Finite Group Databasebeta

← #15749968

Subgroups — #15749968

Order 3328.

206 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 83 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#13114967C211yesmaximal, characteristic
2#13113592C211yesmaximal, characteristic
3C13×#2163C211yesmaximal, characteristic
4C2×C4×C8×C13C2211yescharacteristic
5#11718597—21no—
6#11718585—21no—
7C13×C4⋊C16—21no—
8C13×C22⋊C16—21no—
9C13×#346C412yescomplemented
10#11718143—21no—
11#11718143C412yes—
12#11718049—21no—
13#11718049C412yescomplemented
14C22×C8×C13C2×C411yescharacteristic
15C22×C8×C13D411yescharacteristic
16C2×C42×C13D411yescharacteristic
17C2×C4⋊Dic13—22no—
18C2×#6099—41no—
19C2×C13×C16—22no—
20C4×C8×C13C2×C411yescharacteristic
21C4×C8×C13C2×C411yescharacteristic
22C4×C8×C13D411yescharacteristic
23C4×C8×C13Q811yescharacteristic
24#88071—41no—
25#88071—41no—
26C4⋊#1055—22no—
27C4⋊#1055—41no—
28#7221—131nomaximal, Sylow
29C22×C4×C13C22⋊C411yescharacteristic
30C22×C4×C13D811yescharacteristic
31C22×C4×C13SD1611yescharacteristic
32C22×Dic13—42no—
33C2×C8×C13—41no—
34C2×C8×C13—41no—
35C2×C8×C13C4211yescharacteristic
36C2×C8×C13C22⋊C411yescharacteristic
37C2×C8×C13C4⋊C411yescharacteristic
38C2×C8×C13C4⋊C411yescharacteristic
39C42×C13C22⋊C411yescharacteristic
40C42×C13C4⋊C411yescharacteristic
41C42×C13SD1611yescharacteristic
42C42×C13Q1611yescharacteristic
43C4⋊Dic13—42no—
44C4⋊Dic13—42no—
45#6099—82no—
46C2×#1055—42no—
47C13×C16—42no—
48#2163D1311yescharacteristic
49#1835—131no—
50#1566—131no—
51C23×C13#10211yescharacteristic
52C2×C4×C13—22no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—41no—
56C2×C4×C13#9511yescharacteristic
57C2×C4×C13#10211yescharacteristic
58C2×C4×C13#10311yescharacteristic
59C2×C4×C13#10311yescharacteristic
60C2×C4×C13#10611yescharacteristic
61C2×C4×C13#10711yescharacteristic
62C2×Dic13—82no—
63C2×Dic13—82no—
64C2×Dic13—82no—
65C8×C13—21no—
66C8×C13—21no—
67C8×C13—21no—
68C8×C13—21no—
69#1055—82no—
70#423—261no—
71C2×C4×C8C2×D1311yescharacteristic
72#382—261no—
73C4⋊C16—21no—
74C22⋊C16—21no—
75#346Dic1312yescomplemented
76#340—132no—
77#340—261no—
78#334—132no—
79#334—261no—
80C22×C13—21no—
81C22×C13—21no—
82C22×C13#34011yescharacteristic
83C22×C13#36012yes—
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—21no—
87C4×C13—21no—
88C4×C13—21no—
89C4×C13H(3,ℤ/4)11yescharacteristic
90C4×C13#34411yescharacteristic
91Dic13—162no—
92C2×M16—521no—
93C22×C8C4×D1311yescharacteristic
94C22×C8C22⋊D1311yescharacteristic
95C2×C4⋊C4—262no—
96C2×C42D5211yescharacteristic
97C2×C16—22no—
98C4⋊C8—262no—
99C4⋊C8—521no—
100C4×C8Dic2611yescharacteristic
101C4×C8C4×D1311yescharacteristic
102C4×C8C2×Dic1311yescharacteristic
103C4×C8C22⋊D1311yescharacteristic
104#95—521no—
105#95—521no—
106C2×C13—22no—
107C2×C13#128611yescharacteristic
108C2×C13#138611yescharacteristic
109C2×C13#138911yescharacteristic
110C22×C4—522no—
111C22×C4#609511yescharacteristic
112C22×C4D10411yescharacteristic
113C22×C4#610311yescharacteristic
114M16—1042no—
115C2×C8—41no—
116C2×C8—41no—
117C2×C8—522no—
118C2×C8C4×Dic1311yescharacteristic
119C2×C8#610111yescharacteristic
120C2×C8#610111yescharacteristic
121C2×C8C22⋊Dic1311yescharacteristic
122C4⋊C4—522no—
123C4⋊C4—522no—
124C42#609511yescharacteristic
125C42Dic5211yescharacteristic
126C42C4⋊Dic1311yescharacteristic
127C42#610311yescharacteristic
128C16—42no—
129C13#722111yescharacteristic, complemented, Sylow
130C23#8806111yescharacteristic
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—1042no—
136C2×C4—1042no—
137C2×C4—1042no—
138C2×C4#8805611yescharacteristic
139C2×C4#8805611yescharacteristic
140C2×C4#8805711yescharacteristic
141C2×C4#8805811yescharacteristic
142C2×C4#8806111yescharacteristic
143C2×C4#8807111yescharacteristic
144C8—21no—
145C8—21no—
146C8—21no—
147C8—21no—
148C8—1042no—
149C22—21no—
150C22—21no—
151C22#1171811012yes—
152C22#1171814311yescharacteristic
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—2082no—
159C4#1171812311yescharacteristic
160C4#1171814811yescharacteristic
161C2—22no—
162C2#1311269511yescharacteristic
163C2#1311294211yescharacteristic
164C2#1311295111yescharacteristic
subgroupG/H
centerC22#11718143
commutatorC2×C8×C13C42
FrattiniC2×C4×C8C2×D13
FittingC13×#2163C2
socleC22×C13#340
prime radicalC23×C13#102
cosocleC2×C4×C8×C13C22
hypercenter#2163D13
hypocenterC13#7221
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
9. C13×#346C4semidirect
13. #11718049C4semidirect
75. #346Dic13semidirect
129. C13#7221semidirect

Maximal subgroups

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

subgroupindex
#131149672
#131135922
C13×#21632
#722113