Finite Group Databasebeta

← #482061

Subgroups — #482061

Order 512.

1151 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34937C211yesmaximal, characteristic
2#20637C211yesmaximal, characteristic, complemented
3#17349C211yesmaximal, characteristic, complemented
4#11884C214yesmaximal, complemented
5#11883C212yesmaximal, complemented
6#11882C212yesmaximal, complemented
7#11697C214yesmaximal, complemented
8C2×#532—21no—
9C2×#532C411yescharacteristic
10C2×C4×#41C2211yescharacteristic
11C2×#431—21no—
12C2×#423—21no—
13C2×#413—21no—
14#2548C2211yescharacteristic
15#2547C411yescharacteristic
16#2546C2211yescharacteristic
17#2545—21no—
18#2544—21no—
19#2543C412yes—
20#2543C2212yes—
21#2541C411yescharacteristic
22#2416—21no—
23#2416—21no—
24#2392C412yes—
25#2392C2212yes—
26C4×#121—21no—
27C4×#121—21no—
28#2297—21no—
29C2×C4×C4⋊C4C411yescharacteristic
30#1801—21no—
31#1801C2212yes—
32#1800—21no—
33#1800C2212yes—
34#1742C2212yes—
35#1461C2212yes—
36#1460—21no—
37#1459—21no—
38#1459C2212yes—
39#1458—21no—
40#1458C2212yes—
41#1346C2218yes—
42#1345C2218yes—
43C22×#41—21no—
44C22×#41D411yescharacteristic
45C22×M16—22no—
46#532—41no—
47#532—41no—
48#532—41no—
49#532—41no—
50#532—44no—
51#532—44no—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8C2×C411yescharacteristic
54C2×#127—21no—
55C2×#127C2×C411yescharacteristic
56C2×#124—21no—
57C2×#124—21no—
58C2×#124—21no—
59C2×#121—22no—
60C2×#121—22no—
61C2×#121—21no—
62C2×#121—21no—
63C2×#121—21no—
64C2×#121C2×C412yes—
65C4×#41—41no—
66C4×#41—41no—
67C4×#41—41no—
68C4×#41—41no—
69C2×C4×Q8D411yescharacteristic
70C2×C4×Q8C2311yescharacteristic
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—21no—
74C2×C4×D4C2×C411yescharacteristic
75C2×C4×D4C2×C412yes—
76C2×C4×D4C2×C411yescharacteristic
77C2×C4×D4D411yescharacteristic
78C2×C4×D4D411yescharacteristic
79C2×C4×D4D411yescharacteristic
80C2×C4×D4C2311yescharacteristic
81C2×#117C2×C411yescharacteristic
82C2×#117D411yescharacteristic
83C2×#117C2311yescharacteristic
84C22×C4⋊C4—21no—
85C22×C42—21no—
86C22×C42C2×C411yescharacteristic
87C22×C42D411yescharacteristic
88C22×C42D411yescharacteristic
89#431—22no—
90#431—22no—
91#431—41no—
92#431—41no—
93#423—22no—
94#423—22no—
95#423—41no—
96#423—41no—
97C2×C4⋊C8—41no—
98C2×C4⋊C8—41no—
99C2×C4⋊C8—41no—
100#413—44no—
101C2×#101—22no—
102C2×#100—22no—
103C2×C22⋊C8—22no—
104C2×C4×C8—41no—
105#398C2×C412yes—
106#398C2312yes—
107#397C2×C412yes—
108#397C2×C412yes—
109#396—22no—
110#396—22no—
111#394—22no—
112#394—22no—
113#394C2×C412yes—
114#394C2312yes—
115#392C2×C412yes—
116#392C2×C412yes—
117#391—21no—
118#391—21no—
119#390—21no—
120#390—21no—
121#390—21no—
122#390—21no—
123#389—21no—
124#389—21no—
125#388—22no—
126#388—22no—
127#386—22no—
128#386—22no—
129#386—22no—
130#386—22no—
131#380—21no—
132#380—21no—
133C4×C4⋊C4—21no—
134C4×C4⋊C4—21no—
135C4×C4⋊C4C2×C412yes—
136C4×C4⋊C4C2×C411yescharacteristic
137C4×C4⋊C4C2×C411yescharacteristic
138C4×C22⋊C4—22no—
139C4×C22⋊C4—22no—
140C2×#95C2×C412yes—
141#343—22no—
142#343C2314yes—
143#324—22no—
144#324C2314yes—
145#323—22no—
146#323—22no—
147C2×#41—41no—
148C2×#41—41no—
149C2×#41—42no—
150C2×#41—42no—
151C2×#41—42no—
152C2×#41—44no—
153C2×#41—44no—
154C2×#41D814yes—
155C2×#41SD1614yes—
156C22×Q8—21no—
157C22×Q8C2×D411yescharacteristic
158C22×D4—22no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4C22⋊C411yescharacteristic
164C22×D4C22⋊C411yescharacteristic
165C22×D4C22×C412yes—
166C22×D4C2×D411yescharacteristic
167C23×C4—22no—
168C23×C4—22no—
169C23×C4C22⋊C411yescharacteristic
170C23×C4C22⋊C411yescharacteristic
171C23×C4C22⋊C411yescharacteristic
172C23×C4C22⋊C411yescharacteristic
173C23×C4C22⋊C411yescharacteristic
174C23×C4C22⋊C411yescharacteristic
175C23×C4C22×C411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C2×M16—24no—
179C2×M16—42no—
180C2×M16—44no—
181C2×M16—44no—
182C22×C8—42no—
183C22×C8—42no—
184C4⋊Q8—41no—
185C4⋊Q8—41no—
186C4⋊Q8—42no—
187C4⋊Q8—42no—
188#127—41no—
189#127—41no—
190#127—44no—
191#124—42no—
192#124—42no—
193#124—42no—
194#124—42no—
195#124—44no—
196#121—44no—
197#121—44no—
198#121—42no—
199#121—42no—
200#121—48no—
201#121—44no—
202#121—44no—
203#121—42no—
204#121—42no—
205C4×Q8—41no—
206C4×Q8—41no—
207C4×Q8—41no—
208C4×Q8—41no—
209C4×D4—41no—
210C4×D4—41no—
211C4×D4—41no—
212C4×D4—41no—
213C4×D4—41no—
214C4×D4—41no—
215C4×D4—41no—
216C4×D4—41no—
217C4×D4—41no—
218C4×D4—41no—
219C4×D4—41no—
220C4×D4—41no—
221C4×D4—42no—
222C4×D4—42no—
223C4×D4—48no—
224C4×D4—44no—
225C4×D4—44no—
226C4×D4—41no—
227C4×D4—41no—
228C4×D4—41no—
229C4×D4—41no—
230#117—41no—
231#117—41no—
232#117—41no—
233#117—41no—
234#117—41no—
235#117—41no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—44no—
243C2×C4⋊C4C22⋊C411yescharacteristic
244C2×C4⋊C4C22⋊C411yescharacteristic
245C2×C4⋊C4C22×C412yes—
246C2×C4⋊C4C22×C411yescharacteristic
247C2×C4⋊C4C2×D411yescharacteristic
248C2×C4⋊C4C2×D411yescharacteristic
249C2×C4⋊C4C2411yescharacteristic
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4C22⋊C411yescharacteristic
261C2×C22⋊C4C22⋊C411yescharacteristic
262C2×C22⋊C4C22×C411yescharacteristic
263C2×C22⋊C4C22×C411yescharacteristic
264C2×C22⋊C4C2×D411yescharacteristic
265C2×C22⋊C4C2×D411yescharacteristic
266C2×C42—21no—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—22no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—44no—
282C2×C42C22⋊C411yescharacteristic
283C2×C42C22⋊C411yescharacteristic
284C2×C42C22⋊C411yescharacteristic
285C2×C42C22⋊C411yescharacteristic
286C2×C42C22×C411yescharacteristic
287C2×C42C22×C411yescharacteristic
288C2×C42C2×D411yescharacteristic
289C2×C42C2×D411yescharacteristic
290C2×C42C2×D411yescharacteristic
291C2×C42C2×D411yescharacteristic
292C4⋊C8—42no—
293C4⋊C8—42no—
294C4⋊C8—42no—
295C4⋊C8—42no—
296C4⋊C8—42no—
297C4⋊C8—42no—
298#101—44no—
299#100—44no—
300C22⋊C8—24no—
301C22⋊C8—42no—
302C4×C8—42no—
303C4×C8—42no—
304#95—22no—
305#95—22no—
306#95—22no—
307#95—22no—
308#95—22no—
309#95C22×C412yes—
310#95C22×C412yes—
311C24—22no—
312C24C2×C22⋊C411yescharacteristic
313C24C2×C22⋊C411yescharacteristic
314C24C2×C22⋊C411yescharacteristic
315#41—44no—
316#41—44no—
317#41—44no—
318#41—44no—
319#41—88no—
320#41—88no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8—42no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×Q8C2×D812yes—
327C2×Q8C2×SD1612yes—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—44no—
338C2×D4—44no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—44no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—44no—
345C2×D4—44no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—42no—
349C2×D4—82no—
350C2×D4—82no—
351C2×D4—82no—
352C2×D4#10214yes—
353C2×D4#10214yes—
354C2×D4C2×D812yes—
355C2×D4C2×SD1612yes—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—44no—
388C22×C4—44no—
389C22×C4—81no—
390C22×C4—81no—
391C22×C4—82no—
392C22×C4—81no—
393C22×C4#10214yes—
394C22×C4#10214yes—
395C22×C4C2×C22⋊C411yescharacteristic
396C22×C4C2×C22⋊C411yescharacteristic
397C22×C4C2×C22⋊C411yescharacteristic
398C22×C4C2×C22⋊C411yescharacteristic
399C22×C4C2×C22⋊C411yescharacteristic
400C22×C4C2×C22⋊C411yescharacteristic
401C22×C4C2×C22⋊C411yescharacteristic
402C22×C4C2×C22⋊C411yescharacteristic
403C22×C4C2×C22⋊C411yescharacteristic
404C22×C4C2×D812yes—
405C22×C4C2×SD1612yes—
406C22×C4C23×C411yescharacteristic
407C22×C4C22×D411yescharacteristic
408C22×C4C22×D411yescharacteristic
409M16—44no—
410M16—44no—
411M16—84no—
412C2×C8—44no—
413C2×C8—44no—
414C2×C8—84no—
415C2×C8—84no—
416C4⋊C4—24no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C4⋊C4—44no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—44no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—44no—
438C22⋊C4—44no—
439C22⋊C4—44no—
440C22⋊C4—44no—
441C22⋊C4—44no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—44no—
447C22⋊C4—82no—
448C22⋊C4—82no—
449C42—21no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—21no—
454C42—21no—
455C42—21no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—44no—
468C42—42no—
469C42—42no—
470C42#9911yescharacteristic
471C42#9911yescharacteristic
472C42#9911yescharacteristic
473C42#9911yescharacteristic
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23C2×#10212yes—
494C23C2×#10212yes—
495C23C2×#10212yes—
496C23C22×C22⋊C411yescharacteristic
497Q8—42no—
498Q8—42no—
499Q8—84no—
500D4—44no—
501D4—44no—
502D4—42no—
503D4—42no—
504D4—82no—
505D4—84no—
506D4—88no—
507D4—88no—
508D4—84no—
509D4—88no—
510D4—82no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—88no—
561C2×C4—84no—
562C2×C4—84no—
563C2×C4C2×#9911yescharacteristic
564C2×C4C2×#9911yescharacteristic
565C2×C4C2×#9911yescharacteristic
566C2×C4C2×#9911yescharacteristic
567C2×C4C2×#9911yescharacteristic
568C2×C4C2×#9911yescharacteristic
569C2×C4C2×#10212yes—
570C2×C4C2×#10212yes—
571C2×C4C2×#10212yes—
572C2×C4#42112yes—
573C2×C4C22×D811yescharacteristic
574C2×C4C22×SD1611yescharacteristic
575C8—84no—
576C8—84no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—81no—
593C22—81no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22C22×#9911yescharacteristic
602C22C22×#10211yescharacteristic
603C22C2×#42111yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—22no—
610C4—22no—
611C4—44no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—82no—
619C4—82no—
620C4#151912yes—
621C4#151912yes—
622C4#213212yes—
623C2—21no—
624C2—21no—
625C2—42no—
626C2—42no—
627C2—42no—
628C2—162no—
629C2C2×#151911yescharacteristic
630C2#3334711yescharacteristic
631C2C2×#213211yescharacteristic
subgroupG/H
centerC2×C4C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
socleC22C22×#99
prime radical#34937C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20637C2semidirect
3. #17349C2semidirect
4. #11884C2semidirect
5. #11883C2semidirect
6. #11882C2semidirect
7. #11697C2semidirect

Maximal subgroups

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

subgroupindex
#349372
#206372
#173492
#118842
#118832
#118822
#116972