Finite Group Databasebeta

← #759495

Subgroups — #759495

Order 512.

5110 conjugacy classes of subgroups.

The subgroup lattice has 909 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
4C22×#381C211yesmaximal, characteristic, complemented
5#16395C212yesmaximal, complemented
6#16392C212yesmaximal, complemented
7#14974C214yesmaximal, complemented
8#14919C212yesmaximal, complemented
9#14918C212yesmaximal, complemented
10#14836C212yesmaximal, complemented
11#14735C212yesmaximal, complemented
12#14128C211yesmaximal, characteristic, complemented
13#13999C214yesmaximal, complemented
14#13958C211yesmaximal, characteristic, complemented
15#13877C212yesmaximal, complemented
16#13868C211yesmaximal, characteristic, complemented
17#13867C212yesmaximal
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2212yes—
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26#2482—28no—
27C2×#399C2212yescomplemented
28C2×#397C2212yescomplemented
29C2×#388C2214yescomplemented
30C2×#386—28no—
31C2×#386C2212yes—
32C2×#386C2214yes—
33C2×#386C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2214yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39#2280—28no—
40C2×#381—28no—
41C2×#381C2211yescharacteristic
42C2×#381C2212yes—
43C2×#381C2212yes—
44C2×#381C2211yescharacteristic
45C2×#381C2212yescomplemented
46C2×#381C2212yescomplemented
47C2×#380C2211yescharacteristic, complemented
48C2×#380C2211yescharacteristic, complemented
49C2×#380C2211yescharacteristic, complemented
50C2×#380C2211yescharacteristic, complemented
51C2×#380C2214yescomplemented
52C2×#379C2212yes—
53C2×#379C2212yes—
54C2×#379C2212yes—
55C2×C4×C22⋊C4C2212yescomplemented
56C2×C4×C22⋊C4C2212yescomplemented
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2212yescomplemented
60C22×#95C2212yescomplemented
61#1445C2212yescomplemented
62#1445C2212yescomplemented
63#1445C2214yescomplemented
64#1444C2212yescomplemented
65#1443C2214yescomplemented
66#1443C2214yescomplemented
67#1442C2212yescomplemented
68#1442C2214yescomplemented
69#1440C2214yescomplemented
70#1440C2214yescomplemented
71#1439C2212yescomplemented
72#1439C2214yescomplemented
73#1439C2212yescomplemented
74#1439C2214yescomplemented
75#1439C2214yescomplemented
76#1439C2214yescomplemented
77#1438C2214yes—
78#1438C2214yes—
79#1437C2214yescomplemented
80#1436C2214yescomplemented
81#1434C2214yescomplemented
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2214yescomplemented
87C26C2311yescharacteristic
88C26C2311yescharacteristic
89C23×D4—24no—
90C23×D4—28no—
91C23×D4—28no—
92C23×D4—44no—
93C23×D4C2312yes—
94C23×D4C2312yes—
95C24×C4—28no—
96C24×C4—24no—
97C24×C4—24no—
98C24×C4—44no—
99C24×C4D418yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2314yes—
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—44no—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2314yes—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—28no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—28no—
128C22×C22⋊C4—44no—
129C22×C22⋊C4—44no—
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⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152#399—28no—
153#397—28no—
154#388—216no—
155#386—216no—
156#386—28no—
157#386—28no—
158#386—28no—
159#386—28no—
160#386—48no—
161#385—28no—
162#385—44no—
163#381—24no—
164#381—28no—
165#381—28no—
166#381—28no—
167#381—28no—
168#381D418yescomplemented
169#380—24no—
170#380—24no—
171#380—24no—
172#380—24no—
173#380—48no—
174#379—28no—
175#379—28no—
176#379—44no—
177C4×C22⋊C4—28no—
178C4×C22⋊C4—28no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—28no—
182C2×#95—28no—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C25—22no—
208C25—22no—
209C25—24no—
210C25—24no—
211C25—24no—
212C25—22no—
213C25—24no—
214C25—22no—
215C25—22no—
216C25—24no—
217C25—24no—
218C25—42no—
219C25—42no—
220C25—42no—
221C25—42no—
222C25—42no—
223C25C2×D414yes—
224C25#4118yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C22×D4—232no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—28no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—24no—
238C22×D4—44no—
239C22×D4—464no—
240C22×D4—416no—
241C22×D4—416no—
242C22×D4#4118yes—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—232no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—232no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—28no—
269C23×C4—28no—
270C23×C4—28no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—28no—
275C23×C4—416no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—44no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—432no—
289C23×C4—432no—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4#4114yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2414yes—
305C23×C4C2414yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311#117—416no—
312#117—416no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
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—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—432no—
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—44no—
371C2×C22⋊C4—416no—
372C2×C22⋊C4—416no—
373C2×C22⋊C4—416no—
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⋊C4—44no—
381C2×C22⋊C4C2×D418yes—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—42no—
387C2×C42—42no—
388#95—28no—
389#95—28no—
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—28no—
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—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—28no—
422C24—28no—
423C24—28no—
424C24—28no—
425C24—216no—
426C24—216no—
427C24—232no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—28no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—44no—
447C24—44no—
448C24—416no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—416no—
454C24—416no—
455C24—416no—
456C24—48no—
457C24—48no—
458C24—416no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24—44no—
465C24—48no—
466C24—48no—
467C24—84no—
468C24—88no—
469C24—84no—
470C24—88no—
471C24#123116yes—
472C24C22×D412yes—
473C24C22×D412yes—
474C24C22×D412yes—
475C24C22×D412yes—
476C24C2×#4114yes—
477C24C2×#4114yes—
478C24C2×#4112yes—
479C24C2×#4114yes—
480C24C2×#4114yes—
481C24C2×#4114yes—
482C24H(5,𝔽2)14yes—
483C24H(5,𝔽2)14yes—
484C24C2511yescharacteristic
485C2×D4—216no—
486C2×D4—216no—
487C2×D4—232no—
488C2×D4—416no—
489C2×D4—416no—
490C2×D4—4128no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—416no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
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—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
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—22no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—4128no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—416no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—416no—
599C22×C4—88no—
600C22×C4—88no—
601C22×C4—88no—
602C22×C4—84no—
603C22×C4—84no—
604C22×C4—88no—
605C22×C4#121116yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D418yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—88no—
621C4⋊C4—88no—
622C22⋊C4—216no—
623C22⋊C4—416no—
624C22⋊C4—416no—
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—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—88no—
639C22⋊C4—88no—
640C22⋊C4—88no—
641C42—48no—
642C42—48no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—28no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—28no—
661C23—28no—
662C23—24no—
663C23—24no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—28no—
668C23—22no—
669C23—22no—
670C23—232no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—28no—
678C23—28no—
679C23—232no—
680C23—24no—
681C23—24no—
682C23—28no—
683C23—24no—
684C23—28no—
685C23—416no—
686C23—464no—
687C23—416no—
688C23—464no—
689C23—416no—
690C23—416no—
691C23—416no—
692C23—416no—
693C23—416no—
694C23—416no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—44no—
700C23—44no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—44no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—832no—
720C23—832no—
721C23—88no—
722C23—88no—
723C23—88no—
724C23—88no—
725C23C2×#12114yes—
726C23C2×#12314yes—
727C23C2×#12314yes—
728C23C2×#12314yes—
729C23#52514yes—
730C23#53414yes—
731C23#53514yes—
732C23#54618yes—
733C23#55118yes—
734C23#551116yes—
735C23C23×D411yescharacteristic
736C23C23×D411yescharacteristic
737C23C22×#4111yescharacteristic
738C23C22×#4112yes—
739C23C22×#4112yes—
740C23C2×H(5,𝔽2)12yes—
741C23C2×H(5,𝔽2)12yes—
742C23#58512yes—
743C23#58512yes—
744D4—432no—
745D4—432no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—232no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—416no—
767C2×C4—416no—
768C2×C4—416no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—42no—
772C2×C4—416no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
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—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
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—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—832no—
821C2×C4—88no—
822C2×C4—88no—
823C2×C4C2×#12114yes—
824C2×C4C2×#12114yes—
825C22—24no—
826C22—24no—
827C22—216no—
828C22—216no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—216no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—464no—
845C22—48no—
846C22—42no—
847C22—48no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—48no—
852C22—48no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—832no—
857C22—82no—
858C22—84no—
859C22—82no—
860C22—82no—
861C22—84no—
862C22—82no—
863C22#241218yes—
864C22#248218yescomplemented
865C22C22×#12111yescharacteristic
866C22C22×#12311yescharacteristic
867C22C2×#52511yescharacteristic
868C22C2×#53411yescharacteristic
869C22C2×#53511yescharacteristic
870C22#344911yescharacteristic
871C22#344911yescharacteristic
872C22C2×#54612yes—
873C22D4×#4112yes—
874C22C2×#55112yes—
875C22C2×#55114yes—
876C22#347512yes—
877C22#348812yes—
878C22#349114yes—
879C22#349412yes—
880C22#351314yes—
881C22#353414yes—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—48no—
887C4—44no—
888C4—82no—
889C4—82no—
890C4—84no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C2—28no—
896C2—28no—
897C2—44no—
898C2—84no—
899C2C2×#241211yescharacteristic
900C2#3473711yescharacteristic
901C2C2×#248211yescharacteristic
902C2#3506311yescharacteristic
903C2#3509711yescharacteristic
904C2#3525211yescharacteristic
905C2#3744611yescharacteristic
906C2#5901114yes—
907C2#5919514yes—
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. C22×#381C2semidirect
5. #16395C2semidirect
6. #16392C2semidirect
7. #14974C2semidirect
8. #14919C2semidirect
9. #14918C2semidirect
10. #14836C2semidirect
11. #14735C2semidirect
12. #14128C2semidirect
13. #13999C2semidirect
14. #13958C2semidirect
15. #13877C2semidirect
16. #13868C2semidirect
27. C2×#399C22semidirect
28. C2×#397C22semidirect
29. C2×#388C22semidirect
45. C2×#381C22semidirect
46. C2×#381C22semidirect
47. C2×#380C22semidirect
48. C2×#380C22semidirect
49. C2×#380C22semidirect
50. C2×#380C22semidirect
51. C2×#380C22semidirect
55. C2×C4×C22⋊C4C22semidirect
56. C2×C4×C22⋊C4C22semidirect
59. C22×#95C22semidirect
60. C22×#95C22semidirect
61. #1445C22semidirect
62. #1445C22semidirect
63. #1445C22semidirect
64. #1444C22semidirect
65. #1443C22semidirect
66. #1443C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1440C22semidirect
70. #1440C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
79. #1437C22semidirect
80. #1436C22semidirect
81. #1434C22semidirect
86. C22⋊#95C22semidirect
168. #381D4semidirect
410. #95C2×D4semidirect
411. #95C2×D4semidirect
864. C22#2482semidirect

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
C22×#3812
#163952
#163922
#149742
#149192
#149182
#148362
#147352
#141282
#139992
#139582
#138772
#138682
#138672