Finite Group Databasebeta

← #480763

Subgroups — #480763

Order 512.

919 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34952C211yesmaximal, characteristic
2#17366C211yesmaximal, characteristic
3#17366C211yesmaximal, characteristic
4#11580C212yesmaximal, complemented
5#11579C212yesmaximal, complemented
6#11577C214yesmaximal, complemented
7#11518C214yesmaximal, complemented
8C2×C4×#41C2211yescharacteristic
9C22×C4×Q8C411yescharacteristic
10#2920—21no—
11#2920—21no—
12#2582—21no—
13#2581—21no—
14#2580—21no—
15#2579C412yes—
16#2579C2212yes—
17#2538—21no—
18#2487C411yescharacteristic
19#2487C2211yescharacteristic
20#2409C411yescharacteristic
21#2409C2211yescharacteristic
22#2396—21no—
23#2396—21no—
24C4×C22⋊Q8—21no—
25C4×C22⋊Q8—21no—
26#2297C412yes—
27#2296C2212yes—
28#2285C411yescharacteristic
29#1465—21no—
30#1465—21no—
31#1465C2212yes—
32#1465C2212yes—
33#1464—21no—
34#1464—21no—
35#1464C2212yes—
36#1464C2212yes—
37#1461—21no—
38#1461—21no—
39#1460C2212yes—
40#1460C2212yes—
41#1326C2218yes—
42#1326C2218yes—
43C22×#41C2×C411yescharacteristic
44C23×Q8C2×C411yescharacteristic
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8—21no—
47C4×#41—41no—
48C4×#41—41no—
49C4×#41—41no—
50C4×#41—41no—
51C2×C4×Q8—21no—
52C2×C4×Q8—21no—
53C2×C4×Q8—21no—
54C2×C4×Q8—21no—
55C2×C4×Q8—41no—
56C2×C4×Q8—41no—
57C2×C4×Q8—41no—
58C2×C4×Q8—41no—
59C2×C4×Q8D411yescharacteristic
60C2×C4×Q8D411yescharacteristic
61C2×C4×D4C2×C411yescharacteristic
62C2×C4×D4C2×C411yescharacteristic
63C2×C4×D4D411yescharacteristic
64C2×C4×D4D411yescharacteristic
65C2×C4×D4C2311yescharacteristic
66C2×C4×D4C2311yescharacteristic
67C2×#117C2×C412yes—
68C2×#117D411yescharacteristic
69C2×#117D411yescharacteristic
70C2×#117C2311yescharacteristic
71C22×C4⋊C4C2×C412yes—
72C22×C4⋊C4C2×C411yescharacteristic
73C22×C42C2×C411yescharacteristic
74C22×C42C2×C412yes—
75C22×C42D411yescharacteristic
76C22×C42D411yescharacteristic
77#432—22no—
78#432—22no—
79#432—41no—
80#432—41no—
81#431—22no—
82#431—22no—
83#431—41no—
84#431—41no—
85#423—41no—
86#423—41no—
87#407—22no—
88#407—22no—
89C4×M16—41no—
90C4×M16—41no—
91#400—21no—
92#400—21no—
93#399—21no—
94#399—21no—
95#398—22no—
96#398—22no—
97#396—22no—
98#396—22no—
99#395—21no—
100#395—21no—
101#393—21no—
102#393—21no—
103#391—22no—
104#391—21no—
105#391—21no—
106#390—22no—
107#389—22no—
108#389—22no—
109#389—21no—
110#389—21no—
111#387—22no—
112#387—22no—
113#386C2×C412yes—
114#386C2×C412yes—
115#386C2×C412yes—
116#386C2×C412yes—
117#385—22no—
118#385—22no—
119#385C2×C412yes—
120#385C2×C412yes—
121#385C2312yes—
122#385C2312yes—
123#384—21no—
124#382—21no—
125#380—21no—
126#380—21no—
127#380C2×C412yes—
128#380C2×C411yescharacteristic
129#380C2×C411yescharacteristic
130C4×C4⋊C4—21no—
131C4×C4⋊C4—21no—
132C4×C4⋊C4—22no—
133C4×C4⋊C4—22no—
134C4×C22⋊C4—22no—
135C4×C22⋊C4—22no—
136#324—22no—
137#324—22no—
138#324—22no—
139#324—22no—
140#323—22no—
141#323—22no—
142#323C2314yes—
143#323C2314yes—
144C2×#41—24no—
145C2×#41—41no—
146C2×#41—41no—
147C2×#41—42no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—41no—
151C22×Q8—41no—
152C22×Q8—44no—
153C22×Q8C22⋊C411yescharacteristic
154C22×D4C22⋊C411yescharacteristic
155C22×D4C22×C411yescharacteristic
156C22×D4C22×C411yescharacteristic
157C23×C4C22⋊C411yescharacteristic
158C23×C4C22⋊C411yescharacteristic
159C23×C4C22⋊C411yescharacteristic
160C23×C4C22⋊C411yescharacteristic
161C23×C4C22×C411yescharacteristic
162C23×C4C22×C411yescharacteristic
163C23×C4C22×C411yescharacteristic
164C23×C4C22×C412yes—
165C23×C4C22×C412yes—
166C23×C4C2×D411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C2×M16—42no—
169C2×M16—42no—
170C22⋊Q8—44no—
171C22⋊Q8—44no—
172C4×Q8—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×Q8—42no—
177C4×Q8—42no—
178C4×Q8—42no—
179C4×Q8—42no—
180C4×Q8—42no—
181C4×Q8—42no—
182C4×Q8—41no—
183C4×Q8—41no—
184C4×Q8—41no—
185C4×Q8—41no—
186C4×D4—41no—
187C4×D4—41no—
188C4×D4—41no—
189C4×D4—41no—
190C4×D4—41no—
191C4×D4—41no—
192C4×D4—41no—
193C4×D4—41no—
194C4×D4—41no—
195C4×D4—41no—
196C4×D4—41no—
197C4×D4—41no—
198#117—41no—
199#117—41no—
200#117—41no—
201#117—41no—
202#117—41no—
203#117—41no—
204#117—44no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—42no—
220C2×C4⋊C4—42no—
221C2×C4⋊C4C22⋊C411yescharacteristic
222C2×C4⋊C4C22⋊C411yescharacteristic
223C2×C4⋊C4C2×D411yescharacteristic
224C2×C4⋊C4C2×D411yescharacteristic
225C2×C4⋊C4C2×D411yescharacteristic
226C2×C4⋊C4C2×D411yescharacteristic
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4C22⋊C411yescharacteristic
232C2×C22⋊C4C22⋊C411yescharacteristic
233C2×C22⋊C4C22×C412yes—
234C2×C22⋊C4C22×C412yes—
235C2×C22⋊C4C22×C411yescharacteristic
236C2×C22⋊C4C2×D411yescharacteristic
237C2×C22⋊C4C2×D411yescharacteristic
238C2×C22⋊C4C2411yescharacteristic
239C2×C42—21no—
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—22no—
252C2×C42—22no—
253C2×C42—22no—
254C2×C42—42no—
255C2×C42—42no—
256C2×C42C22⋊C411yescharacteristic
257C2×C42C22⋊C411yescharacteristic
258C2×C42C22⋊C411yescharacteristic
259C2×C42C22⋊C411yescharacteristic
260C2×C42C22⋊C411yescharacteristic
261C2×C42C22⋊C411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C2×C42C2×D411yescharacteristic
264C2×C42C2×D411yescharacteristic
265C2×C42C2×D411yescharacteristic
266C4⋊C8—42no—
267C4⋊C8—42no—
268C4⋊C8—42no—
269C4⋊C8—42no—
270C22⋊C8—24no—
271C22⋊C8—24no—
272C22⋊C8—42no—
273C22⋊C8—42no—
274#97—42no—
275#97—42no—
276C4×C8—42no—
277C4×C8—42no—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—22no—
282#95—22no—
283#95—22no—
284#95—21no—
285#95—21no—
286#95—22no—
287#95—22no—
288#95—22no—
289C24C2×C22⋊C411yescharacteristic
290C24C2×C22⋊C411yescharacteristic
291C24C23×C411yescharacteristic
292#41—48no—
293#41—48no—
294C2×Q8—24no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—42no—
298C2×Q8—42no—
299C2×Q8—44no—
300C2×Q8—44no—
301C2×Q8—48no—
302C2×Q8—44no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8#10114yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—42no—
344C22×C4—44no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—81no—
350C22×C4—81no—
351C22×C4—81no—
352C22×C4—82no—
353C22×C4C2×C22⋊C411yescharacteristic
354C22×C4C2×C22⋊C411yescharacteristic
355C22×C4C2×C22⋊C411yescharacteristic
356C22×C4C2×C22⋊C411yescharacteristic
357C22×C4C2×C22⋊C411yescharacteristic
358C22×C4C2×C22⋊C411yescharacteristic
359C22×C4C2×C22⋊C411yescharacteristic
360C22×C4C2×C22⋊C411yescharacteristic
361C22×C4C2×C22⋊C411yescharacteristic
362C22×C4C2×C22⋊C411yescharacteristic
363C22×C4C22×D411yescharacteristic
364C22×C4C22×D411yescharacteristic
365M16—84no—
366M16—84no—
367C2×C8—44no—
368C2×C8—44no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—44no—
376C4⋊C4—42no—
377C4⋊C4—44no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—44no—
381C4⋊C4—44no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—82no—
387C4⋊C4—82no—
388C4⋊C4—82no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—44no—
398C22⋊C4—44no—
399C22⋊C4—82no—
400C22⋊C4—82no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—44no—
420C42—44no—
421C42—42no—
422C42—42no—
423C42#9911yescharacteristic
424C42#9911yescharacteristic
425C42#9911yescharacteristic
426C42#9911yescharacteristic
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23C22×C22⋊C411yescharacteristic
442C23#56812yes—
443Q8—44no—
444Q8—44no—
445Q8—48no—
446Q8—44no—
447D4—44no—
448D4—44no—
449D4—44no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—44no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—81no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—84no—
505C2×C4C2×#9911yescharacteristic
506C2×C4C2×#9911yescharacteristic
507C2×C4C2×#9911yescharacteristic
508C2×C4C2×#9911yescharacteristic
509C2×C4C2×#9911yescharacteristic
510C2×C4C2×#9911yescharacteristic
511C2×C4C2×#10112yes—
512C2×C4C2×#10112yes—
513C2×C4C2×#10112yes—
514C8—84no—
515C8—84no—
516C22—21no—
517C22—21no—
518C22—22no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—81no—
532C22—81no—
533C22#287911yescharacteristic
534C22C22×#9911yescharacteristic
535C22C22×#10111yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—41no—
545C4—44no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—82no—
552C4—82no—
553C4—82no—
554C4#212012yes—
555C2—21no—
556C2—21no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2#1739711yescharacteristic
561C2C2×#212011yescharacteristic
562C2#3334711yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC22×#41C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11580C2semidirect
5. #11579C2semidirect
6. #11577C2semidirect
7. #11518C2semidirect

Maximal subgroups

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

subgroupindex
#349522
#173662
#115802
#115792
#115772
#115182