Finite Group Databasebeta

← #687701

Subgroups — #687701

Order 512.

3460 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2407C211yesmaximal, characteristic
3C2×#2352C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic, complemented
5#16270C214yesmaximal, complemented
6#15960C214yesmaximal, complemented
7#15293C214yesmaximal, complemented
8#15244C211yesmaximal, characteristic, complemented
9#15241C211yesmaximal, characteristic, complemented
10#15236C211yesmaximal, characteristic, complemented
11#15219C211yesmaximal, characteristic, complemented
12#14798C214yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#14136C211yesmaximal, characteristic, complemented
15#14003C211yesmaximal, characteristic, complemented
16#14002C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13881C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2499—28no—
28#2407—28no—
29C2×#397C2214yes—
30C2×#394C2212yes—
31C2×#392C2212yes—
32#2352—28no—
33#2311—28no—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#388C2212yes—
45C2×#387C2212yes—
46C2×#387C2214yes—
47C2×#386C2212yes—
48C2×#386C2214yes—
49C2×#386C2212yes—
50C2×#385C2212yes—
51C2×#384C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2214yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65#1443C2214yes—
66#1443C2214yes—
67#1443C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2212yes—
72#1440C2212yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2212yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84#1437C2214yes—
85#1437C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90#1434C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C23×D4C2312yes—
105C23×D4C2312yes—
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—42no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4D418yes—
120C2×#117—24no—
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—24no—
124C2×#117—42no—
125C2×#117—42no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—42no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165#397—216no—
166#394—28no—
167#392—28no—
168#391—24no—
169#391—24no—
170#391—24no—
171#391—42no—
172#391D418yescomplemented
173#390—24no—
174#390—24no—
175#390—24no—
176#390—24no—
177#390—42no—
178#388—28no—
179#387—28no—
180#387—216no—
181#386—28no—
182#386—28no—
183#386—216no—
184#385—28no—
185#384—24no—
186#382—24no—
187#382—24no—
188#382—42no—
189#382—42no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—216no—
194C4×C4⋊C4—24no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—42no—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C25C2411yescharacteristic
226C25C2412yes—
227C25C2411yescharacteristic
228C2×#41—232no—
229C2×#41—416no—
230C2×#41—416no—
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8C2×D414yes—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4C2×D414yes—
265C22×D4#4114yes—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4#4114yes—
291C23×C4#4114yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C22⋊Q8—416no—
309#121—416no—
310C4×D4—232no—
311#117—416no—
312#117—416no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—416no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4C2×D414yes—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4C2×D414yes—
395C2×C22⋊C4C2×D414yes—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—42no—
413C2×C42—44no—
414C2×C42C2×D414yes—
415C2×C42C2×D414yes—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—28no—
422#95—24no—
423#95—24no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—28no—
428#95—24no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—42no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95C2×D4116yes—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—21no—
457C24—22no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—24no—
464C24—24no—
465C24—22no—
466C24—24no—
467C24—24no—
468C24—22no—
469C24—22no—
470C24C22×D412yes—
471C24C22×D412yes—
472C24C2×#4114yes—
473C24C2×#4112yes—
474C24C2×#4112yes—
475C24C2511yescharacteristic
476#41—4128no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×D4—216no—
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—84no—
506C2×D4—88no—
507C2×D4—88no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—216no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—88no—
611C22×C4—84no—
612C22×C4—88no—
613C22×C4#123116yes—
614C22×C4C22×D412yes—
615C22×C4C22×D414yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D414yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4112yes—
628C22×C4H(5,𝔽2)12yes—
629C22×C4H(5,𝔽2)12yes—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—416no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—84no—
653C22⋊C4—88no—
654C22⋊C4—88no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—88no—
658C22⋊C4—88no—
659C42—28no—
660C42—28no—
661C42—48no—
662C42—44no—
663C42—44no—
664C42—44no—
665C42—84no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—22no—
690C23—28no—
691C23—28no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—44no—
728C23—42no—
729C23—44no—
730C23—44no—
731C23—42no—
732C23—44no—
733C23—42no—
734C23C2×#12314yes—
735C23C23×D411yescharacteristic
736C23C23×D411yescharacteristic
737C23C22×#4111yescharacteristic
738C23C22×#4111yescharacteristic
739C23C22×#4111yescharacteristic
740C23C2×H(5,𝔽2)11yescharacteristic
741C23C2×H(5,𝔽2)11yescharacteristic
742C23#58512yes—
743C23#58512yes—
744C23#58512yes—
745C23#58512yes—
746Q8—416no—
747D4—416no—
748D4—432no—
749D4—416no—
750D4—816no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—232no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—432no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—416no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—44no—
842C2×C4—816no—
843C2×C4C2×#12314yes—
844C2×C4C2×#12314yes—
845C2×C4#52514yes—
846C2×C4#53814yes—
847C2×C4D4214yes—
848C2×C4#54614yes—
849C2×C4#54614yes—
850C2×C4#55114yes—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—48no—
867C22—42no—
868C22—44no—
869C22—42no—
870C22—48no—
871C22—42no—
872C22—42no—
873C22—44no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—84no—
880C22—82no—
881C22—82no—
882C22—84no—
883C22—82no—
884C22C22×#12311yescharacteristic
885C22C2×#52511yescharacteristic
886C22#344911yescharacteristic
887C22#344911yescharacteristic
888C22C2×#53811yescharacteristic
889C22C2×D4211yescharacteristic
890C22C2×#54611yescharacteristic
891C22C2×#54611yescharacteristic
892C22C2×#55111yescharacteristic
893C22#348712yes—
894C22#349312yes—
895C22#349312yes—
896C22#349312yes—
897C22#350011yescharacteristic
898C22#350011yescharacteristic
899C22#350012yes—
900C22#351212yes—
901C22#352112yes—
902C22#352112yes—
903C22#353912yes—
904C22#355112yes—
905C22#356212yes—
906C22#356212yes—
907C4—24no—
908C4—42no—
909C4—42no—
910C4—42no—
911C4—44no—
912C4—44no—
913C4—44no—
914C4—82no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4—82no—
919C4—82no—
920C4—82no—
921C4—82no—
922C4#241818yes—
923C2—44no—
924C2—82no—
925C2—84no—
926C2C2×#241811yescharacteristic
927C2#3515711yescharacteristic
928C2#3561811yescharacteristic
929C2#3601912yes—
930C2#3768311yescharacteristic
931C2#3809211yescharacteristic
932C2#3894711yescharacteristic
933C2#3935711yescharacteristic
934C2#4268512yes—
935C2#4512912yes—
936C2#4523612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
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×#2499C2semidirect
3. C2×#2352C2semidirect
4. C2×#2311C2semidirect
5. #16270C2semidirect
6. #15960C2semidirect
7. #15293C2semidirect
8. #15244C2semidirect
9. #15241C2semidirect
10. #15236C2semidirect
11. #15219C2semidirect
12. #14798C2semidirect
13. #14340C2semidirect
14. #14136C2semidirect
15. #14003C2semidirect
16. #14002C2semidirect
17. #13937C2semidirect
18. #13881C2semidirect
19. #13839C2semidirect
172. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24072
C2×#23522
C2×#23112
#162702
#159602
#152932
#152442
#152412
#152362
#152192
#147982
#143402
#141362
#140032
#140022
#139372
#138812
#138392