Finite Group Databasebeta

← #13120205

Subgroups — #13120205

Order 1664.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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×#88141C212yesmaximal
2C13×#398C211yesmaximal, characteristic
3#11718645C212yesmaximal
4#11718644C211yesmaximal, characteristic
5#11718637C211yesmaximal, characteristic
6#11718633C212yesmaximal
7#11718308C212yesmaximal
8#11718307C212yesmaximal
9#11718307C212yesmaximal
10C22×Dic26C2212yes—
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×C4×Dic13C2212yes—
22C2×C4×Dic13C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24#88141—28no—
25C13×#95C2211yescharacteristic
26C13×#95C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C2×Dic26—24no—
42C2×Dic26—24no—
43C2×Dic26Q818yescomplemented
44C13×C4⋊C4—24no—
45C13×C4⋊C4—41no—
46C13×C4⋊C4—41no—
47C4⋊Dic13—41no—
48C4⋊Dic13—41no—
49#6101—24no—
50#6101—24no—
51#6101—24no—
52#6101—24no—
53#6101—42no—
54C4×Dic13—24no—
55C4×Dic13—24no—
56C4×Dic13D414yes—
57#2582—131nomaximal, Sylow
58C23×C13C2411yescharacteristic
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13C2×D412yes—
71C2×C4×C13C2×Q814yes—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13C2×D414yes—
81C2×Dic13C2×Q814yes—
82C2×Dic13C2×Q814yes—
83C2×Dic13#4114yes—
84Dic26—216no—
85C2×C4×Q8—132no—
86#398—131no—
87#398—132no—
88#398D1311yescharacteristic
89#391—132no—
90#391—132no—
91#389—132no—
92#389—132no—
93#384—131no—
94C22×C13C22×D411yescharacteristic
95C22×C13C22×Q812yes—
96C22×C13C2×#4112yes—
97C22×C13H(5,𝔽2)11yescharacteristic
98C22×C132−1+411yescharacteristic
99C4×C13—24no—
100C4×C13—22no—
101C4×C13—42no—
102C4×C13—41no—
103C4×C13—41no—
104Dic13—24no—
105Dic13—42no—
106Dic13—42no—
107Dic13C22⋊Q818yes—
108C22×Q8—132no—
109C4×Q8—268no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4—132no—
115C2×C4⋊C4—131no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4C2×D1312yes—
118C2×C4⋊C4C2×D1311yescharacteristic
119C2×C4⋊C4C2×D1311yescharacteristic
120C2×C42—131no—
121C2×C42—132no—
122C2×C42—132no—
123#95—132no—
124#95—132no—
125#95—132no—
126#95—131no—
127#95—132no—
128#95C2×D1312yes—
129#95C2×D1311yescharacteristic
130C2×C13C2×C22⋊Q812yes—
131C2×C13#53711yescharacteristic
132C2×C13#55712yes—
133C2×C13Q8211yescharacteristic
134C2×C13#55911yescharacteristic
135C2×Q8—138no—
136C2×Q8—264no—
137C2×Q8—264no—
138C22×C4—132no—
139C22×C4—132no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4C22×D1311yescharacteristic
143C22×C4C22×D1311yescharacteristic
144C22×C4C22×D1312yes—
145C22×C4C22×D1311yescharacteristic
146C22×C4C22×D1312yes—
147C4⋊C4—24no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—264no—
151C4⋊C4—264no—
152C4⋊C4—264no—
153C4⋊C4—264no—
154C4⋊C4—522no—
155C4⋊C4—521no—
156C4⋊C4—521no—
157C42—134no—
158C42—264no—
159C42—264no—
160C13#258211yescharacteristic, complemented, Sylow
161C23C23×D1311yescharacteristic
162Q8—2616no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—134no—
175C2×C4—134no—
176C2×C4—134no—
177C2×C4—134no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4D4×D1312yes—
187C2×C4Q8×D1314yes—
188C22C2×D4×D1311yescharacteristic
189C22#8825111yescharacteristic
190C22C2×Q8×D1312yes—
191C22#41×D1312yes—
192C22#8825711yescharacteristic
193C4—22no—
194C4—24no—
195C4—42no—
196C4—41no—
197C4—41no—
198C4—138no—
199C4—264no—
200C4—522no—
201C4—522no—
202C2#1171930211yescharacteristic
203C2D13×C22⋊Q812yes—
204C2#1171936911yescharacteristic
205C2#1171939012yes—
206C2#1171942711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#398C2
hypercenter#398D13
hypocenterC13#2582
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. C2×Dic26Q8semidirect
160. C13#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#881412
C13×#3982
#117186452
#117186442
#117186372
#117186332
#117183082
#117183072
#258213