Finite Group Databasebeta

← #16782175

Subgroups — #16782175

Order 3328.

554 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130563C212yesmaximal
2#13129712C212yesmaximal, complemented
3#13129712C212yesmaximal, complemented
4D13×#382C211yesmaximal, characteristic
5C2×C4⋊C4×D13C411yescharacteristic
6C2×C4⋊C4×D13C411yescharacteristic
7C2×C42×D13C2211yescharacteristic
8C2×#88111—22no—
9C2×#88110C2214yes—
10C13×#382C411yescharacteristic
11#11718638C2211yescharacteristic
12#11718638C2211yescharacteristic
13#11718597C411yescharacteristic
14D13×#95—22no—
15#11718311—22no—
16#11718290—22no—
17C22×C4×D13—21no—
18C22×C4×D13—21no—
19C22×C4×D13C2×C411yescharacteristic
20C22×C4×D13D412yes—
21C22×#1057—24no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×C4⋊Dic13C2×C411yescharacteristic
26C2×C4⋊Dic13C2×C411yescharacteristic
27C2×#6101—21no—
28C2×#6101—21no—
29C2×C4×Dic13D412yes—
30C2×C4×Dic13C2311yescharacteristic
31C4⋊C4×D13—42no—
32C4⋊C4×D13—42no—
33C42×D13—24no—
34#88111—28no—
35#88110—28no—
36C13×#95—22no—
37#88071—22no—
38#88071—22no—
39#88071—22no—
40#8718—131nomaximal, Sylow
41C23×D13C22⋊C411yescharacteristic
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13C22⋊C412yes—
45C22×C4×C13C22×C411yescharacteristic
46C22×Dic13—21no—
47C22×Dic13—21no—
48C22×Dic13C22⋊C411yescharacteristic
49C22×Dic13C2×D412yes—
50C2×C4×D13—22no—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—24no—
54C2×C4×D13—24no—
55C2×C4×D13—42no—
56C2×C4×D13—44no—
57C2×C4×D13—42no—
58C2×C4×D13—42no—
59C2×C4×D13—44no—
60C2×#1057—28no—
61C2×#1057—44no—
62C2×#1057—44no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C42×C13—22no—
66C4⋊Dic13—41no—
67C4⋊Dic13—41no—
68#6101—42no—
69#6101—42no—
70C4×Dic13—24no—
71C4×Dic13#4114yes—
72C2×#382—131no—
73#1749—132no—
74#1295—132no—
75#1295—132no—
76C23×C13C2×C22⋊C411yescharacteristic
77C22×D13—21no—
78C22×D13—21no—
79C22×D13—22no—
80C22×D13#10012yes—
81C22×D13#10414yes—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13#11712yes—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—41no—
97C2×Dic13—41no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13#10112yes—
101C2×Dic13#12314yes—
102C4×D13—28no—
103C4×D13—48no—
104C4×D13—84no—
105C4×D13—84no—
106#1057—48no—
107C22×C4⋊C4—131no—
108C22×C4⋊C4—131no—
109C22×C42—131no—
110C2×C22⋊C8—262no—
111C2×#97—134no—
112#382—131no—
113#382—131no—
114#382—131no—
115#382—262no—
116#382#26111yescharacteristic
117C2×#95—262no—
118#336—262no—
119C22×C13#38111yescharacteristic
120C22×C13C2×#10011yescharacteristic
121C22×C13C2×#10111yescharacteristic
122C22×C13C2×#10412yes—
123C22×C13#42112yes—
124C2×D13—22no—
125C2×D13—24no—
126C2×D13—24no—
127C2×D13—22no—
128C2×D13#32914yes—
129C4×C13—22no—
130C4×C13—42no—
131C4×C13—81no—
132C4×C13—81no—
133Dic13—22no—
134Dic13—24no—
135Dic13—81no—
136Dic13—81no—
137C23×C4—131no—
138C23×C4—132no—
139C23×C4—261no—
140C23×C4—261no—
141C22×C8—264no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4—261no—
146C2×C4⋊C4—522no—
147C2×C4⋊C4—522no—
148C2×C4⋊C4C2×#26111yescharacteristic
149C2×C4⋊C4C2×#26111yescharacteristic
150C2×C42—131no—
151C2×C42—132no—
152C2×C42—264no—
153C2×C42C2×#26111yescharacteristic
154C22⋊C8—268no—
155#97—268no—
156#95—22no—
157#95—262no—
158#95—262no—
159#95—262no—
160C2×C13C2×#32911yescharacteristic
161C2×C13#152812yes—
162C2×C13#153311yescharacteristic
163C2×C13#182111yescharacteristic
164C2×C13#182612yes—
165D13—24no—
166C24—131no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—132no—
170C22×C4—131no—
171C22×C4—262no—
172C22×C4—264no—
173C22×C4—262no—
174C22×C4—264no—
175C22×C4—262no—
176C22×C4—261no—
177C22×C4—261no—
178C22×C4—522no—
179C22×C4—522no—
180C22×C4—522no—
181C22×C4—524no—
182C22×C4—524no—
183C22×C4C22⋊#26112yes—
184C22×C4C22×#26111yescharacteristic
185C2×C8—268no—
186C2×C8—524no—
187C2×C8—524no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—521no—
191C4⋊C4—521no—
192C4⋊C4—522no—
193C4⋊C4—522no—
194C42—22no—
195C42—134no—
196C42—264no—
197C13#871811yescharacteristic, complemented, Sylow
198C23—132no—
199C23—134no—
200C23—261no—
201C23—261no—
202C23—262no—
203C23C2×C22⋊#26111yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—134no—
214C2×C4—132no—
215C2×C4—268no—
216C2×C4—261no—
217C2×C4—261no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—528no—
221C2×C4—521no—
222C2×C4—521no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—1044no—
226C2×C4—1044no—
227C2×C4#8823712yes—
228C8—528no—
229C22—134no—
230C22—264no—
231C22—262no—
232C22—262no—
233C22—264no—
234C22#1171913511yescharacteristic
235C22D13⋊#10011yescharacteristic
236C22D13⋊#10111yescharacteristic
237C22D13⋊#10412yes—
238C22#1171916612yes—
239C4—22no—
240C4—42no—
241C4—81no—
242C4—81no—
243C4—262no—
244C4—264no—
245C4—1041no—
246C4—1041no—
247C2—264no—
248C2D13⋊#32911yescharacteristic
249C2#1313029912yes—
250C2#1313031611yescharacteristic
251C2#1313073611yescharacteristic
252C2#1313074412yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#382#261
hypocenterC13#8718
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #13129712C2semidirect
3. #13129712C2semidirect
197. C13#8718semidirect

Maximal subgroups

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

subgroupindex
#131305632
#131297122
D13×#3822
#871813