Finite Group Databasebeta

← #636509

Subgroups — #636509

Order 512.

2478 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2552C211yesmaximal, characteristic, complemented
2C2×#2285C211yesmaximal, characteristic
3#16571C214yesmaximal, complemented
4#16304C214yesmaximal
5#15228C212yesmaximal, complemented
6#15223C212yesmaximal
7#15221C212yesmaximal, complemented
8#15216C212yesmaximal
9#15152C212yesmaximal, complemented
10#15146C212yesmaximal, complemented
11#14686C211yesmaximal, characteristic
12#14340C212yesmaximal
13#14264C212yesmaximal
14#14151C211yesmaximal, characteristic, complemented
15#13911C211yesmaximal, characteristic, complemented
16#13911C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic
18C22×#125C2212yes—
19C22×#117C2212yes—
20C23×C42C2211yescharacteristic
21#2552—28no—
22C2×#400C2214yes—
23C2×#398C2214yes—
24C2×#389C2212yes—
25C2×#389C2212yes—
26C2×#389C2212yes—
27C2×#389C2212yes—
28#2285—28no—
29C2×#384C2212yes—
30C2×#384C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×#384C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#382C2212yes—
35C2×#382C2212yes—
36C2×#382C2212yes—
37C2×#380C2211yescharacteristic
38C2×#380C2212yes—
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2212yes—
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2212yes—
51#1445C2214yes—
52#1445C2214yes—
53#1444C2214yes—
54#1444C2214yes—
55#1442C2214yes—
56#1442C2214yes—
57#1442C2214yes—
58#1442C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82#1434C2212yes—
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C2×#125—28no—
89C2×#125—44no—
90C2×#125—44no—
91C2×#117—28no—
92C2×#117—28no—
93C2×#117—44no—
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2314yes—
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2314yes—
121C22×C42—24no—
122C22×C42—24no—
123C22×C42Q818yes—
124C22×C42C2312yes—
125C22×C42C2312yes—
126C22×C42C2312yes—
127C22×C42C2312yes—
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132#400—48no—
133#398—216no—
134#389—28no—
135#389—28no—
136#389—44no—
137#389—44no—
138#384—24no—
139#384—24no—
140#384—28no—
141#384—24no—
142#384—24no—
143#382—28no—
144#382—44no—
145#382—44no—
146#380—24no—
147#380—24no—
148#380—28no—
149#380—24no—
150#380—24no—
151#380—28no—
152#380—44no—
153#380—44no—
154C4×C4⋊C4—28no—
155C4×C4⋊C4—24no—
156C4×C4⋊C4—24no—
157C4×C4⋊C4—24no—
158C4×C4⋊C4D418yes—
159C4×C22⋊C4—44no—
160C2×#95C2312yes—
161C2×#95C2314yes—
162C2×#95C2312yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2314yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C25C2411yescharacteristic
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—41no—
203C23×C4—41no—
204C23×C4C2×Q814yes—
205C23×C4C2×Q814yes—
206C23×C4C2×Q814yes—
207C23×C4#4114yes—
208C23×C4#4114yes—
209C23×C4C2414yes—
210C23×C4C2412yes—
211C23×C4C2412yes—
212C23×C4C2412yes—
213C23×C4C2414yes—
214C23×C4C2412yes—
215C23×C4C2412yes—
216C23×C4C2412yes—
217C23×C4C2412yes—
218C23×C4C2412yes—
219C23×C4C2411yescharacteristic
220C23×C4C2411yescharacteristic
221C23×C4C2411yescharacteristic
222C23×C4C2411yescharacteristic
223C23×C4C2411yescharacteristic
224C23×C4C2411yescharacteristic
225#125—432no—
226#117—432no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—28no—
235C2×C4⋊C4—28no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4C2×D414yes—
292C2×C4⋊C4C2×D414yes—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4—44no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—24no—
316C2×C42—232no—
317C2×C42—24no—
318C2×C42—24no—
319C2×C42—24no—
320C2×C42—24no—
321C2×C42—24no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—24no—
326C2×C42C2×D418yes—
327C2×C42C2×D414yes—
328C2×C42C2×Q814yes—
329C2×C42C2×Q814yes—
330C2×C42C2×Q814yes—
331C2×C42C2×Q814yes—
332C2×C42#4114yes—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—24no—
337#95—28no—
338#95—24no—
339#95—24no—
340#95—28no—
341#95—24no—
342#95—28no—
343#95—24no—
344#95—24no—
345#95—44no—
346#95—44no—
347#95—42no—
348#95—42no—
349#95—44no—
350#95—44no—
351#95—44no—
352#95—44no—
353#95—44no—
354#95—44no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—44no—
359#95C2×D418yes—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24C22×Q812yes—
373C24C2×#4112yes—
374C24C2×#4112yes—
375C24C2511yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—28no—
392C22×C4—28no—
393C22×C4—28no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4#125116yescomplemented
483C22×C4C22×D414yes—
484C22×C4C22×D414yes—
485C22×C4C22×D412yes—
486C22×C4C22×D412yes—
487C22×C4C22×D412yes—
488C22×C4C22×Q812yes—
489C22×C4C22×Q812yes—
490C22×C4C22×Q812yes—
491C22×C4C22×Q812yes—
492C22×C4C22×Q812yes—
493C22×C4C22×Q812yes—
494C22×C4C2×#4112yes—
495C22×C4C2×#4112yes—
496C22×C4C2×#4112yes—
497C22×C4C2×#4112yes—
498C22×C4C2×#4112yes—
499C22×C4C2×#4112yes—
500C22×C4C2×#4112yes—
501C22×C4H(5,𝔽2)12yes—
502C22×C4H(5,𝔽2)12yes—
503C22×C4H(5,𝔽2)12yes—
504C22×C4H(5,𝔽2)12yes—
505C22×C42−1+412yes—
506C22×C42−1+412yes—
507C22×C42−1+412yes—
508C22×C42−1+412yes—
509C4⋊C4—28no—
510C4⋊C4—28no—
511C4⋊C4—48no—
512C4⋊C4—48no—
513C4⋊C4—48no—
514C4⋊C4—48no—
515C4⋊C4—416no—
516C4⋊C4—416no—
517C4⋊C4—44no—
518C4⋊C4—48no—
519C4⋊C4—44no—
520C4⋊C4—48no—
521C4⋊C4—44no—
522C4⋊C4—44no—
523C4⋊C4—48no—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C4⋊C4—48no—
527C4⋊C4—84no—
528C4⋊C4—84no—
529C4⋊C4—88no—
530C4⋊C4—88no—
531C22⋊C4—48no—
532C22⋊C4—48no—
533C22⋊C4—48no—
534C22⋊C4—48no—
535C22⋊C4—88no—
536C42—28no—
537C42—28no—
538C42—28no—
539C42—216no—
540C42—48no—
541C42—48no—
542C42—48no—
543C42C22⋊Q8116yes—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C2×#12514yes—
579C23C23×D411yescharacteristic
580C23C23×Q811yescharacteristic
581C23C22×#4111yescharacteristic
582C23C22×#4111yescharacteristic
583C23C22×#4111yescharacteristic
584C23C2×H(5,𝔽2)11yescharacteristic
585C23C2×H(5,𝔽2)11yescharacteristic
586C23C2×H(5,𝔽2)11yescharacteristic
587C23C2×H(5,𝔽2)11yescharacteristic
588C23C2×2−1+411yescharacteristic
589C23C2×2−1+411yescharacteristic
590C23C2×2−1+411yescharacteristic
591C23C2×2−1+411yescharacteristic
592C23#58511yescharacteristic
593C23#58511yescharacteristic
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—232no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—416no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—416no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—44no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—44no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—44no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—44no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
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—44no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4C2×C22⋊Q814yes—
693C2×C4C2×C22⋊Q814yes—
694C2×C4C2×C22⋊Q814yes—
695C2×C4C2×#12514yes—
696C2×C4C2×#12514yes—
697C2×C4#53514yes—
698C2×C4#53614yes—
699C2×C4#54214yes—
700C2×C4#54214yes—
701C2×C4#54414yes—
702C2×C4#54414yes—
703C2×C4#54414yes—
704C2×C4#54414yes—
705C2×C4#54614yes—
706C2×C4#54814yes—
707C2×C4#55214yes—
708C2×C4#55314yes—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22C22×C22⋊Q811yescharacteristic
725C22C22×#12511yescharacteristic
726C22C2×#53511yescharacteristic
727C22C2×#53611yescharacteristic
728C22C2×#54211yescharacteristic
729C22C2×#54211yescharacteristic
730C22C2×#54411yescharacteristic
731C22C2×#54411yescharacteristic
732C22C2×#54411yescharacteristic
733C22C2×#54411yescharacteristic
734C22#345811yescharacteristic
735C22C2×#54611yescharacteristic
736C22C2×#54811yescharacteristic
737C22C2×#55211yescharacteristic
738C22C2×#55311yescharacteristic
739C22#348811yescharacteristic
740C22#348911yescharacteristic
741C22#349411yescharacteristic
742C22#349511yescharacteristic
743C22#350611yescharacteristic
744C22#350611yescharacteristic
745C22#350711yescharacteristic
746C22#350711yescharacteristic
747C22#350811yescharacteristic
748C22#350911yescharacteristic
749C22#351111yescharacteristic
750C22#351111yescharacteristic
751C22#354611yescharacteristic
752C22#354711yescharacteristic
753C22#354811yescharacteristic
754C22#354811yescharacteristic
755C22#354811yescharacteristic
756C22#355411yescharacteristic
757C22#355511yescharacteristic
758C22#355611yescharacteristic
759C4—24no—
760C4—24no—
761C4—24no—
762C4—44no—
763C4—42no—
764C4—44no—
765C4—82no—
766C4—84no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4—82no—
771C4—84no—
772C4—82no—
773C4#244218yes—
774C4#262818yes—
775C2—44no—
776C2C2×#262811yescharacteristic
777C2C2×#244211yescharacteristic
778C2#3518111yescharacteristic
779C2#3525311yescharacteristic
780C2#3528611yescharacteristic
781C2#3762411yescharacteristic
782C2#3764311yescharacteristic
783C2#3947011yescharacteristic
784C2#3947111yescharacteristic
785C2#3947811yescharacteristic
786C2#3947911yescharacteristic
787C2#3972411yescharacteristic
788C2#3972511yescharacteristic
789C2#3973611yescharacteristic
790C2#3973711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2552C2semidirect
3. #16571C2semidirect
5. #15228C2semidirect
7. #15221C2semidirect
9. #15152C2semidirect
10. #15146C2semidirect
14. #14151C2semidirect
15. #13911C2semidirect
16. #13911C2semidirect
482. C22×C4#125semidirect

Maximal subgroups

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

subgroupindex
C2×#25522
C2×#22852
#165712
#163042
#152282
#152232
#152212
#152162
#151522
#151462
#146862
#143402
#142642
#141512
#139112
C4×#3802