Finite Group Databasebeta

← #13120785

Subgroups — #13120785

Order 1664.

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

normal subgroups only

This group has 416 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
1C2×#88198C211yesmaximal, characteristic
2C2×#88144C211yesmaximal, characteristic
3C13×#391C211yesmaximal, characteristic
4#11718891C211yesmaximal, characteristic
5#11718635C211yesmaximal, characteristic
6#11718593C211yesmaximal, characteristic
7#11718590C211yesmaximal, characteristic
8#11718321C214yesmaximal
9#11718319C214yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C42×C13C2211yescharacteristic
14#88198—24no—
15C2×C4⋊Dic13C2212yes—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C2×C4×Dic13C2211yescharacteristic
22#88144—24no—
23C13×#95C2214yes—
24#88071C2212yes—
25#88071C2214yes—
26#88071C2214yes—
27#88071C2214yes—
28#88071C2212yes—
29C2×Q8×C13—22no—
30C2×Q8×C13—22no—
31C2×Q8×C13—22no—
32C22×C4×C13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2311yescharacteristic
40C22×Dic13C2311yescharacteristic
41C2×Dic26—22no—
42C2×Dic26—22no—
43C2×Dic26—22no—
44C13×C4⋊C4—22no—
45C42×C13—22no—
46C4⋊Dic13—22no—
47C4⋊Dic13—24no—
48#6101—24no—
49#6101—24no—
50#6101—24no—
51C4×Dic13—22no—
52C4×Dic13D414yes—
53#2642—131nomaximal, Sylow
54C23×C13C2411yescharacteristic
55Q8×C13—44no—
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—24no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13C2×D412yes—
65C2×C4×C13#4112yes—
66C2×C4×C13#4112yes—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—24no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13C2×D412yes—
78C2×Dic13C2×D412yes—
79Dic26—44no—
80C2×C4⋊Q8—131no—
81C2×#125—131no—
82#400—134no—
83#400—134no—
84#391—131no—
85#391—131no—
86#391—131no—
87#391D1311yescharacteristic
88#376—131no—
89C22×C13C22×D411yescharacteristic
90C22×C13C2×#4111yescharacteristic
91C22×C13C2×#4111yescharacteristic
92C22×C132−1+412yes—
93C22×C132−1+412yes—
94C4×C13—42no—
95C4×C13—42no—
96C4×C13—42no—
97C4×C13#12414yes—
98Dic13—22no—
99Dic13—22no—
100Dic13—42no—
101Dic13—42no—
102Dic13—42no—
103C22×Q8—131no—
104C22×Q8C2×D1311yescharacteristic
105C4⋊Q8—264no—
106#125—264no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—131no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4C2×D1311yescharacteristic
113C2×C42—131no—
114C2×C42—131no—
115C2×C42C2×D1311yescharacteristic
116#95—132no—
117#95—132no—
118#95—134no—
119#95—134no—
120#95—134no—
121#95C2×D1314yes—
122C2×C13C2×#12411yescharacteristic
123C2×C13#53611yescharacteristic
124C2×C13#53611yescharacteristic
125C2×C13#54112yes—
126C2×C13#54112yes—
127C2×Q8—22no—
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—262no—
131C2×Q8—262no—
132C2×Q8—262no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—132no—
136C22×C4—132no—
137C22×C4—132no—
138C22×C4C22×D1312yes—
139C22×C4C22×D1312yes—
140C22×C4C22×D1312yes—
141C22×C4C22×D1311yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—264no—
144C4⋊C4—264no—
145C4⋊C4—264no—
146C4⋊C4—264no—
147C4⋊C4—262no—
148C42—22no—
149C42—134no—
150C42—262no—
151C13#264211yescharacteristic, complemented, Sylow
152C23C23×D1311yescharacteristic
153Q8—44no—
154Q8—524no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—132no—
164C2×C4—132no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—264no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4#612712yes—
176C2×C4D4×D1312yes—
177C2×C4#612912yes—
178C22C2×#612711yescharacteristic
179C22C2×D4×D1311yescharacteristic
180C22C2×#612911yescharacteristic
181C22#8825412yes—
182C22#8825712yes—
183C4—42no—
184C4—42no—
185C4—42no—
186C4—262no—
187C4—262no—
188C4—522no—
189C4—522no—
190C4—522no—
191C4#8813914yes—
192C2C2×#8813911yescharacteristic
193C2#1171928812yes—
194C2#1171933012yes—
195C2#1171938011yescharacteristic
196C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#391C2
hypercenter#391D13
hypocenterC13#2642
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
151. C13#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C2×#881442
C13×#3912
#117188912
#117186352
#117185932
#117185902
#117183212
#117183192
#264213