Finite Group Databasebeta

← #874207

Subgroups — #874207

Order 512.

2830 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2567C211yesmaximal, characteristic, complemented
2C2×#2502C211yesmaximal, characteristic
3C2×#2423C211yesmaximal, characteristic
4C2×#2440C211yesmaximal, characteristic
5#16522C214yesmaximal, complemented
6#15629C214yesmaximal, complemented
7#15430C214yesmaximal
8#15196C211yesmaximal, characteristic, complemented
9#15195C211yesmaximal, characteristic
10#15185C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic
12#15145C211yesmaximal, characteristic, complemented
13#15143C211yesmaximal, characteristic, complemented
14#14703C211yesmaximal, characteristic, complemented
15#14692C211yesmaximal, characteristic, complemented
16#14405C214yesmaximal
17#13976C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic
19C4×#388C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C22×C4×Q8C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2567—28no—
26#2502—28no—
27#2440—28no—
28#2423—28no—
29C2×#399C2212yes—
30C2×#398C2212yes—
31C2×#398C2214yes—
32C2×#398C2212yes—
33C2×#398C2214yes—
34C2×#395C2214yes—
35C2×#395C2212yes—
36C2×#395C2214yes—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#389C2214yes—
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#387C2212yes—
49C2×#385C2212yes—
50C2×#385C2214yes—
51C2×#385C2214yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2214yes—
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C2×#384C2214yes—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1445C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1444C2214yes—
74#1444C2214yes—
75#1442C2214yes—
76#1442C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2212yes—
82#1436C2212yes—
83#1436C2214yes—
84#1436C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2214yes—
92#1434C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—42no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—28no—
105C2×C22⋊Q8—48no—
106C2×C22⋊Q8—42no—
107C2×C4×Q8—24no—
108C2×C4×Q8—24no—
109C2×C4×Q8—42no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4C2312yes—
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⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154#399—28no—
155#398—28no—
156#398—28no—
157#398—216no—
158#398—48no—
159#395—216no—
160#395—28no—
161#395—48no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391D418yes—
167#389—24no—
168#389—24no—
169#389—24no—
170#389—216no—
171#388—28no—
172#388Q8116yescomplemented
173#387—28no—
174#385—28no—
175#385—216no—
176#385—48no—
177#384—24no—
178#384—24no—
179#384—24no—
180#384—24no—
181#384—24no—
182#384—24no—
183#384—42no—
184#384—42no—
185#384—48no—
186#384—48no—
187#380—24no—
188#380—24no—
189C4×C4⋊C4—24no—
190C4×C22⋊C4—24no—
191C4×C22⋊C4—24no—
192C4×C22⋊C4D418yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2311yescharacteristic
215C2×#95C2314yes—
216C2×#95C2311yescharacteristic
217C2×#95C2312yes—
218C2×#95C2312yes—
219C43—24no—
220C25C2411yescharacteristic
221C22×Q8—22no—
222C22×Q8—24no—
223C22×Q8—24no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—44no—
230C22×Q8—42no—
231C22×Q8—44no—
232C22×Q8C2×D414yes—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—42no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4C2×D414yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C4⋊Q8—416no—
264C22⋊Q8—432no—
265C22⋊Q8—416no—
266C4×Q8—416no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
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—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—416no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
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⋊C4—44no—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×Q818yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4C2×D414yes—
349C2×C22⋊C4C2×D414yes—
350C2×C22⋊C4C2×Q818yes—
351C2×C22⋊C4C2×Q818yes—
352C2×C22⋊C4C2×Q818yes—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—42no—
375C2×C42C2×D414yes—
376C2×C42C2×D414yes—
377C2×C42C2×D414yes—
378C2×C42C2×Q818yes—
379C2×C42#4114yes—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—28no—
391#95—24no—
392#95—28no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95C2×D414yes—
402#95C2×D414yes—
403#95C2×D4116yes—
404#95C2×Q818yes—
405#95C2×Q818yes—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—22no—
410C24—21no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24C22×D412yes—
416C24C22×Q814yes—
417C24C2511yescharacteristic
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8—48no—
422C2×Q8—48no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—88no—
428C2×Q8—84no—
429C2×Q8—88no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
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—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—48no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—48no—
518C22×C4—88no—
519C22×C4—84no—
520C22×C4—88no—
521C22×C4C22×D414yes—
522C22×C4C22×D412yes—
523C22×C4C22×D414yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×D414yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×Q814yes—
532C22×C4C22×Q814yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q814yes—
535C22×C4C22×Q814yes—
536C22×C4C22×Q814yes—
537C22×C4C2×#4114yes—
538C22×C4C2×#4112yes—
539C22×C4H(5,𝔽2)14yes—
540C22×C4H(5,𝔽2)14yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C42−1+414yes—
543C22×C42−1+412yes—
544C22×C42−1+412yes—
545C22×C42−1+412yes—
546C4⋊C4—28no—
547C4⋊C4—216no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—84no—
563C4⋊C4—88no—
564C4⋊C4—88no—
565C4⋊C4—84no—
566C4⋊C4—88no—
567C4⋊C4—88no—
568C4⋊C4—88no—
569C4⋊C4—88no—
570C4⋊C4—84no—
571C22⋊C4—28no—
572C22⋊C4—216no—
573C22⋊C4—216no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—84no—
577C22⋊C4C4⋊Q8116yes—
578C42—216no—
579C42—28no—
580C42—28no—
581C42—28no—
582C42—28no—
583C42—216no—
584C42—48no—
585C42—44no—
586C42—44no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23C2×C4⋊Q814yes—
610C23C23×D411yescharacteristic
611C23C23×D411yescharacteristic
612C23C23×Q812yes—
613C23C22×#4111yescharacteristic
614C23C2×H(5,𝔽2)12yes—
615C23C2×H(5,𝔽2)11yescharacteristic
616C23C2×H(5,𝔽2)12yes—
617C23C2×2−1+411yescharacteristic
618C23C2×2−1+411yescharacteristic
619C23C2×2−1+411yescharacteristic
620C23C2×2−1+412yes—
621Q8—416no—
622Q8—816no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—28no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—416no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—816no—
717C2×C4C2×C4⋊Q814yes—
718C2×C4C2×C4⋊Q814yes—
719C2×C4#53514yes—
720C2×C4#53614yes—
721C2×C4#53614yes—
722C2×C4#53914yes—
723C2×C4D4214yes—
724C2×C4#54714yes—
725C2×C4#54714yes—
726C2×C4D4×Q818yes—
727C2×C4#55418yes—
728C2×C4#56314yes—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—42no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—42no—
737C22—42no—
738C22—44no—
739C22—42no—
740C22C22×C4⋊Q811yescharacteristic
741C22C2×#53511yescharacteristic
742C22C2×#53611yescharacteristic
743C22C2×#53611yescharacteristic
744C22C2×#53911yescharacteristic
745C22C2×D4211yescharacteristic
746C22C2×#54711yescharacteristic
747C22C2×#54711yescharacteristic
748C22C2×D4×Q812yes—
749C22C2×#55412yes—
750C22#349212yes—
751C22#349811yescharacteristic
752C22#349812yes—
753C22#349911yescharacteristic
754C22#350312yes—
755C22#350312yes—
756C22#350312yes—
757C22#350312yes—
758C22C2×#56311yescharacteristic
759C22#354312yes—
760C22#354412yes—
761C22#354412yes—
762C22#355212yes—
763C4—24no—
764C4—24no—
765C4—28no—
766C4—28no—
767C4—24no—
768C4—42no—
769C4—44no—
770C4—44no—
771C4—44no—
772C4—42no—
773C4—44no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4#268018yes—
781C2—44no—
782C2#3528111yescharacteristic
783C2D4×C4⋊Q811yescharacteristic
784C2#3618011yescharacteristic
785C2#3730311yescharacteristic
786C2#3786311yescharacteristic
787C2#3936111yescharacteristic
788C2#3960412yes—
789C2#3961712yes—
790C2#4600112yes—
791C2C2×#268011yescharacteristic
792C2#5931412yes—
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. #16522C2semidirect
6. #15629C2semidirect
8. #15196C2semidirect
10. #15185C2semidirect
12. #15145C2semidirect
13. #15143C2semidirect
14. #14703C2semidirect
15. #14692C2semidirect
17. #13976C2semidirect
172. #388Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25672
C2×#25022
C2×#24232
C2×#24402
#165222
#156292
#154302
#151962
#151952
#151852
#151822
#151452
#151432
#147032
#146922
#144052
#139762
#138802
C4×#3882