Finite Group Databasebeta

← #13130374

Subgroups — #13130374

Order 1664.

254 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 60 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#11719373C211yesmaximal, characteristic
2#11719053C212yesmaximal, complemented
3#11718303C212yesmaximal, complemented
4#11718297C212yesmaximal, complemented
5C2×#6131C411yescharacteristic
6C2×#6129C411yescharacteristic
7C2×#6118—22no—
8C13×#124C411yescharacteristic
9#88198C2211yescharacteristic
10#88194C2211yescharacteristic
11#88138—22no—
12#88135—22no—
13#88129C411yescharacteristic
14C42×D13C2211yescharacteristic
15#88112—22no—
16#88112C2214yes—
17C2×Q8×C13C2×C411yescharacteristic
18C2×D4×C13C2×C411yescharacteristic
19C2×C22⋊D13—21no—
20C2×C22⋊D13—22no—
21C22×Dic13—21no—
22#6131—42no—
23#6129—42no—
24C2×D52—21no—
25C2×D52C2×C411yescharacteristic
26C2×C4×D13—21no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D412yes—
29C2×Dic26C2×C411yescharacteristic
30C2×#1057—24no—
31#6118—44no—
32C13×C22⋊C4—22no—
33C42×C13C2×C411yescharacteristic
34#6103—22no—
35#6101—22no—
36C4×Dic13D412yes—
37C4×Dic13C2311yescharacteristic
38#1560—131nomaximal, Sylow
39C23×C13—21no—
40C22×D13—21no—
41C22×D13C22⋊C411yescharacteristic
42Q8×C13—41no—
43D4×C13—41no—
44C2×C4×C13—21no—
45C2×C4×C13C22⋊C412yes—
46C2×C4×C13C22×C411yescharacteristic
47C22⋊D13—42no—
48C22⋊D13—42no—
49C22⋊D13—42no—
50C2×Dic13—21no—
51C2×Dic13—42no—
52C2×Dic13C22⋊C411yescharacteristic
53C2×Dic13C2×D412yes—
54D52—41no—
55D52—42no—
56C4×D13—22no—
57C4×D13—22no—
58C4×D13—22no—
59C4×D13—42no—
60Dic26—41no—
61#1057—44no—
62#532—131no—
63#423—132no—
64#333—132no—
65#331—132no—
66C22×C13—41no—
67C22×C13—42no—
68C22×C13C2×C22⋊C411yescharacteristic
69C2×D13—21no—
70C2×D13—22no—
71C2×D13—41no—
72C2×D13—42no—
73C4×C13—21no—
74C4×C13—22no—
75C4×C13—41no—
76Dic13—41no—
77Dic13#10012yes—
78Dic13AGL(1,ℤ/8)12yes—
79Dic13#13712yes—
80C2×#41—131no—
81C2×#41—131no—
82C2×M16—262no—
83C4⋊Q8—131no—
84#127—131no—
85#124—131no—
86#124#26111yescharacteristic
87#121—262no—
88C4×D4—262no—
89C2×C42—131no—
90C4⋊C8—134no—
91C4⋊C8—262no—
92C2×C13—81no—
93C2×C13C2×#10011yescharacteristic
94C2×C13#41712yes—
95D13—41no—
96D13—81no—
97#41—522no—
98#41—522no—
99C2×Q8—131no—
100C2×Q8C2×#26111yescharacteristic
101C2×D4—131no—
102C2×D4—261no—
103C2×D4—262no—
104C2×D4—261no—
105C2×D4C2×#26111yescharacteristic
106C22×C4—132no—
107C22×C4—131no—
108C22×C4—261no—
109C22×C4—261no—
110M16—524no—
111C2×C8—264no—
112C4⋊C4—262no—
113C22⋊C4—22no—
114C22⋊C4—262no—
115C42—132no—
116C42—131no—
117C42C2×#26111yescharacteristic
118C13#156011yescharacteristic, complemented, Sylow
119C23—21no—
120C23—131no—
121C23—261no—
122Q8—41no—
123Q8—521no—
124D4—41no—
125D4—521no—
126D4—522no—
127D4—522no—
128D4—522no—
129D4—522no—
130C2×C4—21no—
131C2×C4—132no—
132C2×C4—131no—
133C2×C4—262no—
134C2×C4—262no—
135C2×C4—262no—
136C2×C4—261no—
137C2×C4—522no—
138C2×C4—522no—
139C2×C4C22⋊#26112yes—
140C2×C4C22×#26111yescharacteristic
141C8—524no—
142C22—41no—
143C22—42no—
144C22—261no—
145C22—262no—
146C22—521no—
147C22—522no—
148C22C2×C22⋊#26111yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—132no—
153C4—132no—
154C4—132no—
155C4—521no—
156C2—81no—
157C2—521no—
158C2—1041no—
159C2D13⋊#10011yescharacteristic
160C2#1171916412yes—
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC22×C13C2×C22⋊C4
prime radical#11719373C2
cosocleC4×Dic13C23
hypercenter#124#261
hypocenterC13#1560
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11719053C2semidirect
3. #11718303C2semidirect
4. #11718297C2semidirect
118. C13#1560semidirect

Maximal subgroups

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

subgroupindex
#117193732
#117190532
#117183032
#117182972
#156013