Finite Group Databasebeta

← #16778663

Subgroups — #16778663

Order 3328.

432 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 114 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#13130622C211yesmaximal, characteristic
2#13130551C211yesmaximal, characteristic
3#13129654C214yesmaximal
4#13123197C211yesmaximal, characteristic
5C2×#88144—21no—
6C2×#88110—21no—
7C2×C4⋊#1057—21no—
8C2×C4×#1057—21no—
9C13×#384C411yescharacteristic
10#11718646—21no—
11#11718646C2212yes—
12#11718638—21no—
13#11718634—21no—
14#11718634C412yes—
15#11718596C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×#1057—22no—
21C22×#1057—22no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4C2×C412yes—
25C2×C42×C13C2×C411yescharacteristic
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—22no—
29C2×C4⋊Dic13C2×C412yes—
30C2×#6101—22no—
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88144—42no—
38#88144—42no—
39#88110—42no—
40C4⋊#1057—24no—
41C4×#1057—24no—
42#88071—22no—
43#88071—22no—
44#7680—131nomaximal, Sylow
45C22×C4×C13—22no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13C22⋊C411yescharacteristic
51C22×Dic13C22⋊C411yescharacteristic
52C22×Dic13C2×D411yescharacteristic
53C22×Dic13C2×D411yescharacteristic
54C2×#1057—24no—
55C2×#1057—24no—
56C2×#1057—42no—
57C2×#1057—42no—
58C2×#1057—42no—
59C2×#1057—42no—
60C13×C4⋊C4—24no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C42×C13—22no—
64C4⋊Dic13—42no—
65C4⋊Dic13—42no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69#6101—44no—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13—22no—
74C4×Dic13—41no—
75C4×Dic13D812yes—
76C4×Dic13SD1612yes—
77#2859—131no—
78#1767—131no—
79#1744—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—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13#10112yes—
90C2×C4×C13#10212yes—
91C2×C4×C13#10412yes—
92C2×C4×C13#10412yes—
93C2×C4×C13#13112yes—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13#10212yes—
107C2×Dic13C2×D811yescharacteristic
108C2×Dic13C2×SD1611yescharacteristic
109C2×Dic13#13712yes—
110#1057—44no—
111#1057—44no—
112C2×#125—261no—
113C2×C4⋊C8—261no—
114C2×#97—261no—
115C2×C4×C8—261no—
116#389—132no—
117#389—132no—
118#389—261no—
119#389—261no—
120#384—131no—
121#384#26111yescharacteristic
122#382—261no—
123C43—131no—
124#336—132no—
125#336—132no—
126#336—261no—
127C22×C13#40811yescharacteristic
128C22×C13#41011yescharacteristic
129C22×C13C2×#10111yescharacteristic
130C22×C13C2×#10211yescharacteristic
131C22×C13#41911yescharacteristic
132C22×C13C2×#10411yescharacteristic
133C22×C13C2×#10411yescharacteristic
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—82no—
137C4×C13#33014yes—
138Dic13—22no—
139Dic13—21no—
140Dic13—21no—
141Dic13—22no—
142Dic13—41no—
143Dic13—82no—
144C22×C8—262no—
145C22×C8—262no—
146#125—522no—
147#125—522no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—262no—
152C2×C4⋊C4—262no—
153C2×C4⋊C4—261no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4C2×#26112yes—
156C2×C42—131no—
157C2×C42—131no—
158C2×C42—131no—
159C2×C42—131no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42C2×#26111yescharacteristic
163C4⋊C8—264no—
164#97—522no—
165C4×C8—264no—
166#95—262no—
167#95—262no—
168C2×C13#147011yescharacteristic
169C2×C13#148511yescharacteristic
170C2×C13#149211yescharacteristic
171C2×C13#150211yescharacteristic
172C2×C13#150611yescharacteristic
173C2×C13C2×#33011yescharacteristic
174C2×C13#154611yescharacteristic
175C22×C4—22no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—262no—
181C22×C4C22⋊#26111yescharacteristic
182C22×C4C22⋊#26111yescharacteristic
183C22×C4C22×#26111yescharacteristic
184C2×C8—264no—
185C2×C8—264no—
186C2×C8—522no—
187C2×C8—522no—
188C2×C8—522no—
189C2×C8—522no—
190C4⋊C4—24no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—522no—
194C4⋊C4—524no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C4⋊C4—522no—
198C4⋊C4—522no—
199C42—22no—
200C42—132no—
201C42—132no—
202C42—262no—
203C42—262no—
204C42—262no—
205C42—262no—
206C42—521no—
207C13#768011yescharacteristic, complemented, Sylow
208C23C2×C22⋊#26111yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—131no—
217C2×C4—132no—
218C2×C4—131no—
219C2×C4—132no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—522no—
230C2×C4—522no—
231C2×C4—522no—
232C2×C4#8811312yes—
233C2×C4#8811512yes—
234C2×C4#8811612yes—
235C2×C4#8811812yes—
236C2×C4#8823812yes—
237C8—524no—
238C8—524no—
239C22C2×#8811311yescharacteristic
240C22C2×#8811511yescharacteristic
241C22C2×#8811611yescharacteristic
242C22#1171914711yescharacteristic
243C22#1171915311yescharacteristic
244C22C2×#8811811yescharacteristic
245C22#1171915611yescharacteristic
246C4—22no—
247C4—22no—
248C4—82no—
249C4—262no—
250C4—261no—
251C4—261no—
252C4—262no—
253C4—521no—
254C4—1042no—
255C4#1171824214yes—
256C2#1313010911yescharacteristic
257C2#1313015911yescharacteristic
258C2#1313018211yescharacteristic
259C2#1313021711yescharacteristic
260C2#1313022811yescharacteristic
261C2C2×#1171824211yescharacteristic
262C2#1313034511yescharacteristic
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#7680
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
207. C13#7680semidirect

Maximal subgroups

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

subgroupindex
#131306222
#131305512
#131296542
#131231972
#768013