Finite Group Databasebeta

← #16782127

Subgroups — #16782127

Order 3328.

530 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 108 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#13130726C212yesmaximal
2#13129674C214yesmaximal
3C2×#11718311C211yesmaximal, characteristic
4C22×#6101C412yes—
5C22×C4×Dic13C2211yescharacteristic
6C2×C22⋊#1057C2214yes—
7C2×C13×#95C411yescharacteristic
8C2×#88071C411yescharacteristic
9C2×#88071C2212yes—
10#11718311—22no—
11#11718311—22no—
12#11718290—22no—
13#11718290—22no—
14C23×C4×C13C2×C412yes—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13C2×C411yescharacteristic
17C23×Dic13C2×C412yes—
18C23×Dic13C2311yescharacteristic
19C22×#1057—24no—
20C2×#6101—22no—
21C2×#6101—22no—
22C2×#6101—44no—
23C2×C4×Dic13—24no—
24C2×C4×Dic13D412yes—
25C2×C4×Dic13D412yes—
26C22⋊#1057—28no—
27C13×#95—22no—
28#88071—22no—
29#88071—24no—
30#8703—131nomaximal, Sylow
31C24×C13C22×C411yescharacteristic
32C22×C4×C13—22no—
33C22×C4×C13—24no—
34C22×C4×C13—22no—
35C22×C4×C13—24no—
36C22×C4×C13—42no—
37C22×C4×C13—42no—
38C22×C4×C13C22⋊C412yes—
39C22×Dic13—22no—
40C22×Dic13—22no—
41C22×Dic13—22no—
42C22×Dic13—22no—
43C22×Dic13—24no—
44C22×Dic13—42no—
45C22×Dic13—42no—
46C22×Dic13—42no—
47C22×Dic13C22⋊C411yescharacteristic
48C22×Dic13C22⋊C411yescharacteristic
49C22×Dic13C2×D412yes—
50C22×Dic13#4114yes—
51C2×#1057—48no—
52C2×#1057—44no—
53#6101—44no—
54#6101—44no—
55C4×Dic13—24no—
56C4×Dic13—24no—
57C2×#382—131no—
58#1817—132no—
59#1280—134no—
60C23×C13—22no—
61C23×C13—21no—
62C23×C13—21no—
63C23×C13C2×C22⋊C411yescharacteristic
64C23×C13#11712yes—
65C23×C13#13114yes—
66C2×C4×C13—22no—
67C2×C4×C13—24no—
68C2×C4×C13—44no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—84no—
73C2×Dic13—28no—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—24no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—44no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C2×Dic13—42no—
83C2×Dic13—84no—
84C2×Dic13#10012yes—
85C2×Dic13#10112yes—
86C2×Dic13#12314yes—
87#1057—84no—
88C22×C4⋊C4—132no—
89C22×C42—131no—
90C2×C22⋊C8—134no—
91#382—262no—
92#382—262no—
93C2×#95—132no—
94C2×#95—131no—
95C2×#95#26111yescharacteristic
96#336—262no—
97#336—262no—
98C22×C13—22no—
99C22×C13—22no—
100C22×C13—24no—
101C22×C13—24no—
102C22×C13#38111yescharacteristic
103C22×C13#40812yes—
104C22×C13#41012yes—
105C22×C13C2×#10011yescharacteristic
106C22×C13C2×#10111yescharacteristic
107C22×C13#43314yes—
108C4×C13—42no—
109C4×C13—82no—
110Dic13—24no—
111Dic13—22no—
112Dic13—22no—
113Dic13—82no—
114C23×C4—131no—
115C23×C4—131no—
116C23×C4—132no—
117C23×C4C2×#26112yes—
118C23×C4C2×#26111yescharacteristic
119C22×C8—264no—
120C2×C4⋊C4—262no—
121C2×C4⋊C4—262no—
122C2×C4⋊C4—524no—
123C2×C42—132no—
124C2×C42—132no—
125C2×C42—264no—
126C22⋊C8—268no—
127#95—22no—
128#95—264no—
129#95—262no—
130C2×C13—24no—
131C2×C13#146912yes—
132C2×C13#147012yes—
133C2×C13#181811yescharacteristic
134C2×C13#182011yescharacteristic
135C2×C13#182111yescharacteristic
136C24C22×#26111yescharacteristic
137C22×C4—22no—
138C22×C4—24no—
139C22×C4—22no—
140C22×C4—24no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—132no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—134no—
147C22×C4—262no—
148C22×C4—262no—
149C22×C4—262no—
150C22×C4—262no—
151C22×C4—264no—
152C22×C4—522no—
153C22×C4—522no—
154C22×C4—522no—
155C22×C4C22⋊#26112yes—
156C2×C8—524no—
157C2×C8—528no—
158C4⋊C4—524no—
159C4⋊C4—524no—
160C42—264no—
161C42—264no—
162C13#870311yescharacteristic, complemented, Sylow
163C23—22no—
164C23—21no—
165C23—21no—
166C23#8823712yes—
167C23#8823814yes—
168C23C2×C22⋊#26111yescharacteristic
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—84no—
176C2×C4—134no—
177C2×C4—132no—
178C2×C4—132no—
179C2×C4—268no—
180C2×C4—264no—
181C2×C4—261no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—261no—
185C2×C4—524no—
186C2×C4—522no—
187C2×C4—522no—
188C2×C4—522no—
189C2×C4—1044no—
190C8—1044no—
191C22—24no—
192C22—24no—
193C22—22no—
194C22—22no—
195C22#1171906814yes—
196C22#1171911612yes—
197C22#1171913511yescharacteristic
198C22#1171914612yes—
199C22D13⋊#10011yescharacteristic
200C22D13⋊#10111yescharacteristic
201C4—42no—
202C4—82no—
203C4—264no—
204C4—262no—
205C4—262no—
206C4—1042no—
207C2—24no—
208C2#1313010512yes—
209C2#1313010812yes—
210C2#1313072911yescharacteristic
211C2#1313073311yescharacteristic
212C2#1313073611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC2×C13×#95C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC2×#95#261
hypocenterC13#8703
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
162. C13#8703semidirect

Maximal subgroups

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

subgroupindex
#131307262
#131296742
C2×#117183112
#870313