Finite Group Databasebeta

← #16778556

Subgroups — #16778556

Order 3328.

384 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130764C212yesmaximal
2#13129654C214yesmaximal
3#125×Dic13C211yesmaximal, characteristic
4C2×C13×#125C411yescharacteristic
5#11718646C2212yes—
6#11718642—22no—
7C4⋊C4×Dic13—22no—
8C4⋊C4×Dic13C412yes—
9#11718597C411yescharacteristic
10C42×Dic13C2211yescharacteristic
11#11718290—22no—
12#11718290—22no—
13#11718290C2214yes—
14C22×#1057—24no—
15C13×#125—24no—
16C2×C13×C4⋊C4—22no—
17C2×C13×C4⋊C4C2×C412yes—
18C2×C42×C13C2×C411yescharacteristic
19C2×C4⋊Dic13—22no—
20C2×C4⋊Dic13C2×C412yes—
21C2×C4×Dic13—22no—
22C2×C4×Dic13C2×C411yescharacteristic
23C2×C4×Dic13D412yes—
24C2×C4×Dic13D412yes—
25C2×C4×Dic13C2311yescharacteristic
26#88071—22no—
27#88071—22no—
28#88071—22no—
29#7650—131nomaximal, Sylow
30C22×C4×C13—22no—
31C22×C4×C13C22⋊C412yes—
32C22×C4×C13C22×C411yescharacteristic
33C22×Dic13—22no—
34C22×Dic13C22⋊C411yescharacteristic
35C22×Dic13C22⋊C411yescharacteristic
36C22×Dic13C2×D412yes—
37C2×#1057—44no—
38C2×#1057—44no—
39C2×#1057—44no—
40C13×C4⋊C4—28no—
41C13×C4⋊C4—22no—
42C13×C4⋊C4M1614yes—
43C42×C13—22no—
44C4⋊Dic13—44no—
45C4⋊Dic13—42no—
46C4×Dic13—22no—
47C4×Dic13—24no—
48C4×Dic13—42no—
49C4×Dic13—41no—
50C4×Dic13—44no—
51C4×#125—131no—
52#1839—132no—
53#1271—134no—
54C23×C13C2×C22⋊C411yescharacteristic
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—22no—
58C2×C4×C13—24no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—42no—
62C2×C4×C13—42no—
63C2×C4×C13C2×M1612yes—
64C2×Dic13—22no—
65C2×Dic13—22no—
66C2×Dic13—22no—
67C2×Dic13—21no—
68C2×Dic13—22no—
69C2×Dic13—42no—
70C2×Dic13—42no—
71C2×Dic13—42no—
72C2×Dic13#10112yes—
73C2×Dic13#13514yes—
74#1057—84no—
75C2×#125#26111yescharacteristic
76#389—132no—
77#387—262no—
78#382—131no—
79C4×C4⋊C4—132no—
80C4×C4⋊C4—262no—
81C43—131no—
82#336—134no—
83#336—262no—
84#336—262no—
85C22×C13#40711yescharacteristic
86C22×C13#41011yescharacteristic
87C22×C13C2×#10111yescharacteristic
88C22×C13#41612yes—
89C22×C13#42112yes—
90C4×C13—22no—
91C4×C13—42no—
92C4×C13—44no—
93Dic13—24no—
94Dic13—22no—
95Dic13—41no—
96Dic13—82no—
97C22×C8—264no—
98#125—24no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—132no—
101C2×C4⋊C4—262no—
102C2×C4⋊C4C2×#26112yes—
103C2×C42—132no—
104C2×C42—131no—
105C2×C42—132no—
106C2×C42—131no—
107C2×C42—262no—
108C2×C42C2×#26111yescharacteristic
109#95—262no—
110#95—262no—
111#95—262no—
112C2×C13#146711yescharacteristic
113C2×C13#148812yes—
114C2×C13#152112yes—
115C2×C13#153411yescharacteristic
116C2×C13#154411yescharacteristic
117C22×C4—22no—
118C22×C4—132no—
119C22×C4—131no—
120C22×C4—131no—
121C22×C4—262no—
122C22×C4C22⋊#26112yes—
123C22×C4C22×#26111yescharacteristic
124C2×C8—524no—
125C2×C8—524no—
126C2×C8—524no—
127C4⋊C4—28no—
128C4⋊C4—22no—
129C4⋊C4—522no—
130C4⋊C4—524no—
131C4⋊C4#612214yes—
132C42—22no—
133C42—262no—
134C42—264no—
135C42—521no—
136C42—522no—
137C42—524no—
138C13#765011yescharacteristic, complemented, Sylow
139C23C2×C22⋊#26111yescharacteristic
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—132no—
149C2×C4—134no—
150C2×C4—262no—
151C2×C4—262no—
152C2×C4—262no—
153C2×C4—261no—
154C2×C4—262no—
155C2×C4—522no—
156C2×C4—522no—
157C2×C4—522no—
158C2×C4C2×#612212yes—
159C8—1044no—
160C22#1171915611yescharacteristic
161C22D13⋊#10111yescharacteristic
162C22#1171916512yes—
163C22#1171916612yes—
164C22#1171916911yescharacteristic
165C4—22no—
166C4—42no—
167C4—44no—
168C4—264no—
169C4—262no—
170C4—521no—
171C4—1042no—
172C2#1313009911yescharacteristic
173C2#1313016712yes—
174C2#1313027912yes—
175C2#1313031911yescharacteristic
176C2#1313034211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#125C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#125#261
hypocenterC13#7650
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
138. C13#7650semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131296542
#125×Dic132
#765013