Finite Group Databasebeta

← #649137

Subgroups — #649137

Order 512.

3586 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2566C211yesmaximal, characteristic, complemented
2C2×#2441C211yesmaximal, characteristic, complemented
3C2×#2339C211yesmaximal, characteristic
4C2×#2297C211yesmaximal, characteristic
5#15439C214yesmaximal, complemented
6#15328C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15238C211yesmaximal, characteristic, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15184C211yesmaximal, characteristic, complemented
11#14769C214yesmaximal, complemented
12#14682C211yesmaximal, characteristic, complemented
13#14028C214yesmaximal, complemented
14#13979C211yesmaximal, characteristic, complemented
15#13979C211yesmaximal, characteristic, complemented
16#13937C211yesmaximal, characteristic
17#13906C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#385C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2566—28no—
27#2441—28no—
28C2×#399C2212yes—
29C2×#396C2214yes—
30C2×#396C2212yes—
31#2339—28no—
32#2297—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2212yes—
46C2×#387C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2214yes—
51C2×#385C2212yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#381C2212yes—
58C2×#380C2211yescharacteristic
59C2×#380C2214yes—
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2214yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C22×#95C2212yes—
67#1445C2214yes—
68#1445C2214yes—
69#1443C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1436C2214yes—
81#1436C2212yes—
82#1436C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87#1434C2214yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41Q818yes—
102C23×Q8C2311yescharacteristic
103C23×D4C2312yes—
104C23×D4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110C2×#125—24no—
111C2×#125—24no—
112C2×#125—42no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—42no—
118C2×C4×D4—42no—
119C2×#117—24no—
120C2×#117—24no—
121C2×#117—42no—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2314yes—
149C22×C42—24no—
150C22×C42—24no—
151C22×C42—42no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#399—28no—
161#396—216no—
162#396—28no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—42no—
168#391—42no—
169#390—24no—
170#390—24no—
171#390—24no—
172#390D418yes—
173#389—24no—
174#389—24no—
175#389—28no—
176#387—28no—
177#386—28no—
178#386—28no—
179#386—216no—
180#385—28no—
181#385—216no—
182#384—24no—
183#384—24no—
184#382—24no—
185#382—42no—
186#382—42no—
187#381—28no—
188#380—24no—
189#380—24no—
190#380—216no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—42no—
193C4×C22⋊C4—24no—
194C4×C22⋊C4—216no—
195C4×C22⋊C4D418yes—
196C2×#95—28no—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C25C2411yescharacteristic
226C25C2412yes—
227C2×#41—232no—
228C2×#41—232no—
229C2×#41—416no—
230C2×#41—416no—
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8C2×Q814yes—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4C2×D414yes—
252C22×D4C2×Q818yes—
253C22×D4C2×Q814yes—
254C22×D4#4114yes—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—28no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4C2×D414yes—
283C23×C4C2×Q818yes—
284C23×C4C2×Q814yes—
285C23×C4#4114yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303#125—416no—
304C4×D4—416no—
305C4×D4—416no—
306#117—416no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
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—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4#4118yescomplemented
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D4116yes—
379C2×C22⋊C4C2×D414yes—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—416no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—28no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—28no—
419#95—28no—
420#95—24no—
421#95—24no—
422#95—44no—
423#95—44no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95C2×D414yes—
432#95C2×D414yes—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—24no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—24no—
444C24—22no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24C22×D412yes—
450C24C22×D414yes—
451C24C22×Q812yes—
452C24C22×Q814yes—
453C24C2×#4114yes—
454C24C2×#4112yes—
455C24C2511yescharacteristic
456#41—4128no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×D4—216no—
465C2×D4—216no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4C22⋊Q8116yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—216no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—216no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—416no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—84no—
583C22×C4—88no—
584C22×C4—84no—
585C22×C4—88no—
586C22×C4—88no—
587C22×C4C22⋊Q8116yes—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D414yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×Q814yes—
598C22×C4C22×Q812yes—
599C22×C4C22×Q812yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C4H(5,𝔽2)12yes—
608C4⋊C4—28no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—88no—
621C4⋊C4—84no—
622C4⋊C4—84no—
623C22⋊C4—28no—
624C22⋊C4—44no—
625C22⋊C4—416no—
626C22⋊C4—416no—
627C22⋊C4—416no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—88no—
635C42—28no—
636C42—28no—
637C42—28no—
638C42—48no—
639C42—48no—
640C42—44no—
641C42—44no—
642C42—44no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—28no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—28no—
660C23—28no—
661C23—24no—
662C23—28no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—28no—
668C23—28no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—44no—
674C23—42no—
675C23—44no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—44no—
680C23—42no—
681C23—44no—
682C23—42no—
683C23—42no—
684C23—44no—
685C23—44no—
686C23—42no—
687C23C2×C22⋊Q818yes—
688C23C2×C22⋊Q814yes—
689C23C23×D411yescharacteristic
690C23C23×D411yescharacteristic
691C23C23×Q811yescharacteristic
692C23C22×#4111yescharacteristic
693C23C22×#4111yescharacteristic
694C23C22×#4112yes—
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23#58512yes—
698C23#58512yes—
699C23#58512yes—
700Q8—416no—
701D4—232no—
702D4—432no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—232no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—816no—
797C2×C4—816no—
798C2×C4C2×C22⋊Q814yes—
799C2×C4C2×C22⋊Q814yes—
800C2×C4C2×C22⋊Q814yes—
801C2×C4#53214yes—
802C2×C4#54314yes—
803C2×C4D4214yes—
804C2×C4#54614yes—
805C2×C4#54614yes—
806C2×C4#55114yes—
807C22—24no—
808C22—24no—
809C22—28no—
810C22—216no—
811C22—24no—
812C22—42no—
813C22—44no—
814C22—44no—
815C22—42no—
816C22—44no—
817C22—44no—
818C22—48no—
819C22—44no—
820C22—42no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—48no—
825C22—44no—
826C22—48no—
827C22—42no—
828C22—44no—
829C22C22×C22⋊Q811yescharacteristic
830C22C22×C22⋊Q811yescharacteristic
831C22C2×#53211yescharacteristic
832C22#344911yescharacteristic
833C22C2×#54311yescharacteristic
834C22C2×D4211yescharacteristic
835C22C2×#54611yescharacteristic
836C22C2×#54611yescharacteristic
837C22D4×#4112yes—
838C22C2×#55111yescharacteristic
839C22#347512yes—
840C22#347512yes—
841C22Q8×#4112yes—
842C22#348512yes—
843C22#349312yes—
844C22#350011yescharacteristic
845C22#350011yescharacteristic
846C22#350412yes—
847C22#350512yes—
848C22#351712yes—
849C22#352112yes—
850C22#353912yes—
851C22#356212yes—
852C4—24no—
853C4—24no—
854C4—42no—
855C4—44no—
856C4—42no—
857C4—44no—
858C4—44no—
859C4—44no—
860C4—44no—
861C4—42no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4#243718yes—
869C2—44no—
870C2—48no—
871C2C2×#243711yescharacteristic
872C2#3494711yescharacteristic
873C2#3562011yescharacteristic
874C2#3612511yescharacteristic
875C2#3621912yes—
876C2#3638611yescharacteristic
877C2#3768211yescharacteristic
878C2#3809211yescharacteristic
879C2#3998512yes—
880C2#5902012yes—
881C2#5928012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2566C2semidirect
2. C2×#2441C2semidirect
5. #15439C2semidirect
6. #15328C2semidirect
7. #15240C2semidirect
8. #15238C2semidirect
9. #15237C2semidirect
10. #15184C2semidirect
11. #14769C2semidirect
12. #14682C2semidirect
13. #14028C2semidirect
14. #13979C2semidirect
15. #13979C2semidirect
17. #13906C2semidirect
18. #13879C2semidirect
19. C4×#385C2semidirect
347. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25662
C2×#24412
C2×#23392
C2×#22972
#154392
#153282
#152402
#152382
#152372
#151842
#147692
#146822
#140282
#139792
#139372
#139062
#138792
C4×#3852