Finite Group Databasebeta

← #636946

Subgroups — #636946

Order 512.

4325 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic
2C2×#2412C211yesmaximal, characteristic
3C22×#385C211yesmaximal, characteristic, complemented
4C22×#381C211yesmaximal, characteristic, complemented
5#16675C214yesmaximal, complemented
6#16661C214yesmaximal, complemented
7#15073C212yesmaximal, complemented
8#15069C212yesmaximal, complemented
9#15014C212yesmaximal, complemented
10#14921C212yesmaximal, complemented
11#14919C212yesmaximal, complemented
12#14912C212yesmaximal, complemented
13#14275C212yesmaximal, complemented
14#14259C212yesmaximal, complemented
15#14134C211yesmaximal, characteristic
16#13877C211yesmaximal, characteristic, complemented
17#13869C211yesmaximal, characteristic, complemented
18C25×C4C2211yescharacteristic
19C22×#123C2212yes—
20C22×#123C2211yescharacteristic
21C22×#120C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27#2849—28no—
28#2412—28no—
29C2×#397C2212yes—
30C2×#394C2212yes—
31C2×#386C2212yes—
32C2×#386C2211yescharacteristic
33C2×#386C2211yescharacteristic
34C2×#386C2212yes—
35C2×#386C2211yescharacteristic
36C2×#386C2212yes—
37C2×#386C2212yes—
38C2×#385—28no—
39C2×#385C2212yes—
40C2×#385C2211yescharacteristic
41C2×#385C2211yescharacteristic
42C2×#385C2214yes—
43C2×#385C2211yescharacteristic
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#381—28no—
48C2×#381C2212yes—
49C2×#381C2214yes—
50C2×#381C2212yes—
51C2×#381C2212yes—
52C2×#381C2211yescharacteristic
53C2×#381C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#379C2211yescharacteristic
57C22×#95C2212yes—
58C22×#95C2212yes—
59C22×#95C2212yes—
60#1445C2214yescomplemented
61#1444C2214yescomplemented
62#1444C2214yescomplemented
63#1443C2214yescomplemented
64#1443C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2214yescomplemented
67#1442C2214yescomplemented
68#1442C2214yescomplemented
69#1441C2214yescomplemented
70#1441C2214yescomplemented
71#1441C2214yescomplemented
72#1440C2214yes—
73#1440C2212yes—
74#1440C2214yescomplemented
75#1439C2214yes—
76#1439C2214yescomplemented
77#1439C2214yescomplemented
78#1439C2214yescomplemented
79#1438C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—44no—
94C24×C4—44no—
95C24×C4D418yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C24×C4C2312yes—
105C2×#123—28no—
106C2×#123—24no—
107C2×#123—44no—
108C2×#123—44no—
109C2×#123—44no—
110C2×#120—24no—
111C2×#120—24no—
112C2×#120—24no—
113C22×C4⋊C4—28no—
114C22×C4⋊C4—44no—
115C22×C4⋊C4—44no—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—28no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—44no—
130C22×C22⋊C4—44no—
131C22×C22⋊C4D418yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153#397—28no—
154#394—28no—
155#386—28no—
156#386—24no—
157#386—24no—
158#386—28no—
159#386—24no—
160#386—28no—
161#386—44no—
162#385—28no—
163#385—24no—
164#385—24no—
165#385—216no—
166#385—28no—
167#385—28no—
168#385—24no—
169#385—44no—
170#381—28no—
171#381—24no—
172#381—28no—
173#381—28no—
174#381—216no—
175#381—44no—
176#380—28no—
177#380—28no—
178#379—24no—
179C2×#95—28no—
180C2×#95—28no—
181C2×#95—28no—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C25—24no—
207C25—24no—
208C25—24no—
209C25—24no—
210C25—44no—
211C25C2×D414yes—
212C25C2×D414yes—
213C25#4114yes—
214C25C2411yescharacteristic
215C25C2411yescharacteristic
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—44no—
232C23×C4—232no—
233C23×C4—24no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—28no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—432no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—416no—
278C23×C4—416no—
279C23×C4—432no—
280C23×C4C2×D418yes—
281C23×C4C2×D418yes—
282C23×C4C2×D418yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2414yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2414yes—
298#123—416no—
299#123—432no—
300#120—416no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—432no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C22⋊C4—232no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—28no—
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—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
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—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—416no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—416no—
370C2×C22⋊C4—416no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D414yes—
376C2×C22⋊C4C2×D418yes—
377C2×C22⋊C4#4118yes—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—28no—
393#95—28no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—24no—
408C24—28no—
409C24—28no—
410C24—216no—
411C24—28no—
412C24—28no—
413C24—216no—
414C24—216no—
415C24—216no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—24no—
429C24—48no—
430C24—48no—
431C24—48no—
432C24—416no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24#121116yes—
437C24C22×D412yes—
438C24C22×D412yes—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C2×#4112yes—
444C24C2×#4112yes—
445C24C2×#4112yes—
446C24C2×#4114yes—
447C24H(5,𝔽2)14yes—
448C24H(5,𝔽2)14yes—
449C242−1+414yes—
450C24C2511yescharacteristic
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—84no—
464C2×D4—84no—
465C22×C4—216no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—216no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—216no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—416no—
547C22×C4—416no—
548C22×C4—48no—
549C22×C4—4128no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—88no—
576C22×C4—88no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—88no—
580C22×C4—88no—
581C22×C4C22×D414yes—
582C22×C4C22×D414yes—
583C22×C4C22×D414yes—
584C22×C4C22×D414yes—
585C22×C4C2×#4118yes—
586C4⋊C4—416no—
587C4⋊C4—416no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—84no—
592C4⋊C4—88no—
593C22⋊C4—216no—
594C22⋊C4—216no—
595C22⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—44no—
612C22⋊C4—84no—
613C22⋊C4—88no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—232no—
637C23—22no—
638C23—232no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—416no—
650C23—432no—
651C23—432no—
652C23—432no—
653C23—464no—
654C23—432no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23C2×#12114yes—
676C23C2×#12114yes—
677C23C2×#12114yes—
678C23#52514yes—
679C23#53414yes—
680C23#53418yes—
681C23#53514yes—
682C23#53614yes—
683C23#53818yes—
684C23#54718yes—
685C23#55218yes—
686C23C23×D411yescharacteristic
687C23C23×D411yescharacteristic
688C23C22×#4111yescharacteristic
689C23C22×#4112yes—
690C23C2×H(5,𝔽2)12yes—
691C23C2×H(5,𝔽2)12yes—
692C23C2×2−1+412yes—
693C23#58514yes—
694D4—88no—
695D4—88no—
696D4—88no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—432no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—432no—
716C2×C4—432no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
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—816no—
775C2×C4—88no—
776C2×C4—816no—
777C2×C4—88no—
778C22—24no—
779C22—24no—
780C22—28no—
781C22—28no—
782C22—28no—
783C22—28no—
784C22—28no—
785C22—28no—
786C22—24no—
787C22—216no—
788C22—216no—
789C22—28no—
790C22—28no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—464no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—48no—
800C22—44no—
801C22—81no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—81no—
806C22—84no—
807C22—82no—
808C22—81no—
809C22#241318yes—
810C22#261718yes—
811C22C22×#12111yescharacteristic
812C22C2×#52511yescharacteristic
813C22C2×#53412yes—
814C22C2×#53411yescharacteristic
815C22C2×#53511yescharacteristic
816C22C2×#53611yescharacteristic
817C22#344912yes—
818C22C2×#53812yes—
819C22C2×#54712yes—
820C22C2×#55212yes—
821C22#348512yes—
822C22#349112yes—
823C22#351314yes—
824C22#351314yes—
825C22#353514yes—
826C22#353514yes—
827C4—44no—
828C4—44no—
829C4—48no—
830C4—44no—
831C4—44no—
832C4—82no—
833C4—81no—
834C4—82no—
835C4—84no—
836C4—81no—
837C4—82no—
838C4—82no—
839C4—81no—
840C2—28no—
841C2—28no—
842C2—44no—
843C2—161no—
844C2C2×#261711yescharacteristic
845C2C2×#241311yescharacteristic
846C2#3506312yes—
847C2#3508911yescharacteristic
848C2#3744712yes—
849C2#3803812yes—
850C2#3803912yes—
851C2#3806514yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#385C2semidirect
4. C22×#381C2semidirect
5. #16675C2semidirect
6. #16661C2semidirect
7. #15073C2semidirect
8. #15069C2semidirect
9. #15014C2semidirect
10. #14921C2semidirect
11. #14919C2semidirect
12. #14912C2semidirect
13. #14275C2semidirect
14. #14259C2semidirect
16. #13877C2semidirect
17. #13869C2semidirect
60. #1445C22semidirect
61. #1444C22semidirect
62. #1444C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
74. #1440C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#24122
C22×#3852
C22×#3812
#166752
#166612
#150732
#150692
#150142
#149212
#149192
#149122
#142752
#142592
#141342
#138772
#138692