Finite Group Databasebeta

← #16782202

Subgroups — #16782202

Order 3328.

522 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 120 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#13130067C212yesmaximal
2#13129664C212yesmaximal, complemented
3#13129660C212yesmaximal, complemented
4#117×Dic13C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×#88180C2211yescharacteristic
7C22×C4×Dic13C411yescharacteristic
8#11719119C2214yes—
9C4⋊C4×Dic13—22no—
10C22⋊C4×Dic13—22no—
11#11718593C411yescharacteristic
12#11718593C2211yescharacteristic
13C42×Dic13C411yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718305—22no—
16#11718285—22no—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13—21no—
19C13×#117—22no—
20C13×#117—22no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C22⋊C4—21no—
23C2×C42×C13C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13D412yes—
26#88180—22no—
27#88180—22no—
28C2×C4⋊Dic13D412yes—
29C2×C4×Dic13—21no—
30C2×C4×Dic13—22no—
31C2×C4×Dic13—22no—
32C2×C4×Dic13—22no—
33C2×C4×Dic13C814yescomplemented
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13C2311yescharacteristic
38C22⋊#1057—24no—
39C4⋊#1057—24no—
40C4×#1057—24no—
41#88071—22no—
42#88071—22no—
43#8730—131nomaximal, Sylow
44C24×C13C22⋊C411yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C2×C812yes—
53C22×C4×C13M1612yes—
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—21no—
56C22×Dic13—24no—
57C22×Dic13—21no—
58C22×Dic13—44no—
59C22×Dic13C22⋊C412yes—
60C22×Dic13C2×D412yes—
61C2×#1057—44no—
62C13×C4⋊C4—24no—
63C13×C22⋊C4—24no—
64C42×C13—21no—
65C42×C13—21no—
66C42×C13M1612yes—
67C42×C13M1612yes—
68C22⋊Dic13—24no—
69C4⋊Dic13—24no—
70C4×Dic13—24no—
71C4×Dic13—21no—
72C4×Dic13—21no—
73C4×Dic13—21no—
74C4×Dic13—21no—
75C4×Dic13—44no—
76C4×Dic13—44no—
77C4×Dic13C2×C812yes—
78C4×Dic13C2×C812yes—
79C4×Dic13#4112yes—
80C4×Dic13#4112yes—
81C4×#117—131no—
82#1458—132no—
83#1276—132no—
84#1274—132no—
85C23×C13—21no—
86C23×C13—21no—
87C23×C13—42no—
88C23×C13C22⋊C812yes—
89C23×C13C2×C22⋊C411yescharacteristic
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13C22⋊C812yes—
101C2×C4×C13#11711yescharacteristic
102C2×C4×C13#11711yescharacteristic
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×C4×C13C2×M1611yescharacteristic
106C2×C4×C13C2×M1611yescharacteristic
107C2×Dic13—24no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—42no—
112C2×Dic13—48no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13#12314yes—
116#1057—84no—
117C2×#117—131no—
118C2×#117#26111yescharacteristic
119C22×C42—131no—
120#431—134no—
121C4×C4⋊C4—262no—
122C4×C22⋊C4—262no—
123#376—131no—
124#376—131no—
125C43—131no—
126C43—131no—
127#324—262no—
128#323—262no—
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13#38111yescharacteristic
135C22×C13C2×C22⋊C811yescharacteristic
136C22×C13#40711yescharacteristic
137C4×C13—22no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13#43111yescharacteristic
141C4×C13#43111yescharacteristic
142C4×C13#43211yescharacteristic
143C4×C13#43211yescharacteristic
144Dic13—24no—
145Dic13—24no—
146Dic13—42no—
147Dic13—42no—
148C23×C4—261no—
149C23×C4C2×#26111yescharacteristic
150#117—22no—
151#117—22no—
152#117—262no—
153#117—262no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—132no—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—132no—
158C2×C42—131no—
159C2×C42—134no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—262no—
164C2×C42—261no—
165C2×C42—262no—
166C2×C42—262no—
167C2×C42C2×#26111yescharacteristic
168C2×C42C2×#26111yescharacteristic
169C4⋊C8—264no—
170C22⋊C8—264no—
171C4×C8—264no—
172#95—262no—
173#95—262no—
174C2×C13—21no—
175C2×C13—21no—
176C2×C13—42no—
177C2×C13#181711yescharacteristic
178C2×C13#182712yes—
179C24C22⋊#26111yescharacteristic
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—132no—
187C22×C4—132no—
188C22×C4—261no—
189C22×C4—264no—
190C22×C4—261no—
191C22×C4—524no—
192C22×C4D13⋊C812yes—
193C22×C4#611812yes—
194C22×C4C22⋊#26111yescharacteristic
195C22×C4C22×#26111yescharacteristic
196C2×C8—524no—
197C4⋊C4—24no—
198C4⋊C4—264no—
199C22⋊C4—24no—
200C22⋊C4—264no—
201C42—21no—
202C42—21no—
203C42—132no—
204C42—132no—
205C42—132no—
206C42—132no—
207C42—264no—
208C42—261no—
209C42—261no—
210C42—261no—
211C42—261no—
212C42—524no—
213C42—524no—
214C42#612212yes—
215C42#612212yes—
216C13#873011yescharacteristic, complemented, Sylow
217C23—21no—
218C23—21no—
219C23—42no—
220C23#8811112yes—
221C23C2×C22⋊#26111yescharacteristic
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—134no—
233C2×C4—264no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—522no—
238C2×C4—528no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4#8811112yes—
242C2×C4C2×D13⋊C811yescharacteristic
243C2×C4C2×#611811yescharacteristic
244C2×C4#8823711yescharacteristic
245C2×C4#8823711yescharacteristic
246C2×C4C2×#612211yescharacteristic
247C2×C4C2×#612211yescharacteristic
248C8—1044no—
249C22—22no—
250C22—22no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C2×#8811111yescharacteristic
255C22#1171913511yescharacteristic
256C22#1171916911yescharacteristic
257C4—22no—
258C4—42no—
259C4—42no—
260C4—264no—
261C4—264no—
262C4—522no—
263C4—522no—
264C4#1171912511yescharacteristic
265C4#1171912511yescharacteristic
266C4#1171913011yescharacteristic
267C4#1171913011yescharacteristic
268C2—21no—
269C2—21no—
270C2—42no—
271C2#1313072711yescharacteristic
272C2#1313074612yes—
subgroupG/H
centerC2×C4#88237
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8730
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129664C2semidirect
3. #13129660C2semidirect
33. C2×C4×Dic13C8semidirect
216. C13#8730semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131296642
#131296602
#117×Dic132
#873013