Finite Group Databasebeta

← #482064

Subgroups — #482064

Order 512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35272C211yesmaximal, characteristic
2#20637C211yesmaximal, characteristic, complemented
3#17349C211yesmaximal, characteristic, complemented
4#11882C214yesmaximal, complemented
5#11880C214yesmaximal, complemented
6#11699C214yesmaximal, complemented
7C2×#535—21no—
8C22×#127C411yescharacteristic
9C2×C4×#41C2211yescharacteristic
10C2×#431—21no—
11C2×#423—21no—
12C2×#413—21no—
13#2856—21no—
14#2856—21no—
15#2619C412yes—
16#2619C2212yes—
17#2548—21no—
18#2548C2212yes—
19#2541—21no—
20#2541C412yes—
21#2408—21no—
22#2408—21no—
23#2408C412yes—
24#2408C2212yes—
25#2309—21no—
26#2285C411yescharacteristic
27#1801—21no—
28#1801C2212yescomplemented
29#1800—21no—
30#1800C2212yes—
31#1742C2212yescomplemented
32#1461C2212yescomplemented
33#1460—21no—
34#1459—21no—
35#1459C2212yes—
36#1458—21no—
37#1458C2212yescomplemented
38#1345C22116yescomplemented
39C22×#41D411yescharacteristic
40C23×D4—21no—
41C23×D4—21no—
42C23×D4C2×C412yes—
43C22×M16—22no—
44#535—44no—
45#535—44no—
46C2×#127—22no—
47C2×#127—21no—
48C2×#127—21no—
49C2×#127—41no—
50C2×#127—41no—
51C2×#127—41no—
52C2×#127—41no—
53C2×#127C2×C412yes—
54C2×#127C2×C412yes—
55C2×#124—22no—
56C2×#121—22no—
57C2×#121—22no—
58C2×#121—22no—
59C2×#121—22no—
60C2×#121—22no—
61C2×#121—22no—
62C2×#120—22no—
63C2×#120—22no—
64C4×#41—41no—
65C4×#41—41no—
66C4×#41—41no—
67C4×#41—41no—
68C2×C4×Q8D411yescharacteristic
69C2×C4×Q8C2311yescharacteristic
70C2×C4×D4C2×C411yescharacteristic
71C2×C4×D4C2×C411yescharacteristic
72C2×C4×D4D411yescharacteristic
73C2×C4×D4D411yescharacteristic
74C2×C4×D4D411yescharacteristic
75C2×C4×D4C2311yescharacteristic
76C2×#117—21no—
77C2×#117C2×C411yescharacteristic
78C2×#117D411yescharacteristic
79C2×#117C2311yescharacteristic
80C22×C42C2×C411yescharacteristic
81C22×C42D411yescharacteristic
82C22×C42D411yescharacteristic
83#431—22no—
84#431—22no—
85#431—41no—
86#431—41no—
87#423—22no—
88#423—22no—
89#423—41no—
90#423—41no—
91C2×C4⋊C8—41no—
92C2×C4⋊C8—41no—
93C2×C4⋊C8—41no—
94#413—44no—
95C2×#101—22no—
96C2×#100—22no—
97C2×C22⋊C8—22no—
98C2×C4×C8—41no—
99#394—22no—
100#394—22no—
101#394C2×C414yes—
102#394C2314yes—
103#392—22no—
104#392—22no—
105#392C2×C414yes—
106#392C2×C414yes—
107#390—22no—
108#390—22no—
109#390—22no—
110#390—22no—
111#390—22no—
112#390—22no—
113#390—22no—
114#390—22no—
115#384—21no—
116#382C2×C412yes—
117#380—21no—
118#380C2×C412yes—
119#379—22no—
120#379—22no—
121C4×C4⋊C4—21no—
122C4×C4⋊C4C2×C412yes—
123#343—22no—
124#343C2314yes—
125#324—22no—
126#324C2314yes—
127#323—22no—
128#323—22no—
129C25—22no—
130C2×#41—41no—
131C2×#41—41no—
132C2×#41—42no—
133C2×#41D814yes—
134C2×#41SD1614yes—
135C22×Q8C2×D411yescharacteristic
136C22×D4—24no—
137C22×D4—24no—
138C22×D4—22no—
139C22×D4—22no—
140C22×D4—22no—
141C22×D4—22no—
142C22×D4—22no—
143C22×D4—42no—
144C22×D4—42no—
145C22×D4—42no—
146C22×D4—42no—
147C22×D4—44no—
148C22×D4—42no—
149C22×D4—42no—
150C22×D4—44no—
151C22×D4—84no—
152C22×D4—84no—
153C22×D4C22⋊C411yescharacteristic
154C22×D4C22⋊C411yescharacteristic
155C22×D4C22×C414yes—
156C22×D4C2×D411yescharacteristic
157C23×C4C22⋊C411yescharacteristic
158C23×C4C22⋊C411yescharacteristic
159C23×C4C22⋊C411yescharacteristic
160C23×C4C22⋊C411yescharacteristic
161C23×C4C22⋊C411yescharacteristic
162C23×C4C22⋊C411yescharacteristic
163C23×C4C22×C411yescharacteristic
164C23×C4C2×D411yescharacteristic
165C23×C4C2×D411yescharacteristic
166C2×M16—24no—
167C2×M16—42no—
168C2×M16—44no—
169C2×M16—44no—
170C22×C8—42no—
171C22×C8—42no—
172#127—42no—
173#127—42no—
174#127—42no—
175#127—42no—
176#127—42no—
177#127—42no—
178#127—48no—
179#127—41no—
180#127—41no—
181#127—41no—
182#127—41no—
183#124—44no—
184#124—44no—
185#121—48no—
186#121—44no—
187#121—44no—
188#121—84no—
189#121—84no—
190#121—84no—
191#121—84no—
192#120—48no—
193#120—44no—
194#120—44no—
195C4×Q8—41no—
196C4×Q8—41no—
197C4×Q8—41no—
198C4×Q8—41no—
199C4×D4—41no—
200C4×D4—41no—
201C4×D4—41no—
202C4×D4—41no—
203C4×D4—41no—
204C4×D4—41no—
205C4×D4—41no—
206C4×D4—41no—
207C4×D4—41no—
208C4×D4—41no—
209C4×D4—41no—
210C4×D4—41no—
211#117—41no—
212#117—41no—
213#117—41no—
214#117—41no—
215#117—41no—
216#117—41no—
217#117—44no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4C22⋊C411yescharacteristic
222C2×C4⋊C4C22⋊C411yescharacteristic
223C2×C4⋊C4C22×C411yescharacteristic
224C2×C4⋊C4C2×D411yescharacteristic
225C2×C4⋊C4C2×D411yescharacteristic
226C2×C4⋊C4C2411yescharacteristic
227C2×C22⋊C4—22no—
228C2×C22⋊C4—24no—
229C2×C22⋊C4—24no—
230C2×C22⋊C4—24no—
231C2×C22⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—24no—
234C2×C22⋊C4C22⋊C411yescharacteristic
235C2×C22⋊C4C22⋊C411yescharacteristic
236C2×C22⋊C4C22×C411yescharacteristic
237C2×C22⋊C4C22×C411yescharacteristic
238C2×C22⋊C4C2×D411yescharacteristic
239C2×C22⋊C4C2×D411yescharacteristic
240C2×C42—21no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42—22no—
253C2×C42C22⋊C411yescharacteristic
254C2×C42C22⋊C411yescharacteristic
255C2×C42C22⋊C411yescharacteristic
256C2×C42C22⋊C411yescharacteristic
257C2×C42C22×C411yescharacteristic
258C2×C42C22×C411yescharacteristic
259C2×C42C2×D411yescharacteristic
260C2×C42C2×D411yescharacteristic
261C2×C42C2×D411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C4⋊C8—42no—
264C4⋊C8—42no—
265C4⋊C8—42no—
266C4⋊C8—42no—
267C4⋊C8—42no—
268C4⋊C8—42no—
269#101—44no—
270#100—44no—
271C22⋊C8—24no—
272C22⋊C8—42no—
273C4×C8—42no—
274C4×C8—42no—
275#95—22no—
276#95C22×C414yes—
277C24—24no—
278C24—44no—
279C24—44no—
280C24—44no—
281C24—84no—
282C24—84no—
283C24C2×C22⋊C411yescharacteristic
284C24C2×C22⋊C411yescharacteristic
285C24C2×C22⋊C411yescharacteristic
286#41—44no—
287#41—44no—
288#41—44no—
289#41—44no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8C2×D812yes—
293C2×Q8C2×SD1612yes—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—44no—
301C2×D4—44no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—44no—
305C2×D4—44no—
306C2×D4—44no—
307C2×D4—44no—
308C2×D4—48no—
309C2×D4—48no—
310C2×D4—42no—
311C2×D4—42no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—44no—
317C2×D4—44no—
318C2×D4—44no—
319C2×D4—88no—
320C2×D4—88no—
321C2×D4—84no—
322C2×D4—88no—
323C2×D4—88no—
324C2×D4—88no—
325C2×D4—88no—
326C2×D4—84no—
327C2×D4—84no—
328C2×D4—84no—
329C2×D4—84no—
330C2×D4—84no—
331C2×D4#10214yes—
332C2×D4#10214yes—
333C2×D4C2×D812yes—
334C2×D4C2×SD1612yes—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4#10214yes—
364C22×C4#10214yes—
365C22×C4C2×C22⋊C411yescharacteristic
366C22×C4C2×C22⋊C411yescharacteristic
367C22×C4C2×C22⋊C411yescharacteristic
368C22×C4C2×C22⋊C411yescharacteristic
369C22×C4C2×C22⋊C411yescharacteristic
370C22×C4C2×C22⋊C411yescharacteristic
371C22×C4C2×C22⋊C411yescharacteristic
372C22×C4C2×C22⋊C411yescharacteristic
373C22×C4C2×C22⋊C411yescharacteristic
374C22×C4C2×D812yes—
375C22×C4C2×SD1612yes—
376C22×C4C23×C411yescharacteristic
377C22×C4C22×D411yescharacteristic
378C22×C4C22×D411yescharacteristic
379M16—44no—
380M16—44no—
381M16—84no—
382C2×C8—44no—
383C2×C8—44no—
384C2×C8—84no—
385C2×C8—84no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C22⋊C4—44no—
404C22⋊C4—48no—
405C22⋊C4—84no—
406C22⋊C4—84no—
407C22⋊C4—84no—
408C22⋊C4—84no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—44no—
428C42#9911yescharacteristic
429C42#9911yescharacteristic
430C42#9911yescharacteristic
431C42#9911yescharacteristic
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—44no—
445C23—44no—
446C23—44no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—88no—
452C23—88no—
453C23—88no—
454C23—168no—
455C23—168no—
456C23C2×#10212yes—
457C23C2×#10212yes—
458C23C2×#10212yes—
459C23C22×C22⋊C411yescharacteristic
460Q8—42no—
461Q8—42no—
462D4—44no—
463D4—44no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468D4—88no—
469D4—88no—
470D4—88no—
471D4—84no—
472D4—84no—
473D4—84no—
474D4—84no—
475D4—168no—
476D4—168no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—81no—
520C2×C4C2×#9911yescharacteristic
521C2×C4C2×#9911yescharacteristic
522C2×C4C2×#9911yescharacteristic
523C2×C4C2×#9911yescharacteristic
524C2×C4C2×#9911yescharacteristic
525C2×C4C2×#9911yescharacteristic
526C2×C4C2×#10212yes—
527C2×C4C2×#10212yes—
528C2×C4C2×#10212yes—
529C2×C4#42112yes—
530C2×C4C22×D811yescharacteristic
531C2×C4C22×SD1611yescharacteristic
532C8—84no—
533C8—84no—
534C22—21no—
535C22—21no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—81no—
550C22—81no—
551C22—84no—
552C22—84no—
553C22—84no—
554C22—84no—
555C22—84no—
556C22—84no—
557C22—84no—
558C22—1616no—
559C22C22×#9911yescharacteristic
560C22C22×#10211yescharacteristic
561C22C2×#42111yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—84no—
575C4#151912yes—
576C4#151912yes—
577C4#212212yes—
578C4#213412yes—
579C2—21no—
580C2—21no—
581C2—42no—
582C2—42no—
583C2—42no—
584C2—164no—
585C2C2×#151911yescharacteristic
586C2C2×#212211yescharacteristic
587C2C2×#213411yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radical#35272C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ 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. #11882C2semidirect
5. #11880C2semidirect
6. #11699C2semidirect
28. #1801C22semidirect
31. #1742C22semidirect
32. #1461C22semidirect
37. #1458C22semidirect
38. #1345C22semidirect

Maximal subgroups

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

subgroupindex
#352722
#206372
#173492
#118822
#118802
#116992