Finite Group Databasebeta

← #13123109

Subgroups — #13123109

Order 1664.

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

normal subgroups only

This group has 356 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×#400C211yesmaximal, characteristic
2#11718647C211yesmaximal, characteristic
3#11718640C212yesmaximal
4#11718638C211yesmaximal, characteristic
5#11718320C212yesmaximal
6#11718319C212yesmaximal
7#11718317C212yesmaximal
8#11718317C212yesmaximal
9#11718311C212yesmaximal
10C22×Dic26C2212yes—
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic13C2212yes—
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×C4×Dic13C2211yescharacteristic
20C13×#95C2212yes—
21C13×#95C2212yes—
22C13×#95C2211yescharacteristic
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2211yescharacteristic
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—42no—
41C2×Dic26—42no—
42C2×Dic26—42no—
43C13×C4⋊C4—41no—
44C13×C4⋊C4—41no—
45C4⋊Dic13—41no—
46C4⋊Dic13—42no—
47C4⋊Dic13—41no—
48#6101—42no—
49#6101—42no—
50#6101—42no—
51C4×Dic13Q814yescomplemented
52#2844—131nomaximal, Sylow
53C23×C13C2411yescharacteristic
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—22no—
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×C13C2×Q812yes—
67C2×Dic13—22no—
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—22no—
77C2×Dic13—22no—
78C2×Dic13C2×Q814yes—
79Dic26—48no—
80#400—131no—
81#400—132no—
82#400—132no—
83#400D1311yescharacteristic
84#395—132no—
85#395—132no—
86#395—132no—
87#382—131no—
88#382—132no—
89C22×C13C22×Q811yescharacteristic
90C22×C13H(5,𝔽2)11yescharacteristic
91C22×C13H(5,𝔽2)12yes—
92C22×C132−1+411yescharacteristic
93C22×C132−1+412yes—
94C4×C13—22no—
95C4×C13—42no—
96C4×C13—41no—
97C4×C13—41no—
98C4×C13—42no—
99Dic13—24no—
100Dic13—42no—
101Dic13—42no—
102Dic13—42no—
103C22×Q8—132no—
104C2×C4⋊C4—132no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—131no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4C2×D1311yescharacteristic
111C2×C4⋊C4C2×D1311yescharacteristic
112C2×C42—131no—
113#95—132no—
114#95—132no—
115#95—132no—
116#95—132no—
117#95—132no—
118#95—132no—
119#95—132no—
120#95—131no—
121#95C2×D1312yes—
122#95C2×D1312yes—
123#95C2×D1311yescharacteristic
124C2×C13#54411yescharacteristic
125C2×C13#54412yes—
126C2×C13H(3,𝔽4)11yescharacteristic
127C2×C13#56311yescharacteristic
128C2×C13#56312yes—
129C2×Q8—522no—
130C2×Q8—522no—
131C2×Q8—522no—
132C22×C4—132no—
133C22×C4—132no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4C22×D1311yescharacteristic
137C22×C4C22×D1311yescharacteristic
138C22×C4C22×D1312yes—
139C22×C4C22×D1312yes—
140C22×C4C22×D1311yescharacteristic
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—522no—
144C4⋊C4—522no—
145C4⋊C4—522no—
146C4⋊C4—521no—
147C4⋊C4—521no—
148C4⋊C4—522no—
149C42—134no—
150C13#284411yescharacteristic, complemented, Sylow
151C23C23×D1311yescharacteristic
152Q8—528no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—134no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4Q8×D1312yes—
178C22#8825111yescharacteristic
179C22C2×Q8×D1311yescharacteristic
180C22#8825612yes—
181C22#8825711yescharacteristic
182C22#8825712yes—
183C4—22no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—42no—
188C4—264no—
189C4—522no—
190C4—522no—
191C4—522no—
192C2#1171932811yescharacteristic
193C2#1171935611yescharacteristic
194C2#1171938811yescharacteristic
195C2#1171939412yes—
196C2#1171941712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#400C2
hypercenter#400D13
hypocenterC13#2844
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
51. C4×Dic13Q8semidirect
150. C13#2844semidirect

Maximal subgroups

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

subgroupindex
C13×#4002
#117186472
#117186402
#117186382
#117183202
#117183192
#117183172
#117183112
#284413