Finite Group Databasebeta

← #626528

Subgroups — #626528

Order 512.

3232 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic
2C2×#2409C211yesmaximal, characteristic
3C2×#2310C211yesmaximal, characteristic, complemented
4C2×#2293C211yesmaximal, characteristic
5#15860C214yesmaximal, complemented
6#15832C214yesmaximal, complemented
7#15717C214yesmaximal, complemented
8#15702C214yesmaximal
9#15237C211yesmaximal, characteristic, complemented
10#15236C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#14703C211yesmaximal, characteristic, complemented
14#14703C211yesmaximal, characteristic, complemented
15#14340C211yesmaximal, characteristic, complemented
16#14258C211yesmaximal, characteristic, complemented
17#14258C211yesmaximal, characteristic, complemented
18#13939C211yesmaximal, characteristic, complemented
19#13922C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2485—28no—
28#2409—28no—
29C2×#397C2212yes—
30C2×#395C2212yes—
31C2×#394C2212yes—
32C2×#393C2212yes—
33#2310—28no—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2214yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45#2293—28no—
46C2×#390C2212yes—
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2212yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#387C2212yes—
54C2×#386C2212yes—
55C2×#385C2212yes—
56C2×#384C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#381C2214yes—
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C43C2211yescharacteristic
67#1446C2214yes—
68#1443C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1440C2214yes—
78#1440C2214yes—
79#1440C2214yes—
80#1440C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2214yes—
92#1434C2214yes—
93#1434C2214yes—
94C22⋊#95C2214yes—
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2312yes—
105C23×D4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2311yescharacteristic
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4D418yes—
118C2×#117—24no—
119C2×#117—24no—
120C2×#117—24no—
121C2×#117—24no—
122C2×#117—42no—
123C2×#117—42no—
124C2×#117—42no—
125C2×#117—42no—
126C2×#117D418yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#397—28no—
164#395—28no—
165#394—28no—
166#393—28no—
167#391—24no—
168#391—24no—
169#391—216no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—42no—
177#391—42no—
178#390—28no—
179#389—28no—
180#389—24no—
181#389—24no—
182#388—28no—
183#388—28no—
184#388—28no—
185#387—28no—
186#386—28no—
187#385—28no—
188#384—42no—
189#382—42no—
190#381—216no—
191#380—24no—
192#380—24no—
193#380—24no—
194#380—24no—
195C4×C4⋊C4—24no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C43—24no—
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C22×Q8—232no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—24no—
236C22×Q8—24no—
237C22×Q8—24no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—42no—
248C22×Q8—42no—
249C22×Q8—416no—
250C22×Q8—416no—
251C22×Q8—416no—
252C22×Q8—416no—
253C22×Q8—416no—
254C22×Q8—416no—
255C22×Q8#4114yes—
256C22×Q8#4114yes—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—24no—
260C22×D4—42no—
261C22×D4C2×D414yes—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4#4114yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C22⋊Q8—416no—
301C22⋊Q8—416no—
302C4×D4—232no—
303#117—416no—
304#117—416no—
305#117—416no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
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—24no—
334C2×C4⋊C4—28no—
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—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D418yes—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4C2×D418yes—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42C2×D414yes—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24C22×D412yes—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C2×#4112yes—
458C24C2511yescharacteristic
459C2×Q8—216no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—48no—
470C2×Q8—48no—
471C2×Q8—4128no—
472C2×Q8—48no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—44no—
484C2×D4—48no—
485C2×D4—48no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
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—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
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—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4#121116yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C42−1+414yes—
609C22×C42−1+414yes—
610C4⋊C4—28no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C4⋊C4—88no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C42—28no—
639C42—28no—
640C42—28no—
641C42—48no—
642C42—48no—
643C42—48no—
644C42—44no—
645C42—44no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23C2×#12114yes—
692C23C23×D411yescharacteristic
693C23C23×D411yescharacteristic
694C23C22×#4111yescharacteristic
695C23C22×#4111yescharacteristic
696C23C22×#4111yescharacteristic
697C23C2×H(5,𝔽2)11yescharacteristic
698C23C2×H(5,𝔽2)11yescharacteristic
699C23C2×2−1+412yes—
700C23C2×2−1+412yes—
701C23#58512yes—
702C23#58512yes—
703Q8—432no—
704Q8—416no—
705Q8—416no—
706D4—416no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—432no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
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—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—416no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4C2×#12114yes—
805C2×C4C2×#12114yes—
806C2×C4#52514yes—
807C2×C4#53414yes—
808C2×C4#53614yes—
809C2×C4#54614yes—
810C2×C4#54614yes—
811C2×C4#55114yes—
812C2×C4#55114yes—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—44no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22C22×#12111yescharacteristic
836C22C2×#52511yescharacteristic
837C22C2×#53411yescharacteristic
838C22C2×#53611yescharacteristic
839C22#344911yescharacteristic
840C22#346112yes—
841C22C2×#54611yescharacteristic
842C22C2×#54611yescharacteristic
843C22C2×#55111yescharacteristic
844C22C2×#55111yescharacteristic
845C22#348912yes—
846C22#348912yes—
847C22#349512yes—
848C22#349911yescharacteristic
849C22#350011yescharacteristic
850C22#351612yes—
851C22#351812yes—
852C22#352312yes—
853C22#352412yes—
854C22#354712yes—
855C22#354712yes—
856C22#355012yes—
857C22#355112yes—
858C4—24no—
859C4—24no—
860C4—44no—
861C4—44no—
862C4—42no—
863C4—44no—
864C4—44no—
865C4—44no—
866C4—42no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4#253418yes—
875C2—44no—
876C2—82no—
877C2C2×#253411yescharacteristic
878C2#3530611yescharacteristic
879C2#3530811yescharacteristic
880C2#3566312yes—
881C2#3737612yes—
882C2#3820312yes—
883C2#3820712yes—
884C2#3894611yescharacteristic
885C2#3894811yescharacteristic
886C2#3895411yescharacteristic
887C2#3895811yescharacteristic
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
3. C2×#2310C2semidirect
5. #15860C2semidirect
6. #15832C2semidirect
7. #15717C2semidirect
9. #15237C2semidirect
10. #15236C2semidirect
11. #15184C2semidirect
12. #15182C2semidirect
13. #14703C2semidirect
14. #14703C2semidirect
15. #14340C2semidirect
16. #14258C2semidirect
17. #14258C2semidirect
18. #13939C2semidirect
19. #13922C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24092
C2×#23102
C2×#22932
#158602
#158322
#157172
#157022
#152372
#152362
#151842
#151822
#147032
#143402
#142582
#139392
#139222