Finite Group Databasebeta

← #4463300

Subgroups — #4463300

Order 512.

1246 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17265C214yesmaximal
2#17264C214yesmaximal
3#17256C214yesmaximal
4#17252C214yesmaximal
5#15256C211yesmaximal, characteristic
6#15249C211yesmaximal, characteristic
7#15121C212yesmaximal
8#15051C214yesmaximal
9#15031C214yesmaximal
10#14286C212yesmaximal
11#13855C211yesmaximal, characteristic
12C2×#389C2212yes—
13C2×#376C2211yescharacteristic
14#1445C2212yes—
15#1445C2212yes—
16#1445C2214yes—
17#1445C2214yes—
18#1445C2214yes—
19#1445C2214yes—
20#1445C2214yes—
21#1444C2212yes—
22#1443C2214yes—
23#1443C2214yes—
24#1443C2214yes—
25#1443C2214yes—
26#1443C2214yes—
27#1443C2214yes—
28#1443C2214yes—
29#1443C2214yes—
30#1442C2214yes—
31#1442C2212yes—
32#1442C2214yes—
33#1442C2214yes—
34#1442C2214yes—
35#1442C2214yes—
36#1442C2214yes—
37#1442C2214yes—
38#1442C2214yes—
39#1441C2214yes—
40#1441C2214yes—
41#1441C2214yes—
42#1441C2214yes—
43#1441C2214yes—
44#1441C2214yes—
45#1441C2214yes—
46#1436C2214yes—
47#1436C2214yes—
48#1436C2214yes—
49#1434C2212yes—
50#1434C2214yes—
51#1434C2214yes—
52#1434C2214yes—
53C4×#95C2211yescharacteristic
54C4×#95C2212yes—
55C4×#95C2212yes—
56C4×#95C2211yescharacteristic
57C22×C4⋊C4C2314yes—
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2314yes—
61C22×C4⋊C4C2314yes—
62C22×C4⋊C4C2314yes—
63C22×C42C2311yescharacteristic
64C22×C42C2312yes—
65C22×C42C2312yes—
66C22×C42C2311yescharacteristic
67C22×C42C2311yescharacteristic
68#389—28no—
69#376—24no—
70C2×#95C2314yes—
71C2×#95C2314yes—
72C2×#95C2312yes—
73C2×#95C2312yes—
74C2×#95C2314yes—
75C2×#95C2314yes—
76C2×#95C2314yes—
77C2×#95C2314yes—
78C2×#95C2314yes—
79C2×#95C2314yes—
80C2×#95C2314yes—
81C2×#95C2314yes—
82C2×#95C2314yes—
83C2×#95C2314yes—
84C2×#95C2314yes—
85C2×#95C2314yes—
86C2×#95C2314yes—
87C2×#95C2312yes—
88C2×#95C2314yes—
89C2×#95C2314yes—
90C2×#95C2314yes—
91C2×#95C2314yes—
92C2×#95C2314yes—
93C2×#95C2314yes—
94C2×#95C2312yes—
95C2×#95C2314yes—
96C2×#95C2314yes—
97C2×#95C2314yes—
98C2×#95C2314yes—
99C2×#95C2314yes—
100C2×#95C2314yes—
101C2×#95C2314yes—
102C2×#95C2314yes—
103C2×#95C2314yes—
104C23×C4C2414yes—
105C23×C4C2414yes—
106C23×C4C2414yes—
107C23×C4C2414yes—
108C23×C4C2412yes—
109C23×C4C2414yes—
110C23×C4C2414yes—
111C23×C4C2411yescharacteristic
112C23×C4C2411yescharacteristic
113C23×C4C2412yes—
114C23×C4C2411yescharacteristic
115C2×C4⋊C4—24no—
116C2×C4⋊C4—28no—
117C2×C4⋊C4—24no—
118C2×C4⋊C4—44no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—44no—
122C2×C4⋊C4—44no—
123C2×C4⋊C4—44no—
124C2×C4⋊C4—44no—
125C2×C4⋊C4—44no—
126C2×C4⋊C4—44no—
127C2×C4⋊C4—44no—
128C2×C4⋊C4—44no—
129C2×C4⋊C4—44no—
130C2×C4⋊C4—44no—
131C2×C4⋊C4—44no—
132C2×C42—22no—
133C2×C42—22no—
134C2×C42—24no—
135C2×C42—24no—
136C2×C42—24no—
137C2×C42—42no—
138C2×C42—41no—
139C2×C42—41no—
140C2×C42—42no—
141C2×C42—42no—
142C2×C42—42no—
143C2×C42—42no—
144C2×C42#4114yes—
145#95—24no—
146#95—24no—
147#95—28no—
148#95—28no—
149#95—44no—
150#95—44no—
151#95—42no—
152#95—42no—
153#95—44no—
154#95—44no—
155#95—44no—
156#95—44no—
157#95—44no—
158#95—44no—
159#95—44no—
160#95—44no—
161#95—44no—
162#95—44no—
163#95—44no—
164#95—44no—
165#95—44no—
166#95—44no—
167#95—44no—
168#95—44no—
169#95—44no—
170#95—44no—
171#95—44no—
172#95—44no—
173#95—44no—
174#95—44no—
175#95—44no—
176#95—44no—
177#95—44no—
178#95—44no—
179C24C2511yescharacteristic
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—24no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—24no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—24no—
191C22×C4—24no—
192C22×C4—24no—
193C22×C4—24no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—24no—
197C22×C4—24no—
198C22×C4—24no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—24no—
202C22×C4—24no—
203C22×C4—24no—
204C22×C4—24no—
205C22×C4—24no—
206C22×C4—24no—
207C22×C4—24no—
208C22×C4—22no—
209C22×C4—24no—
210C22×C4—24no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4C2×#4114yes—
241C22×C4C2×#4112yes—
242C22×C42−1+414yes—
243C4⋊C4—48no—
244C4⋊C4—84no—
245C4⋊C4—88no—
246C4⋊C4—88no—
247C4⋊C4—88no—
248C4⋊C4—88no—
249C42—44no—
250C42—44no—
251C42—44no—
252C42—84no—
253C42—84no—
254C23C22×#4111yescharacteristic
255C23C2×2−1+412yes—
256C23#58514yes—
257C23#58512yes—
258C23#58511yescharacteristic
259C23#58511yescharacteristic
260C23#58514yes—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4#54114yes—
324C22C2×#54111yescharacteristic
325C22#345512yes—
326C22#349111yescharacteristic
327C22#349311yescharacteristic
328C22#351012yes—
329C22#353114yes—
330C22#356412yes—
331C22#356412yes—
332C22#356514yes—
333C22#356614yes—
334C22#356614yes—
335C22#356614yes—
336C22#356714yes—
337C4—24no—
338C4—44no—
339C4—84no—
340C4—84no—
341C4—81no—
342C4—81no—
343C4—84no—
344C4—84no—
345C4—84no—
346C4—84no—
347C4—82no—
348C2#3670011yescharacteristic
349C2#3697911yescharacteristic
350C2#3701312yes—
351C2#3703012yes—
352C2#3743311yescharacteristic
353C2#5279114yes—
354C2#5285714yes—
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#172652
#172642
#172562
#172522
#152562
#152492
#151212
#150512
#150312
#142862
#138552