Finite Group Databasebeta

← #2736541

Subgroups — #2736541

Order 512.

3268 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2813C212yesmaximal, complemented
2C2×#2537C211yesmaximal, characteristic, complemented
3C2×#2422C211yesmaximal, characteristic, complemented
4#17089C214yesmaximal, complemented
5#17087C214yesmaximal, complemented
6#16557C212yesmaximal, complemented
7#16400C212yesmaximal, complemented
8#16360C212yesmaximal, complemented
9#15153C211yesmaximal, characteristic, complemented
10#15135C211yesmaximal, characteristic, complemented
11#15131C212yesmaximal, complemented
12#15129C211yesmaximal, characteristic, complemented
13#15129C212yesmaximal, complemented
14#15126C212yesmaximal, complemented
15#15123C212yesmaximal, complemented
16#13920C211yesmaximal, characteristic, complemented
17C4×#392C211yesmaximal, characteristic, complemented
18C22×#123C2212yes—
19C22×#121C2212yes—
20C22×#121C2211yescharacteristic
21C22×#121C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25#2813—216no—
26#2537—28no—
27#2422—28no—
28C2×#400C2212yes—
29C2×#400C2212yes—
30C2×#399C2212yes—
31C2×#397C2212yes—
32C2×#396C2214yes—
33C2×#394C2214yes—
34C2×#394C2212yes—
35C2×#394C2214yes—
36C2×#394C2214yes—
37C2×#394C2212yes—
38C2×#392C2214yes—
39C2×#392C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2212yes—
42C2×#389C2211yescharacteristic
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#385C2212yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57#1445C2212yes—
58#1445C2214yes—
59#1444C2211yescharacteristic
60#1444C2212yes—
61#1441C2214yes—
62#1441C2212yes—
63#1441C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2211yescharacteristic
75#1439C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2211yescharacteristic
80#1438C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C22⋊#95C2212yes—
85C4×#95C2211yescharacteristic
86C23×D4C2311yescharacteristic
87C23×D4C2312yes—
88C23×D4C2314yes—
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C2×#123—28no—
95C2×#123—28no—
96C2×#123—44no—
97C2×#121—24no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—28no—
101C2×#121—44no—
102C2×#121—44no—
103C2×#121—44no—
104C2×#121—44no—
105C2×C4×D4—24no—
106C2×C4×D4—44no—
107C2×C4×D4—44no—
108C2×C4×D4—44no—
109C2×C4×D4—44no—
110C2×C4×D4—44no—
111C2×C4×D4D418yescomplemented
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C42C2312yes—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148#400—28no—
149#400—44no—
150#399—28no—
151#397—28no—
152#396—216no—
153#394—28no—
154#394—216no—
155#394—28no—
156#394—216no—
157#394—216no—
158#392—216no—
159#392D418yescomplemented
160#390—24no—
161#390—44no—
162#389—24no—
163#389—44no—
164#389—44no—
165#385—28no—
166#384—24no—
167#384—24no—
168#380—28no—
169#380—24no—
170#380—28no—
171#380—28no—
172#380—44no—
173#380—44no—
174#380—44no—
175C4×C22⋊C4—24no—
176C4×C22⋊C4—44no—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2311yescharacteristic
183C2×#95C2312yes—
184C2×#95C2311yescharacteristic
185C2×#95C2311yescharacteristic
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2311yescharacteristic
198C25C2411yescharacteristic
199C25C2412yes—
200C25C2412yes—
201C22×D4—28no—
202C22×D4—24no—
203C22×D4—28no—
204C22×D4—24no—
205C22×D4—22no—
206C22×D4—24no—
207C22×D4—22no—
208C22×D4—24no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—42no—
212C22×D4—42no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4—42no—
216C22×D4—42no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4—44no—
220C22×D4—44no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4—42no—
224C22×D4—44no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4C2×D414yes—
228C22×D4C2×D414yes—
229C22×D4C2×D418yes—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4C2×D418yes—
247C23×C4C2414yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2414yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261#123—432no—
262#121—432no—
263#121—416no—
264#121—432no—
265C4×D4—416no—
266C4×D4—416no—
267C4×D4—432no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4C2×D414yes—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
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⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×D414yes—
358C2×C22⋊C4C2×D418yes—
359C2×C22⋊C4C2×D418yes—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42C2×D414yes—
367#95—22no—
368#95—22no—
369#95—28no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—22no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95C2×D414yes—
388C24—21no—
389C24—22no—
390C24—22no—
391C24—21no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—21no—
399C24—24no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—24no—
420C24—22no—
421C24—22no—
422C24C22×D412yes—
423C24C22×D414yes—
424C24C22×D414yes—
425C24C2511yescharacteristic
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—28no—
429C2×D4—28no—
430C2×D4—48no—
431C2×D4—48no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—416no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—416no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—84no—
448C2×D4—88no—
449C2×D4—88no—
450C2×D4—88no—
451C2×D4—88no—
452C2×D4—88no—
453C2×D4—88no—
454C2×D4—88no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—216no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
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—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4—48no—
530C22×C4—44no—
531C22×C4—48no—
532C22×C4—44no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—88no—
540C22×C4—88no—
541C22×C4C22×D414yes—
542C22×C4C22×D412yes—
543C22×C4C22×D414yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C4H(5,𝔽2)14yes—
550C22×C4H(5,𝔽2)14yes—
551C22×C4H(5,𝔽2)12yes—
552C22×C42−1+412yes—
553C22×C42−1+412yes—
554C4⋊C4—28no—
555C4⋊C4—48no—
556C4⋊C4—44no—
557C4⋊C4—48no—
558C4⋊C4—44no—
559C4⋊C4—48no—
560C4⋊C4—44no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—84no—
565C4⋊C4—88no—
566C4⋊C4—88no—
567C4⋊C4—84no—
568C22⋊C4—28no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—44no—
572C22⋊C4—48no—
573C22⋊C4—416no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—416no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C22⋊C4—88no—
585C22⋊C4—88no—
586C22⋊C4—88no—
587C42—28no—
588C42—44no—
589C42—48no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—44no—
621C23—44no—
622C23—42no—
623C23—42no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—44no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—44no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—44no—
649C23—44no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—44no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23C23×D411yescharacteristic
672C23C23×D411yescharacteristic
673C23C2×H(5,𝔽2)12yes—
674C23C2×H(5,𝔽2)12yes—
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×H(5,𝔽2)11yescharacteristic
677C23C2×2−1+411yescharacteristic
678C23C2×2−1+411yescharacteristic
679C23#58512yes—
680C23#58511yescharacteristic
681C23#58512yes—
682D4—416no—
683D4—432no—
684D4—416no—
685D4—816no—
686D4—832no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—44no—
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—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—816no—
764C2×C4—816no—
765C2×C4—88no—
766C2×C4#53414yes—
767C2×C4#53514yes—
768C2×C4#53714yes—
769C2×C4D4214yes—
770C2×C4#56018yes—
771C2×C4#56218yes—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—42no—
790C22—44no—
791C22—82no—
792C22—81no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—84no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—84no—
801C22—82no—
802C22—81no—
803C22—84no—
804C22—84no—
805C22—82no—
806C22—81no—
807C22—82no—
808C22—81no—
809C22C2×#53411yescharacteristic
810C22C2×#53511yescharacteristic
811C22C2×#53711yescharacteristic
812C22C2×D4211yescharacteristic
813C22#348511yescharacteristic
814C22#348911yescharacteristic
815C22#349611yescharacteristic
816C22#349612yes—
817C22#349612yes—
818C22#349911yescharacteristic
819C22#350011yescharacteristic
820C22C2×#56012yes—
821C22C2×#56212yes—
822C22#353912yes—
823C22#353912yes—
824C22#354012yes—
825C22#354112yes—
826C22#354212yes—
827C22#354612yes—
828C22#354712yes—
829C22#354711yescharacteristic
830C22#354811yescharacteristic
831C22#356512yes—
832C4—24no—
833C4—44no—
834C4—44no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—81no—
839C4—82no—
840C4—82no—
841C4—84no—
842C4—82no—
843C4—82no—
844C4—84no—
845C4#281318yescomplemented
846C2—84no—
847C2—82no—
848C2—84no—
849C2C2×#281311yescharacteristic
850C2#3933811yescharacteristic
851C2#3934011yescharacteristic
852C2#3936211yescharacteristic
853C2#4265011yescharacteristic
854C2#4267911yescharacteristic
855C2#4299211yescharacteristic
856C2#4547812yes—
857C2#4548212yes—
858C2#5304412yes—
859C2#5306212yes—
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×#2813C2semidirect
2. C2×#2537C2semidirect
3. C2×#2422C2semidirect
4. #17089C2semidirect
5. #17087C2semidirect
6. #16557C2semidirect
7. #16400C2semidirect
8. #16360C2semidirect
9. #15153C2semidirect
10. #15135C2semidirect
11. #15131C2semidirect
12. #15129C2semidirect
13. #15129C2semidirect
14. #15126C2semidirect
15. #15123C2semidirect
16. #13920C2semidirect
17. C4×#392C2semidirect
111. C2×C4×D4D4semidirect
159. #392D4semidirect
845. C4#2813semidirect

Maximal subgroups

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

subgroupindex
C2×#28132
C2×#25372
C2×#24222
#170892
#170872
#165572
#164002
#163602
#151532
#151352
#151312
#151292
#151262
#151232
#139202
C4×#3922