Finite Group Databasebeta

← #13122263

Subgroups — #13122263

Order 1664.

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

normal subgroups only

This group has 400 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×#397C211yesmaximal, characteristic
2#11718645C212yesmaximal, complemented
3#11718612C212yesmaximal
4#11718608C211yesmaximal, characteristic
5#11718607C212yesmaximal
6#11718604C211yesmaximal, characteristic
7#11718320C212yesmaximal, complemented
8#11718312C212yesmaximal, complemented
9#11718307C212yesmaximal, complemented
10C23×Dic13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C22⋊C4C2212yes—
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2212yes—
21C13×#95C2212yes—
22C13×#95C2211yescharacteristic
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C24×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2312yes—
36C22×Dic13—22no—
37C22×Dic13—41no—
38C22×Dic13—41no—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C2×Dic26—24no—
44C2×Dic26—41no—
45C13×C4⋊C4—41no—
46C13×C22⋊C4—24no—
47C13×C22⋊C4—41no—
48C22⋊Dic13—24no—
49C22⋊Dic13—41no—
50C4⋊Dic13—42no—
51#6101—42no—
52#6101—42no—
53C4×Dic13—24no—
54#2764—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×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×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—44no—
83C2×Dic13#4114yes—
84Dic26—44no—
85#400—132no—
86#398—132no—
87#397D1311yescharacteristic
88#393—131no—
89#391—132no—
90#388—132no—
91#385—132no—
92#383—132no—
93#381—131no—
94C22×C13—22no—
95C22×C13—24no—
96C22×C13—42no—
97C22×C13—41no—
98C22×C13—41no—
99C22×C13C2×#4111yescharacteristic
100C22×C13C2×#4112yes—
101C22×C13H(5,𝔽2)11yescharacteristic
102C22×C13H(5,𝔽2)11yescharacteristic
103C22×C132−1+412yes—
104C4×C13—42no—
105C4×C13—41no—
106C4×C13—42no—
107C4×C13—41no—
108Dic13—24no—
109Dic13—42no—
110Dic13—42no—
111Dic13—42no—
112C22×Q8—131no—
113C23×C4—131no—
114C2×C4⋊C4—132no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4C2×D1311yescharacteristic
118C2×C22⋊C4—132no—
119C2×C22⋊C4—131no—
120C2×C22⋊C4C2×D1312yes—
121C2×C22⋊C4C2×D1311yescharacteristic
122C2×C42—132no—
123#95—132no—
124#95—132no—
125#95—132no—
126#95—132no—
127#95—132no—
128#95—132no—
129#95—132no—
130#95—131no—
131#95C2×D1311yescharacteristic
132#95C2×D1312yes—
133C2×C13—42no—
134C2×C13#53811yescharacteristic
135C2×C13#54212yes—
136C2×C13#55111yescharacteristic
137C2×C13#55212yes—
138C2×C13#56311yescharacteristic
139C24C22×D1311yescharacteristic
140C2×Q8—264no—
141C2×Q8—521no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4—262no—
147C22×C4—521no—
148C22×C4—521no—
149C22×C4C22×D1311yescharacteristic
150C22×C4C22×D1312yes—
151C22×C4C22×D1311yescharacteristic
152C22×C4C22×D1312yes—
153C4⋊C4—41no—
154C4⋊C4—522no—
155C4⋊C4—522no—
156C4⋊C4—522no—
157C22⋊C4—24no—
158C22⋊C4—41no—
159C22⋊C4—264no—
160C22⋊C4—521no—
161C42—264no—
162C13#276411yescharacteristic, complemented, Sylow
163C23—21no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23#612912yes—
168C23C23×D1311yescharacteristic
169Q8—524no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—134no—
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—
191C2×C4—262no—
192C2×C4—524no—
193C22—22no—
194C22—24no—
195C22—41no—
196C22—41no—
197C22—42no—
198C22C2×#612911yescharacteristic
199C22#8825111yescharacteristic
200C22#41×D1312yes—
201C22#8825611yescharacteristic
202C22#8825712yes—
203C4—42no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—264no—
208C4—522no—
209C4—522no—
210C4—522no—
211C2—42no—
212C2#1171932211yescharacteristic
213C2#1171935512yes—
214C2#1171935611yescharacteristic
215C2#1171938411yescharacteristic
216C2#1171941512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×C13C23
hypercenter#397D13
hypocenterC13#2764
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #11718645C2semidirect
7. #11718320C2semidirect
8. #11718312C2semidirect
9. #11718307C2semidirect
162. C13#2764semidirect

Maximal subgroups

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

subgroupindex
C13×#3972
#117186452
#117186122
#117186082
#117186072
#117186042
#117183202
#117183122
#117183072
#276413