Finite Group Databasebeta

← #24913340

Subgroups — #24913340

Order 10624.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×Dic166C211yesmaximal, characteristic
2#19127640C212yesmaximal
3#19127639C212yesmaximal
4#19127632C212yesmaximal
5#19127621C212yesmaximal
6#19127582C214yesmaximal
7#19127569C211yesmaximal, characteristic
8C2×#125×C83C211yesmaximal, characteristic
9C22×Dic166C2211yescharacteristic
10C4×Dic166—24no—
11C2×C4⋊Dic83C2211yescharacteristic
12C2×Dic83⋊C4C2214yes—
13C2×Dic83⋊C4C2212yes—
14C2×C4×Dic83C2212yes—
15C83⋊#95C2212yes—
16C83⋊#95C2212yes—
17C83⋊#95C2212yes—
18C83⋊#95C2214yes—
19C83⋊#95C2214yes—
20C83⋊#95C2214yes—
21#125×C83—24no—
22C2×C4⋊C4×C83C2212yes—
23C2×C4⋊C4×C83C2212yes—
24C2×C4⋊C4×C83C2211yescharacteristic
25C2×C4⋊C4×C83C2211yescharacteristic
26C2×C42×C83C2211yescharacteristic
27C2×Dic166—22no—
28C2×Dic166—24no—
29C22×Dic83C2314yes—
30C22×Dic83C2312yes—
31C22×Dic83C2312yes—
32C4⋊Dic83—22no—
33Dic83⋊C4—24no—
34Dic83⋊C4—28no—
35C4×Dic83—24no—
36C22×C4×C83C2312yes—
37C22×C4×C83C2312yes—
38C22×C4×C83C2311yescharacteristic
39C22×C4×C83C2311yescharacteristic
40C22×C4×C83C2311yescharacteristic
41C4⋊C4×C83—24no—
42C4⋊C4×C83—22no—
43C4⋊C4×C83—22no—
44C4⋊C4×C83—24no—
45C42×C83D414yes—
46C23×C83C2411yescharacteristic
47C2×C4×C83—22no—
48C2×C4×C83—22no—
49C2×C4×C83—22no—
50C2×C4×C83—22no—
51C2×C4×C83—22no—
52C2×C4×C83—24no—
53C2×C4×C83—24no—
54C2×C4×C83C2×D412yes—
55C2×C4×C83C2×D412yes—
56C2×C4×C83C2×D412yes—
57C2×Dic83—22no—
58C2×Dic83—22no—
59C2×Dic83—22no—
60C2×Dic83—24no—
61C2×Dic83—24no—
62C2×Dic83—24no—
63C2×Dic83—24no—
64C2×Dic83#4114yes—
65Dic166—28no—
66C22×C83C22×D411yescharacteristic
67C22×C83C2×#4112yes—
68C22×C832−1+412yes—
69C22×C832−1+412yes—
70C4×C83—22no—
71C4×C83—22no—
72C4×C83—22no—
73C4×C83—42no—
74C4×C83—42no—
75Dic83—24no—
76Dic83—42no—
77Dic83—44no—
78C2×C83#52511yescharacteristic
79C2×C83#53611yescharacteristic
80C2×C83#53611yescharacteristic
81C2×C83#54114yes—
82#2634—831nomaximal, Sylow
83C83#263411yescharacteristic, complemented, Sylow
84C2×#125D8311yescharacteristic
85C2×C4×Q8—831no—
86#400—832no—
87#400—832no—
88#398—832no—
89#395—832no—
90#387—834no—
91#383—831no—
92C22×Q8—831no—
93#125—24no—
94C4×Q8—1664no—
95C2×C4⋊C4—832no—
96C2×C4⋊C4—831no—
97C2×C4⋊C4—834no—
98C2×C4⋊C4C2×D8312yes—
99C2×C4⋊C4C2×D8312yes—
100C2×C4⋊C4C2×D8311yescharacteristic
101C2×C4⋊C4C2×D8311yescharacteristic
102C2×C42—832no—
103C2×C42C2×D8311yescharacteristic
104#95—832no—
105#95—832no—
106#95—832no—
107#95—834no—
108#95—834no—
109#95—834no—
110C2×Q8—1664no—
111C2×Q8—1662no—
112C22×C4—832no—
113C22×C4—834no—
114C22×C4—832no—
115C22×C4C22×D8312yes—
116C22×C4C22×D8312yes—
117C22×C4C22×D8311yescharacteristic
118C22×C4C22×D8311yescharacteristic
119C22×C4C22×D8311yescharacteristic
120C4⋊C4—24no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—1668no—
125C4⋊C4—1664no—
126C4⋊C4—1662no—
127C42—1664no—
128C42C22⋊D8314yes—
129C23C23×D8311yescharacteristic
130Q8—1668no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—24no—
138C2×C4—834no—
139C2×C4—1662no—
140C2×C4—1664no—
141C2×C4—1664no—
142C2×C4—1664no—
143C2×C4—1664no—
144C2×C4—1662no—
145C2×C4—1662no—
146C2×C4C2×C22⋊D8312yes—
147C2×C4C2×C22⋊D8312yes—
148C2×C4C2×C22⋊D8312yes—
149C22C22×C22⋊D8311yescharacteristic
150C22#41×D8312yes—
151C22#1458183912yes—
152C22#1458184012yes—
153C4—22no—
154C4—22no—
155C4—22no—
156C4—42no—
157C4—42no—
158C4—3322no—
159C4—3324no—
160C4—1664no—
161C2#1912820811yescharacteristic
162C2#1912827211yescharacteristic
163C2#1912827511yescharacteristic
164C2#1912831014yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
FittingC2×#125×C83C2
hypercenterC2×#125D83
hypocenterC83#2634
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
83. C83#2634semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic1662
#191276402
#191276392
#191276322
#191276212
#191275822
#191275692
C2×#125×C832
#263483