Finite Group Databasebeta

← #639831

Subgroups — #639831

Order 512.

4293 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic
2C2×#2623C211yesmaximal, characteristic, complemented
3C22×#381C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic, complemented
5#16395C212yesmaximal, complemented
6#16394C212yesmaximal, complemented
7#16393C212yesmaximal, complemented
8#16392C212yesmaximal, complemented
9#14919C212yesmaximal, complemented
10#14912C212yesmaximal, complemented
11#14836C212yesmaximal, complemented
12#14826C212yesmaximal, complemented
13#14766C212yesmaximal, complemented
14#14735C212yesmaximal, complemented
15#14342C211yesmaximal, characteristic, complemented
16#14263C211yesmaximal, characteristic, complemented
17#14256C211yesmaximal, characteristic, complemented
18#14134C212yesmaximal
19#13877C212yesmaximal, complemented
20C25×C4C2211yescharacteristic
21C22×#123C2211yescharacteristic
22C22×#123C2211yescharacteristic
23C22×#120C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27C23×C22⋊C4C2212yes—
28#2849—28no—
29#2623—28no—
30C2×#400C2212yescomplemented
31C2×#399C2212yescomplemented
32C2×#398C2212yescomplemented
33C2×#397C2212yescomplemented
34C2×#386C2211yescharacteristic
35C2×#386C2211yescharacteristic
36C2×#386C2211yescharacteristic
37C2×#386C2211yescharacteristic
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2214yes—
41C2×#385C2211yescharacteristic
42C2×#385C2211yescharacteristic
43C2×#385C2211yescharacteristic
44C2×#385C2211yescharacteristic
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#381—28no—
48C2×#381C2211yescharacteristic
49C2×#381C2211yescharacteristic
50C2×#381C2211yescharacteristic
51C2×#381C2212yes—
52C2×#381C2212yes—
53C2×#381C2212yes—
54C2×#381C2211yescharacteristic
55C2×#380—28no—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×#380C2214yes—
61C2×#379C2211yescharacteristic
62C22×#95C2212yes—
63C22×#95C2212yes—
64C22×#95C2212yes—
65#1445C2212yescomplemented
66#1445C2212yescomplemented
67#1445C2212yescomplemented
68#1445C2212yescomplemented
69#1445C2214yescomplemented
70#1444C2212yescomplemented
71#1444C2212yescomplemented
72#1443C2214yescomplemented
73#1443C2214yescomplemented
74#1442C2214yescomplemented
75#1442C2212yescomplemented
76#1442C2214yescomplemented
77#1442C2212yescomplemented
78#1441C2212yescomplemented
79#1441C2214yescomplemented
80#1441C2212yescomplemented
81#1440C2214yes—
82#1440C2214yescomplemented
83#1439C2214yes—
84#1439C2214yes—
85#1439C2212yescomplemented
86#1439C2214yescomplemented
87#1439C2212yescomplemented
88#1438C2214yes—
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2214yes—
93C22⋊#95C2212yes—
94C22⋊#95C2214yes—
95C26C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C24×C4—28no—
100C24×C4—24no—
101C24×C4—24no—
102C24×C4—44no—
103C24×C4D418yes—
104C24×C4C2311yescharacteristic
105C24×C4C2314yes—
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2312yes—
113C2×#123—24no—
114C2×#123—24no—
115C2×#123—24no—
116C2×#123—24no—
117C2×#123—44no—
118C2×#120—24no—
119C2×#120—28no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—44no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C22⋊C4—28no—
136C22×C22⋊C4—28no—
137C22×C22⋊C4—28no—
138C22×C22⋊C4—44no—
139C22×C22⋊C4—48no—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2314yes—
160#400—28no—
161#399—28no—
162#398—28no—
163#397—28no—
164#386—24no—
165#386—24no—
166#386—24no—
167#386—24no—
168#386—28no—
169#386—48no—
170#386—44no—
171#385—24no—
172#385—24no—
173#385—24no—
174#385—24no—
175#385—28no—
176#385—44no—
177#381—24no—
178#381—24no—
179#381—24no—
180#381—28no—
181#381—28no—
182#381—28no—
183#381D418yescomplemented
184#380—28no—
185#380—28no—
186#380—28no—
187#380—28no—
188#380—48no—
189#379—24no—
190C2×#95—28no—
191C2×#95—28no—
192C2×#95—28no—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C25—22no—
222C25—22no—
223C25—24no—
224C25—24no—
225C25—24no—
226C25—42no—
227C25—42no—
228C25C2×D414yes—
229C25#4118yes—
230C25C2411yescharacteristic
231C25C2411yescharacteristic
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—42no—
246C22×D4—42no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—232no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—232no—
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—24no—
268C23×C4—24no—
269C23×C4—28no—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—28no—
277C23×C4—416no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—432no—
290C23×C4—432no—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4#4114yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2414yes—
304C23×C4C2414yes—
305C23×C4C2414yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2414yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314#123—416no—
315#123—416no—
316#120—416no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
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—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—416no—
339C2×C4⋊C4—416no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—432no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—432no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4C2×D418yes—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—24no—
402#95—24no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—28no—
412#95—28no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95C2×D418yes—
424#95C2×D418yes—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—232no—
439C24—216no—
440C24—216no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—44no—
458C24—44no—
459C24—416no—
460C24—48no—
461C24—48no—
462C24—48no—
463C24—48no—
464C24—416no—
465C24—416no—
466C24#123116yes—
467C24C22×D412yes—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C2×#4114yes—
472C24C2×#4112yes—
473C24C2×#4114yes—
474C24C2×#4114yes—
475C24H(5,𝔽2)14yes—
476C24H(5,𝔽2)14yes—
477C242−1+414yes—
478C24C2511yescharacteristic
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—416no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—88no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—216no—
495C22×C4—216no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—4128no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—416no—
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—416no—
602C22×C4—88no—
603C22×C4—88no—
604C22×C4—88no—
605C22×C4—88no—
606C22×C4—88no—
607C22×C4—88no—
608C22×C4—88no—
609C22×C4#121116yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D418yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—88no—
628C4⋊C4—88no—
629C22⋊C4—216no—
630C22⋊C4—416no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—416no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—416no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—88no—
648C22⋊C4—88no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—28no—
665C23—28no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—232no—
675C23—22no—
676C23—232no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—28no—
683C23—24no—
684C23—24no—
685C23—28no—
686C23—416no—
687C23—464no—
688C23—416no—
689C23—416no—
690C23—416no—
691C23—464no—
692C23—416no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—44no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—44no—
715C23—44no—
716C23C2×#12114yes—
717C23C2×#12314yes—
718C23C2×#12314yes—
719C23C2×#12314yes—
720C23#53414yes—
721C23#53514yes—
722C23#53614yes—
723C23#539116yes—
724C23#54618yes—
725C23#55118yes—
726C23C23×D411yescharacteristic
727C23C23×D411yescharacteristic
728C23C22×#4111yescharacteristic
729C23C22×#4112yes—
730C23C2×H(5,𝔽2)12yes—
731C23C2×H(5,𝔽2)12yes—
732C23C2×2−1+412yes—
733C23#58512yes—
734C23#58512yes—
735D4—88no—
736D4—88no—
737D4—88no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—232no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—416no—
757C2×C4—416no—
758C2×C4—416no—
759C2×C4—416no—
760C2×C4—416no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—832no—
822C2×C4—816no—
823C2×C4—816no—
824C2×C4C2×#12114yes—
825C2×C4C2×#12114yes—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—216no—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—216no—
839C22—216no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—464no—
846C22—48no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—48no—
851C22—42no—
852C22—81no—
853C22—81no—
854C22—84no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—84no—
860C22—81no—
861C22#241218yes—
862C22#262318yescomplemented
863C22C22×#12111yescharacteristic
864C22C22×#12311yescharacteristic
865C22C2×#53411yescharacteristic
866C22C2×#53511yescharacteristic
867C22C2×#53611yescharacteristic
868C22#344911yescharacteristic
869C22#344911yescharacteristic
870C22C2×#53914yes—
871C22C2×#54612yes—
872C22C2×#55112yes—
873C22#348812yes—
874C22#348912yes—
875C22#349114yes—
876C22#349412yes—
877C22#349512yes—
878C22#353414yes—
879C22#353514yes—
880C4—24no—
881C4—24no—
882C4—48no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—84no—
888C4—81no—
889C4—84no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—84no—
894C4—81no—
895C2—28no—
896C2—28no—
897C2—44no—
898C2—161no—
899C2C2×#262311yescharacteristic
900C2C2×#241211yescharacteristic
901C2#3509711yescharacteristic
902C2#3525211yescharacteristic
903C2#3530611yescharacteristic
904C2#3744611yescharacteristic
905C2#3744711yescharacteristic
906C2#3766114yes—
907C2#3784914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2623C2semidirect
3. C22×#381C2semidirect
4. C22×#380C2semidirect
5. #16395C2semidirect
6. #16394C2semidirect
7. #16393C2semidirect
8. #16392C2semidirect
9. #14919C2semidirect
10. #14912C2semidirect
11. #14836C2semidirect
12. #14826C2semidirect
13. #14766C2semidirect
14. #14735C2semidirect
15. #14342C2semidirect
16. #14263C2semidirect
17. #14256C2semidirect
19. #13877C2semidirect
30. C2×#400C22semidirect
31. C2×#399C22semidirect
32. C2×#398C22semidirect
33. C2×#397C22semidirect
65. #1445C22semidirect
66. #1445C22semidirect
67. #1445C22semidirect
68. #1445C22semidirect
69. #1445C22semidirect
70. #1444C22semidirect
71. #1444C22semidirect
72. #1443C22semidirect
73. #1443C22semidirect
74. #1442C22semidirect
75. #1442C22semidirect
76. #1442C22semidirect
77. #1442C22semidirect
78. #1441C22semidirect
79. #1441C22semidirect
80. #1441C22semidirect
82. #1440C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
183. #381D4semidirect
862. C22#2623semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#26232
C22×#3812
C22×#3802
#163952
#163942
#163932
#163922
#149192
#149122
#148362
#148262
#147662
#147352
#143422
#142632
#142562
#141342
#138772