⋊C4—84no—
556C4⋊C4—84no—
557C4⋊C4—88no—
558C4⋊C4—84no—
559C4⋊C4—84no—
560C22⋊C4—216no—
561C22⋊C4—216no—
562C22⋊C4—416no—
563C22⋊C4—48no—
564C22⋊C4—88no—
565C22⋊C4—84no—
566C22⋊C4—84no—
567C22⋊C4—88no—
568C22⋊C4—88no—
569C42—28no—
570C42—48no—
571C42—44no—
572C42—44no—
573C42—44no—
574C42—44no—
575C42—84no—
576C42—84no—
577C42#121116yes—
578C42C22⋊Q8116yes—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—28no—
583C23—28no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—44no—
589C23—44no—
590C23—44no—
591C23—44no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23C23×D411yescharacteristic
603C23C23×D411yescharacteristic
604C23C23×Q811yescharacteristic
605C23C22×#4111yescharacteristic
606C23C22×#4111yescharacteristic
607C23C2×H(5,𝔽2)11yescharacteristic
608C23C2×H(5,𝔽2)12yes—
609C23C2×2−1+411yescharacteristic
610C23C2×2−1+412yes—
611C23#58512yes—
612C23#58512yes—
613Q8—416no—
614D4—416no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—28no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—28no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—816no—
707C2×C4C2×#12114yes—
708C2×C4C2×#12114yes—
709C2×C4C2×#12114yes—
710C2×C4C2×C22⋊Q814yes—
711C2×C4C2×C22⋊Q814yes—
712C2×C4C2×C22⋊Q814yes—
713C2×C4#53714yes—
714C2×C4D4×Q814yes—
715C2×C4#55014yes—
716C2×C4#55414yes—
717C2×C4#55614yes—
718C22—44no—
719C22—44no—
720C22—48no—
721C22—48no—
722C22—44no—
723C22—82no—
724C22—82no—
725C22—84no—
726C22—84no—
727C22—82no—
728C22—82no—
729C22C22×#12111yescharacteristic
730C22C22×C22⋊Q811yescharacteristic
731C22C2×#53711yescharacteristic
732C22C2×D4×Q811yescharacteristic
733C22C2×#55011yescharacteristic
734C22C2×#55411yescharacteristic
735C22C2×#55611yescharacteristic
736C22#348812yes—
737C22#348912yes—
738C22#349212yes—
739C22#349312yes—
740C22#349811yescharacteristic
741C22#349911yescharacteristic
742C22#350011yescharacteristic
743C22#350011yescharacteristic
744C22#350312yes—
745C22#350412yes—
746C22#350612yes—
747C22#350712yes—
748C22#354112yes—
749C22#354212yes—
750C22#355412yes—
751C22#355512yes—
752C4—24no—
753C4—24no—
754C4—24no—
755C4—24no—
756C4—42no—
757C4—44no—
758C4—44no—
759C4—44no—
760C4—44no—
761C4—42no—
762C4—44no—
763C4—82no—
764C4—82no—
765C4—82no—
766C4—82no—
767C4—82no—
768C4—82no—
769C4#253818yes—
770C2—84no—
771C2C2×#253811yescharacteristic
772C2#3553211yescharacteristic
773C2#3553311yescharacteristic
774C2#3562011yescharacteristic
775C2#3562111yescharacteristic
776C2#3730111yescharacteristic
777C2#3738911yescharacteristic
778C2#4496612yes—
779C2#4498012yes—
780C2#4537012yes—
781C2#4542412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
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×#2565C2semidirect
3. C2×#2330C2semidirect
5. #15866C2semidirect
6. #15441C2semidirect
7. #15361C2semidirect
8. #15305C2semidirect
9. #15237C2semidirect
11. #15184C2semidirect
15. #13926C2semidirect
16. #13911C2semidirect
17. #13910C2semidirect
19. #13856C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#25662
C2×#23302
C2×#23262
#158662
#154412
#153612
#153052
#152372
#152222
#151842
#151342
#141532
#139262
#139112
#139102
#139062
#138562