Finite Group Databasebeta

← #24905966

Subgroups — #24905966

Order 10624.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128214C211yesmaximal, characteristic
2#19127663C211yesmaximal, characteristic, complemented
3#95×D83C211yesmaximal, characteristic, complemented
4#19127438C211yesmaximal, characteristic, complemented
5#19127436C211yesmaximal, characteristic, complemented
6#19127434C211yesmaximal, characteristic, complemented
7#328×C83C211yesmaximal, characteristic, complemented
8C2×#13050591C411yescharacteristic, complemented
9C22×C4×D83—21no—
10C22×C4×D83C2211yescharacteristic
11C2×#13050573—21no—
12#14581777—21no—
13#14581768C411yescharacteristic, complemented
14#14581767C411yescharacteristic, complemented
15#14581766C2211yescharacteristic
16#14581762—21no—
17#14581754—21no—
18(C22⋊D83)⋊C4—21no—
19#14581750C411yescharacteristic, complemented
20C22⋊(C83⋊C8)C2211yescharacteristic
21(C2×D83)⋊C8—21no—
22C83⋊#95—21no—
23C83⋊#95C2211yescharacteristic
24C22⋊Q8×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic
26#95×C83C2211yescharacteristic
27C23×D83D411yescharacteristic
28#13050591—42no—
29C2×D332—21no—
30C2×D332—21no—
31C2×D332C2×C411yescharacteristic, complemented
32C2×C22⋊D83—21no—
33C22×Dic83—21no—
34C22×Dic83D411yescharacteristic
35C2×C4×D83—24no—
36C2×C4×D83—21no—
37C2×C4×D83—42no—
38C2×C4×D83—42no—
39C2×C4×D83—42no—
40C2×C4×D83C2×C411yescharacteristic
41C2×C4×D83C2×C411yescharacteristic
42C2×C4×D83D411yescharacteristic
43C2×C4×D83D411yescharacteristic
44#13050573—42no—
45C2×C83⋊C8—21no—
46C4⋊Dic83C2×C411yescharacteristic, complemented
47Dic83⋊C4—21no—
48(C2×D83)⋊C4—21no—
49(C2×D83)⋊C4—21no—
50(C2×D83)⋊C4—21no—
51(C2×D83)⋊C4—21no—
52C4×Dic83—21no—
53C2×Q8×C83C2×C411yescharacteristic, complemented
54C22×C4×C83—21no—
55C22×C4×C83C2311yescharacteristic
56C2×C8×C83—21no—
57C4⋊C4×C83—21no—
58C4⋊C4×C83C2×C411yescharacteristic, complemented
59C22⋊C4×C83—21no—
60C23×C83C2×D411yescharacteristic
61C22×D83—21no—
62C22×D83—21no—
63C22×D83—22no—
64C22×D83—22no—
65C22×D83—21no—
66C22×D83C22⋊C411yescharacteristic
67C22×D83C22⋊C411yescharacteristic
68Q8×C83—41no—
69C2×C4×C83—22no—
70C2×C4×C83—21no—
71C2×C4×C83—21no—
72C2×C4×C83—41no—
73C2×C4×C83—41no—
74C2×C4×C83—41no—
75C2×C4×C83C22×C411yescharacteristic
76C2×C4×C83C2×D411yescharacteristic
77C22⋊D83—41no—
78C22⋊D83—41no—
79C2×Dic83—22no—
80C2×Dic83—21no—
81C2×Dic83—41no—
82C2×Dic83—41no—
83C2×Dic83—41no—
84C2×Dic83C22⋊C411yescharacteristic
85C2×Dic83C22⋊C411yescharacteristic
86D332—41no—
87D332—42no—
88D332—42no—
89C4×D83—22no—
90C4×D83—22no—
91C4×D83—41no—
92C4×D83—41no—
93C4×D83—42no—
94C4×D83—48no—
95C8×C83—41no—
96C83⋊C8—41no—
97C22×C83—21no—
98C22×C83—21no—
99C22×C83C2×C22⋊C411yescharacteristic
100C22×C83AGL(1,ℤ/8)11yescharacteristic
101C22×C83#13711yescharacteristic
102C2×D83—24no—
103C2×D83—24no—
104C2×D83—21no—
105C2×D83—21no—
106C2×D83—21no—
107C2×D83—21no—
108C2×D83—41no—
109C2×D83—41no—
110C2×D83—41no—
111C2×D83#9912yes—
112C2×D83#10412yes—
113C4×C83—21no—
114C4×C83—21no—
115C4×C83—42no—
116C4×C83—41no—
117C4×C83—41no—
118Dic83—21no—
119Dic83—21no—
120Dic83—42no—
121Dic83—41no—
122C2×C83—21no—
123C2×C83—21no—
124C2×C83C2×#9911yescharacteristic
125C2×C83#41711yescharacteristic
126C2×C83C2×#10411yescharacteristic
127D83—22no—
128D83—22no—
129D83—81no—
130#1504—831nomaximal, Sylow
131C83#150411yescharacteristic, complemented, Sylow
132#525—831no—
133#407—831no—
134C2×#95—831no—
135#328—831no—
136#328D8311yescharacteristic, complemented
137#327—831no—
138#327—831no—
139C2×#41—831no—
140C23×C4—831no—
141C23×C4—1661no—
142C2×M16—1661no—
143#123—1661no—
144C22⋊Q8—831no—
145C22⋊Q8C2×D8311yescharacteristic
146#121—831no—
147#121—831no—
148#120—1661no—
149C4×D4—1661no—
150C4×D4—1661no—
151#117—831no—
152C22⋊C8—831no—
153C22⋊C8—1661no—
154C22⋊C8C2×D8311yescharacteristic
155#95—831no—
156#95—1661no—
157#95C2×D8311yescharacteristic
158C24—831no—
159#41—3322no—
160C2×Q8C4×D8311yescharacteristic, complemented
161C2×D4—831no—
162C2×D4—1661no—
163C2×D4—1661no—
164C2×D4—1661no—
165C22×C4—21no—
166C22×C4—3322no—
167C22×C4—3322no—
168C22×C4—3322no—
169C22×C4—831no—
170C22×C4—831no—
171C22×C4—831no—
172C22×C4—831no—
173C22×C4—831no—
174C22×C4—1661no—
175C22×C4—1664no—
176C22×C4—1661no—
177C22×C4C22×D8311yescharacteristic
178M16—3322no—
179C2×C8—21no—
180C2×C8—1661no—
181C4⋊C4—21no—
182C4⋊C4—831no—
183C4⋊C4—1661no—
184C4⋊C4C4×D8311yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—1661no—
187C22⋊C4—1661no—
188C22⋊C4—1661no—
189C22⋊C4—1661no—
190C42—1661no—
191C23—831no—
192C23—831no—
193C23—1662no—
194C23—1662no—
195C23—1661no—
196C23—1661no—
197C23—1661no—
198C23D4×D8311yescharacteristic
199Q8—41no—
200D4—3321no—
201D4—3322no—
202D4—3322no—
203D4—3321no—
204D4—3321no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3321no—
212C2×C4—3321no—
213C2×C4—3328no—
214C2×C4—3322no—
215C2×C4—3321no—
216C2×C4—3321no—
217C2×C4—3321no—
218C2×C4—831no—
219C2×C4—831no—
220C2×C4—1662no—
221C2×C4—1662no—
222C2×C4—1662no—
223C2×C4—1661no—
224C2×C4C2×C4×D8311yescharacteristic
225C2×C4D4×D8311yescharacteristic
226C8—41no—
227C8—3321no—
228C22—21no—
229C22—21no—
230C22—3321no—
231C22—3321no—
232C22—3321no—
233C22—832no—
234C22—832no—
235C22—1664no—
236C22—1664no—
237C22—1661no—
238C22—1661no—
239C22—1661no—
240C22—1661no—
241C22C22⋊C4×D8311yescharacteristic
242C22#1458181911yescharacteristic
243C22#1458182411yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—3322no—
250C4—3321no—
251C4—1661no—
252C4—1661no—
253C2—21no—
254C2—21no—
255C2—6641no—
256C2—1662no—
257C2—1662no—
258C2#99×D8311yescharacteristic
259C2#1912770111yescharacteristic
260C2#104×D8311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#328×C83C2
socleC22×C83C2×C22⋊C4
prime radical#19128214C2
cosocleC22×C4×C83C23
hypercenter#328D83
hypocenterC83#1504
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19127663C2semidirect
3. #95×D83C2semidirect
4. #19127438C2semidirect
5. #19127436C2semidirect
6. #19127434C2semidirect
7. #328×C83C2semidirect
8. C2×#13050591C4semidirect
13. #14581768C4semidirect
14. #14581767C4semidirect
19. #14581750C4semidirect
31. C2×D332C2×C4semidirect
46. C4⋊Dic83C2×C4semidirect
53. C2×Q8×C83C2×C4semidirect
58. C4⋊C4×C83C2×C4semidirect
131. C83#1504semidirect
136. #328D83semidirect
160. C2×Q8C4×D83semidirect
184. C4⋊C4C4×D83semidirect