Finite Group Databasebeta

← #517274

Subgroups — #517274

Order 512.

6502 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2C2×#2325C211yesmaximal, characteristic, complemented
3C2×C4×#120C212yesmaximal, complemented
4C23×#95C211yesmaximal, characteristic, complemented
5#14694C212yesmaximal, complemented
6#14680C211yesmaximal, characteristic, complemented
7#14275C211yesmaximal, characteristic, complemented
8#14271C211yesmaximal, characteristic, complemented
9#14259C212yesmaximal, complemented
10#14047C214yesmaximal, complemented
11#14023C214yesmaximal, complemented
12#13999C214yesmaximal, complemented
13#13975C214yesmaximal, complemented
14#13784C212yesmaximal, complemented
15#13778C211yesmaximal, characteristic, complemented
16C25×C4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×#121C2212yes—
21C22×#120C2212yes—
22C22×C4×D4C2212yes—
23C22×C4×D4C2214yes—
24#2847C4116yescomplemented
25#2325—28no—
26C4×#120—216no—
27C2×#388C2212yescomplemented
28C2×#387C2212yescomplemented
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#386C2214yes—
32C2×#386C2212yes—
33C2×#386C2214yes—
34C2×#386C2214yes—
35C2×#386C2214yes—
36C2×#386C2212yes—
37C2×#386C2212yescomplemented
38C2×#385C2214yes—
39C2×#385C2212yes—
40C2×#385C2212yescomplemented
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2211yescharacteristic
46C2×#380C2212yes—
47C2×#379C2212yes—
48C2×C4×C22⋊C4C2214yes—
49C2×C4×C22⋊C4C2212yes—
50C22×#95—28no—
51C22×#95C2214yes—
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2214yes—
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57#1445C2212yescomplemented
58#1444C2212yescomplemented
59#1443C2214yescomplemented
60#1442C2214yescomplemented
61#1442C2212yescomplemented
62#1441C2214yescomplemented
63#1440C2214yescomplemented
64#1439C2214yescomplemented
65#1439C2214yescomplemented
66#1438C2212yescomplemented
67#1437C2214yescomplemented
68#1436C2214yescomplemented
69#1436C2214yescomplemented
70#1436C2214yescomplemented
71#1434C2214yescomplemented
72C22⋊#95C2212yes—
73C22⋊#95C2214yes—
74C22⋊#95C2214yes—
75C22⋊#95C2214yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C22⋊#95C2214yescomplemented
79C26C2311yescharacteristic
80C23×D4C2312yes—
81C23×D4C2314yes—
82C23×D4C2311yescharacteristic
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—44no—
91C24×C4—44no—
92C24×C4—44no—
93C24×C4—44no—
94C24×C4—44no—
95C24×C4—44no—
96C24×C4C2×C418yescomplemented
97C24×C4D418yescomplemented
98C24×C4C2314yes—
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2314yes—
102C24×C4C2312yes—
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—44no—
112C2×#121—44no—
113C2×#121C2×C418yescomplemented
114C2×#121C2×C4116yescomplemented
115C2×#120—28no—
116C2×#120—28no—
117C2×#120C2×C4116yescomplemented
118C2×C4×D4—28no—
119C2×C4×D4—216no—
120C2×C4×D4—28no—
121C2×C4×D4—28no—
122C2×C4×D4—48no—
123C2×C4×D4—48no—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C42C2312yes—
145C22×C42C2314yes—
146#388—28no—
147#387—28no—
148#386—28no—
149#386—216no—
150#386—28no—
151#386—28no—
152#386—28no—
153#386—48no—
154#386—48no—
155#386C2×C4132yescomplemented
156#386C2×C4116yescomplemented
157#385—216no—
158#385—28no—
159#385—28no—
160#380—24no—
161#380—24no—
162#380—44no—
163#380—44no—
164#380C2×C4116yescomplemented
165#380C2×C418yescomplemented
166#379—28no—
167C4×C22⋊C4—216no—
168C4×C22⋊C4—28no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—216no—
173C2×#95—216no—
174C2×#95D418yescomplemented
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—24no—
202C25—24no—
203C25—24no—
204C25—24no—
205C25C22×C414yes—
206C25C2×D414yes—
207C25#4114yes—
208C25C2412yes—
209C25C2411yescharacteristic
210C25C2412yes—
211C22×D4—24no—
212C22×D4—28no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—28no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—28no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4C22×C418yes—
228C22×D4C22×C4116yes—
229C22×D4C22×C414yescomplemented
230C23×C4—232no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—28no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—28no—
241C23×C4—28no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—232no—
247C23×C4—232no—
248C23×C4—28no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—28no—
252C23×C4—28no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—28no—
256C23×C4—28no—
257C23×C4—28no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—432no—
262C23×C4—432no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—416no—
286C23×C4—416no—
287C23×C4—416no—
288C23×C4—416no—
289C23×C4—416no—
290C23×C4—416no—
291C23×C4—432no—
292C23×C4—432no—
293C23×C4—432no—
294C23×C4—432no—
295C23×C4C22×C418yes—
296C23×C4C22×C418yes—
297C23×C4C22×C414yes—
298C23×C4C22×C414yes—
299C23×C4C2×D4116yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4#4114yes—
306C23×C4#4114yes—
307C23×C4#4114yes—
308C23×C4C2412yes—
309C23×C4C2414yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2414yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2412yes—
320#121—232no—
321#121—432no—
322#120—264no—
323C4×D4—464no—
324C4×D4—432no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4C22×C414yescomplemented
343C2×C4⋊C4C22×C418yescomplemented
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4C22×C418yes—
378C2×C22⋊C4C22×C4116yes—
379C2×C22⋊C4C22×C418yescomplemented
380C2×C22⋊C4C22×C4116yescomplemented
381C2×C42—28no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—44no—
386C2×C42—44no—
387#95—28no—
388#95—24no—
389#95—24no—
390#95—28no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—28no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95C22×C4116yescomplemented
406#95C22×C418yescomplemented
407#95C2×D418yes—
408#95C2×D418yes—
409C24—28no—
410C24—28no—
411C24—28no—
412C24—216no—
413C24—216no—
414C24—216no—
415C24—28no—
416C24—216no—
417C24—216no—
418C24—216no—
419C24—28no—
420C24—28no—
421C24—216no—
422C24—216no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—216no—
428C24—216no—
429C24—216no—
430C24—216no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24C4×D4116yes—
454C24C23×C414yes—
455C24C23×C412yes—
456C24C23×C414yes—
457C24C22×D412yes—
458C24C22×D412yes—
459C24C22×D414yes—
460C24C2×#4112yes—
461C24C2×#4112yes—
462C24C2×#4114yes—
463C24C2×#4112yes—
464C24C2×#4112yes—
465C24H(5,𝔽2)14yes—
466C24H(5,𝔽2)14yes—
467C24H(5,𝔽2)14yes—
468C242−1+414yes—
469C24C2511yescharacteristic
470C2×D4—232no—
471C2×D4—216no—
472C2×D4—216no—
473C2×D4—216no—
474C2×D4—232no—
475C2×D4—232no—
476C2×D4—28no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—416no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—82no—
487C2×D4—82no—
488C2×D4—84no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—232no—
496C22×C4—28no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—232no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—216no—
534C22×C4—216no—
535C22×C4—232no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—416no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—416no—
572C22×C4—416no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—416no—
578C22×C4—416no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—416no—
583C22×C4—416no—
584C22×C4—416no—
585C22×C4—416no—
586C22×C4—4128no—
587C22×C4—4128no—
588C22×C4—4128no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—416no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—416no—
602C22×C4—48no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—88no—
606C22×C4C4×D4116yescomplemented
607C22×C4#121116yescomplemented
608C22×C4C23×C414yes—
609C22×C4C23×C418yes—
610C22×C4C23×C414yes—
611C22×C4C23×C412yes—
612C22×C4C23×C412yes—
613C22×C4C22×D414yes—
614C22×C4C22×D414yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D414yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4114yes—
623C4⋊C4—28no—
624C4⋊C4—48no—
625C4⋊C4—416no—
626C4⋊C4—48no—
627C4⋊C4—82no—
628C4⋊C4—82no—
629C4⋊C4—84no—
630C22⋊C4—232no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—416no—
634C22⋊C4—416no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—416no—
638C22⋊C4—416no—
639C22⋊C4—48no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—88no—
643C42—416no—
644C42—48no—
645C23—232no—
646C23—232no—
647C23—232no—
648C23—232no—
649C23—232no—
650C23—264no—
651C23—232no—
652C23—264no—
653C23—264no—
654C23—264no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—232no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—28no—
704C23—28no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23C2×C4×D418yes—
724C23C2×C4×D414yes—
725C23C2×C4×D414yes—
726C23C4×#4114yes—
727C23#51818yes—
728C23#52018yes—
729C23C2×#12114yes—
730C23#52514yes—
731C23#52914yes—
732C23#53214yes—
733C23#53418yes—
734C23#53718yes—
735C23#53818yes—
736C23#53918yes—
737C23C24×C411yescharacteristic
738C23C23×D411yescharacteristic
739C23C23×D411yescharacteristic
740C23C22×#4111yescharacteristic
741C23C22×#4111yescharacteristic
742C23C22×#4111yescharacteristic
743C23C22×#4111yescharacteristic
744C23C2×H(5,𝔽2)12yes—
745C23C2×H(5,𝔽2)12yes—
746C23C2×H(5,𝔽2)12yes—
747C23C2×2−1+412yes—
748D4—464no—
749D4—432no—
750D4—88no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—416no—
780C2×C4—416no—
781C2×C4—432no—
782C2×C4—432no—
783C2×C4—464no—
784C2×C4—416no—
785C2×C4—416no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—464no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—816no—
827C2×C4C2×C4×D414yes—
828C2×C4C2×C4×D414yes—
829C2×C4C2×#12118yes—
830C22—2128no—
831C22—28no—
832C22—28no—
833C22—24no—
834C22—28no—
835C22—24no—
836C22—28no—
837C22—24no—
838C22—28no—
839C22—24no—
840C22—28no—
841C22—28no—
842C22—28no—
843C22—28no—
844C22—24no—
845C22—28no—
846C22—24no—
847C22—28no—
848C22—28no—
849C22—28no—
850C22—28no—
851C22—28no—
852C22—28no—
853C22—28no—
854C22—28no—
855C22—48no—
856C22—44no—
857C22—44no—
858C22—48no—
859C22—44no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—84no—
865C22—84no—
866C22C4×#12118yes—
867C22#2325116yescomplemented
868C22C22×C4×D411yescharacteristic
869C22C22×C4×D411yescharacteristic
870C22C2×C4×#4111yescharacteristic
871C22C2×#51812yes—
872C22C2×#52012yes—
873C22C22×#12111yescharacteristic
874C22C2×#52511yescharacteristic
875C22C2×#52911yescharacteristic
876C22C2×#53211yescharacteristic
877C22C2×#53412yes—
878C22C2×#53712yes—
879C22C2×#53812yes—
880C22C2×#53912yes—
881C22#348411yescharacteristic
882C22#348411yescharacteristic
883C22#348411yescharacteristic
884C22#348611yescharacteristic
885C22#349012yes—
886C22#349012yes—
887C22#349012yes—
888C22#349212yes—
889C22#349212yes—
890C22#349212yes—
891C4—24no—
892C4—24no—
893C4—28no—
894C4—48no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—44no—
899C4—44no—
900C4—82no—
901C4—82no—
902C4—84no—
903C2—216no—
904C2—28no—
905C2—84no—
906C2C2×C4×#12111yescharacteristic
907C2C2×#232512yes—
908C2#3419811yescharacteristic
909C2#3420011yescharacteristic
910C2#3421812yes—
911C2#3498111yescharacteristic
912C2#3498811yescharacteristic
913C2#3498911yescharacteristic
914C2#3499712yes—
915C2#3505112yes—
916C2#3522311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2847C2
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×#2325C2semidirect
3. C2×C4×#120C2semidirect
4. C23×#95C2semidirect
5. #14694C2semidirect
6. #14680C2semidirect
7. #14275C2semidirect
8. #14271C2semidirect
9. #14259C2semidirect
10. #14047C2semidirect
11. #14023C2semidirect
12. #13999C2semidirect
13. #13975C2semidirect
14. #13784C2semidirect
15. #13778C2semidirect
24. #2847C4semidirect
27. C2×#388C22semidirect
28. C2×#387C22semidirect
37. C2×#386C22semidirect
40. C2×#385C22semidirect
57. #1445C22semidirect
58. #1444C22semidirect
59. #1443C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1441C22semidirect
63. #1440C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1438C22semidirect
67. #1437C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. #1436C22semidirect
71. #1434C22semidirect
78. C22⋊#95C22semidirect
96. C24×C4C2×C4semidirect
97. C24×C4D4semidirect
113. C2×#121C2×C4semidirect
114. C2×#121C2×C4semidirect
117. C2×#120C2×C4semidirect
155. #386C2×C4semidirect
156. #386C2×C4semidirect
164. #380C2×C4semidirect
165. #380C2×C4semidirect
174. C2×#95D4semidirect
229. C22×D4C22×C4semidirect
342. C2×C4⋊C4C22×C4semidirect
343. C2×C4⋊C4C22×C4semidirect
379. C2×C22⋊C4C22×C4semidirect
380. C2×C22⋊C4C22×C4semidirect
405. #95C22×C4semidirect
406. #95C22×C4semidirect
606. C22×C4C4×D4semidirect
607. C22×C4#121semidirect
867. C22#2325semidirect

Maximal subgroups

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

subgroupindex
C2×#28472
C2×#23252
C2×C4×#1202
C23×#952
#146942
#146802
#142752
#142712
#142592
#140472
#140232
#139992
#139752
#137842
#137782