Finite Group Databasebeta

← #649072

Subgroups — #649072

Order 512.

3072 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic
3C2×#2352C211yesmaximal, characteristic
4C22×#382C211yesmaximal, characteristic, complemented
5#15706C214yesmaximal, complemented
6#15395C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15231C211yesmaximal, characteristic, complemented
11#14737C214yesmaximal
12#14702C211yesmaximal, characteristic, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14050C211yesmaximal, characteristic, complemented
15#14003C211yesmaximal, characteristic, complemented
16#13980C214yesmaximal, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2499—28no—
28#2417—28no—
29C2×#398C2212yes—
30C2×#397C2214yes—
31C2×#396C2212yes—
32#2352—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#388C2212yes—
40C2×#387C2212yes—
41C2×#387C2214yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#385C2214yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#382—28no—
49C2×#382C2214yes—
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2211yescharacteristic
64C22×#95C2214yes—
65#1445C2214yes—
66#1445C2214yes—
67#1444C2214yes—
68#1443C2214yes—
69#1443C2214yes—
70#1443C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1437C2212yes—
79#1436C2212yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89#1434C2214yes—
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4D418yes—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—42no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157#398—28no—
158#397—216no—
159#396—28no—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—42no—
165#389—24no—
166#388—28no—
167#387—28no—
168#387—216no—
169#386—28no—
170#386—28no—
171#386—28no—
172#385—216no—
173#384—24no—
174#384—42no—
175#382—24no—
176#382—24no—
177#382—24no—
178#382—24no—
179#382—216no—
180#382D418yescomplemented
181#380—24no—
182#380—24no—
183#380—24no—
184#380—28no—
185C4×C4⋊C4—24no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—28no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—24no—
190C2×#95—216no—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
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—24no—
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—24no—
251C23×C4—24no—
252C23×C4—28no—
253C23×C4—28no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C2×D414yes—
263C23×C4C2×D414yes—
264C23×C4#4114yes—
265C23×C4#4114yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C22⋊Q8—416no—
284C22⋊Q8—416no—
285C4×D4—232no—
286#117—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—416no—
322C2×C4⋊C4—416no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
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—28no—
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—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4C2×D414yes—
361C2×C22⋊C4C2×D414yes—
362C2×C22⋊C4#4118yes—
363C2×C42—232no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—42no—
383C2×C42—44no—
384C2×C42C2×D414yes—
385C2×C42C2×D414yes—
386C2×C42#4114yes—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—24no—
403#95—24no—
404#95—28no—
405#95—28no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—42no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—42no—
415#95—44no—
416#95C2×D4116yes—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24C22×D412yes—
434C24C22×D412yes—
435C24C2×#4112yes—
436C24C2×#4112yes—
437C24C2×#4114yes—
438C242−1+414yes—
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—28no—
450C2×D4—48no—
451C2×D4—48no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—216no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—416no—
551C22×C4—416no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—88no—
563C22×C4—88no—
564C22×C4#123116yes—
565C22×C4C22×D412yes—
566C22×C4C22×D414yes—
567C22×C4C22×D414yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D414yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C2×#4114yes—
575C22×C4C2×#4114yes—
576C22×C4C2×#4114yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4112yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4H(5,𝔽2)12yes—
583C22×C42−1+412yes—
584C4⋊C4—28no—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—416no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C4⋊C4—48no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—84no—
598C4⋊C4—88no—
599C22⋊C4—28no—
600C22⋊C4—216no—
601C22⋊C4—28no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—84no—
609C22⋊C4—84no—
610C42—216no—
611C42—28no—
612C42—28no—
613C42—28no—
614C42—48no—
615C42—44no—
616C42—44no—
617C42—84no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23C2×#12314yes—
660C23#53214yes—
661C23#53614yes—
662C23#55218yes—
663C23#55618yes—
664C23C23×D411yescharacteristic
665C23C23×D411yescharacteristic
666C23C22×#4111yescharacteristic
667C23C22×#4111yescharacteristic
668C23C22×#4111yescharacteristic
669C23C22×#4112yes—
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×2−1+412yes—
672C23C2×2−1+411yescharacteristic
673C23#58512yes—
674C23#58512yes—
675Q8—88no—
676D4—416no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—232no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—432no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
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—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—416no—
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—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—816no—
774C2×C4—816no—
775C2×C4C2×#12314yes—
776C2×C4C2×#12314yes—
777C2×C4#52514yes—
778C2×C4#53914yes—
779C2×C4D4214yes—
780C2×C4#54714yes—
781C2×C4#54814yes—
782C2×C4#55314yes—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—28no—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—24no—
792C22—28no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22#249918yescomplemented
805C22C22×#12311yescharacteristic
806C22C2×#52511yescharacteristic
807C22C2×#53211yescharacteristic
808C22C2×#53611yescharacteristic
809C22C2×#53911yescharacteristic
810C22C2×D4211yescharacteristic
811C22C2×#54711yescharacteristic
812C22C2×#54811yescharacteristic
813C22D4×#4112yes—
814C22C2×#55212yes—
815C22C2×#55311yescharacteristic
816C22C2×#55612yes—
817C22#347512yes—
818C22#348912yes—
819C22#349312yes—
820C22#349512yes—
821C22#350011yescharacteristic
822C22#350011yescharacteristic
823C22#351212yes—
824C22#351412yes—
825C22#351512yes—
826C22#356112yes—
827C22#356312yes—
828C4—24no—
829C4—44no—
830C4—44no—
831C4—42no—
832C4—44no—
833C4—44no—
834C4—44no—
835C4—42no—
836C4—44no—
837C4—42no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4#244318yes—
845C2—28no—
846C2—82no—
847C2C2×#244311yescharacteristic
848C2C2×#249911yescharacteristic
849C2#3561811yescharacteristic
850C2#3612411yescharacteristic
851C2#3618411yescharacteristic
852C2#3643912yes—
853C2#3767611yescharacteristic
854C2#3786511yescharacteristic
855C2#3915512yes—
856C2#5914012yes—
857C2#5930912yes—
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. C22×#382C2semidirect
5. #15706C2semidirect
6. #15395C2semidirect
7. #15240C2semidirect
8. #15236C2semidirect
9. #15233C2semidirect
10. #15231C2semidirect
12. #14702C2semidirect
13. #14139C2semidirect
14. #14050C2semidirect
15. #14003C2semidirect
16. #13980C2semidirect
17. #13880C2semidirect
18. #13879C2semidirect
180. #382D4semidirect
804. C22#2499semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24172
C2×#23522
C22×#3822
#157062
#153952
#152402
#152362
#152332
#152312
#147372
#147022
#141392
#140502
#140032
#139802
#138802
#138792
C4×#3862