Finite Group Databasebeta

← #15756354

Subgroups — #15756354

Order 3328.

514 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 135 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#13117241C211yesmaximal, characteristic
2#13114813C212yesmaximal
3#13112720C212yesmaximal, complemented
4#13112719C211yesmaximal, characteristic, complemented
5C13×#1296C211yesmaximal, characteristic, complemented
6C2×#88146C412yes—
7C2×C42×D13C2211yescharacteristic
8C2×C13×C4⋊C8C2212yes—
9C13×#384C2211yescharacteristic
10C2×#88060—22no—
11#11718648—22no—
12#11718638C412yes—
13C4⋊C4×Dic13—22no—
14#11718596C2211yescharacteristic
15C2×C4⋊#1055C2212yes—
16#11718142—22no—
17C22×C4×D13C2×C411yescharacteristic
18C22×C4×D13D412yes—
19C22×C8×C13—22no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C42×C13C2311yescharacteristic
23C2×#6103—22no—
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13C2×C412yes—
26C2×C4×Dic13—22no—
27C2×C4×Dic13C2×C411yescharacteristic
28C2×C4×Dic13D412yes—
29C22×#1055—22no—
30#88146—44no—
31C42×D13—22no—
32C42×D13—21no—
33C42×D13—21no—
34C13×C4⋊C8—22no—
35C13×C4⋊C8—22no—
36#88071—24no—
37#88060—44no—
38C4⋊#1055—22no—
39C4⋊#1055—22no—
40#8728—131nomaximal, Sylow
41C23×D13C22⋊C411yescharacteristic
42C22×C4×C13—22no—
43C22×C4×C13C22×C411yescharacteristic
44C22×C4×C13C2×D412yes—
45C22×Dic13—22no—
46C22×Dic13C22⋊C412yes—
47C22×Dic13C22⋊C411yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—21no—
50C2×C4×D13—21no—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—22no—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C8×C13—42no—
59C2×C8×C13—42no—
60C2×C8×C13—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C42×C13#4112yes—
65C42×C13#4111yescharacteristic
66C42×C13#4111yescharacteristic
67#6103—44no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4×Dic13—21no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13—44no—
76C2×#1055—42no—
77C2×#1055—42no—
78C2×#1055—42no—
79#2285—131no—
80#1797—132no—
81#1296—132no—
82#1296—131no—
83#1296D1311yescharacteristic, complemented
84C23×C13C2×C22⋊C411yescharacteristic
85C22×D13—21no—
86C22×D13—21no—
87C22×D13—22no—
88C22×D13—22no—
89C22×D13#10112yes—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—42no—
93C2×C4×C13—44no—
94C2×C4×C13#11711yescharacteristic
95C2×C4×C13#11711yescharacteristic
96C2×C4×C13#12312yes—
97C2×C4×C13#12312yes—
98C2×C4×C13#13512yes—
99C2×C4×C13#13512yes—
100C2×C4×C13AGL(1,ℤ/8)12yes—
101C2×C4×C13#13712yes—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—42no—
108C2×Dic13—44no—
109C2×Dic13#10012yes—
110C4×D13—24no—
111C4×D13—24no—
112C4×D13—42no—
113C4×D13—42no—
114C4×D13—42no—
115C4×D13—42no—
116C8×C13—82no—
117#1055—82no—
118C2×#117—132no—
119C22×C42—131no—
120C2×C4⋊C8—132no—
121C2×C4⋊C8C2×D1312yes—
122C2×C22⋊C8—262no—
123#384—131no—
124#384C2×D1311yescharacteristic
125#382—132no—
126#380—262no—
127C4×C4⋊C4—262no—
128#336—262no—
129C22×C13#38111yescharacteristic
130C22×C13C2×#10011yescharacteristic
131C22×C13C2×#10111yescharacteristic
132C22×C13#41612yes—
133C22×C13#41712yes—
134C2×D13—24no—
135C2×D13—22no—
136C2×D13—41no—
137C2×D13—41no—
138C2×D13—42no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—82no—
142C4×C13#48212yes—
143C4×C13#48212yes—
144C4×C13#48512yes—
145C4×C13#48512yes—
146Dic13—22no—
147Dic13—42no—
148Dic13—82no—
149C23×C4—131no—
150C23×C4—132no—
151C22×C8—22no—
152C22×C8—262no—
153#117—524no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4—262no—
157C2×C4⋊C4C4×D1312yes—
158C2×C22⋊C4—262no—
159C2×C42—131no—
160C2×C42—132no—
161C2×C42—262no—
162C2×C42—261no—
163C2×C42—261no—
164C2×C42—262no—
165C2×C42C22×D1311yescharacteristic
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—262no—
169C4⋊C8—262no—
170C22⋊C8—524no—
171#95—264no—
172C2×C13#154311yescharacteristic
173C2×C13#155212yes—
174C2×C13#156011yescharacteristic
175C2×C13#182111yescharacteristic
176C2×C13#182512yes—
177D13—42no—
178C24—131no—
179C22×C4—22no—
180C22×C4—131no—
181C22×C4—132no—
182C22×C4—262no—
183C22×C4—262no—
184C22×C4—261no—
185C22×C4—261no—
186C22×C4—262no—
187C22×C4—262no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—262no—
192C22×C4—262no—
193C22×C4C2×C4×D1311yescharacteristic
194C22×C4D4×D1312yes—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—522no—
199C2×C8—522no—
200C2×C8—522no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—522no—
205C4⋊C4—522no—
206C4⋊C4—522no—
207C22⋊C4—524no—
208C42—261no—
209C42—262no—
210C42—261no—
211C42—262no—
212C42—524no—
213C42#612712yes—
214C42#612911yescharacteristic
215C42#613111yescharacteristic
216C13#872811yescharacteristic, complemented, Sylow
217C23—132no—
218C23—261no—
219C23—262no—
220C23—262no—
221C23—261no—
222C23C22⋊C4×D1311yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—44no—
227C2×C4—132no—
228C2×C4—264no—
229C2×C4—264no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4—522no—
240C2×C4—524no—
241C2×C4#8812611yescharacteristic
242C2×C4#8813712yes—
243C2×C4#8814611yescharacteristic
244C2×C4#8814812yes—
245C2×C4#8816612yes—
246C2×C4#8816812yes—
247C2×C4#8817012yes—
248C2×C4#8817212yes—
249C8—82no—
250C8—1042no—
251C22—262no—
252C22—264no—
253C22—522no—
254C22—521no—
255C22—521no—
256C22#1171832511yescharacteristic
257C22D13×#10011yescharacteristic
258C22D13×#10111yescharacteristic
259C22#1171843312yes—
260C22#1171846412yes—
261C4—21no—
262C4—21no—
263C4—82no—
264C4—262no—
265C4—522no—
266C4—1042no—
267C4#1171844512yes—
268C4#1171847612yes—
269C4#1171852712yes—
270C4#1171854912yes—
271C2—522no—
272C2#1311349511yescharacteristic
273C2#1311353312yes—
274C2#1311357011yescharacteristic
275C2#1311491511yescharacteristic
276C2#1311492912yes—
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1296D13
hypocenterC13#8728
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #13112720C2semidirect
4. #13112719C2semidirect
5. C13×#1296C2semidirect
83. #1296D13semidirect
216. C13#8728semidirect

Maximal subgroups

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

subgroupindex
#131172412
#131148132
#131127202
#131127192
C13×#12962
#872813