Finite Group Databasebeta

← #13119125

Subgroups — #13119125

Order 1664.

512 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 153 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×#88180C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic
3C13×#381C211yesmaximal, characteristic
4#11718611C212yesmaximal
5#11718604C212yesmaximal
6#11718322C212yesmaximal, complemented
7#11718320C212yesmaximal, complemented
8#11718314C214yesmaximal, complemented
9C23×C4×C13C2211yescharacteristic
10C23×Dic13C2211yescharacteristic
11C23×Dic13C2211yescharacteristic
12C2×C13×C22⋊C4C2212yes—
13C2×C22⋊Dic13C2212yes—
14#88180—24no—
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2214yes—
18C2×#6101—24no—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×C4×Dic13C2212yes—
22C13×#95C2212yes—
23C13×#95C2212yes—
24#88071C2214yes—
25#88071C2214yes—
26#88071C2214yes—
27C24×C13C2311yescharacteristic
28C22×C4×C13—24no—
29C22×C4×C13D414yes—
30C22×C4×C13C2314yes—
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×Dic13—22no—
34C22×Dic13—24no—
35C22×Dic13—22no—
36C22×Dic13—24no—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C13×C22⋊C4—24no—
42C22⋊Dic13—24no—
43C4⋊Dic13—22no—
44C4⋊Dic13—22no—
45C4⋊Dic13—28no—
46#6101—24no—
47#6101—24no—
48C4×Dic13—24no—
49#2484—131nomaximal, Sylow
50C23×C13—22no—
51C23×C13—22no—
52C23×C13C2×D412yes—
53C23×C13#4114yes—
54C23×C13C2411yescharacteristic
55C2×C4×C13—28no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—24no—
59C2×C4×C13—24no—
60C2×C4×C13—24no—
61C2×C4×C13C2×D412yes—
62C2×C4×C13C2×D412yes—
63C2×Dic13—28no—
64C2×Dic13—22no—
65C2×Dic13—22no—
66C2×Dic13—22no—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—24no—
70C2×Dic13—24no—
71C2×Dic13—24no—
72C2×Dic13—44no—
73C2×Dic13#4114yes—
74C2×#117—131no—
75C22×C4⋊C4—131no—
76#400—132no—
77#398—132no—
78#387—134no—
79#385—132no—
80#381—132no—
81#381D1311yescharacteristic
82C22×C13—22no—
83C22×C13—22no—
84C22×C13—28no—
85C22×C13#12314yes—
86C22×C13C22×D411yescharacteristic
87C22×C13C2×#4112yes—
88C22×C13C2×#4112yes—
89C22×C132−1+412yes—
90C4×C13—22no—
91C4×C13—22no—
92C4×C13—44no—
93Dic13—24no—
94Dic13—42no—
95Dic13—42no—
96Dic13—42no—
97C23×C4—131no—
98C23×C4—131no—
99C23×C4C2×D1311yescharacteristic
100#117—264no—
101C2×C4⋊C4—132no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—131no—
104C2×C4⋊C4—131no—
105C2×C4⋊C4—134no—
106C2×C4⋊C4—264no—
107C2×C22⋊C4—132no—
108C2×C22⋊C4C2×D1312yes—
109C2×C42—132no—
110#95—134no—
111#95—134no—
112#95—134no—
113#95C2×D1312yes—
114#95C2×D1312yes—
115C2×C13—24no—
116C2×C13C2×#12311yescharacteristic
117C2×C13#52511yescharacteristic
118C2×C13#53611yescharacteristic
119C2×C13#55214yes—
120C24C22×D1311yescharacteristic
121C22×C4—24no—
122C22×C4—132no—
123C22×C4—132no—
124C22×C4—132no—
125C22×C4—132no—
126C22×C4—264no—
127C22×C4—262no—
128C22×C4—262no—
129C22×C4—264no—
130C22×C4D5214yes—
131C22×C4C22×D1314yes—
132C22×C4C22×D1311yescharacteristic
133C22×C4C22×D1311yescharacteristic
134C4⋊C4—268no—
135C4⋊C4—264no—
136C4⋊C4—264no—
137C4⋊C4—262no—
138C4⋊C4—262no—
139C22⋊C4—24no—
140C22⋊C4—264no—
141C42—264no—
142C13#248411yescharacteristic, complemented, Sylow
143C23—22no—
144C23—22no—
145C23C2×D5212yes—
146C23#612914yes—
147C23C23×D1311yescharacteristic
148C2×C4—28no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—134no—
155C2×C4—268no—
156C2×C4—262no—
157C2×C4—262no—
158C2×C4—262no—
159C2×C4—262no—
160C2×C4—262no—
161C2×C4—264no—
162C2×C4—264no—
163C2×C4—264no—
164C2×C4—524no—
165C2×C4C2×D5212yes—
166C2×C4C2×D5212yes—
167C22—22no—
168C22—22no—
169C22—28no—
170C22#8814014yes—
171C22C22×D5211yescharacteristic
172C22C2×#612912yes—
173C22#41×D1312yes—
174C22#8825712yes—
175C4—22no—
176C4—22no—
177C4—44no—
178C4—264no—
179C4—522no—
180C4—522no—
181C4—522no—
182C2—24no—
183C2C2×#8814011yescharacteristic
184C2#1171922911yescharacteristic
185C2#1171923111yescharacteristic
186C2#1171935514yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC24×C13C23
hypercenter#381D13
hypocenterC13#2484
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #11718322C2semidirect
7. #11718320C2semidirect
8. #11718314C2semidirect
142. C13#2484semidirect

Maximal subgroups

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

subgroupindex
C2×#881802
C22×#61012
C13×#3812
#117186112
#117186042
#117183222
#117183202
#117183142
#248413