Finite Group Databasebeta

← #875305

Subgroups — #875305

Order 512.

3204 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2562C211yesmaximal, characteristic, complemented
2C2×#2407C211yesmaximal, characteristic
3#16797C214yesmaximal, complemented
4#15756C214yesmaximal, complemented
5#15529C214yesmaximal, complemented
6#15238C211yesmaximal, characteristic, complemented
7#15236C211yesmaximal, characteristic, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15229C211yesmaximal, characteristic, complemented
11#15219C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14698C211yesmaximal, characteristic, complemented
14#14427C214yesmaximal, complemented
15#14003C211yesmaximal, characteristic, complemented
16#14002C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2562—28no—
27#2407—28no—
28C2×#400C2212yes—
29C2×#394C2212yes—
30C2×#394C2212yes—
31C2×#392C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#386C2212yes—
45C2×#386C2214yes—
46C2×#386C2212yes—
47C2×#385C2212yes—
48C2×#382C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59#1443C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1438C2214yes—
73#1438C2214yes—
74#1438C2214yes—
75#1437C2214yes—
76#1437C2214yes—
77#1437C2212yes—
78#1436C2214yes—
79#1436C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86#1434C2214yes—
87C22⋊#95C2212yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C22×#41—24no—
94C22×#41—24no—
95C22×#41—24no—
96C22×#41—42no—
97C22×#41—42no—
98C22×#41—42no—
99C22×#41—42no—
100C23×Q8C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C23×D4C2312yes—
103C23×D4C2312yes—
104C23×D4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2312yes—
109C2×#125—24no—
110C2×#125—42no—
111C2×#125—42no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—42no—
118C2×C4×D4—42no—
119C2×C4×D4—42no—
120C2×C4×D4D418yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C42—42no—
150C22×C42—42no—
151C22×C42—42no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159#400—28no—
160#394—28no—
161#394—28no—
162#392—28no—
163#391—24no—
164#391—24no—
165#391—42no—
166#391—42no—
167#391—42no—
168#390—24no—
169#390—24no—
170#390—42no—
171#390—42no—
172#390—42no—
173#388—28no—
174#388—28no—
175#386—28no—
176#386—216no—
177#386—28no—
178#385—28no—
179#382—42no—
180#382—42no—
181#380—24no—
182#380—24no—
183#380—24no—
184#380—24no—
185#380—24no—
186C4×C4⋊C4—24no—
187C4×C22⋊C4—42no—
188C4×C22⋊C4—42no—
189C4×C22⋊C4—42no—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C25C2411yescharacteristic
218C25C2412yes—
219C25C2411yescharacteristic
220C2×#41—416no—
221C2×#41—416no—
222C2×#41—416no—
223C2×#41—416no—
224C2×#41—416no—
225C2×#41—416no—
226C2×#41—416no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8#4114yes—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—28no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—41no—
248C22×D4—41no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—44no—
256C22×D4C2×D414yes—
257C22×D4#4114yes—
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—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4#4118yescomplemented
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302#125—416no—
303C22⋊Q8—416no—
304#121—416no—
305C4×D4—416no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4C2×D414yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
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—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
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⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—416no—
402C2×C42—44no—
403C2×C42C2×D414yes—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—44no—
418#95—44no—
419#95—42no—
420#95—42no—
421#95—44no—
422#95—44no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—24no—
457C24—24no—
458C24—22no—
459C24—24no—
460C24C22×D412yes—
461C24C22×D412yes—
462C24C2×#4114yes—
463C24C2×#4114yes—
464C24C2511yescharacteristic
465#41—4128no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—416no—
490C2×D4—48no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—84no—
496C2×D4—88no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
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—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
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—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
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—24no—
550C22×C4—24no—
551C22×C4—24no—
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—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C4H(5,𝔽2)12yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C4H(5,𝔽2)12yes—
621C4⋊C4—44no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—84no—
642C22⋊C4—88no—
643C22⋊C4—88no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C22⋊C4—88no—
648C22⋊C4—88no—
649C42—28no—
650C42—48no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—84no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—28no—
677C23—22no—
678C23—22no—
679C23—28no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—44no—
706C23—44no—
707C23—42no—
708C23—44no—
709C23—42no—
710C23—44no—
711C23—42no—
712C23—42no—
713C23—44no—
714C23—42no—
715C23—41no—
716C23—42no—
717C23—44no—
718C23—42no—
719C23—44no—
720C23—42no—
721C23—44no—
722C23—44no—
723C23—42no—
724C23#53214yes—
725C23C23×D411yescharacteristic
726C23C22×#4112yes—
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C2×H(5,𝔽2)11yescharacteristic
730C23C2×H(5,𝔽2)11yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23#58512yes—
734C23#58512yes—
735C23#58512yes—
736Q8—416no—
737D4—416no—
738D4—432no—
739D4—416no—
740D4—816no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—432no—
763C2×C4—432no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—416no—
789C2×C4—416no—
790C2×C4—42no—
791C2×C4—42no—
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—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4#53414yes—
835C2×C4#53814yes—
836C2×C4#53814yes—
837C2×C4#54614yes—
838C2×C4#54614yes—
839C2×C4#55114yes—
840C2×C4H(3,𝔽4)14yes—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—44no—
846C22—44no—
847C22—42no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—48no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—48no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—84no—
869C22—82no—
870C22—84no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22C2×#53211yescharacteristic
875C22C2×#53411yescharacteristic
876C22#344911yescharacteristic
877C22C2×#53811yescharacteristic
878C22C2×#53811yescharacteristic
879C22C2×#54611yescharacteristic
880C22C2×#54611yescharacteristic
881C22C2×#55111yescharacteristic
882C22#347512yes—
883C22#348012yes—
884C22#350011yescharacteristic
885C22#350011yescharacteristic
886C22#350512yes—
887C22#350512yes—
888C22#350512yes—
889C22#350612yes—
890C22#352112yes—
891C22#352412yes—
892C22C2×H(3,𝔽4)11yescharacteristic
893C22#353912yes—
894C22#353912yes—
895C22#353912yes—
896C22#355112yes—
897C4—42no—
898C4—42no—
899C4—42no—
900C4—44no—
901C4—44no—
902C4—44no—
903C4—42no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4—82no—
912C4#268418yes—
913C2—44no—
914C2—84no—
915C2—82no—
916C2#3503211yescharacteristic
917C2#3638611yescharacteristic
918C2#3639611yescharacteristic
919C2#3741811yescharacteristic
920C2#3809211yescharacteristic
921C2#3809311yescharacteristic
922C2#3953712yes—
923C2#3979512yes—
924C2#4550912yes—
925C2C2×#268411yescharacteristic
926C2#5937412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
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×#2562C2semidirect
3. #16797C2semidirect
4. #15756C2semidirect
5. #15529C2semidirect
6. #15238C2semidirect
7. #15236C2semidirect
8. #15233C2semidirect
9. #15233C2semidirect
10. #15229C2semidirect
11. #15219C2semidirect
12. #14702C2semidirect
13. #14698C2semidirect
14. #14427C2semidirect
15. #14003C2semidirect
16. #14002C2semidirect
17. #13937C2semidirect
18. #13937C2semidirect
19. C4×#386C2semidirect
285. C23×C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25622
C2×#24072
#167972
#157562
#155292
#152382
#152362
#152332
#152292
#152192
#147022
#146982
#144272
#140032
#140022
#139372
C4×#3862