Finite Group Databasebeta

← #797449

Subgroups — #797449

Order 512.

4776 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2541C211yesmaximal, characteristic, complemented
2C2×#2431C212yesmaximal, complemented
3C2×#2445C212yesmaximal, complemented
4C2×#2339C211yesmaximal, characteristic, complemented
5#16508C212yesmaximal, complemented
6#15561C214yesmaximal, complemented
7#15412C214yesmaximal, complemented
8#15227C211yesmaximal, characteristic, complemented
9#15193C211yesmaximal, characteristic, complemented
10#15124C211yesmaximal, characteristic, complemented
11#14926C212yesmaximal, complemented
12#14762C212yesmaximal, complemented
13#14153C212yesmaximal, complemented
14#14152C212yesmaximal, complemented
15#13998C212yesmaximal, complemented
16C4×#399C211yesmaximal, characteristic, complemented
17#13820C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C22×#127C2212yes—
20C22×#127C2211yescharacteristic
21C22×#124C2212yes—
22C22×#123C2214yes—
23C22×#121C2212yes—
24C22×#121C2212yes—
25C22×#121C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28#2541—28no—
29#2445—216no—
30#2431—216no—
31C2×#399C2211yescharacteristic
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#392C2214yes—
35C2×#392C2214yes—
36C2×#392C2214yes—
37C2×#392C2212yes—
38C2×#392C2212yes—
39#2339—28no—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2212yes—
43C2×#390C2212yes—
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#390C2214yes—
47C2×#390C2212yes—
48C2×#389C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2214yes—
52C2×#386C2214yes—
53C2×#386C2214yes—
54C2×#381C2212yes—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62C22×#95C2212yes—
63#1445C2211yescharacteristic
64#1445C2212yes—
65#1445C2214yes—
66#1445C2212yes—
67#1444C2211yescharacteristic
68#1444C2212yes—
69#1439C2212yes—
70#1439C2211yescharacteristic
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2212yes—
75#1438C2212yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2212yes—
79#1438C2212yes—
80#1437C2214yes—
81#1437C2214yes—
82#1437C2214yes—
83#1437C2214yes—
84C4⋊#95C2211yescharacteristic
85C22⋊#95C2212yes—
86C4×#95C2211yescharacteristic
87C22×#41—24no—
88C22×#41—24no—
89C22×#41—28no—
90C22×#41—24no—
91C22×#41—44no—
92C23×Q8C2311yescharacteristic
93C23×D4C2312yes—
94C23×D4C2312yes—
95C23×D4C2314yes—
96C23×D4C2314yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2314yes—
100C23×D4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C24×C4C2312yes—
105C2×#127—28no—
106C2×#127—28no—
107C2×#127—28no—
108C2×#127—24no—
109C2×#127—44no—
110C2×#124—28no—
111C2×#124—28no—
112C2×#124—44no—
113C2×#123—216no—
114C2×#123—48no—
115C2×#123—48no—
116C2×#121—28no—
117C2×#121—28no—
118C2×#121—28no—
119C2×#121—28no—
120C2×#121—28no—
121C2×#121—48no—
122C2×#121—44no—
123C2×#121—44no—
124C2×C4×D4—24no—
125C2×C4×D4—28no—
126C2×C4×D4—44no—
127C2×C4×D4D418yescomplemented
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2314yes—
159#399—24no—
160#394—216no—
161#394—216no—
162#392—216no—
163#392—216no—
164#392—216no—
165#392—44no—
166#392—44no—
167#391—24no—
168#391—28no—
169#391—24no—
170#390—28no—
171#390—28no—
172#390—28no—
173#390—48no—
174#390D4116yescomplemented
175#389—28no—
176#386—28no—
177#386—28no—
178#386—216no—
179#386—216no—
180#386—216no—
181#381—28no—
182#380—24no—
183C4×C4⋊C4—28no—
184C4×C4⋊C4—24no—
185C4×C4⋊C4—44no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—28no—
188C4×C22⋊C4—44no—
189C2×#95—28no—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2311yescharacteristic
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C25C2414yes—
212C25C2411yescharacteristic
213C25C2412yes—
214C2×#41—232no—
215C2×#41—432no—
216C2×#41—432no—
217C2×#41—416no—
218C2×#41—416no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—24no—
223C22×Q8#4114yes—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—28no—
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—28no—
230C22×D4—28no—
231C22×D4—28no—
232C22×D4—28no—
233C22×D4—28no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—28no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—28no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—28no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4—42no—
269C22×D4—44no—
270C22×D4C2×D414yes—
271C22×D4C2×D418yes—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—28no—
282C23×C4—28no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—42no—
290C23×C4C2×D418yes—
291C23×C4#4114yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2414yes—
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306#127—416no—
307#127—432no—
308#124—432no—
309#123—464no—
310#121—432no—
311#121—432no—
312#121—432no—
313C4×D4—416no—
314C4×D4—416no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D418yes—
335C2×C4⋊C4#4114yescomplemented
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—44no—
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⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D418yes—
385C2×C22⋊C4C2×D4116yes—
386C2×C22⋊C4C2×D4116yes—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—44no—
396C2×C42—44no—
397C2×C42—44no—
398C2×C42C2×D414yes—
399C2×C42C2×D418yes—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—22no—
416#95—22no—
417#95—24no—
418#95—42no—
419#95—44no—
420#95—42no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—21no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24C22×D418yes—
456C24C22×D414yes—
457C24C2×#4112yes—
458C24C2511yescharacteristic
459#41—4128no—
460C2×Q8—28no—
461C2×Q8—216no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—48no—
465C2×D4—216no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—216no—
469C2×D4—216no—
470C2×D4—416no—
471C2×D4—416no—
472C2×D4—416no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—416no—
477C2×D4—416no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—416no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—416no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—88no—
496C2×D4—88no—
497C2×D4—88no—
498C2×D4—84no—
499C2×D4—88no—
500C2×D4—84no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—88no—
504C2×D4—88no—
505C2×D4—88no—
506C2×D4—88no—
507C2×D4—88no—
508C2×D4—88no—
509C2×D4—88no—
510C2×D4—88no—
511C2×D4—88no—
512C2×D4#127116yes—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—216no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—216no—
568C22×C4—216no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—416no—
583C22×C4—416no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—88no—
592C22×C4—88no—
593C22×C4—84no—
594C22×C4—88no—
595C22×C4C22×D412yes—
596C22×C4C22×D414yes—
597C22×C4C22×D414yes—
598C22×C4C22×D418yes—
599C22×C4C22×D414yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D414yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C4H(5,𝔽2)14yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C4H(5,𝔽2)14yes—
613C4⋊C4—28no—
614C4⋊C4—216no—
615C4⋊C4—28no—
616C4⋊C4—216no—
617C4⋊C4—28no—
618C4⋊C4—48no—
619C4⋊C4—416no—
620C4⋊C4—44no—
621C22⋊C4—416no—
622C22⋊C4—48no—
623C22⋊C4—416no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—416no—
628C22⋊C4—416no—
629C22⋊C4—416no—
630C22⋊C4—416no—
631C22⋊C4—416no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—48no—
635C22⋊C4—44no—
636C22⋊C4—84no—
637C22⋊C4—88no—
638C22⋊C4—88no—
639C42—28no—
640C42—216no—
641C42—44no—
642C42—48no—
643C42—88no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—24no—
652C23—24no—
653C23—28no—
654C23—28no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—41no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23C2×#12718yes—
725C23C23×D411yescharacteristic
726C23C23×D412yes—
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C22×#4111yescharacteristic
730C23C2×H(5,𝔽2)12yes—
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×H(5,𝔽2)12yes—
734C23#58512yes—
735C23#58511yescharacteristic
736Q8—416no—
737D4—232no—
738D4—432no—
739D4—816no—
740D4—832no—
741D4—832no—
742D4—832no—
743D4—816no—
744D4—816no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—432no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—416no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—816no—
822C2×C4—816no—
823C2×C4#52514yes—
824C2×C4C2×#12714yes—
825C2×C4#53414yes—
826C2×C4#54614yes—
827C2×C4#54618yes—
828C2×C4#54618yes—
829C22—28no—
830C22—28no—
831C22—28no—
832C22—48no—
833C22—44no—
834C22—44no—
835C22—48no—
836C22—48no—
837C22—44no—
838C22—44no—
839C22—48no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—42no—
845C22—81no—
846C22—81no—
847C22—82no—
848C22—81no—
849C22—81no—
850C22—82no—
851C22—84no—
852C22—84no—
853C22—84no—
854C22—84no—
855C22—84no—
856C22—84no—
857C22—84no—
858C22—84no—
859C22—84no—
860C22—84no—
861C22—84no—
862C22—84no—
863C22—84no—
864C22—84no—
865C22—84no—
866C22C2×#52511yescharacteristic
867C22C22×#12711yescharacteristic
868C22C2×#53411yescharacteristic
869C22C2×#54612yes—
870C22C2×#54612yes—
871C22C2×#54611yescharacteristic
872C22D4×#4112yes—
873C22#348011yescharacteristic
874C22#348311yescharacteristic
875C22#348411yescharacteristic
876C22#348412yes—
877C22#348812yes—
878C22#348811yescharacteristic
879C22#349612yes—
880C22#350011yescharacteristic
881C22#350612yes—
882C22#350812yes—
883C22#350811yescharacteristic
884C22#351711yescharacteristic
885C22#351712yes—
886C22#354312yes—
887C22#354612yes—
888C22#356212yes—
889C4—24no—
890C4—42no—
891C4—44no—
892C4—44no—
893C4—48no—
894C4—42no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—42no—
899C4—44no—
900C4—82no—
901C4—81no—
902C4#253918yes—
903C2—48no—
904C2—82no—
905C2—164no—
906C2C2×#253911yescharacteristic
907C2#3570411yescharacteristic
908C2#3592111yescharacteristic
909C2#3626011yescharacteristic
910C2#3641011yescharacteristic
911C2#3946411yescharacteristic
912C2#4296711yescharacteristic
913C2#4487612yes—
914C2#4488912yes—
915C2#5909712yes—
916C2#5914512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2541C2semidirect
2. C2×#2431C2semidirect
3. C2×#2445C2semidirect
4. C2×#2339C2semidirect
5. #16508C2semidirect
6. #15561C2semidirect
7. #15412C2semidirect
8. #15227C2semidirect
9. #15193C2semidirect
10. #15124C2semidirect
11. #14926C2semidirect
12. #14762C2semidirect
13. #14153C2semidirect
14. #14152C2semidirect
15. #13998C2semidirect
16. C4×#399C2semidirect
17. #13820C2semidirect
127. C2×C4×D4D4semidirect
174. #390D4semidirect
335. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25412
C2×#24312
C2×#24452
C2×#23392
#165082
#155612
#154122
#152272
#151932
#151242
#149262
#147622
#141532
#141522
#139982
C4×#3992
#138202