Finite Group Databasebeta

← #2072791

Subgroups — #2072791

Order 512.

2432 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16955C212yesmaximal, complemented
2#16916C212yesmaximal, complemented
3#16865C212yesmaximal, complemented
4#16247C211yesmaximal, characteristic, complemented
5#15982C211yesmaximal, characteristic, complemented
6#15952C212yesmaximal, complemented
7#15561C211yesmaximal, characteristic, complemented
8#15492C212yesmaximal, complemented
9#15484C212yesmaximal, complemented
10#15412C211yesmaximal, characteristic
11#15369C212yesmaximal, complemented
12#15368C212yesmaximal, complemented
13#15270C212yesmaximal, complemented
14#14706C212yesmaximal, complemented
15#14706C211yesmaximal, characteristic, complemented
16#14533C211yesmaximal, characteristic, complemented
17#14507C211yesmaximal, characteristic, complemented
18#14376C212yesmaximal, complemented
19#14373C212yesmaximal, complemented
20C22×#123C2212yes—
21C22×#123C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#401C2212yes—
24C2×#394C2212yes—
25C2×#392C2211yescharacteristic
26C2×#392C2211yescharacteristic
27C2×#392C2212yes—
28C2×#390C2211yescharacteristic
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#386C2211yescharacteristic
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#385C2211yescharacteristic
38C2×#381C2211yescharacteristic
39C2×#381C2212yes—
40C2×#381C2212yes—
41C2×#381C2211yescharacteristic
42C2×#380C2212yes—
43#1445C2212yes—
44#1445C2211yescharacteristic
45#1445C2212yes—
46#1445C2212yes—
47#1443C2212yes—
48#1443C2212yes—
49#1443C2212yes—
50#1443C2212yes—
51#1443C2212yes—
52#1442C2212yes—
53#1442C2212yes—
54#1442C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1441C2212yes—
59#1441C2212yes—
60#1441C2212yes—
61#1440C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1440C2211yescharacteristic
65#1440C2211yescharacteristic
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1438C2212yes—
79#1438C2212yes—
80#1438C2212yes—
81#1438C2212yes—
82#1438C2211yescharacteristic
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2211yescharacteristic
87#1437C2211yescharacteristic
88#1437C2212yes—
89#1437C2211yescharacteristic
90#1437C2212yes—
91#1437C2211yescharacteristic
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2211yescharacteristic
97#1436C2212yes—
98#1436C2212yes—
99#1436C2211yescharacteristic
100#1434C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C23×D4C2311yescharacteristic
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C23×D4C2312yes—
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C2×#123—24no—
116C2×#123—28no—
117C2×#123—42no—
118C2×#123—44no—
119C2×#123—44no—
120C2×#123—42no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C42—42no—
153C22×C42—44no—
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#401—44no—
159#394—44no—
160#392—24no—
161#392—42no—
162#392—44no—
163#390—42no—
164#386—28no—
165#386—28no—
166#386—44no—
167#386—44no—
168#386—42no—
169#386—44no—
170#386—44no—
171#386—44no—
172#385—42no—
173#381—24no—
174#381—44no—
175#381—42no—
176#381—44no—
177#380—44no—
178C2×#95C2311yescharacteristic
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
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×#95C2312yes—
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C25C2411yescharacteristic
223C25C2412yes—
224C25C2411yescharacteristic
225C22×D4—22no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—42no—
237C22×D4—41no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—41no—
246C22×D4—41no—
247C22×D4—42no—
248C22×D4—42no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—41no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—41no—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289#123—432no—
290#123—416no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4#4114yes—
380C2×C22⋊C4#4118yes—
381C2×C42—41no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—41no—
388C2×C42—416no—
389C2×C42—41no—
390C2×C42—42no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—22no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—41no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—41no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24C2×#4112yes—
465C24C2×#4114yes—
466C24H(5,𝔽2)14yes—
467C24H(5,𝔽2)12yes—
468C24C2511yescharacteristic
469C2×D4—48no—
470C2×D4—44no—
471C2×D4—48no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—82no—
481C2×D4—84no—
482C2×D4—84no—
483C2×D4—84no—
484C2×D4—84no—
485C2×D4—84no—
486C2×D4—82no—
487C2×D4—84no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—82no—
491C2×D4—84no—
492C2×D4—84no—
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
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—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
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—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
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—48no—
601C22×C4—44no—
602C22×C4—48no—
603C22×C4—44no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4C2×#4112yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4114yes—
617C22×C4H(5,𝔽2)14yes—
618C22×C4H(5,𝔽2)12yes—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C22⋊C4—48no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—48no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—82no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—82no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C22⋊C4—84no—
648C22⋊C4—84no—
649C22⋊C4—84no—
650C42—44no—
651C42—48no—
652C42—44no—
653C42—82no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—41no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23#56014yes—
731C23C22×#4111yescharacteristic
732C23C22×#4112yes—
733C23C2×H(5,𝔽2)12yes—
734C23C2×H(5,𝔽2)11yescharacteristic
735C23C2×H(5,𝔽2)12yes—
736C23C2×H(5,𝔽2)11yescharacteristic
737C23#58512yes—
738C23#58512yes—
739C23#58512yes—
740D4—88no—
741D4—816no—
742D4—88no—
743D4—816no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
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—24no—
759C2×C4—432no—
760C2×C4—416no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
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—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—816no—
849C2×C4—88no—
850C22—28no—
851C22—24no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—42no—
857C22—42no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—42no—
867C22—44no—
868C22—42no—
869C22—44no—
870C22—42no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22#345511yescharacteristic
884C22#346012yes—
885C22#347512yes—
886C22#348111yescharacteristic
887C22#349012yes—
888C22#349011yescharacteristic
889C22#350811yescharacteristic
890C22#351312yes—
891C22#351312yes—
892C22#351312yes—
893C22#352112yes—
894C22C2×#56011yescharacteristic
895C22#353311yescharacteristic
896C22#353312yes—
897C22#353412yes—
898C22#353412yes—
899C22#353412yes—
900C22#354612yes—
901C22#355111yescharacteristic
902C22#356212yes—
903C22#356612yes—
904C4—44no—
905C4—44no—
906C4—44no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—81no—
915C4—82no—
916C4—82no—
917C4—81no—
918C4—82no—
919C4—82no—
920C2—44no—
921C2—84no—
922C2—82no—
923C2#3681211yescharacteristic
924C2#3686712yes—
925C2#3875612yes—
926C2#3898812yes—
927C2#4022912yes—
928C2#4553612yes—
929C2#4553711yescharacteristic
930C2#5323612yes—
931C2#5962111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#15412C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16955C2semidirect
2. #16916C2semidirect
3. #16865C2semidirect
4. #16247C2semidirect
5. #15982C2semidirect
6. #15952C2semidirect
7. #15561C2semidirect
8. #15492C2semidirect
9. #15484C2semidirect
11. #15369C2semidirect
12. #15368C2semidirect
13. #15270C2semidirect
14. #14706C2semidirect
15. #14706C2semidirect
16. #14533C2semidirect
17. #14507C2semidirect
18. #14376C2semidirect
19. #14373C2semidirect

Maximal subgroups

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

subgroupindex
#169552
#169162
#168652
#162472
#159822
#159522
#155612
#154922
#154842
#154122
#153692
#153682
#152702
#147062
#145332
#145072
#143762
#143732