Finite Group Databasebeta

← #13122827

Subgroups — #13122827

Order 1664.

344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C13×#389C211yesmaximal, characteristic
2#11718647C212yesmaximal
3#11718643C212yesmaximal
4#11718642C212yesmaximal
5#11718639C212yesmaximal
6#11718589C211yesmaximal, characteristic
7#11718589C211yesmaximal, characteristic
8#11718320C212yesmaximal
9#11718316C212yesmaximal
10C2×C13×C4⋊C4C2212yes—
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C42×C13C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2212yes—
21C13×#95C2212yes—
22#88071C2212yes—
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C13×C4⋊C4—22no—
41C13×C4⋊C4—24no—
42C13×C4⋊C4—41no—
43C42×C13—41no—
44C4⋊Dic13—22no—
45C4⋊Dic13—22no—
46C4⋊Dic13—41no—
47C4⋊Dic13—41no—
48#6101—24no—
49#6101—24no—
50C4×Dic13—42no—
51#2810—131nomaximal, Sylow
52C23×C13C2411yescharacteristic
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13#4112yes—
66C2×C4×C13#4112yes—
67C2×C4×C13#4112yes—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80#400—132no—
81#400—132no—
82#400—132no—
83#389—131no—
84#389—131no—
85#389D1311yescharacteristic
86#387—132no—
87#387—132no—
88#387—132no—
89C22×C13C2×#4111yescharacteristic
90C22×C13C2×#4111yescharacteristic
91C22×C13C2×#4111yescharacteristic
92C22×C13H(5,𝔽2)11yescharacteristic
93C22×C132−1+411yescharacteristic
94C22×C132−1+411yescharacteristic
95C22×C132−1+411yescharacteristic
96C4×C13—22no—
97C4×C13—22no—
98C4×C13—22no—
99C4×C13—42no—
100C4×C13—42no—
101Dic13—42no—
102Dic13—42no—
103Dic13—42no—
104Dic13—42no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—131no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—131no—
110C2×C4⋊C4—131no—
111C2×C4⋊C4C2×D1312yes—
112C2×C4⋊C4C2×D1311yescharacteristic
113C2×C4⋊C4C2×D1311yescharacteristic
114C2×C42—132no—
115C2×C42C2×D1311yescharacteristic
116#95—132no—
117#95—132no—
118#95—132no—
119#95—132no—
120#95—132no—
121#95—132no—
122#95—132no—
123#95—132no—
124#95—132no—
125#95C2×D1312yes—
126C2×C13#53911yescharacteristic
127C2×C13#53911yescharacteristic
128C2×C13#53911yescharacteristic
129C2×C13#55611yescharacteristic
130C2×C13#55611yescharacteristic
131C2×C13#55611yescharacteristic
132C2×C13#56411yescharacteristic
133C22×C4—132no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4C22×D1312yes—
138C22×C4C22×D1312yes—
139C22×C4C22×D1311yescharacteristic
140C22×C4C22×D1311yescharacteristic
141C22×C4C22×D1311yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—264no—
146C4⋊C4—262no—
147C4⋊C4—264no—
148C4⋊C4—262no—
149C4⋊C4—521no—
150C4⋊C4—521no—
151C42—41no—
152C42—522no—
153C13#281011yescharacteristic, complemented, Sylow
154C23C23×D1311yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4#612712yes—
180C2×C4#612912yes—
181C2×C4#613112yes—
182C22C2×#612711yescharacteristic
183C22C2×#612911yescharacteristic
184C22#8825111yescharacteristic
185C22C2×#613111yescharacteristic
186C22#8825411yescharacteristic
187C22#8825711yescharacteristic
188C22#8825711yescharacteristic
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—522no—
195C4—522no—
196C4—522no—
197C4—522no—
198C2#1171922011yescharacteristic
199C2#1171924711yescharacteristic
200C2#1171928911yescharacteristic
201C2#1171930711yescharacteristic
202C2#1171935011yescharacteristic
203C2C13⋊#56411yescharacteristic
204C2#1171943711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#389C2
hypercenter#389D13
hypocenterC13#2810
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
153. C13#2810semidirect

Maximal subgroups

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

subgroupindex
C13×#3892
#117186472
#117186432
#117186422
#117186392
#117185892
#117183202
#117183162
#281013