Finite Group Databasebeta

← #474725

Subgroups — #474725

Order 512.

936 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15218C211yesmaximal, characteristic
2#15151C211yesmaximal, characteristic
3#11385C212yesmaximal
4#11316C212yesmaximal
5#11293C212yesmaximal
6#11227C212yesmaximal
7#11207C212yesmaximal
8#10880C212yesmaximal
9#10834C211yesmaximal, characteristic
10C22×#125C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×C4×C8C2211yescharacteristic
13C2×#398—22no—
14C2×#389C2212yes—
15C2×#389C2212yes—
16C2×#384C2211yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×#340C2212yes—
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#336C2212yes—
27C2×#336C2212yes—
28#1445—22no—
29#1444—22no—
30#1441—22no—
31C4⋊#95C2211yescharacteristic
32C4⋊#95C2212yes—
33C4⋊#95C2211yescharacteristic
34C4⋊#95C2212yes—
35C23×C8C2312yes—
36C23×C8C2312yes—
37C2×#125—24no—
38C2×#125—42no—
39C2×#125—41no—
40C2×#125—41no—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4D412yes—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C42C2311yescharacteristic
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C2×C4⋊C8—22no—
54C2×C4⋊C8—41no—
55C2×C4⋊C8—41no—
56C2×C4×C8—22no—
57C2×C4×C8—41no—
58C2×C4×C8—41no—
59#398—48no—
60#389—24no—
61#389—24no—
62#389—24no—
63#389—42no—
64#384—41no—
65#384—41no—
66C4×C4⋊C4—41no—
67C4×C4⋊C4—41no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—22no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95D412yes—
77#340—24no—
78#340—42no—
79#340—42no—
80#340—42no—
81#340—42no—
82#340—42no—
83#340—42no—
84#340Q818yes—
85#336—42no—
86#336—42no—
87C23×C4—22no—
88C23×C4—22no—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4C2×D412yes—
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D412yes—
94C23×C4C2×D411yescharacteristic
95C23×C4C2411yescharacteristic
96C22×C8—22no—
97C22×C8—22no—
98C22×C8—22no—
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8C2×Q814yes—
110#125—44no—
111#125—48no—
112#125—44no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—24no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—42no—
137C2×C4⋊C4—44no—
138C2×C4⋊C4—44no—
139C2×C4⋊C4—44no—
140C2×C4⋊C4—44no—
141C2×C4⋊C4—44no—
142C2×C4⋊C4—44no—
143C2×C4⋊C4—44no—
144C2×C4⋊C4—44no—
145C2×C4⋊C4—44no—
146C2×C4⋊C4—44no—
147C2×C4⋊C4—44no—
148C2×C4⋊C4—82no—
149C2×C4⋊C4C2×Q814yes—
150C2×C4⋊C4C2×Q814yes—
151C2×C4⋊C4#4114yes—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—22no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—22no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42#4112yes—
165C2×C42#4112yes—
166C4⋊C8—44no—
167C4×C8—44no—
168#95—42no—
169#95—44no—
170#95—44no—
171#95—44no—
172#95—44no—
173#95—44no—
174#95—44no—
175#95—82no—
176#95—82no—
177C24C22×D411yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—24no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4#12412yes—
227C22×C4#12412yes—
228C22×C4#13514yes—
229C22×C4AGL(1,ℤ/8)14yes—
230C22×C4C22×Q812yes—
231C22×C4C2×#4111yescharacteristic
232C22×C4C2×#4112yes—
233C22×C4C2×#4111yescharacteristic
234C22×C4H(5,𝔽2)11yescharacteristic
235C22×C4H(5,𝔽2)11yescharacteristic
236C22×C4H(5,𝔽2)11yescharacteristic
237C22×C4H(5,𝔽2)12yes—
238C22×C42−1+411yescharacteristic
239C22×C42−1+412yes—
240C2×C8—24no—
241C2×C8—24no—
242C2×C8—24no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—24no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—48no—
261C4⋊C4—416no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—88no—
273C4⋊C4—88no—
274C4⋊C4—88no—
275C42—22no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—42no—
280C42—42no—
281C42—41no—
282C42—41no—
283C42—41no—
284C42—41no—
285C23C2×#12411yescharacteristic
286C23#53411yescharacteristic
287C23#53711yescharacteristic
288C23#54612yes—
289C23D4×Q812yes—
290C23C2×#13512yes—
291C23C2×AGL(1,ℤ/8)12yes—
292C23#57712yes—
293C23#57812yes—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4#49014yes—
346C2×C4#53312yes—
347C2×C4#53811yescharacteristic
348C2×C4#53812yes—
349C2×C4#53811yescharacteristic
350C2×C4#53911yescharacteristic
351C2×C4#53911yescharacteristic
352C2×C4#54112yes—
353C2×C4#54212yes—
354C2×C4#54412yes—
355C2×C4#54412yes—
356C2×C4#55111yescharacteristic
357C2×C4#55412yes—
358C2×C4#55412yes—
359C2×C4#55612yes—
360C2×C4Q8211yescharacteristic
361C2×C4#56011yescharacteristic
362C2×C4#56212yes—
363C2×C4#56311yescharacteristic
364C8—44no—
365C8—82no—
366C22#249212yes—
367C22#263911yescharacteristic
368C22#269711yescharacteristic
369C22#270412yes—
370C22#273411yescharacteristic
371C22#313111yescharacteristic
372C22C2×#49011yescharacteristic
373C22#313712yes—
374C22#318812yes—
375C22#320112yes—
376C22#324712yes—
377C22#326011yescharacteristic
378C22#326111yescharacteristic
379C22#329612yes—
380C22#330012yes—
381C22#333012yes—
382C22#333212yes—
383C22#338112yes—
384C22#338312yes—
385C22#338412yes—
386C22#338612yes—
387C4—24no—
388C4—44no—
389C4—42no—
390C4—84no—
391C4—84no—
392C4—82no—
393C4—84no—
394C4—162no—
395C4#258611yescharacteristic
396C4#266612yes—
397C4#278812yes—
398C4#278911yescharacteristic
399C4#279211yescharacteristic
400C4#283011yescharacteristic
401C2#1700411yescharacteristic
402C2#2781812yes—
403C2#2782212yes—
404C2#3018911yescharacteristic
405C2#3019611yescharacteristic
406C2#3167412yes—
407C2#3187412yes—
408C2#3187612yes—
409C2#3268812yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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
#152182
#151512
#113852
#113162
#112932
#112272
#112072
#108802
#108342