Finite Group Databasebeta

← #13123102

Subgroups — #13123102

Order 1664.

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

normal subgroups only

This group has 348 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×#395C211yesmaximal, characteristic
2#11718890C212yesmaximal
3#11718647C211yesmaximal, characteristic
4#11718645C212yesmaximal
5#11718641C212yesmaximal
6#11718637C211yesmaximal, characteristic
7#11718319C212yesmaximal
8#11718318C212yesmaximal
9#11718312C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2212yes—
13C2×C4⋊Dic13C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×#6101C2212yes—
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C13×#95C2212yes—
22C13×#95C2211yescharacteristic
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C2×Q8×C13—42no—
32C2×Q8×C13—41no—
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C13×C4⋊C4—41no—
43C13×C4⋊C4—42no—
44C4⋊Dic13—41no—
45C4⋊Dic13—41no—
46#6101—42no—
47#6101—42no—
48#6101—42no—
49#6101—42no—
50#6101—42no—
51C4×Dic13Q814yescomplemented
52#2843—131nomaximal, Sylow
53C23×C13C2411yescharacteristic
54Q8×C13—44no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—21no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13C2×Q812yes—
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—24no—
77C2×Dic13—22no—
78C2×Dic13C2×Q814yes—
79#400—131no—
80#400—132no—
81#398—132no—
82#398—132no—
83#398—132no—
84#395—132no—
85#395D1311yescharacteristic
86#384—131no—
87#383—132no—
88C22×C13C22×Q811yescharacteristic
89C22×C13H(5,𝔽2)12yes—
90C22×C13H(5,𝔽2)11yescharacteristic
91C22×C132−1+412yes—
92C22×C132−1+411yescharacteristic
93C4×C13—22no—
94C4×C13—41no—
95C4×C13—42no—
96C4×C13—41no—
97C4×C13—42no—
98Dic13—24no—
99Dic13—42no—
100Dic13—42no—
101Dic13—42no—
102C22×Q8C2×D1311yescharacteristic
103C2×C4⋊C4—132no—
104C2×C4⋊C4—132no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—131no—
110C2×C4⋊C4C2×D1311yescharacteristic
111C2×C4⋊C4C2×D1312yes—
112C2×C42—131no—
113#95—132no—
114#95—132no—
115#95—132no—
116#95—132no—
117#95—132no—
118#95—132no—
119#95—131no—
120#95—132no—
121#95C2×D1312yes—
122#95C2×D1311yescharacteristic
123C2×C13#54412yes—
124C2×C13#54411yescharacteristic
125C2×C13#56011yescharacteristic
126C2×C13#56311yescharacteristic
127C2×C13#56312yes—
128C2×Q8—42no—
129C2×Q8—41no—
130C22×C4—132no—
131C22×C4—132no—
132C22×C4—132no—
133C22×C4—132no—
134C22×C4C22×D1312yes—
135C22×C4C22×D1312yes—
136C22×C4C22×D1311yescharacteristic
137C22×C4C22×D1311yescharacteristic
138C22×C4C22×D1311yescharacteristic
139C4⋊C4—41no—
140C4⋊C4—42no—
141C4⋊C4—522no—
142C4⋊C4—522no—
143C4⋊C4—522no—
144C4⋊C4—522no—
145C4⋊C4—522no—
146C4⋊C4—521no—
147C4⋊C4—521no—
148C42—134no—
149C13#284311yescharacteristic, complemented, Sylow
150C23C23×D1311yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—134no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—264no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4Q8×D1312yes—
176C22#8825112yes—
177C22#8825111yescharacteristic
178C22C2×Q8×D1311yescharacteristic
179C22#8825412yes—
180C22#8825711yescharacteristic
181C4—22no—
182C4—41no—
183C4—42no—
184C4—41no—
185C4—42no—
186C4—264no—
187C4—522no—
188C4—522no—
189C4—522no—
190C2#1171930011yescharacteristic
191C2#1171932811yescharacteristic
192C2#1171935112yes—
193C2#1171943412yes—
194C2#1171944011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2843
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic13Q8semidirect
149. C13#2843semidirect

Maximal subgroups

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

subgroupindex
C13×#3952
#117188902
#117186472
#117186452
#117186412
#117186372
#117183192
#117183182
#117183122
#284313