Finite Group Databasebeta

← #13120958

Subgroups — #13120958

Order 1664.

448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 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×#88144C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic
3C13×#384C211yesmaximal, characteristic
4#11718645C214yesmaximal
5#11718640C214yesmaximal
6#11718638C211yesmaximal, characteristic
7#11718637C211yesmaximal, characteristic
8#11718597C211yesmaximal, characteristic
9#11718593C211yesmaximal, characteristic
10C22×Dic26C2212yes—
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2214yes—
14C2×C42×C13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2214yes—
21C2×C4×Dic13C2211yescharacteristic
22C2×C4×Dic13C2211yescharacteristic
23#88144—24no—
24#88142—24no—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2214yes—
28#88071C2214yes—
29C22×C4×C13C2312yes—
30C22×C4×C13C2312yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×Dic13C2312yes—
34C22×Dic13C2312yes—
35C22×Dic13C2311yescharacteristic
36C22×Dic13C2311yescharacteristic
37C22×Dic13C2312yes—
38C2×Dic26—24no—
39C2×Dic26—44no—
40C13×C4⋊C4—22no—
41C13×C4⋊C4—22no—
42C13×C4⋊C4—44no—
43C42×C13Q814yescomplemented
44C4⋊Dic13—22no—
45C4⋊Dic13—22no—
46C4⋊Dic13—24no—
47#6101—24no—
48#6101—24no—
49#6101—44no—
50C4×Dic13D414yes—
51C4×Dic13Q814yescomplemented
52#2660—131nomaximal, Sylow
53C23×C13C2411yescharacteristic
54C2×C4×C13—22no—
55C2×C4×C13—22no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—24no—
59C2×C4×C13—24no—
60C2×C4×C13C2×D412yes—
61C2×C4×C13C2×Q814yes—
62C2×C4×C13C2×Q812yes—
63C2×C4×C13C2×Q812yes—
64C2×Dic13—22no—
65C2×Dic13—22no—
66C2×Dic13—22no—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—24no—
71C2×Dic13—24no—
72C2×Dic13C2×D412yes—
73C2×Dic13C2×D412yes—
74C2×Dic13C2×Q814yes—
75Dic26—48no—
76C2×C4⋊Q8—131no—
77C2×#125—131no—
78#398—134no—
79#395—134no—
80#384—131no—
81#384D1311yescharacteristic
82#382—131no—
83#382—131no—
84#376—131no—
85C22×C13C22×D411yescharacteristic
86C22×C13C22×Q811yescharacteristic
87C22×C13C22×Q811yescharacteristic
88C22×C13H(5,𝔽2)12yes—
89C22×C132−1+412yes—
90C4×C13—24no—
91C4×C13—42no—
92C4×C13—42no—
93C4×C13C4⋊Q814yes—
94Dic13—22no—
95Dic13—22no—
96Dic13—24no—
97Dic13—42no—
98Dic13—42no—
99C22×Q8—132no—
100C4⋊Q8—264no—
101#125—264no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—131no—
104C2×C4⋊C4—132no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—131no—
107C2×C4⋊C4—134no—
108C2×C4⋊C4C2×D1311yescharacteristic
109C2×C4⋊C4C2×D1311yescharacteristic
110C2×C4⋊C4C2×D1314yes—
111C2×C42—131no—
112C2×C42—131no—
113C2×C42C2×D1311yescharacteristic
114#95—132no—
115#95—132no—
116#95—134no—
117#95—134no—
118C2×C13C2×C4⋊Q811yescharacteristic
119C2×C13#53511yescharacteristic
120C2×C13#53611yescharacteristic
121C2×C13#54412yes—
122C2×C13#54412yes—
123C2×Q8—264no—
124C2×Q8—524no—
125C22×C4—132no—
126C22×C4—131no—
127C22×C4—131no—
128C22×C4—132no—
129C22×C4—132no—
130C22×C4C22×D1312yes—
131C22×C4C22×D1312yes—
132C22×C4C22×D1312yes—
133C22×C4C22×D1311yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—44no—
137C4⋊C4—264no—
138C4⋊C4—264no—
139C4⋊C4—264no—
140C4⋊C4—262no—
141C4⋊C4—262no—
142C4⋊C4—524no—
143C42—134no—
144C42—134no—
145C42Dic2614yescomplemented
146C13#266011yescharacteristic, complemented, Sylow
147C23C23×D1311yescharacteristic
148Q8—528no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—132no—
156C2×C4—132no—
157C2×C4—134no—
158C2×C4—262no—
159C2×C4—262no—
160C2×C4—262no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—264no—
165C2×C4—264no—
166C2×C4C2×Dic2614yes—
167C2×C4C2×Dic2612yes—
168C2×C4D4×D1312yes—
169C2×C4Q8×D1312yes—
170C22C22×Dic2611yescharacteristic
171C22C2×D4×D1311yescharacteristic
172C22#8825112yes—
173C22C2×Q8×D1311yescharacteristic
174C22#8825412yes—
175C4—24no—
176C4—42no—
177C4—42no—
178C4—262no—
179C4—264no—
180C4—262no—
181C4—522no—
182C4—522no—
183C4#8814214yes—
184C2C2×#8814211yescharacteristic
185C2#1171920512yes—
186C2#1171942011yescharacteristic
187C2#1171942911yescharacteristic
188C2#1171943412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#384C2
hypercenter#384D13
hypocenterC13#2660
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
43. C42×C13Q8semidirect
51. C4×Dic13Q8semidirect
145. C42Dic26semidirect
146. C13#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#881442
C2×#881422
C13×#3842
#117186452
#117186402
#117186382
#117186372
#117185972
#117185932
#266013