Finite Group Databasebeta

← #617547

Subgroups — #617547

Order 512.

2814 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2567C211yesmaximal, characteristic, complemented
2C2×#2628C211yesmaximal, characteristic
3C2×#2323C211yesmaximal, characteristic
4C2×#2296C211yesmaximal, characteristic
5#15888C214yesmaximal, complemented
6#15623C214yesmaximal, complemented
7#15426C214yesmaximal
8#15294C214yesmaximal
9#15237C211yesmaximal, characteristic, complemented
10#15196C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#15151C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic
14#14686C211yesmaximal, characteristic
15#14340C211yesmaximal, characteristic
16#14258C211yesmaximal, characteristic
17#14155C211yesmaximal, characteristic, complemented
18#13942C211yesmaximal, characteristic, complemented
19#13909C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2628—28no—
27#2567—28no—
28C2×#400C2212yes—
29C2×#399C2212yes—
30C2×#398C2214yes—
31C2×#395C2212yes—
32C2×#395C2214yes—
33C2×#393C2212yes—
34#2323—28no—
35#2296—28no—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2214yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2214yes—
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#387C2212yes—
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2214yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#1445C2214yes—
69#1445C2214yes—
70#1444C2214yes—
71#1443C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1440C2214yes—
81#1439C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93#1434C2214yes—
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×Q8C2312yes—
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8Q818yescomplemented
105C2×C4×Q8—24no—
106C2×C4×Q8—24no—
107C2×C4×Q8—24no—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—42no—
113C2×#117D418yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—42no—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156#400—28no—
157#399—28no—
158#398—48no—
159#395—28no—
160#395—216no—
161#393—28no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—48no—
166#391—42no—
167#391—42no—
168#389—216no—
169#389—28no—
170#389—28no—
171#389—24no—
172#389—24no—
173#389—24no—
174#389—28no—
175#388—28no—
176#388—28no—
177#387—28no—
178#385—28no—
179#385—28no—
180#384—24no—
181#384—24no—
182#384—42no—
183#382—24no—
184#382—42no—
185#380—24no—
186#380—24no—
187#380—24no—
188#380—48no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4D418yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—24no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—44no—
233C22×Q8—44no—
234C22×Q8C2×Q814yes—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4C2×D414yes—
247C23×C4C2×Q814yes—
248C23×C4#4114yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C4⋊Q8—416no—
268C22⋊Q8—232no—
269C4×Q8—416no—
270#117—232no—
271#117—416no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×D418yes—
336C2×C4⋊C4C2×Q814yes—
337C2×C4⋊C4C2×Q818yes—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
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—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4C2×D414yes—
354C2×C22⋊C4C2×D414yes—
355C2×C22⋊C4C2×Q818yes—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—416no—
375C2×C42—42no—
376C2×C42—44no—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42C2×D414yes—
382C2×C42#4114yes—
383#95—24no—
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—28no—
396#95—28no—
397#95—24no—
398#95—24no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95C2×D418yes—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24C22×D412yes—
420C24C22×Q812yes—
421C24C2×#4112yes—
422C24C2511yescharacteristic
423C2×Q8—28no—
424C2×Q8—28no—
425C2×Q8—28no—
426C2×Q8—416no—
427C2×Q8—44no—
428C2×Q8—48no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8—88no—
433C2×Q8—84no—
434C2×Q8—84no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—216no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
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—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
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—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4C22⋊Q8116yes—
528C22×C4C22×D412yes—
529C22×C4C22×D414yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D414yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×Q814yes—
540C22×C4C22×Q814yes—
541C22×C4C22×Q812yes—
542C22×C4C22×Q812yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4H(5,𝔽2)14yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C42−1+414yes—
551C22×C42−1+414yes—
552C22×C42−1+412yes—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—216no—
557C4⋊C4—216no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—44no—
563C4⋊C4—48no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—88no—
571C4⋊C4—88no—
572C4⋊C4—88no—
573C4⋊C4—84no—
574C4⋊C4—84no—
575C4⋊C4—84no—
576C22⋊C4—216no—
577C22⋊C4—28no—
578C22⋊C4—28no—
579C22⋊C4—48no—
580C22⋊C4—84no—
581C22⋊C4—84no—
582C22⋊C4—84no—
583C42—28no—
584C42—28no—
585C42—28no—
586C42—48no—
587C42—48no—
588C42—44no—
589C42—44no—
590C42—84no—
591C42#121116yes—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23C2×C22⋊Q814yes—
615C23C23×D411yescharacteristic
616C23C23×D411yescharacteristic
617C23C23×Q811yescharacteristic
618C23C22×#4111yescharacteristic
619C23C22×#4111yescharacteristic
620C23C2×H(5,𝔽2)11yescharacteristic
621C23C2×H(5,𝔽2)12yes—
622C23C2×2−1+412yes—
623C23C2×2−1+412yes—
624C23C2×2−1+411yescharacteristic
625C23#58512yes—
626Q8—416no—
627Q8—816no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—232no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—28no—
665C2×C4—24no—
666C2×C4—432no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4C2×#12114yes—
724C2×C4C2×#12114yes—
725C2×C4C2×#12114yes—
726C2×C4C2×C22⋊Q814yes—
727C2×C4C2×C22⋊Q814yes—
728C2×C4#53618yes—
729C2×C4#53714yes—
730C2×C4#54614yes—
731C2×C4D4×Q814yes—
732C2×C4#55214yes—
733C2×C4#55414yes—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—44no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—42no—
745C22C22×#12111yescharacteristic
746C22C22×C22⋊Q811yescharacteristic
747C22C2×#53612yes—
748C22C2×#53711yescharacteristic
749C22#346012yes—
750C22C2×#54611yescharacteristic
751C22C2×D4×Q811yescharacteristic
752C22C2×#55211yescharacteristic
753C22C2×#55411yescharacteristic
754C22#348812yes—
755C22#349212yes—
756C22#349512yes—
757C22#349811yescharacteristic
758C22#349911yescharacteristic
759C22#349911yescharacteristic
760C22#350011yescharacteristic
761C22#350212yes—
762C22#350312yes—
763C22#350912yes—
764C22#353612yes—
765C22#354112yes—
766C22#355012yes—
767C22#355512yes—
768C4—24no—
769C4—24no—
770C4—28no—
771C4—24no—
772C4—44no—
773C4—42no—
774C4—44no—
775C4—44no—
776C4—44no—
777C4—42no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4#241718yes—
786C2—44no—
787C2C2×#241711yescharacteristic
788C2#3525611yescharacteristic
789C2#3531611yescharacteristic
790C2#3553211yescharacteristic
791C2#3566811yescharacteristic
792C2#3729911yescharacteristic
793C2#3738911yescharacteristic
794C2#3783812yes—
795C2#3798112yes—
796C2#3959712yes—
797C2#3969112yes—
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. C2×#2567C2semidirect
5. #15888C2semidirect
6. #15623C2semidirect
9. #15237C2semidirect
10. #15196C2semidirect
11. #15184C2semidirect
12. #15151C2semidirect
17. #14155C2semidirect
18. #13942C2semidirect
19. #13909C2semidirect
104. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25672
C2×#26282
C2×#23232
C2×#22962
#158882
#156232
#154262
#152942
#152372
#151962
#151842
#151512
#147022
#146862
#143402
#142582
#141552
#139422
#139092