Finite Group Databasebeta

← #878971

Subgroups — #878971

Order 512.

2174 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17078C211yesmaximal, characteristic, complemented
2#17073C211yesmaximal, characteristic, complemented
3#16959C212yesmaximal, complemented
4#15959C212yesmaximal
5#15788C212yesmaximal
6#15488C212yesmaximal
7#15276C212yesmaximal
8#14944C212yesmaximal, complemented
9#14943C212yesmaximal, complemented
10#14891C212yesmaximal
11#14702C211yesmaximal, characteristic
12#14697C211yesmaximal, characteristic
13#14570C212yesmaximal, complemented
14#14467C211yesmaximal, characteristic, complemented
15#14446C211yesmaximal, characteristic, complemented
16#14214C212yesmaximal, complemented
17#14211C212yesmaximal, complemented
18#13938C212yesmaximal
19#13756C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#398C2212yes—
25C2×#398C2212yes—
26C2×#396C2212yes—
27C2×#395C2212yes—
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2212yes—
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2212yes—
34C2×#387C2212yes—
35C2×#387C2212yes—
36C2×#387C2212yes—
37C2×#385C2212yes—
38C2×#383C2212yes—
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C4⋊C4C2212yes—
43#1445C2212yes—
44#1445C2212yes—
45#1445C2212yes—
46#1445C2212yes—
47#1444C2212yes—
48#1444C2212yes—
49#1444C2212yes—
50#1444C2212yes—
51#1444C2212yes—
52#1444C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1441C2212yes—
60#1441C2212yes—
61#1441C2212yes—
62#1441C2212yes—
63#1441C2212yes—
64#1441C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89C4⋊#95C2212yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C4⋊#95C2211yescharacteristic
98#1434C2212yes—
99#1434C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C23×Q8C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×#117—24no—
115C2×#117—42no—
116C2×#117—42no—
117C2×#117—42no—
118C2×#117—42no—
119C2×#117Q818yescomplemented
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C42—24no—
149C22×C42—42no—
150C22×C42—42no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159#398—28no—
160#398—28no—
161#396—44no—
162#395—28no—
163#391—24no—
164#391—42no—
165#391—44no—
166#389—24no—
167#389—42no—
168#389—44no—
169#387—44no—
170#387—44no—
171#387—44no—
172#385—44no—
173#383—44no—
174#380—24no—
175#380—42no—
176#380—42no—
177C4×C4⋊C4—44no—
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×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C25C2411yescharacteristic
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—41no—
229C22×Q8—41no—
230C22×Q8—41no—
231C22×Q8—41no—
232C22×Q8#4114yes—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4—41no—
252C23×C4—41no—
253C23×C4C2×Q814yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C22⋊Q8—416no—
273#117—416no—
274#117—416no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4C2×Q814yes—
338C2×C4⋊C4C2×Q814yes—
339C2×C4⋊C4#4114yes—
340C2×C4⋊C4#4114yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
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⋊C4C2×Q818yes—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—42no—
369C2×C42—41no—
370C2×C42—41no—
371C2×C42—41no—
372C2×C42—41no—
373C2×C42—41no—
374C2×C42—41no—
375C2×C42—416no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42C2×Q818yes—
383C2×C42#4114yes—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
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—
429#95—42no—
430#95—42no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24C22×Q812yes—
444C24H(5,𝔽2)12yes—
445C242−1+412yes—
446C24C2511yescharacteristic
447C2×Q8—28no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—82no—
451C2×Q8—82no—
452C2×Q8—82no—
453C2×Q8—82no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
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—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—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4C22×Q814yes—
583C22×C4C22×Q814yes—
584C22×C4C22×Q812yes—
585C22×C4C22×Q812yes—
586C22×C4C2×#4114yes—
587C22×C4C2×#4114yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C42−1+412yes—
600C22×C42−1+412yes—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C4⋊C4—84no—
622C4⋊C4—84no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C42—216no—
630C42—44no—
631C42—44no—
632C42—44no—
633C42—48no—
634C42—44no—
635C42—84no—
636C42—84no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#54414yes—
672C23C23×Q811yescharacteristic
673C23C22×#4111yescharacteristic
674C23C22×#4111yescharacteristic
675C23C22×#4111yescharacteristic
676C23C22×#4111yescharacteristic
677C23C2×H(5,𝔽2)11yescharacteristic
678C23C2×H(5,𝔽2)11yescharacteristic
679C23C2×H(5,𝔽2)11yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×2−1+411yescharacteristic
683C23C2×2−1+411yescharacteristic
684C23C2×2−1+411yescharacteristic
685C23#58511yescharacteristic
686C23#58511yescharacteristic
687Q8—88no—
688C2×C4—232no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
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—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—416no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
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—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—42no—
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#53314yes—
814C2×C4#54314yes—
815C2×C4#55314yes—
816C2×C4#55614yes—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22C2×#53311yescharacteristic
833C22C2×#54311yescharacteristic
834C22C2×#54411yescharacteristic
835C22#345911yescharacteristic
836C22#345911yescharacteristic
837C22C2×#55311yescharacteristic
838C22C2×#55611yescharacteristic
839C22Q8×#4111yescharacteristic
840C22Q8×#4111yescharacteristic
841C22#348111yescharacteristic
842C22#348211yescharacteristic
843C22#348311yescharacteristic
844C22#349011yescharacteristic
845C22#349011yescharacteristic
846C22#349011yescharacteristic
847C22#349211yescharacteristic
848C22#349211yescharacteristic
849C22#349211yescharacteristic
850C22#349411yescharacteristic
851C22#349511yescharacteristic
852C22#350311yescharacteristic
853C22#350311yescharacteristic
854C22#351711yescharacteristic
855C22#351811yescharacteristic
856C22#352011yescharacteristic
857C22#352311yescharacteristic
858C22#352911yescharacteristic
859C22#353411yescharacteristic
860C22#353511yescharacteristic
861C22#353711yescharacteristic
862C22#353811yescharacteristic
863C22#354811yescharacteristic
864C22#354811yescharacteristic
865C22#356111yescharacteristic
866C22#356311yescharacteristic
867C4—24no—
868C4—24no—
869C4—24no—
870C4—24no—
871C4—42no—
872C4—44no—
873C4—44no—
874C4—42no—
875C4—44no—
876C4—44no—
877C4—44no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C2—44no—
886C2#3505211yescharacteristic
887C2#3648011yescharacteristic
888C2#3648111yescharacteristic
889C2#3730711yescharacteristic
890C2#3794011yescharacteristic
891C2#3795611yescharacteristic
892C2#3844611yescharacteristic
893C2#3844711yescharacteristic
894C2#3876111yescharacteristic
895C2#3880111yescharacteristic
896C2#4623311yescharacteristic
897C2#4631511yescharacteristic
898C2#5229111yescharacteristic
899C2#5921811yescharacteristic
900C2#6004411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17078C2semidirect
2. #17073C2semidirect
3. #16959C2semidirect
8. #14944C2semidirect
9. #14943C2semidirect
13. #14570C2semidirect
14. #14467C2semidirect
15. #14446C2semidirect
16. #14214C2semidirect
17. #14211C2semidirect
119. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#170782
#170732
#169592
#159592
#157882
#154882
#152762
#149442
#149432
#148912
#147022
#146972
#145702
#144672
#144462
#142142
#142112
#139382
#137562