Finite Group Databasebeta

← #627988

Subgroups — #627988

Order 512.

4258 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2626C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C2×#2312C211yesmaximal, characteristic, complemented
4C22×#390C211yesmaximal, characteristic
5#15696C214yesmaximal, complemented
6#15666C214yesmaximal, complemented
7#15631C214yesmaximal, complemented
8#15615C214yesmaximal, complemented
9#14727C212yesmaximal, complemented
10#14724C212yesmaximal
11#14702C211yesmaximal, characteristic, complemented
12#14697C211yesmaximal, characteristic, complemented
13#14338C211yesmaximal, characteristic, complemented
14#14043C212yesmaximal, complemented
15#13971C212yesmaximal, complemented
16C24×D4C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2626—28no—
25#2626—28no—
26C2×#399C2212yescomplemented
27C2×#399C2212yescomplemented
28C2×#397C2214yescomplemented
29C2×#396C2212yescomplemented
30C2×#396C2214yescomplemented
31C2×#396C2212yescomplemented
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#393C2212yescomplemented
35C2×#393C2212yescomplemented
36#2312—28no—
37C2×#391C2212yescomplemented
38C2×#390—28no—
39C2×#390C2214yes—
40C2×#390C2214yes—
41C2×#389C2214yescomplemented
42C2×#389C2212yescomplemented
43C2×#388C2214yescomplemented
44C2×#388C2214yescomplemented
45C2×#388C2214yescomplemented
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#379C2212yes—
53C2×#379C2212yes—
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×C4×C22⋊C4C2212yes—
57#1444C2214yescomplemented
58#1441C2214yescomplemented
59#1440C2214yescomplemented
60#1440C2214yescomplemented
61#1440C2214yescomplemented
62#1439C2214yescomplemented
63#1439C2212yescomplemented
64#1439C2212yescomplemented
65#1439C2214yescomplemented
66#1439C2214yescomplemented
67#1438C2214yes—
68#1438C2214yes—
69#1437C2214yescomplemented
70#1436C2214yescomplemented
71#1436C2214yescomplemented
72#1436C2214yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C26C2311yescharacteristic
80C26C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—44no—
86C23×D4—44no—
87C23×D4C2314yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C2×C22⋊Q8—24no—
94C2×C22⋊Q8—24no—
95C2×C22⋊Q8—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—44no—
98C22×C4⋊C4C2314yes—
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4—44no—
118C22×C22⋊C4D418yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C42—24no—
140C22×C42—44no—
141C22×C42C2312yes—
142C22×C42C2312yes—
143C22×C42C2314yes—
144#399—28no—
145#399—28no—
146#397—48no—
147#396—216no—
148#396—28no—
149#396—28no—
150#394—48no—
151#394—48no—
152#393—28no—
153#393—28no—
154#391—44no—
155#390—216no—
156#390—216no—
157#389—48no—
158#389—44no—
159#388—216no—
160#388—216no—
161#388—48no—
162#385—28no—
163#385—28no—
164#385—28no—
165#380—24no—
166#380—24no—
167#380D418yescomplemented
168#379—28no—
169#379—28no—
170#379—28no—
171#379—28no—
172C4×C22⋊C4—28no—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C25—22no—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—42no—
202C25—42no—
203C25—42no—
204C25—42no—
205C25—42no—
206C25—42no—
207C25—42no—
208C25—42no—
209C25C2×D414yes—
210C25#4114yes—
211C25C2412yes—
212C25C2412yes—
213C25C2411yescharacteristic
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—42no—
218C22×Q8—42no—
219C22×D4—232no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—416no—
228C22×D4—416no—
229C22×D4—432no—
230C22×D4—432no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4#4114yes—
255C23×C4#4114yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C22⋊Q8—416no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—416no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4C2×D418yescomplemented
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—232no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—416no—
340C2×C22⋊C4—416no—
341C2×C22⋊C4—416no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C2×D418yes—
357C2×C22⋊C4C2×D418yes—
358C2×C22⋊C4C2×D418yes—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—28no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—416no—
367C2×C42—44no—
368C2×C42—44no—
369#95—28no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95C2×D418yescomplemented
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—28no—
390C24—28no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—28no—
412C24—28no—
413C24—28no—
414C24—28no—
415C24—44no—
416C24—44no—
417C24—44no—
418C24—48no—
419C24—44no—
420C24—48no—
421C24—44no—
422C24—48no—
423C24—48no—
424C24—44no—
425C24—44no—
426C24—48no—
427C24—48no—
428C24—44no—
429C24—48no—
430C24—48no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—84no—
440C24—84no—
441C24—84no—
442C24—84no—
443C24—84no—
444C24—84no—
445C24—84no—
446C24—84no—
447C24—84no—
448C24—84no—
449C24—84no—
450C24—84no—
451C24—84no—
452C24—84no—
453C24—84no—
454C24—84no—
455C24C22×D414yes—
456C24C22×D412yes—
457C24C22×D412yes—
458C24C2×#4114yes—
459C24C2×#4112yes—
460C24C2×#4112yes—
461C24C2×#4112yes—
462C242−1+412yes—
463C242−1+412yes—
464C24C2511yescharacteristic
465C2×Q8—48no—
466C2×Q8—44no—
467C2×Q8—82no—
468C2×Q8—82no—
469C2×Q8—84no—
470C2×D4—232no—
471C2×D4—416no—
472C2×D4—416no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—4128no—
476C2×D4—416no—
477C2×D4—416no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—216no—
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—216no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—28no—
509C22×C4—24no—
510C22×C4—22no—
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—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4—84no—
557C22×C4—84no—
558C22×C4#121116yes—
559C22×C4C22×D418yes—
560C22×C4C22×D414yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4114yes—
568C22×C4H(5,𝔽2)14yes—
569C22×C4H(5,𝔽2)14yes—
570C22×C4H(5,𝔽2)14yes—
571C4⋊C4—48no—
572C4⋊C4—416no—
573C4⋊C4—44no—
574C4⋊C4—48no—
575C4⋊C4—416no—
576C4⋊C4—82no—
577C4⋊C4—82no—
578C4⋊C4—84no—
579C4⋊C4—84no—
580C4⋊C4—84no—
581C4⋊C4—88no—
582C22⋊C4—216no—
583C22⋊C4—216no—
584C22⋊C4—216no—
585C22⋊C4—416no—
586C22⋊C4—416no—
587C22⋊C4—416no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—88no—
594C22⋊C4—88no—
595C22⋊C4—88no—
596C22⋊C4—88no—
597C22⋊C4—84no—
598C22⋊C4—84no—
599C22⋊C4—84no—
600C22⋊C4—84no—
601C22⋊C4—88no—
602C42—48no—
603C42—48no—
604C42—88no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—28no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—28no—
633C23—416no—
634C23—416no—
635C23—416no—
636C23—416no—
637C23—42no—
638C23—416no—
639C23—416no—
640C23—42no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—88no—
674C23—88no—
675C23—88no—
676C23—816no—
677C23—88no—
678C23—816no—
679C23—88no—
680C23—816no—
681C23—816no—
682C23—88no—
683C23—88no—
684C23—816no—
685C23—88no—
686C23—816no—
687C23—816no—
688C23—816no—
689C23C2×#12114yes—
690C23#52514yes—
691C23#53614yes—
692C23#54714yes—
693C23#54814yes—
694C23#55214yes—
695C23#55614yes—
696C23C23×D411yescharacteristic
697C23C23×D411yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4111yescharacteristic
700C23C22×#4111yescharacteristic
701C23C2×H(5,𝔽2)12yes—
702C23C2×H(5,𝔽2)12yes—
703C23C2×H(5,𝔽2)12yes—
704C23C2×2−1+411yescharacteristic
705C23C2×2−1+411yescharacteristic
706C23#58512yes—
707Q8—88no—
708D4—464no—
709C2×C4—232no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—88no—
778C2×C4—88no—
779C2×C4C2×#12114yes—
780C2×C4C2×#12114yes—
781C2×C4#53818yes—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—28no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—48no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—48no—
804C22—832no—
805C22—832no—
806C22—82no—
807C22—84no—
808C22—84no—
809C22—82no—
810C22—82no—
811C22—84no—
812C22—82no—
813C22—84no—
814C22—84no—
815C22—84no—
816C22#241518yes—
817C22C22×#12111yescharacteristic
818C22C2×#52511yescharacteristic
819C22C2×#53611yescharacteristic
820C22C2×#53812yes—
821C22#345912yes—
822C22C2×#54711yescharacteristic
823C22C2×#54811yescharacteristic
824C22C2×#55211yescharacteristic
825C22C2×#55611yescharacteristic
826C22#348411yescharacteristic
827C22#348411yescharacteristic
828C22#348411yescharacteristic
829C22#348511yescharacteristic
830C22#349012yes—
831C22#349612yes—
832C22#349812yes—
833C22#350512yes—
834C22#350612yes—
835C22#350812yes—
836C22#353612yes—
837C22#353612yes—
838C22#356112yes—
839C22#356112yes—
840C4—24no—
841C4—24no—
842C4—28no—
843C4—44no—
844C4—44no—
845C4—48no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—84no—
852C2—28no—
853C2—84no—
854C2—84no—
855C2C2×#241511yescharacteristic
856C2#3498611yescharacteristic
857C2#3498811yescharacteristic
858C2#3535811yescharacteristic
859C2#3552811yescharacteristic
860C2#3671811yescharacteristic
861C2#3696611yescharacteristic
862C2#3937512yes—
863C2#3942012yes—
864C2#3951112yes—
865C2#3954012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2626C2semidirect
2. C2×#2626C2semidirect
3. C2×#2312C2semidirect
5. #15696C2semidirect
6. #15666C2semidirect
7. #15631C2semidirect
8. #15615C2semidirect
9. #14727C2semidirect
11. #14702C2semidirect
12. #14697C2semidirect
13. #14338C2semidirect
14. #14043C2semidirect
15. #13971C2semidirect
26. C2×#399C22semidirect
27. C2×#399C22semidirect
28. C2×#397C22semidirect
29. C2×#396C22semidirect
30. C2×#396C22semidirect
31. C2×#396C22semidirect
34. C2×#393C22semidirect
35. C2×#393C22semidirect
37. C2×#391C22semidirect
41. C2×#389C22semidirect
42. C2×#389C22semidirect
43. C2×#388C22semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
57. #1444C22semidirect
58. #1441C22semidirect
59. #1440C22semidirect
60. #1440C22semidirect
61. #1440C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
69. #1437C22semidirect
70. #1436C22semidirect
71. #1436C22semidirect
72. #1436C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
167. #380D4semidirect
298. C2×C4⋊C4C2×D4semidirect
384. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26262
C2×#23122
C22×#3902
#156962
#156662
#156312
#156152
#147272
#147242
#147022
#146972
#143382
#140432
#139712