Finite Group Databasebeta

← #639833

Subgroups — #639833

Order 512.

3766 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2625C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic
4C2×#2280C211yesmaximal, characteristic
5#16394C212yesmaximal, complemented
6#16393C212yesmaximal, complemented
7#16391C214yesmaximal
8#15183C212yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#14841C212yesmaximal, complemented
11#14840C212yesmaximal, complemented
12#14837C214yesmaximal, complemented
13#14343C211yesmaximal, characteristic, complemented
14#14264C211yesmaximal, characteristic, complemented
15#14258C211yesmaximal, characteristic, complemented
16#14138C212yesmaximal, complemented
17#13951C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#117C2212yes—
24C22×#117C2211yescharacteristic
25#2848—28no—
26#2625—28no—
27C2×#400C2212yescomplemented
28C2×#398C2212yescomplemented
29C2×#397C2214yes—
30C2×#391C2212yescomplemented
31C2×#391C2212yescomplemented
32C2×#389C2212yescomplemented
33C2×#389C2212yescomplemented
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yes—
37#2280—28no—
38#2280—28no—
39C2×#381C2212yes—
40C2×#381C2212yes—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#379C2212yes—
52C2×#379C2212yes—
53C2×#379C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58#1445C2212yescomplemented
59#1445C2212yescomplemented
60#1445C2214yescomplemented
61#1444C2212yescomplemented
62#1443C2214yescomplemented
63#1442C2214yescomplemented
64#1442C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2214yescomplemented
67#1441C2212yescomplemented
68#1440C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1436C2214yescomplemented
80#1436C2214yescomplemented
81C4⋊#95C2212yescomplemented
82C4⋊#95C2212yescomplemented
83C4⋊#95C2212yescomplemented
84C4⋊#95C2212yescomplemented
85C4⋊#95C2214yescomplemented
86#1434C2214yescomplemented
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—28no—
92C24×C4—44no—
93C24×C4D418yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—28no—
106C2×C22⋊Q8—44no—
107C2×#117—24no—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—28no—
111C2×#117—24no—
112C2×#117—28no—
113C2×#117—44no—
114C2×#117—44no—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
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×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2314yes—
148#400—28no—
149#398—28no—
150#397—216no—
151#391—28no—
152#391—44no—
153#389—28no—
154#389—44no—
155#385—28no—
156#385—28no—
157#385—28no—
158#381—28no—
159#381—28no—
160#380—24no—
161#380—24no—
162#380—24no—
163#380—24no—
164#380—24no—
165#380—24no—
166#380—24no—
167#380—24no—
168#380—28no—
169#380D418yes—
170#379—28no—
171#379—28no—
172#379—28no—
173C4×C22⋊C4—28no—
174C4×C22⋊C4—28no—
175C4×C22⋊C4—28no—
176C4×C22⋊C4—28no—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C25—22no—
202C25—22no—
203C25—24no—
204C25—24no—
205C25—42no—
206C25—42no—
207C25—41no—
208C25—41no—
209C25—41no—
210C25—41no—
211C25C2×D414yes—
212C25C2411yescharacteristic
213C25C2411yescharacteristic
214C25C2411yescharacteristic
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—24no—
219C22×Q8—24no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—24no—
228C23×C4—232no—
229C23×C4—232no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—416no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—432no—
245C23×C4—432no—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2×D414yes—
249C23×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4#4114yes—
254C23×C4#4118yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C22⋊Q8—416no—
270C22⋊Q8—416no—
271C22⋊Q8—416no—
272#117—432no—
273#117—416no—
274#117—416no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4C2×D418yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
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—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4C2×D418yes—
356C2×C42—28no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—28no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—44no—
365#95—28no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95C2×D418yes—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—22no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—28no—
416C24—28no—
417C24—28no—
418C24—44no—
419C24—44no—
420C24—44no—
421C24—44no—
422C24—48no—
423C24—48no—
424C24—48no—
425C24—48no—
426C24—48no—
427C24—48no—
428C24—48no—
429C24—48no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24C22×D412yes—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C2×#4112yes—
443C24C2×#4114yes—
444C242−1+414yes—
445C24C2511yescharacteristic
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—48no—
450C2×Q8—48no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—216no—
461C22×C4—216no—
462C22×C4—216no—
463C22×C4—216no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
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—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—4128no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4#121116yes—
553C22×C4#123116yes—
554C22×C4C22×D412yes—
555C22×C4C22×D418yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C2×#4112yes—
562C22×C4C2×#4114yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4114yes—
565C22×C4H(5,𝔽2)14yes—
566C4⋊C4—216no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—48no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C4⋊C4—48no—
576C4⋊C4—44no—
577C4⋊C4—48no—
578C4⋊C4—88no—
579C4⋊C4—88no—
580C22⋊C4—48no—
581C22⋊C4—416no—
582C22⋊C4—416no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C42—416no—
597C42—48no—
598C42—48no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—416no—
638C23—416no—
639C23—416no—
640C23—416no—
641C23—416no—
642C23—416no—
643C23—432no—
644C23—432no—
645C23—416no—
646C23—432no—
647C23—432no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—42no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23C2×#12114yes—
677C23C2×#12314yes—
678C23#53614yes—
679C23C23×D411yescharacteristic
680C23C23×D411yescharacteristic
681C23C22×#4111yescharacteristic
682C23C22×#4112yes—
683C23C2×H(5,𝔽2)12yes—
684C23C2×2−1+412yes—
685C23#58511yescharacteristic
686C23#58511yescharacteristic
687C23#58512yes—
688C23#58511yescharacteristic
689C23#58511yescharacteristic
690Q8—88no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—232no—
700C2×C4—232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—416no—
708C2×C4—416no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
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—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4C2×#12114yes—
775C2×C4C2×#12114yes—
776C2×C4C2×#12314yes—
777C2×C4C2×#12314yes—
778C2×C4#53414yes—
779C2×C4#54618yes—
780C2×C4#55118yes—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—464no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—42no—
814C22—42no—
815C22C22×#12111yescharacteristic
816C22C22×#12311yescharacteristic
817C22C2×#53411yescharacteristic
818C22C2×#53611yescharacteristic
819C22#344911yescharacteristic
820C22#344911yescharacteristic
821C22#344911yescharacteristic
822C22#345512yes—
823C22#345512yes—
824C22C2×#54612yes—
825C22C2×#55112yes—
826C22#348511yescharacteristic
827C22#348711yescharacteristic
828C22#348912yes—
829C22#349311yescharacteristic
830C22#349311yescharacteristic
831C22#349512yes—
832C22#349512yes—
833C22#349512yes—
834C22#353912yes—
835C22#354012yes—
836C22#354112yes—
837C22#354112yes—
838C4—24no—
839C4—24no—
840C4—48no—
841C4—42no—
842C4—84no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4#241218yes—
852C2—44no—
853C2—44no—
854C2—44no—
855C2#3463511yescharacteristic
856C2C2×#241211yescharacteristic
857C2#3515011yescharacteristic
858C2#3530611yescharacteristic
859C2#3531111yescharacteristic
860C2#3743811yescharacteristic
861C2#3744511yescharacteristic
862C2#3766812yes—
863C2#3767112yes—
864C2#3785612yes—
865C2#3785912yes—
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
2. C2×#2625C2semidirect
5. #16394C2semidirect
6. #16393C2semidirect
8. #15183C2semidirect
9. #15179C2semidirect
10. #14841C2semidirect
11. #14840C2semidirect
12. #14837C2semidirect
13. #14343C2semidirect
14. #14264C2semidirect
15. #14258C2semidirect
16. #14138C2semidirect
17. #13951C2semidirect
27. C2×#400C22semidirect
28. C2×#398C22semidirect
30. C2×#391C22semidirect
31. C2×#391C22semidirect
32. C2×#389C22semidirect
33. C2×#389C22semidirect
58. #1445C22semidirect
59. #1445C22semidirect
60. #1445C22semidirect
61. #1444C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
79. #1436C22semidirect
80. #1436C22semidirect
81. C4⋊#95C22semidirect
82. C4⋊#95C22semidirect
83. C4⋊#95C22semidirect
84. C4⋊#95C22semidirect
85. C4⋊#95C22semidirect
86. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#26252
C2×#22802
#163942
#163932
#163912
#151832
#151792
#148412
#148402
#148372
#143432
#142642
#142582
#141382
#139512