Finite Group Databasebeta

← #13126042

Subgroups — #13126042

Order 1664.

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

normal subgroups only

This group has 324 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
1C2×C13×#125C211yesmaximal, characteristic
2#11719175C211yesmaximal, characteristic
3#11718730C212yesmaximal, complemented
4#11718726C212yesmaximal, complemented
5#11718724C214yesmaximal, complemented
6#11718632C212yesmaximal
7#11718631C212yesmaximal
8#11718587C211yesmaximal, characteristic
9C13×#125—21no—
10C13×#125—21no—
11C13×#125C2212yes—
12C13×#125C2212yes—
13C2×C13×C4⋊C4—21no—
14C2×C13×C4⋊C4—21no—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C42×C13C2211yescharacteristic
18#88180—21no—
19#88178—21no—
20#88178C2212yes—
21#88124—21no—
22#88123C2211yescharacteristic
23#88123C2211yescharacteristic
24C4×Dic26—21no—
25C4×Dic26C2212yes—
26C22⋊#1055C2212yes—
27#88050C2214yes—
28#88050C2214yes—
29#88048C2214yes—
30#88047C2214yes—
31C4⋊#1055C2212yes—
32#88043C2212yes—
33C22×C4×C13—21no—
34C22×C4×C13—21no—
35C22×C4×C13D411yescharacteristic
36C22×C4×C13D411yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C2×Dic26—21no—
39C2×Dic26C2312yes—
40C13×C4⋊C4—22no—
41C13×C4⋊C4—22no—
42C13×C4⋊C4—22no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4—21no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4C2312yes—
47C13×C4⋊C4C2312yes—
48C42×C13D411yescharacteristic
49C42×C13D411yescharacteristic
50C42×C13C2311yescharacteristic
51C42×C13C2311yescharacteristic
52C22⋊Dic13—22no—
53C4⋊Dic13—21no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13C2312yes—
57#6101—22no—
58#6101—22no—
59C4×Dic13—22no—
60C2×#1055C2314yes—
61#3236—131nomaximal, Sylow
62C23×C13C2×D411yescharacteristic
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—41no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13C2×D411yescharacteristic
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2411yescharacteristic
76C2×Dic13—22no—
77C2×Dic13—22no—
78Dic26—24no—
79Dic26—42no—
80#1055—24no—
81#533—131no—
82C2×#125D1311yescharacteristic
83#501—132no—
84#491—132no—
85#484—132no—
86#483—132no—
87#479—134no—
88#432—131no—
89C22×C13—21no—
90C22×C13—21no—
91C22×C13#13712yes—
92C22×C13C22×D411yescharacteristic
93C4×C13—21no—
94C4×C13—21no—
95C4×C13—21no—
96C4×C13—21no—
97C4×C13—21no—
98C4×C13—42no—
99C4×C13—42no—
100C4×C132−1+412yes—
101Dic13—42no—
102Dic13—42no—
103C4⋊Q8—131no—
104C4⋊Q8—131no—
105#125—21no—
106#125—21no—
107#125—261no—
108#125C2×D1312yes—
109#125C2×D1312yes—
110C22⋊Q8—132no—
111C22⋊Q8—261no—
112C4×Q8—132no—
113C4×Q8—261no—
114#117—261no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4C2×D1311yescharacteristic
118C2×C4⋊C4C2×D1311yescharacteristic
119C2×C42C2×D1311yescharacteristic
120#107—134no—
121#106—134no—
122C4⋊C8—132no—
123#103—134no—
124#103—134no—
125C22⋊C8—132no—
126#97—132no—
127C2×C13—22no—
128C2×C13#53611yescharacteristic
129C2×C13C2×#13711yescharacteristic
130C2×C13#57511yescharacteristic
131C2×Q8—132no—
132C2×Q8—261no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4C22⋊D1311yescharacteristic
136C22×C4C22⋊D1311yescharacteristic
137C22×C4C22×D1311yescharacteristic
138C2×C8—134no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—132no—
146C4⋊C4—261no—
147C4⋊C4—261no—
148C4⋊C4—262no—
149C4⋊C4—262no—
150C4⋊C4—261no—
151C4⋊C4C22×D1312yes—
152C4⋊C4C22×D1312yes—
153C22⋊C4—262no—
154C42—262no—
155C42C22⋊D1311yescharacteristic
156C42C22⋊D1311yescharacteristic
157C42C22×D1311yescharacteristic
158C42C22×D1311yescharacteristic
159C13#323611yescharacteristic, complemented, Sylow
160C23C2×C22⋊D1311yescharacteristic
161Q8—264no—
162Q8—522no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4C2×C22⋊D1311yescharacteristic
173C2×C4C2×C22⋊D1311yescharacteristic
174C2×C4C2×C22⋊D1311yescharacteristic
175C2×C4C2×C22⋊D1311yescharacteristic
176C2×C4C2×C22⋊D1311yescharacteristic
177C2×C4C23×D1311yescharacteristic
178C8—264no—
179C22—21no—
180C22—21no—
181C22#8820512yes—
182C22C22×C22⋊D1311yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—42no—
190C4—522no—
191C4—522no—
192C4#8825412yes—
193C2—22no—
194C2#1171952111yescharacteristic
195C2#1171952711yescharacteristic
196C2C2×#8820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#125C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenterC2×#125D13
hypocenterC13#3236
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #11718730C2semidirect
4. #11718726C2semidirect
5. #11718724C2semidirect
159. C13#3236semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1252
#117191752
#117187302
#117187262
#117187242
#117186322
#117186312
#117185872
#323613