Finite Group Databasebeta

← #16779852

Subgroups — #16779852

Order 3328.

604 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 140 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#13131283C212yesmaximal
2#13129716C214yesmaximal
3#13123467C211yesmaximal, characteristic
4C2×C42×D13C2211yescharacteristic
5#11719136—22no—
6#11719135—22no—
7C4×C22⋊#261C2214yes—
8#11719061C414yescomplemented
9#11719060C414yescomplemented
10C4×C4⋊#261—22no—
11#11719057—22no—
12C4×C13×M16C411yescharacteristic, complemented
13#11718787C2212yes—
14#11718779C412yescomplemented
15C4×#6099C411yescharacteristic, complemented
16#11718366—22no—
17#11718346—22no—
18C22×C4×D13D412yes—
19C22×C4×D13C2311yescharacteristic
20C2×C22⋊#261—24no—
21C2×C4⋊#261—24no—
22C2×C4×#261—24no—
23C2×C13×M16C2×C412yes—
24C2×C42×C13C2×C411yescharacteristic
25C2×C4×Dic13C2×C411yescharacteristic
26C2×C4×Dic13Q812yes—
27C2×#6099C2×C412yes—
28C42×D13C2×C412yes—
29C42×D13C2×C412yes—
30C42×D13D412yes—
31C42×D13D412yes—
32(C2×#261)⋊C4—24no—
33(C2×#261)⋊C4—24no—
34(C2×#261)⋊C4—24no—
35(C2×#261)⋊C4C2×C418yes—
36C13×#97—21no—
37C4×C8×C13—21no—
38#88060—24no—
39#88054—24no—
40#88043—21no—
41C4×#1055—21no—
42#8050—131nomaximal, Sylow
43C23×D13C2×D411yescharacteristic
44C22×#261—28no—
45C22×C4×C13C4⋊C412yes—
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13C4⋊C412yes—
48C22×Dic13C2×Q811yescharacteristic
49C2×C4×D13—42no—
50C2×C4×D13—44no—
51C2×C4×D13C22⋊C412yes—
52C2×C4×D13C22⋊C412yes—
53C2×C4×D13C22⋊C412yes—
54C2×C4×D13C22⋊C412yes—
55C2×C4×D13C22×C412yes—
56C2×C4×D13C2×D412yes—
57C22⋊#261—48no—
58C4⋊#261—48no—
59C4×#261—48no—
60C13×M16—42no—
61C2×C8×C13—22no—
62C42×C13C4212yes—
63C42×C13C22⋊C411yescharacteristic
64C42×C13C22⋊C411yescharacteristic
65C4×Dic13C4211yescharacteristic
66C4×Dic13C4211yescharacteristic
67C4×Dic13C22⋊C412yes—
68C4×Dic13C4⋊C412yes—
69C4×Dic13C4⋊C412yes—
70C4×Dic13C4⋊C412yes—
71C4×Dic13C4⋊C412yes—
72#6099—42no—
73C2×#1055—22no—
74#2920—131no—
75#2283—132no—
76#1297—134no—
77C23×C13C2×C4⋊C411yescharacteristic
78C22×D13—24no—
79C22×D13—41no—
80C22×D13C2×C22⋊C412yes—
81C2×#261—48no—
82C2×#261—48no—
83C2×#261—48no—
84C2×C4×C13—22no—
85C2×C4×C13—42no—
86C2×C4×C13#9512yes—
87C2×C4×C13#9512yes—
88C2×C4×C13C2×C4211yescharacteristic
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C2×Dic13—42no—
91C2×Dic13—41no—
92C2×Dic13#9512yes—
93C2×Dic13#9512yes—
94C2×Dic13C2×C4⋊C412yes—
95C4×D13—24no—
96C4×D13—24no—
97C4×D13—24no—
98C4×D13—42no—
99C4×D13—42no—
100C4×D13—42no—
101C8×C13—42no—
102#1055—42no—
103C22×C42—131no—
104#432—262no—
105#431—262no—
106#423—132no—
107#407—132no—
108C4×M16—131no—
109C4×M16#26111yescharacteristic, complemented
110#383—134no—
111#382—134no—
112#381—262no—
113#380—262no—
114C4×C4⋊C4—262no—
115C4×C22⋊C4—134no—
116#376—262no—
117C22×C13—22no—
118C22×C13—21no—
119C22×C13C2×#9511yescharacteristic
120C2×D13—22no—
121C2×D13—22no—
122C2×D13—44no—
123C2×D13#42114yes—
124#261—88no—
125C4×C13—22no—
126C4×C13—22no—
127C4×C13—21no—
128C4×C13#41012yes—
129Dic13—22no—
130Dic13—22no—
131Dic13—22no—
132C23×C4—132no—
133C23×C4—131no—
134C2×M16—132no—
135C2×M16C2×#26112yes—
136C2×C4⋊C4—264no—
137C2×C22⋊C4—264no—
138C2×C42—132no—
139C2×C42—131no—
140C2×C42—132no—
141C2×C42—132no—
142C2×C42—132no—
143C2×C42—132no—
144C2×C42—264no—
145C2×C42C2×#26111yescharacteristic
146C4⋊C8—264no—
147C22⋊C8—264no—
148#97—21no—
149#97—261no—
150C4×C8—21no—
151C4×C8—261no—
152#95—138no—
153#95—264no—
154#95—264no—
155#95—264no—
156C2×C13—41no—
157C2×C13#173312yes—
158C2×C13#174011yescharacteristic
159D13—24no—
160C24—131no—
161C22×C4—132no—
162C22×C4—131no—
163C22×C4—132no—
164C22×C4—132no—
165C22×C4—132no—
166C22×C4—132no—
167C22×C4—132no—
168C22×C4—132no—
169C22×C4—268no—
170C22×C4—522no—
171C22×C4—524no—
172C22×C4C4⋊#26112yes—
173C22×C4C22×#26111yescharacteristic
174M16—42no—
175M16—522no—
176C2×C8—22no—
177C2×C8—262no—
178C4⋊C4—528no—
179C22⋊C4—528no—
180C42—132no—
181C42—132no—
182C42—132no—
183C42—132no—
184C42—131no—
185C42—131no—
186C42—132no—
187C42—528no—
188C42C4×#26112yes—
189C42C22⋊#26111yescharacteristic
190C42C22⋊#26111yescharacteristic
191C13#805011yescharacteristic, complemented, Sylow
192C23—132no—
193C23—264no—
194C23—521no—
195C23C2×C4⋊#26111yescharacteristic
196C2×C4—22no—
197C2×C4—42no—
198C2×C4—132no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—264no—
202C2×C4—264no—
203C2×C4—264no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—521no—
209C2×C4—528no—
210C2×C4—528no—
211C2×C4—528no—
212C2×C4(C2×#261)⋊C412yes—
213C2×C4(C2×#261)⋊C412yes—
214C2×C4C2×C4×#26111yescharacteristic
215C2×C4C2×C22⋊#26111yescharacteristic
216C8—42no—
217C8—522no—
218C22—22no—
219C22—21no—
220C22—134no—
221C22—262no—
222C22—262no—
223C22—524no—
224C22C2×(C2×#261)⋊C411yescharacteristic
225C4—22no—
226C4—22no—
227C4—21no—
228C4—262no—
229C4—262no—
230C4—262no—
231C4—1048no—
232C4#1171911612yes—
233C2—41no—
234C2—264no—
235C2#1313051812yes—
236C2#1313053511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC4×C13×M16C4
socleC22×C13C2×#95
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenterC4×M16#261
hypocenterC13#8050
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
8. #11719061C4semidirect
9. #11719060C4semidirect
12. C4×C13×M16C4semidirect
14. #11718779C4semidirect
15. C4×#6099C4semidirect
109. C4×M16#261semidirect
191. C13#8050semidirect

Maximal subgroups

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

subgroupindex
#131312832
#131297162
#131234672
#805013