Finite Group Databasebeta

← #13120032

Subgroups — #13120032

Order 1664.

548 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 169 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#11718882C211yesmaximal, characteristic
4#11718882C211yesmaximal, characteristic
5#11718871C214yesmaximal, complemented
6#11718638C211yesmaximal, characteristic, complemented
7#11718637C211yesmaximal, characteristic, complemented
8#11718609C214yesmaximal, complemented
9C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2212yes—
12C4×D4×C13—24no—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2212yes—
15C2×C42×C13C2211yescharacteristic
16C2×C22⋊Dic13C2214yes—
17C2×C22⋊Dic13C2214yes—
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2214yes—
24C2×C4×Dic13C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26#88124—24no—
27#88071C2212yes—
28#88071C2214yes—
29C24×C13C2312yes—
30C2×D4×C13—22no—
31C2×D4×C13—22no—
32C2×D4×C13Q814yes—
33C22×C4×C13—24no—
34C22×C4×C13—44no—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C13×C4⋊C4—22no—
44C13×C22⋊C4—24no—
45C42×C13D414yes—
46C22⋊Dic13—28no—
47C22⋊Dic13—44no—
48C4⋊Dic13—22no—
49C4⋊Dic13—22no—
50C4⋊Dic13—24no—
51#6101—24no—
52#6101—24no—
53#6101—44no—
54C4×Dic13—22no—
55C4×Dic13—22no—
56#2566—131nomaximal, Sylow
57C23×C13—22no—
58C23×C13—24no—
59C23×C13—22no—
60C23×C13—24no—
61C23×C13C2×Q814yes—
62C23×C13C2411yescharacteristic
63D4×C13—28no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—24no—
68C2×C4×C13—48no—
69C2×C4×C13C2×D412yes—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×D412yes—
72C2×C4×C13C2×Q812yes—
73C2×C4×C13#4112yes—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—24no—
81C2×Dic13—24no—
82C2×Dic13—22no—
83C2×Dic13#4114yes—
84C2×#125—131no—
85C2×C4×D4D1311yescharacteristic
86#396—134no—
87#390—131no—
88#390—131no—
89#385—134no—
90#384—131no—
91#382—131no—
92C4×C4⋊C4—131no—
93C22×C13—24no—
94C22×C13—28no—
95C22×C13—42no—
96C22×C13—42no—
97C22×C13—44no—
98C22×C13C22×D411yescharacteristic
99C22×C13C22×Q811yescharacteristic
100C22×C13C2×#4111yescharacteristic
101C22×C13C2×#4112yes—
102C22×C13H(5,𝔽2)12yes—
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—42no—
106C4×C13C22⋊Q814yes—
107Dic13—24no—
108Dic13—42no—
109Dic13—42no—
110Dic13—42no—
111C22×D4C2×D1311yescharacteristic
112C23×C4C2×D1312yes—
113#125—264no—
114C4×D4—24no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—134no—
121C2×C4⋊C4C2×D1311yescharacteristic
122C2×C22⋊C4—134no—
123C2×C22⋊C4—134no—
124C2×C22⋊C4C2×D1312yes—
125C2×C42—131no—
126C2×C42—131no—
127C2×C42C2×D1311yescharacteristic
128#95—132no—
129#95—134no—
130C2×C13—44no—
131C2×C13C2×C22⋊Q811yescharacteristic
132C2×C13#53211yescharacteristic
133C2×C13#53511yescharacteristic
134C2×C13#55312yes—
135C2×C13#55412yes—
136C24C22×D1312yes—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4Dic2614yes—
140C22×C4—24no—
141C22×C4—44no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4C22×D1312yes—
147C22×C4C22×D1311yescharacteristic
148C22×C4C22×D1311yescharacteristic
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—264no—
152C4⋊C4—264no—
153C4⋊C4—264no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—524no—
157C22⋊C4—24no—
158C22⋊C4—268no—
159C22⋊C4—524no—
160C42—262no—
161C42—262no—
162C42C22⋊D1314yes—
163C13#256611yescharacteristic, complemented, Sylow
164C23—22no—
165C23—24no—
166C23—24no—
167C23—22no—
168C23C2×Dic2614yes—
169C23C23×D1311yescharacteristic
170D4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—48no—
176C2×C4—134no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—264no—
182C2×C4—264no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4C2×Dic2612yes—
187C2×C4#612712yes—
188C2×C4C2×C22⋊D1312yes—
189C2×C4C2×C22⋊D1312yes—
190C2×C4C2×C22⋊D1312yes—
191C22—24no—
192C22—28no—
193C22—42no—
194C22—44no—
195C22—42no—
196C22C22×Dic2611yescharacteristic
197C22C2×#612711yescharacteristic
198C22#8825112yes—
199C22#41×D1312yes—
200C22C22×C22⋊D1311yescharacteristic
201C4—22no—
202C4—22no—
203C4—42no—
204C4—264no—
205C4—522no—
206C4—522no—
207C4—522no—
208C4#8817814yes—
209C2—44no—
210C2#1171924412yes—
211C2#1171926312yes—
212C2C2×#8817811yescharacteristic
213C2#1171951011yescharacteristic
214C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C4×D4×C13C2
prime radicalC22×D4×C13C22
hypercenterC2×C4×D4D13
hypocenterC13#2566
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
5. #11718871C2semidirect
6. #11718638C2semidirect
7. #11718637C2semidirect
8. #11718609C2semidirect
9. C4×C4⋊Dic13C2semidirect
163. C13#2566semidirect

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
#117188822
#117188712
#117186382
#117186372
#117186092
C4×C4⋊Dic132
#256613