Finite Group Databasebeta

← #13120035

Subgroups — #13120035

Order 1664.

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

normal subgroups only

This group has 548 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×#88147C211yesmaximal, characteristic
2C2×#88144C211yesmaximal, characteristic, complemented
3C13×#382C211yesmaximal, characteristic, complemented
4#11718649C211yesmaximal, characteristic
5#11718637C211yesmaximal, characteristic, complemented
6#11718600C211yesmaximal, characteristic
7C4×#6101C211yesmaximal, characteristic, complemented
8#11718337C214yesmaximal, complemented
9#11718329C214yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15C2×#6103C2212yes—
16C2×#6103C2214yes—
17C2×#6103C2214yes—
18C2×C4⋊Dic13C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2214yes—
23C2×C4×Dic13C2211yescharacteristic
24C2×C4×Dic13C2211yescharacteristic
25#88147—24no—
26#88144—24no—
27C13×#95C2214yes—
28#88071C2212yes—
29C23×D13C2312yes—
30C22×C4×C13C2312yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×Dic13C2312yes—
35C22×Dic13C2311yescharacteristic
36C22×Dic13C2311yescharacteristic
37C22×Dic13C2312yes—
38C2×D52—22no—
39C2×D52—22no—
40C2×D52Q814yes—
41C2×C4×D13—24no—
42C2×C4×D13—44no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4—22no—
45C42×C13—22no—
46#6103—24no—
47#6103—28no—
48#6103—44no—
49C4⋊Dic13—22no—
50C4⋊Dic13—24no—
51#6101—24no—
52#6101—24no—
53#6101—44no—
54C4×Dic13—22no—
55C4×Dic13D414yes—
56#2566—131nomaximal, Sylow
57C23×C13C2411yescharacteristic
58C22×D13—22no—
59C22×D13—24no—
60C22×D13—22no—
61C22×D13—24no—
62C22×D13C2×Q814yes—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—24no—
67C2×C4×C13—22no—
68C2×C4×C13—24no—
69C2×C4×C13—22no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×Q812yes—
72C2×C4×C13#4112yes—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—24no—
79C2×Dic13C2×D412yes—
80C2×Dic13C2×D412yes—
81C2×Dic13#4114yes—
82D52—28no—
83C4×D13—48no—
84C2×#125—131no—
85C2×C4×D4—131no—
86#396—134no—
87#390—131no—
88#390—131no—
89#385—134no—
90#384—131no—
91#382D1311yescharacteristic, complemented
92C4×C4⋊C4—131no—
93C22×C13C22×D411yescharacteristic
94C22×C13C22×Q811yescharacteristic
95C22×C13C2×#4111yescharacteristic
96C22×C13C2×#4112yes—
97C22×C13H(5,𝔽2)12yes—
98C2×D13—24no—
99C2×D13—28no—
100C2×D13—42no—
101C2×D13—42no—
102C2×D13—44no—
103C4×C13—42no—
104C4×C13—42no—
105C4×C13—42no—
106C4×C13C22⋊Q814yes—
107Dic13—22no—
108Dic13—22no—
109Dic13—24no—
110Dic13—42no—
111C22×D4—131no—
112C23×C4—132no—
113#125—264no—
114C4×D4—264no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—132no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—134no—
120C2×C4⋊C4C2×D1311yescharacteristic
121C2×C4⋊C4C2×D1311yescharacteristic
122C2×C22⋊C4—132no—
123C2×C22⋊C4—134no—
124C2×C22⋊C4—134no—
125C2×C42—131no—
126C2×C42—131no—
127C2×C42C2×D1311yescharacteristic
128#95—132no—
129#95C2×D1314yes—
130C2×C13C2×C22⋊Q811yescharacteristic
131C2×C13#53211yescharacteristic
132C2×C13#53511yescharacteristic
133C2×C13#55312yes—
134C2×C13#55412yes—
135D13—44no—
136C24—132no—
137C2×D4—134no—
138C2×D4—262no—
139C2×D4—262no—
140C22×C4—131no—
141C22×C4—132no—
142C22×C4—131no—
143C22×C4—132no—
144C22×C4—264no—
145C22×C4—524no—
146C22×C4C22×D1312yes—
147C22×C4C22×D1312yes—
148C22×C4C22×D1312yes—
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—264no—
153C4⋊C4—264no—
154C4⋊C4—264no—
155C4⋊C4—262no—
156C4⋊C4—524no—
157C22⋊C4—264no—
158C22⋊C4—268no—
159C22⋊C4—524no—
160C42—22no—
161C42—134no—
162C42—262no—
163C13#256611yescharacteristic, complemented, Sylow
164C23—134no—
165C23—262no—
166C23—262no—
167C23—264no—
168C23—264no—
169C23C23×D1311yescharacteristic
170D4—268no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—132no—
179C2×C4—132no—
180C2×C4—134no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—264no—
187C2×C4—528no—
188C2×C4#612712yes—
189C2×C4D4×D1312yes—
190C2×C4Q8×D1312yes—
191C22—264no—
192C22—268no—
193C22—524no—
194C22—522no—
195C22—522no—
196C22C2×#612711yescharacteristic
197C22C2×D4×D1311yescharacteristic
198C22C2×Q8×D1311yescharacteristic
199C22#41×D1312yes—
200C22#8825612yes—
201C4—42no—
202C4—42no—
203C4—42no—
204C4—264no—
205C4—262no—
206C4—262no—
207C4—522no—
208C4#8815014yes—
209C2—524no—
210C2C2×#8815011yescharacteristic
211C2#1171923512yes—
212C2#1171937311yescharacteristic
213C2#1171937911yescharacteristic
214C2#1171939512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#382C2
prime radicalC22×D52C22
hypercenter#382D13
hypocenterC13#2566
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#88144C2semidirect
3. C13×#382C2semidirect
5. #11718637C2semidirect
7. C4×#6101C2semidirect
8. #11718337C2semidirect
9. #11718329C2semidirect
91. #382D13semidirect
163. C13#2566semidirect

Maximal subgroups

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

subgroupindex
C2×#881472
C2×#881442
C13×#3822
#117186492
#117186372
#117186002
C4×#61012
#117183372
#117183292
#256613