Finite Group Databasebeta

← #15760521

Subgroups — #15760521

Order 3328.

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

normal subgroups only

This group has 400 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#13125218C211yesmaximal, characteristic
2#13123938C211yesmaximal, characteristic
3#13113522C212yesmaximal
4#13112725C212yesmaximal
5C13×#1561C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#423C2212yes—
9#11718754—22no—
10#11718730C414yes—
11#11718685—22no—
12Q8×#1055—22no—
13#11718665—22no—
14#11718661—22no—
15#11718586C2212yes—
16C4×#6099C2211yescharacteristic
17C13×#332—22no—
18#11718078—22no—
19#11718078—22no—
20C22×Dic26—21no—
21C2×C13×M16—22no—
22C13×C4⋊Q8D412yes—
23C13×#125C2×C412yes—
24C13×C22⋊Q8—22no—
25C4×Q8×C13—22no—
26C13×#117D412yes—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13—22no—
29C2×#6099—21no—
30#88123—22no—
31#88123—21no—
32#88123C2×C412yes—
33C13×C4⋊C8—22no—
34C13×C4⋊C8—22no—
35C22⋊#1055—22no—
36#88050—28no—
37C4⋊#1055—24no—
38C4⋊#1055D412yes—
39C4⋊#1055D412yes—
40#88043—22no—
41#88043C2×C412yes—
42C4×#1055—22no—
43C4×#1055—22no—
44C4×#1055—21no—
45#9436—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C22×C4×C13C2×D411yescharacteristic
48C22×C4×C13#4112yes—
49C22×Dic13—41no—
50C2×Dic26—22no—
51C2×Dic26—44no—
52C2×Dic26—41no—
53C13×M16—82no—
54C2×C8×C13—42no—
55C13×C4⋊C4—24no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4C22⋊C414yes—
58C13×C22⋊C4—22no—
59C42×C13—22no—
60C42×C13C22×C411yescharacteristic
61C42×C13C2×D412yes—
62C42×C13C2×D411yescharacteristic
63C4⋊Dic13—24no—
64C4⋊Dic13—42no—
65#6099—42no—
66C2×#1055—22no—
67C2×#1055—22no—
68C2×#1055—22no—
69#3139—131no—
70#2986—131no—
71#1561D1311yescharacteristic
72#1549—132no—
73#1299—132no—
74C23×C13#12311yescharacteristic
75Q8×C13—42no—
76Q8×C13—42no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—24no—
81C2×C4×C13C2×C22⋊C411yescharacteristic
82C2×C4×C13C4×D412yes—
83C2×C4×C13#12011yescharacteristic
84C2×C4×C13#12112yes—
85C2×Dic13—42no—
86C2×Dic13—82no—
87Dic26—44no—
88Dic26—82no—
89C8×C13—82no—
90#1055—42no—
91#1055—42no—
92#1055—42no—
93#533C2×D1311yescharacteristic
94C2×C4⋊Q8—131no—
95#491—134no—
96#487—262no—
97#446—262no—
98C8×Q8—262no—
99#433—262no—
100#431—132no—
101#423C2×D1312yes—
102#419—262no—
103C4×M16—131no—
104#332—22no—
105#332—262no—
106#332—262no—
107C22×C13—21no—
108C22×C13—22no—
109C22×C13#38611yescharacteristic
110C4×C13—21no—
111C4×C13—22no—
112C4×C13—44no—
113C4×C13#45412yes—
114C4×C13#47112yes—
115C4×C13#47312yes—
116Dic13—82no—
117C22×Q8—261no—
118C2×M16—22no—
119C2×M16—261no—
120C4⋊Q8—132no—
121C4⋊Q8—262no—
122C4⋊Q8—261no—
123C4⋊Q8C22⋊D1312yes—
124#125C4×D1312yes—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117D5212yes—
128C2×C4⋊C4—262no—
129C2×C42C22×D1311yescharacteristic
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—132no—
133C4⋊C8—132no—
134C4⋊C8—264no—
135#103—268no—
136C22⋊C8—262no—
137#97—132no—
138#97—262no—
139C4×C8—262no—
140C4×C8—262no—
141C4×C8—261no—
142C2×C13—41no—
143C2×C13#188811yescharacteristic
144C2×C13#190812yes—
145C2×Q8—22no—
146C2×Q8—262no—
147C2×Q8—524no—
148C2×Q8—521no—
149C22×C4—521no—
150C22×C4C2×D5211yescharacteristic
151C22×C4#612912yes—
152M16—82no—
153M16—522no—
154C2×C8—42no—
155C2×C8—262no—
156C2×C8—262no—
157C2×C8—262no—
158C4⋊C4—24no—
159C4⋊C4—22no—
160C4⋊C4—264no—
161C4⋊C4—522no—
162C4⋊C4#610314yes—
163C22⋊C4—22no—
164C42—22no—
165C42C2×C4×D1311yescharacteristic
166C42D4×D1312yes—
167C42C2×C22⋊D1311yescharacteristic
168C13#943611yescharacteristic, complemented, Sylow
169C23#8814011yescharacteristic
170Q8—42no—
171Q8—42no—
172Q8—524no—
173Q8—1042no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—522no—
179C2×C4—1042no—
180C2×C4#8813512yes—
181C2×C4#8813611yescharacteristic
182C2×C4C2×#610311yescharacteristic
183C2×C4#8819312yes—
184C8—82no—
185C8—522no—
186C8—522no—
187C8—522no—
188C22—21no—
189C22—22no—
190C22#1171861911yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—1042no—
195C4#1171841412yes—
196C4#1171886112yes—
197C4#1171886512yes—
198C2—41no—
199C2#1311523711yescharacteristic
200C2#1311534912yes—
subgroupG/H
centerC22#11718619
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1561C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#1561D13
hypocenterC13#9436
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
168. C13#9436semidirect

Maximal subgroups

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

subgroupindex
#131252182
#131239382
#131135222
#131127252
C13×#15612
#943613