Finite Group Databasebeta

← #4310324

Subgroups — #4310324

Order 512.

2966 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16831C211yesmaximal, characteristic, complemented
2#16718C212yesmaximal, complemented
3#16481C212yesmaximal, complemented
4#16415C212yesmaximal, complemented
5#16403C212yesmaximal, complemented
6#16391C211yesmaximal, characteristic
7#16391C212yesmaximal
8#16358C211yesmaximal, characteristic, complemented
9#16306C212yesmaximal, complemented
10#16297C211yesmaximal, characteristic
11#14834C212yesmaximal, complemented
12#14797C212yesmaximal, complemented
13#14753C212yesmaximal, complemented
14#14740C212yesmaximal, complemented
15#14693C212yesmaximal
16#14319C211yesmaximal, characteristic, complemented
17#14313C211yesmaximal, characteristic, complemented
18#14269C212yesmaximal, complemented
19C4×#379C211yesmaximal, characteristic
20C25×C4C2211yescharacteristic
21C2×#400C2212yescomplemented
22C2×#398C2212yescomplemented
23C2×#397C2211yescharacteristic
24C2×#397C2212yes—
25C2×#393C2211yescharacteristic
26C2×#393C2212yes—
27C2×#391C2211yescharacteristic, complemented
28C2×#389C2211yescharacteristic, complemented
29C2×#387C2212yescomplemented
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#385C2212yes—
33C2×#385C2212yes—
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#379C2212yes—
37C2×#379C2211yescharacteristic
38C2×#379C2211yescharacteristic
39C2×#379C2212yes—
40C2×C4×C22⋊C4C2212yes—
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44#1446C2211yescharacteristic, complemented
45#1446C2212yescomplemented
46#1445C2212yescomplemented
47#1445C2212yescomplemented
48#1445C2212yescomplemented
49#1445C2211yescharacteristic, complemented
50#1444C2211yescharacteristic, complemented
51#1444C2211yescharacteristic, complemented
52#1443C2212yescomplemented
53#1443C2212yescomplemented
54#1443C2212yescomplemented
55#1443C2212yescomplemented
56#1443C2212yescomplemented
57#1443C2212yescomplemented
58#1443C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1442C2212yescomplemented
62#1442C2212yescomplemented
63#1442C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1440C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2211yescharacteristic
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2211yescharacteristic
90#1436C2212yescomplemented
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1434C2211yescharacteristic, complemented
95#1434C2212yescomplemented
96#1434C2211yescharacteristic, complemented
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C26C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C24×C4—24no—
110C24×C4—44no—
111C24×C4—42no—
112C24×C4—42no—
113C24×C4—44no—
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C24×C4C2312yes—
117C24×C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#400—44no—
152#398—44no—
153#397—24no—
154#397—44no—
155#393—24no—
156#393—44no—
157#391—42no—
158#389—42no—
159#387—44no—
160#385—28no—
161#385—44no—
162#385—44no—
163#385—44no—
164#385—44no—
165#385—44no—
166#379—28no—
167#379—24no—
168#379—24no—
169#379—44no—
170C4×C22⋊C4—44no—
171C4×C22⋊C4—42no—
172C4×C22⋊C4—42no—
173C4×C22⋊C4—44no—
174C2×#95C2311yescharacteristic
175C2×#95C2312yes—
176C2×#95C2311yescharacteristic
177C2×#95C2312yes—
178C2×#95C2312yes—
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×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2312yes—
207C2×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C25—22no—
223C25—22no—
224C25—24no—
225C25—24no—
226C25—41no—
227C25—42no—
228C25—41no—
229C25—41no—
230C25—42no—
231C25—41no—
232C25#4114yes—
233C25C2411yescharacteristic
234C25C2412yes—
235C22×Q8—22no—
236C22×Q8—41no—
237C22×Q8—41no—
238C22×Q8—42no—
239C22×Q8—42no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—41no—
261C23×C4—42no—
262C23×C4—41no—
263C23×C4—432no—
264C23×C4—416no—
265C23×C4—416no—
266C23×C4—432no—
267C23×C4—416no—
268C23×C4#4114yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
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—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
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—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4#4114yes—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381#95—24no—
382#95—24no—
383#95—22no—
384#95—24no—
385#95—22no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—41no—
394#95—41no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—41no—
405#95—41no—
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—42no—
417#95—42no—
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—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—28no—
450C24—216no—
451C24—44no—
452C24—48no—
453C24—44no—
454C24—48no—
455C24—44no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—44no—
461C24—44no—
462C24—48no—
463C24—44no—
464C24—44no—
465C24—44no—
466C24—48no—
467C24—48no—
468C24—48no—
469C24—44no—
470C24—44no—
471C24—48no—
472C24C2×#4112yes—
473C24C2×#4112yes—
474C24C2×#4112yes—
475C24C2×#4114yes—
476C24H(5,𝔽2)14yes—
477C242−1+414yes—
478C24C2511yescharacteristic
479C2×Q8—44no—
480C2×Q8—84no—
481C2×Q8—82no—
482C2×Q8—84no—
483C2×Q8—82no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—216no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
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—22no—
533C22×C4—21no—
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—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—21no—
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—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—4128no—
606C22×C4—44no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4H(5,𝔽2)14yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C4H(5,𝔽2)12yes—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—84no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C4⋊C4—82no—
622C4⋊C4—82no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C22⋊C4—44no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—44no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—44no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C42—82no—
647C42—82no—
648C42—84no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—416no—
680C23—432no—
681C23—416no—
682C23—432no—
683C23—416no—
684C23—416no—
685C23—416no—
686C23—416no—
687C23—432no—
688C23—416no—
689C23—432no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23#52914yes—
717C23#53918yes—
718C23C22×#4111yescharacteristic
719C23C22×#4111yescharacteristic
720C23C22×#4111yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)12yes—
724C23C2×H(5,𝔽2)12yes—
725C23C2×2−1+412yes—
726C23#58511yescharacteristic
727C23#58511yescharacteristic
728C23#58512yes—
729Q8—88no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—432no—
744C2×C4—416no—
745C2×C4—432no—
746C2×C4—416no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
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—42no—
789C2×C4—42no—
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—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
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—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
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#53814yes—
841C22—24no—
842C22—28no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—464no—
847C22—42no—
848C22—44no—
849C22—42no—
850C22—44no—
851C22—44no—
852C22—42no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—42no—
857C22—42no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—42no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22C2×#52911yescharacteristic
869C22C2×#53811yescharacteristic
870C22C2×#53912yes—
871C22#345511yescharacteristic
872C22#345911yescharacteristic
873C22#345911yescharacteristic
874C22#345911yescharacteristic
875C22#345912yes—
876C22#346011yescharacteristic
877C22#349012yes—
878C22#349512yes—
879C22#351312yes—
880C22#352012yes—
881C22#353211yescharacteristic
882C22#353211yescharacteristic
883C22#353212yes—
884C22#353312yes—
885C22#353512yes—
886C22#353811yescharacteristic
887C22#354011yescharacteristic
888C22#354012yes—
889C22#354112yes—
890C22#354112yes—
891C4—24no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—44no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—81no—
901C4—82no—
902C4—82no—
903C4—81no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C2—44no—
909C2—48no—
910C2#3457011yescharacteristic
911C2#3499912yes—
912C2#3672511yescharacteristic
913C2#3673312yes—
914C2#3685812yes—
915C2#3687111yescharacteristic
916C2#3692911yescharacteristic
917C2#3738111yescharacteristic
918C2#3745712yes—
919C2#3748611yescharacteristic
920C2#3752811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16831C2semidirect
2. #16718C2semidirect
3. #16481C2semidirect
4. #16415C2semidirect
5. #16403C2semidirect
8. #16358C2semidirect
9. #16306C2semidirect
11. #14834C2semidirect
12. #14797C2semidirect
13. #14753C2semidirect
14. #14740C2semidirect
16. #14319C2semidirect
17. #14313C2semidirect
18. #14269C2semidirect
21. C2×#400C22semidirect
22. C2×#398C22semidirect
27. C2×#391C22semidirect
28. C2×#389C22semidirect
29. C2×#387C22semidirect
44. #1446C22semidirect
45. #1446C22semidirect
46. #1445C22semidirect
47. #1445C22semidirect
48. #1445C22semidirect
49. #1445C22semidirect
50. #1444C22semidirect
51. #1444C22semidirect
52. #1443C22semidirect
53. #1443C22semidirect
54. #1443C22semidirect
55. #1443C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1443C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
90. #1436C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect

Maximal subgroups

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

subgroupindex
#168312
#167182
#164812
#164152
#164032
#163912
#163582
#163062
#162972
#148342
#147972
#147532
#147402
#146932
#143192
#143132
#142692
C4×#3792