Finite Group Databasebeta

← #16790252

Subgroups — #16790252

Order 3328.

370 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 160 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×#11718260C214yesmaximal
2C2×C4⋊#6092C212yesmaximal
3#13114524C211yesmaximal, characteristic
4C22×#6092C2214yes—
5C2×C13×#97C411yescharacteristic
6C2×#88055C412yes—
7C2×C8×Dic13C2212yes—
8#11718593C411yescharacteristic
9C2×C4×#1055C2211yescharacteristic
10#11718260—28no—
11C4⋊#6092—24no—
12C22×C8×C13C2×C412yes—
13C2×C42×C13C2×C411yescharacteristic
14C2×C4×Dic13C2×C412yes—
15C22×#1055C2×C411yescharacteristic
16C22×#1055C2311yescharacteristic
17C2×#6092—24no—
18C2×#6092—28no—
19C13×#97—22no—
20#88071C814yes—
21#88055—24no—
22C8×Dic13D414yes—
23C8×Dic13Q814yes—
24C4×#1055D412yes—
25C4×#1055Q812yes—
26#12899—131nomaximal, Sylow
27C22×C4×C13C2×C812yes—
28C22×C4×C13C22×C411yescharacteristic
29C22×Dic13C2×C814yes—
30C2×C8×C13—22no—
31C2×C8×C13—22no—
32C2×C8×C13C4⋊C414yes—
33C42×C13C4⋊C412yes—
34C42×C13M1612yes—
35C4×Dic13C4⋊C414yes—
36C4×Dic13M1614yes—
37C2×#1055—22no—
38C2×#1055C4⋊C412yes—
39C2×#1055C2×D411yescharacteristic
40C2×#1055C2×D412yes—
41C2×#1055C2×Q811yescharacteristic
42C2×#1055C2×Q812yes—
43#6092—44no—
44C2×C4⋊C16—132no—
45C2×C4⋊C16—134no—
46#1726—131no—
47C23×C13C22×C811yescharacteristic
48C2×C4×C13—24no—
49C2×C4×C13C4⋊C814yes—
50C2×C4×C13C2×C4⋊C411yescharacteristic
51C2×C4×C13C2×C4⋊C412yes—
52C2×C4×C13C2×M1612yes—
53C2×C4×C13C2×M1611yescharacteristic
54C2×Dic13—28no—
55C2×Dic13C4⋊C818yes—
56C8×C13—24no—
57#1055—22no—
58#1055#12711yescharacteristic
59#1055C4⋊Q811yescharacteristic
60#1055C4⋊Q812yes—
61C22×C16—134no—
62C2×#97—132no—
63C2×#97#26111yescharacteristic
64C2×C4×C8—132no—
65C2×C4×C8—131no—
66#376—131no—
67C4⋊C16—264no—
68C4⋊C16—268no—
69C22×C13C2×C4⋊C812yes—
70C22×C13C2×C4⋊C811yescharacteristic
71C22×C13#50414yes—
72C4×C13—24no—
73C4×C13#38411yescharacteristic
74C4×C13#42311yescharacteristic
75C4×C13#42312yes—
76Dic13—28no—
77C22×C8—131no—
78C22×C8—131no—
79C22×C8C2×#26112yes—
80C2×C42—132no—
81C2×C42C2×#26111yescharacteristic
82C2×C16—264no—
83C2×C16—268no—
84#97—22no—
85#97—264no—
86C4×C8—134no—
87C4×C8—134no—
88C4×C8—132no—
89C4×C8—132no—
90#95—134no—
91C2×C13#184211yescharacteristic
92C2×C13#215114yes—
93C2×C13#215112yes—
94C22×C4—134no—
95C22×C4D13⋊C812yes—
96C22×C4C22×#26111yescharacteristic
97C2×C8—22no—
98C2×C8—22no—
99C2×C8—131no—
100C2×C8—132no—
101C2×C8—131no—
102C2×C8—132no—
103C2×C8—132no—
104C2×C8—262no—
105C2×C8C4⋊#26114yes—
106C42—134no—
107C42—134no—
108C42C4⋊#26112yes—
109C42#612212yes—
110C16—524no—
111C13#1289911yescharacteristic, complemented, Sylow
112C23C2×D13⋊C811yescharacteristic
113C2×C4—24no—
114C2×C4—138no—
115C2×C4—268no—
116C2×C4#8811214yes—
117C2×C4D13⋊M1612yes—
118C2×C4C2×C4⋊#26111yescharacteristic
119C2×C4C2×C4⋊#26112yes—
120C2×C4C2×#612211yescharacteristic
121C8—24no—
122C8—131no—
123C8—131no—
124C8—132no—
125C8—262no—
126C22D13⋊(C4⋊C8)12yes—
127C22#1171909614yes—
128C22C2×#8811211yescharacteristic
129C4—24no—
130C4—268no—
131C4#1171905311yescharacteristic
132C4#1171905911yescharacteristic
133C4#1171912912yes—
134C2#1313076911yescharacteristic
135C2#1313117214yes—
136C2#1313117312yes—
subgroupG/H
center, FrattiniC22×C4C22×#261
commutator, socle, prime radicalC23×C13C22×C8
FittingC2×C13×#97C4
cosocleC22×#1055C23
hypercenterC2×#97#261
hypocenterC13#12899
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
111. C13#12899semidirect

Maximal subgroups

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

subgroupindex
C2×#117182602
C2×C4⋊#60922
#131145242
#1289913