Finite Group Databasebeta

← #16778483

Subgroups — #16778483

Order 3328.

658 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130562C212yesmaximal
2#13129657C214yesmaximal, complemented
3C2×#11718635C211yesmaximal, characteristic
4C23×Dic26C411yescharacteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88110—22no—
9C2×#88071—22no—
10#11718635—22no—
11#11718635C412yes—
12#11718635C2212yes—
13#11718290C2214yes—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C22×Dic26—21no—
19C22×Dic26—24no—
20C22×Dic26—42no—
21C22×Dic26—42no—
22C22×Dic26C2×C412yes—
23C22×#1057—24no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—42no—
26C2×C13×C4⋊C4C2×C412yes—
27C2×C4×Dic13—42no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13D412yes—
30C2×C4×Dic13C2311yescharacteristic
31C22⋊#1057—28no—
32#88110—44no—
33#88071—24no—
34#88071—24no—
35#7629—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—42no—
42C22×C4×C13—44no—
43C22×C4×C13C22⋊C411yescharacteristic
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13—24no—
46C22×Dic13—24no—
47C22×Dic13—22no—
48C22×Dic13—24no—
49C22×Dic13—42no—
50C22×Dic13—42no—
51C22×Dic13—42no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C2×D412yes—
54C2×Dic26—24no—
55C2×Dic26—22no—
56C2×Dic26—42no—
57C2×Dic26—416no—
58C2×Dic26—42no—
59C2×Dic26—42no—
60C2×Dic26—42no—
61C2×Dic26M1614yes—
62C2×#1057—28no—
63C2×#1057—44no—
64C2×#1057—44no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C4×Dic13—24no—
68C4×Dic13—41no—
69C4×Dic13—41no—
70C2×#391—131no—
71#1749—132no—
72#1272—134no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13#10012yes—
77C23×C13#10414yes—
78C23×C13C2×C22⋊C411yescharacteristic
79C2×C4×C13—28no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13—44no—
86C2×C4×C13—84no—
87C2×C4×C13#9912yes—
88C2×C4×C13C2×M1612yes—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—24no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—48no—
96C2×Dic13—48no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13#13714yes—
100Dic26—48no—
101Dic26—44no—
102Dic26—44no—
103#1057—48no—
104C23×Q8—131no—
105C22×C4⋊C4#26111yescharacteristic
106C22×C42—131no—
107C2×C22⋊C8—262no—
108C2×#97—262no—
109#391—132no—
110#391—132no—
111#391—262no—
112C2×#95—262no—
113#336—134no—
114C22×C13—22no—
115C22×C13—22no—
116C22×C13—24no—
117C22×C13—24no—
118C22×C13#32914yes—
119C22×C13#40711yescharacteristic
120C22×C13C2×#9911yescharacteristic
121C22×C13C2×#10011yescharacteristic
122C22×C13#41912yes—
123C22×C13C2×#10412yes—
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—82no—
127Dic13—24no—
128Dic13—44no—
129Dic13—42no—
130C22×Q8—132no—
131C22×Q8—264no—
132C22×Q8—261no—
133C22×Q8—522no—
134C22×Q8—522no—
135C23×C4—21no—
136C23×C4—132no—
137C23×C4—261no—
138C23×C4C2×#26111yescharacteristic
139C22×C8—264no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—42no—
142C2×C4⋊C4C2×#26112yes—
143C2×C42—132no—
144C2×C42—131no—
145C2×C42—131no—
146C2×C42—522no—
147C22⋊C8—268no—
148#97—524no—
149#95—264no—
150#95—264no—
151C2×C13—24no—
152C2×C13#146211yescharacteristic
153C2×C13#149112yes—
154C2×C13#150812yes—
155C2×C13C2×#32911yescharacteristic
156C2×C13#155811yescharacteristic
157C24C22⋊#26111yescharacteristic
158C2×Q8—134no—
159C2×Q8—264no—
160C2×Q8—262no—
161C2×Q8—5216no—
162C2×Q8—522no—
163C2×Q8—522no—
164C2×Q8—522no—
165C2×Q8—522no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—44no—
171C22×C4—42no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4—264no—
175C22×C4—264no—
176C22×C4—264no—
177C22×C4—262no—
178C22×C4—522no—
179C22×C4—522no—
180C22×C4—522no—
181C22×C4C22⋊#26111yescharacteristic
182C22×C4C22×#26111yescharacteristic
183C2×C8—268no—
184C2×C8—524no—
185C2×C8—524no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C42—264no—
189C42—521no—
190C42—521no—
191C13#762911yescharacteristic, complemented, Sylow
192C23—21no—
193C23—21no—
194C23—22no—
195C23#8811614yes—
196C23#8812112yes—
197C23C2×C22⋊#26111yescharacteristic
198Q8—524no—
199Q8—528no—
200Q8—524no—
201C2×C4—28no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—44no—
208C2×C4—84no—
209C2×C4—134no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—264no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—528no—
217C2×C4—528no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4#8810712yes—
221C2×C4D13⋊M1612yes—
222C8—528no—
223C22—22no—
224C22—22no—
225C22—24no—
226C22—24no—
227C22#1171829314yes—
228C22C2×#8810711yescharacteristic
229C22#1171912611yescharacteristic
230C22C2×#8811612yes—
231C22#1171915312yes—
232C22C2×#8812111yescharacteristic
233C4—22no—
234C4—22no—
235C4—82no—
236C4—264no—
237C4—524no—
238C4—522no—
239C2—24no—
240C2#1313008311yescharacteristic
241C2#1313018012yes—
242C2#1313023512yes—
243C2C2×#1171829311yescharacteristic
244C2#1313036911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#7629
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129657C2semidirect
191. C13#7629semidirect

Maximal subgroups

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

subgroupindex
#131305622
#131296572
C2×#117186352
#762913