Finite Group Databasebeta

← #13120241

Subgroups — #13120241

Order 1664.

412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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#11718640C212yesmaximal
3#11718640C211yesmaximal, characteristic
4C4⋊C4×Dic13C212yesmaximal
5#11718635C211yesmaximal, characteristic
6#11718633C212yesmaximal
7#11718315C212yesmaximal
8#11718314C212yesmaximal
9#11718307C212yesmaximal
10C22×Dic26C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic13C2212yes—
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×C4×Dic13C2212yes—
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C13×#95C2212yes—
23C13×#95C2211yescharacteristic
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×Dic26—22no—
41C2×Dic26—24no—
42C2×Dic26—41no—
43C2×Dic26—41no—
44C2×Dic26—41no—
45C13×C4⋊C4—24no—
46C13×C4⋊C4—41no—
47C13×C4⋊C4—41no—
48C4⋊Dic13Q818yescomplemented
49#6101—24no—
50#6101—42no—
51#6101—42no—
52C4×Dic13—24no—
53C4×Dic13—41no—
54C4×Dic13—42no—
55#2586—131nomaximal, Sylow
56C23×C13C2411yescharacteristic
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13C2×Q814yes—
69C2×C4×C13#4112yes—
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—
81C2×Dic13#4114yes—
82Dic26—44no—
83Dic26—44no—
84#398D1311yescharacteristic
85#395—131no—
86#395—132no—
87#391—131no—
88#391—132no—
89#389—132no—
90#387—132no—
91#387—132no—
92C4×C4⋊C4—132no—
93C22×C13C22×Q812yes—
94C22×C13C2×#4111yescharacteristic
95C22×C13C2×#4112yes—
96C22×C13H(5,𝔽2)11yescharacteristic
97C22×C13H(5,𝔽2)11yescharacteristic
98C4×C13—24no—
99C4×C13—22no—
100C4×C13—42no—
101C4×C13—41no—
102C4×C13—41no—
103Dic13—24no—
104Dic13—24no—
105Dic13—24no—
106Dic13—42no—
107C22×Q8—131no—
108C22×Q8—131no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4C2×D1312yes—
114C2×C4⋊C4C2×D1311yescharacteristic
115C2×C4⋊C4C2×D1311yescharacteristic
116C2×C42—132no—
117C2×C42—131no—
118C2×C42—132no—
119#95—132no—
120#95—132no—
121#95—131no—
122#95—132no—
123#95—132no—
124#95—132no—
125#95—132no—
126#95C2×D1311yescharacteristic
127#95C2×D1312yes—
128C2×C13#53312yes—
129C2×C13#53811yescharacteristic
130C2×C13#55111yescharacteristic
131C2×C13#55412yes—
132C2×C13Q8211yescharacteristic
133C2×Q8—264no—
134C2×Q8—262no—
135C2×Q8—521no—
136C2×Q8—521no—
137C2×Q8—521no—
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—138no—
151C4⋊C4—264no—
152C4⋊C4—522no—
153C4⋊C4—522no—
154C42—264no—
155C42—521no—
156C42—522no—
157C13#258611yescharacteristic, complemented, Sylow
158C23C23×D1311yescharacteristic
159Q8—524no—
160Q8—524no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—134no—
173C2×C4—134no—
174C2×C4—134no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4#612912yes—
185C2×C4Q8×D1314yes—
186C22C2×#612911yescharacteristic
187C22#8825111yescharacteristic
188C22C2×Q8×D1312yes—
189C22#41×D1312yes—
190C22#8825611yescharacteristic
191C4—22no—
192C4—24no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—264no—
197C4—264no—
198C4—264no—
199C4—522no—
200C2#1171932211yescharacteristic
201C2#1171932712yes—
202C2#1171936411yescharacteristic
203C2#1171939512yes—
204C2#1171942711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#398C2
hypercenter#398D13
hypocenterC13#2586
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
48. C4⋊Dic13Q8semidirect
157. C13#2586semidirect

Maximal subgroups

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

subgroupindex
C13×#3982
#117186402
C4⋊C4×Dic132
#117186352
#117186332
#117183152
#117183142
#117183072
#258613