Finite Group Databasebeta

← #120938

Subgroups — #120938

Order 512.

523 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21933C211yesmaximal, characteristic
2#8104C211yesmaximal, characteristic
3#8057C211yesmaximal, characteristic
4#8055C211yesmaximal, characteristic
5C2×#1298C211yesmaximal, characteristic
6#8008C211yesmaximal, characteristic
7#7925C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C2×#407C2211yescharacteristic
12C22×C22⋊C8C2211yescharacteristic
13C22×C22⋊C8C2211yescharacteristic
14#2280C2211yescharacteristic
15#1851—22no—
16#1850—22no—
17#1798—22no—
18#1305C414yes—
19#1298—22no—
20#1298—22no—
21#1298—22no—
22#1293—22no—
23#1282—22no—
24C24×C4C2311yescharacteristic
25C22×M16—21no—
26C22×M16—21no—
27C22×M16—21no—
28C22×M16Q812yes—
29C23×C8—21no—
30C23×C8—21no—
31C2×#117—21no—
32C2×C4⋊C8—24no—
33#407—21no—
34#407—21no—
35#407—21no—
36#407—21no—
37#407—21no—
38#407—21no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407—21no—
44#407—21no—
45#407—21no—
46#407—21no—
47#407C2×C412yes—
48#407C2×C412yes—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8—21no—
60C2×C22⋊C8—21no—
61C2×C22⋊C8—21no—
62C2×C22⋊C8—21no—
63C2×C22⋊C8—21no—
64C2×C22⋊C8—21no—
65C2×C22⋊C8—21no—
66C2×C22⋊C8D412yes—
67C2×C22⋊C8D412yes—
68C2×C22⋊C8D412yes—
69#381—21no—
70#380—21no—
71#380C2×C412yes—
72#379Q812yes—
73C4×C22⋊C4—21no—
74C4×C22⋊C4D412yes—
75#336—24no—
76C25C2×Q811yescharacteristic
77C23×C4—82no—
78C23×C4C22×C411yescharacteristic
79C23×C4C2×D411yescharacteristic
80C23×C4C2×D411yescharacteristic
81C23×C4C2×D411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4C2×Q811yescharacteristic
84C23×C4#4111yescharacteristic
85C23×C4#4111yescharacteristic
86C23×C4#4111yescharacteristic
87C23×C4#4111yescharacteristic
88C23×C4#4111yescharacteristic
89C23×C4#4111yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C2×M16—22no—
93C2×M16—22no—
94C2×M16—22no—
95C2×M16—22no—
96C2×M16—41no—
97C2×M16—41no—
98C2×M16—41no—
99C2×M16—41no—
100C2×M16—82no—
101C2×M16—82no—
102C2×M16—82no—
103C2×M16—82no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—82no—
115C22×C8—82no—
116#117—82no—
117C2×C4⋊C4—22no—
118C2×C22⋊C4—22no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4C4⋊C414yes—
121C2×C42—22no—
122C4⋊C8—84no—
123C22⋊C8—22no—
124C22⋊C8—22no—
125C22⋊C8—22no—
126C22⋊C8—22no—
127C22⋊C8—22no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—22no—
131C22⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147#95—22no—
148#95—22no—
149C24—42no—
150C24—42no—
151C24—81no—
152C24C2×C4⋊C411yescharacteristic
153C24C22⋊Q811yescharacteristic
154C24C22⋊Q811yescharacteristic
155C24#12511yescharacteristic
156C24#12511yescharacteristic
157C24#12511yescharacteristic
158C24C4⋊Q811yescharacteristic
159C22×C4—24no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—81no—
168C22×C4—81no—
169C22×C4—81no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—81no—
173C22×C4—81no—
174C22×C4#11711yescharacteristic
175C22×C4#11711yescharacteristic
176C22×C4C4×D411yescharacteristic
177C22×C4C4×D411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×Q811yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4C22⋊Q811yescharacteristic
185C22×C4C22⋊Q811yescharacteristic
186C22×C4C22⋊Q811yescharacteristic
187C22×C4#12311yescharacteristic
188C22×C4#12311yescharacteristic
189C22×C4#12311yescharacteristic
190C22×C4#12311yescharacteristic
191C22×C4#12311yescharacteristic
192C22×C4#12411yescharacteristic
193C22×C4#12411yescharacteristic
194C22×C4#12411yescharacteristic
195C22×C4#12411yescharacteristic
196C22×C4#12511yescharacteristic
197C22×C4#12511yescharacteristic
198C22×C4#12611yescharacteristic
199C22×C4#12611yescharacteristic
200C22×C4#12611yescharacteristic
201C22×C4#12611yescharacteristic
202M16—82no—
203M16—82no—
204M16—82no—
205M16—82no—
206M16—82no—
207M16—82no—
208M16—82no—
209M16—82no—
210C2×C8—44no—
211C2×C8—44no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—82no—
219C2×C8—82no—
220C2×C8—82no—
221C2×C8—82no—
222C2×C8—82no—
223C2×C8—82no—
224C2×C8—82no—
225C2×C8—82no—
226C4⋊C4—82no—
227C22⋊C4—44no—
228C22⋊C4—44no—
229C22⋊C4—82no—
230C42—44no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—88no—
253C23#38211yescharacteristic
254C23#38511yescharacteristic
255C23#38911yescharacteristic
256C23#39811yescharacteristic
257C23#39811yescharacteristic
258C23#40011yescharacteristic
259C23#40011yescharacteristic
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4#38711yescharacteristic
292C2×C4#38711yescharacteristic
293C2×C4#38811yescharacteristic
294C2×C4#38811yescharacteristic
295C2×C4#39311yescharacteristic
296C2×C4#39411yescharacteristic
297C2×C4#39711yescharacteristic
298C2×C4#40011yescharacteristic
299C8—82no—
300C8—82no—
301C8—82no—
302C8—82no—
303C8—82no—
304C8—82no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—44no—
325C22—44no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22#144211yescharacteristic
332C22#185812yes—
333C22#210312yes—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—84no—
342C4#203212yes—
343C2—22no—
344C2—22no—
345C2—41no—
346C2—41no—
347C2—41no—
348C2—41no—
349C2—41no—
350C2#1126411yescharacteristic
351C2#1127911yescharacteristic
352C2#1129711yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
socleC22#1442
prime radicalC25C2×Q8
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#219332
#81042
#80572
#80552
C2×#12982
#80082
#79252