Finite Group Databasebeta

← #15750012

Subgroups — #15750012

Order 3328.

280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114832C212yesmaximal
2C13×#1984C211yesmaximal, characteristic
3C2×C4×Q8×C13C2211yescharacteristic
4C2×C13×C4⋊C8C411yescharacteristic
5C2×C4×C8×C13C411yescharacteristic
6C2×#88076—22no—
7#11718585—22no—
8C13×#336—22no—
9#11718122C414yes—
10C22×Q8×C13D411yescharacteristic
11C22×C8×C13—21no—
12C22×C8×C13—21no—
13C4×Q8×C13—41no—
14C4×Q8×C13—41no—
15C2×C13×C4⋊C4C2×C412yes—
16C2×C13×C4⋊C4Q811yescharacteristic
17C2×C42×C13C2×C411yescharacteristic
18C2×C42×C13D412yes—
19C2×#6099—24no—
20C13×C4⋊C8—41no—
21C4×C8×C13—41no—
22#88076—42no—
23#88076—42no—
24C4⋊#1055—42no—
25C4⋊#1055—42no—
26#7238—131nomaximal, Sylow
27C2×Q8×C13—41no—
28C2×Q8×C13—41no—
29C2×Q8×C13D811yescharacteristic
30C2×Q8×C13SD1612yes—
31C2×Q8×C13Q1611yescharacteristic
32C22×C4×C13C4211yescharacteristic
33C22×C4×C13C22⋊C412yes—
34C22×C4×C13C22⋊C411yescharacteristic
35C22×C4×C13C4⋊C412yes—
36C22×C4×C13C4⋊C411yescharacteristic
37C2×C8×C13—22no—
38C2×C8×C13—41no—
39C2×C8×C13—41no—
40C2×C8×C13—42no—
41C2×C8×C13—41no—
42C13×C4⋊C4—42no—
43C13×C4⋊C4—41no—
44C42×C13—21no—
45C42×C13—21no—
46C42×C13—22no—
47C42×C13—22no—
48#6099—44no—
49#6099—44no—
50C2×#1055—44no—
51#1984D1311yescharacteristic
52#1801—132no—
53C23×C13#9511yescharacteristic
54Q8×C13—41no—
55Q8×C13—42no—
56Q8×C13—41no—
57C2×C4×C13—22no—
58C2×C4×C13—21no—
59C2×C4×C13—22no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—22no—
65C2×C4×C13—41no—
66C2×C4×C13—42no—
67C2×C4×C13#9911yescharacteristic
68C2×C4×C13#9911yescharacteristic
69C2×C4×C13#10212yes—
70C2×C4×C13#10312yes—
71C2×C4×C13#10611yescharacteristic
72C2×C4×C13#10711yescharacteristic
73C8×C13—42no—
74C8×C13—81no—
75#1055—84no—
76C2×C4×Q8C2×D1311yescharacteristic
77#423—262no—
78C2×C4⋊C8Dic1311yescharacteristic
79C2×#101—262no—
80C2×C4×C8Dic1311yescharacteristic
81#343—134no—
82#336—22no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13H(3,ℤ/4)11yescharacteristic
86C22×C13#34011yescharacteristic
87C22×C13#34211yescharacteristic
88C4×C13—22no—
89C4×C13—22no—
90C4×C13—21no—
91C4×C13—21no—
92C4×C13—21no—
93C4×C13—41no—
94C4×C13—42no—
95C4×C13#35511yescharacteristic
96C4×C13#35611yescharacteristic
97C22×Q8D5211yescharacteristic
98C2×M16—264no—
99C22×C8—21no—
100C22×C8—21no—
101C4×Q8—41no—
102C4×Q8—41no—
103C2×C4⋊C4Dic2611yescharacteristic
104C2×C4⋊C4C4×D1312yes—
105C2×C42C2×Dic1311yescharacteristic
106C2×C42C22⋊D1312yes—
107C4⋊C8—41no—
108C4⋊C8—522no—
109C4⋊C8—522no—
110#101—522no—
111#101—522no—
112C4×C8—41no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13#128911yescharacteristic
116C2×C13#139211yescharacteristic
117C2×C13#139411yescharacteristic
118C2×Q8—41no—
119C2×Q8—41no—
120C2×Q8#609512yes—
121C2×Q8D10411yescharacteristic
122C2×Q8Dic5211yescharacteristic
123C22×C4C4×Dic1311yescharacteristic
124C22×C4#610112yes—
125C22×C4C4⋊Dic1311yescharacteristic
126C22×C4#610312yes—
127C22×C4C22⋊Dic1311yescharacteristic
128M16—524no—
129M16—524no—
130C2×C8—22no—
131C2×C8—41no—
132C2×C8—41no—
133C2×C8—42no—
134C2×C8—41no—
135C2×C8—524no—
136C4⋊C4—41no—
137C4⋊C4—42no—
138C42—21no—
139C42—21no—
140C42—22no—
141C42—22no—
142C13#723811yescharacteristic, complemented, Sylow
143C23#8807111yescharacteristic
144Q8—42no—
145Q8—41no—
146Q8—41no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4#8805612yes—
158C2×C4#8805711yescharacteristic
159C2×C4#8805811yescharacteristic
160C2×C4#8806112yes—
161C2×C4#8807411yescharacteristic
162C2×C4#8807411yescharacteristic
163C8—42no—
164C8—81no—
165C8—1044no—
166C22—21no—
167C22—21no—
168C22#1171811811yescharacteristic
169C22#1171814311yescharacteristic
170C22#1171814911yescharacteristic
171C4—22no—
172C4—22no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—42no—
178C4#1171813411yescharacteristic
179C4#1171814011yescharacteristic
180C2—21no—
181C2—21no—
182C2#1311270411yescharacteristic
183C2#1311295911yescharacteristic
184C2#1311296311yescharacteristic
subgroupG/H
centerC22#11718118
commutatorC22×C4×C13C42
FrattiniC2×C4×Q8C2×D13
FittingC13×#1984C2
socleC22×C13#342
prime radicalC23×C13#95
cosocleC2×C4×Q8×C13C22
hypercenter#1984D13
hypocenterC13#7238
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1984

Complements

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

NH ≅ G/Ntype
142. C13#7238semidirect

Maximal subgroups

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

subgroupindex
#131148322
C13×#19842
#723813