Finite Group Databasebeta

← #876609

Subgroups — #876609

Order 512.

4902 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2679C211yesmaximal, characteristic, complemented
2C2×#2404C212yesmaximal, complemented
3C2×#2297C211yesmaximal, characteristic, complemented
4#17077C212yesmaximal, complemented
5#16652C212yesmaximal, complemented
6#15376C214yesmaximal, complemented
7#15257C214yesmaximal, complemented
8#14886C212yesmaximal, complemented
9#14838C214yesmaximal, complemented
10#14698C212yesmaximal, complemented
11#14440C211yesmaximal, characteristic, complemented
12#14357C212yesmaximal, complemented
13#13995C214yesmaximal, complemented
14C23×#41C2211yescharacteristic
15C22×#121C2212yes—
16C22×#120C2212yes—
17C22×#120C2214yes—
18C22×#120C2212yescomplemented
19C22×#117C2211yescharacteristic, complemented
20C23×C22⋊C4C2212yescomplemented
21C23×C42C2211yescharacteristic, complemented
22#2679—28no—
23#2404—216no—
24C2×#394C2212yes—
25C2×#394C2214yes—
26C2×#393C2214yescomplemented
27C2×#392C2214yes—
28C2×#392C2212yes—
29#2297—28no—
30C2×#391C2211yescharacteristic, complemented
31C2×#391C2211yescharacteristic, complemented
32C2×#390C2211yescharacteristic
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2211yescharacteristic
37C2×#386C2212yes—
38C2×#386C2214yes—
39C2×#386C2214yes—
40C2×#386C2212yescomplemented
41C2×#386C2214yescomplemented
42C2×#386C2214yescomplemented
43C2×#386C2214yescomplemented
44C2×#385C2214yescomplemented
45C2×#381C2212yescomplemented
46C2×#380C2212yescomplemented
47C2×#379C2214yescomplemented
48C2×C4×C22⋊C4C2214yescomplemented
49#1443C2214yescomplemented
50#1442C2214yescomplemented
51#1441C2212yescomplemented
52#1440C2214yescomplemented
53#1440C2214yescomplemented
54#1439C2214yescomplemented
55#1439C2212yescomplemented
56#1439C2214yescomplemented
57#1439C2214yescomplemented
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1438C2214yes—
61#1438C2214yes—
62#1438C2214yes—
63#1438C2214yescomplemented
64#1437C2214yescomplemented
65#1437C2214yescomplemented
66#1437C2214yescomplemented
67C4⋊#95C2212yescomplemented
68C4⋊#95C2212yescomplemented
69#1434C2212yescomplemented
70C26C2312yes—
71C22×#41—24no—
72C22×#41—24no—
73C22×#41—42no—
74C22×#41—42no—
75C22×#41—42no—
76C22×#41—42no—
77C22×#41D418yescomplemented
78C23×Q8C2311yescharacteristic
79C23×D4C2314yes—
80C23×D4C2314yes—
81C23×D4C2312yes—
82C23×D4C2312yes—
83C23×D4C2312yes—
84C23×D4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2312yes—
87C24×C4C2312yes—
88C24×C4C2312yes—
89C2×#121—28no—
90C2×#121—44no—
91C2×#121—44no—
92C2×#120—28no—
93C2×#120—28no—
94C2×#120—28no—
95C2×#120—28no—
96C2×#120—216no—
97C2×#120—216no—
98C2×#120—48no—
99C2×#120—44no—
100C2×#120—44no—
101C2×#117—24no—
102C2×#117—42no—
103C2×#117—42no—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C22⋊C4—28no—
111C22×C22⋊C4—44no—
112C22×C22⋊C4—44no—
113C22×C22⋊C4C2314yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2314yes—
116C22×C22⋊C4C2314yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
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×C42—24no—
131C22×C42—42no—
132C22×C42—42no—
133C22×C42C2312yes—
134C22×C42C2312yes—
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137#394—28no—
138#394—216no—
139#393—216no—
140#392—216no—
141#392—44no—
142#391—24no—
143#391—24no—
144#390—24no—
145#390—28no—
146#390—44no—
147#390—44no—
148#390D418yescomplemented
149#386—28no—
150#386—28no—
151#386—216no—
152#386—216no—
153#386—216no—
154#386—48no—
155#386—48no—
156#385—48no—
157#381—28no—
158#380—44no—
159#379—48no—
160C4×C22⋊C4—216no—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C25—24no—
176C25—28no—
177C25—24no—
178C25—24no—
179C25—42no—
180C25—42no—
181C25—44no—
182C25—44no—
183C25—42no—
184C25—42no—
185C25—44no—
186C25C2414yes—
187C25C2412yes—
188C25C2411yescharacteristic
189C2×#41—232no—
190C2×#41—416no—
191C2×#41—416no—
192C2×#41—416no—
193C2×#41—416no—
194C2×#41—416no—
195C2×#41—416no—
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8—41no—
199C22×Q8—41no—
200C22×Q8—41no—
201C22×Q8—41no—
202C22×Q8C2×D414yes—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—28no—
208C22×D4—28no—
209C22×D4—28no—
210C22×D4—28no—
211C22×D4—28no—
212C22×D4—28no—
213C22×D4—28no—
214C22×D4—28no—
215C22×D4—28no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4—41no—
222C22×D4—41no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—44no—
230C22×D4—42no—
231C22×D4—44no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4C2×D418yes—
239C22×D4C2×D414yes—
240C22×D4C2×D414yes—
241C22×D4#4114yes—
242C22×D4#4118yescomplemented
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
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—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4C2×D414yes—
268C23×C4C2×D418yes—
269C23×C4C2412yes—
270C23×C4C2414yes—
271C23×C4C2414yes—
272C23×C4C2414yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279#121—432no—
280#120—464no—
281#120—432no—
282#120—432no—
283#117—416no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4C2×D414yes—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—432no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
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×C42—24no—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—42no—
359C2×C42—41no—
360C2×C42—41no—
361C2×C42—42no—
362C2×C42—41no—
363C2×C42—41no—
364C2×C42—416no—
365C2×C42C2×D414yes—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—42no—
380C24—21no—
381C24—24no—
382C24—21no—
383C24—22no—
384C24—24no—
385C24—24no—
386C24—21no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—416no—
411C24—48no—
412C24—416no—
413C24—416no—
414C24—48no—
415C24—416no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—84no—
420C24—84no—
421C24—88no—
422C24—84no—
423C24—84no—
424C24—88no—
425C24—88no—
426C24—88no—
427C24—88no—
428C24—88no—
429C24—88no—
430C24—84no—
431C24—84no—
432C24—88no—
433C24C22×D414yes—
434C24C22×D414yes—
435C24C22×D412yes—
436C24C2×#4118yes—
437C24C2×#4114yes—
438C24H(5,𝔽2)12yes—
439C24H(5,𝔽2)12yes—
440C24C2511yescharacteristic
441#41—4128no—
442C2×Q8—28no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×D4—216no—
450C2×D4—216no—
451C2×D4—216no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—48no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—416no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—416no—
467C2×D4—416no—
468C2×D4—48no—
469C2×D4—416no—
470C2×D4—416no—
471C2×D4—416no—
472C2×D4—416no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4—84no—
479C2×D4—84no—
480C2×D4—88no—
481C2×D4—88no—
482C2×D4—88no—
483C2×D4—88no—
484C2×D4—88no—
485C2×D4—88no—
486C2×D4—88no—
487C2×D4—84no—
488C2×D4#121116yescomplemented
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—216no—
509C22×C4—216no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—216no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
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—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—88no—
566C22×C4—88no—
567C22×C4—84no—
568C22×C4—84no—
569C22×C4C22×D414yes—
570C22×C4C22×D414yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D414yes—
575C22×C4C2×#4112yes—
576C22×C4C2×#4114yes—
577C22×C4H(5,𝔽2)14yes—
578C22×C4H(5,𝔽2)12yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C4H(5,𝔽2)14yes—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—48no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C22⋊C4—232no—
588C22⋊C4—416no—
589C22⋊C4—48no—
590C22⋊C4—416no—
591C22⋊C4—416no—
592C22⋊C4—416no—
593C22⋊C4—416no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—416no—
597C22⋊C4—416no—
598C22⋊C4—416no—
599C22⋊C4—88no—
600C22⋊C4—88no—
601C22⋊C4—88no—
602C22⋊C4—88no—
603C22⋊C4—88no—
604C42—44no—
605C42—48no—
606C42—48no—
607C42—44no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—28no—
613C23—24no—
614C23—28no—
615C23—28no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—28no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—28no—
628C23—28no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—42no—
640C23—44no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—44no—
647C23—42no—
648C23—44no—
649C23—41no—
650C23—42no—
651C23—44no—
652C23—42no—
653C23—44no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—44no—
659C23—432no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—832no—
689C23—816no—
690C23—816no—
691C23—816no—
692C23—832no—
693C23—832no—
694C23—832no—
695C23—816no—
696C23—816no—
697C23—816no—
698C23C2×#12118yes—
699C23#53414yes—
700C23C23×D411yescharacteristic
701C23C23×D411yescharacteristic
702C23C22×#4111yescharacteristic
703C23C22×#4112yes—
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×H(5,𝔽2)11yescharacteristic
706C23C2×H(5,𝔽2)11yescharacteristic
707C23C2×H(5,𝔽2)11yescharacteristic
708C23C2×H(5,𝔽2)12yes—
709C23C2×H(5,𝔽2)12yes—
710C23#58512yes—
711Q8—416no—
712D4—416no—
713D4—432no—
714D4—816no—
715D4—816no—
716D4—832no—
717D4—832no—
718C2×C4—232no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
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—44no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—816no—
785C2×C4C2×#12114yes—
786C2×C4#53414yes—
787C2×C4#54618yes—
788C22—28no—
789C22—216no—
790C22—24no—
791C22—28no—
792C22—48no—
793C22—44no—
794C22—48no—
795C22—44no—
796C22—48no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—44no—
801C22—42no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—42no—
806C22—42no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—48no—
811C22—48no—
812C22—48no—
813C22—48no—
814C22—48no—
815C22—48no—
816C22—48no—
817C22—864no—
818C22—84no—
819C22—84no—
820C22—84no—
821C22—84no—
822C22—84no—
823C22—84no—
824C22—84no—
825C22—84no—
826C22C22×#12111yescharacteristic
827C22C2×#53411yescharacteristic
828C22C2×#53411yescharacteristic
829C22#345912yes—
830C22C2×#54612yes—
831C22D4×#4112yes—
832C22#348112yes—
833C22#348111yescharacteristic
834C22#348411yescharacteristic
835C22#348411yescharacteristic
836C22#348812yes—
837C22#349012yes—
838C22#349011yescharacteristic
839C22#349011yescharacteristic
840C22#349812yes—
841C22#351412yes—
842C22#351912yes—
843C22#352911yescharacteristic
844C22#353412yes—
845C22#353712yes—
846C22#354911yescharacteristic
847C22#354911yescharacteristic
848C22#355812yes—
849C4—28no—
850C4—24no—
851C4—24no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—84no—
856C4—82no—
857C4—84no—
858C4—84no—
859C2—44no—
860C2—48no—
861C2—88no—
862C2#3498111yescharacteristic
863C2#3625812yes—
864C2#3729711yescharacteristic
865C2#3774412yes—
866C2#3842412yes—
867C2#3876012yes—
868C2#4622511yescharacteristic
869C2#4628711yescharacteristic
870C2#5216311yescharacteristic
871C2#5904111yescharacteristic
872C2#6004511yescharacteristic
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×#2679C2semidirect
2. C2×#2404C2semidirect
3. C2×#2297C2semidirect
4. #17077C2semidirect
5. #16652C2semidirect
6. #15376C2semidirect
7. #15257C2semidirect
8. #14886C2semidirect
9. #14838C2semidirect
10. #14698C2semidirect
11. #14440C2semidirect
12. #14357C2semidirect
13. #13995C2semidirect
18. C22×#120C22semidirect
19. C22×#117C22semidirect
20. C23×C22⋊C4C22semidirect
21. C23×C42C22semidirect
26. C2×#393C22semidirect
30. C2×#391C22semidirect
31. C2×#391C22semidirect
40. C2×#386C22semidirect
41. C2×#386C22semidirect
42. C2×#386C22semidirect
43. C2×#386C22semidirect
44. C2×#385C22semidirect
45. C2×#381C22semidirect
46. C2×#380C22semidirect
47. C2×#379C22semidirect
48. C2×C4×C22⋊C4C22semidirect
49. #1443C22semidirect
50. #1442C22semidirect
51. #1441C22semidirect
52. #1440C22semidirect
53. #1440C22semidirect
54. #1439C22semidirect
55. #1439C22semidirect
56. #1439C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
63. #1438C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1437C22semidirect
67. C4⋊#95C22semidirect
68. C4⋊#95C22semidirect
69. #1434C22semidirect
77. C22×#41D4semidirect
148. #390D4semidirect
242. C22×D4#41semidirect
488. C2×D4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#26792
C2×#24042
C2×#22972
#170772
#166522
#153762
#152572
#148862
#148382
#146982
#144402
#143572
#139952