Finite Group Databasebeta

← #919771

Subgroups — #919771

Order 512.

3908 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2C2×#2395C211yesmaximal, characteristic, complemented
3#17093C214yesmaximal, complemented
4#17015C212yesmaximal, complemented
5#16932C212yesmaximal, complemented
6#16391C212yesmaximal, complemented
7#16298C212yesmaximal, complemented
8#15268C214yesmaximal, complemented
9#15183C212yesmaximal, complemented
10#15134C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#14257C212yesmaximal, complemented
13#14022C212yesmaximal, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13902C212yesmaximal, complemented
16C24×D4C2211yescharacteristic
17C22×#121C2212yes—
18C22×#120C2212yes—
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic, complemented
21#2408—28no—
22#2395—28no—
23C2×#400C2211yescharacteristic, complemented
24C2×#399C2211yescharacteristic
25C2×#398C2211yescharacteristic, complemented
26C2×#397C2211yescharacteristic
27C2×#397C2212yescomplemented
28C2×#396C2214yescomplemented
29C2×#396C2214yescomplemented
30C2×#394C2212yes—
31C2×#394C2212yes—
32C2×#394C2214yescomplemented
33C2×#392C2212yes—
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#389C2212yescomplemented
41C2×#388C2214yescomplemented
42C2×#384C2211yescharacteristic, complemented
43C2×#380C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2212yescomplemented
46C2×#379C2212yes—
47C2×#379C2214yes—
48C2×#379C2214yes—
49C2×C4×C4⋊C4C2212yescomplemented
50C2×C4×C4⋊C4C2211yescharacteristic, complemented
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic, complemented
53#1445C2214yescomplemented
54#1443C2214yescomplemented
55#1440C2214yes—
56#1440C2214yescomplemented
57#1440C2214yescomplemented
58#1439C2212yes—
59#1439C2214yes—
60#1439C2214yescomplemented
61#1439C2214yescomplemented
62#1439C2214yescomplemented
63#1439C2214yescomplemented
64#1439C2214yescomplemented
65#1439C2212yescomplemented
66#1439C2214yescomplemented
67#1438C2214yes—
68#1438C2214yes—
69#1438C2214yescomplemented
70#1438C2214yescomplemented
71#1438C2214yescomplemented
72#1437C2214yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C26C2312yes—
78C23×D4—28no—
79C23×D4—24no—
80C23×D4—42no—
81C23×D4—42no—
82C23×D4—44no—
83C23×D4C2312yes—
84C23×D4C2311yescharacteristic
85C23×D4C2312yes—
86C23×D4C2314yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C2×#121—28no—
90C2×#121—28no—
91C2×#121—44no—
92C2×#120—28no—
93C2×#120—44no—
94C2×#120—44no—
95C2×C4×D4—42no—
96C2×C4×D4—42no—
97C2×C4×D4D418yes—
98C2×#117—24no—
99C2×#117—42no—
100C2×#117—42no—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C22⋊C4C2314yes—
113C22×C22⋊C4C2312yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2314yes—
117C22×C22⋊C4C2314yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2311yescharacteristic
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2311yescharacteristic
135C22×C42C2312yes—
136#400—24no—
137#399—24no—
138#398—24no—
139#397—24no—
140#397—28no—
141#396—48no—
142#396—48no—
143#394—28no—
144#394—28no—
145#394—48no—
146#392—28no—
147#390—28no—
148#390—28no—
149#390—44no—
150#390—44no—
151#390—44no—
152#390—44no—
153#389—44no—
154#388—48no—
155#384—42no—
156#380—24no—
157#380—44no—
158#380—44no—
159#379—28no—
160#379—48no—
161#379—48no—
162C4×C4⋊C4—28no—
163C4×C4⋊C4—42no—
164C4×C22⋊C4—28no—
165C4×C22⋊C4—24no—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2311yescharacteristic
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2311yescharacteristic
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C25—24no—
184C25—28no—
185C25—24no—
186C25—24no—
187C25—44no—
188C25—42no—
189C25—42no—
190C25—42no—
191C25—42no—
192C25—44no—
193C25—44no—
194C25C2411yescharacteristic
195C25C2414yes—
196C25C2411yescharacteristic
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—28no—
200C22×D4—28no—
201C22×D4—28no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—432no—
212C22×D4—41no—
213C22×D4—41no—
214C22×D4—44no—
215C22×D4—42no—
216C22×D4—42no—
217C22×D4—416no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4—44no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4—416no—
224C22×D4—432no—
225C22×D4—416no—
226C22×D4C2×D414yes—
227C22×D4#4118yes—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4C2×D414yes—
237C23×C4C2×D414yes—
238C23×C4C2414yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2414yes—
242C23×C4C2412yes—
243C23×C4C2414yes—
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250#121—432no—
251#120—432no—
252C4×D4—416no—
253#117—416no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4—41no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4C2×D414yes—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—28no—
292C2×C22⋊C4—28no—
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—24no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—41no—
311C2×C22⋊C4—41no—
312C2×C22⋊C4—41no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
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—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4C2×D414yes—
345C2×C22⋊C4C2×D414yes—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42C2×D414yes—
358#95—24no—
359#95—22no—
360#95—24no—
361#95—22no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—44no—
366#95—42no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—22no—
383C24—24no—
384C24—22no—
385C24—24no—
386C24—24no—
387C24—22no—
388C24—24no—
389C24—24no—
390C24—24no—
391C24—21no—
392C24—24no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—24no—
407C24—416no—
408C24—48no—
409C24—416no—
410C24—416no—
411C24—48no—
412C24—416no—
413C24—48no—
414C24—48no—
415C24—48no—
416C24—88no—
417C24—84no—
418C24—84no—
419C24—84no—
420C24—84no—
421C24—88no—
422C24—88no—
423C24—88no—
424C24—88no—
425C24—88no—
426C24—88no—
427C24—88no—
428C24—84no—
429C24—84no—
430C24C22×D412yes—
431C24C22×D412yes—
432C24C2×#4118yes—
433C24H(5,𝔽2)12yes—
434C242−1+412yes—
435C24C2511yescharacteristic
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—216no—
439C2×D4—216no—
440C2×D4—216no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—416no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—416no—
450C2×D4—48no—
451C2×D4—4128no—
452C2×D4—416no—
453C2×D4—416no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—88no—
459C2×D4—88no—
460C2×D4—88no—
461C2×D4—88no—
462C2×D4—88no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C2×#4114yes—
543C22×C4H(5,𝔽2)14yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C4H(5,𝔽2)12yes—
548C22×C4H(5,𝔽2)14yes—
549C4⋊C4—44no—
550C4⋊C4—48no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—84no—
558C4⋊C4—88no—
559C4⋊C4—84no—
560C22⋊C4—44no—
561C22⋊C4—44no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—416no—
565C22⋊C4—416no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—416no—
570C22⋊C4—88no—
571C22⋊C4—88no—
572C22⋊C4—88no—
573C22⋊C4—88no—
574C22⋊C4—88no—
575C22⋊C4—88no—
576C22⋊C4—88no—
577C22⋊C4—88no—
578C22⋊C4—88no—
579C22⋊C4—88no—
580C42—28no—
581C42—48no—
582C42—48no—
583C42—84no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—28no—
600C23—28no—
601C23—24no—
602C23—28no—
603C23—24no—
604C23—28no—
605C23—28no—
606C23—28no—
607C23—28no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—432no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—42no—
623C23—44no—
624C23—44no—
625C23—41no—
626C23—44no—
627C23—44no—
628C23—42no—
629C23—44no—
630C23—42no—
631C23—44no—
632C23—42no—
633C23—44no—
634C23—42no—
635C23—44no—
636C23—41no—
637C23—44no—
638C23—41no—
639C23—41no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—41no—
645C23—41no—
646C23—42no—
647C23—44no—
648C23—44no—
649C23—42no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—42no—
654C23—44no—
655C23—42no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—41no—
660C23—41no—
661C23—44no—
662C23—42no—
663C23—44no—
664C23—44no—
665C23—832no—
666C23—816no—
667C23—816no—
668C23—816no—
669C23—832no—
670C23—832no—
671C23—832no—
672C23—816no—
673C23—816no—
674C23—816no—
675C23#53714yes—
676C23C23×D411yescharacteristic
677C23C22×#4112yes—
678C23C2×H(5,𝔽2)11yescharacteristic
679C23C2×H(5,𝔽2)11yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)11yescharacteristic
683C23C2×H(5,𝔽2)12yes—
684C23C2×H(5,𝔽2)12yes—
685C23C2×2−1+411yescharacteristic
686C23#58512yes—
687D4—416no—
688D4—432no—
689D4—432no—
690D4—832no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4#53414yes—
764C2×C4#53514yes—
765C2×C4#53818yes—
766C2×C4#54618yes—
767C2×C4#55114yes—
768C2×C4#56014yes—
769C22—24no—
770C22—28no—
771C22—42no—
772C22—42no—
773C22—44no—
774C22—44no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—42no—
782C22—48no—
783C22—44no—
784C22—48no—
785C22—48no—
786C22—42no—
787C22—48no—
788C22—42no—
789C22—48no—
790C22—44no—
791C22—48no—
792C22—864no—
793C22—81no—
794C22—84no—
795C22—81no—
796C22—84no—
797C22—82no—
798C22—84no—
799C22—84no—
800C22—82no—
801C22—84no—
802C22—84no—
803C22—81no—
804C22—81no—
805C22—84no—
806C22—84no—
807C22C2×#53411yescharacteristic
808C22C2×#53511yescharacteristic
809C22C2×#53711yescharacteristic
810C22C2×#53812yes—
811C22C2×#54612yes—
812C22C2×#55111yescharacteristic
813C22#348812yes—
814C22#351312yes—
815C22#351412yes—
816C22#351912yes—
817C22#352012yes—
818C22C2×#56011yescharacteristic
819C22#353611yescharacteristic
820C22#353611yescharacteristic
821C22#353711yescharacteristic
822C22#353711yescharacteristic
823C22#354312yes—
824C22#354312yes—
825C22#354612yes—
826C22#354612yes—
827C22#354911yescharacteristic
828C22#355111yescharacteristic
829C22#356112yes—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—82no—
836C4—84no—
837C4—82no—
838C4—82no—
839C4—84no—
840C4—84no—
841C4#269718yes—
842C2—44no—
843C2—82no—
844C2—88no—
845C2#3727311yescharacteristic
846C2#3743911yescharacteristic
847C2#3802412yes—
848C2#3891012yes—
849C2#4261612yes—
850C2#4264212yes—
851C2#4508811yescharacteristic
852C2#4521411yescharacteristic
853C2C2×#269711yescharacteristic
854C2#5296911yescharacteristic
855C2#5301811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2408C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2395C2semidirect
3. #17093C2semidirect
4. #17015C2semidirect
5. #16932C2semidirect
6. #16391C2semidirect
7. #16298C2semidirect
8. #15268C2semidirect
9. #15183C2semidirect
10. #15134C2semidirect
11. #15126C2semidirect
12. #14257C2semidirect
13. #14022C2semidirect
14. #13906C2semidirect
15. #13902C2semidirect
20. C22×#117C22semidirect
23. C2×#400C22semidirect
25. C2×#398C22semidirect
27. C2×#397C22semidirect
28. C2×#396C22semidirect
29. C2×#396C22semidirect
32. C2×#394C22semidirect
40. C2×#389C22semidirect
41. C2×#388C22semidirect
42. C2×#384C22semidirect
45. C2×#380C22semidirect
49. C2×C4×C4⋊C4C22semidirect
50. C2×C4×C4⋊C4C22semidirect
52. C2×C4×C22⋊C4C22semidirect
53. #1445C22semidirect
54. #1443C22semidirect
56. #1440C22semidirect
57. #1440C22semidirect
60. #1439C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
69. #1438C22semidirect
70. #1438C22semidirect
71. #1438C22semidirect
72. #1437C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
C2×#23952
#170932
#170152
#169322
#163912
#162982
#152682
#151832
#151342
#151262
#142572
#140222
#139062
#139022