Finite Group Databasebeta

← #15760524

Subgroups — #15760524

Order 3328.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123938C211yesmaximal, characteristic
2#13113574C211yesmaximal, characteristic
3#13113521C212yesmaximal
4#13112726C212yesmaximal
5C13×#3139C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C2×C13×C4⋊Q8C2211yescharacteristic
8C13×#491C414yes—
9C13×#487—22no—
10C13×#419—22no—
11C4×C13×M16C2211yescharacteristic
12#11718685—22no—
13Q8×#1055—22no—
14#11718661—22no—
15#11718586C2212yes—
16#11718585C2212yes—
17#11718139—22no—
18#11718139—22no—
19#11718139—22no—
20C22×Q8×C13—21no—
21C2×C13×M16—21no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8C2×C412yes—
25C13×C4⋊Q8D412yes—
26C13×#125C2×C412yes—
27C13×C22⋊Q8—22no—
28C4×Q8×C13—22no—
29C13×#117D412yes—
30C2×C13×C4⋊C4—22no—
31C2×C42×C13C2311yescharacteristic
32C2×#6099—22no—
33C13×#103—28no—
34C13×#97C2×C412yes—
35C4×C8×C13—21no—
36C22⋊#1055—22no—
37C4⋊#1055—24no—
38C4⋊#1055—22no—
39C4⋊#1055—22no—
40C4⋊#1055D412yes—
41C4⋊#1055D412yes—
42#88043—22no—
43C4×#1055—22no—
44C4×#1055—22no—
45#9436—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C2×Q8×C13—22no—
48C2×Q8×C13—44no—
49C2×Q8×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13#4112yes—
53C13×M16—42no—
54C2×C8×C13—22no—
55C13×C4⋊C4—24no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—24no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4C22⋊C414yes—
60C13×C22⋊C4—22no—
61C42×C13—22no—
62C42×C13C22×C411yescharacteristic
63C42×C13C2×D412yes—
64C42×C13C2×D411yescharacteristic
65#6099—82no—
66C2×#1055—22no—
67C2×#1055—22no—
68C2×#1055—42no—
69#3139D1311yescharacteristic
70#2986—131no—
71#1561—131no—
72#1549—132no—
73#1299—132no—
74C23×C13#12311yescharacteristic
75Q8×C13—44no—
76Q8×C13—42no—
77Q8×C13—42no—
78Q8×C13—82no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—24no—
83C2×C4×C13—42no—
84C2×C4×C13—82no—
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13C4×D412yes—
87C2×C4×C13#12011yescharacteristic
88C2×C4×C13#12112yes—
89C8×C13—42no—
90#1055—42no—
91#1055—42no—
92#1055—82no—
93#533C2×D1311yescharacteristic
94C2×C4⋊Q8C2×D1311yescharacteristic
95#491Dic1314yes—
96#487—22no—
97#446—262no—
98C8×Q8—262no—
99#433—262no—
100#431—132no—
101#423—132no—
102#419—22no—
103C4×M16C2×D1311yescharacteristic
104#332—262no—
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—82no—
114C4×C13#45412yes—
115C4×C13#47112yes—
116C4×C13#47312yes—
117C22×Q8—21no—
118C2×M16—21no—
119C2×M16—262no—
120C4⋊Q8—22no—
121C4⋊Q8—21no—
122C4⋊Q8C2×Dic1312yes—
123C4⋊Q8C22⋊D1312yes—
124#125C2×Dic1312yes—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117C22⋊D1312yes—
128C2×C4⋊C4—22no—
129C2×C42C22×D1311yescharacteristic
130C4⋊C8—132no—
131C4⋊C8—132no—
132C4⋊C8—264no—
133C4⋊C8—262no—
134C4⋊C8—262no—
135#103—28no—
136C22⋊C8—262no—
137#97—262no—
138#97C2×Dic1312yes—
139C4×C8—21no—
140C4×C8—262no—
141C4×C8—262no—
142C2×C13—41no—
143C2×C13#188811yescharacteristic
144C2×C13#190812yes—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8—44no—
148C2×Q8—41no—
149C22×C4—41no—
150C22×C4#612912yes—
151C22×C4C2×C22⋊D1311yescharacteristic
152M16—42no—
153M16—1042no—
154C2×C8—22no—
155C2×C8—262no—
156C2×C8—262no—
157C2×C8—522no—
158C4⋊C4—24no—
159C4⋊C4—22no—
160C4⋊C4—24no—
161C4⋊C4—42no—
162C4⋊C4C22⋊Dic1314yes—
163C22⋊C4—22no—
164C42—22no—
165C42D4×D1312yes—
166C42C22×Dic1311yescharacteristic
167C42C2×C22⋊D1311yescharacteristic
168C13#943611yescharacteristic, complemented, Sylow
169C23#8818911yescharacteristic
170Q8—44no—
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—42no—
179C2×C4—82no—
180C2×C4D4×Dic1312yes—
181C2×C4#8819111yescharacteristic
182C2×C4#8819312yes—
183C2×C4C2×C22⋊Dic1311yescharacteristic
184C8—42no—
185C8—522no—
186C8—522no—
187C8—1042no—
188C22—21no—
189C22—22no—
190C22#1171888111yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—82no—
195C4#1171872312yes—
196C4#1171886412yes—
197C4#1171886512yes—
198C2—41no—
199C2#1311524011yescharacteristic
200C2#1311535312yes—
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3139C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#3139D13
hypocenterC13#9436
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
168. C13#9436semidirect

Maximal subgroups

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

subgroupindex
#131239382
#131135742
#131135212
#131127262
C13×#31392
#943613