Finite Group Databasebeta

← #120952

Subgroups — #120952

Order 512.

442 conjugacy classes of subgroups.

The subgroup lattice has 303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21356C211yesmaximal, characteristic
2#8124C211yesmaximal, characteristic
3#7973C211yesmaximal, characteristic
4#7940C211yesmaximal, characteristic
5#7928C211yesmaximal, characteristic
6#7883C211yesmaximal, characteristic
7#7870C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2283C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1939—22no—
16#1851—22no—
17#1767—22no—
18#1308—22no—
19#1288—22no—
20#1284C414yes—
21#1282—22no—
22#1278—22no—
23#1276—22no—
24C22×M16—21no—
25C2×#117—21no—
26C22×C42C2311yescharacteristic
27#432—21no—
28#432—21no—
29#432—21no—
30#432—21no—
31#432—21no—
32#432—21no—
33#432—21no—
34#432D412yes—
35#431—21no—
36#431—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#423—21no—
44#423—21no—
45C2×C4⋊C8—24no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8Q812yes—
48#407—21no—
49#407C2×C412yes—
50C2×C22⋊C8—21no—
51C2×C22⋊C8D412yes—
52C4×M16—21no—
53C4×M16—21no—
54C4×M16—21no—
55C4×M16—21no—
56C4×M16—21no—
57C4×M16—21no—
58C2×#97—21no—
59C2×#97—21no—
60C2×C4×C8—21no—
61C2×C4×C8D412yes—
62#383—21no—
63#382—21no—
64#381C2×C412yes—
65#380—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4Q811yescharacteristic
69C4×C4⋊C4Q811yescharacteristic
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C4×C22⋊C4C2×C412yes—
73#376—21no—
74#376—21no—
75C43D412yes—
76#336—24no—
77C23×C4C22×C411yescharacteristic
78C23×C4C2×D411yescharacteristic
79C23×C4#4111yescharacteristic
80C2×M16—22no—
81C2×M16—44no—
82C2×M16—41no—
83C2×M16—41no—
84C2×M16—41no—
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—22no—
88#117—44no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—41no—
92C2×C22⋊C4—22no—
93C2×C22⋊C4—22no—
94C2×C42—22no—
95C2×C42—22no—
96C2×C42—41no—
97C2×C42C4⋊C412yes—
98C2×C42C4⋊C412yes—
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42C2×Q811yescharacteristic
103C2×C42C2×Q811yescharacteristic
104C2×C42#4111yescharacteristic
105C2×C42#4111yescharacteristic
106C2×C42#4111yescharacteristic
107C2×C42#4111yescharacteristic
108C2×C42#4111yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111C4⋊C8—22no—
112C4⋊C8—22no—
113C4⋊C8—22no—
114C4⋊C8—48no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C22⋊C8—22no—
121C22⋊C8—22no—
122C22⋊C8—22no—
123C22⋊C8—22no—
124C22⋊C8—22no—
125C22⋊C8—41no—
126C22⋊C8—41no—
127C22⋊C8—41no—
128#97—22no—
129#97—41no—
130#97—41no—
131#97—41no—
132#97—41no—
133#97—41no—
134C4×C8—22no—
135C4×C8—22no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8—41no—
139C4×C8—41no—
140#95—22no—
141#95—21no—
142#95—21no—
143#95—22no—
144#95—22no—
145#95—41no—
146#95—41no—
147C24C4×D411yescharacteristic
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—42no—
155C22×C4C2×C4⋊C411yescharacteristic
156C22×C4#11711yescharacteristic
157C22×C4#11711yescharacteristic
158C22×C4C4×D411yescharacteristic
159C22×C4C4×D411yescharacteristic
160C22×C4C4×Q811yescharacteristic
161C22×C4#12011yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4C22⋊Q811yescharacteristic
164C22×C4C22⋊Q811yescharacteristic
165C22×C4C22⋊Q811yescharacteristic
166C22×C4#12311yescharacteristic
167C22×C4#12311yescharacteristic
168C22×C4#12311yescharacteristic
169C22×C4#12411yescharacteristic
170C22×C4#12511yescharacteristic
171C22×C4#12611yescharacteristic
172C22×C4#12611yescharacteristic
173M16—44no—
174M16—44no—
175M16—42no—
176M16—42no—
177M16—82no—
178C2×C8—24no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—44no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—82no—
187C4⋊C4—24no—
188C4⋊C4—42no—
189C4⋊C4—82no—
190C22⋊C4—44no—
191C22⋊C4—42no—
192C22⋊C4—42no—
193C42—42no—
194C42—42no—
195C42—44no—
196C42—44no—
197C42—82no—
198C42#12111yescharacteristic
199C42#12111yescharacteristic
200C42C22⋊Q811yescharacteristic
201C42C22⋊Q811yescharacteristic
202C42#12311yescharacteristic
203C42#12311yescharacteristic
204C42#12411yescharacteristic
205C42#12411yescharacteristic
206C42#12411yescharacteristic
207C42#12511yescharacteristic
208C42#12511yescharacteristic
209C42#12511yescharacteristic
210C42#12511yescharacteristic
211C42#12611yescharacteristic
212C42#12611yescharacteristic
213C42C4⋊Q811yescharacteristic
214C23—21no—
215C23—21no—
216C23—41no—
217C23—41no—
218C23#38511yescharacteristic
219C23#38711yescharacteristic
220C23#38811yescharacteristic
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—24no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4#38211yescharacteristic
251C2×C4#38711yescharacteristic
252C2×C4#38811yescharacteristic
253C2×C4#38911yescharacteristic
254C2×C4#39311yescharacteristic
255C2×C4#39411yescharacteristic
256C2×C4#39711yescharacteristic
257C2×C4#39811yescharacteristic
258C2×C4#39811yescharacteristic
259C2×C4#40011yescharacteristic
260C2×C4#40011yescharacteristic
261C2×C4#40011yescharacteristic
262C8—44no—
263C8—82no—
264C8—82no—
265C8—82no—
266C8—82no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—81no—
276C22—81no—
277C22#144211yescharacteristic
278C22#186811yescharacteristic
279C22#186811yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—44no—
291C4—82no—
292C4—162no—
293C4#203112yes—
294C4#210212yes—
295C2—21no—
296C2—21no—
297C2—41no—
298C2—41no—
299C2#1126111yescharacteristic
300C2#1128211yescharacteristic
301C2#1128811yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1442
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#213562
#81242
#79732
#79402
#79282
#78832
#78702