Finite Group Databasebeta

← #401488

Subgroups — #401488

Order 512.

1122 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1948C212yesmaximal
2C2×#1948C211yesmaximal, characteristic
3C2×#1920C211yesmaximal, characteristic
4#15145C211yesmaximal, characteristic
5#13821C211yesmaximal, characteristic
6#11371C211yesmaximal, characteristic
7#11322C211yesmaximal, characteristic
8#11228C211yesmaximal, characteristic
9#11227C212yesmaximal
10#11207C212yesmaximal
11#10908C212yesmaximal
12C22×#106C2212yes—
13C22×#106C2211yescharacteristic
14C22×C4⋊C8C2212yes—
15C22×C4⋊C8C2211yescharacteristic
16C2×#398—22no—
17C2×#389C2211yescharacteristic
18C2×#389C2212yes—
19C2×#384C2211yescharacteristic
20C2×#384C2212yes—
21C2×C4×C4⋊C4—21no—
22C2×C4×C4⋊C4C2212yes—
23C2×C4×C4⋊C4C2211yescharacteristic
24#1948—28no—
25#1948—24no—
26#1920—24no—
27C2×#340C2211yescharacteristic
28C2×#340C2211yescharacteristic
29C2×#340C2211yescharacteristic
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#336C2211yescharacteristic
36C2×#336C2212yes—
37#1444—21no—
38#1444—21no—
39#1436—22no—
40C4⋊#95C2212yes—
41C4⋊#95C2211yescharacteristic
42#1434—21no—
43C4×#95C2211yescharacteristic
44C23×C8C2311yescharacteristic
45C23×C8C2311yescharacteristic
46C23×C8C2312yes—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2312yes—
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C42—21no—
60C22×C42—22no—
61C22×C42C2311yescharacteristic
62C22×C42C2312yes—
63C2×#106—22no—
64C2×#106—22no—
65C2×#106—24no—
66C2×#106—24no—
67C2×#106—24no—
68C2×#106D414yes—
69C2×C4⋊C8—24no—
70C2×C4⋊C8—24no—
71C2×C4⋊C8—24no—
72C2×C4⋊C8—22no—
73C2×C4⋊C8—24no—
74#398—48no—
75#389—24no—
76#389—22no—
77#389—22no—
78#389Q818yes—
79#384—24no—
80#384—22no—
81#384—22no—
82#384—42no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4—24no—
85C4×C4⋊C4—42no—
86C4×C4⋊C4—44no—
87C4×C4⋊C4D414yes—
88C2×#95—22no—
89C2×#95—21no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—21no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95D412yes—
97C2×#95D411yescharacteristic
98C2×#95D411yescharacteristic
99#340—24no—
100#340—24no—
101#340—22no—
102#340—22no—
103#340—22no—
104#340—24no—
105#340—24no—
106#340—42no—
107#336—22no—
108#336—24no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—22no—
113C23×C4—22no—
114C23×C4—21no—
115C23×C4C2×D411yescharacteristic
116C23×C4C2×D412yes—
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D412yes—
119C23×C4C2411yescharacteristic
120C22×C8—21no—
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—21no—
129C22×C8—22no—
130C22×C8—21no—
131C22×C8—22no—
132C22×C8—21no—
133C22×C8—22no—
134C22×C8—21no—
135C22×C8C2×D412yes—
136C22×C8#4114yes—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—28no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4—44no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—82no—
175C2×C4⋊C4—82no—
176C2×C4⋊C4—82no—
177C2×C4⋊C4C2×D412yes—
178C2×C4⋊C4C2×D412yes—
179C2×C4⋊C4C2×D412yes—
180C2×C4⋊C4C2×D412yes—
181C2×C4⋊C4C2×Q814yes—
182C2×C4⋊C4C2×Q814yes—
183C2×C4⋊C4#4112yes—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—22no—
190C2×C42—24no—
191C2×C42—42no—
192C2×C42—42no—
193C2×C42—44no—
194C2×C42—44no—
195C2×C42—82no—
196C2×C42C2×D412yes—
197C2×C42C2×Q814yes—
198C2×C42#4112yes—
199C2×C42#4114yes—
200#106—28no—
201#106—48no—
202C4⋊C8—28no—
203C4⋊C8—216no—
204#95—24no—
205#95—28no—
206#95—24no—
207#95—22no—
208#95—44no—
209#95—44no—
210#95—42no—
211#95—42no—
212#95—44no—
213#95—81no—
214#95SD1614yes—
215C24C22×D411yescharacteristic
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—24no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—41no—
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—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4#12112yes—
269C22×C4#12112yes—
270C22×C4C22⋊Q814yes—
271C22×C4C22⋊Q814yes—
272C22×C4C2×SD1612yes—
273C22×C4C2×SD1614yes—
274C22×C4AGL(1,ℤ/8)14yes—
275C22×C4#13712yes—
276C22×C4C22×D411yescharacteristic
277C22×C4C22×D411yescharacteristic
278C22×C4C22×Q812yes—
279C22×C4C2×#4111yescharacteristic
280C22×C4C2×#4112yes—
281C22×C4C2×#4112yes—
282C22×C4C2×#4111yescharacteristic
283C22×C4H(5,𝔽2)11yescharacteristic
284C22×C42−1+412yes—
285C22×C42−1+411yescharacteristic
286C2×C8—22no—
287C2×C8—24no—
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—42no—
292C2×C8—41no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—41no—
297C2×C8—42no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—42no—
302C2×C8—42no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—42no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—416no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—88no—
325C4⋊C4—84no—
326C4⋊C4—84no—
327C4⋊C4—84no—
328C4⋊C4—88no—
329C4⋊C4#12114yes—
330C4⋊C4C4⋊Q814yes—
331C42—22no—
332C42—24no—
333C42—22no—
334C42—24no—
335C42—24no—
336C42—24no—
337C42—24no—
338C42—48no—
339C42—88no—
340C23C2×#12111yescharacteristic
341C23C2×C22⋊Q812yes—
342C23D4211yescharacteristic
343C23#54712yes—
344C23#54811yescharacteristic
345C23C22×SD1611yescharacteristic
346C23C2×AGL(1,ℤ/8)12yes—
347C23C2×#13711yescharacteristic
348C23#57712yes—
349C23#57711yescharacteristic
350C23#57811yescharacteristic
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—81no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—81no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—81no—
409C2×C4#46114yes—
410C2×C4#47618yes—
411C2×C4C2×#12111yescharacteristic
412C2×C4#52511yescharacteristic
413C2×C4#52512yes—
414C2×C4#52912yes—
415C2×C4C2×C4⋊Q811yescharacteristic
416C2×C4#53211yescharacteristic
417C2×C4#53312yes—
418C2×C4#53611yescharacteristic
419C2×C4#53711yescharacteristic
420C2×C4#53912yes—
421C2×C4#54112yes—
422C2×C4#54711yescharacteristic
423C2×C4D4×Q812yes—
424C2×C4#55212yes—
425C2×C4#55311yescharacteristic
426C2×C4#55412yes—
427C2×C4#55712yes—
428C2×C4#55712yes—
429C8—42no—
430C8—44no—
431C8—81no—
432C22#241311yescharacteristic
433C22#241611yescharacteristic
434C22#244912yes—
435C22#245312yes—
436C22#285711yescharacteristic
437C22C2×#46111yescharacteristic
438C22#303811yescharacteristic
439C22#304311yescharacteristic
440C22#304611yescharacteristic
441C22C2×#47612yes—
442C22#307912yes—
443C22#308212yes—
444C22#308412yes—
445C22#326512yes—
446C22#327611yescharacteristic
447C22D4×SD1611yescharacteristic
448C22#333512yes—
449C22#334412yes—
450C22#334512yes—
451C22#335312yes—
452C22#335911yescharacteristic
453C22#336812yes—
454C22#337211yescharacteristic
455C4—24no—
456C4—28no—
457C4—42no—
458C4—44no—
459C4—44no—
460C4—44no—
461C4—82no—
462C4—84no—
463C4—161no—
464C4—162no—
465C4#239211yescharacteristic
466C4#246212yes—
467C4#254611yescharacteristic
468C4#258411yescharacteristic
469C4#258512yes—
470C4#266411yescharacteristic
471C2#1481811yescharacteristic
472C2#2458011yescharacteristic
473C2#2459211yescharacteristic
474C2#2473011yescharacteristic
475C2#2474211yescharacteristic
476C2#2633812yes—
477C2#2635312yes—
478C2#2651012yes—
479C2#2652212yes—
480C2#3319711yescharacteristic
481C2#3320411yescharacteristic
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×#19482
C2×#19202
#151452
#138212
#113712
#113222
#112282
#112272
#112072
#109082