Finite Group Databasebeta

← #24907449

Subgroups — #24907449

Order 10624.

380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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×D4×Dic83C211yesmaximal, characteristic
2C2×#14581707C211yesmaximal, characteristic
3#19127559C212yesmaximal, complemented
4#19127467C212yesmaximal, complemented
5C2×#99×C83C211yesmaximal, characteristic
6C23×Dic83C411yescharacteristic, complemented
7C23×Dic83C2211yescharacteristic
8D4×Dic83—22no—
9D4×Dic83—22no—
10C2×C4⋊Dic83C411yescharacteristic, complemented
11C2×Dic83⋊C4—22no—
12C2×C22⋊Dic83C411yescharacteristic, complemented
13C2×C22⋊Dic83C2212yes—
14C2×C22⋊Dic83C2211yescharacteristic
15C2×C4×Dic83C411yescharacteristic, complemented
16#14581707—22no—
17C83⋊#95—22no—
18C22×D4×C83C2211yescharacteristic
19C2×C22⋊C4×C83C2212yes—
20#99×C83—22no—
21C22×Dic83—21no—
22C22×Dic83—21no—
23C22×Dic83—22no—
24C22×Dic83—42no—
25C22×Dic83—42no—
26C22×Dic83C2×C411yescharacteristic
27C22×Dic83C2×C411yescharacteristic
28C22×Dic83C2×C411yescharacteristic
29C22×Dic83C2×C411yescharacteristic
30C22×Dic83D412yes—
31C22×Dic83D412yes—
32C4⋊Dic83—22no—
33Dic83⋊C4—44no—
34C22⋊Dic83—22no—
35C22⋊Dic83—22no—
36C22⋊Dic83—22no—
37C22⋊Dic83—22no—
38C4×Dic83—21no—
39C4×Dic83—21no—
40C24×C83C2×C411yescharacteristic
41C24×C83C2311yescharacteristic
42C2×D4×C83—22no—
43C2×D4×C83—22no—
44C2×D4×C83D412yes—
45C2×D4×C83Q812yes—
46C22×C4×C83—22no—
47C22×C4×C83C2×C411yescharacteristic
48C22⋊C4×C83—22no—
49C22⋊C4×C83—22no—
50C23×C83—21no—
51C23×C83—21no—
52C23×C83—41no—
53C23×C83—41no—
54C23×C83—41no—
55C23×C83—41no—
56C23×C83C4⋊C412yescomplemented
57C23×C83C22×C411yescharacteristic
58C23×C83C2×D412yes—
59C23×C83C2×D411yescharacteristic
60C23×C83C2×Q811yescharacteristic
61C23×C83#4112yes—
62D4×C83—24no—
63D4×C83—24no—
64C2×C4×C83—21no—
65C2×C4×C83—21no—
66C2×C4×C83—42no—
67C2×C4×C83—42no—
68C2×C4×C83—42no—
69C2×C4×C83C4⋊C412yescomplemented
70C2×Dic83—24no—
71C2×Dic83—22no—
72C2×Dic83—21no—
73C2×Dic83—21no—
74C2×Dic83—41no—
75C2×Dic83—42no—
76C2×Dic83—42no—
77C2×Dic83—42no—
78C2×Dic83—41no—
79C2×Dic83—41no—
80C2×Dic83—42no—
81C2×Dic83—42no—
82C2×Dic83—42no—
83C2×Dic83C22⋊C411yescharacteristic
84C2×Dic83C22⋊C412yes—
85C2×Dic83C22⋊C411yescharacteristic
86C22×C83—22no—
87C22×C83—21no—
88C22×C83—22no—
89C22×C83—21no—
90C22×C83—22no—
91C22×C83—41no—
92C22×C83—41no—
93C22×C83—42no—
94C22×C83—42no—
95C22×C83—42no—
96C22×C83—41no—
97C22×C83—41no—
98C22×C83C2×C22⋊C411yescharacteristic
99C22×C83C2×C4⋊C411yescharacteristic
100C22×C83#11711yescharacteristic
101C22×C83#12112yes—
102C22×C83C22⋊Q812yes—
103C4×C83—22no—
104C4×C83—82no—
105Dic83—21no—
106Dic83—22no—
107Dic83—41no—
108Dic83—41no—
109Dic83—82no—
110Dic83#9912yescomplemented
111C2×C83—22no—
112C2×C83—21no—
113C2×C83—21no—
114C2×C83—22no—
115C2×C83—42no—
116C2×C83#38011yescharacteristic
117C2×C83C2×#9911yescharacteristic
118C2×C83#41011yescharacteristic
119#1799—831nomaximal, Sylow
120C83#179911yescharacteristic, complemented, Sylow
121C2×C4×D4—831no—
122C2×#99—831no—
123C2×#99D8311yescharacteristic
124#380—832no—
125#342—832no—
126C22×D4C2×D8311yescharacteristic
127C23×C4—831no—
128C23×C4—831no—
129C4×D4—1662no—
130C4×D4—1662no—
131C2×C4⋊C4—831no—
132C2×C4⋊C4—1662no—
133C2×C22⋊C4—831no—
134C2×C22⋊C4—831no—
135C2×C22⋊C4—832no—
136C2×C22⋊C4C2×D8312yes—
137C2×C42—831no—
138#99—22no—
139#99—1662no—
140#95—1662no—
141C24C4×D8311yescharacteristic
142C24C22×D8311yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4Dic16612yes—
146C2×D4C22⋊D8312yes—
147C22×C4—22no—
148C22×C4—3322no—
149C22×C4—3322no—
150C22×C4—831no—
151C22×C4—832no—
152C22×C4—831no—
153C22×C4—831no—
154C22×C4—831no—
155C22×C4—832no—
156C22×C4—1662no—
157C22×C4—1661no—
158C22×C4—1661no—
159C22×C4C4×D8311yescharacteristic
160C4⋊C4—3324no—
161C4⋊C4—1662no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—1662no—
165C22⋊C4—1662no—
166C22⋊C4—1662no—
167C22⋊C4—1662no—
168C42—1661no—
169C42—1661no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23Dic83⋊C412yescomplemented
177C23C2×C4×D8311yescharacteristic
178C23D4×D8312yes—
179C23C2×C22⋊D8311yescharacteristic
180C23C2×Dic16611yescharacteristic
181C23#1305058912yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—3322no—
190C2×C4—3322no—
191C2×C4—3321no—
192C2×C4—3321no—
193C2×C4—3322no—
194C2×C4—3322no—
195C2×C4—3322no—
196C2×C4—3322no—
197C2×C4—3321no—
198C2×C4—831no—
199C2×C4—831no—
200C2×C4—832no—
201C2×C4—1661no—
202C2×C4—1661no—
203C2×C4—1664no—
204C2×C4—1662no—
205C2×C4Dic83⋊C412yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C22⋊C4×D8311yescharacteristic
219C22C2×Dic83⋊C411yescharacteristic
220C22#1458174811yescharacteristic
221C22#1458176412yes—
222C22#1458176912yes—
223C4—22no—
224C4—82no—
225C4—3321no—
226C4—3321no—
227C4—832no—
228C4—6642no—
229C4—1661no—
230C4—1662no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2#1912755911yescharacteristic
237C2#99×D8311yescharacteristic
238C2#1912767311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC23×C83C22×C4
FrattiniC24C22×D83
FittingC2×#99×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC22×D4×C83C22
cosocleC24×C83C23
hypercenterC2×#99D83
hypocenterC83#1799
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #19127559C2semidirect
4. #19127467C2semidirect
6. C23×Dic83C4semidirect
10. C2×C4⋊Dic83C4semidirect
12. C2×C22⋊Dic83C4semidirect
15. C2×C4×Dic83C4semidirect
56. C23×C83C4⋊C4semidirect
69. C2×C4×C83C4⋊C4semidirect
110. Dic83#99semidirect
120. C83#1799semidirect
176. C23Dic83⋊C4semidirect
205. C2×C4Dic83⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic832
C2×#145817072
#191275592
#191274672
C2×#99×C832
#179983