Finite Group Databasebeta

← #989192

Subgroups — #989192

Order 512.

4710 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2491C212yesmaximal, complemented
2C2×#2408C212yesmaximal, complemented
3#17107C212yesmaximal, complemented
4#16537C214yesmaximal, complemented
5#16249C212yesmaximal, complemented
6#15763C212yesmaximal, complemented
7#15259C214yesmaximal, complemented
8#15219C212yesmaximal, complemented
9#15125C211yesmaximal, characteristic, complemented
10#15123C212yesmaximal, complemented
11#14366C212yesmaximal, complemented
12#14002C212yesmaximal, complemented
13#13905C212yesmaximal, complemented
14#13902C211yesmaximal, characteristic, complemented
15C4×#392C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic, complemented
18C22×#124C2214yescomplemented
19C22×#121C2212yes—
20C22×#121C2212yes—
21C22×#120C2214yes—
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic, complemented
24#2491—216no—
25#2408—216no—
26C2×#394C2214yes—
27C2×#394C2214yescomplemented
28C2×#393C2212yes—
29C2×#393C2214yescomplemented
30C2×#392C2211yescharacteristic
31C2×#392C2214yes—
32C2×#392C2214yescomplemented
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#388C2214yescomplemented
38C2×#382C2212yescomplemented
39C2×#380C2212yes—
40C2×#380C2211yescharacteristic
41C2×#380C2212yescomplemented
42C2×#380C2212yescomplemented
43C2×#379C2212yes—
44C2×#379C2214yes—
45C2×#379C2212yes—
46C2×C4×C4⋊C4C2212yescomplemented
47C2×C4×C22⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2212yescomplemented
49#1446C2212yescomplemented
50#1445C2214yescomplemented
51#1444C2211yescharacteristic, complemented
52#1442C2212yescomplemented
53#1440C2214yescomplemented
54#1440C2214yescomplemented
55#1440C2214yescomplemented
56#1440C2214yescomplemented
57#1439C2212yes—
58#1439C2211yescharacteristic
59#1439C2214yescomplemented
60#1439C2212yescomplemented
61#1438C2212yes—
62#1438C2212yes—
63#1438C2212yes—
64#1438C2214yes—
65#1438C2214yescomplemented
66#1438C2214yescomplemented
67#1438C2211yescharacteristic, complemented
68#1438C2214yescomplemented
69#1438C2214yescomplemented
70#1437C2214yes—
71#1437C2214yescomplemented
72#1437C2214yescomplemented
73#1437C2214yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2211yescharacteristic, complemented
76C4×#95C2211yescharacteristic, complemented
77C26C2312yes—
78C23×Q8C2312yes—
79C23×D4—28no—
80C23×D4—24no—
81C23×D4—44no—
82C23×D4—42no—
83C23×D4—42no—
84C23×D4C2312yes—
85C23×D4C2312yes—
86C23×D4C2312yes—
87C23×D4C2311yescharacteristic
88C23×D4C2314yes—
89C23×D4C2314yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C2×C4⋊Q8—28no—
93C2×C4⋊Q8—42no—
94C2×#124—216no—
95C2×#124—48no—
96C2×#124—48no—
97C2×#121—28no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—44no—
101C2×#121—44no—
102C2×#121—44no—
103C2×#120—216no—
104C2×#120—48no—
105C2×#120—48no—
106C2×C4×D4—28no—
107C2×C4×D4—28no—
108C2×C4×D4—44no—
109C2×C4×D4—42no—
110C2×C4×D4—44no—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2311yescharacteristic
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2314yes—
142#394—216no—
143#394—216no—
144#393—216no—
145#393—44no—
146#392—216no—
147#392—24no—
148#392—48no—
149#390—28no—
150#390—28no—
151#390—44no—
152#390D4116yescomplemented
153#388—216no—
154#382—44no—
155#380—28no—
156#380—28no—
157#380—42no—
158#380—44no—
159#379—216no—
160#379—28no—
161#379—44no—
162C4×C4⋊C4—28no—
163C4×C22⋊C4—28no—
164C4×C22⋊C4—42no—
165C2×#95C2314yes—
166C2×#95C2311yescharacteristic
167C2×#95C2312yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2311yescharacteristic
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2311yescharacteristic
182C2×#95C2311yescharacteristic
183C25—28no—
184C25—24no—
185C25—24no—
186C25—24no—
187C25—42no—
188C25—42no—
189C25—44no—
190C25—44no—
191C25—42no—
192C25—44no—
193C25—42no—
194C25C2414yes—
195C25C2412yes—
196C25C2411yescharacteristic
197C22×Q8—28no—
198C22×Q8—24no—
199C22×Q8—44no—
200C22×Q8—42no—
201C22×Q8—42no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—28no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—28no—
209C22×D4—28no—
210C22×D4—28no—
211C22×D4—28no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—28no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—432no—
223C22×D4—42no—
224C22×D4—41no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4—44no—
229C22×D4—42no—
230C22×D4—41no—
231C22×D4—416no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4—44no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—416no—
242C22×D4—432no—
243C22×D4—416no—
244C22×D4C2×D418yes—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4#4114yes—
257C23×C4C2414yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C4⋊Q8—416no—
270#124—464no—
271#121—432no—
272#121—432no—
273#120—464no—
274C4×D4—432no—
275C4×D4—416no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4C2×D418yes—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—28no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4C2×D4116yes—
353C2×C22⋊C4C2×D4116yes—
354C2×C22⋊C4#4114yes—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—28no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—44no—
363C2×C42—44no—
364C2×C42C2×D418yes—
365#95—24no—
366#95—24no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—22no—
371#95—42no—
372#95—41no—
373#95—42no—
374#95—41no—
375#95—41no—
376#95—42no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—42no—
382#95—44no—
383C24—22no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—22no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—24no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—22no—
397C24—24no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—24no—
417C24—24no—
418C24—22no—
419C24—416no—
420C24—48no—
421C24—416no—
422C24—416no—
423C24—48no—
424C24—416no—
425C24—48no—
426C24—48no—
427C24—48no—
428C24—88no—
429C24—84no—
430C24—84no—
431C24—88no—
432C24—84no—
433C24—88no—
434C24—84no—
435C24—88no—
436C24—88no—
437C24—84no—
438C24—88no—
439C24—88no—
440C24—84no—
441C24—88no—
442C24C22×D418yes—
443C24C2×#4112yes—
444C24C2×#4112yes—
445C24H(5,𝔽2)14yes—
446C24H(5,𝔽2)12yes—
447C24C2511yescharacteristic
448C2×Q8—416no—
449C2×Q8—48no—
450C2×Q8—88no—
451C2×Q8—84no—
452C2×Q8—84no—
453C2×D4—216no—
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—416no—
461C2×D4—44no—
462C2×D4—48no—
463C2×D4—416no—
464C2×D4—416no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—44no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—416no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—4128no—
475C2×D4—48no—
476C2×D4—416no—
477C2×D4—416no—
478C2×D4—416no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—88no—
484C2×D4—88no—
485C2×D4—88no—
486C2×D4—88no—
487C2×D4—88no—
488C2×D4—88no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—28no—
527C22×C4—216no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4C22×D414yes—
565C22×C4C22×D418yes—
566C22×C4C22×D414yes—
567C22×C4C22×D414yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4H(5,𝔽2)14yes—
575C22×C4H(5,𝔽2)12yes—
576C4⋊C4—216no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—44no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C22⋊C4—216no—
583C22⋊C4—416no—
584C22⋊C4—416no—
585C22⋊C4—44no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—416no—
589C22⋊C4—44no—
590C22⋊C4—48no—
591C22⋊C4—416no—
592C22⋊C4—416no—
593C22⋊C4—416no—
594C22⋊C4—416no—
595C22⋊C4—416no—
596C22⋊C4—416no—
597C22⋊C4—48no—
598C22⋊C4—88no—
599C22⋊C4—88no—
600C22⋊C4—84no—
601C22⋊C4—88no—
602C22⋊C4—88no—
603C42—216no—
604C42—416no—
605C42—44no—
606C42—44no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—24no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—28no—
623C23—24no—
624C23—28no—
625C23—28no—
626C23—24no—
627C23—24no—
628C23—28no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—41no—
642C23—42no—
643C23—432no—
644C23—42no—
645C23—42no—
646C23—44no—
647C23—42no—
648C23—44no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—44no—
653C23—42no—
654C23—42no—
655C23—44no—
656C23—42no—
657C23—44no—
658C23—44no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—44no—
670C23—42no—
671C23—44no—
672C23—42no—
673C23—44no—
674C23—44no—
675C23—42no—
676C23—44no—
677C23—42no—
678C23—44no—
679C23—42no—
680C23—44no—
681C23—44no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—42no—
691C23—42no—
692C23—44no—
693C23—42no—
694C23—44no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—832no—
701C23—816no—
702C23—816no—
703C23—816no—
704C23—832no—
705C23—832no—
706C23—832no—
707C23—816no—
708C23—816no—
709C23—816no—
710C23#55514yes—
711C23C23×D412yes—
712C23C22×#4111yescharacteristic
713C23C22×#4111yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)12yes—
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)12yes—
719C23C2×H(5,𝔽2)11yescharacteristic
720C23#58512yes—
721C23#58511yescharacteristic
722Q8—816no—
723D4—432no—
724D4—416no—
725D4—432no—
726D4—432no—
727D4—832no—
728D4—832no—
729C2×C4—22no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—416no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—41no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—816no—
798C2×C4#53518yes—
799C2×C4#53814yes—
800C2×C4D4214yes—
801C2×C4#54618yes—
802C2×C4H(3,𝔽4)14yes—
803C22—24no—
804C22—28no—
805C22—42no—
806C22—44no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—44no—
815C22—48no—
816C22—44no—
817C22—48no—
818C22—44no—
819C22—48no—
820C22—44no—
821C22—48no—
822C22—48no—
823C22—44no—
824C22—48no—
825C22—44no—
826C22—48no—
827C22—44no—
828C22—864no—
829C22—82no—
830C22—84no—
831C22—84no—
832C22—82no—
833C22—84no—
834C22—82no—
835C22—82no—
836C22—84no—
837C22—82no—
838C22—82no—
839C22—84no—
840C22—82no—
841C22—84no—
842C22—84no—
843C22—82no—
844C22—84no—
845C22C2×#53512yes—
846C22C2×#53811yescharacteristic
847C22C2×D4211yescharacteristic
848C22C2×#54612yes—
849C22D4×#4112yes—
850C22C2×#55511yescharacteristic
851C22#348412yes—
852C22#348412yes—
853C22#349412yes—
854C22#350012yes—
855C22#350511yescharacteristic
856C22#350611yescharacteristic
857C22#350811yescharacteristic
858C22#351912yes—
859C22C2×H(3,𝔽4)11yescharacteristic
860C22#353711yescharacteristic
861C22#353711yescharacteristic
862C22#354212yes—
863C22#354212yes—
864C22#354612yes—
865C22#355111yescharacteristic
866C22#355811yescharacteristic
867C22#355812yes—
868C4—48no—
869C4—42no—
870C4—44no—
871C4—42no—
872C4—42no—
873C4—44no—
874C4—42no—
875C4—82no—
876C4—84no—
877C4—84no—
878C4—81no—
879C4#267018yes—
880C2—44no—
881C2—84no—
882C2—88no—
883C2#3950311yescharacteristic
884C2#3987612yes—
885C2#4242612yes—
886C2#4298211yescharacteristic
887C2#4487112yes—
888C2#4535511yescharacteristic
889C2#4564511yescharacteristic
890C2C2×#267011yescharacteristic
891C2#5296711yescharacteristic
892C2#5902612yes—
893C2#5981811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2491C2semidirect
2. C2×#2408C2semidirect
3. #17107C2semidirect
4. #16537C2semidirect
5. #16249C2semidirect
6. #15763C2semidirect
7. #15259C2semidirect
8. #15219C2semidirect
9. #15125C2semidirect
10. #15123C2semidirect
11. #14366C2semidirect
12. #14002C2semidirect
13. #13905C2semidirect
14. #13902C2semidirect
15. C4×#392C2semidirect
17. C22×C4⋊Q8C22semidirect
18. C22×#124C22semidirect
23. C22×C4×D4C22semidirect
27. C2×#394C22semidirect
29. C2×#393C22semidirect
32. C2×#392C22semidirect
37. C2×#388C22semidirect
38. C2×#382C22semidirect
41. C2×#380C22semidirect
42. C2×#380C22semidirect
46. C2×C4×C4⋊C4C22semidirect
48. C2×C4×C22⋊C4C22semidirect
49. #1446C22semidirect
50. #1445C22semidirect
51. #1444C22semidirect
52. #1442C22semidirect
53. #1440C22semidirect
54. #1440C22semidirect
55. #1440C22semidirect
56. #1440C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
65. #1438C22semidirect
66. #1438C22semidirect
67. #1438C22semidirect
68. #1438C22semidirect
69. #1438C22semidirect
71. #1437C22semidirect
72. #1437C22semidirect
73. #1437C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. C4×#95C22semidirect
152. #390D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24912
C2×#24082
#171072
#165372
#162492
#157632
#152592
#152192
#151252
#151232
#143662
#140022
#139052
#139022
C4×#3922