Finite Group Databasebeta

← #16782208

Subgroups — #16782208

Order 3328.

522 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130069C212yesmaximal
2#13129664C212yesmaximal, complemented
3#13129660C212yesmaximal, complemented
4C4×#88126C211yesmaximal, characteristic
5C2×#88126C411yescharacteristic
6C2×#88126C2211yescharacteristic
7C2×C42×D13C411yescharacteristic
8#11719119C2214yes—
9C43×C13C411yescharacteristic
10C4×#6103—22no—
11#11718593C411yescharacteristic
12#11718593C2211yescharacteristic
13C4×#6101—22no—
14C42×Dic13C2211yescharacteristic
15#11718287—22no—
16#11718286—22no—
17C22×C4×D13—21no—
18C22×C4×D13C2×C411yescharacteristic
19C2×C42×C13—22no—
20C2×C42×C13C2×C411yescharacteristic
21C2×C42×C13C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×#6103—21no—
24C2×#6103D412yes—
25C2×#6101—21no—
26C2×#6101D412yes—
27C2×C4×Dic13—21no—
28C2×C4×Dic13—22no—
29C2×C4×Dic13C2×C411yescharacteristic
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13C2311yescharacteristic
32#88126—22no—
33#88126—22no—
34#88126—22no—
35#88126C814yescomplemented
36C42×D13—22no—
37C42×D13—22no—
38C22⋊#1057—24no—
39C4⋊#1057—24no—
40C4×#1057—24no—
41#88071—22no—
42#88071—22no—
43#8731—131nomaximal, Sylow
44C23×D13C22⋊C411yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22⋊C412yes—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—21no—
50C22×Dic13—21no—
51C22×Dic13C22⋊C411yescharacteristic
52C22×Dic13C2×D412yes—
53C2×C4×D13—21no—
54C2×C4×D13—21no—
55C2×C4×D13—21no—
56C2×C4×D13—21no—
57C2×C4×D13—24no—
58C2×C4×D13—44no—
59C2×C4×D13C2×C812yes—
60C2×C4×D13M1612yes—
61C2×#1057—44no—
62C42×C13—21no—
63C42×C13—21no—
64C42×C13—21no—
65C42×C13—21no—
66C42×C13—44no—
67C42×C13C2×C812yes—
68C42×C13M1612yes—
69#6103—24no—
70#6103—24no—
71#6101—24no—
72#6101—24no—
73C4×Dic13—24no—
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13—44no—
77C4×Dic13C2×C812yes—
78C4×Dic13M1612yes—
79C4×Dic13#4112yes—
80C4×Dic13#4112yes—
81C4×#117—131no—
82#1458—132no—
83#1276—132no—
84#1274—132no—
85C23×C13C2×C22⋊C411yescharacteristic
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—42no—
89C22×D13C22⋊C812yes—
90C2×C4×C13—24no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13#11711yescharacteristic
97C2×C4×C13#11711yescharacteristic
98C2×C4×C13C22×C811yescharacteristic
99C2×C4×C13C2×M1611yescharacteristic
100C2×C4×C13C2×M1611yescharacteristic
101C2×C4×C13C2×M1611yescharacteristic
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13C22⋊C812yes—
110C2×Dic13#12314yes—
111C4×D13—22no—
112C4×D13—22no—
113C4×D13—22no—
114C4×D13—22no—
115C4×D13—48no—
116#1057—84no—
117C2×#117—131no—
118C2×#117—131no—
119C22×C42—131no—
120#431—134no—
121C4×C4⋊C4—262no—
122C4×C22⋊C4—262no—
123#376—131no—
124#376—131no—
125C43—131no—
126C43#26111yescharacteristic
127#324—262no—
128#323—262no—
129C22×C13—22no—
130C22×C13#38111yescharacteristic
131C22×C13C2×C22⋊C811yescharacteristic
132C22×C13#40711yescharacteristic
133C2×D13—22no—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—42no—
137C4×C13—24no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13#43111yescharacteristic
141C4×C13#43111yescharacteristic
142C4×C13#43211yescharacteristic
143C4×C13#43211yescharacteristic
144Dic13—22no—
145Dic13—24no—
146Dic13—42no—
147Dic13—42no—
148C23×C4—131no—
149C23×C4—261no—
150#117—134no—
151#117—262no—
152#117—262no—
153#117—262no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—261no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—261no—
158C2×C42—22no—
159C2×C42—131no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—262no—
163C2×C42—261no—
164C2×C42—262no—
165C2×C42—262no—
166C2×C42C2×#26111yescharacteristic
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#181711yescharacteristic
177C2×C13#182712yes—
178D13—42no—
179C24—131no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—131no—
183C22×C4—132no—
184C22×C4—132no—
185C22×C4—132no—
186C22×C4—264no—
187C22×C4—261no—
188C22×C4—261no—
189C22×C4—261no—
190C22×C4—261no—
191C22×C4—261no—
192C22×C4—261no—
193C22×C4—524no—
194C22×C4C22⋊#26112yes—
195C22×C4C22×#26111yescharacteristic
196C2×C8—524no—
197C4⋊C4—264no—
198C4⋊C4—264no—
199C22⋊C4—264no—
200C22⋊C4—264no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—44no—
206C42—132no—
207C42—132no—
208C42—132no—
209C42—132no—
210C42—264no—
211C42—261no—
212C42—261no—
213C42—524no—
214C42D13⋊C812yes—
215C42#611812yes—
216C13#873111yescharacteristic, complemented, Sylow
217C23—132no—
218C23—261no—
219C23—261no—
220C23—522no—
221C23C2×C22⋊#26111yescharacteristic
222C2×C4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—132no—
229C2×C4—134no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—528no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4C2×D13⋊C811yescharacteristic
243C2×C4C2×#611811yescharacteristic
244C2×C4D13⋊M1611yescharacteristic
245C2×C4D13⋊M1611yescharacteristic
246C2×C4#8823711yescharacteristic
247C2×C4#8823711yescharacteristic
248C8—1044no—
249C22—22no—
250C22—262no—
251C22—522no—
252C22—522no—
253C22—522no—
254C22D13⋊(C22⋊C8)11yescharacteristic
255C22#1171912711yescharacteristic
256C22#1171913511yescharacteristic
257C4—24no—
258C4—42no—
259C4—42no—
260C4—262no—
261C4—264no—
262C4—522no—
263C4—522no—
264C4#1171904911yescharacteristic
265C4#1171905111yescharacteristic
266C4#1171905411yescharacteristic
267C4#1171905511yescharacteristic
268C2—21no—
269C2—21no—
270C2—522no—
271C2#1313072811yescharacteristic
272C2#1313074512yes—
subgroupG/H
centerC2×C4#88237
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC43×C13C4
socleC22×C13#381
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC43#261
hypocenterC13#8731
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
2. #13129664C2semidirect
3. #13129660C2semidirect
35. #88126C8semidirect
216. C13#8731semidirect

Maximal subgroups

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

subgroupindex
#131300692
#131296642
#131296602
C4×#881262
#873113