Finite Group Databasebeta

← #13120317

Subgroups — #13120317

Order 1664.

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

normal subgroups only

This group has 596 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×C13×#121C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic, complemented
3#11718883C212yesmaximal, complemented
4#11718881C212yesmaximal, complemented
5#11718881C212yesmaximal, complemented
6C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
7#11718643C212yesmaximal, complemented
8#11718606C214yesmaximal, complemented
9C22×D4×C13C2212yes—
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C13×#121—24no—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2214yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2214yes—
20C2×#6101—24no—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×C4×Dic13C2212yes—
24#88071C2214yes—
25#88071C2214yes—
26#88071C2212yes—
27C24×C13C2312yes—
28C24×C13C2311yescharacteristic
29C2×D4×C13—24no—
30C2×D4×C13—28no—
31C2×D4×C13—22no—
32C2×D4×C13—42no—
33C22×C4×C13—42no—
34C22×C4×C13D414yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13—22no—
39C22×Dic13—24no—
40C22×Dic13—22no—
41C22×Dic13—42no—
42C22×Dic13C2314yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C13×C4⋊C4—22no—
46C13×C22⋊C4—24no—
47C22⋊Dic13—24no—
48C22⋊Dic13—28no—
49C22⋊Dic13—44no—
50#6101—24no—
51#6101—24no—
52C4×Dic13—42no—
53#2591—131nomaximal, Sylow
54C23×C13—22no—
55C23×C13—22no—
56C23×C13—22no—
57C23×C13—24no—
58C23×C13—24no—
59C23×C13—24no—
60C23×C13C2×D412yes—
61C23×C13#4114yes—
62C23×C13C2411yescharacteristic
63D4×C13—44no—
64D4×C13—48no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—24no—
69C2×C4×C13—44no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D412yes—
72C2×Dic13—28no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—24no—
77C2×Dic13—24no—
78C2×Dic13—24no—
79C2×Dic13—24no—
80C2×Dic13—44no—
81C2×Dic13#4114yes—
82C2×#121D1311yescharacteristic
83C22×C4⋊C4—131no—
84#400—132no—
85#394—132no—
86#388—134no—
87#386—132no—
88#386—132no—
89C4×C22⋊C4—131no—
90C22×C13—22no—
91C22×C13—22no—
92C22×C13—28no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13—42no—
96C22×C13—48no—
97C22×C13#12414yes—
98C22×C13C22×D411yescharacteristic
99C22×C13C2×#4112yes—
100C22×C13C2×#4112yes—
101C22×C13H(5,𝔽2)12yes—
102C4×C13—22no—
103C4×C13—22no—
104C4×C13—42no—
105Dic13—24no—
106Dic13—42no—
107Dic13—44no—
108C22×D4C2×D1312yes—
109C22×D4C2×D1311yescharacteristic
110C23×C4—131no—
111C23×C4—131no—
112C23×C4C2×D1311yescharacteristic
113#121—24no—
114C2×C4⋊C4—132no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—264no—
117C2×C4⋊C4C2×D1311yescharacteristic
118C2×C22⋊C4—132no—
119C2×C22⋊C4—134no—
120C2×C22⋊C4—134no—
121C2×C22⋊C4C2×D1312yes—
122C2×C42—132no—
123#95—132no—
124#95—134no—
125#95—134no—
126C2×C13—24no—
127C2×C13—82no—
128C2×C13#52511yescharacteristic
129C2×C13C2×#12411yescharacteristic
130C2×C13#53411yescharacteristic
131C2×C13#55314yes—
132C24C22×D1312yes—
133C24C22×D1311yescharacteristic
134C2×D4—28no—
135C2×D4—24no—
136C2×D4—22no—
137C2×D4—42no—
138C22×C4—42no—
139C22×C4—132no—
140C22×C4—134no—
141C22×C4—132no—
142C22×C4—264no—
143C22×C4—262no—
144C22×C4—262no—
145C22×C4—522no—
146C22×C4C22⋊D1314yes—
147C22×C4C22×D1312yes—
148C22×C4C22×D1311yescharacteristic
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—264no—
152C4⋊C4—264no—
153C22⋊C4—24no—
154C22⋊C4—268no—
155C22⋊C4—264no—
156C22⋊C4—524no—
157C42—522no—
158C13#259111yescharacteristic, complemented, Sylow
159C23—22no—
160C23—22no—
161C23—24no—
162C23—24no—
163C23—24no—
164C23—22no—
165C23#612914yes—
166C23C2×C22⋊D1312yes—
167C23C23×D1311yescharacteristic
168D4—44no—
169D4—48no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—44no—
175C2×C4—134no—
176C2×C4—268no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—264no—
180C2×C4—264no—
181C2×C4—264no—
182C2×C4—264no—
183C2×C4—262no—
184C2×C4—524no—
185C2×C4C2×C22⋊D1312yes—
186C2×C4C2×C22⋊D1312yes—
187C22—22no—
188C22—22no—
189C22—28no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—48no—
194C22#8819014yes—
195C22C2×#612912yes—
196C22#8825112yes—
197C22#41×D1312yes—
198C22C22×C22⋊D1311yescharacteristic
199C4—22no—
200C4—22no—
201C4—42no—
202C4—264no—
203C4—522no—
204C4—524no—
205C2—24no—
206C2—82no—
207C2#1171930614yes—
208C2C2×#8819011yescharacteristic
209C2#1171950911yescharacteristic
210C2#1171953311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2591
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C22×#6101C2semidirect
3. #11718883C2semidirect
4. #11718881C2semidirect
5. #11718881C2semidirect
6. C4×C22⋊Dic13C2semidirect
7. #11718643C2semidirect
8. #11718606C2semidirect
158. C13#2591semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C22×#61012
#117188832
#117188812
C4×C22⋊Dic132
#117186432
#117186062
#259113