Finite Group Databasebeta

← #15774759

Subgroups — #15774759

Order 3328.

212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C16×Dic26C212yesmaximal
2C8×Dic52C211yesmaximal, characteristic
3#13112900C211yesmaximal, characteristic
4#13112816C212yesmaximal
5C13×#1312C211yesmaximal, characteristic
6C4×Dic52C411yescharacteristic
7C8×Dic26C2212yes—
8C4×C13×C16C2211yescharacteristic
9C4×C13×C16C2211yescharacteristic
10C82×C13C2211yescharacteristic
11#11718093—22no—
12C16×Dic13—22no—
13C4⋊#6090C2212yes—
14#11718050C411yescharacteristic
15#11718048C412yes—
16C2×Dic52C811yescharacteristic
17C4×Dic26C2×C412yes—
18C2×C13×C16—21no—
19C2×C13×C16D412yes—
20C4×C8×C13C2×C411yescharacteristic
21C4×C8×C13C2×C411yescharacteristic
22C4×C8×C13C2311yescharacteristic
23#88058C811yescharacteristic
24#88056C812yes—
25#88054—22no—
26C8×Dic13—22no—
27C2×#6090—22no—
28C4⋊#1055C2×C412yes—
29#12059—131nomaximal, Sylow
30C2×Dic26C2×C812yes—
31C2×C8×C13—21no—
32C2×C8×C13C2×C811yescharacteristic
33C2×C8×C13C2×C811yescharacteristic
34C2×C8×C13C2×D411yescharacteristic
35C2×C8×C13#4111yescharacteristic
36C42×C13C22×C411yescharacteristic
37C4⋊Dic13C2×C812yes—
38#6101—22no—
39C4×Dic13—22no—
40C2×#1055—22no—
41Dic52C1614yescomplemented
42C13×C16—22no—
43C13×C16—41no—
44#6090—42no—
45Q8×C16—132no—
46C8×Q16—131no—
47#1367—131no—
48Q8⋊C16—132no—
49#1312D1311yescharacteristic
50C2×C4×C13C4×D411yescharacteristic
51C2×C4×C13C22×C811yescharacteristic
52C2×C4×C13#13111yescharacteristic
53C2×Dic13—22no—
54C2×Dic13—22no—
55Dic26—22no—
56Dic26C2×C1614yes—
57C8×C13—21no—
58C8×C13—21no—
59C8×C13—41no—
60C8×C13C2×C1612yes—
61C8×C13#13712yes—
62#1055—42no—
63C8×Q8—132no—
64C4×Q16—131no—
65C4⋊C16—132no—
66C4⋊C16—262no—
67C4×C16—262no—
68C4×C16C2×D1311yescharacteristic
69C4×C16C2×D1311yescharacteristic
70#335—131no—
71Q8⋊C8—132no—
72C82C2×D1311yescharacteristic
73C22×C13C8×D411yescharacteristic
74C4×C13—21no—
75C4×C13#44111yescharacteristic
76C4×C13#44411yescharacteristic
77C4×C13C22×C1611yescharacteristic
78C4×C13#50411yescharacteristic
79Dic13—24no—
80Dic13—42no—
81C2×Q16—131no—
82C4×Q8—132no—
83C2×C16—21no—
84C2×C16—262no—
85C2×C16D5212yes—
86#107—131no—
87C4⋊C8—132no—
88C4⋊C8—262no—
89#103—132no—
90C4×C8—262no—
91C4×C8C4×D1311yescharacteristic
92C4×C8C4×D1311yescharacteristic
93C4×C8C22×D1311yescharacteristic
94C2×C13#157911yescharacteristic
95C2×C13D4×C1611yescharacteristic
96C2×C13#217111yescharacteristic
97C2×Q8—132no—
98Q16—134no—
99C2×C8—21no—
100C2×C8—262no—
101C2×C8C8×D1311yescharacteristic
102C2×C8C8×D1311yescharacteristic
103C2×C8C2×D5211yescharacteristic
104C2×C8#612711yescharacteristic
105C4⋊C4—132no—
106C4⋊C4—262no—
107C42—262no—
108C42C2×C4×D1311yescharacteristic
109C16—22no—
110C16—41no—
111C16—522no—
112C13#1205911yescharacteristic, complemented, Sylow
113Q8—134no—
114Q8—262no—
115C2×C4—262no—
116C2×C4—262no—
117C2×C4C4×D5211yescharacteristic
118C2×C4C2×C8×D1311yescharacteristic
119C2×C4#8815511yescharacteristic
120C8—21no—
121C8—21no—
122C8—41no—
123C8—522no—
124C8C16×D1312yes—
125C8#8816312yes—
126C22C8×D5211yescharacteristic
127C4—21no—
128C4—264no—
129C4—522no—
130C4#1171837711yescharacteristic
131C4#1171837811yescharacteristic
132C4C2×C16×D1311yescharacteristic
133C4#1171856211yescharacteristic
134C2#1311365611yescharacteristic
135C2C16×D5211yescharacteristic
136C2#1311667911yescharacteristic
subgroupG/H
centerC2×C8C2×D52
commutatorC4×C13C22×C16
FrattiniC4×C8C22×D13
FittingC13×#1312C2
socle, prime radicalC22×C13C8×D4
cosocleC4×C8×C13C23
hypercenter#1312D13
hypocenterC13#12059
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C16 ◁ #1312

Complements

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

NH ≅ G/Ntype
41. Dic52C16semidirect
112. C13#12059semidirect

Maximal subgroups

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

subgroupindex
C16×Dic262
C8×Dic522
#131129002
#131128162
C13×#13122
#1205913