Finite Group Databasebeta

← #24906005

Subgroups — #24906005

Order 10624.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#19127560C211yesmaximal, characteristic, complemented
4#19127438C211yesmaximal, characteristic, complemented
5#19127436C211yesmaximal, characteristic, complemented
6#19127434C211yesmaximal, characteristic, complemented
7#328×C83C211yesmaximal, characteristic, complemented
8C2×#13050591C411yescharacteristic, complemented
9C22×C4×D83C2211yescharacteristic
10C2×#13050573—21no—
11#14581777—21no—
12#14581768C411yescharacteristic, complemented
13#14581767C411yescharacteristic, complemented
14#14581766C2211yescharacteristic
15#14581762—21no—
16#14581754—21no—
17(C22⋊D83)⋊C4—21no—
18#14581750C411yescharacteristic, complemented
19C2×Dic83⋊C4—21no—
20C2×(C2×D83)⋊C4—21no—
21C22⋊(C83⋊C8)C2211yescharacteristic
22(C2×D83)⋊C8—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
32C2×C22⋊D83—21no—
33C22×Dic83—21no—
34C22×Dic83D411yescharacteristic
35C2×C4×D83—21no—
36C2×C4×D83—42no—
37C2×C4×D83C2×C411yescharacteristic
38C2×C4×D83C2×C411yescharacteristic
39C2×C4×D83D411yescharacteristic
40C2×C4×D83D411yescharacteristic
41#13050573—42no—
42C2×C83⋊C8—21no—
43C4⋊Dic83C2×C411yescharacteristic
44Dic83⋊C4—21no—
45Dic83⋊C4—42no—
46(C2×D83)⋊C4—21no—
47(C2×D83)⋊C4—21no—
48(C2×D83)⋊C4—21no—
49(C2×D83)⋊C4—21no—
50(C2×D83)⋊C4—42no—
51C4×Dic83—21no—
52C2×Q8×C83C2×C411yescharacteristic
53C22×C4×C83—21no—
54C22×C4×C83C2311yescharacteristic
55C2×C8×C83—21no—
56C4⋊C4×C83—21no—
57C4⋊C4×C83C2×C411yescharacteristic
58C22⋊C4×C83—21no—
59C23×C83C2×D411yescharacteristic
60C22×D83—21no—
61C22×D83—21no—
62C22×D83—21no—
63C22×D83—41no—
64C22×D83—41no—
65C22×D83C22⋊C411yescharacteristic
66C22×D83C22⋊C411yescharacteristic
67Q8×C83—41no—
68C2×C4×C83—21no—
69C2×C4×C83—21no—
70C2×C4×C83—41no—
71C2×C4×C83—41no—
72C2×C4×C83—41no—
73C2×C4×C83—41no—
74C2×C4×C83C22×C411yescharacteristic
75C2×C4×C83C2×D411yescharacteristic
76C22⋊D83—41no—
77C22⋊D83—41no—
78C2×Dic83—22no—
79C2×Dic83—21no—
80C2×Dic83—41no—
81C2×Dic83—41no—
82C2×Dic83—41no—
83C2×Dic83C22⋊C411yescharacteristic
84C2×Dic83C22⋊C411yescharacteristic
85D332—41no—
86D332—42no—
87D332—42no—
88C4×D83—22no—
89C4×D83—22no—
90C4×D83—41no—
91C4×D83—41no—
92C4×D83—42no—
93C8×C83—41no—
94C83⋊C8—41no—
95C22×C83—21no—
96C22×C83—21no—
97C22×C83C2×C22⋊C411yescharacteristic
98C22×C83AGL(1,ℤ/8)11yescharacteristic
99C22×C83#13711yescharacteristic
100C2×D83—21no—
101C2×D83—21no—
102C2×D83—21no—
103C2×D83—21no—
104C2×D83—21no—
105C2×D83—21no—
106C2×D83—42no—
107C2×D83—42no—
108C2×D83—41no—
109C2×D83—41no—
110C2×D83—41no—
111C4×C83—21no—
112C4×C83—21no—
113C4×C83—41no—
114C4×C83—41no—
115C4×C83—81no—
116Dic83—21no—
117Dic83—41no—
118Dic83—81no—
119Dic83#9912yes—
120C2×C83—21no—
121C2×C83—21no—
122C2×C83C2×#9911yescharacteristic
123C2×C83#41711yescharacteristic
124C2×C83#42111yescharacteristic
125D83—41no—
126D83—41no—
127D83—81no—
128#1513—831nomaximal, Sylow
129C83#151311yescharacteristic, complemented, Sylow
130#525—831no—
131#407—831no—
132#380—831no—
133#328—831no—
134#328D8311yescharacteristic, complemented
135#327—831no—
136#327—831no—
137C2×#41—831no—
138C23×C4—831no—
139C2×M16—1661no—
140#123—1661no—
141C22⋊Q8—831no—
142C22⋊Q8C2×D8311yescharacteristic
143#121—831no—
144#121—831no—
145#120—1661no—
146C4×D4—1661no—
147C4×D4—1661no—
148#117—831no—
149C2×C4⋊C4—1661no—
150C2×C22⋊C4—1661no—
151C22⋊C8—831no—
152C22⋊C8—1661no—
153C22⋊C8C2×D8311yescharacteristic
154#95—831no—
155#95C2×D8311yescharacteristic
156C24—831no—
157#41—3322no—
158C2×Q8C4×D8311yescharacteristic
159C2×D4—831no—
160C2×D4—1661no—
161C2×D4—1661no—
162C2×D4—1661no—
163C22×C4—21no—
164C22×C4—3322no—
165C22×C4—831no—
166C22×C4—831no—
167C22×C4—831no—
168C22×C4—831no—
169C22×C4—831no—
170C22×C4—1661no—
171C22×C4—1661no—
172C22×C4C22×D8311yescharacteristic
173M16—3322no—
174C2×C8—21no—
175C2×C8—1661no—
176C4⋊C4—21no—
177C4⋊C4—3322no—
178C4⋊C4—831no—
179C4⋊C4—1661no—
180C4⋊C4C4×D8311yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—3322no—
183C22⋊C4—1661no—
184C22⋊C4—1661no—
185C22⋊C4—1661no—
186C22⋊C4—1661no—
187C42—1661no—
188C23—3321no—
189C23—3321no—
190C23—831no—
191C23—831no—
192C23—1661no—
193C23—1661no—
194C23—1661no—
195C23D4×D8311yescharacteristic
196Q8—41no—
197D4—3321no—
198D4—3322no—
199D4—3322no—
200D4—3321no—
201D4—3321no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—3321no—
209C2×C4—3321no—
210C2×C4—3322no—
211C2×C4—3321no—
212C2×C4—3321no—
213C2×C4—3321no—
214C2×C4—831no—
215C2×C4—831no—
216C2×C4—1662no—
217C2×C4—1662no—
218C2×C4—1661no—
219C2×C4—1662no—
220C2×C4C2×C4×D8311yescharacteristic
221C2×C4D4×D8311yescharacteristic
222C8—41no—
223C8—3321no—
224C22—21no—
225C22—21no—
226C22—3322no—
227C22—3322no—
228C22—3321no—
229C22—3321no—
230C22—3321no—
231C22—1661no—
232C22—1661no—
233C22—1661no—
234C22—1661no—
235C22—1661no—
236C22—1661no—
237C22C22⋊C4×D8311yescharacteristic
238C22#1458181911yescharacteristic
239C22#1458182411yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—3321no—
246C4—832no—
247C4—6641no—
248C4—1661no—
249C2—21no—
250C2—21no—
251C2—3321no—
252C2—3321no—
253C2—6641no—
254C2#99×D8311yescharacteristic
255C2#1912770111yescharacteristic
256C2#1912771611yescharacteristic
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#1513
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. #19127560C2semidirect
4. #19127438C2semidirect
5. #19127436C2semidirect
6. #19127434C2semidirect
7. #328×C83C2semidirect
8. C2×#13050591C4semidirect
12. #14581768C4semidirect
13. #14581767C4semidirect
18. #14581750C4semidirect
129. C83#1513semidirect
134. #328D83semidirect