Finite Group Databasebeta

← #15783285

Subgroups — #15783285

Order 3328.

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

normal subgroups only

This group has 318 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#13116521C212yesmaximal
2#13113009C214yesmaximal, complemented
3C13×#3142C211yesmaximal, characteristic
4C13×#532C2211yescharacteristic
5C2×C13×#125C411yescharacteristic
6C13×#491C2212yes—
7C13×#490C412yes—
8C13×#488—22no—
9C13×#417—22no—
10C4×C13×M16C411yescharacteristic
11#11718898—22no—
12#11718140C2214yes—
13#11718134—22no—
14C2×C13×#41D412yes—
15C2×C13×M16—21no—
16C13×C4⋊Q8C2311yescharacteristic
17C13×#127C2×C411yescharacteristic
18C13×#125—21no—
19C13×#125—41no—
20C13×#125C2×C412yes—
21C13×#124D412yes—
22C13×#121—41no—
23C4×D4×C13—41no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—41no—
26C2×C42×C13C2×C411yescharacteristic
27C2×#6099—42no—
28C13×#103—24no—
29C13×#102—24no—
30C13×#97C2×C412yes—
31C4×C8×C13—21no—
32#88076—24no—
33#88073—42no—
34#13600—131nomaximal, Sylow
35C13×#41—42no—
36C13×#41—42no—
37C2×Q8×C13C2×D412yes—
38C2×D4×C13—22no—
39C2×D4×C13—41no—
40C2×D4×C13C22⋊C412yes—
41C22×C4×C13—21no—
42C22×C4×C13—22no—
43C22×C4×C13—41no—
44C22×C4×C13C22⋊C411yescharacteristic
45C13×M16—42no—
46C2×C8×C13—22no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—41no—
49C13×C4⋊C4—42no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—41no—
52C13×C22⋊C4—42no—
53C42×C13—21no—
54C42×C13C22⋊C411yescharacteristic
55C42×C13C22×C411yescharacteristic
56#6099—44no—
57#6099—82no—
58C2×#1055—82no—
59#3142D1311yescharacteristic
60#2132—132no—
61#1413—134no—
62C23×C13—22no—
63C23×C13#9911yescharacteristic
64Q8×C13—42no—
65D4×C13—42no—
66D4×C13—82no—
67D4×C13—82no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—42no—
73C2×C4×C13—42no—
74C2×C4×C13—42no—
75C2×C4×C13—81no—
76C2×C4×C13—82no—
77C2×C4×C13#9911yescharacteristic
78C2×C4×C13C2×C22⋊C411yescharacteristic
79C8×C13—42no—
80#1055—84no—
81#532C2×D1311yescharacteristic
82C2×#125Dic1311yescharacteristic
83#491C2×D1312yes—
84#490Dic1312yes—
85#488—22no—
86#417—22no—
87#413—262no—
88C4×M16Dic1311yescharacteristic
89#356—134no—
90#355—262no—
91C22×C13—21no—
92C22×C13—41no—
93C22×C13—42no—
94C22×C13—82no—
95C22×C13C2×#9911yescharacteristic
96C4×C13—21no—
97C4×C13—41no—
98C4×C13—41no—
99C4×C13—42no—
100C4×C13—82no—
101C4×C13#35412yes—
102C2×#41C22⋊D1312yes—
103C2×M16—21no—
104C2×M16—522no—
105C4⋊Q8C22×D1311yescharacteristic
106#127C2×Dic1311yescharacteristic
107#125—21no—
108#125—41no—
109#125C2×Dic1312yes—
110#124C22⋊D1312yes—
111#121—41no—
112C4×D4—41no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—41no—
115C2×C42C2×Dic1311yescharacteristic
116#103—24no—
117#102—24no—
118#101—264no—
119#100—522no—
120#97C2×Dic1312yes—
121C4×C8—21no—
122C2×C13—21no—
123C2×C13—41no—
124C2×C13—82no—
125C2×C13C2×#35411yescharacteristic
126#41—42no—
127#41—42no—
128C2×Q8C2×C22⋊D1312yes—
129C2×D4—22no—
130C2×D4—41no—
131C2×D4C22⋊Dic1312yes—
132C22×C4—21no—
133C22×C4—22no—
134C22×C4—41no—
135C22×C4C22⋊Dic1311yescharacteristic
136M16—42no—
137M16—524no—
138M16—1042no—
139C2×C8—22no—
140C2×C8—1042no—
141C4⋊C4—22no—
142C4⋊C4—41no—
143C4⋊C4—42no—
144C4⋊C4—42no—
145C4⋊C4—41no—
146C22⋊C4—42no—
147C42—21no—
148C42C22⋊Dic1311yescharacteristic
149C42C22×Dic1311yescharacteristic
150C13#1360011yescharacteristic, complemented, Sylow
151C23—22no—
152C23#8807411yescharacteristic
153Q8—42no—
154D4—42no—
155D4—82no—
156D4—82no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—82no—
166C2×C4#8807411yescharacteristic
167C2×C4C2×C22⋊Dic1311yescharacteristic
168C8—42no—
169C8—1044no—
170C22—21no—
171C22—41no—
172C22—42no—
173C22—82no—
174C22C2×#8807411yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—42no—
179C4—82no—
180C4#1171813312yes—
181C2—21no—
182C2—41no—
183C2—82no—
184C2C2×#1171813311yescharacteristic
subgroupG/H
centerC2C2×#11718133
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC13×#3142C2
socleC2×C13C2×#354
prime radicalC13×#532C22
cosocleC13×C4⋊Q8C23
hypercenter#3142D13
hypocenterC13#13600
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3142

Complements

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

NH ≅ G/Ntype
2. #13113009C2semidirect
150. C13#13600semidirect

Maximal subgroups

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

subgroupindex
#131165212
#131130092
C13×#31422
#1360013