Finite Group Databasebeta

← #1409260

Subgroups — #1409260

Order 512.

4048 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2541C211yesmaximal, characteristic, complemented
2C2×#2445C211yesmaximal, characteristic, complemented
3C2×#2661C212yesmaximal, complemented
4#16551C214yesmaximal, complemented
5#16500C212yesmaximal, complemented
6#16291C214yesmaximal, complemented
7#16250C212yesmaximal, complemented
8#15147C211yesmaximal, characteristic, complemented
9#15142C212yesmaximal, complemented
10#15142C211yesmaximal, characteristic, complemented
11#15127C211yesmaximal, characteristic, complemented
12#15127C212yesmaximal, complemented
13#14762C212yesmaximal, complemented
14#14154C212yesmaximal, complemented
15#14141C212yesmaximal, complemented
16C4×#398C211yesmaximal, characteristic, complemented
17#13820C211yesmaximal, characteristic, complemented
18C22×#127C2212yes—
19C22×#127C2211yescharacteristic
20C22×#127C2212yes—
21C22×#127C2211yescharacteristic
22C22×#123C2212yes—
23C22×#121C2212yes—
24C22×#121C2212yes—
25C22×C4×D4C2211yescharacteristic
26#2661—216no—
27#2541—28no—
28#2445—28no—
29C2×#398C2211yescharacteristic
30C2×#397C2212yes—
31C2×#394C2212yes—
32C2×#394C2214yes—
33C2×#394C2212yes—
34C2×#394C2212yes—
35C2×#394C2214yes—
36C2×#394C2212yes—
37C2×#392C2214yes—
38C2×#392C2212yes—
39C2×#392C2214yes—
40C2×#392C2212yes—
41C2×#392C2214yes—
42C2×#392C2214yes—
43C2×#392C2214yes—
44C2×#392C2214yes—
45C2×#390C2214yes—
46C2×#390C2211yescharacteristic
47C2×#390C2212yes—
48C2×#390C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2212yes—
53C2×#390C2212yes—
54C2×#390C2212yes—
55C2×#390C2214yes—
56C2×#389C2211yescharacteristic
57C2×#388C2214yes—
58C2×#386C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C4⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64#1445C2211yescharacteristic
65#1444C2211yescharacteristic
66#1442C2212yes—
67#1441C2211yescharacteristic
68#1441C2212yes—
69#1440C2214yes—
70#1440C2214yes—
71#1439C2212yes—
72#1439C2214yes—
73#1438C2214yes—
74#1438C2212yes—
75#1438C2214yes—
76#1438C2212yes—
77#1438C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80#1437C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C4×#95C2211yescharacteristic
86C23×D4C2312yes—
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2314yes—
90C23×D4C2312yes—
91C23×D4C2312yes—
92C23×D4C2312yes—
93C23×D4C2314yes—
94C23×D4C2314yes—
95C23×D4C2312yes—
96C23×D4C2314yes—
97C24×C4C2312yes—
98C2×#127—24no—
99C2×#127—28no—
100C2×#127—24no—
101C2×#127—28no—
102C2×#127—44no—
103C2×#127—44no—
104C2×#127—44no—
105C2×#127—44no—
106C2×#127—44no—
107C2×#127—44no—
108C2×#123—28no—
109C2×#123—28no—
110C2×#123—44no—
111C2×#121—28no—
112C2×#121—28no—
113C2×#121—28no—
114C2×#121—48no—
115C2×#121—44no—
116C2×C4×D4—44no—
117C2×C4×D4D418yescomplemented
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2314yes—
153#398D418yescomplemented
154#397—28no—
155#394—28no—
156#394—216no—
157#394—28no—
158#394—28no—
159#394—48no—
160#394—44no—
161#392—216no—
162#392—28no—
163#392—216no—
164#392—44no—
165#392—48no—
166#392—48no—
167#392—48no—
168#392—48no—
169#390—24no—
170#390—216no—
171#390—24no—
172#390—28no—
173#390—24no—
174#390—28no—
175#390—28no—
176#390—44no—
177#390—44no—
178#390—44no—
179#390—48no—
180#389—24no—
181#388—216no—
182#386—28no—
183C4×C4⋊C4—24no—
184C4×C4⋊C4—24no—
185C4×C4⋊C4—44no—
186C4×C4⋊C4—44no—
187C4×C22⋊C4—28no—
188C2×#95C2311yescharacteristic
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C25C2412yes—
207C25C2414yes—
208C25C2412yes—
209C22×D4—28no—
210C22×D4—28no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—22no—
216C22×D4—28no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—28no—
221C22×D4—24no—
222C22×D4—28no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—28no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4—28no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—28no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—42no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—42no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—42no—
273C22×D4C2×D414yes—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×D418yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2414yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293#127—416no—
294#127—432no—
295#127—416no—
296#127—432no—
297#123—432no—
298#121—432no—
299#121—432no—
300C4×D4—416no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4C2×D414yes—
325C2×C4⋊C4C2×D414yes—
326C2×C4⋊C4C2×D414yes—
327C2×C4⋊C4C2×D418yes—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
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—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
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⋊C4C2×D418yes—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—28no—
393C2×C42—44no—
394C2×C42—44no—
395C2×C42C2×D414yes—
396C2×C42#4118yes—
397#95—24no—
398#95—22no—
399#95—24no—
400#95—22no—
401#95—24no—
402#95—28no—
403#95—24no—
404#95—24no—
405#95—22no—
406#95—24no—
407#95—24no—
408#95—42no—
409#95—42no—
410#95—44no—
411#95—42no—
412#95—44no—
413#95C2×D414yes—
414#95C2×D418yes—
415C24—22no—
416C24—24no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—22no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—22no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—22no—
449C24—22no—
450C24—24no—
451C24C22×D414yes—
452C24C2511yescharacteristic
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—416no—
457C2×D4—416no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—416no—
463C2×D4—48no—
464C2×D4—416no—
465C2×D4—416no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—416no—
469C2×D4—416no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—48no—
473C2×D4—44no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—416no—
486C2×D4—88no—
487C2×D4—88no—
488C2×D4—88no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C2×D4—84no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C2×D4—84no—
497C2×D4—88no—
498C2×D4—88no—
499C2×D4—88no—
500C2×D4—88no—
501C2×D4—88no—
502C2×D4—84no—
503C2×D4—88no—
504C2×D4—84no—
505C2×D4—88no—
506C2×D4—88no—
507C2×D4—88no—
508C2×D4—88no—
509C2×D4—88no—
510C2×D4—88no—
511C2×D4—88no—
512C2×D4—88no—
513C2×D4—88no—
514C2×D4—88no—
515C2×D4—88no—
516C2×D4—88no—
517C2×D4—88no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
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—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—216no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—88no—
585C22×C4—88no—
586C22×C4C22×D412yes—
587C22×C4C22×D414yes—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4114yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C4H(5,𝔽2)14yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)14yes—
602C22×C4H(5,𝔽2)14yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C4H(5,𝔽2)12yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—44no—
612C4⋊C4—48no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—416no—
617C22⋊C4—416no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—416no—
622C22⋊C4—416no—
623C22⋊C4—84no—
624C22⋊C4—88no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C22⋊C4—84no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C22⋊C4—84no—
633C22⋊C4—88no—
634C42—28no—
635C42—216no—
636C42—44no—
637C42—44no—
638C42—48no—
639C42—88no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—42no—
651C23—44no—
652C23—42no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—42no—
664C23—44no—
665C23—44no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—42no—
682C23—42no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
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—42no—
716C23—44no—
717C23—42no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23C23×D411yescharacteristic
722C23C23×D411yescharacteristic
723C23C22×#4112yes—
724C23C2×H(5,𝔽2)12yes—
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)11yescharacteristic
728C23C2×H(5,𝔽2)12yes—
729C23C2×H(5,𝔽2)12yes—
730C23C2×H(5,𝔽2)11yescharacteristic
731C23#58511yescharacteristic
732D4—416no—
733D4—816no—
734D4—832no—
735D4—816no—
736D4—832no—
737D4—832no—
738D4—816no—
739D4—816no—
740D4—832no—
741D4—816no—
742D4—88no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—41no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—816no—
819C2×C4#53214yes—
820C2×C4#53414yes—
821C2×C4#53514yes—
822C2×C4#53818yes—
823C2×C4#54018yes—
824C2×C4D4214yes—
825C2×C4#55018yes—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—84no—
834C22—84no—
835C22—84no—
836C22—84no—
837C22—84no—
838C22—82no—
839C22—82no—
840C22—84no—
841C22—84no—
842C22—84no—
843C22—84no—
844C22—84no—
845C22—82no—
846C22—84no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—84no—
851C22—82no—
852C22—82no—
853C22—84no—
854C22—84no—
855C22—84no—
856C22—84no—
857C22—84no—
858C22—84no—
859C22—84no—
860C22—84no—
861C22—84no—
862C22—84no—
863C22C2×#53211yescharacteristic
864C22C2×#53411yescharacteristic
865C22C2×#53511yescharacteristic
866C22C2×#53812yes—
867C22C2×#54012yes—
868C22C2×D4211yescharacteristic
869C22C2×#55012yes—
870C22#348411yescharacteristic
871C22#348811yescharacteristic
872C22#349611yescharacteristic
873C22#349811yescharacteristic
874C22#349812yes—
875C22#349811yescharacteristic
876C22#350612yes—
877C22#350812yes—
878C22#350812yes—
879C22#353712yes—
880C22#354312yes—
881C22#354312yes—
882C22#354312yes—
883C22#354611yescharacteristic
884C22#354911yescharacteristic
885C22#355812yes—
886C4—24no—
887C4—28no—
888C4—44no—
889C4—42no—
890C4—42no—
891C4—44no—
892C4—44no—
893C4—42no—
894C4—42no—
895C4—44no—
896C4—82no—
897C4—81no—
898C4—84no—
899C4#266118yescomplemented
900C2—84no—
901C2—164no—
902C2—162no—
903C2C2×#266111yescharacteristic
904C2#3593011yescharacteristic
905C2#3612811yescharacteristic
906C2#3933611yescharacteristic
907C2#3934211yescharacteristic
908C2#3938312yes—
909C2#3938612yes—
910C2#4243011yescharacteristic
911C2#4252912yes—
912C2#4296611yescharacteristic
913C2#4297712yes—
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×#2445C2semidirect
3. C2×#2661C2semidirect
4. #16551C2semidirect
5. #16500C2semidirect
6. #16291C2semidirect
7. #16250C2semidirect
8. #15147C2semidirect
9. #15142C2semidirect
10. #15142C2semidirect
11. #15127C2semidirect
12. #15127C2semidirect
13. #14762C2semidirect
14. #14154C2semidirect
15. #14141C2semidirect
16. C4×#398C2semidirect
17. #13820C2semidirect
117. C2×C4×D4D4semidirect
153. #398D4semidirect
899. C4#2661semidirect

Maximal subgroups

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

subgroupindex
C2×#25412
C2×#24452
C2×#26612
#165512
#165002
#162912
#162502
#151472
#151422
#151272
#147622
#141542
#141412
C4×#3982
#138202