Finite Group Databasebeta

← #674180

Subgroups — #674180

Order 512.

3610 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C212yesmaximal
2C2×#2440C212yesmaximal, complemented
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
5#15305C214yesmaximal, complemented
6#15276C214yesmaximal, complemented
7#15158C212yesmaximal, complemented
8#15133C212yesmaximal, complemented
9#15131C212yesmaximal, complemented
10#15131C212yesmaximal, complemented
11#14712C211yesmaximal, characteristic, complemented
12#14018C212yesmaximal
13#13910C211yesmaximal, characteristic, complemented
14#13910C211yesmaximal, characteristic, complemented
15#13907C212yesmaximal, complemented
16#13906C211yesmaximal, characteristic
17C4×#390C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2214yes—
20C22×C4×Q8C2212yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2212yes—
24#2538—216no—
25#2440—216no—
26C2×#398C2214yes—
27C2×#396C2214yes—
28C2×#396C2214yes—
29C2×#395C2214yes—
30D4×C4⋊C4—28no—
31C4×C4⋊Q8—28no—
32C2×#391C2212yes—
33C2×#390C2212yes—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#385C2214yes—
48C2×#385C2214yes—
49C2×#384C2211yescharacteristic
50C2×#384C2212yes—
51C2×#384C2212yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2214yes—
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64C2×C43C2211yescharacteristic
65#1444C2214yes—
66#1444C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1437C2212yes—
77#1437C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C22⋊#95C2214yes—
87C23×Q8C2312yes—
88C23×D4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2314yes—
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8D418yescomplemented
94C2×C22⋊Q8—216no—
95C2×C22⋊Q8—216no—
96C2×C22⋊Q8—48no—
97C2×C4×Q8—28no—
98C2×C4×Q8—28no—
99C2×C4×Q8—44no—
100C2×C4×D4—28no—
101C2×C4×D4—24no—
102C2×C4×D4—28no—
103C2×C4×D4—24no—
104C2×C4×D4—44no—
105C2×C4×D4Q818yescomplemented
106C22×C4⋊C4—28no—
107C22×C4⋊C4—28no—
108C22×C4⋊C4—28no—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C42C2312yes—
142C22×C42C2311yescharacteristic
143C22×C42C2312yes—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#398—216no—
152#396—216no—
153#396—216no—
154#395—216no—
155#391—28no—
156#390—28no—
157#390D418yes—
158#390Q818yescomplemented
159#389—24no—
160#389—24no—
161#389—28no—
162#389—28no—
163#389—28no—
164#389—28no—
165#389—28no—
166#389—28no—
167#389—44no—
168#389—44no—
169#389—44no—
170#385—216no—
171#385—216no—
172#384—24no—
173#384—28no—
174#384—28no—
175#384—24no—
176#384—24no—
177#380—28no—
178#380—28no—
179#380—216no—
180#380—44no—
181C4×C4⋊C4—28no—
182C4×C4⋊C4—24no—
183C4×C4⋊C4—24no—
184C4×C4⋊C4D418yes—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—44no—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C43—24no—
207C25C2412yes—
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8—24no—
211C22×Q8—24no—
212C22×Q8—42no—
213C22×Q8—42no—
214C22×Q8C2×D418yes—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4C2×D414yes—
220C22×D4C2×Q814yes—
221C22×D4C2×Q814yes—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—28no—
229C23×C4—28no—
230C23×C4—28no—
231C23×C4—28no—
232C23×C4—44no—
233C23×C4—44no—
234C23×C4—44no—
235C23×C4C2×Q818yes—
236C23×C4C2414yes—
237C23×C4C2412yes—
238C23×C4C2414yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2411yescharacteristic
243C23×C4C2412yes—
244C23×C4C2411yescharacteristic
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2411yescharacteristic
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C4⋊Q8—232no—
253C22⋊Q8—464no—
254C4×Q8—432no—
255C4×D4—232no—
256C4×D4—432no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—432no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D418yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D414yes—
325C2×C4⋊C4C2×D414yes—
326C2×C4⋊C4C2×D414yes—
327C2×C4⋊C4C2×Q814yes—
328C2×C4⋊C4C2×Q814yes—
329C2×C4⋊C4#4114yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4C2×D418yes—
350C2×C22⋊C4C2×D418yes—
351C2×C22⋊C4C2×Q818yes—
352C2×C22⋊C4C2×Q818yes—
353C2×C22⋊C4C2×Q818yes—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—41no—
376C2×C42—41no—
377C2×C42C2×D418yes—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381C2×C42C2×Q814yes—
382C2×C42C2×Q814yes—
383C2×C42#4114yes—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—28no—
390#95—28no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—24no—
396#95—42no—
397#95—42no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95C2×D418yes—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24C22×D414yes—
416C24C22×Q814yes—
417C24C22×Q814yes—
418C24C2511yescharacteristic
419C2×Q8—216no—
420C2×Q8—216no—
421C2×Q8—48no—
422C2×Q8—48no—
423C2×Q8—48no—
424C2×Q8—48no—
425C2×Q8—48no—
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—28no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4C4⋊Q8116yescomplemented
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—216no—
492C22×C4—216no—
493C22×C4—216no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—416no—
516C22×C4—416no—
517C22×C4—416no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—416no—
523C22×C4—88no—
524C22×C4—88no—
525C22×C4—88no—
526C22×C4C22×D412yes—
527C22×C4C22×D414yes—
528C22×C4C22×D414yes—
529C22×C4C22×D414yes—
530C22×C4C22×D414yes—
531C22×C4C22×D414yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×Q812yes—
541C22×C4C22×Q814yes—
542C22×C4C22×Q814yes—
543C22×C4C22×Q812yes—
544C22×C4C22×Q812yes—
545C22×C4C22×Q812yes—
546C22×C4C22×Q812yes—
547C22×C4C22×Q812yes—
548C22×C4C2×#4114yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C42−1+412yes—
557C22×C42−1+412yes—
558C22×C42−1+412yes—
559C4⋊C4—216no—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—28no—
563C4⋊C4—28no—
564C4⋊C4—28no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—416no—
570C4⋊C4—416no—
571C4⋊C4—48no—
572C4⋊C4—416no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C4⋊C4—48no—
576C4⋊C4—416no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—84no—
580C4⋊C4—88no—
581C4⋊C4—88no—
582C4⋊C4#121116yes—
583C22⋊C4—216no—
584C22⋊C4—216no—
585C22⋊C4—216no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—416no—
589C22⋊C4—416no—
590C22⋊C4—88no—
591C42—28no—
592C42—216no—
593C42—28no—
594C42—28no—
595C42—44no—
596C42—44no—
597C42—44no—
598C42—48no—
599C42—48no—
600C42C22⋊Q8116yescomplemented
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23C2×C4⋊Q818yes—
636C23C23×D411yescharacteristic
637C23C23×D411yescharacteristic
638C23C23×D411yescharacteristic
639C23C23×Q811yescharacteristic
640C23C23×Q811yescharacteristic
641C23C22×#4111yescharacteristic
642C23C22×#4111yescharacteristic
643C23C2×H(5,𝔽2)11yescharacteristic
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×H(5,𝔽2)11yescharacteristic
646C23C2×2−1+411yescharacteristic
647C23C2×2−1+411yescharacteristic
648C23C2×2−1+411yescharacteristic
649C23#58511yescharacteristic
650C23#58511yescharacteristic
651Q8—432no—
652D4—232no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—432no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—832no—
749C2×C4C2×#12118yes—
750C2×C4C2×#12114yes—
751C2×C4C2×C22⋊Q814yes—
752C2×C4C2×C22⋊Q814yes—
753C2×C4C2×C22⋊Q814yes—
754C2×C4C2×C4⋊Q814yes—
755C2×C4#53714yes—
756C2×C4#54414yes—
757C2×C4D4214yes—
758C2×C4D4214yes—
759C2×C4#54714yes—
760C2×C4D4×Q814yes—
761C2×C4D4×Q814yes—
762C2×C4D4×Q814yes—
763C2×C4#55014yes—
764C2×C4#55414yes—
765C2×C4#55414yes—
766C2×C4#55614yes—
767C22—28no—
768C22—28no—
769C22—28no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22C22×#12111yescharacteristic
783C22C22×C22⋊Q811yescharacteristic
784C22C22×C4⋊Q811yescharacteristic
785C22C2×#53711yescharacteristic
786C22C2×#54411yescharacteristic
787C22C2×D4211yescharacteristic
788C22C2×D4211yescharacteristic
789C22C2×#54711yescharacteristic
790C22C2×D4×Q811yescharacteristic
791C22C2×D4×Q811yescharacteristic
792C22C2×D4×Q811yescharacteristic
793C22C2×#55011yescharacteristic
794C22D4×#4111yescharacteristic
795C22C2×#55411yescharacteristic
796C22C2×#55411yescharacteristic
797C22C2×#55611yescharacteristic
798C22Q8×#4111yescharacteristic
799C22#348811yescharacteristic
800C22#348911yescharacteristic
801C22#349611yescharacteristic
802C22#349611yescharacteristic
803C22#349711yescharacteristic
804C22#349911yescharacteristic
805C22#350111yescharacteristic
806C22#350311yescharacteristic
807C22#350311yescharacteristic
808C22#350411yescharacteristic
809C22#350611yescharacteristic
810C22#350711yescharacteristic
811C22#351911yescharacteristic
812C22#352311yescharacteristic
813C22#354711yescharacteristic
814C22#354811yescharacteristic
815C22#354811yescharacteristic
816C22#355511yescharacteristic
817C4—24no—
818C4—24no—
819C4—28no—
820C4—24no—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—42no—
825C4—42no—
826C4—44no—
827C4—44no—
828C4—84no—
829C4—82no—
830C4—84no—
831C4#244018yescomplemented
832C4#253818yescomplemented
833C2—48no—
834C2C2×#244011yescharacteristic
835C2C2×#253811yescharacteristic
836C2#3551911yescharacteristic
837C2D4×#12111yescharacteristic
838C2D4×C4⋊Q811yescharacteristic
839C2#3626111yescharacteristic
840C2Q8×#12111yescharacteristic
841C2#3896511yescharacteristic
842C2#3934011yescharacteristic
843C2#3937011yescharacteristic
844C2#3959811yescharacteristic
845C2#5942811yescharacteristic
846C2#5942911yescharacteristic
847C2#5981511yescharacteristic
848C2#5982311yescharacteristic
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
2. C2×#2440C2semidirect
4. C2×C4×C4⋊Q8C2semidirect
5. #15305C2semidirect
6. #15276C2semidirect
7. #15158C2semidirect
8. #15133C2semidirect
9. #15131C2semidirect
10. #15131C2semidirect
11. #14712C2semidirect
13. #13910C2semidirect
14. #13910C2semidirect
15. #13907C2semidirect
93. C2×C4⋊Q8D4semidirect
105. C2×C4×D4Q8semidirect
158. #390Q8semidirect
432. C2×D4C4⋊Q8semidirect
600. C42C22⋊Q8semidirect
831. C4#2440semidirect
832. C4#2538semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24402
C2×D4×C4⋊C42
C2×C4×C4⋊Q82
#153052
#152762
#151582
#151332
#151312
#147122
#140182
#139102
#139072
#139062
C4×#3902