Finite Group Databasebeta

← #482660

Subgroups — #482660

Order 512.

969 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35249C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic, complemented
3#17365C211yesmaximal, characteristic, complemented
4#11908C212yesmaximal, complemented
5#11882C212yesmaximal, complemented
6#11833C214yesmaximal, complemented
7#11762C214yesmaximal, complemented
8C2×#532C411yescharacteristic
9C22×C4×Q8C2211yescharacteristic
10#2920—21no—
11C2×#423—21no—
12C22×#101—21no—
13#2854—21no—
14#2854—21no—
15#2632C412yes—
16#2632C2212yes—
17#2580—21no—
18#2580—21no—
19#2567C411yescharacteristic
20#2567C2211yescharacteristic
21#2548C411yescharacteristic
22#2548C2211yescharacteristic
23#2501—21no—
24#2436—21no—
25#2406C412yes—
26#2406C2212yes—
27#2326—21no—
28#2326—21no—
29#2283C411yescharacteristic
30#1801—21no—
31#1801—21no—
32#1801C2212yes—
33#1801C2212yes—
34C2×#343C2212yes—
35#1467—21no—
36#1467C2212yes—
37#1463—21no—
38#1463C2212yes—
39#1461—21no—
40#1461C2212yes—
41#1354C2218yes—
42#1345C2218yes—
43C22×#41C2×C412yes—
44C23×Q8D411yescharacteristic
45C22×M16—22no—
46#532—41no—
47#532—41no—
48#532—41no—
49#532—41no—
50C2×C4⋊Q8C2×C411yescharacteristic
51C2×#127C2×C411yescharacteristic
52C2×#124—21no—
53C2×#124—21no—
54C2×#124C2×C412yes—
55C2×#123—22no—
56C2×#123—22no—
57C2×#121—21no—
58C2×#121—21no—
59C2×C4×Q8—41no—
60C2×C4×Q8—41no—
61C2×C4×Q8—41no—
62C2×C4×Q8—41no—
63C2×C4×Q8C2×C411yescharacteristic
64C2×C4×Q8C2×C411yescharacteristic
65C2×C4×Q8D411yescharacteristic
66C2×C4×Q8D411yescharacteristic
67C2×C4×Q8D411yescharacteristic
68C2×C4×Q8D411yescharacteristic
69C2×C4×Q8C2311yescharacteristic
70C2×C4×Q8C2311yescharacteristic
71C2×C4×D4—21no—
72C2×C4×D4—21no—
73C22×C4⋊C4C2×C411yescharacteristic
74C22×C4⋊C4D411yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C42C2×C411yescharacteristic
77C22×C42D411yescharacteristic
78C22×C42D411yescharacteristic
79#432—22no—
80#432—41no—
81#431—22no—
82#431—41no—
83#423—22no—
84#423—22no—
85#423—41no—
86#423—41no—
87#423—41no—
88C2×C4⋊C8—41no—
89C2×C4⋊C8—41no—
90C2×#101—22no—
91C2×#101—22no—
92C2×#101—44no—
93#407—22no—
94C4×M16—41no—
95#399—22no—
96#399—22no—
97#395C2×C412yes—
98#395C2×C412yes—
99#395C2×C412yes—
100#395C2312yes—
101#394C2×C412yes—
102#394C2×C412yes—
103#394C2×C412yes—
104#394C2312yes—
105#393—22no—
106#393—22no—
107#391—21no—
108#391—21no—
109#390—21no—
110#390—21no—
111#390—21no—
112#390—21no—
113#390—21no—
114#390—21no—
115#389—21no—
116#389—21no—
117#389—21no—
118#389—21no—
119#388—22no—
120#388—22no—
121#388—22no—
122#388—22no—
123#386—22no—
124#386—22no—
125#385—22no—
126#385—22no—
127#385—22no—
128#385—22no—
129#384—21no—
130#384—21no—
131#383C2×C412yes—
132#382—21no—
133#381C2×C412yes—
134#380—21no—
135C4×C4⋊C4C2×C411yescharacteristic
136C4×C4⋊C4C2×C411yescharacteristic
137C4×C22⋊C4—21no—
138#376—21no—
139#343—22no—
140#343C2314yes—
141#324—22no—
142#324—22no—
143#324—22no—
144#324C2314yes—
145C2×#41—42no—
146C2×#41—42no—
147C2×#41—84no—
148C22×Q8—22no—
149C22×Q8—22no—
150C22×Q8—41no—
151C22×Q8—41no—
152C22×Q8—42no—
153C22×Q8C22⋊C411yescharacteristic
154C22×Q8C22⋊C411yescharacteristic
155C22×Q8C22×C412yes—
156C22×Q8C2×D411yescharacteristic
157C22×Q8C2×D411yescharacteristic
158C22×D4—22no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4C22×C412yes—
162C23×C4—22no—
163C23×C4C22⋊C411yescharacteristic
164C23×C4C22⋊C411yescharacteristic
165C23×C4C22⋊C411yescharacteristic
166C23×C4C22⋊C411yescharacteristic
167C23×C4C22×C411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C2×M16—24no—
171C2×M16—42no—
172C2×M16—42no—
173C2×M16—44no—
174C2×M16—44no—
175C22×C8—42no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178#127—41no—
179#127—41no—
180#124—42no—
181#124—42no—
182#124—44no—
183#124—42no—
184#124—42no—
185#123—84no—
186#123—84no—
187#121—42no—
188#121—42no—
189#121—41no—
190#121—41no—
191#121—41no—
192#121—41no—
193C4×Q8—41no—
194C4×Q8—41no—
195C4×Q8—41no—
196C4×Q8—41no—
197C4×Q8—41no—
198C4×Q8—41no—
199C4×Q8—41no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×Q8—41no—
204C4×Q8—41no—
205C4×Q8—41no—
206C4×Q8—41no—
207C4×Q8—41no—
208C4×Q8—41no—
209C4×D4—42no—
210C4×D4—42no—
211C4×D4—42no—
212C4×D4—42no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4C22⋊C411yescharacteristic
228C2×C4⋊C4C22⋊C411yescharacteristic
229C2×C4⋊C4C22⋊C411yescharacteristic
230C2×C4⋊C4C22⋊C411yescharacteristic
231C2×C4⋊C4C22×C411yescharacteristic
232C2×C4⋊C4C22×C411yescharacteristic
233C2×C4⋊C4C22×C411yescharacteristic
234C2×C4⋊C4C2×D411yescharacteristic
235C2×C4⋊C4C2×D411yescharacteristic
236C2×C4⋊C4C2×D411yescharacteristic
237C2×C4⋊C4C2×D411yescharacteristic
238C2×C4⋊C4C2411yescharacteristic
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42C22⋊C411yescharacteristic
265C2×C42C22⋊C411yescharacteristic
266C2×C42C22⋊C411yescharacteristic
267C2×C42C22⋊C411yescharacteristic
268C2×C42C22⋊C411yescharacteristic
269C2×C42C22⋊C411yescharacteristic
270C2×C42C22×C411yescharacteristic
271C2×C42C22×C411yescharacteristic
272C2×C42C2×D411yescharacteristic
273C2×C42C2×D411yescharacteristic
274C2×C42C2×D411yescharacteristic
275C2×C42C2×D411yescharacteristic
276C4⋊C8—42no—
277C4⋊C8—42no—
278C4⋊C8—42no—
279C4⋊C8—42no—
280C4⋊C8—42no—
281C4⋊C8—42no—
282#101—44no—
283#101—44no—
284C22⋊C8—24no—
285C22⋊C8—42no—
286#97—42no—
287C4×C8—42no—
288#95—22no—
289#95—22no—
290#95—22no—
291#95—22no—
292#95—22no—
293#95—22no—
294#95—22no—
295#95C22×C412yes—
296#95C22×C412yes—
297C24—22no—
298C24C2×C22⋊C411yescharacteristic
299#41—88no—
300#41—88no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—44no—
314C2×Q8—44no—
315C2×Q8—44no—
316C2×Q8—44no—
317C2×Q8—42no—
318C2×Q8—82no—
319C2×Q8AGL(1,ℤ/8)12yes—
320C2×Q8#13712yes—
321C2×D4—42no—
322C2×D4—42no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—42no—
326C2×D4—44no—
327C2×D4—44no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—42no—
333C2×D4—82no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—42no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—44no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—82no—
362C22×C4—82no—
363C22×C4#9911yescharacteristic
364C22×C4#9911yescharacteristic
365C22×C4#9911yescharacteristic
366C22×C4#9911yescharacteristic
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×C22⋊C411yescharacteristic
375C22×C4C2×C22⋊C411yescharacteristic
376C22×C4C2×C22⋊C411yescharacteristic
377C22×C4C2×C22⋊C411yescharacteristic
378C22×C4C23×C411yescharacteristic
379C22×C4C22×D411yescharacteristic
380C22×C4C22×D411yescharacteristic
381M16—44no—
382M16—44no—
383M16—84no—
384M16—84no—
385C2×C8—44no—
386C2×C8—44no—
387C2×C8—84no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—82no—
406C4⋊C4—82no—
407C4⋊C4—82no—
408C4⋊C4—82no—
409C22⋊C4—44no—
410C22⋊C4—44no—
411C22⋊C4—44no—
412C22⋊C4—42no—
413C22⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—82no—
419C22⋊C4—82no—
420C22⋊C4—82no—
421C22⋊C4—82no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—21no—
433C42—21no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42—21no—
440C42—21no—
441C42—21no—
442C42—21no—
443C42—21no—
444C42—21no—
445C42—21no—
446C42—42no—
447C42—42no—
448C23—22no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23C2×#9911yescharacteristic
460C23C2×#9911yescharacteristic
461C23C22×C22⋊C411yescharacteristic
462Q8—42no—
463Q8—42no—
464Q8—44no—
465Q8—44no—
466Q8—42no—
467Q8—42no—
468Q8—84no—
469D4—82no—
470D4—84no—
471D4—84no—
472D4—84no—
473D4—84no—
474D4—82no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—88no—
531C2×C4C2×#9911yescharacteristic
532C2×C4C2×#9911yescharacteristic
533C2×C4C2×#9911yescharacteristic
534C2×C4C2×#9911yescharacteristic
535C2×C4#41712yes—
536C2×C4#41712yes—
537C2×C4#42112yes—
538C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
539C2×C4C2×#13711yescharacteristic
540C8—84no—
541C8—84no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—42no—
550C22—42no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22#212212yes—
559C22C22×#9911yescharacteristic
560C22C2×#41711yescharacteristic
561C22C2×#42111yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—82no—
579C4—82no—
580C4—82no—
581C4#213312yes—
582C2—21no—
583C2—21no—
584C2—22no—
585C2—41no—
586C2—162no—
587C2#1759211yescharacteristic
588C2C2×#212211yescharacteristic
589C2C2×#213311yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC2×#532C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1801C2semidirect
3. #17365C2semidirect
4. #11908C2semidirect
5. #11882C2semidirect
6. #11833C2semidirect
7. #11762C2semidirect

Maximal subgroups

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

subgroupindex
#352492
C2×#18012
#173652
#119082
#118822
#118332
#117622