Finite Group Databasebeta

← #535921

Subgroups — #535921

Order 512.

4484 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2388C211yesmaximal, characteristic
2C2×D4×C4⋊C4C212yesmaximal, complemented
3C2×#2311C212yesmaximal, complemented
4#14575C212yesmaximal, complemented
5#14535C212yesmaximal, complemented
6#14518C214yesmaximal, complemented
7#14236C212yesmaximal, complemented
8#14189C214yesmaximal, complemented
9#14171C212yesmaximal, complemented
10#13906C211yesmaximal, characteristic, complemented
11#13880C212yesmaximal, complemented
12#13876C212yesmaximal, complemented
13#13872C211yesmaximal, characteristic, complemented
14#13871C212yesmaximal, complemented
15#13801C212yesmaximal, complemented
16C23×#41C2211yescharacteristic
17C22×C4×D4C2212yes—
18C22×C4×D4C2214yes—
19C22×C4×D4C2211yescharacteristic
20C22×#117C2212yes—
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23#2388C4116yescomplemented
24C2×#395C2211yescharacteristic
25C2×#394C2212yes—
26C2×#394C2211yescharacteristic
27C2×#393C2211yescharacteristic
28C2×#392C2211yescharacteristic
29C2×#392C2212yes—
30D4×C4⋊C4—216no—
31#2311—216no—
32C2×#391C2214yes—
33C2×#390C2214yes—
34C2×#390C2212yes—
35C2×#389C2214yes—
36C2×#388C2214yes—
37C2×#386C2214yes—
38C2×#386C2214yes—
39C2×#386C2212yes—
40C2×#385C2214yes—
41C2×#385C2214yes—
42C2×#385C2214yes—
43C2×#385C2214yes—
44C2×#384C2212yes—
45C2×#384C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56#1444C2214yes—
57#1444C2214yes—
58#1442C2214yes—
59#1441C2212yes—
60#1440C2214yes—
61#1439C2212yes—
62#1439C2214yes—
63#1439C2212yes—
64#1439C2212yes—
65#1438C2214yes—
66#1437C2214yes—
67#1437C2214yes—
68#1437C2214yes—
69#1436C2214yes—
70#1436C2214yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75#1434C2214yes—
76C22⋊#95C2212yes—
77C4×#95C2214yes—
78C22×#41—28no—
79C22×#41—28no—
80C22×#41—42no—
81C22×#41—42no—
82C22×#41C2×C418yescomplemented
83C23×Q8C2311yescharacteristic
84C23×D4C2312yes—
85C23×D4C2311yescharacteristic
86C23×D4C2312yes—
87C23×D4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2314yes—
93C2×C4×D4—28no—
94C2×C4×D4—28no—
95C2×C4×D4—216no—
96C2×C4×D4—48no—
97C2×C4×D4—42no—
98C2×C4×D4—42no—
99C2×C4×D4—48no—
100C2×C4×D4C2×C4116yescomplemented
101C2×C4×D4C2×C418yescomplemented
102C2×#117—28no—
103C2×#117—28no—
104C2×#117—44no—
105C22×C4⋊C4—28no—
106C22×C4⋊C4—28no—
107C22×C4⋊C4—28no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—44no—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2314yes—
136C22×C42C2314yes—
137C22×C42C2314yes—
138C22×C42C2312yes—
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141#395C2×C418yescomplemented
142#394C2×C418yescomplemented
143#394C2×C4116yescomplemented
144#393C2×C418yescomplemented
145#392C2×C418yes—
146#392C2×C4116yescomplemented
147#391—216no—
148#390—216no—
149#390—44no—
150#389—216no—
151#388—48no—
152#386—216no—
153#386—216no—
154#386—44no—
155#385—216no—
156#385—216no—
157#385—48no—
158#385—48no—
159#384—28no—
160#384—42no—
161#380—28no—
162#380—28no—
163#380—28no—
164#380—28no—
165#380—42no—
166#380D4116yescomplemented
167C4×C4⋊C4—28no—
168C4×C4⋊C4—42no—
169C4×C22⋊C4C2×C418yescomplemented
170C4×C22⋊C4C2×C4116yescomplemented
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2311yescharacteristic
186C2×#95C2312yes—
187C2×#95C2311yescharacteristic
188C2×#95C2314yes—
189C25C2411yescharacteristic
190C25C2412yes—
191C25C2411yescharacteristic
192C2×#41—264no—
193C2×#41—416no—
194C2×#41—416no—
195C2×#41—432no—
196C2×#41—416no—
197C22×Q8—24no—
198C22×Q8—24no—
199C22×Q8—41no—
200C22×Q8—41no—
201C22×Q8C22×C414yes—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—22no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—41no—
219C22×D4—41no—
220C22×D4—42no—
221C22×D4—42no—
222C22×D4—41no—
223C22×D4—41no—
224C22×D4C22×C418yes—
225C22×D4C22×C414yes—
226C22×D4C22×C414yes—
227C22×D4C22×C418yes—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—28no—
241C23×C4—24no—
242C23×C4—28no—
243C23×C4—28no—
244C23×C4—42no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4—44no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—42no—
252C23×C4C22×C414yes—
253C23×C4C22×C414yes—
254C23×C4C22×C418yes—
255C23×C4C2×D418yes—
256C23×C4#4118yes—
257C23×C4C2414yes—
258C23×C4C2414yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2414yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C4×D4—264no—
270C4×D4—416no—
271C4×D4—464no—
272#117—432no—
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—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—416no—
293C2×C4⋊C4—432no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4C22×C418yes—
306C2×C4⋊C4C22×C414yes—
307C2×C4⋊C4C2×D418yes—
308C2×C4⋊C4C2×D418yes—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4C22×C418yes—
344C2×C22⋊C4C22×C418yes—
345C2×C22⋊C4C22×C418yes—
346C2×C22⋊C4C22×C418yes—
347C2×C22⋊C4C22×C418yes—
348C2×C22⋊C4C22×C414yes—
349C2×C22⋊C4C22×C414yes—
350C2×C22⋊C4C2×D4116yes—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—28no—
356C2×C42—28no—
357C2×C42—28no—
358C2×C42—28no—
359C2×C42—24no—
360C2×C42—44no—
361C2×C42—44no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42C22×C418yes—
365C2×C42C22×C414yes—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—42no—
375#95—42no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95C22×C414yes—
380#95C22×C418yes—
381#95C22×C414yes—
382#95C22×C418yes—
383#95C2×D4116yes—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—21no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24C23×C412yes—
415C24C23×C414yes—
416C24C23×C412yes—
417C24C22×D414yes—
418C24C2×#4114yes—
419C24H(5,𝔽2)12yes—
420C242−1+412yes—
421C24C2511yescharacteristic
422#41—4128no—
423C2×Q8—216no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—48no—
427C2×Q8—44no—
428C2×D4—216no—
429C2×D4—216no—
430C2×D4—216no—
431C2×D4—216no—
432C2×D4—216no—
433C2×D4—216no—
434C2×D4—216no—
435C2×D4—216no—
436C2×D4—28no—
437C2×D4—216no—
438C2×D4—216no—
439C2×D4—28no—
440C2×D4—44no—
441C2×D4—48no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—44no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—216no—
467C22×C4—216no—
468C22×C4—216no—
469C22×C4—216no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—48no—
521C22×C4—416no—
522C22×C4—416no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—416no—
530C22×C4—88no—
531C22×C4—88no—
532C22×C4—88no—
533C22×C4—88no—
534C22×C4—84no—
535C22×C4—88no—
536C22×C4—84no—
537C22×C4—88no—
538C22×C4C4×D4132yescomplemented
539C22×C4C23×C414yes—
540C22×C4C23×C412yes—
541C22×C4C23×C412yes—
542C22×C4C23×C412yes—
543C22×C4C23×C414yes—
544C22×C4C23×C414yes—
545C22×C4C23×C412yes—
546C22×C4C23×C412yes—
547C22×C4C22×D418yes—
548C22×C4C22×D418yes—
549C22×C4C22×D414yes—
550C22×C4C22×D414yes—
551C22×C4C2×#4114yes—
552C22×C4C2×#4114yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C4H(5,𝔽2)14yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C42−1+414yes—
558C22×C42−1+412yes—
559C4⋊C4—216no—
560C4⋊C4—216no—
561C4⋊C4—216no—
562C4⋊C4—44no—
563C4⋊C4—416no—
564C4⋊C4—48no—
565C4⋊C4—416no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—84no—
569C4⋊C4—88no—
570C4⋊C4—84no—
571C22⋊C4—216no—
572C22⋊C4—216no—
573C22⋊C4—216no—
574C22⋊C4—216no—
575C22⋊C4—216no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—416no—
579C22⋊C4—416no—
580C22⋊C4—416no—
581C22⋊C4—88no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C22⋊C4—84no—
585C42—216no—
586C42—28no—
587C42—416no—
588C42—416no—
589C42—84no—
590C23—24no—
591C23—24no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
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—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—41no—
626C23—42no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—41no—
652C23—42no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23C2×C4×D418yes—
670C23#52014yes—
671C23C24×C411yescharacteristic
672C23C23×D412yes—
673C23C22×#4112yes—
674C23C2×H(5,𝔽2)11yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×H(5,𝔽2)11yescharacteristic
677C23C2×H(5,𝔽2)12yes—
678C23C2×H(5,𝔽2)11yescharacteristic
679C23C2×2−1+411yescharacteristic
680C23C2×2−1+412yes—
681C23C2×2−1+411yescharacteristic
682Q8—416no—
683D4—264no—
684D4—416no—
685D4—432no—
686D4—416no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—264no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—44no—
741C2×C4—41no—
742C2×C4—416no—
743C2×C4—416no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—816no—
759C2×C4—832no—
760C2×C4C2×C4×D418yes—
761C2×C4C2×C4×D418yes—
762C2×C4#51814yes—
763C2×C4#52014yes—
764C2×C4#52018yes—
765C2×C4D4214yes—
766C2×C4#54618yes—
767C2×C4#55114yes—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—44no—
774C22—42no—
775C22—44no—
776C22—42no—
777C22—44no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22—81no—
800C22—81no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—82no—
805C22C22×C4×D412yes—
806C22C2×#51811yescharacteristic
807C22C2×#52011yescharacteristic
808C22C2×#52011yescharacteristic
809C22C2×#52012yes—
810C22C2×D4211yescharacteristic
811C22C2×#54612yes—
812C22C2×#55111yescharacteristic
813C22#348412yes—
814C22#348612yes—
815C22#349212yes—
816C22#349212yes—
817C22#349812yes—
818C22#349912yes—
819C22#351112yes—
820C22#351112yes—
821C22#353611yescharacteristic
822C22#353611yescharacteristic
823C22#353711yescharacteristic
824C22#353811yescharacteristic
825C22#354812yes—
826C22#354911yescharacteristic
827C22#355011yescharacteristic
828C4—24no—
829C4—28no—
830C4—28no—
831C4—42no—
832C4—48no—
833C4—48no—
834C4—42no—
835C4—42no—
836C4—44no—
837C4—84no—
838C4—84no—
839C4#235818yes—
840C2—44no—
841C2—48no—
842C2—82no—
843C2C2×#235811yescharacteristic
844C2#3420012yes—
845C2#3420712yes—
846C2#3436011yescharacteristic
847C2#3436811yescharacteristic
848C2#4486912yes—
849C2#4487011yescharacteristic
850C2#4491411yescharacteristic
851C2#4491512yes—
852C2#4532111yescharacteristic
853C2#4533011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2388C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×D4×C4⋊C4C2semidirect
3. C2×#2311C2semidirect
4. #14575C2semidirect
5. #14535C2semidirect
6. #14518C2semidirect
7. #14236C2semidirect
8. #14189C2semidirect
9. #14171C2semidirect
10. #13906C2semidirect
11. #13880C2semidirect
12. #13876C2semidirect
13. #13872C2semidirect
14. #13871C2semidirect
15. #13801C2semidirect
23. #2388C4semidirect
82. C22×#41C2×C4semidirect
100. C2×C4×D4C2×C4semidirect
101. C2×C4×D4C2×C4semidirect
141. #395C2×C4semidirect
142. #394C2×C4semidirect
143. #394C2×C4semidirect
144. #393C2×C4semidirect
146. #392C2×C4semidirect
166. #380D4semidirect
169. C4×C22⋊C4C2×C4semidirect
170. C4×C22⋊C4C2×C4semidirect
538. C22×C4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23882
C2×D4×C4⋊C42
C2×#23112
#145752
#145352
#145182
#142362
#141892
#141712
#139062
#138802
#138762
#138722
#138712
#138012