Finite Group Databasebeta

← #719707

Subgroups — #719707

Order 512.

3190 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×#2542C211yesmaximal, characteristic
2C2×#2566C211yesmaximal, characteristic
3C2×#2550C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic
5#16521C214yesmaximal, complemented
6#15406C214yesmaximal, complemented
7#15276C214yesmaximal, complemented
8#15234C211yesmaximal, characteristic, complemented
9#15228C211yesmaximal, characteristic, complemented
10#15196C211yesmaximal, characteristic, complemented
11#15143C211yesmaximal, characteristic, complemented
12#14720C214yesmaximal, complemented
13#14354C211yesmaximal, characteristic, complemented
14#13979C211yesmaximal, characteristic
15#13977C211yesmaximal, characteristic
16#13941C211yesmaximal, characteristic
17#13910C211yesmaximal, characteristic, complemented
18#13848C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C22⋊Q8C2214yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27#2566—28no—
28#2550—28no—
29#2542—28no—
30C2×#399C2214yes—
31C2×#398C2212yes—
32C2×#396C2214yes—
33C2×#395C2212yes—
34C2×#395C2214yes—
35D4×C4⋊C4—28no—
36C2×#391C2212yes—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2214yes—
47C2×#385C2212yes—
48C2×#385C2214yes—
49C2×#385C2212yes—
50C2×#385C2214yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×#376C2211yescharacteristic
66#1444C2214yes—
67#1444C2214yes—
68#1444C2212yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1442C2212yes—
74#1442C2214yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1437C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2312yes—
96C23×D4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2312yes—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—42no—
103C2×#125—24no—
104C2×#125—24no—
105C2×#125—42no—
106C2×C22⋊Q8—216no—
107C2×C22⋊Q8—48no—
108C2×C22⋊Q8—48no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—42no—
116C2×C4×D4—42no—
117C2×C4×D4Q818yescomplemented
118C22×C4⋊C4—28no—
119C22×C4⋊C4—48no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160#399—216no—
161#398—28no—
162#396—216no—
163#395—28no—
164#395—48no—
165#391—28no—
166#390—24no—
167#390—24no—
168#390D418yes—
169#390Q818yescomplemented
170#389—24no—
171#389—24no—
172#389—24no—
173#389—24no—
174#389—28no—
175#389—48no—
176#385—216no—
177#385—28no—
178#385—28no—
179#385—48no—
180#384—24no—
181#384—24no—
182#384—24no—
183#384—24no—
184#384—42no—
185#382—24no—
186#382—24no—
187#382—42no—
188#380—28no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4D418yes—
194#376—24no—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C25C2412yes—
222C22×Q8—24no—
223C22×Q8—24no—
224C22×Q8—28no—
225C22×Q8—44no—
226C22×Q8—42no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4C2×D414yes—
232C22×D4C2×Q814yes—
233C22×D4C2×Q814yes—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—28no—
241C23×C4—44no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4C2×Q818yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C4⋊Q8—416no—
268#125—416no—
269C22⋊Q8—464no—
270C4×D4—232no—
271C4×D4—416no—
272C4×D4—416no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—432no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2×D414yes—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×Q814yes—
340C2×C4⋊C4C2×Q814yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4C2×D4116yes—
360C2×C22⋊C4C2×Q818yes—
361C2×C22⋊C4C2×Q8116yes—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—44no—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42C2×D414yes—
382C2×C42C2×Q814yes—
383C2×C42C2×Q814yes—
384C2×C42#4114yes—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—28no—
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—28no—
400#95—24no—
401#95—24no—
402#95—44no—
403#95—42no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95C2×D414yes—
410#95C2×D414yes—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—24no—
415C24—22no—
416C24—24no—
417C24—22no—
418C24—24no—
419C24C22×D414yes—
420C24C22×Q814yes—
421C24C22×Q814yes—
422C24C2511yescharacteristic
423C2×Q8—416no—
424C2×Q8—48no—
425C2×Q8—48no—
426C2×Q8—84no—
427C2×Q8—88no—
428C2×D4—28no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4C4⋊Q8116yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
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—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—216no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—416no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—416no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—416no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—84no—
521C22×C4—88no—
522C22×C4—84no—
523C22×C4—88no—
524C22×C4—88no—
525C22×C4C22×D412yes—
526C22×C4C22×D414yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D414yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×Q814yes—
536C22×C4C22×Q814yes—
537C22×C4C22×Q814yes—
538C22×C4C22×Q812yes—
539C22×C4C22×Q812yes—
540C22×C4C22×Q812yes—
541C22×C4C22×Q812yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4H(5,𝔽2)14yes—
546C22×C4H(5,𝔽2)14yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C42−1+414yes—
549C22×C42−1+412yes—
550C4⋊C4—216no—
551C4⋊C4—216no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—44no—
557C4⋊C4—48no—
558C4⋊C4—416no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—416no—
566C4⋊C4—48no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—84no—
572C4⋊C4—88no—
573C4⋊C4—84no—
574C4⋊C4—88no—
575C22⋊C4—216no—
576C22⋊C4—416no—
577C22⋊C4—416no—
578C22⋊C4—416no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—416no—
582C42—28no—
583C42—28no—
584C42—28no—
585C42—28no—
586C42—44no—
587C42—44no—
588C42—84no—
589C42C22⋊Q8116yescomplemented
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—28no—
597C23—28no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—42no—
603C23—42no—
604C23—44no—
605C23—42no—
606C23—42no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23C2×C4⋊Q818yes—
613C23C23×D411yescharacteristic
614C23C23×D411yescharacteristic
615C23C23×Q811yescharacteristic
616C23C23×Q811yescharacteristic
617C23C22×#4111yescharacteristic
618C23C2×H(5,𝔽2)12yes—
619C23C2×H(5,𝔽2)11yescharacteristic
620C23C2×H(5,𝔽2)12yes—
621C23C2×2−1+411yescharacteristic
622C23C2×2−1+412yes—
623C23#58512yes—
624Q8—816no—
625D4—232no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—28no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—432no—
666C2×C4—42no—
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—42no—
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—44no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
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—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—816no—
718C2×C4—816no—
719C2×C4C2×C22⋊Q814yes—
720C2×C4C2×C22⋊Q814yes—
721C2×C4C2×C22⋊Q814yes—
722C2×C4C2×C4⋊Q814yes—
723C2×C4#53514yes—
724C2×C4#54414yes—
725C2×C4D4214yes—
726C2×C4#54714yes—
727C2×C4D4×Q814yes—
728C2×C4#55414yes—
729C22—216no—
730C22—28no—
731C22—48no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—48no—
736C22—44no—
737C22—44no—
738C22—48no—
739C22—44no—
740C22C22×C22⋊Q811yescharacteristic
741C22C22×C4⋊Q811yescharacteristic
742C22C2×#53511yescharacteristic
743C22#344911yescharacteristic
744C22C2×#54411yescharacteristic
745C22C2×D4211yescharacteristic
746C22C2×#54711yescharacteristic
747C22C2×D4×Q811yescharacteristic
748C22C2×#55411yescharacteristic
749C22#348412yes—
750C22#348912yes—
751C22#349212yes—
752C22#349811yescharacteristic
753C22#349911yescharacteristic
754C22#350112yes—
755C22#350112yes—
756C22#350312yes—
757C22#350312yes—
758C22#350612yes—
759C22#354312yes—
760C22#355212yes—
761C22#355412yes—
762C22#355912yes—
763C4—24no—
764C4—24no—
765C4—24no—
766C4—42no—
767C4—44no—
768C4—42no—
769C4—42no—
770C4—44no—
771C4—44no—
772C4—44no—
773C4—44no—
774C4—44no—
775C4—44no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4#244018yes—
781C2—48no—
782C2C2×#244011yescharacteristic
783C2#3517211yescharacteristic
784C2#3553211yescharacteristic
785C2#3592812yes—
786C2#3767411yescharacteristic
787C2#3768011yescharacteristic
788C2#3961111yescharacteristic
789C2#3961611yescharacteristic
790C2#4249912yes—
791C2#4490812yes—
792C2#4525512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2550C2semidirect
5. #16521C2semidirect
6. #15406C2semidirect
7. #15276C2semidirect
8. #15234C2semidirect
9. #15228C2semidirect
10. #15196C2semidirect
11. #15143C2semidirect
12. #14720C2semidirect
13. #14354C2semidirect
17. #13910C2semidirect
18. #13848C2semidirect
117. C2×C4×D4Q8semidirect
169. #390Q8semidirect
589. C42C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#25662
C2×#25502
C2×D4×C4⋊C42
#165212
#154062
#152762
#152342
#152282
#151962
#151432
#147202
#143542
#139792
#139772
#139412
#139102
#138482
#137852