Finite Group Databasebeta

← #719814

Subgroups — #719814

Order 512.

4294 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic, complemented
2C2×#2535C211yesmaximal, characteristic, complemented
3C2×#2428C212yesmaximal, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#2328C211yesmaximal, characteristic, complemented
6#16512C214yesmaximal, complemented
7#15390C214yesmaximal, complemented
8#15263C214yesmaximal, complemented
9#15220C212yesmaximal, complemented
10#15126C212yesmaximal, complemented
11#14719C214yesmaximal, complemented
12#14276C211yesmaximal, characteristic, complemented
13#13970C212yesmaximal, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13847C211yesmaximal, characteristic, complemented
16C22×#127C2211yescharacteristic
17C22×#121C2212yes—
18C22×#121C2212yes—
19C22×#121C2212yes—
20C22×#121C2214yes—
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26#2537—28no—
27#2535—28no—
28#2428—216no—
29C2×#397C2212yes—
30C2×#394C2214yes—
31C2×#394C2214yes—
32C2×#394C2214yes—
33C2×#392C2212yes—
34C2×#392C2214yes—
35D4×C4⋊C4—28no—
36#2328—28no—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#386C2214yes—
43C2×#386C2214yes—
44C2×#386C2214yes—
45C2×#386C2214yes—
46C2×#386C2214yes—
47C2×#385C2214yes—
48C2×#384C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×#376C2211yescharacteristic
59#1445C2212yes—
60#1443C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1440C2214yes—
65#1440C2214yes—
66#1439C2214yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2212yes—
72#1439C2212yes—
73#1438C2214yes—
74#1438C2212yes—
75#1438C2214yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C22⋊#95C2214yes—
79C22⋊#95C2214yes—
80C23×D4C2311yescharacteristic
81C23×D4C2311yescharacteristic
82C23×D4C2314yes—
83C23×D4C2311yescharacteristic
84C23×D4C2314yes—
85C23×D4C2314yes—
86C24×C4C2312yes—
87C24×C4C2314yes—
88C24×C4C2312yes—
89C24×C4C2312yes—
90C2×#127—24no—
91C2×#127—24no—
92C2×#127D418yescomplemented
93C2×#121—216no—
94C2×#121—28no—
95C2×#121—28no—
96C2×#121—28no—
97C2×#121—28no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—48no—
101C2×#121—48no—
102C2×#121—48no—
103C2×#121—44no—
104C2×C4×D4—28no—
105C2×C4×D4—28no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—44no—
115C2×C4×D4D418yescomplemented
116C22×C4⋊C4—28no—
117C22×C4⋊C4—48no—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C42C2312yes—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#397—28no—
150#394—216no—
151#394—216no—
152#394—48no—
153#392—216no—
154#392—28no—
155#390—24no—
156#390—28no—
157#390—24no—
158#389—28no—
159#389—28no—
160#386—216no—
161#386—216no—
162#386—216no—
163#386—216no—
164#386—48no—
165#385—216no—
166#384D418yescomplemented
167#382—24no—
168#382—24no—
169#380—28no—
170#380—28no—
171#380—28no—
172#380—28no—
173C4×C4⋊C4—24no—
174C4×C22⋊C4—28no—
175C4×C22⋊C4—44no—
176#376—24no—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C25C2412yes—
196C25C2412yes—
197C25C2412yes—
198C22×D4—24no—
199C22×D4—28no—
200C22×D4—28no—
201C22×D4—28no—
202C22×D4—28no—
203C22×D4—28no—
204C22×D4—28no—
205C22×D4—28no—
206C22×D4—28no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—28no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—42no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4—44no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—44no—
230C22×D4—44no—
231C22×D4—44no—
232C22×D4—44no—
233C22×D4C2×D414yes—
234C22×D4C2×D414yes—
235C22×D4C2×D414yes—
236C22×D4C2×D4116yes—
237C22×D4#4114yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—28no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—28no—
250C23×C4—28no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4C2×D418yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2414yes—
267C23×C4C2412yes—
268C23×C4C2414yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274#127—232no—
275#121—464no—
276#121—432no—
277#121—432no—
278#121—432no—
279C4×D4—232no—
280C4×D4—432no—
281C4×D4—416no—
282C4×D4—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—432no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4C2×D418yes—
310C2×C4⋊C4C2×D414yes—
311C2×C4⋊C4C2×D418yes—
312C2×C4⋊C4C2×D418yes—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
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—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
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—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4C2×D418yes—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42C2×D414yes—
370C2×C42C2×D414yes—
371C2×C42C2×D414yes—
372C2×C42#4114yes—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—24no—
383#95—24no—
384#95—28no—
385#95—44no—
386#95—42no—
387#95—42no—
388#95—44no—
389#95—44no—
390#95—44no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—24no—
398C24—24no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—24no—
419C24—22no—
420C24—24no—
421C24—22no—
422C24—22no—
423C24C22×D414yes—
424C24C22×D414yes—
425C24C22×D414yes—
426C24C2×#4114yes—
427C24H(5,𝔽2)14yes—
428C24C2511yescharacteristic
429C2×D4—28no—
430C2×D4—232no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—44no—
443C2×D4—416no—
444C2×D4—416no—
445C2×D4—416no—
446C2×D4—416no—
447C2×D4—416no—
448C2×D4—416no—
449C2×D4—416no—
450C2×D4—416no—
451C2×D4—416no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—88no—
458C2×D4—88no—
459C2×D4—88no—
460C2×D4—88no—
461C2×D4—88no—
462C2×D4—88no—
463C2×D4—88no—
464C2×D4—88no—
465C2×D4—88no—
466C2×D4—88no—
467C2×D4—88no—
468C2×D4#121116yescomplemented
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—216no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—416no—
530C22×C4—416no—
531C22×C4—48no—
532C22×C4—416no—
533C22×C4—48no—
534C22×C4—416no—
535C22×C4—416no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—88no—
547C22×C4—88no—
548C22×C4—88no—
549C22×C4—88no—
550C22×C4—88no—
551C22×C4—88no—
552C22×C4C22×D414yes—
553C22×C4C22×D414yes—
554C22×C4C22×D418yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4112yes—
566C22×C4H(5,𝔽2)14yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C42−1+412yes—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—216no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—416no—
575C4⋊C4—44no—
576C4⋊C4—416no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—48no—
580C22⋊C4—216no—
581C22⋊C4—216no—
582C22⋊C4—48no—
583C22⋊C4—416no—
584C22⋊C4—416no—
585C22⋊C4—416no—
586C22⋊C4—416no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—416no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—88no—
593C22⋊C4—88no—
594C22⋊C4—88no—
595C22⋊C4—88no—
596C42—28no—
597C42—44no—
598C42—48no—
599C42#121116yescomplemented
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—28no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—28no—
611C23—28no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—28no—
618C23—28no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—44no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—44no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—44no—
659C23—42no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—42no—
665C23—44no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—42no—
670C23—44no—
671C23—42no—
672C23—42no—
673C23—44no—
674C23—42no—
675C23—44no—
676C23—42no—
677C23—42no—
678C23—44no—
679C23—42no—
680C23C2×#12118yes—
681C23C23×D411yescharacteristic
682C23C23×D411yescharacteristic
683C23C23×D411yescharacteristic
684C23C22×#4111yescharacteristic
685C23C22×#4111yescharacteristic
686C23C2×H(5,𝔽2)11yescharacteristic
687C23C2×H(5,𝔽2)12yes—
688C23C2×H(5,𝔽2)12yes—
689C23C2×2−1+411yescharacteristic
690C23#58512yes—
691C23#58512yes—
692D4—232no—
693D4—416no—
694D4—416no—
695D4—832no—
696D4—832no—
697D4—832no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—432no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—816no—
767C2×C4—832no—
768C2×C4—816no—
769C2×C4C2×#12114yes—
770C2×C4C2×#12114yes—
771C2×C4C2×#12114yes—
772C2×C4C2×#12114yes—
773C2×C4#53714yes—
774C2×C4D4214yes—
775C2×C4#54714yes—
776C2×C4#54814yes—
777C2×C4#55314yes—
778C22—28no—
779C22—216no—
780C22—44no—
781C22—44no—
782C22—48no—
783C22—44no—
784C22—48no—
785C22—44no—
786C22—48no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—48no—
795C22—44no—
796C22—44no—
797C22—48no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—82no—
802C22—82no—
803C22—84no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—84no—
813C22—82no—
814C22—82no—
815C22C22×#12111yescharacteristic
816C22C22×#12111yescharacteristic
817C22C2×#53711yescharacteristic
818C22#346012yes—
819C22C2×D4211yescharacteristic
820C22C2×#54711yescharacteristic
821C22C2×#54811yescharacteristic
822C22C2×#55311yescharacteristic
823C22#348411yescharacteristic
824C22#348412yes—
825C22#348411yescharacteristic
826C22#348512yes—
827C22#348711yescharacteristic
828C22#348711yescharacteristic
829C22#348812yes—
830C22#349412yes—
831C22#349612yes—
832C22#351312yes—
833C22#351412yes—
834C22#353712yes—
835C22#353912yes—
836C22#354712yes—
837C22#355912yes—
838C4—24no—
839C4—24no—
840C4—44no—
841C4—48no—
842C4—44no—
843C4—44no—
844C4—82no—
845C4—82no—
846C4—84no—
847C4—82no—
848C4—82no—
849C4#241618yes—
850C2—48no—
851C2—84no—
852C2—84no—
853C2C2×#241611yescharacteristic
854C2#3516811yescharacteristic
855C2#3556311yescharacteristic
856C2#3576112yes—
857C2#3776412yes—
858C2#3925612yes—
859C2#4244512yes—
860C2#4493811yescharacteristic
861C2#4527111yescharacteristic
862C2#4535511yescharacteristic
863C2#4538711yescharacteristic
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×#2537C2semidirect
2. C2×#2535C2semidirect
3. C2×#2428C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. C2×#2328C2semidirect
6. #16512C2semidirect
7. #15390C2semidirect
8. #15263C2semidirect
9. #15220C2semidirect
10. #15126C2semidirect
11. #14719C2semidirect
12. #14276C2semidirect
13. #13970C2semidirect
14. #13941C2semidirect
15. #13847C2semidirect
92. C2×#127D4semidirect
115. C2×C4×D4D4semidirect
166. #384D4semidirect
468. C2×D4#121semidirect
599. C42#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#25352
C2×#24282
C2×D4×C4⋊C42
C2×#23282
#165122
#153902
#152632
#152202
#151262
#147192
#142762
#139702
#139412
#138472