Finite Group Databasebeta

← #13123016

Subgroups — #13123016

Order 1664.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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#11718647C211yesmaximal, characteristic
3#11718645C212yesmaximal
4#11718642C212yesmaximal
5#11718640C212yesmaximal
6#11718635C211yesmaximal, characteristic
7C13⋊#401C212yesmaximal
8#11718321C212yesmaximal
9#11718320C212yesmaximal
10C22×Dic26C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic13C2212yes—
15C2×C4⋊Dic13C2211yescharacteristic
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×C4×Dic13C2211yescharacteristic
19C13×#95C2212yes—
20C13×#95C2211yescharacteristic
21#88071C2211yescharacteristic
22#88071C2212yes—
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×Dic26—22no—
41C2×Dic26—41no—
42C2×Dic26—41no—
43C13×C4⋊C4—24no—
44C13×C4⋊C4—41no—
45C13×C4⋊C4—41no—
46C4⋊Dic13—42no—
47C4⋊Dic13—41no—
48#6101—42no—
49#6101—42no—
50C4×Dic13—41no—
51#2833—131nomaximal, Sylow
52C23×C13C2411yescharacteristic
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—22no—
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#4112yes—
66C2×Dic13—22no—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—24no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77Dic26—44no—
78#401—132no—
79#400—131no—
80#400—132no—
81#400—132no—
82#398—132no—
83#398D1311yescharacteristic
84#395—132no—
85#391—131no—
86#387—132no—
87C22×C13C2×#4111yescharacteristic
88C22×C13H(5,𝔽2)11yescharacteristic
89C22×C13H(5,𝔽2)11yescharacteristic
90C22×C132−1+412yes—
91C22×C132−1+412yes—
92C4×C13—22no—
93C4×C13—42no—
94C4×C13—42no—
95C4×C13—41no—
96C4×C13—41no—
97Dic13—42no—
98Dic13—42no—
99Dic13—42no—
100Dic13—42no—
101C22×Q8—131no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—132no—
104C2×C4⋊C4—132no—
105C2×C4⋊C4—131no—
106C2×C4⋊C4C2×D1312yes—
107C2×C4⋊C4C2×D1311yescharacteristic
108C2×C4⋊C4C2×D1311yescharacteristic
109C2×C42—131no—
110#95—132no—
111#95—132no—
112#95—132no—
113#95—132no—
114#95—132no—
115#95—132no—
116#95—132no—
117#95—132no—
118#95—132no—
119#95—131no—
120#95C2×D1312yes—
121#95C2×D1311yescharacteristic
122C2×C13#53811yescharacteristic
123C2×C13#54112yes—
124C2×C13#56311yescharacteristic
125C2×C13#56311yescharacteristic
126C2×C13#56312yes—
127C2×Q8—262no—
128C2×Q8—521no—
129C2×Q8—521no—
130C22×C4—132no—
131C22×C4—132no—
132C22×C4—132no—
133C22×C4—132no—
134C22×C4C22×D1312yes—
135C22×C4C22×D1311yescharacteristic
136C22×C4C22×D1311yescharacteristic
137C22×C4C22×D1312yes—
138C22×C4C22×D1311yescharacteristic
139C4⋊C4—24no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—522no—
143C4⋊C4—522no—
144C4⋊C4—521no—
145C4⋊C4—522no—
146C42—521no—
147C13#283311yescharacteristic, complemented, Sylow
148C23C23×D1311yescharacteristic
149Q8—524no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—264no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4#612912yes—
174C22C2×#612911yescharacteristic
175C22#8825111yescharacteristic
176C22#8825412yes—
177C22#8825611yescharacteristic
178C22#8825712yes—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4—522no—
185C4—522no—
186C4—522no—
187C4—522no—
188C2#1171932211yescharacteristic
189C2#1171933012yes—
190C2#1171935611yescharacteristic
191C2#1171940412yes—
192C2#1171944011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#398C2
hypercenter#398D13
hypocenterC13#2833
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
147. C13#2833semidirect

Maximal subgroups

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

subgroupindex
C13×#3982
#117186472
#117186452
#117186422
#117186402
#117186352
C13⋊#4012
#117183212
#117183202
#283313