Finite Group Databasebeta

← #759499

Subgroups — #759499

Order 512.

4978 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic, complemented
4C2×#2280C211yesmaximal, characteristic, complemented
5#16401C212yesmaximal, complemented
6#16398C212yesmaximal, complemented
7#15002C214yesmaximal, complemented
8#14842C212yesmaximal, complemented
9#14839C212yesmaximal, complemented
10#14727C212yesmaximal, complemented
11#14724C212yesmaximal
12#14199C214yesmaximal, complemented
13#14128C211yesmaximal, characteristic, complemented
14#13962C212yesmaximal, complemented
15#13958C211yesmaximal, characteristic, complemented
16#13868C212yesmaximal, complemented
17#13868C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×#117C2212yes—
22C22×#117C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26#2482—28no—
27C2×#399C2212yescomplemented
28C2×#397C2212yescomplemented
29C2×#397C2214yescomplemented
30C2×#394C2214yes—
31C2×#394C2214yes—
32C2×#388C2214yescomplemented
33C2×#386—28no—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40#2280—28no—
41#2280—28no—
42C2×#381C2211yescharacteristic
43C2×#381C2212yes—
44C2×#381C2211yescharacteristic
45C2×#380C2211yescharacteristic, complemented
46C2×#380C2212yescomplemented
47C2×#380C2211yescharacteristic, complemented
48C2×#380C2212yescomplemented
49C2×#380C2211yescharacteristic, complemented
50C2×#380C2211yescharacteristic, complemented
51C2×#379C2212yes—
52C2×#379C2212yes—
53C2×#379C2212yes—
54C2×#379C2212yes—
55C2×C4×C22⋊C4C2212yescomplemented
56C2×C4×C22⋊C4C2212yescomplemented
57C2×C4×C22⋊C4C2212yescomplemented
58C2×C4×C22⋊C4C2212yescomplemented
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61#1445C2212yescomplemented
62#1445C2212yescomplemented
63#1444C2212yescomplemented
64#1442C2212yescomplemented
65#1441C2214yescomplemented
66#1441C2214yescomplemented
67#1440C2214yescomplemented
68#1440C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2212yescomplemented
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1439C2212yescomplemented
74#1438C2214yes—
75#1438C2214yes—
76#1437C2214yescomplemented
77#1437C2214yescomplemented
78#1437C2214yescomplemented
79#1436C2214yescomplemented
80C4⋊#95C2214yescomplemented
81#1434C2214yescomplemented
82#1434C2214yescomplemented
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C26C2311yescharacteristic
89C23×D4—24no—
90C23×D4—28no—
91C23×D4—44no—
92C23×D4—44no—
93C23×D4C2312yes—
94C23×D4C2312yes—
95C24×C4—24no—
96C24×C4—24no—
97C24×C4—28no—
98C24×C4—44no—
99C24×C4D418yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—28no—
113C2×#117—24no—
114C2×#117—28no—
115C2×#117—44no—
116C2×#117—44no—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—28no—
130C22×C22⋊C4—44no—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C42C2312yes—
152C22×C42C2314yes—
153C22×C42C2312yes—
154#399—28no—
155#397—28no—
156#397—48no—
157#394—216no—
158#394—48no—
159#388—216no—
160#386—28no—
161#386—28no—
162#386—28no—
163#386—28no—
164#385—28no—
165#385—44no—
166#381—24no—
167#381—28no—
168#381D418yescomplemented
169#380—24no—
170#380—24no—
171#380—24no—
172#380—24no—
173#380—28no—
174#380—28no—
175#379—28no—
176#379—28no—
177#379—28no—
178#379—44no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—28no—
182C4×C22⋊C4—28no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C25—24no—
208C25—24no—
209C25—24no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—24no—
214C25—24no—
215C25—22no—
216C25—22no—
217C25—24no—
218C25—24no—
219C25—42no—
220C25—42no—
221C25—42no—
222C25—42no—
223C25—42no—
224C25C2×D414yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C22×D4—232no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—28no—
235C22×D4—24no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—464no—
240C22×D4—416no—
241C22×D4—416no—
242C22×D4#4118yes—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—232no—
250C23×C4—232no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—416no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—432no—
277C23×C4—432no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4#4114yes—
290C23×C4#4118yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2414yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2414yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304#117—432no—
305#117—416no—
306#117—416no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
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×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
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—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—416no—
371C2×C22⋊C4—416no—
372C2×C22⋊C4—416no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4C2×D418yes—
381C2×C42—28no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—28no—
386C2×C42—24no—
387C2×C42—44no—
388C2×C42—42no—
389C2×C42—42no—
390#95—24no—
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—24no—
400#95—28no—
401#95—28no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95C2×D418yescomplemented
411#95C2×D418yescomplemented
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—232no—
417C24—28no—
418C24—28no—
419C24—28no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—24no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—44no—
448C24—44no—
449C24—48no—
450C24—48no—
451C24—416no—
452C24—48no—
453C24—48no—
454C24—416no—
455C24—416no—
456C24—48no—
457C24—48no—
458C24—416no—
459C24—416no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—48no—
464C24—48no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24—48no—
469C24—48no—
470C24—84no—
471C24—84no—
472C24—88no—
473C24—88no—
474C24C22×D412yes—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C22×D412yes—
478C24C2×#4114yes—
479C24C2×#4114yes—
480C24C2×#4112yes—
481C24C2×#4114yes—
482C24H(5,𝔽2)14yes—
483C24H(5,𝔽2)14yes—
484C24C2511yescharacteristic
485C2×D4—216no—
486C2×D4—216no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—416no—
490C2×D4—4128no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—416no—
495C2×D4—48no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—28no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—4128no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—416no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—88no—
595C22×C4#121116yes—
596C22×C4#123116yes—
597C22×C4C22×D418yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4114yes—
609C4⋊C4—416no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—88no—
615C4⋊C4—88no—
616C22⋊C4—216no—
617C22⋊C4—416no—
618C22⋊C4—416no—
619C22⋊C4—416no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—88no—
634C22⋊C4—88no—
635C22⋊C4—88no—
636C42—416no—
637C42—48no—
638C42—48no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—28no—
646C23—24no—
647C23—28no—
648C23—24no—
649C23—28no—
650C23—28no—
651C23—232no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—28no—
667C23—24no—
668C23—28no—
669C23—28no—
670C23—24no—
671C23—28no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—28no—
676C23—28no—
677C23—416no—
678C23—416no—
679C23—416no—
680C23—416no—
681C23—464no—
682C23—416no—
683C23—464no—
684C23—416no—
685C23—416no—
686C23—416no—
687C23—416no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—44no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—44no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—832no—
719C23—832no—
720C23—88no—
721C23—88no—
722C23—88no—
723C23—88no—
724C23C2×#12114yes—
725C23C2×#12314yes—
726C23#52514yes—
727C23#53414yes—
728C23#53514yes—
729C23#54618yes—
730C23#55118yes—
731C23C23×D411yescharacteristic
732C23C23×D411yescharacteristic
733C23C22×#4111yescharacteristic
734C23C22×#4112yes—
735C23C22×#4112yes—
736C23C2×H(5,𝔽2)12yes—
737C23C2×H(5,𝔽2)12yes—
738C23#58512yes—
739C23#58512yes—
740D4—432no—
741D4—432no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—232no—
747C2×C4—232no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—416no—
766C2×C4—416no—
767C2×C4—416no—
768C2×C4—416no—
769C2×C4—416no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—88no—
815C2×C4—88no—
816C2×C4C2×#12114yes—
817C2×C4C2×#12114yes—
818C2×C4C2×#12314yes—
819C2×C4C2×#12314yes—
820C22—216no—
821C22—24no—
822C22—216no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—464no—
835C22—48no—
836C22—48no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—48no—
842C22—48no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—48no—
848C22—48no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—832no—
853C22—84no—
854C22—82no—
855C22—82no—
856C22—84no—
857C22—82no—
858C22—82no—
859C22#241218yes—
860C22C22×#12111yescharacteristic
861C22C22×#12311yescharacteristic
862C22C2×#52511yescharacteristic
863C22C2×#53411yescharacteristic
864C22C2×#53511yescharacteristic
865C22#344911yescharacteristic
866C22#344911yescharacteristic
867C22C2×#54612yes—
868C22D4×#4112yes—
869C22C2×#55112yes—
870C22#347512yes—
871C22#347514yes—
872C22#348812yes—
873C22#349014yes—
874C22#349412yes—
875C22#349414yes—
876C22#353314yes—
877C4—24no—
878C4—24no—
879C4—24no—
880C4—24no—
881C4—48no—
882C4—44no—
883C4—82no—
884C4—84no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C2—28no—
891C2—44no—
892C2—44no—
893C2—84no—
894C2C2×#241211yescharacteristic
895C2#3473711yescharacteristic
896C2#3480911yescharacteristic
897C2#3505011yescharacteristic
898C2#3525211yescharacteristic
899C2#3526211yescharacteristic
900C2#3744311yescharacteristic
901C2#5900714yes—
902C2#5919314yes—
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×#2482C2semidirect
3. C2×#2280C2semidirect
4. C2×#2280C2semidirect
5. #16401C2semidirect
6. #16398C2semidirect
7. #15002C2semidirect
8. #14842C2semidirect
9. #14839C2semidirect
10. #14727C2semidirect
12. #14199C2semidirect
13. #14128C2semidirect
14. #13962C2semidirect
15. #13958C2semidirect
16. #13868C2semidirect
17. #13868C2semidirect
27. C2×#399C22semidirect
28. C2×#397C22semidirect
29. C2×#397C22semidirect
32. C2×#388C22semidirect
45. C2×#380C22semidirect
46. C2×#380C22semidirect
47. C2×#380C22semidirect
48. C2×#380C22semidirect
49. C2×#380C22semidirect
50. C2×#380C22semidirect
55. C2×C4×C22⋊C4C22semidirect
56. C2×C4×C22⋊C4C22semidirect
57. C2×C4×C22⋊C4C22semidirect
58. C2×C4×C22⋊C4C22semidirect
61. #1445C22semidirect
62. #1445C22semidirect
63. #1444C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1440C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
76. #1437C22semidirect
77. #1437C22semidirect
78. #1437C22semidirect
79. #1436C22semidirect
80. C4⋊#95C22semidirect
81. #1434C22semidirect
82. #1434C22semidirect
168. #381D4semidirect
410. #95C2×D4semidirect
411. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
C22×#3862
C2×#22802
#164012
#163982
#150022
#148422
#148392
#147272
#147242
#141992
#141282
#139622
#139582
#138682