Finite Group Databasebeta

← #24905343

Subgroups — #24905343

Order 10624.

276 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 89 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#19127561C211yesmaximal, characteristic
2C2×C83⋊#95C211yesmaximal, characteristic
3C2×C22⋊C8×C83C211yesmaximal, characteristic
4C23×Dic83—21no—
5C2×C4⋊Dic83C412yescomplemented
6C2×C22⋊Dic83—21no—
7C83⋊#95—21no—
8C83⋊#95—21no—
9C83⋊#95C412yescomplemented
10C23×C4×C83C2211yescharacteristic
11C22×C8×C83—21no—
12C22⋊C8×C83—21no—
13C22⋊C8×C83C412yescomplemented
14C22×Dic83—24no—
15C22×Dic83—22no—
16C22×Dic83—22no—
17C22×Dic83—42no—
18C22×Dic83—41no—
19C22×Dic83—41no—
20C4⋊Dic83—42no—
21C22⋊Dic83—41no—
22C22⋊Dic83—41no—
23C24×C83D411yescharacteristic
24C22×C4×C83—42no—
25C22×C4×C83C2×C411yescharacteristic
26C22×C4×C83C2×C411yescharacteristic
27C22×C4×C83C2×C411yescharacteristic
28C22×C4×C83D411yescharacteristic
29C22×C4×C83D411yescharacteristic
30C22×C4×C83Q811yescharacteristic
31C2×C8×C83—22no—
32C2×C8×C83—42no—
33C23×C83—22no—
34C23×C83—22no—
35C23×C83C22⋊C411yescharacteristic
36C23×C83C22⋊C411yescharacteristic
37C23×C83C4⋊C411yescharacteristic
38C23×C83D811yescharacteristic
39C23×C83SD1611yescharacteristic
40C23×C83SD1611yescharacteristic
41C23×C83Q1611yescharacteristic
42C2×C4×C83—22no—
43C2×C4×C83—22no—
44C2×C4×C83—41no—
45C2×C4×C83—41no—
46C2×C4×C83—41no—
47C2×C4×C83—41no—
48C2×C4×C83C4211yescharacteristic
49C2×C4×C83C22⋊C411yescharacteristic
50C2×C4×C83C4⋊C411yescharacteristic
51C2×C4×C83C4⋊C411yescharacteristic
52C2×Dic83—24no—
53C2×Dic83—44no—
54C2×Dic83—44no—
55C2×Dic83—42no—
56C2×Dic83—42no—
57C2×Dic83—42no—
58C2×Dic83—42no—
59C2×Dic83—42no—
60C8×C83—42no—
61C22×C83—22no—
62C22×C83—22no—
63C22×C83—22no—
64C22×C83—22no—
65C22×C83—21no—
66C22×C83—21no—
67C22×C83—21no—
68C22×C83—21no—
69C22×C83#9511yescharacteristic
70C22×C83#9912yes—
71C22×C83#10211yescharacteristic
72C22×C83#10211yescharacteristic
73C22×C83#10311yescharacteristic
74C22×C83#10311yescharacteristic
75C22×C83#10412yes—
76C22×C83#10611yescharacteristic
77C22×C83#10711yescharacteristic
78C4×C83—21no—
79C4×C83—21no—
80C4×C83—21no—
81C4×C83—21no—
82Dic83—44no—
83Dic83—82no—
84C2×C83—21no—
85C2×C83—21no—
86C2×C83—21no—
87C2×C83—21no—
88C2×C83#32712yes—
89C2×C83#32812yes—
90C2×C83#33911yescharacteristic
91C2×C83#34011yescharacteristic
92C2×C83#34211yescharacteristic
93#1294—831nomaximal, Sylow
94C83#129411yescharacteristic, complemented, Sylow
95C2×C22⋊C8D8311yescharacteristic
96#380—831no—
97C2×#95—831no—
98C23×C4—1661no—
99C23×C4C2×D8311yescharacteristic
100C22×C8—21no—
101C2×C4⋊C4—832no—
102C2×C22⋊C4—1661no—
103C22⋊C8—21no—
104C22⋊C8Dic8312yescomplemented
105#95—832no—
106#95—1661no—
107#95—1661no—
108C24D33211yescharacteristic
109C22×C4—42no—
110C22×C4—3322no—
111C22×C4—3321no—
112C22×C4—3321no—
113C22×C4—1662no—
114C22×C4—1664no—
115C22×C4—1662no—
116C22×C4Dic16611yescharacteristic
117C22×C4C4×D8311yescharacteristic
118C22×C4C4×D8311yescharacteristic
119C22×C4C2×Dic8311yescharacteristic
120C22×C4C22⋊D8311yescharacteristic
121C22×C4C22⋊D8311yescharacteristic
122C2×C8—22no—
123C2×C8—42no—
124C4⋊C4—3322no—
125C22⋊C4—3321no—
126C22⋊C4—3321no—
127C23—22no—
128C23—22no—
129C23(C2×D83)⋊C411yescharacteristic
130C23(C2×D83)⋊C411yescharacteristic
131C23C4⋊Dic8311yescharacteristic
132C23D66411yescharacteristic
133C23#1305057911yescharacteristic
134C23#1305057911yescharacteristic
135C23Dic33211yescharacteristic
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—3324no—
143C2×C4—3324no—
144C2×C4—3322no—
145C2×C4—3322no—
146C2×C4—3322no—
147C2×C4—3322no—
148C2×C4—3322no—
149C2×C4—1664no—
150C2×C4C4×Dic8311yescharacteristic
151C2×C4C22⋊Dic8311yescharacteristic
152C2×C4Dic83⋊C411yescharacteristic
153C2×C4Dic83⋊C411yescharacteristic
154C8—42no—
155C22—22no—
156C22—22no—
157C22—22no—
158C22—22no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22C83⋊#9511yescharacteristic
164C22#1458170612yes—
165C22#1458171411yescharacteristic
166C22#1458171411yescharacteristic
167C22#1458171711yescharacteristic
168C22#1458171711yescharacteristic
169C22#1458171812yes—
170C22#1458172411yescharacteristic
171C22#1458172611yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—3324no—
177C4—6642no—
178C2—21no—
179C2—21no—
180C2—21no—
181C2—21no—
182C2#1912743612yes—
183C2#1912743912yes—
184C2#1912746211yescharacteristic
185C2#1912746411yescharacteristic
186C2#1912746711yescharacteristic
subgroupG/H
centerC23(C2×D83)⋊C4
commutatorC2×C4×C83C42
FrattiniC23×C4C2×D83
FittingC2×C22⋊C8×C83C2
socleC23×C83C22⋊C4
prime radicalC24×C83D4
cosocleC23×C4×C83C22
hypercenterC2×C22⋊C8D83
hypocenterC83#1294
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Dic83C4semidirect
9. C83⋊#95C4semidirect
13. C22⋊C8×C83C4semidirect
94. C83#1294semidirect
104. C22⋊C8Dic83semidirect