Finite Group Databasebeta

← #13122637

Subgroups — #13122637

Order 1664.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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#11718645C212yesmaximal
4#11718644C211yesmaximal, characteristic
5#11718637C211yesmaximal, characteristic
6#11718634C212yesmaximal
7#11718315C212yesmaximal
8#11718314C212yesmaximal
9#11718308C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic13C2211yescharacteristic
14C2×C4⋊Dic13C2211yescharacteristic
15C2×C4⋊Dic13C2212yes—
16C2×#6101C2212yes—
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C2×C4×Dic13C2212yes—
23C13×#95C2212yes—
24C13×#95C2211yescharacteristic
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C2×Q8×C13—41no—
32C2×Q8×C13—42no—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C13×C4⋊C4—42no—
43C13×C4⋊C4—41no—
44C4⋊Dic13—41no—
45C4⋊Dic13—41no—
46C4⋊Dic13Q818yescomplemented
47#6101—24no—
48#6101—42no—
49#6101—42no—
50#6101—42no—
51#6101—42no—
52C4×Dic13—22no—
53C4×Dic13—42no—
54#2792—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56Q8×C13—44no—
57C2×C4×C13—22no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13C2×Q814yes—
69C2×C4×C13#4112yes—
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×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13C2×Q814yes—
81C2×Dic13C2×Q814yes—
82#398—131no—
83#398—132no—
84#395—132no—
85#395D1311yescharacteristic
86#389—132no—
87#389—132no—
88#387—132no—
89#387—132no—
90#384—131no—
91C22×C13C22×Q812yes—
92C22×C13C2×#4111yescharacteristic
93C22×C13H(5,𝔽2)11yescharacteristic
94C22×C13H(5,𝔽2)12yes—
95C22×C132−1+411yescharacteristic
96C4×C13—22no—
97C4×C13—24no—
98C4×C13—41no—
99C4×C13—42no—
100C4×C13—41no—
101Dic13—24no—
102Dic13—24no—
103Dic13—42no—
104Dic13—42no—
105C22×Q8C2×D1311yescharacteristic
106C2×C4⋊C4—132no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—131no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4C2×D1311yescharacteristic
115C2×C4⋊C4C2×D1312yes—
116C2×C42—131no—
117C2×C42—132no—
118#95—132no—
119#95—132no—
120#95—132no—
121#95—132no—
122#95—132no—
123#95—131no—
124#95C2×D1311yescharacteristic
125#95C2×D1312yes—
126C2×C13#53911yescharacteristic
127C2×C13#54412yes—
128C2×C13#55412yes—
129C2×C13Q8211yescharacteristic
130C2×C13#56011yescharacteristic
131C2×Q8—41no—
132C2×Q8—42no—
133C22×C4—132no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4C22×D1312yes—
138C22×C4C22×D1311yescharacteristic
139C22×C4C22×D1311yescharacteristic
140C22×C4C22×D1312yes—
141C22×C4C22×D1311yescharacteristic
142C4⋊C4—42no—
143C4⋊C4—41no—
144C4⋊C4—138no—
145C4⋊C4—264no—
146C4⋊C4—522no—
147C4⋊C4—522no—
148C4⋊C4—522no—
149C4⋊C4—522no—
150C4⋊C4—521no—
151C4⋊C4—521no—
152C42—262no—
153C42—522no—
154C13#279211yescharacteristic, complemented, Sylow
155C23C23×D1311yescharacteristic
156Q8—44no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—134no—
169C2×C4—134no—
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×C4—262no—
180C2×C4Q8×D1314yes—
181C2×C4#613112yes—
182C22#8825111yescharacteristic
183C22#8825112yes—
184C22C2×Q8×D1312yes—
185C22C2×#613111yescharacteristic
186C22#8825711yescharacteristic
187C4—24no—
188C4—22no—
189C4—41no—
190C4—41no—
191C4—42no—
192C4—264no—
193C4—264no—
194C4—522no—
195C4—522no—
196C2#1171930011yescharacteristic
197C2#1171932812yes—
198C2#1171935011yescharacteristic
199C2#1171942711yescharacteristic
200C2#1171943512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2792
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
46. C4⋊Dic13Q8semidirect
154. C13#2792semidirect

Maximal subgroups

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

subgroupindex
C13×#3952
#117188902
#117186452
#117186442
#117186372
#117186342
#117183152
#117183142
#117183082
#279213