Finite Group Databasebeta

← #15760544

Subgroups — #15760544

Order 3328.

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

normal subgroups only

This group has 434 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#13117942C211yesmaximal, characteristic
2#13113463C211yesmaximal, characteristic
3#13113348C212yesmaximal
4#13112730C212yesmaximal
5C13×#3166C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×C13×#125C2211yescharacteristic
8C13×#501C414yescomplemented
9C13×#499—22no—
10C13×#428—22no—
11C4×C13×M16C2211yescharacteristic
12#11718642—22no—
13#11718642—22no—
14C4⋊C4×Dic13—22no—
15#11718593C2212yes—
16#11718587C2212yes—
17#11718135—22no—
18#11718130—22no—
19#11718130—22no—
20C2×C13×M16—21no—
21C13×C4⋊Q8C2×C412yes—
22C13×#125—21no—
23C13×#125—22no—
24C13×#125C2×C412yes—
25C13×#125D412yes—
26C13×C22⋊Q8—22no—
27C4×Q8×C13—22no—
28C13×#117—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4D412yes—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—22no—
33C2×C4×Dic13—22no—
34C2×C4×Dic13—22no—
35C13×#107—24no—
36C13×#106—24no—
37C13×#97C2×C412yes—
38C4×C8×C13—21no—
39#88071—22no—
40#88071—22no—
41#88071—22no—
42#88071D412yes—
43#88071D412yes—
44C22⋊#1055—22no—
45C4⋊#1055—22no—
46#88043—22no—
47#9440—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13C2×D412yes—
51C22×C4×C13C2×D411yescharacteristic
52C22×Dic13—22no—
53C22×Dic13—22no—
54C13×M16—24no—
55C2×C8×C13—22no—
56C13×C4⋊C4—24no—
57C13×C4⋊C4—24no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4C22⋊C414yes—
63C13×C22⋊C4—41no—
64C42×C13—41no—
65C42×C13C22×C411yescharacteristic
66C42×C13C2×D411yescharacteristic
67C42×C13#4112yes—
68C4⋊Dic13—44no—
69C4×Dic13—44no—
70C4×Dic13—44no—
71C2×#1055—42no—
72#3166D1311yescharacteristic
73#2371—131no—
74#1534—131no—
75#1506—132no—
76#1300—132no—
77C23×C13#12011yescharacteristic
78Q8×C13—82no—
79C2×C4×C13—22no—
80C2×C4×C13—24no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13C4×D412yes—
87C2×C4×C13#12112yes—
88C2×C4×C13#12311yescharacteristic
89C2×Dic13—24no—
90C2×Dic13—42no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C8×C13—24no—
96#1055—82no—
97#533C2×D1311yescharacteristic
98C2×#125C2×D1311yescharacteristic
99#501Dic1314yescomplemented
100#499—22no—
101#432—132no—
102#428—22no—
103C4×M16C2×D1311yescharacteristic
104#387—262no—
105#387—262no—
106C4×C4⋊C4—262no—
107#376—132no—
108#330—262no—
109#328—262no—
110#328—262no—
111C22×C13—22no—
112C22×C13#38611yescharacteristic
113C22×C13#45612yes—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—44no—
119C4×C13—82no—
120Dic13—44no—
121Dic13—82no—
122C2×M16—21no—
123C4⋊Q8C2×Dic1312yes—
124#125—22no—
125#125—21no—
126#125C2×Dic1312yes—
127#125C22⋊D1312yes—
128C22⋊Q8—22no—
129C4×Q8—22no—
130#117—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—262no—
133C2×C4⋊C4C22⋊D1312yes—
134C2×C42—262no—
135C2×C42—262no—
136C2×C42C22×D1311yescharacteristic
137#107—24no—
138#106—24no—
139C4⋊C8—262no—
140C22⋊C8—262no—
141#97—262no—
142#97C2×Dic1312yes—
143C4×C8—21no—
144#95—132no—
145#95—132no—
146#95—262no—
147#95—262no—
148#95—262no—
149C2×C13—22no—
150C2×C13#188611yescharacteristic
151C2×C13#190612yes—
152C2×Q8—22no—
153C22×C4—22no—
154C22×C4—262no—
155C22×C4—262no—
156C22×C4D4×D1312yes—
157C22×C4C2×C22⋊D1311yescharacteristic
158M16—24no—
159C2×C8—22no—
160C2×C8—522no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—42no—
167C4⋊C4—524no—
168C4⋊C4C22⋊Dic1314yes—
169C22⋊C4—41no—
170C42—41no—
171C42—524no—
172C42—524no—
173C42#612912yes—
174C42C22×Dic1311yescharacteristic
175C42C2×C22⋊D1311yescharacteristic
176C13#944011yescharacteristic, complemented, Sylow
177C23#8819111yescharacteristic
178Q8—82no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—264no—
186C2×C4—522no—
187C2×C4—522no—
188C2×C4—522no—
189C2×C4—522no—
190C2×C4—522no—
191C2×C4D4×Dic1312yes—
192C2×C4#8818911yescharacteristic
193C2×C4#8819312yes—
194C2×C4C2×C22⋊Dic1311yescharacteristic
195C8—24no—
196C8—1042no—
197C22—22no—
198C22#1171875612yes—
199C22#1171888111yescharacteristic
200C4—21no—
201C4—21no—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—82no—
206C4—524no—
207C4—1042no—
208C2—22no—
209C2#1311523011yescharacteristic
210C2#1311533912yes—
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3166C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#3166D13
hypocenterC13#9440
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
8. C13×#501C4semidirect
99. #501Dic13semidirect
176. C13#9440semidirect

Maximal subgroups

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

subgroupindex
#131179422
#131134632
#131133482
#131127302
C13×#31662
#944013