Finite Group Databasebeta

← #16778515

Subgroups — #16778515

Order 3328.

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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#13130553C211yesmaximal, characteristic
2#13130553C211yesmaximal, characteristic
3#13129655C214yesmaximal
4#13117403C211yesmaximal, characteristic
5C2×#88141—21no—
6C2×#88123C411yescharacteristic
7C2×#88110—21no—
8C2×#88110—21no—
9C13×#384C411yescharacteristic
10C4⋊C4×Dic13—21no—
11C4⋊C4×Dic13C412yes—
12#11718635—21no—
13#11718634—21no—
14#11718634C2212yes—
15C42×Dic13C2211yescharacteristic
16#11718290—21no—
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×Dic26—21no—
21C22×#1057—22no—
22C22×#1057—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13C2×C412yes—
29C2×#6101—22no—
30C2×C4×Dic13—22no—
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88141—44no—
38#88123—24no—
39#88110—24no—
40#88110—24no—
41#88071—22no—
42#88071—22no—
43#7638—131nomaximal, Sylow
44C22×C4×C13—22no—
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C22×Dic13—22no—
49C22×Dic13C22⋊C411yescharacteristic
50C22×Dic13C22⋊C411yescharacteristic
51C22×Dic13C2×D411yescharacteristic
52C22×Dic13C2×D411yescharacteristic
53C2×Dic26—24no—
54C2×Dic26—42no—
55C2×Dic26—42no—
56C2×#1057—24no—
57C2×#1057—24no—
58C2×#1057—42no—
59C2×#1057—42no—
60C2×#1057—42no—
61C2×#1057—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C42×C13—22no—
66C4⋊Dic13—24no—
67C4⋊Dic13—22no—
68C4⋊Dic13M1614yes—
69#6101—44no—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13—41no—
76C4×Dic13—44no—
77C4×C4⋊Q8—131no—
78#1745—131no—
79#1745—131no—
80#1271—134no—
81C23×C13C2×C22⋊C411yescharacteristic
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13#10412yes—
92C2×C4×C13#10412yes—
93C2×C4×C13C2×M1612yes—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—24no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13#10112yes—
107C2×Dic13AGL(1,ℤ/8)12yes—
108C2×Dic13#13712yes—
109Dic26—48no—
110#1057—44no—
111#1057—44no—
112C2×C4⋊Q8—131no—
113C2×C4×Q8—261no—
114C2×#97—261no—
115C2×#97—261no—
116#391—261no—
117#389—132no—
118#389—261no—
119#384#26111yescharacteristic
120C4×C4⋊C4—132no—
121C4×C4⋊C4—261no—
122C43—131no—
123#336—132no—
124#336—132no—
125#336—261no—
126#336—261no—
127C22×C13#40711yescharacteristic
128C22×C13#41011yescharacteristic
129C22×C13C2×#10111yescharacteristic
130C22×C13#41811yescharacteristic
131C22×C13#41911yescharacteristic
132C22×C13C2×#10411yescharacteristic
133C22×C13C2×#10411yescharacteristic
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—82no—
138Dic13—22no—
139Dic13—22no—
140Dic13—22no—
141Dic13—44no—
142Dic13—41no—
143C22×Q8—261no—
144C22×C8—262no—
145C22×C8—262no—
146C4⋊Q8—264no—
147C4×Q8—524no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4—262no—
153C2×C4⋊C4C2×#26112yes—
154C2×C42—131no—
155C2×C42—131no—
156C2×C42—131no—
157C2×C42—131no—
158C2×C42—131no—
159C2×C42—131no—
160C2×C42—262no—
161C2×C42C2×#26111yescharacteristic
162#97—264no—
163#97—264no—
164#95—262no—
165#95—262no—
166C2×C13#146711yescharacteristic
167C2×C13#149011yescharacteristic
168C2×C13#149111yescharacteristic
169C2×C13#150511yescharacteristic
170C2×C13#150611yescharacteristic
171C2×C13#152611yescharacteristic
172C2×C13#155611yescharacteristic
173C2×Q8—264no—
174C2×Q8—522no—
175C2×Q8—522no—
176C22×C4—22no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—131no—
181C22×C4—262no—
182C22×C4C22⋊#26111yescharacteristic
183C22×C4C22⋊#26111yescharacteristic
184C22×C4C22×#26111yescharacteristic
185C2×C8—264no—
186C2×C8—264no—
187C2×C8—522no—
188C2×C8—522no—
189C2×C8—522no—
190C2×C8—522no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—134no—
195C4⋊C4—264no—
196C4⋊C4—262no—
197C4⋊C4—524no—
198C42—22no—
199C42—262no—
200C42—262no—
201C42—262no—
202C42—262no—
203C42—262no—
204C42—521no—
205C42—524no—
206C13#763811yescharacteristic, complemented, Sylow
207C23C2×C22⋊#26111yescharacteristic
208Q8—528no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—132no—
219C2×C4—132no—
220C2×C4—132no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—264no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—522no—
232C2×C4—522no—
233C2×C4#8811612yes—
234C2×C4#8811812yes—
235C2×C4D13⋊M1612yes—
236C8—524no—
237C8—524no—
238C22#1171912611yescharacteristic
239C22#1171913811yescharacteristic
240C22C2×#8811611yescharacteristic
241C22#1171914211yescharacteristic
242C22#1171915311yescharacteristic
243C22C2×#8811811yescharacteristic
244C22D13⋊#10111yescharacteristic
245C4—22no—
246C4—22no—
247C4—22no—
248C4—82no—
249C4—262no—
250C4—262no—
251C4—262no—
252C4—521no—
253C4—524no—
254C2#1313010011yescharacteristic
255C2#1313017711yescharacteristic
256C2#1313018011yescharacteristic
257C2#1313022511yescharacteristic
258C2#1313023011yescharacteristic
259C2#1313029411yescharacteristic
260C2#1313036611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#7638
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
206. C13#7638semidirect

Maximal subgroups

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

subgroupindex
#131305532
#131296552
#131174032
#763813