Finite Group Databasebeta

← #455283

Subgroups — #455283

Order 512.

1258 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#475C211yesmaximal, characteristic
2C2×#2072C212yesmaximal
3C2×#1865C211yesmaximal, characteristic
4#15143C211yesmaximal, characteristic
5#13931C211yesmaximal, characteristic
6#11384C211yesmaximal, characteristic
7#11323C212yesmaximal
8#11257C212yesmaximal
9#11255C211yesmaximal, characteristic
10#11227C211yesmaximal, characteristic
11#11190C212yesmaximal
12C22×C4⋊Q8C2211yescharacteristic
13C22×C4×Q8C2211yescharacteristic
14C2×#475—28no—
15C2×#475—24no—
16C22×#106C2212yes—
17C22×#106C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2212yes—
22C2×#395—21no—
23C2×#395—21no—
24C2×#391C2212yes—
25C2×#389C2211yescharacteristic
26C2×#384C2212yes—
27#2072—28no—
28#1865—24no—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2211yescharacteristic
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2212yes—
35C2×#336C2212yes—
36C2×#336C2211yescharacteristic
37#1445—22no—
38#1444—22no—
39C4⋊#95C2212yes—
40C4⋊#95C2212yes—
41C4⋊#95C2211yescharacteristic
42#1434—21no—
43#1434—21no—
44C4×#95C2211yescharacteristic
45C23×Q8—21no—
46C23×Q8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C23×C8C2312yes—
49C23×C8C2311yescharacteristic
50C2×C4⋊Q8—24no—
51C2×C4⋊Q8—22no—
52C2×C4⋊Q8—22no—
53C2×C4⋊Q8—42no—
54C2×C4×Q8—22no—
55C2×C4×Q8—24no—
56C2×C4×Q8—42no—
57C2×C4×Q8D414yes—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4C2311yescharacteristic
64C22×C4⋊C4C2312yes—
65C22×C4⋊C4C2312yes—
66C22×C4⋊C4C2311yescharacteristic
67C22×C4⋊C4C2311yescharacteristic
68C22×C42—21no—
69C22×C42C2312yes—
70C22×C42C2311yescharacteristic
71#475—232no—
72C2×#106—24no—
73C2×#106—24no—
74C2×#106—24no—
75C2×#106—22no—
76C2×#106—42no—
77C2×C4⋊C8—24no—
78C2×C4⋊C8—22no—
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—22no—
82C2×#103—22no—
83C2×#103—22no—
84C2×#103—24no—
85C2×#103—22no—
86C2×#103D418yes—
87#395—44no—
88#395—44no—
89#391—24no—
90#391—42no—
91#389—22no—
92#389—22no—
93#384—24no—
94#384—42no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—21no—
102C2×#95—22no—
103C2×#95—21no—
104C2×#95D411yescharacteristic
105C2×#95D412yes—
106C2×#95D411yescharacteristic
107#340—24no—
108#340—24no—
109#340—22no—
110#340—24no—
111#340—42no—
112#336—24no—
113#336—24no—
114#336—22no—
115C22×Q8—21no—
116C22×Q8—22no—
117C22×Q8—21no—
118C22×Q8—21no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—21no—
122C22×Q8—21no—
123C22×Q8—44no—
124C22×Q8—42no—
125C22×Q8—42no—
126C22×Q8—42no—
127C22×Q8—82no—
128C22×Q8C2×D414yes—
129C22×Q8C2×D412yes—
130C23×C4—21no—
131C23×C4—22no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—22no—
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D412yes—
138C23×C4C2×D412yes—
139C23×C4C2×D411yescharacteristic
140C23×C4C2411yescharacteristic
141C22×C8—21no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—21no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—21no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—21no—
155C22×C8—21no—
156C22×C8C2×D414yes—
157C22×C8#4112yes—
158C4⋊Q8—28no—
159C4⋊Q8—48no—
160C4⋊Q8—44no—
161C4×Q8—28no—
162C4×Q8—44no—
163C4×Q8—48no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—44no—
192C2×C4⋊C4—44no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—82no—
199C2×C4⋊C4—82no—
200C2×C4⋊C4C2×D412yes—
201C2×C4⋊C4C2×D414yes—
202C2×C4⋊C4#4112yes—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—24no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—44no—
213C2×C42C2×D412yes—
214C2×C42#4112yes—
215#106—216no—
216#106—44no—
217C4⋊C8—28no—
218#103—28no—
219#103—216no—
220#103—44no—
221#95—22no—
222#95—24no—
223#95—44no—
224#95—44no—
225#95—44no—
226#95—42no—
227#95—44no—
228#95—42no—
229#95—44no—
230#95—82no—
231#95—81no—
232#95SD1614yes—
233C24C22×D411yescharacteristic
234C2×Q8—22no—
235C2×Q8—24no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—24no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—24no—
244C2×Q8—48no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—88no—
253C2×Q8—88no—
254C2×Q8—84no—
255C2×Q8—84no—
256C2×Q8#12014yes—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4#12112yes—
312C22×C4#12112yes—
313C22×C4C2×SD1614yes—
314C22×C4C2×SD1612yes—
315C22×C4AGL(1,ℤ/8)12yes—
316C22×C4#13714yes—
317C22×C4C22×D411yescharacteristic
318C22×C4C22×D412yes—
319C22×C4C2×#4111yescharacteristic
320C22×C4C2×#4111yescharacteristic
321C22×C4C2×#4111yescharacteristic
322C22×C4H(5,𝔽2)12yes—
323C22×C42−1+412yes—
324C22×C42−1+411yescharacteristic
325C22×C42−1+411yescharacteristic
326C22×C42−1+412yes—
327C2×C8—24no—
328C2×C8—22no—
329C2×C8—24no—
330C2×C8—24no—
331C2×C8—24no—
332C2×C8—42no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—42no—
343C2×C8—42no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—48no—
351C4⋊C4—48no—
352C4⋊C4—42no—
353C4⋊C4—41no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—88no—
365C4⋊C4—88no—
366C4⋊C4—84no—
367C42—22no—
368C42—22no—
369C42—24no—
370C42—48no—
371C42—42no—
372C42—42no—
373C42—42no—
374C42—42no—
375C23C2×#12111yescharacteristic
376C23#53612yes—
377C23D4212yes—
378C23#54711yescharacteristic
379C23#54811yescharacteristic
380C23C22×SD1611yescharacteristic
381C23C2×AGL(1,ℤ/8)11yescharacteristic
382C23C2×#13712yes—
383C23#57711yescharacteristic
384C23#57712yes—
385C23#57811yescharacteristic
386Q8—24no—
387Q8—24no—
388Q8—42no—
389Q8—42no—
390Q8—44no—
391Q8—44no—
392Q8—816no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—81no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—81no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4#46014yes—
453C2×C4C2×#12011yescharacteristic
454C2×C4#52511yescharacteristic
455C2×C4#53411yescharacteristic
456C2×C4#53611yescharacteristic
457C2×C4#53611yescharacteristic
458C2×C4#53611yescharacteristic
459C2×C4#53612yes—
460C2×C4#53612yes—
461C2×C4#53912yes—
462C2×C4#54112yes—
463C2×C4#54212yes—
464C2×C4#54612yes—
465C2×C4#54712yes—
466C2×C4#54712yes—
467C2×C4#55211yescharacteristic
468C2×C4#55611yescharacteristic
469C2×C4#56312yes—
470C2×C4#56312yes—
471C8—42no—
472C8—44no—
473C8—81no—
474C22#241011yescharacteristic
475C22#241511yescharacteristic
476C22#262111yescharacteristic
477C22#267412yes—
478C22#268012yes—
479C22C2×#46011yescharacteristic
480C22#303911yescharacteristic
481C22#304311yescharacteristic
482C22#304611yescharacteristic
483C22#322912yes—
484C22#323912yes—
485C22#324212yes—
486C22#324412yes—
487C22#326512yes—
488C22#327012yes—
489C22#327812yes—
490C22D4×SD1612yes—
491C22#333511yescharacteristic
492C22#334412yes—
493C22#335311yescharacteristic
494C22#335911yescharacteristic
495C22#336912yes—
496C22#337311yescharacteristic
497C4—24no—
498C4—42no—
499C4—44no—
500C4—44no—
501C4—44no—
502C4—84no—
503C4—82no—
504C4—82no—
505C4—161no—
506C4—162no—
507C4#240611yescharacteristic
508C4#261411yescharacteristic
509C4#263811yescharacteristic
510C4#268912yes—
511C4#269812yes—
512C4#281711yescharacteristic
513C2#1626211yescharacteristic
514C2#2435611yescharacteristic
515C2#2437411yescharacteristic
516C2#2467811yescharacteristic
517C2#2469811yescharacteristic
518C2#2986611yescharacteristic
519C2#2987311yescharacteristic
520C2#3080812yes—
521C2#3082412yes—
522C2#3108912yes—
523C2#3110312yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ 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
C22×#4752
C2×#20722
C2×#18652
#151432
#139312
#113842
#113232
#112572
#112552
#112272
#111902