Finite Group Databasebeta

← #16779814

Subgroups — #16779814

Order 3328.

726 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 184 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
1C2×#11719128C212yesmaximal
2#13129714C214yesmaximal, complemented
3C2×#11718637C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×#6101—22no—
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11719128—24no—
10#11719128C418yescomplemented
11C2×#88112C2214yes—
12C2×#88110—22no—
13#11718637—22no—
14#11718637C412yes—
15#11718637C2212yes—
16C23×C4×C13—21no—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13—21no—
19C23×Dic13D412yes—
20C22×#1057—24no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—42no—
23C2×C13×C4⋊C4C2×C412yes—
24C2×C4⋊Dic13—21no—
25C2×C4⋊Dic13—42no—
26C2×C4⋊Dic13C2×C412yes—
27C2×#6101—24no—
28C2×#6101—24no—
29C2×#6101—48no—
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13C2×C414yes—
32C2×C4×Dic13D412yes—
33C2×C4×Dic13D412yes—
34C2×C4×Dic13Q812yes—
35C2×C4×Dic13C2311yescharacteristic
36C22⋊#1057—28no—
37#88112—24no—
38#88112C2×C418yescomplemented
39#88110—28no—
40#8040—131nomaximal, Sylow
41C24×C13C22⋊C411yescharacteristic
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—44no—
46C22×C4×C13—42no—
47C22×C4×C13C4212yes—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C4⋊C412yes—
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—24no—
52C22×Dic13—24no—
53C22×Dic13—22no—
54C22×Dic13—44no—
55C22×Dic13—42no—
56C22×Dic13C22⋊C412yes—
57C22×Dic13C22⋊C414yes—
58C22×Dic13C4⋊C414yes—
59C22×Dic13C2×D412yes—
60C2×#1057—28no—
61C2×#1057—44no—
62C2×#1057—44no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C4⋊Dic13—42no—
66C4⋊Dic13—42no—
67#6101—48no—
68#6101—48no—
69C4×Dic13C4212yes—
70C4×Dic13C22⋊C414yes—
71C4×Dic13C4⋊C412yes—
72C4×Dic13C4⋊C414yes—
73C4×Dic13C22×C412yes—
74C4×Dic13C2×D411yescharacteristic
75C4×Dic13C2×Q811yescharacteristic
76C2×#432—132no—
77C2×#384—131no—
78#1296—134no—
79C23×C13—22no—
80C23×C13—22no—
81C23×C13#9512yes—
82C23×C13#10012yes—
83C23×C13#10112yes—
84C23×C13C2×C22⋊C411yescharacteristic
85C2×C4×C13—24no—
86C2×C4×C13—24no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—42no—
92C2×C4×C13—44no—
93C2×C4×C13—84no—
94C2×C4×C13#9512yes—
95C2×C4×C13C2×C4211yescharacteristic
96C2×C4×C13C2×C4⋊C411yescharacteristic
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—28no—
100C2×Dic13—28no—
101C2×Dic13—42no—
102C2×Dic13—44no—
103C2×Dic13—84no—
104C2×Dic13#9514yes—
105C2×Dic13C2×C22⋊C412yes—
106C2×Dic13C2×C4⋊C412yes—
107C2×Dic13AGL(1,ℤ/8)14yes—
108C2×Dic13#13714yes—
109#1057—48no—
110C22×C4⋊C4—131no—
111C22×C4⋊C4—262no—
112C22×C4⋊C4#26111yescharacteristic
113C22×C42—131no—
114#432—138no—
115#432—264no—
116C2×C4⋊C8—134no—
117C2×C22⋊C8—262no—
118C2×#97—262no—
119#384—132no—
120#384—132no—
121#384—262no—
122C22×C13—22no—
123C22×C13—24no—
124C22×C13—22no—
125C22×C13—24no—
126C22×C13#34314yes—
127C22×C13C2×#9511yescharacteristic
128C22×C13C2×#10011yescharacteristic
129C22×C13C2×#10111yescharacteristic
130C22×C13#41812yes—
131C22×C13#41912yes—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13—82no—
136Dic13—24no—
137Dic13—82no—
138Dic13#41714yes—
139Dic13#42814yes—
140C23×C4—21no—
141C23×C4—132no—
142C23×C4—261no—
143C23×C4C2×#26111yescharacteristic
144C22×C8—264no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—264no—
149C2×C4⋊C4—264no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4—522no—
152C2×C4⋊C4—528no—
153C2×C4⋊C4C2×#26112yes—
154C2×C42—134no—
155C2×C42—132no—
156C2×C42—132no—
157C2×C42—132no—
158C2×C42—131no—
159C2×C42—131no—
160C4⋊C8—138no—
161C4⋊C8—264no—
162C22⋊C8—268no—
163#97—268no—
164C2×C13—24no—
165C2×C13#155511yescharacteristic
166C2×C13#155612yes—
167C2×C13#155811yescharacteristic
168C2×C13#173612yes—
169C2×C13C2×#34311yescharacteristic
170C24C22⋊#26111yescharacteristic
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—44no—
175C22×C4—42no—
176C22×C4—132no—
177C22×C4—134no—
178C22×C4—134no—
179C22×C4—132no—
180C22×C4—264no—
181C22×C4—264no—
182C22×C4—262no—
183C22×C4—524no—
184C22×C4—522no—
185C22×C4C4×#26112yes—
186C22×C4C4⋊#26112yes—
187C22×C4C22⋊#26111yescharacteristic
188C22×C4C22×#26111yescharacteristic
189C2×C8—268no—
190C2×C8—524no—
191C2×C8—524no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—522no—
195C4⋊C4—522no—
196C4⋊C4—528no—
197C4⋊C4—528no—
198C42—134no—
199C42—134no—
200C42—132no—
201C42—132no—
202C42—131no—
203C42—132no—
204C42—131no—
205C13#804011yescharacteristic, complemented, Sylow
206C23—22no—
207C23—22no—
208C23#8811312yes—
209C23(C2×#261)⋊C412yes—
210C23#8812112yes—
211C23C2×C22⋊#26111yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—24no—
215C2×C4—24no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—84no—
221C2×C4—132no—
222C2×C4—132no—
223C2×C4—134no—
224C2×C4—134no—
225C2×C4—134no—
226C2×C4—268no—
227C2×C4—268no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—522no—
231C2×C4—524no—
232C2×C4—1044no—
233C2×C4(C2×#261)⋊C412yes—
234C2×C4C2×C4×#26111yescharacteristic
235C2×C4C2×C4⋊#26111yescharacteristic
236C8—528no—
237C22—24no—
238C22—22no—
239C22—24no—
240C22—22no—
241C22#1171829114yes—
242C22C2×#8811311yescharacteristic
243C22C2×(C2×#261)⋊C411yescharacteristic
244C22#1171913812yes—
245C22#1171915312yes—
246C22C2×#8812111yescharacteristic
247C4—22no—
248C4—21no—
249C4—21no—
250C4—82no—
251C4—134no—
252C4—134no—
253C4—264no—
254C4—1042no—
255C2—24no—
256C2#1313036311yescharacteristic
257C2#1313036512yes—
258C2#1313036911yescharacteristic
259C2#1313052312yes—
260C2C2×#1171829111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#8040
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129714C2semidirect
10. #11719128C4semidirect
38. #88112C2×C4semidirect
205. C13#8040semidirect

Maximal subgroups

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

subgroupindex
C2×#117191282
#131297142
C2×#117186372
#804013