Finite Group Databasebeta

← #402392

Subgroups — #402392

Order 512.

1078 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1865C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3#15153C211yesmaximal, characteristic
4#13817C211yesmaximal, characteristic
5#11357C211yesmaximal, characteristic
6#11255C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11190C212yesmaximal
9#11190C212yesmaximal
10#10908C212yesmaximal
11#10807C212yesmaximal
12C22×C4×Q8C2211yescharacteristic
13C22×#106C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2211yescharacteristic
16C22×#103C2212yes—
17C22×#103C2211yescharacteristic
18C2×#400—21no—
19C2×#400—21no—
20C2×#391C2212yes—
21C2×#389C2211yescharacteristic
22C2×#384C2211yescharacteristic
23C2×C4×C4⋊C4C2212yes—
24#1865—24no—
25#1803—24no—
26C2×#340C2211yescharacteristic
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#336C2211yescharacteristic
33C2×#336C2212yes—
34C2×#336C2212yes—
35#1445—22no—
36#1436—22no—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40#1434—21no—
41C4×#95—21no—
42C4×#95C2211yescharacteristic
43C23×Q8C2311yescharacteristic
44C23×C8C2312yes—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C2×C4×Q8—22no—
48C2×C4×Q8—24no—
49C2×C4×Q8—42no—
50C2×C4×Q8D414yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C42—21no—
61C22×C42—22no—
62C22×C42C2312yes—
63C22×C42C2311yescharacteristic
64C2×#106—22no—
65C2×#106—24no—
66C2×C4⋊C8—22no—
67C2×C4⋊C8—42no—
68C2×#103—22no—
69C2×#103—22no—
70C2×#103—22no—
71C2×#103—24no—
72C2×#103—22no—
73C2×#103—24no—
74C2×#103—24no—
75C2×#103—42no—
76#400—44no—
77#400—44no—
78#391—24no—
79#391—24no—
80#389—22no—
81#389—22no—
82#384—22no—
83#384—22no—
84C4×C4⋊C4—24no—
85C4×C4⋊C4—42no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—21no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95D411yescharacteristic
97C2×#95D412yes—
98C2×#95D411yescharacteristic
99#340—24no—
100#340—22no—
101#340—24no—
102#340—24no—
103#340—24no—
104#340—42no—
105#336—24no—
106#336—22no—
107#336—42no—
108C22×Q8—21no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—21no—
112C22×Q8—21no—
113C22×Q8—22no—
114C22×Q8—21no—
115C22×Q8—21no—
116C22×Q8C2×D412yes—
117C22×Q8#4114yes—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—21no—
124C23×C4C2×D412yes—
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D412yes—
127C23×C4C2×D411yescharacteristic
128C23×C4C2411yescharacteristic
129C22×C8—21no—
130C22×C8—22no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—21no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—21no—
144C22×C8—21no—
145C22×C8#4112yes—
146C4×Q8—28no—
147C4×Q8—44no—
148C4×Q8—48no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4C2×D412yes—
182C2×C4⋊C4#4114yes—
183C2×C4⋊C4#4112yes—
184C2×C4⋊C4#4114yes—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—24no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—44no—
195C2×C42—44no—
196C2×C42—44no—
197C2×C42—82no—
198C2×C42C2×D412yes—
199C2×C42#4112yes—
200#106—44no—
201C4⋊C8—44no—
202#103—28no—
203#103—44no—
204#103—48no—
205#95—28no—
206#95—28no—
207#95—22no—
208#95—42no—
209#95—44no—
210#95—44no—
211#95—44no—
212#95—42no—
213#95—44no—
214#95—44no—
215#95—42no—
216#95—81no—
217#95SD1614yes—
218C24C22×D411yescharacteristic
219C2×Q8—24no—
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—24no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8#12414yes—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4#12112yes—
293C22×C4#12112yes—
294C22×C4C2×SD1614yes—
295C22×C4C2×SD1612yes—
296C22×C4AGL(1,ℤ/8)12yes—
297C22×C4C22×D411yescharacteristic
298C22×C4C2×#4112yes—
299C22×C4C2×#4111yescharacteristic
300C22×C4C2×#4111yescharacteristic
301C22×C4C2×#4112yes—
302C22×C4C2×#4112yes—
303C22×C4C2×#4111yescharacteristic
304C22×C4H(5,𝔽2)12yes—
305C22×C42−1+411yescharacteristic
306C22×C42−1+411yescharacteristic
307C2×C8—22no—
308C2×C8—24no—
309C2×C8—41no—
310C2×C8—42no—
311C2×C8—41no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—42no—
317C2×C8—41no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C4⋊C4—22no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—48no—
331C4⋊C4—41no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—41no—
341C4⋊C4—42no—
342C4⋊C4—84no—
343C4⋊C4—84no—
344C4⋊C4—84no—
345C4⋊C4#12314yes—
346C42—22no—
347C42—22no—
348C42—24no—
349C42—48no—
350C42—42no—
351C42—42no—
352C42—42no—
353C42—42no—
354C42—88no—
355C23C2×#12111yescharacteristic
356C23#52512yes—
357C23#54612yes—
358C23#54711yescharacteristic
359C23#54811yescharacteristic
360C23C22×SD1611yescharacteristic
361C23C2×AGL(1,ℤ/8)11yescharacteristic
362C23#57512yes—
363C23#57711yescharacteristic
364C23#57812yes—
365C23#57811yescharacteristic
366Q8—24no—
367Q8—24no—
368Q8—44no—
369Q8—42no—
370Q8—42no—
371Q8—44no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—82no—
426C2×C4—81no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4#46014yes—
432C2×C4C2×#12311yescharacteristic
433C2×C4#52511yescharacteristic
434C2×C4C2×#12411yescharacteristic
435C2×C4#52912yes—
436C2×C4#52912yes—
437C2×C4#52912yes—
438C2×C4#53211yescharacteristic
439C2×C4#53411yescharacteristic
440C2×C4#53611yescharacteristic
441C2×C4#53912yes—
442C2×C4#54212yes—
443C2×C4#55112yes—
444C2×C4#55212yes—
445C2×C4#55212yes—
446C2×C4#55211yescharacteristic
447C2×C4#55312yes—
448C2×C4#55312yes—
449C2×C4#55611yescharacteristic
450C8—42no—
451C8—82no—
452C8—81no—
453C22#241211yescharacteristic
454C22#241511yescharacteristic
455C22#246012yes—
456C22#246812yes—
457C22#285011yescharacteristic
458C22C2×#46011yescharacteristic
459C22#304011yescharacteristic
460C22#304411yescharacteristic
461C22#304611yescharacteristic
462C22#310312yes—
463C22#311512yes—
464C22#312012yes—
465C22#312712yes—
466C22#329812yes—
467C22#330812yes—
468C22#331512yes—
469C22#332312yes—
470C22#333511yescharacteristic
471C22#334912yes—
472C22#335311yescharacteristic
473C22#335911yescharacteristic
474C22#337311yescharacteristic
475C22#337712yes—
476C4—24no—
477C4—44no—
478C4—42no—
479C4—44no—
480C4—44no—
481C4—82no—
482C4—84no—
483C4—82no—
484C4—162no—
485C4—161no—
486C4#239511yescharacteristic
487C4#250311yescharacteristic
488C4#253012yes—
489C4#257712yes—
490C4#259111yescharacteristic
491C4#266311yescharacteristic
492C2#1484111yescharacteristic
493C2#2452811yescharacteristic
494C2#2454511yescharacteristic
495C2#2467811yescharacteristic
496C2#2469911yescharacteristic
497C2#2675612yes—
498C2#2677612yes—
499C2#2709812yes—
500C2#2711812yes—
501C2#3302511yescharacteristic
502C2#3304111yescharacteristic
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
C2×#18652
C2×#18032
#151532
#138172
#113572
#112552
#112272
#111902
#109082
#108072