Finite Group Databasebeta

← #649785

Subgroups — #649785

Order 512.

4174 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#125C211yesmaximal, characteristic, complemented
2C2×#2442C212yesmaximal, complemented
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4#15996C214yesmaximal, complemented
5#15847C214yesmaximal, complemented
6#15228C212yesmaximal, complemented
7#15216C212yesmaximal, complemented
8#14843C212yesmaximal, complemented
9#14728C212yesmaximal, complemented
10#14697C211yesmaximal, characteristic, complemented
11#14054C212yesmaximal, complemented
12#14015C212yesmaximal
13#13907C211yesmaximal, characteristic, complemented
14#13881C211yesmaximal, characteristic, complemented
15#13872C211yesmaximal, characteristic
16#13872C212yesmaximal
17C4×#386C211yesmaximal, characteristic
18C22×#125—216no—
19C22×#125—28no—
20C22×#125C2212yes—
21C22×#125C2214yes—
22C22×#125C2212yes—
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2212yes—
29C23×C4⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2442—216no—
32C2×#400C2214yes—
33C2×#398C2214yes—
34D4×C4⋊C4—28no—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#386C2212yes—
39C2×#386C2211yescharacteristic
40C2×#386C2211yescharacteristic
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2214yes—
44C2×#385C2212yes—
45C2×#384C2211yescharacteristic
46C2×#382C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2214yes—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56#1445C2214yes—
57#1444C2214yes—
58#1444C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1441C2214yes—
63#1441C2212yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1439C2214yes—
68#1439C2212yes—
69#1439C2214yes—
70#1437C2212yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2214yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2211yescharacteristic
85C22⋊#95C2211yescharacteristic
86C4×#95C2212yes—
87C23×D4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2312yes—
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C2×#125—2128no—
96C2×#125—28no—
97C2×#125—216no—
98C2×#125—216no—
99C2×#125—28no—
100C2×#125—216no—
101C2×#125—28no—
102C2×#125—28no—
103C2×#125—28no—
104C2×#125D4116yescomplemented
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—28no—
108C2×C4×D4—28no—
109C2×C4×D4—44no—
110C2×C4×D4Q818yes—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—28no—
113C22×C4⋊C4—28no—
114C22×C4⋊C4—28no—
115C22×C4⋊C4—216no—
116C22×C4⋊C4—216no—
117C22×C4⋊C4—28no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—28no—
120C22×C4⋊C4D418yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C42—24no—
150C22×C42—28no—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156#400—216no—
157#398—216no—
158#389—28no—
159#389—28no—
160#389—28no—
161#386—24no—
162#386—28no—
163#386—24no—
164#385—28no—
165#385—28no—
166#385—216no—
167#385—44no—
168#384—24no—
169#382—28no—
170#380—24no—
171#380—24no—
172#380—24no—
173#380—216no—
174#380—28no—
175#380—44no—
176C4×C4⋊C4—24no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—28no—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C25C2411yescharacteristic
204C25C2411yescharacteristic
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4C2×Q814yes—
210C22×D4#4114yes—
211C22×D4#4114yes—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—28no—
220C23×C4—28no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—28no—
236C23×C4—44no—
237C23×C4—42no—
238C23×C4—44no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—44no—
242C23×C4C2×D418yes—
243C23×C4C2×D414yes—
244C23×C4C2×Q814yes—
245C23×C4C2×Q814yes—
246C23×C4#4114yes—
247C23×C4C2414yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2414yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262#125—2128no—
263#125—264no—
264#125—264no—
265C4×D4—232no—
266C4×D4—432no—
267C2×C4⋊C4—232no—
268C2×C4⋊C4—264no—
269C2×C4⋊C4—264no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—232no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—416no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4C2×D418yes—
311C2×C4⋊C4C2×D4116yes—
312C2×C4⋊C4C2×D4116yes—
313C2×C4⋊C4C2×D414yes—
314C2×C4⋊C4C2×D418yes—
315C2×C4⋊C4C2×D418yes—
316C2×C4⋊C4C2×D414yes—
317C2×C4⋊C4C2×Q814yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4C2×Q814yes—
347C2×C22⋊C4C2×Q814yes—
348C2×C42—232no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—42no—
362C2×C42C2×D418yes—
363C2×C42C2×Q814yes—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—28no—
368#95—24no—
369#95—24no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—28no—
378#95—24no—
379#95—44no—
380#95—42no—
381#95—44no—
382#95—44no—
383#95—42no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24C22×D412yes—
401C24C22×Q812yes—
402C24C22×Q812yes—
403C24C2×#4112yes—
404C24C2×#4112yes—
405C24C2×#4112yes—
406C24C2×#4112yes—
407C24C2×#4112yes—
408C24H(5,𝔽2)12yes—
409C242−1+412yes—
410C24C2511yescharacteristic
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—28no—
417C2×D4#125116yescomplemented
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—216no—
434C22×C4—216no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—216no—
466C22×C4—28no—
467C22×C4—216no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—48no—
500C22×C4—416no—
501C22×C4—416no—
502C22×C4—416no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—416no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—416no—
510C22×C4—44no—
511C22×C4—48no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—84no—
521C22×C4—88no—
522C22×C4C22⋊Q8116yes—
523C22×C4C22×D414yes—
524C22×C4C22×D418yes—
525C22×C4C22×D414yes—
526C22×C4C22×D414yes—
527C22×C4C22×D414yes—
528C22×C4C22×D418yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D414yes—
532C22×C4C22×Q812yes—
533C22×C4C22×Q812yes—
534C22×C4C22×Q812yes—
535C22×C4C22×Q812yes—
536C22×C4C22×Q812yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C42−1+414yes—
542C4⋊C4—216no—
543C4⋊C4—232no—
544C4⋊C4—232no—
545C4⋊C4—216no—
546C4⋊C4—232no—
547C4⋊C4—232no—
548C4⋊C4—216no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C4⋊C4—88no—
557C4⋊C4—84no—
558C4⋊C4—88no—
559C4⋊C4#120116yes—
560C22⋊C4—28no—
561C22⋊C4—28no—
562C22⋊C4—48no—
563C22⋊C4—416no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C42—216no—
571C42—216no—
572C42—28no—
573C42—48no—
574C42—48no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23C2×C22⋊Q814yes—
614C23C2×#12514yes—
615C23C2×#12514yescomplemented
616C23#54414yes—
617C23#54614yes—
618C23#54814yes—
619C23#55214yes—
620C23#55314yes—
621C23C23×D411yescharacteristic
622C23C23×D412yes—
623C23C23×Q811yescharacteristic
624C23C22×#4111yescharacteristic
625C23C22×#4111yescharacteristic
626C23C22×#4111yescharacteristic
627C23C2×H(5,𝔽2)11yescharacteristic
628C23C2×2−1+412yes—
629C23C2×2−1+411yescharacteristic
630C23#58512yes—
631C23#58512yes—
632D4—232no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—28no—
647C2×C4—232no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—28no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—28no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—28no—
663C2×C4—24no—
664C2×C4—432no—
665C2×C4—416no—
666C2×C4—432no—
667C2×C4—416no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—816no—
721C2×C4C2×#12018yes—
722C2×C4C2×#12014yes—
723C2×C4C2×C22⋊Q814yes—
724C2×C4C2×C22⋊Q814yes—
725C2×C4C2×#12514yescomplemented
726C2×C4#53614yes—
727C2×C4#54818yes—
728C2×C4D4×Q818yes—
729C22—28no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—28no—
740C22—24no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—44no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22#244218yescomplemented
751C22C22×#12011yescharacteristic
752C22C22×C22⋊Q811yescharacteristic
753C22C22×#12511yescharacteristic
754C22C2×#53611yescharacteristic
755C22C2×#54411yescharacteristic
756C22C2×#54611yescharacteristic
757C22C2×#54812yes—
758C22C2×#54811yescharacteristic
759C22C2×D4×Q812yes—
760C22D4×#4112yes—
761C22D4×#4112yes—
762C22C2×#55211yescharacteristic
763C22C2×#55311yescharacteristic
764C22#348511yescharacteristic
765C22#348711yescharacteristic
766C22#348812yes—
767C22#348912yes—
768C22#350412yes—
769C22#351212yes—
770C22#351512yes—
771C22#351512yes—
772C22#355912yes—
773C22#356312yes—
774C4—28no—
775C4—24no—
776C4—24no—
777C4—42no—
778C4—44no—
779C4—48no—
780C4—44no—
781C4—44no—
782C4—42no—
783C4—82no—
784C4—84no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#240918yes—
789C2—28no—
790C2—44no—
791C2C2×#240911yescharacteristic
792C2C2×#244211yescharacteristic
793C2#3563911yescharacteristic
794C2D4×#12512yes—
795C2#3621211yescharacteristic
796C2#3642811yescharacteristic
797C2#3768712yes—
798C2#3890711yescharacteristic
799C2#3912211yescharacteristic
800C2#5913912yes—
801C2#5914012yes—
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. C23×#125C2semidirect
2. C2×#2442C2semidirect
4. #15996C2semidirect
5. #15847C2semidirect
6. #15228C2semidirect
7. #15216C2semidirect
8. #14843C2semidirect
9. #14728C2semidirect
10. #14697C2semidirect
11. #14054C2semidirect
13. #13907C2semidirect
14. #13881C2semidirect
104. C2×#125D4semidirect
417. C2×D4#125semidirect
615. C23C2×#125semidirect
725. C2×C4C2×#125semidirect
750. C22#2442semidirect

Maximal subgroups

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

subgroupindex
C23×#1252
C2×#24422
C2×D4×C4⋊C42
#159962
#158472
#152282
#152162
#148432
#147282
#146972
#140542
#140152
#139072
#138812
#138722
C4×#3862