Finite Group Databasebeta

← #449432

Subgroups — #449432

Order 512.

898 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15218C211yesmaximal, characteristic
2#13955C211yesmaximal, characteristic
3#11385C212yesmaximal
4#11268C212yesmaximal
5#11257C212yesmaximal
6#11220C212yesmaximal
7#10908C212yesmaximal
8#10881C212yesmaximal
9#10875C211yesmaximal, characteristic
10C22×#125C2211yescharacteristic
11C22×#106C2212yes—
12C22×#97C2211yescharacteristic
13C2×#389C2212yes—
14C2×#382C2211yescharacteristic
15C2×C4×C4⋊C4C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17C2×#340C2212yes—
18C2×#340C2212yes—
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#336C2212yes—
25C2×#336C2211yescharacteristic
26C2×#336C2212yes—
27#1444—22no—
28#1442—22no—
29#1441—22no—
30C4⋊#95C2212yes—
31C4⋊#95C2211yescharacteristic
32C4⋊#95C2212yes—
33C4⋊#95C2212yes—
34#1434—22no—
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⋊C4D412yes—
44C22×C4⋊C4C2312yes—
45C22×C4⋊C4C2312yes—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2312yes—
48C22×C42—21no—
49C22×C42C2311yescharacteristic
50C22×C42C2311yescharacteristic
51C22×C42C2311yescharacteristic
52C2×#106—24no—
53C2×#106—24no—
54C2×#106—42no—
55C2×#97—41no—
56C2×#97—42no—
57#389—24no—
58#389—42no—
59#382—41no—
60#382—41no—
61C4×C4⋊C4—24no—
62C4×C4⋊C4—41no—
63C4×C4⋊C4—41no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—22no—
67C2×#95—22no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—21no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95D412yes—
76#340—24no—
77#340—24no—
78#340—24no—
79#340—24no—
80#340—42no—
81#340—42no—
82#340—42no—
83#336—42no—
84#336—41no—
85#336Q818yes—
86C23×C4—22no—
87C23×C4—22no—
88C23×C4—22no—
89C23×C4—22no—
90C23×C4C2×D412yes—
91C23×C4C2×D412yes—
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C23×C4C2411yescharacteristic
95C22×C8—22no—
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×C8C2×Q814yes—
108C22×C8C2×Q814yes—
109#125—44no—
110#125—48no—
111#125—44no—
112C2×C4⋊C4—22no—
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—22no—
126C2×C4⋊C4—22no—
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—42no—
134C2×C4⋊C4—42no—
135C2×C4⋊C4—42no—
136C2×C4⋊C4—44no—
137C2×C4⋊C4—44no—
138C2×C4⋊C4—44no—
139C2×C4⋊C4—44no—
140C2×C4⋊C4—44no—
141C2×C4⋊C4—82no—
142C2×C4⋊C4#4114yes—
143C2×C4⋊C4#4114yes—
144C2×C4⋊C4#4114yes—
145C2×C42—22no—
146C2×C42—21no—
147C2×C42—21no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—22no—
156C2×C42—24no—
157C2×C42—82no—
158C2×C42C2×Q814yes—
159#106—48no—
160#97—44no—
161#95—24no—
162#95—42no—
163#95—44no—
164#95—44no—
165#95—44no—
166#95—44no—
167#95—42no—
168#95—42no—
169#95—82no—
170#95—82no—
171#95—82no—
172#95—82no—
173C24C22×D411yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—24no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—24no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—42no—
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×C4C4⋊Q812yes—
225C22×C4C4⋊Q812yes—
226C22×C4C22×Q812yes—
227C22×C4C2×#4112yes—
228C22×C4C2×#4112yes—
229C22×C4C2×#4112yes—
230C22×C4H(5,𝔽2)11yescharacteristic
231C22×C4H(5,𝔽2)12yes—
232C22×C4H(5,𝔽2)11yescharacteristic
233C22×C42−1+412yes—
234C2×C8—24no—
235C2×C8—24no—
236C2×C8—24no—
237C2×C8—24no—
238C2×C8—24no—
239C2×C8—24no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C4⋊C4—24no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—48no—
255C4⋊C4—416no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—88no—
267C42—24no—
268C42—24no—
269C42—42no—
270C42—42no—
271C42—41no—
272C42—41no—
273C42—41no—
274C42—41no—
275C42—84no—
276C23#52511yescharacteristic
277C23C2×C4⋊Q811yescharacteristic
278C23#53411yescharacteristic
279C23#54612yes—
280C23#54812yes—
281C23#57512yes—
282C23#57512yes—
283C23#57712yes—
284C23#57712yes—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
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#52912yes—
338C2×C4#53312yes—
339C2×C4#53812yes—
340C2×C4#54212yes—
341C2×C4#54212yes—
342C2×C4#54412yes—
343C2×C4#55112yes—
344C2×C4#55111yescharacteristic
345C2×C4#55212yes—
346C2×C4#55412yes—
347C2×C4#55412yes—
348C2×C4#55412yes—
349C2×C4#55511yescharacteristic
350C2×C4#55712yes—
351C2×C4H(3,𝔽4)11yescharacteristic
352C2×C4#56311yescharacteristic
353C8—44no—
354C8—44no—
355C22#247712yes—
356C22#255012yes—
357C22#258311yescharacteristic
358C22#268411yescharacteristic
359C22#273111yescharacteristic
360C22#311112yes—
361C22#312311yescharacteristic
362C22#312611yescharacteristic
363C22#316211yescharacteristic
364C22#316312yes—
365C22#316611yescharacteristic
366C22#319712yes—
367C22#320412yes—
368C22#330712yes—
369C22#331712yes—
370C22#332312yes—
371C22#332612yes—
372C22#337112yes—
373C22#337112yes—
374C22#337612yes—
375C22#337612yes—
376C4—42no—
377C4—42no—
378C4—82no—
379C4—82no—
380C4—84no—
381C4—84no—
382C4—84no—
383C4—162no—
384C4#252012yes—
385C4#257412yes—
386C4#276312yes—
387C4#277412yes—
388C2#1594411yescharacteristic
389C2#2744912yes—
390C2#2745112yes—
391C2#2879612yes—
392C2#2880512yes—
393C2#2930511yescharacteristic
394C2#2930711yescharacteristic
395C2#3127512yes—
396C2#3264312yes—
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
#139552
#113852
#112682
#112572
#112202
#109082
#108812
#108752