Finite Group Databasebeta

← #13120002

Subgroups — #13120002

Order 1664.

532 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 157 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×D4×C13C211yesmaximal, characteristic
2C2×#88124C211yesmaximal, characteristic, complemented
3#11718883C212yesmaximal
4#11718873C212yesmaximal, complemented
5#11718873C212yesmaximal, complemented
6#11718643C212yesmaximal, complemented
7#11718606C214yesmaximal, complemented
8C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
9C22×D4×C13C2211yescharacteristic
10C23×C4×C13C2212yes—
11C4×D4×C13—24no—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C22⋊C4C2212yes—
14C2×C42×C13C2211yescharacteristic
15C2×C22⋊Dic13C2214yes—
16C2×C22⋊Dic13C2214yes—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2212yes—
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2212yes—
23#88124—24no—
24#88071C2212yes—
25#88071C2214yes—
26#88071C2214yes—
27C24×C13C2312yes—
28C2×D4×C13—24no—
29C2×D4×C13—22no—
30C22×C4×C13—24no—
31C22×C4×C13—24no—
32C22×C4×C13—24no—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×Dic13C2314yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C13×C4⋊C4—22no—
41C13×C22⋊C4—24no—
42C42×C13D414yes—
43C22⋊Dic13—28no—
44C22⋊Dic13—44no—
45C4⋊Dic13—22no—
46C4⋊Dic13—22no—
47C4⋊Dic13—24no—
48#6101—24no—
49#6101—24no—
50C4×Dic13—42no—
51#2562—131nomaximal, Sylow
52C23×C13—22no—
53C23×C13—22no—
54C23×C13—22no—
55C23×C13—22no—
56C23×C13—22no—
57C23×C13—22no—
58C23×C13#4114yes—
59C23×C13C2411yescharacteristic
60D4×C13—28no—
61C2×C4×C13—22no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—48no—
68C2×C4×C13C2×D412yes—
69C2×C4×C13C2×D412yes—
70C2×C4×C13C2×D412yes—
71C2×C4×C13#4114yes—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—24no—
75C2×Dic13—24no—
76C2×Dic13—24no—
77C2×Dic13—24no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×#125—131no—
81C2×C4×D4D1311yescharacteristic
82#400—132no—
83#394—132no—
84#388—134no—
85#380—132no—
86#380—132no—
87C4×C4⋊C4—131no—
88C22×C13—24no—
89C22×C13—24no—
90C22×C13—24no—
91C22×C13—42no—
92C22×C13—42no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13C22×D411yescharacteristic
96C22×C13C2×#4112yes—
97C22×C13C2×#4112yes—
98C22×C13H(5,𝔽2)11yescharacteristic
99C22×C132−1+411yescharacteristic
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—42no—
103C4×C13#12414yes—
104Dic13—42no—
105Dic13—42no—
106Dic13—44no—
107C22×D4C2×D1311yescharacteristic
108C23×C4C2×D1312yes—
109#125—264no—
110C4×D4—24no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4—131no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4C2×D1311yescharacteristic
117C2×C22⋊C4—134no—
118C2×C22⋊C4—134no—
119C2×C22⋊C4C2×D1312yes—
120C2×C42—132no—
121C2×C42C2×D1311yescharacteristic
122#95—132no—
123#95—134no—
124#95—134no—
125C2×C13—44no—
126C2×C13#52511yescharacteristic
127C2×C13C2×#12411yescharacteristic
128C2×C13#53711yescharacteristic
129C2×C13#55212yes—
130C2×C13#55312yes—
131C24C22×D1312yes—
132C2×D4—24no—
133C2×D4—22no—
134C22×C4—24no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—134no—
138C22×C4—132no—
139C22×C4—132no—
140C22×C4C22×D1312yes—
141C22×C4C22×D1311yescharacteristic
142C22×C4C22×D1311yescharacteristic
143C22×C4C22×D1311yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—264no—
146C4⋊C4—264no—
147C4⋊C4—264no—
148C4⋊C4—262no—
149C4⋊C4—262no—
150C22⋊C4—24no—
151C22⋊C4—268no—
152C22⋊C4—524no—
153C42—522no—
154C42C22⋊D1314yes—
155C13#256211yescharacteristic, complemented, Sylow
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23#612714yes—
163C23C23×D1311yescharacteristic
164D4—28no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—48no—
172C2×C4—264no—
173C2×C4—264no—
174C2×C4—264no—
175C2×C4—264no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4#612914yes—
181C2×C4C2×C22⋊D1312yes—
182C2×C4C2×C22⋊D1312yes—
183C2×C4C2×C22⋊D1312yes—
184C22—24no—
185C22—24no—
186C22—24no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C2×#612712yes—
192C22C2×#612912yes—
193C22#8825611yescharacteristic
194C22#8825711yescharacteristic
195C22C22×C22⋊D1311yescharacteristic
196C4—22no—
197C4—22no—
198C4—42no—
199C4—522no—
200C4—524no—
201C4—522no—
202C4#8819014yes—
203C2—44no—
204C2#1171924612yes—
205C2#1171927012yes—
206C2#1171949611yescharacteristic
207C2C2×#8819011yescharacteristic
208C2#1171953811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C4×D4×C13C2
prime radicalC22×D4×C13C22
hypercenterC2×C4×D4D13
hypocenterC13#2562
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#88124C2semidirect
4. #11718873C2semidirect
5. #11718873C2semidirect
6. #11718643C2semidirect
7. #11718606C2semidirect
8. C4×C4⋊Dic13C2semidirect
155. C13#2562semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C132
C2×#881242
#117188832
#117188732
#117186432
#117186062
C4×C4⋊Dic132
#256213