Finite Group Databasebeta

← #16781163

Subgroups — #16781163

Order 3328.

802 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 132 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#13130692C212yesmaximal
2C2×#11718245C214yesmaximal, complemented
3C2×#11719222C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7#11719222—28no—
8C2×#88144C412yes—
9C2×#88142C2212yes—
10C2×#88132—22no—
11C2×C4×Dic26—22no—
12C2×C22⋊#1057—22no—
13C2×#88112C2214yes—
14#11718290—22no—
15#11718245—28no—
16C23×C4×C13C2×C411yescharacteristic
17C23×Dic13D412yes—
18C22×Dic26—22no—
19C22×#1057—24no—
20C13×#117—24no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C13×C22⋊C4—21no—
23C2×C42×C13—21no—
24C2×C22⋊Dic13—21no—
25#88180—24no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13C2×C412yes—
28C2×#6101—22no—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13—24no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13C2311yescharacteristic
35#88144—24no—
36#88144—24no—
37#88142—24no—
38#88142D418yes—
39#88132—216no—
40C4×Dic26—216no—
41C22⋊#1057—44no—
42#88112—28no—
43#8345—131nomaximal, Sylow
44C24×C13C22⋊C411yescharacteristic
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—22no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—24no—
53C22×Dic13—24no—
54C22×Dic13—22no—
55C22×Dic13—22no—
56C22×Dic13C22⋊C412yes—
57C22×Dic13C2×D412yes—
58C2×Dic26—28no—
59C2×Dic26—44no—
60C2×Dic26—42no—
61C2×Dic26—42no—
62C2×#1057—44no—
63C2×#1057—44no—
64C2×#1057—44no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4C22⋊C414yes—
67C13×C22⋊C4—24no—
68C42×C13—24no—
69C22⋊Dic13—24no—
70C4⋊Dic13—28no—
71C4⋊Dic13—22no—
72C4⋊Dic13C22⋊C414yes—
73#6101—28no—
74#6101—28no—
75C4×Dic13—24no—
76C4×Dic13—22no—
77C4×Dic13—24no—
78C4×Dic13C2×D414yes—
79C2×#533—131no—
80#1797—132no—
81C2×#332—134no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13#10112yes—
87C23×C13C2×C22⋊C411yescharacteristic
88C2×C4×C13—28no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—24no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13#10112yes—
97C2×C4×C13C2×C22⋊C412yes—
98C2×Dic13—22no—
99C2×Dic13—24no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—44no—
105C2×Dic13—44no—
106C2×Dic13#12014yes—
107C2×Dic13#13514yes—
108C2×Dic13AGL(1,ℤ/8)12yes—
109C2×Dic13#13712yes—
110Dic26—48no—
111Dic26—48no—
112#1057—84no—
113#533—268no—
114C2×C4⋊Q8—132no—
115C2×#125—132no—
116C2×C22⋊Q8—262no—
117C2×C4×Q8—262no—
118C2×#117—131no—
119C2×#117#26111yescharacteristic
120C22×C42—131no—
121C2×C4⋊C8—134no—
122C2×C22⋊C8—262no—
123#336—262no—
124#332—268no—
125C22×C13—24no—
126C22×C13—22no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—42no—
130C22×C13#37911yescharacteristic
131C22×C13C2×#10111yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C22×C13#41612yes—
134C22×C13#41712yes—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—44no—
138Dic13—44no—
139Dic13—42no—
140Dic13#44914yes—
141Dic13#45214yes—
142C22×Q8—262no—
143C23×C4—132no—
144C23×C4C2×#26111yescharacteristic
145C22×C8—264no—
146C4⋊Q8—138no—
147C4⋊Q8—264no—
148#125—264no—
149#125—264no—
150C22⋊Q8—2616no—
151C4×Q8—2616no—
152#117—24no—
153#117—264no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—262no—
156C2×C4⋊C4—262no—
157C2×C4⋊C4—262no—
158C2×C4⋊C4C2×#26112yes—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—261no—
161C2×C42—21no—
162C2×C42—131no—
163C2×C42—132no—
164C2×C42—131no—
165C2×C42—264no—
166C2×C42—261no—
167C4⋊C8—268no—
168C22⋊C8—524no—
169C2×C13—42no—
170C2×C13#154411yescharacteristic
171C2×C13#155212yes—
172C2×C13#156111yescharacteristic
173C2×C13#178411yescharacteristic
174C2×C13#178812yes—
175C24C22⋊#26111yescharacteristic
176C2×Q8—268no—
177C2×Q8—522no—
178C2×Q8—522no—
179C2×Q8—524no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—132no—
185C22×C4—132no—
186C22×C4—262no—
187C22×C4—264no—
188C22×C4—262no—
189C22×C4—264no—
190C22×C4—262no—
191C22×C4C22⋊#26111yescharacteristic
192C22×C4C22×#26111yescharacteristic
193C2×C8—524no—
194C2×C8—524no—
195C2×C8—524no—
196C4⋊C4—22no—
197C4⋊C4—134no—
198C4⋊C4—268no—
199C4⋊C4—268no—
200C4⋊C4—268no—
201C4⋊C4—262no—
202C4⋊C4C22⋊#26114yes—
203C22⋊C4—24no—
204C22⋊C4—264no—
205C42—24no—
206C42—134no—
207C42—264no—
208C42—264no—
209C42—262no—
210C13#834511yescharacteristic, complemented, Sylow
211C23—21no—
212C23—21no—
213C23—22no—
214C23—22no—
215C23#8811312yes—
216C23C2×C22⋊#26111yescharacteristic
217Q8—528no—
218Q8—528no—
219C2×C4—28no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—24no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—134no—
228C2×C4—132no—
229C2×C4—132no—
230C2×C4—134no—
231C2×C4—262no—
232C2×C4—264no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—524no—
236C2×C4—524no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4#8811312yes—
240C2×C4C2×C22⋊#26112yes—
241C8—1044no—
242C22—24no—
243C22—22no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22C2×#8811311yescharacteristic
248C22C2×#8811311yescharacteristic
249C22#1171916412yes—
250C22#1171916512yes—
251C22#1171917111yescharacteristic
252C4—22no—
253C4—22no—
254C4—44no—
255C4—134no—
256C4—134no—
257C4—522no—
258C4—524no—
259C2—42no—
260C2#1313034111yescharacteristic
261C2#1313035712yes—
262C2#1313037511yescharacteristic
263C2#1313067011yescharacteristic
264C2#1313067612yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8345
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11718245C2semidirect
210. C13#8345semidirect

Maximal subgroups

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

subgroupindex
#131306922
C2×#117182452
C2×#117192222
#834513