Finite Group Databasebeta

← #617618

Subgroups — #617618

Order 512.

3236 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2563C211yesmaximal, characteristic, complemented
2C2×#2547C211yesmaximal, characteristic, complemented
3C2×#2535C211yesmaximal, characteristic
4C2×#2290C211yesmaximal, characteristic, complemented
5#15737C214yesmaximal, complemented
6#15687C214yesmaximal, complemented
7#15390C214yesmaximal, complemented
8#15314C214yesmaximal, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15219C211yesmaximal, characteristic, complemented
12#15130C211yesmaximal, characteristic, complemented
13#14698C211yesmaximal, characteristic, complemented
14#14682C211yesmaximal, characteristic, complemented
15#14340C211yesmaximal, characteristic, complemented
16#14282C211yesmaximal, characteristic, complemented
17#14257C211yesmaximal, characteristic, complemented
18#13909C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2212yes—
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2563—28no—
29#2547—28no—
30#2535—28no—
31C2×#397C2212yes—
32C2×#397C2212yes—
33C2×#397C2212yes—
34C2×#394C2214yes—
35C2×#393C2214yes—
36C2×#392C2212yes—
37C2×#391C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42#2290—28no—
43C2×#388C2212yes—
44C2×#387C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2214yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2214yes—
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#1446C2214yes—
68#1445C2214yes—
69#1443C2214yes—
70#1443C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1437C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×Q8C2312yes—
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×#124—28no—
108C2×#124—48no—
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—42no—
114C2×#121—42no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4D418yes—
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—42no—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C42—24no—
155C22×C42—24no—
156C22×C42—42no—
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164#397—28no—
165#397—28no—
166#397—28no—
167#394—48no—
168#393—216no—
169#392—28no—
170#391—28no—
171#390—24no—
172#390—24no—
173#390—24no—
174#390—24no—
175#388—28no—
176#387—28no—
177#386—28no—
178#386—28no—
179#386—28no—
180#386—48no—
181#385—28no—
182#384—42no—
183#382—24no—
184#382—24no—
185#382—24no—
186#382—42no—
187#380—24no—
188#380—24no—
189#380—24no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—216no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4D418yescomplemented
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198#376—24no—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C25C2411yescharacteristic
225C25C2412yes—
226C25C2411yescharacteristic
227C22×Q8—24no—
228C22×Q8—24no—
229C22×Q8—24no—
230C22×Q8—44no—
231C22×Q8—44no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—28no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4C2×D414yes—
253C22×D4#4114yes—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C4⋊Q8—416no—
297#124—432no—
298#121—416no—
299#121—416no—
300C4×D4—232no—
301C4×D4—416no—
302#117—416no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
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—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
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—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D418yes—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
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—28no—
350C2×C22⋊C4—28no—
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—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
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⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4C2×D414yes—
386C2×C22⋊C4C2×D414yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—416no—
400C2×C42—44no—
401C2×C42—42no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406C2×C42#4114yes—
407C2×C42#4114yes—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—28no—
414#95—28no—
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—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95C2×D418yes—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—21no—
450C24—22no—
451C24—24no—
452C24—21no—
453C24—22no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24C22×D412yes—
463C24C22×D412yes—
464C24C2×#4114yes—
465C24H(5,𝔽2)14yes—
466C24C2511yescharacteristic
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—48no—
470C2×Q8—88no—
471C2×Q8—88no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—44no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—416no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—88no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
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—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
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—22no—
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—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—48no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—88no—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D414yes—
599C22×C4C22×D414yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4H(5,𝔽2)12yes—
613C22×C42−1+412yes—
614C4⋊C4—28no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—44no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—88no—
626C22⋊C4—28no—
627C22⋊C4—28no—
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—48no—
637C22⋊C4—48no—
638C22⋊C4—88no—
639C22⋊C4—88no—
640C22⋊C4—88no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—88no—
644C42—28no—
645C42—28no—
646C42—28no—
647C42—48no—
648C42—48no—
649C42—44no—
650C42#121116yes—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—28no—
674C23—28no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—41no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—44no—
698C23—42no—
699C23—44no—
700C23—42no—
701C23—44no—
702C23—42no—
703C23—44no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—44no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23—42no—
715C23—44no—
716C23—42no—
717C23—44no—
718C23—42no—
719C23#53514yes—
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C22×#4111yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C2×H(5,𝔽2)12yes—
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×2−1+411yescharacteristic
728C23#58512yes—
729C23#58512yes—
730C23#58512yes—
731Q8—816no—
732D4—416no—
733D4—416no—
734D4—816no—
735D4—816no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—432no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—416no—
781C2×C4—416no—
782C2×C4—42no—
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—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—816no—
825C2×C4C2×#12114yes—
826C2×C4C2×#12114yes—
827C2×C4C2×#12114yes—
828C2×C4#52914yes—
829C2×C4#54214yes—
830C2×C4#54614yes—
831C2×C4#54614yes—
832C2×C4#54714yes—
833C2×C4#54814yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—42no—
845C22—42no—
846C22—44no—
847C22—42no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—44no—
852C22—48no—
853C22—48no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—84no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—84no—
866C22—82no—
867C22C22×#12111yescharacteristic
868C22C2×#52911yescharacteristic
869C22C2×#53511yescharacteristic
870C22#344911yescharacteristic
871C22#344912yes—
872C22C2×#54211yescharacteristic
873C22C2×#54611yescharacteristic
874C22C2×#54611yescharacteristic
875C22C2×#54711yescharacteristic
876C22C2×#54811yescharacteristic
877C22#348812yes—
878C22#349312yes—
879C22#349412yes—
880C22#349412yes—
881C22#350011yescharacteristic
882C22#350011yescharacteristic
883C22#351012yes—
884C22#351312yes—
885C22#352112yes—
886C22#354012yes—
887C22#354212yes—
888C22#355912yes—
889C22#356512yes—
890C4—24no—
891C4—24no—
892C4—42no—
893C4—42no—
894C4—44no—
895C4—44no—
896C4—44no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4#242718yes—
906C2—44no—
907C2—82no—
908C2—84no—
909C2C2×#242711yescharacteristic
910C2#3525211yescharacteristic
911C2#3532711yescharacteristic
912C2#3555012yes—
913C2#3736312yes—
914C2#3784512yes—
915C2#3786411yescharacteristic
916C2#3787011yescharacteristic
917C2#3808211yescharacteristic
918C2#3809411yescharacteristic
919C2#3911812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2535C2
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×#2563C2semidirect
2. C2×#2547C2semidirect
4. C2×#2290C2semidirect
5. #15737C2semidirect
6. #15687C2semidirect
7. #15390C2semidirect
8. #15314C2semidirect
9. #15233C2semidirect
10. #15233C2semidirect
11. #15219C2semidirect
12. #15130C2semidirect
13. #14698C2semidirect
14. #14682C2semidirect
15. #14340C2semidirect
16. #14282C2semidirect
17. #14257C2semidirect
18. #13909C2semidirect
19. #13785C2semidirect
195. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25632
C2×#25472
C2×#25352
C2×#22902
#157372
#156872
#153902
#153142
#152332
#152192
#151302
#146982
#146822
#143402
#142822
#142572
#139092
#137852