Finite Group Databasebeta

← #16782238

Subgroups — #16782238

Order 3328.

450 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#13130087C212yesmaximal
2#13129687C214yesmaximal, complemented
3#13117318C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C2211yescharacteristic
6C22×C4×Dic13C411yescharacteristic
7#11719128C2214yes—
8#11718634—22no—
9#11718607—22no—
10C4×#6101C412yes—
11C4×#6101C2212yes—
12#11718305—22no—
13#11718285—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13—21no—
16C13×#117—42no—
17C2×C13×C4⋊C4—21no—
18C2×C13×C22⋊C4—21no—
19C2×C42×C13C2×C412yes—
20C2×C22⋊Dic13D412yes—
21#88180—24no—
22C2×C4⋊Dic13D412yes—
23C2×#6101—22no—
24C2×#6101—22no—
25C2×C4×Dic13—21no—
26C2×C4×Dic13—42no—
27C2×C4×Dic13C2×C411yescharacteristic
28C2×C4×Dic13C2×C412yes—
29C2×C4×Dic13C2311yescharacteristic
30C22⋊#1057—24no—
31#88112—24no—
32#88110—24no—
33#88071—22no—
34#88071—22no—
35#8742—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13C22⋊C411yescharacteristic
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13—44no—
45C22×Dic13—42no—
46C22×Dic13C22⋊C412yes—
47C22×Dic13C2×D412yes—
48C2×#1057—44no—
49C13×C4⋊C4—42no—
50C13×C22⋊C4—42no—
51C42×C13—42no—
52C22⋊Dic13—24no—
53C4⋊Dic13—24no—
54#6101—44no—
55#6101—44no—
56C4×Dic13—22no—
57C4×Dic13—42no—
58C4×Dic13—42no—
59C4×Dic13#4114yes—
60#2296—131no—
61#1464—132no—
62#1285—134no—
63C23×C13—21no—
64C23×C13—21no—
65C23×C13—42no—
66C23×C13#10012yes—
67C23×C13C2×C22⋊C411yescharacteristic
68C2×C4×C13—28no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—42no—
74C2×C4×C13—42no—
75C2×C4×C13—42no—
76C2×C4×C13#10112yes—
77C2×C4×C13#11712yes—
78C2×Dic13—24no—
79C2×Dic13—22no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C2×Dic13—48no—
83C2×Dic13—42no—
84C2×Dic13—42no—
85C2×Dic13#12314yes—
86#1057—84no—
87C2×#117—131no—
88C2×#117#26111yescharacteristic
89C22×C42—131no—
90#432—134no—
91#389—262no—
92#385—262no—
93C4×C4⋊C4—132no—
94C4×C4⋊C4—132no—
95#324—262no—
96#323—262no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13#38111yescharacteristic
103C22×C13C2×#10011yescharacteristic
104C22×C13C2×#10111yescharacteristic
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—82no—
108Dic13—24no—
109Dic13—44no—
110Dic13—42no—
111C23×C4—261no—
112C23×C4C2×#26111yescharacteristic
113#117—42no—
114#117—264no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—132no—
117C2×C4⋊C4—262no—
118C2×C4⋊C4—262no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—132no—
121C2×C42—131no—
122C2×C42—131no—
123C2×C42—132no—
124C2×C42—261no—
125C2×C42—522no—
126C2×C42C2×#26112yes—
127C4⋊C8—264no—
128C22⋊C8—264no—
129#97—264no—
130#95—262no—
131#95—262no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13—42no—
135C2×C13#182111yescharacteristic
136C2×C13#182712yes—
137C24C22⋊#26111yescharacteristic
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4—262no—
145C22×C4—524no—
146C22×C4—522no—
147C22×C4C22⋊#26111yescharacteristic
148C22×C4C22×#26111yescharacteristic
149C2×C8—524no—
150C4⋊C4—42no—
151C4⋊C4—264no—
152C4⋊C4—524no—
153C4⋊C4—524no—
154C22⋊C4—42no—
155C22⋊C4—264no—
156C42—42no—
157C42—134no—
158C42—262no—
159C42—522no—
160C42—522no—
161C13#874211yescharacteristic, complemented, Sylow
162C23—21no—
163C23—21no—
164C23—42no—
165C23#8812112yes—
166C23C2×C22⋊#26111yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—134no—
176C2×C4—264no—
177C2×C4—262no—
178C2×C4—522no—
179C2×C4—522no—
180C2×C4—528no—
181C2×C4—522no—
182C2×C4—522no—
183C2×C4#8811312yes—
184C2×C4#8823712yes—
185C8—1044no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C2×#8811311yescharacteristic
192C22#1171913511yescharacteristic
193C22C2×#8812111yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—264no—
198C4—524no—
199C4—522no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2#1313073511yescharacteristic
204C2#1313074612yes—
subgroupG/H
centerC22#11719135
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8742
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129687C2semidirect
161. C13#8742semidirect

Maximal subgroups

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

subgroupindex
#131300872
#131296872
#131173182
#874213