Finite Group Databasebeta

← #4380781

Subgroups — #4380781

Order 512.

2564 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic, complemented
2C2×#2486C211yesmaximal, characteristic
3C2×#2638C211yesmaximal, characteristic
4C2×#2313C211yesmaximal, characteristic, complemented
5#16396C212yesmaximal, complemented
6#16257C212yesmaximal
7#15812C212yesmaximal, complemented
8#15786C212yesmaximal, complemented
9#15778C212yesmaximal, complemented
10#15769C212yesmaximal, complemented
11#15740C212yesmaximal, complemented
12#15737C212yesmaximal, complemented
13#15648C212yesmaximal, complemented
14#15629C212yesmaximal, complemented
15#14837C212yesmaximal, complemented
16#14761C212yesmaximal
17#14660C211yesmaximal, characteristic, complemented
18#14295C211yesmaximal, characteristic, complemented
19#13940C211yesmaximal, characteristic
20C22×#123C2211yescharacteristic
21C22×#123C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2638—28no—
26#2502—28no—
27#2486—28no—
28C2×#398C2211yescharacteristic
29C2×#398C2212yes—
30C2×#398C2212yes—
31C2×#398C2212yes—
32C2×#398C2212yes—
33C2×#397C2212yes—
34C2×#397C2211yescharacteristic
35C2×#397C2212yes—
36C2×#396C2212yes—
37C2×#395C2211yescharacteristic
38C2×#394C2212yes—
39C2×#393C2211yescharacteristic
40#2313—28no—
41C2×#391C2212yes—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#388C2212yes—
45C2×#387C2212yes—
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#387C2212yes—
49C2×#387C2212yes—
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#384C2212yes—
54C2×#381C2211yescharacteristic
55C2×#381C2211yescharacteristic
56C2×#381C2211yescharacteristic
57C2×#381C2211yescharacteristic
58C2×#380C2212yes—
59C2×#380C2211yescharacteristic
60C2×#380C2212yes—
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2212yes—
63#1446C2212yes—
64#1445C2212yes—
65#1445C2212yes—
66#1444C2212yes—
67#1444C2212yes—
68#1444C2212yes—
69#1443C2212yes—
70#1443C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1442C2212yes—
74#1442C2212yes—
75#1442C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1441C2212yes—
80#1441C2212yes—
81#1441C2212yes—
82#1441C2212yes—
83#1441C2212yes—
84#1441C2212yes—
85#1441C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1438C2212yes—
97#1437C2212yes—
98#1437C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105C4⋊#95C2212yes—
106#1434C2211yescharacteristic
107#1434C2211yescharacteristic
108#1434C2212yes—
109C22⋊#95C2211yescharacteristic
110C22⋊#95C2211yescharacteristic
111C23×Q8C2311yescharacteristic
112C23×D4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C2×#123—24no—
118C2×#123—24no—
119C2×#123—42no—
120C2×#123—42no—
121C2×#123—42no—
122C2×#123—42no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C4×D4—24no—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4D418yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168#398—28no—
169#398—28no—
170#398—28no—
171#398—24no—
172#398—44no—
173#397—28no—
174#397—28no—
175#397—24no—
176#396—44no—
177#395—24no—
178#394—28no—
179#393—24no—
180#391—28no—
181#389—28no—
182#389—44no—
183#388—44no—
184#387—28no—
185#387—28no—
186#387—28no—
187#387—28no—
188#387—28no—
189#385—28no—
190#385—28no—
191#385—28no—
192#384—28no—
193#381—24no—
194#381—24no—
195#381—24no—
196#381D418yes—
197#380—24no—
198#380—28no—
199#380—28no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—28no—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2312yes—
247C25C2411yescharacteristic
248C25C2411yescharacteristic
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—42no—
253C22×Q8—42no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—41no—
260C22×D4—41no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—41no—
271C23×C4—41no—
272C23×C4—41no—
273C23×C4—41no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—41no—
277C23×C4—41no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4#4114yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302#123—416no—
303#123—416no—
304C22⋊Q8—416no—
305C4×D4—416no—
306C2×C4⋊C4—232no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C2×D418yes—
360C2×C4⋊C4C2×D418yes—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4C2×D418yes—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—22no—
425#95—22no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95C2×D418yes—
458#95C2×D414yes—
459#95C2×D414yes—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—21no—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C2×#4112yes—
481C24H(5,𝔽2)12yes—
482C24C2511yescharacteristic
483C2×Q8—48no—
484C2×Q8—44no—
485C2×Q8—84no—
486C2×Q8—82no—
487C2×Q8—82no—
488C2×D4—28no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
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—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—48no—
596C22×C4—48no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—48no—
604C22×C4—44no—
605C22×C4—84no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4#121116yes—
617C22×C4C22×D414yes—
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D414yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4H(5,𝔽2)12yes—
628C22×C42−1+414yes—
629C22×C42−1+414yes—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—84no—
641C4⋊C4—84no—
642C4⋊C4—84no—
643C4⋊C4—84no—
644C4⋊C4—84no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C4⋊C4—84no—
648C22⋊C4—216no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—48no—
659C22⋊C4—44no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C42—48no—
663C42—44no—
664C42—84no—
665C42—84no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23C2×#12114yes—
712C23C23×D411yescharacteristic
713C23C23×D411yescharacteristic
714C23C22×#4111yescharacteristic
715C23C2×H(5,𝔽2)11yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×2−1+412yes—
718C23C2×2−1+412yes—
719C23#58512yes—
720C23#58512yes—
721C23#58511yescharacteristic
722C23#58511yescharacteristic
723Q8—88no—
724D4—416no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—416no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
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—42no—
795C2×C4—42no—
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—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
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—88no—
836C2×C4—88no—
837C2×C4—88no—
838C2×C4C2×#12114yes—
839C2×C4C2×#12114yes—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—42no—
844C22—42no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—42no—
854C22—44no—
855C22—42no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—82no—
860C22—82no—
861C22—81no—
862C22C22×#12111yescharacteristic
863C22#344912yes—
864C22#348411yescharacteristic
865C22#348512yes—
866C22#348511yescharacteristic
867C22#348612yes—
868C22#348811yescharacteristic
869C22#348811yescharacteristic
870C22#349111yescharacteristic
871C22#349111yescharacteristic
872C22#349411yescharacteristic
873C22#349411yescharacteristic
874C22#349912yes—
875C22#350911yescharacteristic
876C22#350911yescharacteristic
877C22#353512yes—
878C22#354112yes—
879C22#355312yes—
880C22#355412yes—
881C22#355712yes—
882C22#355912yes—
883C22#356412yes—
884C22#356512yes—
885C4—24no—
886C4—24no—
887C4—44no—
888C4—44no—
889C4—44no—
890C4—44no—
891C4—42no—
892C4—44no—
893C4—44no—
894C4—81no—
895C4—82no—
896C4—81no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C2—44no—
903C2—82no—
904C2#3508911yescharacteristic
905C2#3551411yescharacteristic
906C2#3566711yescharacteristic
907C2#4059912yes—
908C2#4141712yes—
909C2#4682112yes—
910C2#4720812yes—
911C2#5066211yescharacteristic
912C2#5066511yescharacteristic
913C2#5104311yescharacteristic
914C2#5104411yescharacteristic
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×#2502C2semidirect
4. C2×#2313C2semidirect
5. #16396C2semidirect
7. #15812C2semidirect
8. #15786C2semidirect
9. #15778C2semidirect
10. #15769C2semidirect
11. #15740C2semidirect
12. #15737C2semidirect
13. #15648C2semidirect
14. #15629C2semidirect
15. #14837C2semidirect
17. #14660C2semidirect
18. #14295C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#24862
C2×#26382
C2×#23132
#163962
#162572
#158122
#157862
#157782
#157692
#157402
#157372
#156482
#156292
#148372
#147612
#146602
#142952
#139402