Finite Group Databasebeta

← #15749813

Subgroups — #15749813

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
1#13116639C211yesmaximal, characteristic
2#13113125C211yesmaximal, characteristic
3C4×C13×M32C211yesmaximal, characteristic
4C2×C13×M32—21no—
5C2×C4×C8×C13C2211yescharacteristic
6#11718586C411yescharacteristic
7C4×#6099C411yescharacteristic
8C13×#346—21no—
9C4×C13×C16C412yes—
10C22⋊#6090—21no—
11C4⋊#6090C412yes—
12#11718053—21no—
13#11718047—21no—
14#11718046—21no—
15C22×C8×C13D411yescharacteristic
16C22×C8×C13Q811yescharacteristic
17C2×C42×C13C2×C411yescharacteristic
18C2×#6099—21no—
19C13×M32—24no—
20C2×C13×C16—22no—
21C4×C8×C13C2×C411yescharacteristic
22C4×C8×C13C2×C411yescharacteristic
23C4×C8×C13D411yescharacteristic
24C4×C8×C13D411yescharacteristic
25C22⋊#1055C812yes—
26C2×#6090—22no—
27C4⋊#1055—21no—
28#88043C812yes—
29C4×#1055—21no—
30C4×#1055—21no—
31#7164—131nomaximal, Sylow
32C22×C4×C13C4⋊C411yescharacteristic
33C22×C4×C13C2×C811yescharacteristic
34C22×C4×C13M1611yescharacteristic
35C2×C8×C13—22no—
36C2×C8×C13—22no—
37C2×C8×C13C22⋊C411yescharacteristic
38C2×C8×C13C22⋊C411yescharacteristic
39C2×C8×C13C4⋊C411yescharacteristic
40C2×C8×C13C4⋊C411yescharacteristic
41C42×C13C4211yescharacteristic
42C42×C13C22⋊C411yescharacteristic
43C42×C13C2×C811yescharacteristic
44C42×C13M1611yescharacteristic
45#6099—42no—
46C2×#1055—22no—
47C2×#1055—22no—
48C13×C16—24no—
49#6090—42no—
50#2163—131no—
51C4×M32D1311yescharacteristic
52#1451—131no—
53C23×C13C4⋊C811yescharacteristic
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—22no—
57C2×C4×C13—41no—
58C2×C4×C13#9511yescharacteristic
59C2×C4×C13C4×C811yescharacteristic
60C2×C4×C13#9711yescharacteristic
61C2×C4×C13C22⋊C811yescharacteristic
62C2×C4×C13C22⋊C811yescharacteristic
63C2×C4×C13C4⋊C811yescharacteristic
64C8×C13—21no—
65C8×C13—21no—
66C8×C13#10412yes—
67C8×C13#10812yes—
68#1055—42no—
69#1055—42no—
70C2×M32—21no—
71#431—131no—
72C4×M16—131no—
73C2×C4×C8C2×D1311yescharacteristic
74C4⋊C16—132no—
75C22⋊C16—261no—
76#346—21no—
77#346—261no—
78C4×C16Dic1312yes—
79#322—261no—
80#322—261no—
81C22×C13—21no—
82C22×C13—21no—
83C22×C13—21no—
84C22×C13#33611yescharacteristic
85C4×C13—21no—
86C4×C13—21no—
87C4×C13—21no—
88C4×C13—21no—
89C4×C13#33911yescharacteristic
90C4×C13#34111yescharacteristic
91C4×C13#34712yes—
92C2×M16—261no—
93C22×C8Dic2611yescharacteristic
94C22×C8C22⋊D1311yescharacteristic
95C2×C42C4×D1311yescharacteristic
96M32—24no—
97C2×C16—22no—
98C2×C16—262no—
99C4⋊C8—261no—
100C22⋊C8—132no—
101#97—132no—
102C4×C8—261no—
103C4×C8—261no—
104C4×C8C4×D1311yescharacteristic
105C4×C8D5211yescharacteristic
106C4×C8C2×Dic1311yescharacteristic
107C4×C8C22⋊D1311yescharacteristic
108C2×C13—41no—
109C2×C13#127811yescharacteristic
110C2×C13#137511yescharacteristic
111C2×C13#137811yescharacteristic
112C22×C4C8×D1311yescharacteristic
113C22×C4#609411yescharacteristic
114C22×C4#610111yescharacteristic
115M16—522no—
116C2×C8—22no—
117C2×C8—22no—
118C2×C8—262no—
119C2×C8—262no—
120C2×C8#610111yescharacteristic
121C2×C8C4⋊Dic1311yescharacteristic
122C2×C8#610311yescharacteristic
123C2×C8C22⋊Dic1311yescharacteristic
124C42C8×D1311yescharacteristic
125C42#609411yescharacteristic
126C42C4×Dic1311yescharacteristic
127C42#610311yescharacteristic
128C16—24no—
129C16—522no—
130C13#716411yescharacteristic, complemented, Sylow
131C23#8805411yescharacteristic
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4C8×Dic1311yescharacteristic
137C2×C4#8805411yescharacteristic
138C2×C4#8805511yescharacteristic
139C2×C4#8806011yescharacteristic
140C2×C4#8806011yescharacteristic
141C2×C4#8807111yescharacteristic
142C8—21no—
143C8—21no—
144C8—522no—
145C8—522no—
146C8#8804512yes—
147C8#8805912yes—
148C22—21no—
149C22—21no—
150C22—21no—
151C22#1171814211yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4#1171810412yes—
157C4#1171811511yescharacteristic
158C4#1171814411yescharacteristic
159C2—41no—
160C2#1311267311yescharacteristic
161C2#1311291511yescharacteristic
162C2#1311292111yescharacteristic
subgroupG/H
centerC2×C4#88071
commutatorC2×C4×C13C4×C8
FrattiniC2×C4×C8C2×D13
FittingC4×C13×M32C2
socleC22×C13#336
prime radicalC23×C13C4⋊C8
cosocleC2×C4×C8×C13C22
hypercenterC4×M32D13
hypocenterC13#7164
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C4×M32

Complements

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

NH ≅ G/Ntype
130. C13#7164semidirect

Maximal subgroups

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

subgroupindex
#131166392
#131131252
C4×C13×M322
#716413