Finite Group Databasebeta

← #13122636

Subgroups — #13122636

Order 1664.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#398C211yesmaximal, characteristic
2#11718646C212yesmaximal
3#11718644C212yesmaximal
4#11718640C211yesmaximal, characteristic
5#11718639C212yesmaximal
6#11718637C211yesmaximal, characteristic
7#11718317C212yesmaximal
8#11718313C212yesmaximal
9#11718308C212yesmaximal
10C22×Dic26C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic13C2212yes—
15C2×C4⋊Dic13C2212yes—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C2×C4×Dic13C2212yes—
23C13×#95C2211yescharacteristic
24C13×#95C2212yes—
25#88071C2212yes—
26#88071C2211yescharacteristic
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×Dic26—42no—
41C2×Dic26—41no—
42C13×C4⋊C4—24no—
43C13×C4⋊C4—41no—
44C13×C4⋊C4—41no—
45C4⋊Dic13—42no—
46C4⋊Dic13—41no—
47C4⋊Dic13—42no—
48#6101—42no—
49#6101—42no—
50#6101—42no—
51#6101Q818yescomplemented
52C4×Dic13—22no—
53C4×Dic13—42no—
54#2792—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—22no—
67C2×C4×C13C2×Q814yes—
68C2×C4×C13#4112yes—
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×Dic13C2×Q814yes—
80C2×Dic13C2×Q814yes—
81Dic26—44no—
82#398—132no—
83#398D1311yescharacteristic
84#395—131no—
85#395—132no—
86#389—132no—
87#389—132no—
88#387—132no—
89#387—132no—
90#384—131no—
91C22×C13C22×Q812yes—
92C22×C13C2×#4111yescharacteristic
93C22×C13H(5,𝔽2)11yescharacteristic
94C22×C13H(5,𝔽2)12yes—
95C22×C132−1+411yescharacteristic
96C4×C13—22no—
97C4×C13—24no—
98C4×C13—42no—
99C4×C13—41no—
100C4×C13—41no—
101Dic13—24no—
102Dic13—24no—
103Dic13—42no—
104Dic13—42no—
105C22×Q8—131no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—131no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4C2×D1312yes—
114C2×C4⋊C4C2×D1311yescharacteristic
115C2×C4⋊C4C2×D1311yescharacteristic
116C2×C42—131no—
117C2×C42—132no—
118#95—131no—
119#95—132no—
120#95—132no—
121#95—132no—
122#95—132no—
123#95—132no—
124#95C2×D1312yes—
125#95C2×D1311yescharacteristic
126C2×C13#53911yescharacteristic
127C2×C13#54412yes—
128C2×C13#55412yes—
129C2×C13Q8211yescharacteristic
130C2×C13#56011yescharacteristic
131C2×Q8—521no—
132C2×Q8—522no—
133C22×C4—132no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4C22×D1312yes—
138C22×C4C22×D1311yescharacteristic
139C22×C4C22×D1311yescharacteristic
140C22×C4C22×D1311yescharacteristic
141C22×C4C22×D1312yes—
142C4⋊C4—24no—
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—138no—
146C4⋊C4—522no—
147C4⋊C4—522no—
148C4⋊C4—522no—
149C4⋊C4—521no—
150C4⋊C4—522no—
151C4⋊C4—522no—
152C42—262no—
153C42—522no—
154C13#279211yescharacteristic, complemented, Sylow
155C23C23×D1311yescharacteristic
156Q8—524no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—134no—
169C2×C4—134no—
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—262no—
180C2×C4#612912yes—
181C2×C4Q8×D1314yes—
182C22C2×#612911yescharacteristic
183C22#8825111yescharacteristic
184C22C2×Q8×D1312yes—
185C22#8825612yes—
186C22#8825711yescharacteristic
187C4—22no—
188C4—24no—
189C4—42no—
190C4—41no—
191C4—41no—
192C4—264no—
193C4—264no—
194C4—522no—
195C4—522no—
196C2#1171930711yescharacteristic
197C2#1171934012yes—
198C2#1171937111yescharacteristic
199C2#1171939412yes—
200C2#1171942711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#398C2
hypercenter#398D13
hypocenterC13#2792
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
51. #6101Q8semidirect
154. C13#2792semidirect

Maximal subgroups

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

subgroupindex
C13×#3982
#117186462
#117186442
#117186402
#117186392
#117186372
#117183172
#117183132
#117183082
#279213