Finite Group Databasebeta

← #579923

Subgroups — #579923

Order 512.

2398 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2563C211yesmaximal, characteristic
2#14635C211yesmaximal, characteristic, complemented
3#14596C211yesmaximal, characteristic, complemented
4#14575C211yesmaximal, characteristic, complemented
5#14553C212yesmaximal, complemented
6#14455C212yesmaximal, complemented
7#14438C212yesmaximal
8#14420C212yesmaximal, complemented
9#14370C212yesmaximal, complemented
10#14243C212yesmaximal, complemented
11#14213C211yesmaximal, characteristic, complemented
12#14107C212yesmaximal, complemented
13#14106C212yesmaximal, complemented
14#14047C212yesmaximal, complemented
15#14028C212yesmaximal, complemented
16#13960C211yesmaximal, characteristic
17#13928C212yesmaximal, complemented
18#13791C212yesmaximal
19#13784C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22#2563C4116yescomplemented
23C2×#393C2211yescharacteristic
24C2×#393C2211yescharacteristic
25C2×#393C2211yescharacteristic
26C2×#393C2211yescharacteristic
27C2×#391C2212yes—
28C2×#391C2212yes—
29C2×#390C2212yes—
30C2×#387C2212yes—
31C2×#387C2212yes—
32C2×#386C2211yescharacteristic
33C2×#386C2212yes—
34C2×#386C2211yescharacteristic
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#382C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2212yes—
40C2×#380C2212yes—
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2212yes—
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47#1446C2212yes—
48#1446C2212yes—
49#1445C2212yes—
50#1445C2212yes—
51#1444C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1442C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1441C2211yescharacteristic
60#1441C2212yes—
61#1441C2212yes—
62#1441C2212yes—
63#1441C2212yes—
64#1441C2211yescharacteristic
65#1439C2211yescharacteristic
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2211yescharacteristic
71#1437C2212yes—
72#1437C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1436C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87C4⋊#95C2212yes—
88#1434C2212yes—
89#1434C2212yes—
90#1434C2212yes—
91#1434C2212yes—
92#1434C2212yes—
93#1434C2212yes—
94#1434C2212yes—
95#1434C2212yes—
96#1434C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2211yescharacteristic
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C4×#95C2212yes—
107C4×#95C2212yes—
108C23×Q8C2311yescharacteristic
109C23×Q8C2311yescharacteristic
110C23×D4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8C2×C418yescomplemented
119C2×C4×D4—42no—
120C2×C4×D4—42no—
121C2×C4×D4C2×C418yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2312yes—
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152#393C2×C418yescomplemented
153#393C2×C418yescomplemented
154#393C2×C418yescomplemented
155#393C2×C418yescomplemented
156#391—44no—
157#391—44no—
158#390C2×C4116yes—
159#387—44no—
160#387—44no—
161#386—24no—
162#386—28no—
163#386Q818yescomplemented
164#385—44no—
165#385—44no—
166#382C2×C4116yescomplemented
167#380—42no—
168#380C2×C4116yescomplemented
169#380C2×C4116yescomplemented
170C4×C4⋊C4C2×C418yescomplemented
171C4×C22⋊C4—42no—
172C4×C22⋊C4—44no—
173C4×C22⋊C4—44no—
174C2×#95—42no—
175C2×#95—42no—
176C2×#95C2312yes—
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×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C22×Q8—41no—
228C22×Q8—41no—
229C22×Q8—41no—
230C22×Q8—41no—
231C22×Q8—42no—
232C22×Q8—42no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8C22×C414yes—
236C22×Q8C22×C414yes—
237C22×D4—41no—
238C22×D4—41no—
239C22×D4—41no—
240C22×D4—41no—
241C22×D4C22×C414yes—
242C22×D4C2×Q814yes—
243C22×D4#4114yes—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—41no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4—42no—
262C23×C4—41no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4C22×C414yes—
269C23×C4C22×C414yes—
270C23×C4C2×Q814yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C4⋊Q8—416no—
289C4×D4—416no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
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—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4C22×C418yes—
315C2×C4⋊C4C22×C414yes—
316C2×C4⋊C4C22×C418yes—
317C2×C4⋊C4C22×C418yes—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
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⋊C4C22×C414yes—
350C2×C22⋊C4C22×C414yes—
351C2×C22⋊C4C22×C418yes—
352C2×C22⋊C4C22×C418yes—
353C2×C22⋊C4C22×C418yes—
354C2×C22⋊C4C22×C418yes—
355C2×C22⋊C4C2×Q814yes—
356C2×C22⋊C4C2×Q818yes—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—42no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42C22×C414yes—
377C2×C42C22×C418yes—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—42no—
390#95—41no—
391#95—41no—
392#95—42no—
393#95—42no—
394#95—42no—
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—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—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95C22×C414yes—
421#95C22×C414yes—
422#95C22×C418yes—
423#95C22×C418yes—
424#95C22×C418yes—
425#95C22×C418yes—
426#95C2×Q818yes—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24C23×C412yes—
444C24C23×C412yes—
445C24C22×Q812yes—
446C24C22×Q812yes—
447C24C2×#4112yes—
448C24C2×#4112yes—
449C24C2511yescharacteristic
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—48no—
453C2×Q8—48no—
454C2×Q8—84no—
455C2×Q8—84no—
456C2×Q8—82no—
457C2×Q8—82no—
458C2×Q8—82no—
459C2×Q8—82no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4C4×Q8116yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
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—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—28no—
528C22×C4—28no—
529C22×C4—22no—
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—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—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—84no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—84no—
576C22×C4—82no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—82no—
583C22×C4—84no—
584C22×C4—82no—
585C22×C4—84no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—84no—
589C22×C4C23×C412yes—
590C22×C4C23×C412yes—
591C22×C4C23×C414yes—
592C22×C4C23×C414yes—
593C22×C4C23×C412yes—
594C22×C4C23×C414yes—
595C22×C4C23×C414yes—
596C22×C4C23×C412yes—
597C22×C4C23×C412yes—
598C22×C4C22×Q814yes—
599C22×C4C22×Q814yes—
600C22×C4C22×Q812yes—
601C22×C4C2×#4112yes—
602C22×C4H(5,𝔽2)14yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C4H(5,𝔽2)12yes—
605C4⋊C4—216no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—48no—
609C4⋊C4—84no—
610C4⋊C4—84no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—48no—
622C22⋊C4—44no—
623C22⋊C4—48no—
624C22⋊C4—44no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C42—28no—
629C42—48no—
630C42—84no—
631C42—84no—
632C42—84no—
633C42—84no—
634C42—84no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23C2×C4×Q814yes—
680C23C2×C4×Q814yes—
681C23C24×C411yescharacteristic
682C23C23×Q811yescharacteristic
683C23C22×#4111yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×H(5,𝔽2)11yescharacteristic
686C23C2×H(5,𝔽2)12yes—
687C23#58511yescharacteristic
688C23#58511yescharacteristic
689C23#58512yes—
690C23#58512yes—
691C23#58512yes—
692Q8—88no—
693Q8—88no—
694D4—416no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
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—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
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—42no—
804C2×C4—88no—
805C2×C4—88no—
806C2×C4—88no—
807C2×C4—816no—
808C2×C4—88no—
809C2×C4C2×C4×Q814yes—
810C2×C4#51814yes—
811C22—28no—
812C22—28no—
813C22—24no—
814C22—24no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—44no—
826C22—44no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22C22×C4×Q811yescharacteristic
834C22C2×#51811yescharacteristic
835C22#342812yes—
836C22#342811yescharacteristic
837C22C4×H(5,𝔽2)12yes—
838C22#350111yescharacteristic
839C22#350112yes—
840C22#350111yescharacteristic
841C22#350412yes—
842C22#350511yescharacteristic
843C22#350511yescharacteristic
844C22#351312yes—
845C22#352112yes—
846C22#354212yes—
847C22#354511yescharacteristic
848C22#354512yes—
849C22#354511yescharacteristic
850C22#354512yes—
851C22#354911yescharacteristic
852C22#355111yescharacteristic
853C22#355112yes—
854C22#356612yes—
855C22#356612yes—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—44no—
862C4—44no—
863C4—42no—
864C4—44no—
865C4—44no—
866C4—44no—
867C4—44no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C2—44no—
874C2—44no—
875C2#3421211yescharacteristic
876C2#3433312yes—
877C2#3436611yescharacteristic
878C2#3441511yescharacteristic
879C2#3450312yes—
880C2#4684211yescharacteristic
881C2#4684412yes—
882C2#4684911yescharacteristic
883C2#4692912yes—
884C2#4693511yescharacteristic
885C2#4760411yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14635C2semidirect
3. #14596C2semidirect
4. #14575C2semidirect
5. #14553C2semidirect
6. #14455C2semidirect
8. #14420C2semidirect
9. #14370C2semidirect
10. #14243C2semidirect
11. #14213C2semidirect
12. #14107C2semidirect
13. #14106C2semidirect
14. #14047C2semidirect
15. #14028C2semidirect
17. #13928C2semidirect
22. #2563C4semidirect
118. C2×C4⋊Q8C2×C4semidirect
152. #393C2×C4semidirect
153. #393C2×C4semidirect
154. #393C2×C4semidirect
155. #393C2×C4semidirect
163. #386Q8semidirect
166. #382C2×C4semidirect
168. #380C2×C4semidirect
169. #380C2×C4semidirect
170. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25632
#146352
#145962
#145752
#145532
#144552
#144382
#144202
#143702
#142432
#142132
#141072
#141062
#140472
#140282
#139602
#139282
#137912
#137842