Finite Group Databasebeta

← #13122326

Subgroups — #13122326

Order 1664.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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×#382C211yesmaximal, characteristic
2#11718647C211yesmaximal, characteristic
3#11718644C211yesmaximal, characteristic
4#11718633C212yesmaximal
5#11718594C212yesmaximal
6#11718321C212yesmaximal
7#11718318C212yesmaximal
8#11718313C212yesmaximal
9#11718312C212yesmaximal
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C42×C13C2211yescharacteristic
13C2×C4⋊Dic13C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×#6101C2212yes—
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×C4×Dic13C2212yes—
20C13×#95C2212yes—
21C13×#95C2212yes—
22#88071C2211yescharacteristic
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2211yescharacteristic
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—
40C13×C4⋊C4—41no—
41C13×C4⋊C4—41no—
42C42×C13—22no—
43C4⋊Dic13—41no—
44C4⋊Dic13—41no—
45#6101—24no—
46#6101—24no—
47#6101—24no—
48#6101—42no—
49C4×Dic13—24no—
50#2769—131nomaximal, Sylow
51C23×C13C2411yescharacteristic
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13—22no—
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#4112yes—
65C2×Dic13—22no—
66C2×Dic13—22no—
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#4114yes—
77#400—131no—
78#400—132no—
79#398—131no—
80#398—132no—
81#389—132no—
82#387—132no—
83#387—132no—
84#383—132no—
85#382D1311yescharacteristic
86C22×C13C2×#4111yescharacteristic
87C22×C13C2×#4112yes—
88C22×C13H(5,𝔽2)11yescharacteristic
89C22×C132−1+411yescharacteristic
90C22×C132−1+412yes—
91C4×C13—22no—
92C4×C13—42no—
93C4×C13—42no—
94C4×C13—41no—
95C4×C13—41no—
96Dic13—24no—
97Dic13—42no—
98Dic13—42no—
99Dic13—42no—
100C2×C4⋊C4—132no—
101C2×C4⋊C4—132no—
102C2×C4⋊C4—132no—
103C2×C4⋊C4—132no—
104C2×C4⋊C4—131no—
105C2×C4⋊C4—131no—
106C2×C4⋊C4C2×D1311yescharacteristic
107C2×C4⋊C4C2×D1311yescharacteristic
108C2×C42—132no—
109C2×C42C2×D1311yescharacteristic
110#95—131no—
111#95—132no—
112#95—132no—
113#95—132no—
114#95—132no—
115#95—131no—
116#95—132no—
117#95—132no—
118#95—132no—
119#95C2×D1312yes—
120#95C2×D1312yes—
121C2×C13#53911yescharacteristic
122C2×C13#54112yes—
123C2×C13#55212yes—
124C2×C13#55511yescharacteristic
125C2×C13#56311yescharacteristic
126C22×C4—132no—
127C22×C4—132no—
128C22×C4—132no—
129C22×C4—132no—
130C22×C4C22×D1312yes—
131C22×C4C22×D1311yescharacteristic
132C22×C4C22×D1311yescharacteristic
133C22×C4C22×D1312yes—
134C22×C4C22×D1311yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—264no—
138C4⋊C4—264no—
139C4⋊C4—264no—
140C4⋊C4—522no—
141C4⋊C4—521no—
142C4⋊C4—521no—
143C42—22no—
144C42—264no—
145C13#276911yescharacteristic, complemented, Sylow
146C23C23×D1311yescharacteristic
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—134no—
160C2×C4—262no—
161C2×C4—262no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4#612712yes—
172C22C2×#612711yescharacteristic
173C22#8825111yescharacteristic
174C22#8825411yescharacteristic
175C22#41×D1312yes—
176C22#8825712yes—
177C4—22no—
178C4—42no—
179C4—42no—
180C4—41no—
181C4—41no—
182C4—264no—
183C4—522no—
184C4—522no—
185C4—522no—
186C2#1171922011yescharacteristic
187C2#1171923412yes—
188C2#1171937511yescharacteristic
189C2#1171937711yescharacteristic
190C2#1171940112yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#382C2
hypercenter#382D13
hypocenterC13#2769
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
145. C13#2769semidirect

Maximal subgroups

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

subgroupindex
C13×#3822
#117186472
#117186442
#117186332
#117185942
#117183212
#117183182
#117183132
#117183122
#276913