Finite Group Databasebeta

← #790690

Subgroups — #790690

Order 512.

4278 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2C2×#2561C212yesmaximal, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4#16632C212yesmaximal, complemented
5#15399C214yesmaximal, complemented
6#15284C214yesmaximal, complemented
7#15147C211yesmaximal, characteristic, complemented
8#15144C211yesmaximal, characteristic, complemented
9#15125C211yesmaximal, characteristic, complemented
10#14765C212yesmaximal, complemented
11#14717C212yesmaximal, complemented
12#14001C212yesmaximal, complemented
13#13916C212yesmaximal, complemented
14#13902C212yesmaximal
15#13876C212yesmaximal, complemented
16C4×#397C211yesmaximal, characteristic, complemented
17#13820C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic, complemented
20C22×C22⋊Q8C2212yescomplemented
21C22×C22⋊Q8C2212yescomplemented
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C22⋊C4C2212yes—
25#2561—216no—
26#2542—28no—
27C2×#399C2214yescomplemented
28C2×#397C2211yescharacteristic
29C2×#397C2212yescomplemented
30C2×#393C2212yes—
31C2×#393C2212yescomplemented
32C2×#393C2212yescomplemented
33D4×C22⋊C4—28no—
34C2×#390C2211yescharacteristic
35C2×#390C2212yes—
36C2×#390C2211yescharacteristic
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#388C2214yes—
41C2×#388C2214yescomplemented
42C2×#388C2214yescomplemented
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#384C2212yescomplemented
46C2×#381C2214yescomplemented
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#379C2214yes—
50C2×#379C2212yes—
51C2×#379C2214yes—
52C2×C4×C4⋊C4C2211yescharacteristic, complemented
53C2×C4×C4⋊C4C2212yescomplemented
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yescomplemented
57#1446C2212yescomplemented
58#1445C2211yescharacteristic, complemented
59#1443C2212yescomplemented
60#1442C2212yescomplemented
61#1442C2211yescharacteristic, complemented
62#1442C2214yescomplemented
63#1440C2212yes—
64#1440C2214yescomplemented
65#1440C2214yescomplemented
66#1440C2214yescomplemented
67#1439C2212yes—
68#1439C2211yescharacteristic
69#1439C2214yes—
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1439C2212yescomplemented
73#1439C2214yescomplemented
74#1438C2214yes—
75#1438C2214yes—
76#1437C2214yescomplemented
77#1436C2214yescomplemented
78C4⋊#95C2211yescharacteristic, complemented
79C4⋊#95C2212yescomplemented
80C4⋊#95C2212yescomplemented
81C4⋊#95C2212yescomplemented
82C22⋊#95C2214yescomplemented
83C22⋊#95C2212yescomplemented
84C4×#95C2211yescharacteristic, complemented
85C4×#95C2212yescomplemented
86C26C2312yes—
87C23×Q8C2312yes—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—28no—
91C23×D4—24no—
92C23×D4—44no—
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C23×D4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—44no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—48no—
105C2×C22⋊Q8—44no—
106C2×C4×D4—24no—
107C2×C4×D4—28no—
108C2×C4×D4—44no—
109C2×C4×D4D418yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C22⋊C4—28no—
120C22×C22⋊C4—28no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C42C2311yescharacteristic
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2311yescharacteristic
146C22×C42C2314yes—
147#399—216no—
148#397—28no—
149#397D418yescomplemented
150#393—28no—
151#393—28no—
152#393—44no—
153#390—28no—
154#390—28no—
155#390—28no—
156#390—24no—
157#390—24no—
158#390—44no—
159#388—216no—
160#388—216no—
161#388—48no—
162#386—28no—
163#386—28no—
164#384—28no—
165#381—216no—
166#380—24no—
167#380—44no—
168#379—216no—
169#379—28no—
170#379—48no—
171C4×C4⋊C4—24no—
172C4×C4⋊C4—44no—
173C4×C22⋊C4—28no—
174C4×C22⋊C4—24no—
175C4×C22⋊C4—28no—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2311yescharacteristic
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2311yescharacteristic
187C2×#95C2311yescharacteristic
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C25—24no—
200C25—24no—
201C25—24no—
202C25—24no—
203C25—28no—
204C25—24no—
205C25—42no—
206C25—44no—
207C25—42no—
208C25—44no—
209C25—44no—
210C25C2412yes—
211C25C2412yes—
212C25C2411yescharacteristic
213C22×Q8—24no—
214C22×Q8—24no—
215C22×Q8—24no—
216C22×Q8—44no—
217C22×Q8—44no—
218C22×D4—232no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—28no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—432no—
231C22×D4—44no—
232C22×D4—432no—
233C22×D4—416no—
234C22×D4—416no—
235C22×D4C2×D414yes—
236C22×D4#4114yes—
237C22×D4#4118yes—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—28no—
246C23×C4—24no—
247C23×C4—42no—
248C23×C4—44no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4C2×D418yes—
252C23×C4#4114yes—
253C23×C4C2414yes—
254C23×C4C2414yes—
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C4⋊Q8—416no—
268C22⋊Q8—432no—
269C22⋊Q8—432no—
270C4×D4—416no—
271C4×D4—416no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4C2×D414yes—
294C2×C4⋊C4C2×D414yescomplemented
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—432no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—41no—
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⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4C2×D414yes—
350C2×C22⋊C4C2×D418yes—
351C2×C22⋊C4C2×D418yes—
352C2×C42—24no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—28no—
362C2×C42—44no—
363C2×C42—44no—
364C2×C42C2×D414yes—
365#95—22no—
366#95—22no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—22no—
377#95—42no—
378#95—44no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95C2×D414yescomplemented
387#95C2×D418yescomplemented
388C24—22no—
389C24—21no—
390C24—21no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—21no—
404C24—22no—
405C24—216no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—48no—
417C24—416no—
418C24—416no—
419C24—48no—
420C24—48no—
421C24—48no—
422C24—416no—
423C24—416no—
424C24—48no—
425C24—48no—
426C24—48no—
427C24—48no—
428C24—84no—
429C24—88no—
430C24—88no—
431C24—84no—
432C24—88no—
433C24—88no—
434C24—88no—
435C24—88no—
436C24—88no—
437C24—88no—
438C24C22×D414yes—
439C24C22×D412yes—
440C24C2×#4114yes—
441C24C2×#4118yes—
442C24C2×#4112yes—
443C242−1+412yes—
444C24C2511yescharacteristic
445C2×Q8—48no—
446C2×Q8—48no—
447C2×Q8—48no—
448C2×Q8—88no—
449C2×Q8—88no—
450C2×D4—216no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—416no—
458C2×D4—4128no—
459C2×D4—416no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—48no—
465C2×D4#124116yes—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—216no—
504C22×C4—216no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—416no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—88no—
545C22×C4—88no—
546C22×C4—84no—
547C22×C4—88no—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D414yes—
551C22×C4C22×D414yes—
552C22×C4C22×D414yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4114yes—
560C22×C4H(5,𝔽2)14yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)14yes—
563C4⋊C4—28no—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—416no—
567C4⋊C4—416no—
568C4⋊C4—48no—
569C4⋊C4—44no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C22⋊C4—216no—
573C22⋊C4—28no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—416no—
577C22⋊C4—416no—
578C22⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—416no—
581C22⋊C4—48no—
582C22⋊C4—416no—
583C22⋊C4—416no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—84no—
587C22⋊C4—88no—
588C22⋊C4—84no—
589C22⋊C4—88no—
590C22⋊C4—88no—
591C22⋊C4—88no—
592C42—28no—
593C42—48no—
594C42—44no—
595C42—48no—
596C42—88no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—24no—
602C23—28no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—28no—
607C23—28no—
608C23—24no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—28no—
616C23—28no—
617C23—22no—
618C23—24no—
619C23—28no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—28no—
624C23—28no—
625C23—24no—
626C23—432no—
627C23—432no—
628C23—41no—
629C23—41no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—41no—
634C23—44no—
635C23—44no—
636C23—41no—
637C23—42no—
638C23—44no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—44no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—44no—
653C23—44no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—44no—
658C23—42no—
659C23—42no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—816no—
667C23—816no—
668C23—832no—
669C23—816no—
670C23—832no—
671C23—832no—
672C23—832no—
673C23—816no—
674C23—816no—
675C23C2×#12418yes—
676C23#54714yes—
677C23C23×D411yescharacteristic
678C23C23×D411yescharacteristic
679C23C22×#4111yescharacteristic
680C23C22×#4111yescharacteristic
681C23C22×#4112yes—
682C23C2×H(5,𝔽2)12yes—
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)12yes—
685C23C2×2−1+411yescharacteristic
686C23#58511yescharacteristic
687C23#58512yes—
688Q8—816no—
689D4—232no—
690D4—432no—
691D4—416no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—416no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—816no—
770C2×C4—816no—
771C2×C4#52514yes—
772C2×C4C2×#12414yes—
773C2×C4#53414yes—
774C2×C4D4214yes—
775C2×C4#55118yes—
776C2×C4#55118yes—
777C22—24no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—48no—
786C22—44no—
787C22—48no—
788C22—44no—
789C22—42no—
790C22—48no—
791C22—44no—
792C22—48no—
793C22—44no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—48no—
802C22—48no—
803C22—44no—
804C22—864no—
805C22—82no—
806C22—82no—
807C22—84no—
808C22—84no—
809C22—82no—
810C22—82no—
811C22C2×#52511yescharacteristic
812C22C22×#12411yescharacteristic
813C22C2×#53411yescharacteristic
814C22C2×D4211yescharacteristic
815C22C2×#54711yescharacteristic
816C22D4×#4111yescharacteristic
817C22D4×#4112yes—
818C22C2×#55112yes—
819C22C2×#55112yes—
820C22#348411yescharacteristic
821C22#348911yescharacteristic
822C22#349412yes—
823C22#349812yes—
824C22#350011yescharacteristic
825C22#350611yescharacteristic
826C22#351312yes—
827C22#351412yes—
828C22#351412yes—
829C22#352011yescharacteristic
830C22#352012yes—
831C22#354312yes—
832C22#356112yes—
833C22#356212yes—
834C4—24no—
835C4—44no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—44no—
840C4—44no—
841C4—42no—
842C4—82no—
843C4—84no—
844C4—81no—
845C4—82no—
846C4—84no—
847C4#256118yescomplemented
848C2—48no—
849C2—44no—
850C2—84no—
851C2C2×#256111yescharacteristic
852C2#3573011yescharacteristic
853C2#3593911yescharacteristic
854C2#3610011yescharacteristic
855C2D4×#12411yescharacteristic
856C2#3933611yescharacteristic
857C2#4294311yescharacteristic
858C2#4490312yes—
859C2#4508112yes—
860C2#5927312yes—
861C2#5947612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2542C2semidirect
2. C2×#2561C2semidirect
4. #16632C2semidirect
5. #15399C2semidirect
6. #15284C2semidirect
7. #15147C2semidirect
8. #15144C2semidirect
9. #15125C2semidirect
10. #14765C2semidirect
11. #14717C2semidirect
12. #14001C2semidirect
13. #13916C2semidirect
15. #13876C2semidirect
16. C4×#397C2semidirect
17. #13820C2semidirect
19. C22×C4⋊Q8C22semidirect
20. C22×C22⋊Q8C22semidirect
21. C22×C22⋊Q8C22semidirect
27. C2×#399C22semidirect
29. C2×#397C22semidirect
31. C2×#393C22semidirect
32. C2×#393C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
45. C2×#384C22semidirect
46. C2×#381C22semidirect
52. C2×C4×C4⋊C4C22semidirect
53. C2×C4×C4⋊C4C22semidirect
56. C2×C4×C22⋊C4C22semidirect
57. #1446C22semidirect
58. #1445C22semidirect
59. #1443C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
64. #1440C22semidirect
65. #1440C22semidirect
66. #1440C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
76. #1437C22semidirect
77. #1436C22semidirect
78. C4⋊#95C22semidirect
79. C4⋊#95C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect
82. C22⋊#95C22semidirect
83. C22⋊#95C22semidirect
84. C4×#95C22semidirect
85. C4×#95C22semidirect
149. #397D4semidirect
294. C2×C4⋊C4C2×D4semidirect
386. #95C2×D4semidirect
387. #95C2×D4semidirect
847. C4#2561semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#25612
C2×D4×C22⋊C42
#166322
#153992
#152842
#151472
#151442
#151252
#147652
#147172
#140012
#139162
#139022
#138762
C4×#3972
#138202