Finite Group Databasebeta

← #649088

Subgroups — #649088

Order 512.

3430 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2567C211yesmaximal, characteristic, complemented
2C2×#2440C211yesmaximal, characteristic
3C2×#2360C211yesmaximal, characteristic
4C22×#384C211yesmaximal, characteristic
5#15625C214yesmaximal, complemented
6#15438C214yesmaximal, complemented
7#15199C211yesmaximal, characteristic, complemented
8#15196C211yesmaximal, characteristic, complemented
9#15184C211yesmaximal, characteristic, complemented
10#15143C211yesmaximal, characteristic, complemented
11#14720C214yesmaximal
12#14702C211yesmaximal, characteristic
13#14139C211yesmaximal, characteristic
14#14048C211yesmaximal, characteristic, complemented
15#14043C214yesmaximal
16#13976C211yesmaximal, characteristic, complemented
17#13910C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic
19C4×#385C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C22×C4×Q8C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2214yes—
27C23×C42C2211yescharacteristic
28#2567—28no—
29#2440—28no—
30C2×#398C2212yes—
31C2×#395C2212yes—
32C2×#395C2214yes—
33C2×#395C2214yes—
34#2360—28no—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#389C2212yes—
41C2×#389C2211yescharacteristic
42C2×#389C2214yes—
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2214yes—
46C2×#387C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2214yes—
50C2×#385C2212yes—
51C2×#384—28no—
52C2×#384C2214yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66C2×C4×C22⋊C4C2211yescharacteristic
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1444C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1436C2212yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2212yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2312yes—
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—42no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—48no—
108C2×C22⋊Q8Q818yescomplemented
109C2×C4×Q8—24no—
110C2×C4×Q8—24no—
111C2×C4×Q8—42no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—216no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—48no—
120C22×C4⋊C4—48no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163#398—28no—
164#395—216no—
165#395—28no—
166#395—48no—
167#391—24no—
168#391—24no—
169#391—24no—
170#391—24no—
171#391—42no—
172#389—216no—
173#389—24no—
174#389—24no—
175#389—24no—
176#389—28no—
177#389—48no—
178#387—28no—
179#385—28no—
180#385—28no—
181#385—48no—
182#385Q8116yescomplemented
183#384—24no—
184#384—24no—
185#384—24no—
186#384—216no—
187#384—24no—
188#384—24no—
189#384—42no—
190#384D418yes—
191#380—24no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4—24no—
194C4×C4⋊C4—24no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4D418yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2312yes—
224C25C2411yescharacteristic
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—24no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—44no—
234C22×Q8—42no—
235C22×Q8—44no—
236C22×Q8C2×Q814yes—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—28no—
250C23×C4—28no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—44no—
254C23×C4—42no—
255C23×C4—44no—
256C23×C4—42no—
257C23×C4C2×D414yes—
258C23×C4C2×Q818yes—
259C23×C4C2×Q814yes—
260C23×C4#4114yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C4⋊Q8—416no—
280C22⋊Q8—232no—
281C22⋊Q8—432no—
282C4×Q8—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—416no—
327C2×C4⋊C4—416no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—464no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D414yes—
351C2×C4⋊C4C2×D4116yes—
352C2×C4⋊C4C2×Q814yes—
353C2×C4⋊C4C2×Q818yes—
354C2×C4⋊C4C2×Q818yes—
355C2×C4⋊C4C2×Q818yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4C2×D414yes—
364C2×C22⋊C4C2×D414yes—
365C2×C22⋊C4C2×Q818yes—
366C2×C22⋊C4C2×Q818yes—
367C2×C22⋊C4C2×Q818yes—
368C2×C42—232no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—42no—
390C2×C42—44no—
391C2×C42C2×D414yes—
392C2×C42C2×D414yes—
393C2×C42C2×D414yes—
394C2×C42#4114yes—
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—28no—
404#95—28no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—28no—
409#95—24no—
410#95—24no—
411#95—28no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95C2×D414yes—
418#95C2×D414yes—
419#95C2×Q818yes—
420#95C2×Q818yes—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—22no—
427C24C22×D412yes—
428C24C22×Q812yes—
429C24C22×Q814yes—
430C24C2×#4112yes—
431C24H(5,𝔽2)14yes—
432C24C2511yescharacteristic
433C2×Q8—28no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—48no—
437C2×Q8—48no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—88no—
443C2×Q8—84no—
444C2×Q8—88no—
445C22×C4—216no—
446C22×C4—216no—
447C22×C4—216no—
448C22×C4—216no—
449C22×C4—216no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—216no—
473C22×C4—28no—
474C22×C4—216no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
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—21no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—21no—
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—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—416no—
537C22×C4—416no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—84no—
541C22×C4—84no—
542C22×C4—88no—
543C22×C4—88no—
544C22×C4C22⋊Q8116yes—
545C22×C4C22×D412yes—
546C22×C4C22×D414yes—
547C22×C4C22×D412yes—
548C22×C4C22×D414yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D414yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×Q814yes—
556C22×C4C22×Q814yes—
557C22×C4C22×Q814yes—
558C22×C4C22×Q814yes—
559C22×C4C22×Q812yes—
560C22×C4C22×Q814yes—
561C22×C4C22×Q814yes—
562C22×C4C22×Q814yes—
563C22×C4C22×Q814yes—
564C22×C4C22×Q812yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4H(5,𝔽2)14yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C42−1+414yes—
572C22×C42−1+412yes—
573C4⋊C4—28no—
574C4⋊C4—216no—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—216no—
578C4⋊C4—216no—
579C4⋊C4—416no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—416no—
583C4⋊C4—416no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—416no—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—84no—
595C4⋊C4—88no—
596C4⋊C4—84no—
597C4⋊C4—88no—
598C22⋊C4—216no—
599C22⋊C4—28no—
600C22⋊C4—216no—
601C22⋊C4—48no—
602C22⋊C4C4⋊Q8116yes—
603C42—216no—
604C42—28no—
605C42—28no—
606C42—28no—
607C42—28no—
608C42—48no—
609C42—44no—
610C42—44no—
611C42—84no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23C2×C22⋊Q814yes—
631C23C2×C4⋊Q814yes—
632C23#53514yes—
633C23#55418yes—
634C23Q8218yes—
635C23C23×D411yescharacteristic
636C23C23×D411yescharacteristic
637C23C23×Q811yescharacteristic
638C23C23×Q812yes—
639C23C22×#4111yescharacteristic
640C23C22×#4111yescharacteristic
641C23C2×H(5,𝔽2)12yes—
642C23C2×H(5,𝔽2)11yescharacteristic
643C23C2×H(5,𝔽2)12yes—
644C23C2×2−1+411yescharacteristic
645C23C2×2−1+412yes—
646Q8—416no—
647Q8—816no—
648C2×C4—264no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—232no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
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—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
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—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—816no—
743C2×C4—816no—
744C2×C4C2×C22⋊Q814yes—
745C2×C4C2×C22⋊Q814yes—
746C2×C4#52514yes—
747C2×C4C2×C4⋊Q814yes—
748C2×C4C2×C4⋊Q814yes—
749C2×C4#53914yes—
750C2×C4D4214yes—
751C2×C4#54714yes—
752C2×C4D4×Q818yes—
753C2×C4D4×Q814yes—
754C2×C4#55418yes—
755C2×C4#55414yes—
756C22—28no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—28no—
764C22—24no—
765C22—24no—
766C22#256718yescomplemented
767C22C22×C22⋊Q811yescharacteristic
768C22C2×#52511yescharacteristic
769C22C22×C4⋊Q811yescharacteristic
770C22C2×#53511yescharacteristic
771C22C2×#53911yescharacteristic
772C22C2×D4211yescharacteristic
773C22C2×#54711yescharacteristic
774C22C2×D4×Q811yescharacteristic
775C22C2×D4×Q812yes—
776C22C2×#55412yes—
777C22C2×#55411yescharacteristic
778C22C2×#55412yes—
779C22C2×Q8212yes—
780C22#348412yes—
781C22#349212yes—
782C22#349212yes—
783C22#349811yescharacteristic
784C22#349911yescharacteristic
785C22#350312yes—
786C22#350312yes—
787C22#350312yes—
788C22#354312yes—
789C22#354412yes—
790C4—24no—
791C4—24no—
792C4—24no—
793C4—28no—
794C4—28no—
795C4—44no—
796C4—44no—
797C4—42no—
798C4—44no—
799C4—44no—
800C4—44no—
801C4—44no—
802C4—42no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4#244918yes—
808C2—28no—
809C2C2×#244911yescharacteristic
810C2C2×#256711yescharacteristic
811C2#3553211yescharacteristic
812C2D4×C4⋊Q811yescharacteristic
813C2#3618011yescharacteristic
814C2#3654612yes—
815C2#3767411yescharacteristic
816C2#3786311yescharacteristic
817C2#3960412yes—
818C2#5915112yes—
819C2#5932212yes—
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. #15625C2semidirect
6. #15438C2semidirect
7. #15199C2semidirect
8. #15196C2semidirect
9. #15184C2semidirect
10. #15143C2semidirect
14. #14048C2semidirect
16. #13976C2semidirect
17. #13910C2semidirect
108. C2×C22⋊Q8Q8semidirect
182. #385Q8semidirect
766. C22#2567semidirect

Maximal subgroups

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

subgroupindex
C2×#25672
C2×#24402
C2×#23602
C22×#3842
#156252
#154382
#151992
#151962
#151842
#151432
#147202
#147022
#141392
#140482
#140432
#139762
#139102
#138802
C4×#3852