Finite Group Databasebeta

← #16782243

Subgroups — #16782243

Order 3328.

384 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 72 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#13130089C212yesmaximal
2#13129687C214yesmaximal, complemented
3#13117333C211yesmaximal, characteristic
4C2×#88126C2211yescharacteristic
5#11719128C2214yes—
6C43×C13C411yescharacteristic
7#11718601—22no—
8C4×#6103C412yes—
9#11718594—22no—
10#11718593C411yescharacteristic
11C4×#6101C2212yes—
12#11718287—22no—
13#11718286—22no—
14C22×C4×D13C2×C411yescharacteristic
15C2×C42×C13—22no—
16C2×C42×C13C2×C411yescharacteristic
17C2×C42×C13C2×C412yes—
18C2×#6103—22no—
19C2×#6103D412yes—
20C2×#6101—22no—
21C2×#6101D412yes—
22C2×C4×Dic13C2×C412yes—
23C2×C4×Dic13C2311yescharacteristic
24#88126—24no—
25C22⋊#1057—24no—
26#88112—24no—
27#88110—24no—
28#88071—22no—
29#88071—22no—
30#88071—22no—
31#8744—131nomaximal, Sylow
32C23×D13C22⋊C411yescharacteristic
33C22×C4×C13—22no—
34C22×C4×C13C22⋊C412yes—
35C22×C4×C13C22×C411yescharacteristic
36C22×Dic13—22no—
37C22×Dic13C22⋊C411yescharacteristic
38C22×Dic13C2×D412yes—
39C2×C4×D13—22no—
40C2×C4×D13—42no—
41C2×#1057—44no—
42C42×C13—22no—
43C42×C13—42no—
44C42×C13—44no—
45#6103—24no—
46#6103—44no—
47#6101—24no—
48#6101—44no—
49C4×Dic13—42no—
50C4×Dic13#4114yes—
51#2298—131no—
52#1464—132no—
53#1285—134no—
54C23×C13C2×C22⋊C411yescharacteristic
55C22×D13—21no—
56C22×D13—22no—
57C22×D13—42no—
58C2×C4×C13—22no—
59C2×C4×C13—24no—
60C2×C4×C13—22no—
61C2×C4×C13—42no—
62C2×C4×C13—42no—
63C2×C4×C13—42no—
64C2×C4×C13#11712yes—
65C2×Dic13—21no—
66C2×Dic13—22no—
67C2×Dic13—42no—
68C2×Dic13—42no—
69C2×Dic13—42no—
70C2×Dic13—42no—
71C2×Dic13#12314yes—
72C4×D13—44no—
73#1057—84no—
74C2×#117—131no—
75#432—134no—
76#388—262no—
77#387—262no—
78C4×C4⋊C4—132no—
79C4×C22⋊C4—132no—
80#376—131no—
81C43#26111yescharacteristic
82#324—262no—
83#323—262no—
84C22×C13—22no—
85C22×C13#38111yescharacteristic
86C22×C13#41312yes—
87C2×D13—41no—
88C2×D13—42no—
89C2×D13—82no—
90C4×C13—22no—
91C4×C13—44no—
92C4×C13—42no—
93Dic13—24no—
94Dic13—41no—
95Dic13—82no—
96C23×C4—131no—
97#117—264no—
98C2×C4⋊C4—132no—
99C2×C4⋊C4—262no—
100C2×C22⋊C4—132no—
101C2×C22⋊C4—262no—
102C2×C42—22no—
103C2×C42—131no—
104C2×C42—132no—
105C2×C42C2×#26111yescharacteristic
106C2×C42C2×#26112yes—
107C4⋊C8—264no—
108C22⋊C8—264no—
109#97—264no—
110#95—262no—
111#95—262no—
112#95—262no—
113C2×C13—22no—
114C2×C13#182211yescharacteristic
115C2×C13#182712yes—
116D13—81no—
117C24—131no—
118C22×C4—22no—
119C22×C4—132no—
120C22×C4—131no—
121C22×C4—262no—
122C22×C4—262no—
123C22×C4—522no—
124C22×C4C22⋊#26112yes—
125C22×C4C22×#26111yescharacteristic
126C2×C8—524no—
127C4⋊C4—264no—
128C4⋊C4—524no—
129C22⋊C4—264no—
130C22⋊C4—524no—
131C42—22no—
132C42—42no—
133C42—44no—
134C42—134no—
135C42—522no—
136C13#874411yescharacteristic, complemented, Sylow
137C23—261no—
138C23—262no—
139C23—522no—
140C23C2×C22⋊#26111yescharacteristic
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—134no—
148C2×C4—262no—
149C2×C4—261no—
150C2×C4—524no—
151C2×C4—522no—
152C2×C4—522no—
153C2×C4—522no—
154C2×C4—522no—
155C2×C4#8823712yes—
156C8—1044no—
157C22—22no—
158C22—521no—
159C22—522no—
160C22—1042no—
161C22#1171913212yes—
162C22#1171913511yescharacteristic
163C4—22no—
164C4—44no—
165C4—42no—
166C4—264no—
167C4—521no—
168C4—1042no—
169C2—22no—
170C2—1041no—
171C2#1313073711yescharacteristic
172C2#1313074512yes—
subgroupG/H
centerC22#11719135
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC43×C13C4
socleC22×C13#381
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC43#261
hypocenterC13#8744
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C43

Complements

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

NH ≅ G/Ntype
2. #13129687C2semidirect
136. C13#8744semidirect

Maximal subgroups

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

subgroupindex
#131300892
#131296872
#131173332
#874413