Finite Group Databasebeta

← #13119308

Subgroups — #13119308

Order 1664.

708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 181 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×C13×#121C211yesmaximal, characteristic
2C2×#88189C214yesmaximal, complemented
3C22×C4⋊Dic13C211yesmaximal, characteristic, complemented
4#11718882C212yesmaximal, complemented
5C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
6#11718637C212yesmaximal, complemented
7#11718610C214yesmaximal, complemented
8C22×D4×C13C2212yes—
9C22×D4×C13C2211yescharacteristic
10C23×C4×C13C2211yescharacteristic
11C23×Dic13C2212yes—
12C13×#121—24no—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2212yes—
15C2×C22⋊Dic13C2218yes—
16C2×C22⋊Dic13C2212yes—
17#88189—216no—
18C2×C4⋊Dic13—24no—
19C2×C4⋊Dic13C2212yes—
20C2×C4⋊Dic13C2212yes—
21C2×#6101C2218yes—
22C2×C4×Dic13C2212yes—
23#88071C2212yes—
24C24×C13C2312yes—
25C24×C13C2311yescharacteristic
26C2×D4×C13—28no—
27C2×D4×C13—24no—
28C2×D4×C13—22no—
29C2×D4×C13—24no—
30C22×C4×C13—24no—
31C22×C4×C13D414yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2311yescharacteristic
35C22×Dic13—24no—
36C22×Dic13—28no—
37C22×Dic13C2314yes—
38C22×Dic13C2314yes—
39C13×C4⋊C4—22no—
40C13×C22⋊C4—24no—
41C22⋊Dic13—216no—
42C22⋊Dic13D418yescomplemented
43C4⋊Dic13—24no—
44C4⋊Dic13—24no—
45#6101—216no—
46C4×Dic13—24no—
47#2501—131nomaximal, Sylow
48C23×C13—22no—
49C23×C13—22no—
50C23×C13—24no—
51C23×C13—22no—
52C23×C13—24no—
53C23×C13—24no—
54C23×C13C2×D414yes—
55C23×C13C2×D412yes—
56C23×C13C2411yescharacteristic
57D4×C13—48no—
58D4×C13—44no—
59C2×C4×C13—22no—
60C2×C4×C13—28no—
61C2×C4×C13—24no—
62C2×C4×C13—22no—
63C2×C4×C13C2×D412yes—
64C2×C4×C13C2×D412yes—
65C2×C4×C13#4114yes—
66C2×Dic13—24no—
67C2×Dic13—24no—
68C2×Dic13—28no—
69C2×Dic13—24no—
70C2×Dic13—48no—
71C2×Dic13C2×D418yes—
72C2×#123—134no—
73C2×#121D1311yescharacteristic
74C22×C4⋊C4—131no—
75#399—134no—
76#390—132no—
77#384—132no—
78C4×C22⋊C4—131no—
79C22×C13—22no—
80C22×C13—22no—
81C22×C13—28no—
82C22×C13—42no—
83C22×C13—42no—
84C22×C13—42no—
85C22×C13—48no—
86C22×C13#12714yes—
87C22×C13C22×D412yes—
88C22×C13C22×D411yescharacteristic
89C22×C13C2×#4112yes—
90C22×C132−1+412yes—
91C4×C13—22no—
92C4×C13—42no—
93C4×C13#12314yescomplemented
94Dic13—28no—
95Dic13—44no—
96C22×D4C2×D1312yes—
97C22×D4C2×D1311yescharacteristic
98C23×C4—132no—
99C23×C4C2×D1311yescharacteristic
100#123—2616no—
101#121—24no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—132no—
104C2×C4⋊C4—138no—
105C2×C4⋊C4—264no—
106C2×C4⋊C4C2×D1311yescharacteristic
107C2×C22⋊C4—132no—
108C2×C22⋊C4—138no—
109C2×C22⋊C4C2×D1312yes—
110C2×C42—132no—
111#95—132no—
112C2×C13—24no—
113C2×C13—82no—
114C2×C13C2×#12311yescharacteristic
115C2×C13C2×#12711yescharacteristic
116C2×C13#53611yescharacteristic
117C2×C13#54714yes—
118C24C22×D1312yes—
119C24C22×D1311yescharacteristic
120C2×D4—28no—
121C2×D4—24no—
122C2×D4—24no—
123C2×D4—22no—
124C22×C4—24no—
125C22×C4—134no—
126C22×C4—134no—
127C22×C4—268no—
128C22×C4—264no—
129C22×C4C22⋊D1314yes—
130C22×C4C22×D1312yes—
131C22×C4C22×D1311yescharacteristic
132C22×C4C22×D1311yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—2616no—
135C4⋊C4—264no—
136C4⋊C4—264no—
137C22⋊C4—24no—
138C22⋊C4—138no—
139C22⋊C4—2616no—
140C42—264no—
141C13#250111yescharacteristic, complemented, Sylow
142C23—22no—
143C23—22no—
144C23—24no—
145C23—24no—
146C23—24no—
147C23—22no—
148C23D4×D1314yes—
149C23C2×C22⋊D1312yes—
150C23C23×D1311yescharacteristic
151D4—48no—
152D4—44no—
153C2×C4—22no—
154C2×C4—28no—
155C2×C4—24no—
156C2×C4—22no—
157C2×C4—138no—
158C2×C4—264no—
159C2×C4—264no—
160C2×C4—268no—
161C2×C4—264no—
162C2×C4—528no—
163C2×C4#612914yes—
164C2×C4C2×C22⋊D1312yes—
165C2×C4C2×C22⋊D1312yes—
166C22—22no—
167C22—22no—
168C22—28no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—48no—
173C22#8819414yes—
174C22C2×D4×D1312yes—
175C22C2×#612912yes—
176C22#8825712yes—
177C22C22×C22⋊D1311yescharacteristic
178C4—22no—
179C4—42no—
180C4—268no—
181C4—524no—
182C4#8818914yescomplemented
183C2—24no—
184C2—82no—
185C2#1171931614yes—
186C2C2×#8818911yescharacteristic
187C2C2×#8819411yescharacteristic
188C2#1171953011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2501
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#88189C2semidirect
3. C22×C4⋊Dic13C2semidirect
4. #11718882C2semidirect
5. C4×C22⋊Dic13C2semidirect
6. #11718637C2semidirect
7. #11718610C2semidirect
42. C22⋊Dic13D4semidirect
93. C4×C13#123semidirect
141. C13#2501semidirect
182. C4#88189semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881892
C22×C4⋊Dic132
#117188822
C4×C22⋊Dic132
#117186372
#117186102
#250113