Finite Group Databasebeta

← #846396

Subgroups — #846396

Order 512.

4086 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2684C212yesmaximal
2C2×#2547C211yesmaximal, characteristic, complemented
3C2×C4×#120C211yesmaximal, characteristic
4#16470C212yesmaximal, complemented
5#16391C212yesmaximal, complemented
6#15824C214yesmaximal, complemented
7#15494C214yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#15125C212yesmaximal, complemented
11#14680C212yesmaximal, complemented
12#14473C212yesmaximal, complemented
13#13994C212yesmaximal, complemented
14#13872C212yesmaximal, complemented
15#13872C211yesmaximal, characteristic, complemented
16C25×C4C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic, complemented
18C22×#124C2212yes—
19C22×#120C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic, complemented
23#2684—216no—
24#2547—28no—
25C2×#397C2212yes—
26C2×#397C2214yes—
27C2×#397C2212yescomplemented
28C2×#394C2214yes—
29C2×#393C2214yes—
30C4×#120—28no—
31C2×#391C2212yescomplemented
32C2×#389C2212yescomplemented
33C2×#388C2214yes—
34C2×#386C2214yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2211yescharacteristic
38C2×#385C2211yescharacteristic
39C2×#385C2212yes—
40C2×#380C2212yes—
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2212yescomplemented
47C2×#380C2211yescharacteristic, complemented
48C2×#379C2211yescharacteristic
49C2×#379C2214yes—
50C2×C4×C4⋊C4C2211yescharacteristic, complemented
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic
53#1446C2214yescomplemented
54#1443C2214yescomplemented
55#1442C2214yescomplemented
56#1442C2214yescomplemented
57#1442C2214yescomplemented
58#1441C2214yescomplemented
59#1441C2214yescomplemented
60#1441C2212yescomplemented
61#1440C2214yes—
62#1440C2214yes—
63#1440C2214yes—
64#1440C2214yescomplemented
65#1439C2214yes—
66#1439C2212yes—
67#1439C2214yes—
68C4⋊#95C2212yescomplemented
69C4⋊#95C2212yescomplemented
70C4⋊#95C2212yescomplemented
71C4⋊#95C2212yescomplemented
72#1434C2214yescomplemented
73C22⋊#95C2214yes—
74C22⋊#95C2214yes—
75C22⋊#95C2214yes—
76C22⋊#95C2212yescomplemented
77C22⋊#95C2214yescomplemented
78C26C2311yescharacteristic
79C23×Q8C2312yes—
80C23×D4C2312yes—
81C23×D4C2311yescharacteristic
82C24×C4—24no—
83C24×C4—28no—
84C24×C4—42no—
85C24×C4—44no—
86C24×C4—42no—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2312yes—
93C2×C4⋊Q8—24no—
94C2×C4⋊Q8—42no—
95C2×C4⋊Q8—42no—
96C2×#124—28no—
97C2×#124—28no—
98C2×#124—28no—
99C2×#120—24no—
100C2×#120—24no—
101C2×#120D418yes—
102C2×C4×D4—28no—
103C2×C4×D4—28no—
104C2×C4×D4—42no—
105C2×C4×D4—42no—
106C2×C4×D4—44no—
107C2×C4×D4D418yes—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—44no—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C42C2312yes—
136C22×C42C2312yes—
137C22×C42C2311yescharacteristic
138#397—216no—
139#397—28no—
140#397—28no—
141#394—216no—
142#393—216no—
143#391—28no—
144#389—44no—
145#388—216no—
146#386—28no—
147#386—216no—
148#386—24no—
149#386—28no—
150#385—28no—
151#385—24no—
152#380—28no—
153#380—28no—
154#380—28no—
155#380—44no—
156#380—44no—
157#380—44no—
158#380—44no—
159#380—42no—
160#379—216no—
161#379—24no—
162C4×C4⋊C4—24no—
163C4×C22⋊C4—24no—
164C4×C22⋊C4—28no—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C25—22no—
187C25—22no—
188C25—24no—
189C25—24no—
190C25—42no—
191C25—41no—
192C25—41no—
193C25—42no—
194C25—41no—
195C25—41no—
196C25C2×D414yes—
197C25C2411yescharacteristic
198C25C2411yescharacteristic
199C25C2412yes—
200C22×Q8—24no—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—42no—
204C22×Q8—42no—
205C22×Q8—42no—
206C22×Q8—42no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—41no—
212C22×D4—41no—
213C22×D4—42no—
214C22×D4—41no—
215C22×D4—41no—
216C22×D4—42no—
217C22×D4C2×D418yes—
218C22×D4C2×D414yes—
219C22×D4C2×D414yes—
220C22×D4#4114yes—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—41no—
242C23×C4—42no—
243C23×C4—41no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—432no—
249C23×C4—416no—
250C23×C4—42no—
251C23×C4—44no—
252C23×C4—42no—
253C23×C4—44no—
254C23×C4—416no—
255C23×C4—432no—
256C23×C4—416no—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4#4118yes—
260C23×C4C2414yes—
261C23×C4C2414yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C4⋊Q8—416no—
273#124—432no—
274#120—232no—
275C4×D4—416no—
276C4×D4—432no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
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—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—416no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4C2×D414yes—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4C2×D418yes—
349C2×C22⋊C4C2×D414yes—
350C2×C22⋊C4C2×D414yes—
351C2×C22⋊C4C2×D414yes—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42C2×D414yes—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—42no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—21no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—21no—
393C24—22no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—22no—
410C24—28no—
411C24—216no—
412C24—48no—
413C24—44no—
414C24—44no—
415C24—48no—
416C24—44no—
417C24—48no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—44no—
422C24—44no—
423C24—48no—
424C24—44no—
425C24—48no—
426C24—44no—
427C24—44no—
428C24—48no—
429C24—48no—
430C24—44no—
431C24—44no—
432C24—48no—
433C24C22×D412yes—
434C24C22×D412yes—
435C24C22×D412yes—
436C24C22×D412yes—
437C24C22×D414yes—
438C24C2×#4112yes—
439C24C2×#4112yes—
440C24C2×#4114yes—
441C242−1+414yes—
442C24C2511yescharacteristic
443C2×Q8—48no—
444C2×Q8—48no—
445C2×Q8—48no—
446C2×Q8—84no—
447C2×Q8—84no—
448C2×Q8—84no—
449C2×Q8—84no—
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—48no—
462C2×D4—48no—
463C2×D4#121116yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—216no—
495C22×C4—216no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—4128no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—88no—
559C22×C4—84no—
560C22×C4—84no—
561C22×C4—88no—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C2×#4114yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4114yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4H(5,𝔽2)14yes—
575C4⋊C4—44no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—88no—
584C22⋊C4—28no—
585C22⋊C4—216no—
586C22⋊C4—44no—
587C22⋊C4—44no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—44no—
592C22⋊C4—416no—
593C22⋊C4—416no—
594C22⋊C4—416no—
595C22⋊C4—84no—
596C22⋊C4—88no—
597C22⋊C4—88no—
598C22⋊C4—88no—
599C22⋊C4—88no—
600C42—28no—
601C42—48no—
602C42—48no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—432no—
646C23—416no—
647C23—432no—
648C23—416no—
649C23—416no—
650C23—416no—
651C23—416no—
652C23—416no—
653C23—432no—
654C23—432no—
655C23—416no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C2×#12114yes—
693C23C2×#12114yes—
694C23#54718yes—
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4112yes—
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×H(5,𝔽2)12yes—
702C23C2×2−1+412yes—
703C23#58511yescharacteristic
704C23#58511yescharacteristic
705C23#58512yes—
706Q8—816no—
707D4—416no—
708D4—432no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—432no—
728C2×C4—416no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—432no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
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—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—816no—
785C2×C4C2×#12114yes—
786C2×C4#53414yes—
787C2×C4#53818yes—
788C2×C4#54618yes—
789C2×C4#55114yes—
790C2×C4H(3,𝔽4)14yes—
791C22—28no—
792C22—28no—
793C22—28no—
794C22—28no—
795C22—28no—
796C22—24no—
797C22—24no—
798C22—464no—
799C22—44no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—44no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—42no—
812C22—44no—
813C22—42no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22C22×#12111yescharacteristic
830C22C2×#53411yescharacteristic
831C22#344911yescharacteristic
832C22C2×#53812yes—
833C22C2×#54612yes—
834C22C2×#54712yes—
835C22C2×#55111yescharacteristic
836C22#347512yes—
837C22#348912yes—
838C22#349312yes—
839C22#349512yes—
840C22#349612yes—
841C22#349611yescharacteristic
842C22#349611yescharacteristic
843C22#350511yescharacteristic
844C22#350511yescharacteristic
845C22#352012yes—
846C22C2×H(3,𝔽4)11yescharacteristic
847C22#353811yescharacteristic
848C22#354011yescharacteristic
849C22#354012yes—
850C22#354112yes—
851C22#354112yes—
852C4—24no—
853C4—44no—
854C4—42no—
855C4—42no—
856C4—44no—
857C4—42no—
858C4—84no—
859C4—84no—
860C4—84no—
861C4—84no—
862C4—82no—
863C4#268418yescomplemented
864C2—44no—
865C2—48no—
866C2—44no—
867C2#3500011yescharacteristic
868C2#3615312yes—
869C2#3737411yescharacteristic
870C2#3784412yes—
871C2#3934912yes—
872C2#3990812yes—
873C2#4547911yescharacteristic
874C2#4566711yescharacteristic
875C2C2×#268411yescharacteristic
876C2#5919811yescharacteristic
877C2#5920211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×#2547C2semidirect
4. #16470C2semidirect
5. #16391C2semidirect
6. #15824C2semidirect
7. #15494C2semidirect
8. #15132C2semidirect
9. #15129C2semidirect
10. #15125C2semidirect
11. #14680C2semidirect
12. #14473C2semidirect
13. #13994C2semidirect
14. #13872C2semidirect
15. #13872C2semidirect
17. C22×C4⋊Q8C22semidirect
22. C23×C4⋊C4C22semidirect
27. C2×#397C22semidirect
31. C2×#391C22semidirect
32. C2×#389C22semidirect
46. C2×#380C22semidirect
47. C2×#380C22semidirect
50. C2×C4×C4⋊C4C22semidirect
53. #1446C22semidirect
54. #1443C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
64. #1440C22semidirect
68. C4⋊#95C22semidirect
69. C4⋊#95C22semidirect
70. C4⋊#95C22semidirect
71. C4⋊#95C22semidirect
72. #1434C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
863. C4#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#26842
C2×#25472
C2×C4×#1202
#164702
#163912
#158242
#154942
#151322
#151292
#151252
#146802
#144732
#139942
#138722