Finite Group Databasebeta

← #16778531

Subgroups — #16778531

Order 3328.

646 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 124 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
2#13129657C214yesmaximal, complemented
3C2×#11718635C211yesmaximal, characteristic
4C23×Dic26C411yescharacteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88112—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—44no—
32#88112—44no—
33#88071—24no—
34#88071—24no—
35#7643—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—44no—
42C22×C4×C13—42no—
43C22×C4×C13C22⋊C411yescharacteristic
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13—24no—
46C22×Dic13—22no—
47C22×Dic13—42no—
48C22×Dic13—42no—
49C22×Dic13—42no—
50C22×Dic13—42no—
51C22×Dic13C22⋊C412yes—
52C22×Dic13SD1614yes—
53C22×Dic13Q1614yes—
54C22×Dic13C2×D412yes—
55C2×Dic26—24no—
56C2×Dic26—22no—
57C2×Dic26—42no—
58C2×Dic26—416no—
59C2×Dic26—42no—
60C2×Dic26—42no—
61C2×Dic26—42no—
62C2×Dic26M1614yes—
63C2×#1057—44no—
64C2×#1057—44no—
65C2×#1057—44no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C4×Dic13—24no—
69C4×Dic13—41no—
70C4×Dic13—41no—
71C2×#391—131no—
72#1797—132no—
73#1272—134no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—22no—
77C23×C13#10012yes—
78C23×C13#10314yes—
79C23×C13C2×C22⋊C411yescharacteristic
80C2×C4×C13—28no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—42no—
86C2×C4×C13—44no—
87C2×C4×C13—84no—
88C2×C4×C13#9912yes—
89C2×C4×C13C2×M1612yes—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—24no—
95C2×Dic13—44no—
96C2×Dic13—44no—
97C2×Dic13—48no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13#10314yes—
101C2×Dic13C2×SD1612yes—
102C2×Dic13C2×Q1612yes—
103Dic26—48no—
104Dic26—44no—
105Dic26—44no—
106#1057—84no—
107C23×Q8—131no—
108C22×C4⋊C4#26111yescharacteristic
109C22×C42—131no—
110C2×C4⋊C8—262no—
111C2×C22⋊C8—262no—
112#391—132no—
113#391—132no—
114#391—262no—
115C2×#95—262no—
116#336—134no—
117C22×C13—22no—
118C22×C13—24no—
119C22×C13—24no—
120C22×C13—22no—
121C22×C13#33314yes—
122C22×C13#40711yescharacteristic
123C22×C13C2×#9911yescharacteristic
124C22×C13C2×#10011yescharacteristic
125C22×C13C2×#10312yes—
126C22×C13#42112yes—
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—82no—
130Dic13—22no—
131Dic13—24no—
132Dic13—22no—
133Dic13—44no—
134C22×Q8—132no—
135C22×Q8—264no—
136C22×Q8—261no—
137C22×Q8—522no—
138C22×Q8—522no—
139C23×C4—21no—
140C23×C4—132no—
141C23×C4—261no—
142C23×C4C2×#26111yescharacteristic
143C22×C8—264no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—42no—
146C2×C4⋊C4C2×#26112yes—
147C2×C42—132no—
148C2×C42—131no—
149C2×C42—131no—
150C2×C42—522no—
151C4⋊C8—524no—
152C22⋊C8—524no—
153#95—264no—
154#95—264no—
155C2×C13—24no—
156C2×C13#146211yescharacteristic
157C2×C13#148712yes—
158C2×C13#152012yes—
159C2×C13#153311yescharacteristic
160C2×C13C2×#33311yescharacteristic
161C24C22⋊#26111yescharacteristic
162C2×Q8—134no—
163C2×Q8—264no—
164C2×Q8—262no—
165C2×Q8—5216no—
166C2×Q8—522no—
167C2×Q8—522no—
168C2×Q8—522no—
169C2×Q8—522no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—44no—
175C22×C4—42no—
176C22×C4—132no—
177C22×C4—132no—
178C22×C4—134no—
179C22×C4—134no—
180C22×C4—264no—
181C22×C4—262no—
182C22×C4—522no—
183C22×C4—522no—
184C22×C4—522no—
185C22×C4—522no—
186C22×C4C22⋊#26111yescharacteristic
187C22×C4C22×#26111yescharacteristic
188C2×C8—524no—
189C2×C8—524no—
190C2×C8—524no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C42—264no—
194C42—521no—
195C42—521no—
196C13#764311yescharacteristic, complemented, Sylow
197C23—21no—
198C23—21no—
199C23—22no—
200C23#8811714yes—
201C23#8812112yes—
202C23C2×C22⋊#26111yescharacteristic
203Q8—524no—
204Q8—528no—
205Q8—524no—
206C2×C4—28no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—44no—
213C2×C4—84no—
214C2×C4—132no—
215C2×C4—134no—
216C2×C4—132no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—264no—
222C2×C4—524no—
223C2×C4—524no—
224C2×C4—528no—
225C2×C4—522no—
226C2×C4—522no—
227C2×C4#8810712yes—
228C2×C4D13⋊M1612yes—
229C8—1044no—
230C22—24no—
231C22—22no—
232C22—22no—
233C22—24no—
234C22#1171830314yes—
235C22C2×#8810711yescharacteristic
236C22#1171912611yescharacteristic
237C22#1171914012yes—
238C22C2×#8811712yes—
239C22C2×#8812111yescharacteristic
240C4—22no—
241C4—22no—
242C4—82no—
243C4—262no—
244C4—264no—
245C4—262no—
246C4—524no—
247C2—24no—
248C2#1313008311yescharacteristic
249C2#1313016612yes—
250C2#1313027512yes—
251C2#1313031511yescharacteristic
252C2C2×#1171830311yescharacteristic
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#7643
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
196. C13#7643semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131296572
C2×#117186352
#764313