Finite Group Databasebeta

← #13122351

Subgroups — #13122351

Order 1664.

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

normal subgroups only

This group has 392 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×#381C211yesmaximal, characteristic
2#11718871C212yesmaximal
3#11718614C211yesmaximal, characteristic
4#11718610C211yesmaximal, characteristic
5#11718605C212yesmaximal
6#11718321C212yesmaximal, complemented
7#11718319C212yesmaximal, complemented
8#11718313C212yesmaximal, complemented
9#11718308C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C2×C13×C22⋊C4C2211yescharacteristic
12C2×C13×C22⋊C4C2211yescharacteristic
13C2×C22⋊Dic13C2212yes—
14C2×C22⋊Dic13C2212yes—
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×C4×Dic13C2212yes—
22C13×#95C2212yes—
23C13×#95C2212yes—
24#88071C2212yes—
25#88071C2211yescharacteristic
26#88071C2212yes—
27#88071C2212yes—
28#88071C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31C24×C13C2311yescharacteristic
32C22×C4×C13—22no—
33C22×C4×C13—41no—
34C22×C4×C13—41no—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C13×C22⋊C4—41no—
44C13×C22⋊C4—41no—
45C22⋊Dic13—24no—
46C22⋊Dic13—24no—
47C4⋊Dic13—41no—
48C4⋊Dic13—41no—
49#6101—24no—
50#6101—24no—
51#6101—42no—
52#6101—42no—
53C4×Dic13—42no—
54#2771—131nomaximal, Sylow
55C23×C13—22no—
56C23×C13—21no—
57C23×C13—21no—
58C23×C13—22no—
59C23×C13#4112yes—
60C23×C13C2411yescharacteristic
61C2×C4×C13—22no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—44no—
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×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13#4114yes—
84#400—132no—
85#400—132no—
86#399—131no—
87#397—131no—
88#389—132no—
89#388—132no—
90#387—132no—
91#385—132no—
92#381D1311yescharacteristic
93C22×C13—22no—
94C22×C13—24no—
95C22×C13—42no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13C2×#4111yescharacteristic
99C22×C13C2×#4112yes—
100C22×C13H(5,𝔽2)11yescharacteristic
101C22×C13H(5,𝔽2)11yescharacteristic
102C22×C132−1+412yes—
103C4×C13—42no—
104C4×C13—42no—
105C4×C13—41no—
106C4×C13—41no—
107Dic13—24no—
108Dic13—42no—
109Dic13—42no—
110Dic13—42no—
111C23×C4C2×D1311yescharacteristic
112C2×C4⋊C4—132no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4—132no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—131no—
117C2×C4⋊C4—131no—
118C2×C22⋊C4—132no—
119C2×C22⋊C4—132no—
120C2×C22⋊C4C2×D1311yescharacteristic
121C2×C22⋊C4C2×D1311yescharacteristic
122C2×C42—132no—
123#95—132no—
124#95—132no—
125#95—131no—
126#95—132no—
127#95—132no—
128#95—132no—
129#95—131no—
130#95C2×D1312yes—
131#95C2×D1312yes—
132C2×C13—42no—
133C2×C13#53811yescharacteristic
134C2×C13#53912yes—
135C2×C13#55212yes—
136C2×C13#55911yescharacteristic
137C2×C13#56311yescharacteristic
138C24C22×D1311yescharacteristic
139C22×C4—22no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4C22×D1311yescharacteristic
147C22×C4C22×D1312yes—
148C22×C4C22×D1312yes—
149C22×C4C22×D1311yescharacteristic
150C4⋊C4—264no—
151C4⋊C4—264no—
152C4⋊C4—522no—
153C4⋊C4—522no—
154C4⋊C4—521no—
155C4⋊C4—521no—
156C22⋊C4—41no—
157C22⋊C4—41no—
158C22⋊C4—264no—
159C22⋊C4—264no—
160C42—522no—
161C13#277111yescharacteristic, complemented, Sylow
162C23—21no—
163C23—21no—
164C23—22no—
165C23—22no—
166C23#612712yes—
167C23C23×D1311yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—134no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C22—22no—
192C22—24no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22C2×#612711yescharacteristic
197C22#8825111yescharacteristic
198C22#8825111yescharacteristic
199C22#41×D1312yes—
200C22#8825712yes—
201C4—42no—
202C4—41no—
203C4—42no—
204C4—41no—
205C4—264no—
206C4—522no—
207C4—522no—
208C4—522no—
209C2—42no—
210C2#1171919911yescharacteristic
211C2#1171923612yes—
212C2#1171935611yescharacteristic
213C2#1171936512yes—
214C2#1171936911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC24×C13C23
hypercenter#381D13
hypocenterC13#2771
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #11718321C2semidirect
7. #11718319C2semidirect
8. #11718313C2semidirect
9. #11718308C2semidirect
161. C13#2771semidirect

Maximal subgroups

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

subgroupindex
C13×#3812
#117188712
#117186142
#117186102
#117186052
#117183212
#117183192
#117183132
#117183082
#277113