Finite Group Databasebeta

← #15760462

Subgroups — #15760462

Order 3328.

422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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#13118017C211yesmaximal, characteristic
2#13113562C211yesmaximal, characteristic
3#13113387C212yesmaximal
4#13112701C212yesmaximal
5C13×#3139C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×C13×C4⋊Q8C2211yescharacteristic
8C13×#491—22no—
9C13×#487C414yescomplemented
10C13×#419—22no—
11C4×C13×M16C2211yescharacteristic
12#11718891—22no—
13#11718642—24no—
14#11718598C2212yes—
15#11718587C2212yes—
16#11718138—22no—
17#11718130—24no—
18C22×Q8×C13D412yes—
19C2×C13×M16—21no—
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8C2×C412yes—
22C13×C4⋊Q8C2×C412yes—
23C13×C4⋊Q8D412yes—
24C13×#125—21no—
25C13×C22⋊Q8—22no—
26C4×Q8×C13—22no—
27C13×#117—21no—
28C2×C13×C4⋊C4—22no—
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—22no—
31C2×C4×Dic13—22no—
32C13×#103—28no—
33C13×#97—21no—
34C4×C8×C13C2×C412yes—
35#88071—24no—
36#88071—22no—
37#88071—22no—
38#88071D414yes—
39C22⋊#1055—22no—
40C4⋊#1055—22no—
41#88043—22no—
42#9426—131nomaximal, Sylow
43C2×Q8×C13—22no—
44C2×Q8×C13—22no—
45C2×Q8×C13—42no—
46C2×Q8×C13—42no—
47C2×Q8×C13C22⋊C414yes—
48C22×C4×C13—22no—
49C22×C4×C13C2×D412yes—
50C22×C4×C13C2×D411yescharacteristic
51C22×Dic13—24no—
52C13×M16—42no—
53C2×C8×C13—22no—
54C13×C4⋊C4—24no—
55C13×C4⋊C4—24no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—42no—
59C13×C22⋊C4—41no—
60C42×C13—41no—
61C42×C13C22×C411yescharacteristic
62C42×C13C2×D411yescharacteristic
63C42×C13#4112yes—
64C4⋊Dic13—82no—
65C4×Dic13—82no—
66C2×#1055—42no—
67#3139D1311yescharacteristic
68#2381—131no—
69#1558—131no—
70#1515—132no—
71#1288—132no—
72C23×C13#12011yescharacteristic
73Q8×C13—44no—
74Q8×C13—82no—
75Q8×C13—82no—
76C2×C4×C13—22no—
77C2×C4×C13—24no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13C2×C22⋊C411yescharacteristic
83C2×C4×C13C4×D412yes—
84C2×C4×C13#12112yes—
85C2×C4×C13#12311yescharacteristic
86C2×Dic13—48no—
87C2×Dic13—44no—
88C8×C13—42no—
89#1055—82no—
90#533C2×D1311yescharacteristic
91C2×C4⋊Q8C2×D1311yescharacteristic
92#491—22no—
93#487Dic1314yescomplemented
94#432—132no—
95#419—22no—
96C4×M16C2×D1311yescharacteristic
97#391—262no—
98#387—264no—
99#383—132no—
100#333—262no—
101#328—264no—
102C22×C13—22no—
103C22×C13#38611yescharacteristic
104C22×C13#45512yes—
105C4×C13—21no—
106C4×C13—21no—
107C4×C13—22no—
108C4×C13—22no—
109C4×C13—44no—
110C4×C13—82no—
111Dic13—84no—
112C22×Q8C22⋊D1312yes—
113C2×M16—21no—
114C4⋊Q8—22no—
115C4⋊Q8C2×Dic1312yes—
116C4⋊Q8C2×Dic1312yes—
117C4⋊Q8C22⋊D1312yes—
118#125—21no—
119C22⋊Q8—22no—
120C4×Q8—22no—
121#117—21no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—262no—
124C2×C42—262no—
125C2×C42C22×D1311yescharacteristic
126C4⋊C8—262no—
127#103—28no—
128C22⋊C8—262no—
129#97—21no—
130#97—262no—
131C4×C8C2×Dic1312yes—
132#95—134no—
133#95—264no—
134#95—262no—
135#95—262no—
136C2×C13—22no—
137C2×C13#188511yescharacteristic
138C2×C13#190512yes—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8C22⋊Dic1314yes—
144C22×C4—22no—
145C22×C4—264no—
146C22×C4D4×D1312yes—
147C22×C4C2×C22⋊D1311yescharacteristic
148M16—42no—
149C2×C8—22no—
150C2×C8—522no—
151C4⋊C4—24no—
152C4⋊C4—24no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—42no—
156C4⋊C4—1042no—
157C22⋊C4—41no—
158C42—41no—
159C42—1042no—
160C42#612912yes—
161C42C22×Dic1311yescharacteristic
162C42C2×C22⋊D1311yescharacteristic
163C13#942611yescharacteristic, complemented, Sylow
164C23#8819111yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—82no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—528no—
175C2×C4—524no—
176C2×C4D4×Dic1312yes—
177C2×C4#8818911yescharacteristic
178C2×C4#8819312yes—
179C2×C4C2×C22⋊Dic1311yescharacteristic
180C8—42no—
181C8—1042no—
182C22—22no—
183C22#1171872212yes—
184C22#1171888111yescharacteristic
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—82no—
191C4—1044no—
192C2—22no—
193C2#1311522511yescharacteristic
194C2#1311533212yes—
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3139C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#3139D13
hypocenterC13#9426
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
9. C13×#487C4semidirect
93. #487Dic13semidirect
163. C13#9426semidirect

Maximal subgroups

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

subgroupindex
#131180172
#131135622
#131133872
#131127012
C13×#31392
#942613