Finite Group Databasebeta

← #15750607

Subgroups — #15750607

Order 3328.

182 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#11718091C211yesmaximal, characteristic
2C2×#11718094C211yesmaximal, characteristic
3C2×C13×M64C211yesmaximal, characteristic
4C22×C13×C16C2211yescharacteristic
5C2×C8×Dic13C411yescharacteristic
6C22×#6090C411yescharacteristic
7C13×M64—21no—
8C13×M64—21no—
9C2×C13×C32C412yescomplemented
10#11718094—21no—
11#11718094—21no—
12#11718091—21no—
13#11718091—21no—
14C2×#88034C412yescomplemented
15C22×C8×C13C2×C411yescharacteristic
16C2×C4×Dic13C811yescharacteristic
17C22×#1055C811yescharacteristic
18C2×C13×C16C2×C411yescharacteristic
19C2×C13×C16C2×C411yescharacteristic
20C2×C13×C16D411yescharacteristic
21C2×C13×C16D411yescharacteristic
22C2×C13×C16D411yescharacteristic
23C2×C13×C16Q811yescharacteristic
24C8×Dic13—21no—
25C8×Dic13—21no—
26C2×#6090—21no—
27C2×#6090—21no—
28C2×#6090C812yes—
29C13×C32—22no—
30#88034—22no—
31#7466—131nomaximal, Sylow
32C22×C4×C13C2×C811yescharacteristic
33C22×Dic13—21no—
34C2×C8×C13C4211yescharacteristic
35C2×C8×C13C22⋊C411yescharacteristic
36C2×C8×C13C4⋊C411yescharacteristic
37C2×C8×C13C2×C811yescharacteristic
38C2×C8×C13M1611yescharacteristic
39C2×C8×C13M1611yescharacteristic
40C4×Dic13—21no—
41C4×Dic13C1612yes—
42C2×#1055—21no—
43C2×#1055—21no—
44C2×#1055C1612yes—
45C13×C16C22⋊C411yescharacteristic
46C13×C16C22⋊C411yescharacteristic
47C13×C16C4⋊C411yescharacteristic
48C13×C16C4⋊C411yescharacteristic
49#6090—22no—
50C2×M64—131no—
51C2×M64D1311yescharacteristic
52C2×#346—131no—
53C23×C13M3211yescharacteristic
54C2×C4×C13C4×C811yescharacteristic
55C2×C4×C13C22⋊C811yescharacteristic
56C2×C4×C13C4⋊C811yescharacteristic
57C2×C4×C13C2×C1611yescharacteristic
58C2×C4×C13C2×C1611yescharacteristic
59C2×C4×C13M3211yescharacteristic
60C2×Dic13—22no—
61C2×Dic13—42no—
62C8×C13#9511yescharacteristic
63C8×C13#9711yescharacteristic
64C8×C13C22⋊C811yescharacteristic
65C8×C13C4⋊C811yescharacteristic
66#1055—22no—
67C22×C16—131no—
68C22×C16C2×D1311yescharacteristic
69C2×C4×C8—131no—
70M64—21no—
71M64—21no—
72M64—261no—
73M64—261no—
74C2×C32—132no—
75C2×C32Dic1312yescomplemented
76#346—261no—
77#346—261no—
78C22×C13—22no—
79C22×C13#34611yescharacteristic
80C22×C13C22⋊C1611yescharacteristic
81C22×C13C4⋊C1611yescharacteristic
82C4×C13#33611yescharacteristic
83C4×C13C4×C1611yescharacteristic
84C4×C13C22⋊C1611yescharacteristic
85C4×C13C4⋊C1611yescharacteristic
86Dic13—42no—
87C22×C8—131no—
88C22×C8C4×D1311yescharacteristic
89C2×C42—131no—
90C2×C16—132no—
91C2×C16—261no—
92C2×C16—261no—
93C2×C16Dic2611yescharacteristic
94C2×C16C4×D1311yescharacteristic
95C2×C16D5211yescharacteristic
96C2×C16C2×Dic1311yescharacteristic
97C2×C16C22⋊D1311yescharacteristic
98C2×C16C22⋊D1311yescharacteristic
99C4×C8—261no—
100C4×C8—261no—
101C32—22no—
102C32—262no—
103C2×C13—21no—
104C2×C13—21no—
105C2×C13#137411yescharacteristic
106C2×C13#139812yes—
107C22×C4—261no—
108C22×C4C8×D1311yescharacteristic
109C2×C8—132no—
110C2×C8—261no—
111C2×C8—261no—
112C2×C8C8×D1311yescharacteristic
113C2×C8#609411yescharacteristic
114C2×C8#609411yescharacteristic
115C2×C8C4×Dic1311yescharacteristic
116C2×C8#610111yescharacteristic
117C2×C8#610311yescharacteristic
118C42—132no—
119C42—261no—
120C16—262no—
121C16#610111yescharacteristic
122C16C4⋊Dic1311yescharacteristic
123C16#610311yescharacteristic
124C16C22⋊Dic1311yescharacteristic
125C13#746611yescharacteristic, complemented, Sylow
126C23#8803811yescharacteristic
127C2×C4—262no—
128C2×C4—522no—
129C2×C4C16×D1311yescharacteristic
130C2×C4C16×D1311yescharacteristic
131C2×C4#8803811yescharacteristic
132C2×C4C8×Dic1311yescharacteristic
133C2×C4#8805411yescharacteristic
134C2×C4#8806011yescharacteristic
135C8—262no—
136C8#8805411yescharacteristic
137C8#8805511yescharacteristic
138C8#8806011yescharacteristic
139C8#8807111yescharacteristic
140C22—22no—
141C22#1171809311yescharacteristic
142C22#1171809411yescharacteristic
143C22#1171809911yescharacteristic
144C4—522no—
145C4C16×Dic1311yescharacteristic
146C4#1171809311yescharacteristic
147C4#1171809911yescharacteristic
148C4#1171814211yescharacteristic
149C2—21no—
150C2—21no—
151C2#1311291311yescharacteristic
152C2#1311297112yes—
subgroupG/H
centerC2×C8C4×Dic13
commutatorC4×C13C4×C16
FrattiniC22×C16C2×D13
FittingC2×C13×M64C2
socleC22×C13#346
prime radicalC23×C13M32
cosocleC22×C13×C16C22
hypercenterC2×M64D13
hypocenterC13#7466
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×M64

Complements

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

NH ≅ G/Ntype
9. C2×C13×C32C4semidirect
14. C2×#88034C4semidirect
75. C2×C32Dic13semidirect
125. C13#7466semidirect

Maximal subgroups

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

subgroupindex
C2×#117180912
C2×#117180942
C2×C13×M642
#746613