Finite Group Databasebeta

← #649080

Subgroups — #649080

Order 512.

2956 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2415C211yesmaximal, characteristic
3C2×#2354C211yesmaximal, characteristic
4C2×#2285C211yesmaximal, characteristic, complemented
5#15479C214yesmaximal
6#15393C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15145C211yesmaximal, characteristic, complemented
11#14782C214yesmaximal, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14191C214yesmaximal, complemented
14#14138C211yesmaximal, characteristic, complemented
15#14050C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2499—28no—
28#2415—28no—
29C2×#398C2214yes—
30C2×#397C2212yes—
31C2×#397C2214yes—
32C2×#394C2212yes—
33#2354—28no—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2212yes—
40C2×#389C2211yescharacteristic
41C2×#389C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#387C2214yes—
46C2×#386C2212yes—
47#2285—28no—
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2214yes—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2214yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1445C2214yes—
66#1445C2214yes—
67#1444C2214yes—
68#1443C2214yes—
69#1443C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1437C2212yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2212yes—
83#1436C2214yes—
84#1436C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—42no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4D418yes—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—42no—
116C2×#117—42no—
117C2×#117—42no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42—24no—
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160#398—216no—
161#397—28no—
162#397—216no—
163#394—28no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—24no—
168#391—42no—
169#390—28no—
170#389—28no—
171#389—24no—
172#388—28no—
173#388—28no—
174#388—28no—
175#387—216no—
176#386—28no—
177#384—24no—
178#384—24no—
179#384—24no—
180#384—24no—
181#382—24no—
182#382—42no—
183#382D418yescomplemented
184#380—24no—
185#380—24no—
186#380—24no—
187#380—216no—
188C4×C4⋊C4—28no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—216no—
191C4×C22⋊C4—24no—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—24no—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—24no—
233C22×D4—42no—
234C22×D4C2×D414yes—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4#4114yes—
255C23×C4#4114yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C22⋊Q8—416no—
274C22⋊Q8—416no—
275C4×D4—232no—
276#117—416no—
277#117—416no—
278#117—416no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
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—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4C2×D414yes—
359C2×C22⋊C4C2×D414yes—
360C2×C42—232no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—22no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—44no—
387C2×C42C2×D414yes—
388C2×C42C2×D414yes—
389C2×C42#4114yes—
390#95—24no—
391#95—28no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—28no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—24no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—42no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95C2×D4116yes—
416#95#4118yes—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24C22×D412yes—
436C24C22×D412yes—
437C24C2×#4112yes—
438C24C2×#4112yes—
439C24C2511yescharacteristic
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—48no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—216no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
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—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
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—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—48no—
552C22×C4#123116yes—
553C22×C4C22×D412yes—
554C22×C4C22×D414yes—
555C22×C4C22×D412yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C2×#4114yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4114yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C42−1+414yes—
573C22×C42−1+412yes—
574C4⋊C4—28no—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—416no—
578C4⋊C4—416no—
579C4⋊C4—416no—
580C4⋊C4—48no—
581C4⋊C4—44no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—84no—
590C22⋊C4—28no—
591C22⋊C4—28no—
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—48no—
601C22⋊C4—84no—
602C22⋊C4—84no—
603C42—216no—
604C42—28no—
605C42—28no—
606C42—28no—
607C42—48no—
608C42—48no—
609C42—48no—
610C42—48no—
611C42—44no—
612C42—44no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23C2×#12314yes—
659C23C23×D411yescharacteristic
660C23C23×D411yescharacteristic
661C23C22×#4111yescharacteristic
662C23C22×#4111yescharacteristic
663C23C22×#4111yescharacteristic
664C23C22×#4112yes—
665C23C2×H(5,𝔽2)11yescharacteristic
666C23C2×2−1+411yescharacteristic
667C23C2×2−1+412yes—
668C23#58512yes—
669C23#58512yes—
670Q8—88no—
671D4—416no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—232no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—432no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4C2×#12314yes—
767C2×C4C2×#12314yes—
768C2×C4#52514yes—
769C2×C4#53214yes—
770C2×C4#53914yes—
771C2×C4D4214yes—
772C2×C4#54714yes—
773C2×C4#54814yes—
774C2×C4#55314yes—
775C2×C4#55618yes—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—44no—
780C22—42no—
781C22—42no—
782C22—44no—
783C22—42no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22C22×#12311yescharacteristic
799C22C2×#52511yescharacteristic
800C22C2×#53211yescharacteristic
801C22#344911yescharacteristic
802C22C2×#53911yescharacteristic
803C22C2×D4211yescharacteristic
804C22C2×#54711yescharacteristic
805C22C2×#54811yescharacteristic
806C22D4×#4112yes—
807C22C2×#55311yescharacteristic
808C22C2×#55612yes—
809C22#347512yes—
810C22#347512yes—
811C22#348912yes—
812C22#349312yes—
813C22#349512yes—
814C22#349911yescharacteristic
815C22#350011yescharacteristic
816C22#350712yes—
817C22#350912yes—
818C22#351712yes—
819C22#355412yes—
820C22#356512yes—
821C4—28no—
822C4—24no—
823C4—24no—
824C4—44no—
825C4—44no—
826C4—42no—
827C4—44no—
828C4—44no—
829C4—42no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4#244318yes—
838C2—44no—
839C2—82no—
840C2C2×#244311yescharacteristic
841C2#3481011yescharacteristic
842C2#3561911yescharacteristic
843C2#3612511yescharacteristic
844C2#3618811yescharacteristic
845C2#3643912yes—
846C2#3768011yescharacteristic
847C2#3787111yescharacteristic
848C2#3991312yes—
849C2#5913812yes—
850C2#5924312yes—
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×#2499C2semidirect
4. C2×#2285C2semidirect
6. #15393C2semidirect
7. #15240C2semidirect
8. #15233C2semidirect
9. #15182C2semidirect
10. #15145C2semidirect
11. #14782C2semidirect
12. #14702C2semidirect
13. #14191C2semidirect
14. #14138C2semidirect
15. #14050C2semidirect
16. #14000C2semidirect
17. #13879C2semidirect
18. #13879C2semidirect
183. #382D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24152
C2×#23542
C2×#22852
#154792
#153932
#152402
#152332
#151822
#151452
#147822
#147022
#141912
#141382
#140502
#140002
#138792
C4×#3862