Finite Group Databasebeta

← #24905977

Subgroups — #24905977

Order 10624.

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

normal subgroups only

This group has 346 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#121×D83C211yesmaximal, characteristic
2#19127663C211yesmaximal, characteristic, complemented
3#19127548C211yesmaximal, characteristic, complemented
4#19127436C211yesmaximal, characteristic, complemented
5#19127435C211yesmaximal, characteristic, complemented
6#19127434C211yesmaximal, characteristic, complemented
7#327×C83C211yesmaximal, characteristic, complemented
8C2×D4×D83—21no—
9C2×D4×D83C411yescharacteristic, complemented
10C22×C4×D83C2211yescharacteristic
11C2×#13050573—21no—
12#14581767C411yescharacteristic, complemented
13#14581766C2211yescharacteristic
14#14581765—21no—
15#14581764—21no—
16#14581763C411yescharacteristic, complemented
17C4⋊C4×D83C411yescharacteristic, complemented
18C2×(C2×D83)⋊C4—21no—
19C22⋊C4×D83—21no—
20C2×C4×Dic83—21no—
21C22⋊(C83⋊C8)C2211yescharacteristic, complemented
22(C2×D83)⋊C8—21no—
23C83⋊#95C2211yescharacteristic, complemented
24#121×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic, complemented
26#95×C83C2211yescharacteristic, complemented
27C23×D83—21no—
28C23×D83D411yescharacteristic
29C2×D332—21no—
30C2×D332C2×C411yescharacteristic
31C2×C22⋊D83—21no—
32C2×C22⋊D83—21no—
33C2×C22⋊D83—21no—
34D4×D83—42no—
35D4×D83—42no—
36D4×D83—42no—
37C22×Dic83—21no—
38C22×Dic83D411yescharacteristic
39C2×C4×D83—21no—
40C2×C4×D83—42no—
41C2×C4×D83C2×C411yescharacteristic
42C2×C4×D83C2×C411yescharacteristic
43C2×C4×D83D411yescharacteristic
44C2×C4×D83D411yescharacteristic
45#13050573—42no—
46C2×C83⋊C8—21no—
47C4⋊Dic83C2×C411yescharacteristic
48Dic83⋊C4—21no—
49C22⋊Dic83—21no—
50(C2×D83)⋊C4—24no—
51(C2×D83)⋊C4—21no—
52(C2×D83)⋊C4—21no—
53C4×Dic83—42no—
54C2×D4×C83—21no—
55C2×D4×C83C2×C411yescharacteristic
56C22×C4×C83—21no—
57C22×C4×C83C2311yescharacteristic
58C2×C8×C83—21no—
59C4⋊C4×C83C2×C411yescharacteristic
60C22⋊C4×C83—21no—
61C23×C83—21no—
62C23×C83C2×D411yescharacteristic
63C22×D83—21no—
64C22×D83—21no—
65C22×D83—22no—
66C22×D83—21no—
67C22×D83—41no—
68C22×D83—42no—
69C22×D83—42no—
70C22×D83—42no—
71C22×D83C22⋊C411yescharacteristic
72C22×D83C22⋊C411yescharacteristic
73D4×C83—41no—
74D4×C83—41no—
75D4×C83—41no—
76C2×C4×C83—22no—
77C2×C4×C83—21no—
78C2×C4×C83—41no—
79C2×C4×C83—41no—
80C2×C4×C83—41no—
81C2×C4×C83C22×C411yescharacteristic
82C2×C4×C83C2×D411yescharacteristic
83C22⋊D83—42no—
84C22⋊D83—41no—
85C22⋊D83—41no—
86C22⋊D83—42no—
87C2×Dic83—22no—
88C2×Dic83—22no—
89C2×Dic83—21no—
90C2×Dic83—41no—
91C2×Dic83—41no—
92C2×Dic83C22⋊C411yescharacteristic
93C2×Dic83C22⋊C411yescharacteristic
94D332—41no—
95D332—42no—
96C4×D83—22no—
97C4×D83—22no—
98C4×D83—41no—
99C4×D83—41no—
100C4×D83—42no—
101C8×C83—41no—
102C83⋊C8—41no—
103C22×C83—21no—
104C22×C83—21no—
105C22×C83—41no—
106C22×C83—41no—
107C22×C83—41no—
108C22×C83C2×C22⋊C411yescharacteristic
109C22×C83AGL(1,ℤ/8)11yescharacteristic
110C22×C83AGL(1,ℤ/8)11yescharacteristic
111C2×D83—21no—
112C2×D83—21no—
113C2×D83—21no—
114C2×D83—21no—
115C2×D83—21no—
116C2×D83—42no—
117C2×D83—42no—
118C2×D83—41no—
119C2×D83—41no—
120C2×D83—41no—
121C2×D83—84no—
122C2×D83#10412yes—
123C4×C83—21no—
124C4×C83—21no—
125C4×C83—42no—
126C4×C83—41no—
127Dic83—21no—
128Dic83—42no—
129Dic83—41no—
130Dic83#9912yes—
131C2×C83—21no—
132C2×C83—21no—
133C2×C83—81no—
134C2×C83C2×#9911yescharacteristic
135C2×C83#41811yescharacteristic
136C2×C83C2×#10411yescharacteristic
137D83—22no—
138D83—41no—
139D83—81no—
140#1507—831nomaximal, Sylow
141C83#150711yescharacteristic, complemented, Sylow
142C2×#121—831no—
143#407—831no—
144C4×C22⋊C4—831no—
145#327—831no—
146#327—831no—
147#327—831no—
148#327D8311yescharacteristic, complemented
149C22×D4—831no—
150C22×D4—1661no—
151C23×C4—831no—
152C2×M16—1661no—
153#121—831no—
154#121—831no—
155#121—831no—
156#121—1661no—
157#121—1661no—
158#121C2×D8311yescharacteristic
159C2×C4⋊C4—831no—
160C2×C22⋊C4—1661no—
161C2×C22⋊C4—1661no—
162C2×C42—1661no—
163C22⋊C8—831no—
164C22⋊C8—1661no—
165C22⋊C8C2×D8311yescharacteristic, complemented
166#95—831no—
167#95C2×D8311yescharacteristic, complemented
168C24—831no—
169C24—1661no—
170C2×D4—21no—
171C2×D4—3322no—
172C2×D4—3322no—
173C2×D4—3322no—
174C2×D4—831no—
175C2×D4—1661no—
176C2×D4—1661no—
177C2×D4—1661no—
178C2×D4—1661no—
179C2×D4C4×D8311yescharacteristic
180C22×C4—21no—
181C22×C4—3322no—
182C22×C4—831no—
183C22×C4—831no—
184C22×C4—831no—
185C22×C4—831no—
186C22×C4—831no—
187C22×C4—1661no—
188C22×C4—1661no—
189C22×C4C22×D8311yescharacteristic
190M16—3322no—
191C2×C8—21no—
192C2×C8—1661no—
193C4⋊C4—831no—
194C4⋊C4—1661no—
195C4⋊C4C4×D8311yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—1661no—
198C22⋊C4—1664no—
199C22⋊C4—1661no—
200C22⋊C4—1661no—
201C42—3322no—
202C23—21no—
203C23—3321no—
204C23—3322no—
205C23—3322no—
206C23—3322no—
207C23—831no—
208C23—831no—
209C23—1662no—
210C23—1661no—
211C23—1661no—
212C23—1661no—
213C23D4×D8311yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—3321no—
218D4—3322no—
219D4—3322no—
220D4—3321no—
221D4—3321no—
222D4—3322no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—3321no—
229C2×C4—3321no—
230C2×C4—3322no—
231C2×C4—3321no—
232C2×C4—3321no—
233C2×C4—831no—
234C2×C4—831no—
235C2×C4—1662no—
236C2×C4—1662no—
237C2×C4—1662no—
238C2×C4—1661no—
239C2×C4—1662no—
240C2×C4C2×C4×D8311yescharacteristic
241C2×C4D4×D8311yescharacteristic
242C8—41no—
243C8—3321no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—3322no—
250C22—3322no—
251C22—3321no—
252C22—3321no—
253C22—3321no—
254C22—832no—
255C22—6644no—
256C22—1661no—
257C22—1661no—
258C22—1661no—
259C22—1661no—
260C22—1661no—
261C22C22⋊C4×D8311yescharacteristic
262C22#1458181611yescharacteristic
263C22#1458181911yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—41no—
268C4—3322no—
269C4—3321no—
270C4—832no—
271C4—1661no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—3321no—
276C2—6641no—
277C2—1662no—
278C2#99×D8311yescharacteristic
279C2#1912770411yescharacteristic
280C2#104×D8311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#327×C83C2
socleC22×C83C2×C22⋊C4
prime radical#121×D83C2
cosocleC22×C4×C83C23
hypercenter#327D83
hypocenterC83#1507
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #19127663C2semidirect
3. #19127548C2semidirect
4. #19127436C2semidirect
5. #19127435C2semidirect
6. #19127434C2semidirect
7. #327×C83C2semidirect
9. C2×D4×D83C4semidirect
12. #14581767C4semidirect
16. #14581763C4semidirect
17. C4⋊C4×D83C4semidirect
21. C22⋊(C83⋊C8)C22semidirect
23. C83⋊#95C22semidirect
25. C22⋊C8×C83C22semidirect
26. #95×C83C22semidirect
141. C83#1507semidirect
148. #327D83semidirect
165. C22⋊C8C2×D83semidirect
167. #95C2×D83semidirect