Finite Group Databasebeta

← #15749969

Subgroups — #15749969

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#13116639C211yesmaximal, characteristic
2#13114967C211yesmaximal, characteristic
3C13×#1566C211yesmaximal, characteristic
4C13×#423—21no—
5C2×C4×C8×C13C2211yescharacteristic
6#11718597—21no—
7C13×#334—21no—
8C13×#334C412yescomplemented
9#11718143—21no—
10#11718143C412yes—
11C22⋊#6090—21no—
12C4⋊#6090—21no—
13#11718053C412yescomplemented
14C2×C13×M16—41no—
15C22×C8×C13C2×C411yescharacteristic
16C22×C8×C13D411yescharacteristic
17C2×C42×C13D411yescharacteristic
18C2×C4⋊Dic13—22no—
19C13×C4⋊C8—22no—
20C13×C4⋊C8—41no—
21C4×C8×C13C2×C411yescharacteristic
22C4×C8×C13C2×C411yescharacteristic
23C4×C8×C13D411yescharacteristic
24C4×C8×C13Q811yescharacteristic
25#88071—41no—
26#88071—41no—
27C2×#6090—22no—
28#7221—131nomaximal, Sylow
29C22×C4×C13C22⋊C411yescharacteristic
30C22×C4×C13D811yescharacteristic
31C22×C4×C13SD1611yescharacteristic
32C22×Dic13—42no—
33C13×M16—82no—
34C2×C8×C13—41no—
35C2×C8×C13—41no—
36C2×C8×C13—42no—
37C2×C8×C13C4211yescharacteristic
38C2×C8×C13C22⋊C411yescharacteristic
39C2×C8×C13C4⋊C411yescharacteristic
40C2×C8×C13C4⋊C411yescharacteristic
41C42×C13C22⋊C411yescharacteristic
42C42×C13C4⋊C411yescharacteristic
43C42×C13SD1611yescharacteristic
44C42×C13Q1611yescharacteristic
45C4⋊Dic13—42no—
46C4⋊Dic13—42no—
47#6090—42no—
48#2163—131no—
49#1835—131no—
50#1566D1311yescharacteristic
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—
69C8×C13—82no—
70#423—21no—
71C2×C4×C8C2×D1311yescharacteristic
72#382—261no—
73C4⋊C16—261no—
74C22⋊C16—261no—
75#346—132no—
76#340—132no—
77#340—261no—
78#334—21no—
79#334Dic1312yescomplemented
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—41no—
93C22×C8C4×D1311yescharacteristic
94C22×C8D5211yescharacteristic
95C2×C4⋊C4—262no—
96C2×C42C22⋊D1311yescharacteristic
97C2×C16—262no—
98C4⋊C8—22no—
99C4⋊C8—41no—
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#610311yescharacteristic
112C22×C4#610411yescharacteristic
113C22×C4#610611yescharacteristic
114M16—82no—
115C2×C8—41no—
116C2×C8—41no—
117C2×C8—42no—
118C2×C8C4×Dic1311yescharacteristic
119C2×C8#610111yescharacteristic
120C2×C8C4⋊Dic1311yescharacteristic
121C2×C8#610311yescharacteristic
122C4⋊C4—522no—
123C4⋊C4—522no—
124C42#610111yescharacteristic
125C42#610511yescharacteristic
126C42#610711yescharacteristic
127C42C22⋊Dic1311yescharacteristic
128C16—522no—
129C13#722111yescharacteristic, complemented, Sylow
130C23#8804911yescharacteristic
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—1042no—
136C2×C4—1042no—
137C2×C4—1042no—
138C2×C4#8804711yescharacteristic
139C2×C4#8804811yescharacteristic
140C2×C4#8805011yescharacteristic
141C2×C4#8807111yescharacteristic
142C2×C4#8807211yescharacteristic
143C2×C4#8807511yescharacteristic
144C8—21no—
145C8—21no—
146C8—21no—
147C8—21no—
148C8—82no—
149C22—21no—
150C22—21no—
151C22#1171808012yes—
152C22#1171812111yescharacteristic
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—2082no—
159C4#1171814911yescharacteristic
160C4#1171815111yescharacteristic
161C2—22no—
162C2#1311269611yescharacteristic
163C2#1311294311yescharacteristic
164C2#1311295011yescharacteristic
subgroupG/H
centerC22#11718121
commutatorC2×C8×C13C42
FrattiniC2×C4×C8C2×D13
FittingC13×#1566C2
socleC22×C13#340
prime radicalC23×C13#102
cosocleC2×C4×C8×C13C22
hypercenter#1566D13
hypocenterC13#7221
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1566

Complements

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

NH ≅ G/Ntype
8. C13×#334C4semidirect
13. #11718053C4semidirect
79. #334Dic13semidirect
129. C13#7221semidirect

Maximal subgroups

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

subgroupindex
#131166392
#131149672
C13×#15662
#722113