Finite Group Databasebeta

← #15775518

Subgroups — #15775518

Order 3328.

360 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 59 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#13123108C211yesmaximal, characteristic, complemented
2#13113873C212yesmaximal
3#13112862C212yesmaximal, complemented
4#13112780C211yesmaximal, characteristic, complemented
5C13×#2040C211yesmaximal, characteristic
6C13×#537C2211yescharacteristic
7C2×C13×#104—21no—
8C13×#417—21no—
9C13×#382C2211yescharacteristic
10#11718695—22no—
11#11718647C2212yes—
12#11718640—21no—
13#11718597—21no—
14#11718321—22no—
15#11718317—22no—
16C13×#343C2211yescharacteristic
17#11718129—22no—
18#11718120C2212yes—
19C2×C13×#41—21no—
20C22×Dic26—21no—
21C2×C13×M16—21no—
22C13×C22⋊Q8—41no—
23C13×#121—22no—
24C13×#121—41no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13D412yes—
31C2×#6101—22no—
32C13×#104—42no—
33C13×#103—41no—
34C13×#102—41no—
35C13×#95—22no—
36#88072—42no—
37#88071—22no—
38#88071—21no—
39#88071—22no—
40#88071—22no—
41#88071D412yes—
42C22⋊#1055—22no—
43#88048—42no—
44#12185—131nomaximal, Sylow
45C13×#41—41no—
46C13×#41—41no—
47C13×#41—41no—
48C13×#41—41no—
49C2×Q8×C13—21no—
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13—41no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—41no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13—22no—
60C2×Dic26—82no—
61C2×Dic26—81no—
62C13×M16—41no—
63C13×M16—41no—
64C2×C8×C13—41no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C22⋊C4—42no—
69C42×C13—21no—
70C42×C13SD1612yes—
71C4⋊Dic13—42no—
72C4⋊Dic13—81no—
73C4⋊Dic13—81no—
74#6101—82no—
75C2×#1055—42no—
76#2844—131no—
77#2040D1311yescharacteristic
78#1616—132no—
79#1353—132no—
80#1324—131no—
81C23×C13—41no—
82C23×C13#12011yescharacteristic
83Q8×C13—41no—
84Q8×C13—41no—
85D4×C13—41no—
86D4×C13—41no—
87D4×C13—82no—
88D4×C13—81no—
89D4×C13—81no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—81no—
101C2×C4×C13—81no—
102C2×C4×C13C2×SD1611yescharacteristic
103C2×C4×C13#13711yescharacteristic
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110Dic26—84no—
111C8×C13—81no—
112#1055—82no—
113#537C2×D1311yescharacteristic
114#481—262no—
115C2×#104—21no—
116#417—21no—
117#400—132no—
118#400—262no—
119#395—262no—
120#395—261no—
121#382—261no—
122#382C2×D1311yescharacteristic
123#343C2×D1311yescharacteristic
124#327—262no—
125#324—132no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—81no—
129C22×C13—81no—
130C22×C13—81no—
131C22×C13#44811yescharacteristic
132C22×C13#45411yescharacteristic
133C22×C13B(4,𝔽2)11yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—42no—
138C4×C13—81no—
139C4×C13—81no—
140Dic13—82no—
141Dic13—82no—
142C2×#41—21no—
143C22×Q8—261no—
144C2×M16—21no—
145C22⋊Q8—41no—
146#121—22no—
147#121—41no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C4⋊C4C22×D1311yescharacteristic
154C2×C42C22⋊D1311yescharacteristic
155#106—522no—
156#104—42no—
157#103—41no—
158#102—41no—
159#102—522no—
160C22⋊C8—262no—
161#95—22no—
162#95—132no—
163#95—262no—
164#95—261no—
165#95—262no—
166#95—262no—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13—161no—
170C2×C13#159911yescharacteristic
171C2×C13#220111yescharacteristic
172C2×C13#220211yescharacteristic
173#41—41no—
174#41—41no—
175#41—41no—
176#41—41no—
177C2×Q8—21no—
178C2×Q8—1042no—
179C2×Q8—1041no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—41no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—262no—
187C22×C4—262no—
188C22×C4D4×D1312yes—
189C22×C4C2×C22⋊D1311yescharacteristic
190M16—41no—
191M16—41no—
192C2×C8—41no—
193C2×C8—522no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—522no—
198C4⋊C4—1042no—
199C4⋊C4—1041no—
200C4⋊C4—1041no—
201C22⋊C4—42no—
202C42—21no—
203C42#610512yes—
204C13#1218511yescharacteristic, complemented, Sylow
205C23—41no—
206C23#8819111yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—1044no—
210D4—41no—
211D4—41no—
212D4—82no—
213D4—81no—
214D4—81no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4—522no—
231C2×C4—522no—
232C2×C4—522no—
233C2×C4C2×#610511yescharacteristic
234C2×C4#8820511yescharacteristic
235C8—81no—
236C8—1042no—
237C22—21no—
238C22—21no—
239C22—81no—
240C22—81no—
241C22—81no—
242C22#1171869311yescharacteristic
243C22#1171870111yescharacteristic
244C22#1171872311yescharacteristic
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—81no—
250C4—81no—
251C4—1042no—
252C4—1042no—
253C2—21no—
254C2—21no—
255C2—161no—
256C2#1311377511yescharacteristic
257C2#1311684811yescharacteristic
258C2#1311685211yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2040C2
socleC22×C13B(4,𝔽2)
prime radicalC13×#537C22
hypercenter#2040D13
hypocenterC13#12185
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2040

Complements

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

NH ≅ G/Ntype
1. #13123108C2semidirect
3. #13112862C2semidirect
4. #13112780C2semidirect
204. C13#12185semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131138732
#131128622
#131127802
C13×#20402
#1218513