Finite Group Databasebeta

← #785612

Subgroups — #785612

Order 512.

2986 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2477C212yesmaximal, complemented
2C2×#2359C212yesmaximal, complemented
3#16269C212yesmaximal, complemented
4#15965C211yesmaximal, characteristic, complemented
5#15949C211yesmaximal, characteristic, complemented
6#15521C211yesmaximal, characteristic, complemented
7#15506C211yesmaximal, characteristic, complemented
8#15444C212yesmaximal, complemented
9#15270C212yesmaximal
10#15080C212yesmaximal, complemented
11#15001C211yesmaximal, characteristic, complemented
12#14797C212yesmaximal, complemented
13#14738C212yesmaximal, complemented
14#14175C211yesmaximal, characteristic
15#14140C212yesmaximal, complemented
16#14086C212yesmaximal, complemented
17#14068C212yesmaximal, complemented
18#14063C212yesmaximal, complemented
19C4×#399C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2212yes—
24#2477—216no—
25C2×#400C2212yes—
26C2×#399C2211yescharacteristic
27C2×#397C2212yes—
28C2×#394C2212yes—
29C2×#393C2212yes—
30C2×#392C2211yescharacteristic
31#2359—216no—
32C2×#391C2212yes—
33C2×#389C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#387C2212yes—
40C2×#387C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C22×#95C2212yes—
57#1446C2211yescharacteristic
58#1446C2211yescharacteristic
59#1445C2212yes—
60#1445C2211yescharacteristic
61#1444C2211yescharacteristic
62#1444C2212yes—
63#1444C2211yescharacteristic
64#1444C2212yes—
65#1443C2212yes—
66#1443C2212yes—
67#1443C2212yes—
68#1443C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1442C2211yescharacteristic
72#1442C2212yes—
73#1442C2211yescharacteristic
74#1442C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1439C2212yes—
83#1439C2211yescharacteristic
84#1439C2212yes—
85#1439C2211yescharacteristic
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1438C2211yescharacteristic
90#1438C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1434C2212yes—
98#1434C2212yes—
99#1434C2212yes—
100#1434C2211yescharacteristic
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2211yescharacteristic
108C4×#95C2211yescharacteristic
109C23×Q8C2311yescharacteristic
110C23×D4C2312yes—
111C23×D4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2312yes—
116C2×#123—28no—
117C2×#123—28no—
118C2×#123—28no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8—42no—
121C2×C4×D4—28no—
122C2×C4×D4—42no—
123C2×#117—28no—
124C2×#117—28no—
125C2×#117—44no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161#400—28no—
162#399—24no—
163#397—28no—
164#394—28no—
165#393—28no—
166#392—24no—
167#391—28no—
168#389—28no—
169#388—28no—
170#388—28no—
171#388D4116yescomplemented
172#387—28no—
173#387—28no—
174#387—28no—
175#387—28no—
176#386—28no—
177#386—28no—
178#386—28no—
179#386—28no—
180#386—28no—
181#385—28no—
182#385—28no—
183#385—28no—
184#385—28no—
185C4×C4⋊C4—28no—
186C4×C4⋊C4—42no—
187C4×C22⋊C4—28no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—42no—
191C2×#95—28no—
192C2×#95C2311yescharacteristic
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C2×#95C2311yescharacteristic
235C2×#95C2312yes—
236C2×#95C2312yes—
237C25C2411yescharacteristic
238C25C2412yes—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—41no—
242C22×Q8—42no—
243C22×Q8—41no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—41no—
251C22×D4—41no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4#4114yes—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—41no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299#123—264no—
300C22⋊Q8—416no—
301C4×D4—416no—
302#117—432no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4C2×D418yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
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—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
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⋊C4C2×D418yes—
383C2×C22⋊C4C2×D418yes—
384C2×C22⋊C4C2×D418yes—
385C2×C22⋊C4#4118yes—
386C2×C22⋊C4#4114yes—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C2×D418yes—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—41no—
436#95—42no—
437#95—42no—
438#95—41no—
439#95—42no—
440#95—42no—
441#95—41no—
442#95—42no—
443#95—41no—
444#95—41no—
445#95—42no—
446#95C2×D418yes—
447#95C2×D418yes—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24C22×D414yes—
471C24C2×#4112yes—
472C24C2×#4114yes—
473C24C2×#4114yes—
474C24C2511yescharacteristic
475C2×Q8—44no—
476C2×Q8—48no—
477C2×Q8—84no—
478C2×Q8—82no—
479C2×Q8—82no—
480C2×D4—216no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—44no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—84no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—216no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
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—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
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—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
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—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
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—48no—
588C22×C4—44no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—44no—
601C22×C4—84no—
602C22×C4—82no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4C22×D414yes—
613C22×C4C22×D414yes—
614C22×C4C22×D414yes—
615C22×C4C22×D414yes—
616C22×C4C22×D414yes—
617C22×C4C22×D414yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4112yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C42−1+412yes—
625C4⋊C4—216no—
626C4⋊C4—216no—
627C4⋊C4—216no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—44no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C22⋊C4—216no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—216no—
641C22⋊C4—48no—
642C22⋊C4—44no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—44no—
651C22⋊C4—84no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C42—48no—
655C42—48no—
656C42—44no—
657C42—48no—
658C42—44no—
659C42—84no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—22no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—41no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—41no—
717C23#52518yes—
718C23C23×D412yes—
719C23C22×#4111yescharacteristic
720C23C22×#4112yes—
721C23C22×#4111yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×2−1+411yescharacteristic
724C23#58511yescharacteristic
725C23#58512yes—
726C23#58511yescharacteristic
727C23#58512yes—
728C23#58511yescharacteristic
729Q8—88no—
730D4—416no—
731D4—816no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—432no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
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—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
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—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—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—88no—
840C2×C4—816no—
841C2×C4—816no—
842C2×C4D4214yes—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—42no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—82no—
868C22—82no—
869C22C2×#52512yes—
870C22#345911yescharacteristic
871C22C2×D4211yescharacteristic
872C22D4×#4112yes—
873C22D4×#4112yes—
874C22#347512yes—
875C22#347511yescharacteristic
876C22#348111yescharacteristic
877C22#348512yes—
878C22#348912yes—
879C22#350012yes—
880C22#350511yescharacteristic
881C22#350711yescharacteristic
882C22#351012yes—
883C22#351512yes—
884C22#351511yescharacteristic
885C22#352112yes—
886C22#352112yes—
887C22#353311yescharacteristic
888C22#353511yescharacteristic
889C22#355111yescharacteristic
890C22#356612yes—
891C22#356811yescharacteristic
892C4—24no—
893C4—42no—
894C4—44no—
895C4—44no—
896C4—44no—
897C4—42no—
898C4—42no—
899C4—44no—
900C4—44no—
901C4—44no—
902C4—42no—
903C4—44no—
904C4—81no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—82no—
909C2—48no—
910C2—82no—
911C2#3465511yescharacteristic
912C2#3607012yes—
913C2#3622412yes—
914C2#3958111yescharacteristic
915C2#4225211yescharacteristic
916C2#4352711yescharacteristic
917C2#4445512yes—
918C2#4483111yescharacteristic
919C2#5916512yes—
920C2#5981811yescharacteristic
921C2#6000411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
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×#2477C2semidirect
2. C2×#2359C2semidirect
3. #16269C2semidirect
4. #15965C2semidirect
5. #15949C2semidirect
6. #15521C2semidirect
7. #15506C2semidirect
8. #15444C2semidirect
10. #15080C2semidirect
11. #15001C2semidirect
12. #14797C2semidirect
13. #14738C2semidirect
15. #14140C2semidirect
16. #14086C2semidirect
17. #14068C2semidirect
18. #14063C2semidirect
19. C4×#399C2semidirect
171. #388D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24772
C2×#23592
#162692
#159652
#159492
#155212
#155062
#154442
#152702
#150802
#150012
#147972
#147382
#141752
#141402
#140862
#140682
#140632
C4×#3992