Finite Group Databasebeta

← #24905810

Subgroups — #24905810

Order 10624.

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

normal subgroups only

This group has 280 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
1C2×#14581777C211yesmaximal, characteristic
2#19127663C211yesmaximal, characteristic, complemented
3C22⋊C8×D83C211yesmaximal, characteristic, complemented
4#19127427C211yesmaximal, characteristic, complemented
5#19127424C211yesmaximal, characteristic, complemented
6#19127424C211yesmaximal, characteristic, complemented
7#324×C83C211yesmaximal, characteristic, complemented
8C22×D332C411yescharacteristic
9C22×C4×D83C2211yescharacteristic
10C2×#13050573—21no—
11C2×C8×D83—21no—
12#14581777—21no—
13#14581777—21no—
14#14581777—21no—
15#14581777—21no—
16C2×Dic83⋊C4C411yescharacteristic
17C2×(C2×D83)⋊C4C411yescharacteristic
18C2×(C2×D83)⋊C4C411yescharacteristic
19C2×(C2×D83)⋊C4C2211yescharacteristic
20C22⋊(C83⋊C8)C2211yescharacteristic
21C22⋊(C83⋊C8)C2211yescharacteristic
22(C2×D83)⋊C8—21no—
23(C2×D83)⋊C8—21no—
24C2×C4⋊C4×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic
26C22⋊C8×C83C2211yescharacteristic
27C23×D83C2×C411yescharacteristic
28C23×D83C2×C411yescharacteristic
29C2×D332—21no—
30C2×D332—21no—
31C2×D332—42no—
32C22×Dic83C2×C411yescharacteristic
33C22×Dic83C2×C411yescharacteristic
34C2×C4×D83—42no—
35C2×C4×D83D411yescharacteristic
36C2×C4×D83D411yescharacteristic
37C2×C4×D83D411yescharacteristic
38C2×C4×D83D411yescharacteristic
39#13050573—42no—
40C2×C83⋊C8—21no—
41C2×C83⋊C8—21no—
42C8×D83—42no—
43Dic83⋊C4—21no—
44Dic83⋊C4—21no—
45(C2×D83)⋊C4—21no—
46(C2×D83)⋊C4—21no—
47(C2×D83)⋊C4—21no—
48(C2×D83)⋊C4—21no—
49(C2×D83)⋊C4—21no—
50(C2×D83)⋊C4—21no—
51C22×C4×C83C2×C411yescharacteristic
52C22×C4×C83C2×C411yescharacteristic
53C22×C4×C83C2311yescharacteristic
54C2×C8×C83—21no—
55C2×C8×C83—21no—
56C4⋊C4×C83—21no—
57C4⋊C4×C83—21no—
58C23×C83C22×C411yescharacteristic
59C22×D83—21no—
60C22×D83—21no—
61C22×D83—22no—
62C22×D83—21no—
63C22×D83—21no—
64C22×D83—21no—
65C22×D83—41no—
66C22×D83—41no—
67C22×D83—41no—
68C22×D83C22⋊C411yescharacteristic
69C22×D83C22⋊C411yescharacteristic
70C2×C4×C83—21no—
71C2×C4×C83—21no—
72C2×C4×C83—21no—
73C2×C4×C83—21no—
74C2×C4×C83—41no—
75C2×C4×C83—41no—
76C2×C4×C83C2×D411yescharacteristic
77C2×C4×C83C2×D411yescharacteristic
78C2×Dic83—21no—
79C2×Dic83—41no—
80C2×Dic83—41no—
81C2×Dic83C22⋊C411yescharacteristic
82C2×Dic83C22⋊C411yescharacteristic
83D332—42no—
84D332—42no—
85C4×D83—22no—
86C4×D83—22no—
87C4×D83—41no—
88C4×D83—41no—
89C8×C83—41no—
90C8×C83—41no—
91C83⋊C8—41no—
92C83⋊C8—41no—
93C22×C83—21no—
94C22×C83—21no—
95C22×C83C2×C22⋊C411yescharacteristic
96C22×C83#13111yescharacteristic
97C22×C83#13111yescharacteristic
98C2×D83—21no—
99C2×D83—21no—
100C2×D83—21no—
101C2×D83—21no—
102C2×D83—21no—
103C2×D83—42no—
104C2×D83—42no—
105C2×D83—41no—
106C2×D83—41no—
107C2×D83—41no—
108C2×D83—81no—
109C2×D83—81no—
110C2×D83#9912yes—
111C4×C83—21no—
112C4×C83—21no—
113C4×C83—41no—
114C4×C83—41no—
115Dic83—21no—
116Dic83—21no—
117Dic83—41no—
118C2×C83—21no—
119C2×C83—21no—
120C2×C83#40811yescharacteristic
121C2×C83C2×#9911yescharacteristic
122C2×C83#41311yescharacteristic
123D83—22no—
124D83—41no—
125D83—81no—
126#1468—831nomaximal, Sylow
127C83#146811yescharacteristic, complemented, Sylow
128C2×#123—831no—
129#407—831no—
130C2×C22⋊C8—831no—
131#324—831no—
132#324D8311yescharacteristic, complemented
133#323—831no—
134#323—831no—
135C22×D4—831no—
136C23×C4—831no—
137C2×M16—1661no—
138C22×C8—1661no—
139#123—1661no—
140#123—1661no—
141#123—1661no—
142#123—1661no—
143C2×C4⋊C4—831no—
144C2×C4⋊C4C2×D8311yescharacteristic
145C2×C22⋊C4—831no—
146C2×C22⋊C4—831no—
147C2×C22⋊C4—831no—
148C22⋊C8—831no—
149C22⋊C8—831no—
150C22⋊C8—1661no—
151C22⋊C8—1661no—
152C22⋊C8C2×D8311yescharacteristic
153C22⋊C8C2×D8311yescharacteristic
154C24—831no—
155C24—831no—
156C2×D4—3322no—
157C2×D4—1661no—
158C2×D4—1661no—
159C22×C4—3322no—
160C22×C4—831no—
161C22×C4—831no—
162C22×C4—831no—
163C22×C4—831no—
164C22×C4—831no—
165C22×C4—831no—
166C22×C4C4×D8311yescharacteristic
167C22×C4C4×D8311yescharacteristic
168C22×C4C22×D8311yescharacteristic
169M16—3322no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—3322no—
173C2×C8—1661no—
174C2×C8—1661no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—1661no—
178C4⋊C4—1661no—
179C22⋊C4—1661no—
180C22⋊C4—1661no—
181C22⋊C4—1661no—
182C22⋊C4—1661no—
183C22⋊C4—1661no—
184C22⋊C4—1661no—
185C23—3321no—
186C23—3321no—
187C23—3321no—
188C23—831no—
189C23—831no—
190C23—1662no—
191C23—1661no—
192C23—1661no—
193C23—1661no—
194C23—1661no—
195C23—1661no—
196C23C2×C4×D8311yescharacteristic
197D4—3322no—
198D4—3322no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—3321no—
206C2×C4—3321no—
207C2×C4—3321no—
208C2×C4—3321no—
209C2×C4—831no—
210C2×C4—831no—
211C2×C4—1662no—
212C2×C4—1662no—
213C2×C4—1661no—
214C2×C4D4×D8311yescharacteristic
215C2×C4D4×D8311yescharacteristic
216C8—41no—
217C8—41no—
218C8—3321no—
219C8—3321no—
220C22—21no—
221C22—21no—
222C22—3322no—
223C22—3322no—
224C22—3321no—
225C22—3321no—
226C22—3321no—
227C22—832no—
228C22—6641no—
229C22—6641no—
230C22—1661no—
231C22—1661no—
232C22—1661no—
233C22—1661no—
234C22—1661no—
235C22C22⋊C4×D8311yescharacteristic
236C22#1458179811yescharacteristic
237C22#1458180011yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—3321no—
243C4—1661no—
244C4—1661no—
245C2—21no—
246C2—21no—
247C2—3321no—
248C2—6641no—
249C2—1662no—
250C2#1912766611yescharacteristic
251C2#99×D8311yescharacteristic
252C2#1912768411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC23×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#324×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC22×D332C4
cosocleC22×C4×C83C23
hypercenter#324D83
hypocenterC83#1468
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #19127663C2semidirect
3. C22⋊C8×D83C2semidirect
4. #19127427C2semidirect
5. #19127424C2semidirect
6. #19127424C2semidirect
7. #324×C83C2semidirect
127. C83#1468semidirect
132. #324D83semidirect