Finite Group Databasebeta

← #416999

Subgroups — #416999

Order 512.

1060 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2647C211yesmaximal, characteristic
2C2×#1992C211yesmaximal, characteristic
3C2×#1991C211yesmaximal, characteristic
4#14283C211yesmaximal, characteristic
5#11293C212yesmaximal
6#11293C212yesmaximal
7#11292C212yesmaximal
8#11292C212yesmaximal
9#10843C211yesmaximal, characteristic
10#10841C211yesmaximal, characteristic
11#10694C211yesmaximal, characteristic
12C22×#125C2211yescharacteristic
13C22×#97C2211yescharacteristic
14C22×C4×C8C2211yescharacteristic
15#2647—24no—
16#2647—24no—
17C2×#400—22no—
18C2×#398—22no—
19C2×#389C2212yes—
20C2×#389C2212yes—
21C2×#384C2211yescharacteristic
22C2×#384C2211yescharacteristic
23C2×#382C2211yescharacteristic
24C2×#376C2211yescharacteristic
25#1992—24no—
26#1991—24no—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39#1441—22no—
40#1441—22no—
41C4⋊#95C2212yes—
42C4⋊#95C2212yes—
43C23×C8C2311yescharacteristic
44C23×C8C2311yescharacteristic
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C2×#125—22no—
48C2×#125—22no—
49C2×#125—22no—
50C2×#125—22no—
51C2×#125—22no—
52C2×#125Q814yes—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2312yes—
61C22×C4⋊C4C2312yes—
62C22×C42C2311yescharacteristic
63C22×C42C2311yescharacteristic
64C22×C42C2311yescharacteristic
65C2×#97—22no—
66C2×#97—22no—
67C2×#97—22no—
68C2×C4×C8—22no—
69C2×C4×C8—22no—
70C2×C4×C8—22no—
71#400—216no—
72#398—216no—
73#389—24no—
74#389—24no—
75#389—24no—
76#389—24no—
77#384—22no—
78#384—22no—
79#384—22no—
80#384D414yes—
81#382—22no—
82#382D414yes—
83#376—22no—
84#376—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95D412yes—
93C2×#95D412yes—
94#340—24no—
95#340—24no—
96#340—24no—
97#340—24no—
98#340—24no—
99#340—24no—
100#340—24no—
101#340—24no—
102#336—22no—
103#336—22no—
104#336—22no—
105#336—22no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—22no—
110C23×C4C2×D411yescharacteristic
111C23×C4C2×D412yes—
112C23×C4C2×D411yescharacteristic
113C23×C4C2×D412yes—
114C23×C4C2411yescharacteristic
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—21no—
118C22×C8—21no—
119C22×C8—21no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—21no—
126C22×C8—21no—
127C22×C8—21no—
128C22×C8—21no—
129C22×C8—21no—
130C22×C8—21no—
131C22×C8—21no—
132C22×C8—21no—
133C22×C8—21no—
134C22×C8—21no—
135C22×C8—21no—
136C22×C8—21no—
137C22×C8—21no—
138C22×C8—21no—
139C22×C8#4112yes—
140C22×C8#4112yes—
141C22×C8#4112yes—
142C22×C8#4112yes—
143#125—28no—
144#125—28no—
145#125—44no—
146#125—44no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—28no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—28no—
170C2×C4⋊C4—28no—
171C2×C4⋊C4—28no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4—82no—
176C2×C4⋊C4—82no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4—82no—
179C2×C4⋊C4—82no—
180C2×C4⋊C4—82no—
181C2×C4⋊C4—82no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4C2×D414yes—
184C2×C4⋊C4C2×D414yes—
185C2×C4⋊C4C2×Q814yes—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42C2×D412yes—
199C2×C42C2×D412yes—
200C2×C42C2×Q812yes—
201C2×C42#4112yes—
202C2×C42#4112yes—
203C2×C42#4112yes—
204#97—44no—
205C4×C8—44no—
206#95—28no—
207#95—28no—
208#95—28no—
209#95—24no—
210#95—24no—
211#95—82no—
212#95—82no—
213#95—82no—
214#95—82no—
215C24C22×D411yescharacteristic
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—21no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4#12014yes—
266C22×C4C22⋊Q814yes—
267C22×C4#12414yes—
268C22×C4C22×D411yescharacteristic
269C22×C4C22×D411yescharacteristic
270C22×C4C22×Q811yescharacteristic
271C22×C4C2×#4111yescharacteristic
272C22×C4C2×#4111yescharacteristic
273C22×C4C2×#4111yescharacteristic
274C22×C4C2×#4111yescharacteristic
275C22×C4C2×#4111yescharacteristic
276C22×C4C2×#4111yescharacteristic
277C22×C4C2×#4111yescharacteristic
278C22×C42−1+411yescharacteristic
279C22×C42−1+411yescharacteristic
280C22×C42−1+411yescharacteristic
281C22×C42−1+411yescharacteristic
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—416no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—88no—
328C4⋊C4—88no—
329C4⋊C4—88no—
330C4⋊C4—88no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42C22⋊Q814yes—
340C42C22⋊Q814yes—
341C42#12414yes—
342C42#12414yes—
343C23C2×#12011yescharacteristic
344C23C2×C22⋊Q811yescharacteristic
345C23C2×#12411yescharacteristic
346C23#53211yescharacteristic
347C23#53211yescharacteristic
348C23#53611yescharacteristic
349C23#53611yescharacteristic
350C23#57612yes—
351C23#57712yes—
352C23#57712yes—
353C23#57812yes—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4#39318yes—
406C2×C4C2×C22⋊Q811yescharacteristic
407C2×C4C2×C22⋊Q811yescharacteristic
408C2×C4C2×#12411yescharacteristic
409C2×C4C2×#12411yescharacteristic
410C2×C4#52911yescharacteristic
411C2×C4#52911yescharacteristic
412C2×C4#52911yescharacteristic
413C2×C4#52911yescharacteristic
414C2×C4#54111yescharacteristic
415C2×C4#54111yescharacteristic
416C2×C4#54111yescharacteristic
417C2×C4#54111yescharacteristic
418C2×C4#54711yescharacteristic
419C2×C4#54711yescharacteristic
420C2×C4#54711yescharacteristic
421C2×C4#54711yescharacteristic
422C2×C4#54811yescharacteristic
423C2×C4#54811yescharacteristic
424C2×C4#54811yescharacteristic
425C2×C4#54811yescharacteristic
426C2×C4#55211yescharacteristic
427C2×C4#55211yescharacteristic
428C2×C4#55211yescharacteristic
429C2×C4#55211yescharacteristic
430C2×C4#55711yescharacteristic
431C2×C4#55711yescharacteristic
432C2×C4#55711yescharacteristic
433C2×C4#55711yescharacteristic
434C8—42no—
435C8—42no—
436C8—42no—
437C8—42no—
438C22C2×#39311yescharacteristic
439C22#243211yescharacteristic
440C22#243211yescharacteristic
441C22#256511yescharacteristic
442C22#256511yescharacteristic
443C22#264211yescharacteristic
444C22#286111yescharacteristic
445C22#301212yes—
446C22#301312yes—
447C22#308312yes—
448C22#308412yes—
449C22#313612yes—
450C22#313712yes—
451C22#317411yescharacteristic
452C22#317411yescharacteristic
453C22#317611yescharacteristic
454C22#317711yescharacteristic
455C22#317812yes—
456C22#317912yes—
457C22#324112yes—
458C22#324212yes—
459C22#324312yes—
460C22#324412yes—
461C4—28no—
462C4—81no—
463C4—84no—
464C4—81no—
465C4—82no—
466C4—84no—
467C4—84no—
468C4—162no—
469C4#245311yescharacteristic
470C4#245311yescharacteristic
471C4#245311yescharacteristic
472C4#245311yescharacteristic
473C4#248911yescharacteristic
474C4#248911yescharacteristic
475C4#248911yescharacteristic
476C4#248911yescharacteristic
477C2#1523811yescharacteristic
478C2#2345812yes—
479C2#2568211yescharacteristic
480C2#2568311yescharacteristic
481C2#2568412yes—
482C2#2918511yescharacteristic
483C2#2918611yescharacteristic
484C2#2918812yes—
485C2#3023212yes—
486C2#3328411yescharacteristic
487C2#3328511yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#26472
C2×#19922
C2×#19912
#142832
#112932
#112922
#108432
#108412
#106942