Finite Group Databasebeta

← #946473

Subgroups — #946473

Order 512.

3386 conjugacy classes of subgroups.

The subgroup lattice has 961 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2432C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic, complemented
4C2×#2407C211yesmaximal, characteristic
5#17094C214yesmaximal, complemented
6#16346C214yesmaximal, complemented
7#16333C214yesmaximal, complemented
8#15975C214yesmaximal, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15222C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15195C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#15178C211yesmaximal, characteristic, complemented
15#14273C211yesmaximal, characteristic, complemented
16#14261C211yesmaximal, characteristic, complemented
17#14136C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19#13847C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2499—28no—
30#2432—28no—
31#2415—28no—
32#2407—28no—
33C2×#397C2212yes—
34C2×#397C2214yes—
35C2×#394C2212yes—
36C2×#394C2212yes—
37C2×#394C2214yes—
38C2×#392C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2212yes—
51C2×#389C2211yescharacteristic
52C2×#388C2212yes—
53C2×#387C2214yes—
54C2×#386C2212yes—
55C2×#385C2212yes—
56C2×#385C2214yes—
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#1445C2212yes—
68#1444C2214yes—
69#1443C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1438C2212yes—
86#1438C2214yes—
87#1438C2214yes—
88#1438C2214yes—
89#1437C2214yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2214yes—
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—42no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2312yes—
106C23×D4C2312yes—
107C23×D4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—42no—
113C2×C4⋊Q8—42no—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—42no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×#121—24no—
127C2×#121—24no—
128C2×#121—42no—
129C2×C4×D4—42no—
130C2×C4×D4—42no—
131C2×C4×D4D418yes—
132C2×#117—24no—
133C2×#117—24no—
134C2×#117—42no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173#397—28no—
174#397—216no—
175#394—28no—
176#394—28no—
177#394—216no—
178#392—28no—
179#391—24no—
180#391—24no—
181#391—24no—
182#391—42no—
183#391—42no—
184#391—42no—
185#391D418yescomplemented
186#390—24no—
187#390—24no—
188#390—42no—
189#390—42no—
190#389—28no—
191#389—24no—
192#388—28no—
193#387—216no—
194#386—28no—
195#385—28no—
196#385—216no—
197#384—24no—
198#382—24no—
199#380—24no—
200#380—24no—
201C4×C4⋊C4—42no—
202C4×C22⋊C4—24no—
203C4×C22⋊C4—24no—
204C4×C22⋊C4—42no—
205C4×C22⋊C4—42no—
206#376—42no—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C25C2411yescharacteristic
232C25C2411yescharacteristic
233C25C2412yes—
234C2×#41—416no—
235C2×#41—416no—
236C2×#41—416no—
237C2×#41—416no—
238C2×#41—416no—
239C2×#41—416no—
240C2×#41—416no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8C2×D414yes—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—41no—
267C22×D4—41no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4—42no—
271C22×D4—42no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4C2×D414yes—
278C22×D4#4114yes—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C4⋊Q8—416no—
317#124—416no—
318C22⋊Q8—416no—
319C22⋊Q8—416no—
320C22⋊Q8—416no—
321#121—416no—
322C4×D4—416no—
323#117—416no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4C2×D414yes—
414C2×C22⋊C4C2×D414yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—42no—
431C2×C42C2×D414yes—
432C2×C42C2×D414yes—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—28no—
438#95—24no—
439#95—24no—
440#95—28no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95C2×D4116yes—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—24no—
478C24—22no—
479C24—24no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—24no—
484C24—24no—
485C24—22no—
486C24—22no—
487C24C22×D412yes—
488C24C22×D412yes—
489C24C2×#4114yes—
490C24C2511yescharacteristic
491#41—4128no—
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—84no—
528C2×D4—88no—
529C2×D4—88no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—22no—
618C22×C4—24no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D414yes—
638C22×C4C22×D414yes—
639C22×C4C22×D414yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C2×#4112yes—
644C22×C4H(5,𝔽2)12yes—
645C22×C4H(5,𝔽2)12yes—
646C22×C4H(5,𝔽2)12yes—
647C22×C4H(5,𝔽2)12yes—
648C22×C42−1+414yes—
649C4⋊C4—28no—
650C4⋊C4—44no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—416no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—416no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—48no—
665C22⋊C4—416no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—416no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—88no—
680C22⋊C4—88no—
681C42—28no—
682C42—28no—
683C42—48no—
684C42—44no—
685C42—44no—
686C42—44no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—28no—
705C23—28no—
706C23—42no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—44no—
720C23—42no—
721C23—44no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—44no—
735C23—42no—
736C23—44no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—44no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—44no—
746C23—44no—
747C23—42no—
748C23—42no—
749C23—44no—
750C23—42no—
751C23—42no—
752C23—44no—
753C23—44no—
754C23—42no—
755C23—42no—
756C23C23×D411yescharacteristic
757C23C23×D411yescharacteristic
758C23C22×#4111yescharacteristic
759C23C2×H(5,𝔽2)11yescharacteristic
760C23C2×H(5,𝔽2)11yescharacteristic
761C23C2×H(5,𝔽2)11yescharacteristic
762C23C2×H(5,𝔽2)11yescharacteristic
763C23C2×2−1+412yes—
764C23#58512yes—
765C23#58512yes—
766C23#58512yes—
767Q8—416no—
768Q8—88no—
769D4—416no—
770D4—432no—
771D4—416no—
772D4—816no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—432no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
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—42no—
823C2×C4—44no—
824C2×C4—416no—
825C2×C4—416no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—44no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4#53414yes—
868C2×C4#53514yes—
869C2×C4#53814yes—
870C2×C4D4214yes—
871C2×C4#54614yes—
872C2×C4#54614yes—
873C2×C4#56014yes—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—48no—
883C22—44no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—44no—
889C22—42no—
890C22—44no—
891C22—42no—
892C22—48no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—84no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22—84no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22C2×#53411yescharacteristic
908C22C2×#53511yescharacteristic
909C22#344911yescharacteristic
910C22#344911yescharacteristic
911C22C2×#53811yescharacteristic
912C22C2×D4211yescharacteristic
913C22C2×#54611yescharacteristic
914C22C2×#54611yescharacteristic
915C22#348712yes—
916C22#348912yes—
917C22#349911yescharacteristic
918C22#350011yescharacteristic
919C22#351512yes—
920C22#352112yes—
921C22C2×#56011yescharacteristic
922C22#353912yes—
923C22#354012yes—
924C22#354012yes—
925C22#354112yes—
926C22#354112yes—
927C22#354712yes—
928C22#355412yes—
929C22#356212yes—
930C4—42no—
931C4—44no—
932C4—42no—
933C4—44no—
934C4—42no—
935C4—42no—
936C4—44no—
937C4—44no—
938C4—82no—
939C4—82no—
940C4—82no—
941C4—82no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4#267818yes—
946C2—82no—
947C2—82no—
948C2—84no—
949C2#3738811yescharacteristic
950C2#3745511yescharacteristic
951C2#3768011yescharacteristic
952C2#3768311yescharacteristic
953C2#3808811yescharacteristic
954C2#3809411yescharacteristic
955C2#4270912yes—
956C2#4288712yes—
957C2#4541212yes—
958C2C2×#267811yescharacteristic
959C2#5305112yes—
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
2. C2×#2432C2semidirect
3. C2×#2415C2semidirect
5. #17094C2semidirect
6. #16346C2semidirect
7. #16333C2semidirect
8. #15975C2semidirect
9. #15236C2semidirect
10. #15222C2semidirect
11. #15215C2semidirect
12. #15195C2semidirect
13. #15180C2semidirect
14. #15178C2semidirect
15. #14273C2semidirect
16. #14261C2semidirect
17. #14136C2semidirect
18. #13937C2semidirect
19. #13847C2semidirect
185. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24322
C2×#24152
C2×#24072
#170942
#163462
#163332
#159752
#152362
#152222
#152152
#151952
#151802
#151782
#142732
#142612
#141362
#139372
#138472