Finite Group Databasebeta

← #15774113

Subgroups — #15774113

Order 3328.

326 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 79 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#13116648C212yesmaximal, complemented
2#13112869C214yesmaximal, complemented
3C13×#3138C211yesmaximal, characteristic
4C13×#533C411yescharacteristic
5C2×C13×#127C411yescharacteristic
6C13×#490C412yes—
7C13×#490C2212yes—
8C13×#486—22no—
9C13×#418—22no—
10C4×C13×M16C2211yescharacteristic
11#11718145—22no—
12#11718058C2214yescomplemented
13#11718055—22no—
14C22×D4×C13—21no—
15C22×D4×C13—41no—
16C2×C13×M16D412yes—
17C13×C4⋊Q8—21no—
18C13×#127—21no—
19C13×#127—41no—
20C13×#127C2×C412yes—
21C13×#125C2×C412yes—
22C13×C22⋊Q8—41no—
23C4×Q8×C13—41no—
24C13×#117—21no—
25C2×C42×C13C2×C411yescharacteristic
26C13×#102—24no—
27C13×#102—24no—
28C13×#97C2×C411yescharacteristic
29C13×#97C2311yescharacteristic
30C4×C8×C13D412yes—
31#88052—24no—
32#11915—131nomaximal, Sylow
33C24×C13—41no—
34C2×Q8×C13—41no—
35C2×D4×C13—22no—
36C2×D4×C13—44no—
37C2×D4×C13—42no—
38C2×D4×C13—42no—
39C2×D4×C13—41no—
40C2×D4×C13—84no—
41C22×C4×C13—21no—
42C22×C4×C13C22⋊C411yescharacteristic
43C13×M16—42no—
44C2×C8×C13C22⋊C412yes—
45C2×C8×C13C2×D412yes—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—42no—
48C13×C4⋊C4—41no—
49C13×C22⋊C4—41no—
50C42×C13—21no—
51C42×C13—41no—
52C42×C13C22⋊C411yescharacteristic
53C42×C13C22×C411yescharacteristic
54#6090—44no—
55#3138D1311yescharacteristic
56#2165—132no—
57#1355—134no—
58C23×C13—42no—
59C23×C13—82no—
60C23×C13—84no—
61C23×C13#10011yescharacteristic
62Q8×C13—82no—
63D4×C13—44no—
64D4×C13—82no—
65D4×C13—84no—
66D4×C13—84no—
67C2×C4×C13—21no—
68C2×C4×C13—22no—
69C2×C4×C13—21no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13#10011yescharacteristic
73C2×C4×C13C2×C22⋊C411yescharacteristic
74C8×C13—22no—
75C8×C13—22no—
76#533Dic1311yescharacteristic
77C2×#127Dic1311yescharacteristic
78#490Dic1312yes—
79#490C2×D1312yes—
80#486—22no—
81#418—22no—
82C4×M16C2×D1311yescharacteristic
83#364—262no—
84#349—262no—
85#347—134no—
86C22×C13—21no—
87C22×C13—41no—
88C22×C13—84no—
89C22×C13—82no—
90C22×C13—164no—
91C22×C13C2×#10011yescharacteristic
92C4×C13—22no—
93C4×C13—21no—
94C4×C13—41no—
95C4×C13—82no—
96C4×C13#42112yes—
97C22×D4—21no—
98C22×D4—41no—
99C2×M16C22⋊D1312yes—
100C4⋊Q8—21no—
101#127—21no—
102#127—41no—
103#127C2×Dic1312yes—
104#125C2×Dic1312yes—
105C22⋊Q8—41no—
106C4×Q8—41no—
107#117—21no—
108C2×C42C2×Dic1311yescharacteristic
109M32—264no—
110#102—24no—
111#102—24no—
112#97C2×Dic1311yescharacteristic
113#97C22×D1311yescharacteristic
114C4×C8C22⋊D1312yes—
115C2×C13—21no—
116C2×C13—41no—
117C2×C13—162no—
118C2×C13#153311yescharacteristic
119C24—41no—
120C2×Q8—41no—
121C2×D4—22no—
122C2×D4—44no—
123C2×D4—42no—
124C2×D4—42no—
125C2×D4—41no—
126C2×D4—84no—
127C22×C4—21no—
128C22×C4C22⋊Dic1311yescharacteristic
129M16—42no—
130C2×C8C22⋊Dic1312yes—
131C2×C8C2×C22⋊D1312yes—
132C4⋊C4—22no—
133C4⋊C4—42no—
134C4⋊C4—41no—
135C22⋊C4—41no—
136C42—21no—
137C42—41no—
138C42C22⋊Dic1311yescharacteristic
139C42C22×Dic1311yescharacteristic
140C16—524no—
141C13#1191511yescharacteristic, complemented, Sylow
142C23—42no—
143C23—82no—
144C23—84no—
145C23#8807311yescharacteristic
146Q8—82no—
147D4—44no—
148D4—82no—
149D4—84no—
150D4—84no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4#8807311yescharacteristic
157C2×C4C2×C22⋊Dic1311yescharacteristic
158C8—22no—
159C8—22no—
160C22—21no—
161C22—41no—
162C22—84no—
163C22—82no—
164C22—164no—
165C22C2×#8807311yescharacteristic
166C4—22no—
167C4—21no—
168C4—41no—
169C4—82no—
170C4#1171889712yes—
171C2—21no—
172C2—41no—
173C2—162no—
174C2#1311346011yescharacteristic
subgroupG/H
centerC2#13113460
commutatorC42×C13C22×C4
Frattini#97C22×D13
FittingC13×#3138C2
socleC2×C13#1533
prime radicalC2×C13×#127C4
cosocleC13×#97C23
hypercenter#3138D13
hypocenterC13#11915
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #13116648C2semidirect
2. #13112869C2semidirect
12. #11718058C22semidirect
141. C13#11915semidirect

Maximal subgroups

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

subgroupindex
#131166482
#131128692
C13×#31382
#1191513