Finite Group Databasebeta

← #13122819

Subgroups — #13122819

Order 1664.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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#11718645C212yesmaximal
4#11718635C211yesmaximal, characteristic
5#11718318C212yesmaximal
6#11718314C212yesmaximal
7#11718313C212yesmaximal
8#11718308C212yesmaximal
9#11718307C212yesmaximal
10C22×Dic26C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic13C2212yes—
14C2×C4⋊Dic13C2211yescharacteristic
15C2×#6101C2212yes—
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×C4×Dic13C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C13×#95C2212yes—
22C13×#95C2211yescharacteristic
23C13×#95C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2211yescharacteristic
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—41no—
41C2×Dic26—41no—
42C2×Dic26Q814yes—
43C13×C4⋊C4—41no—
44C13×C4⋊C4—41no—
45C4⋊Dic13—24no—
46C4⋊Dic13—41no—
47#6101—24no—
48#6101—24no—
49#6101—42no—
50#6101—42no—
51C4×Dic13—41no—
52C4×Dic13—42no—
53#2809—131nomaximal, Sylow
54C23×C13C2411yescharacteristic
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—21no—
64C2×C4×C13—22no—
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—22no—
77C2×Dic13—22no—
78C2×Dic13C2×Q814yes—
79C2×Dic13#4114yes—
80Dic26—44no—
81#400—131no—
82#400D1311yescharacteristic
83#398—132no—
84#398—132no—
85#391—131no—
86#391—132no—
87#389—132no—
88#387—132no—
89#387—132no—
90C22×C13C22×Q811yescharacteristic
91C22×C13C2×#4112yes—
92C22×C13H(5,𝔽2)11yescharacteristic
93C22×C13H(5,𝔽2)11yescharacteristic
94C22×C132−1+412yes—
95C4×C13—22no—
96C4×C13—42no—
97C4×C13—42no—
98C4×C13—41no—
99C4×C13—41no—
100Dic13—24no—
101Dic13—24no—
102Dic13—42no—
103Dic13—42no—
104C22×Q8—131no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—131no—
111C2×C4⋊C4C2×D1311yescharacteristic
112C2×C4⋊C4C2×D1311yescharacteristic
113C2×C42—132no—
114C2×C42—131no—
115#95—131no—
116#95—132no—
117#95—132no—
118#95—132no—
119#95—132no—
120#95—132no—
121#95—132no—
122#95C2×D1311yescharacteristic
123#95C2×D1312yes—
124#95C2×D1312yes—
125C2×C13#53912yes—
126C2×C13#54311yescharacteristic
127C2×C13#55511yescharacteristic
128C2×C13#55712yes—
129C2×C13#56311yescharacteristic
130C2×Q8—134no—
131C2×Q8—521no—
132C2×Q8—521no—
133C22×C4—132no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4C22×D1311yescharacteristic
138C22×C4C22×D1311yescharacteristic
139C22×C4C22×D1312yes—
140C22×C4C22×D1312yes—
141C22×C4C22×D1311yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—264no—
145C4⋊C4—264no—
146C4⋊C4—264no—
147C4⋊C4—522no—
148C4⋊C4—522no—
149C4⋊C4—521no—
150C42—521no—
151C42—522no—
152C13#280911yescharacteristic, complemented, Sylow
153C23C23×D1311yescharacteristic
154Q8—524no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—134no—
168C2×C4—134no—
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×C4—262no—
178C2×C4—262no—
179C2×C4Q8×D1312yes—
180C22#8825111yescharacteristic
181C22C2×Q8×D1311yescharacteristic
182C22#41×D1312yes—
183C22#8825611yescharacteristic
184C22#8825712yes—
185C4—22no—
186C4—41no—
187C4—41no—
188C4—42no—
189C4—42no—
190C4—264no—
191C4—264no—
192C4—522no—
193C4—522no—
194C2#1171933911yescharacteristic
195C2#1171935611yescharacteristic
196C2#1171937511yescharacteristic
197C2#1171939012yes—
198C2#1171941212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#400C2
hypercenter#400D13
hypocenterC13#2809
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
152. C13#2809semidirect

Maximal subgroups

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

subgroupindex
C13×#4002
#117186472
#117186452
#117186352
#117183182
#117183142
#117183132
#117183082
#117183072
#280913