Finite Group Databasebeta

← #16778107

Subgroups — #16778107

Order 3328.

294 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 46 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#13131109C212yesmaximal
2#13115663C211yesmaximal, characteristic
3#11719182C2211yescharacteristic
4#11719116—22no—
5C13×#423C411yescharacteristic, complemented
6C2×#88065—22no—
7C42×Dic13C411yescharacteristic, complemented
8#11718226C414yescomplemented
9#11718225—22no—
10C2×#6127D412yes—
11#88237—42no—
12C2×C13×M16—21no—
13C2×C42×C13C2×C411yescharacteristic
14#88184—41no—
15C2×C4×Dic13—21no—
16C2×C4×Dic13—41no—
17#88129C2×C412yes—
18#88128D411yescharacteristic
19C4×D52—41no—
20#88123Q811yescharacteristic
21#88119—42no—
22#88107—24no—
23C13×C4⋊C8—41no—
24#88065—44no—
25#7500—131nomaximal, Sylow
26C22×C4×C13—21no—
27C22×C4×C13C22⋊C411yescharacteristic
28C2×C22⋊D13—22no—
29C22×Dic13—41no—
30#6127—42no—
31#6127—42no—
32C2×D52—41no—
33C2×D52C22⋊C412yes—
34C2×C4×D13—22no—
35C2×Dic26C4⋊C412yes—
36C22⋊#261—44no—
37C4⋊#261—82no—
38C4×#261—82no—
39C13×M16—42no—
40C2×C8×C13—41no—
41C42×C13—21no—
42C42×C13C4211yescharacteristic
43C42×C13C4⋊C411yescharacteristic
44#6103—42no—
45C4⋊Dic13—41no—
46C4×Dic13—22no—
47C4×Dic13—41no—
48C4×Dic13—44no—
49#2126—132no—
50#1962—131no—
51C23×C13#9911yescharacteristic
52C22×D13—22no—
53C2×#261—84no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—42no—
59C2×C4×C13#9511yescharacteristic
60C2×C4×C13#9911yescharacteristic
61C22⋊D13—82no—
62C2×Dic13—22no—
63C2×Dic13—42no—
64C2×Dic13—44no—
65D52—42no—
66D52—82no—
67C4×D13—42no—
68C4×D13—42no—
69Dic26—42no—
70C8×C13—81no—
71#532—131no—
72#423#26111yescharacteristic, complemented
73C2×#104—262no—
74#410—262no—
75C43—131no—
76#354—134no—
77#353—262no—
78C22×C13—21no—
79C22×C13—41no—
80C22×C13#34211yescharacteristic
81C2×D13—42no—
82C2×D13—82no—
83#261—164no—
84C4×C13—22no—
85C4×C13—21no—
86C4×C13—41no—
87C4×C13#35311yescharacteristic
88C4×C13#35411yescharacteristic
89Dic13—44no—
90Dic13—42no—
91C2×#41—132no—
92C2×M16—21no—
93C4⋊Q8—131no—
94#127—131no—
95#124—132no—
96#121—521no—
97C4×D4—521no—
98#117—522no—
99C2×C42—261no—
100C2×C42—521no—
101C2×C42C2×#26111yescharacteristic
102C4⋊C8—41no—
103#104—524no—
104#99—264no—
105#99—522no—
106C2×C13—21no—
107C2×C13—41no—
108C2×C13#139311yescharacteristic
109D13—82no—
110#41—522no—
111#41—522no—
112C2×Q8—132no—
113C2×D4—132no—
114C2×D4—262no—
115C2×D4—521no—
116C22×C4—21no—
117C22×C4—262no—
118C22×C4—521no—
119C22×C4C22⋊#26111yescharacteristic
120M16—42no—
121C2×C8—41no—
122C4⋊C4—521no—
123C4⋊C4—1042no—
124C22⋊C4—522no—
125C22⋊C4—524no—
126C42—21no—
127C42—262no—
128C42—521no—
129C42—524no—
130C42—1042no—
131C42C4×#26111yescharacteristic
132C42C4⋊#26111yescharacteristic
133C13#750011yescharacteristic, complemented, Sylow
134C23—262no—
135C23#8810711yescharacteristic
136Q8—522no—
137D4—522no—
138D4—1042no—
139D4—1042no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—262no—
146C2×C4—522no—
147C2×C4—524no—
148C2×C4—522no—
149C2×C4—522no—
150C2×C4—1044no—
151C2×C4(C2×#261)⋊C411yescharacteristic
152C2×C4#8811911yescharacteristic
153C8—81no—
154C22—21no—
155C22—41no—
156C22—522no—
157C22—1042no—
158C22#1171828911yescharacteristic
159C4—22no—
160C4—21no—
161C4—41no—
162C4—524no—
163C4—522no—
164C4—2084no—
165C4#1171829411yescharacteristic
166C4#1171830011yescharacteristic
167C2—21no—
168C2—41no—
169C2—1042no—
170C2#1312993111yescharacteristic
subgroupG/H
centerC4#11718300
commutatorC42×C13C42
FrattiniC2×C42C2×#261
FittingC13×#423C4
socleC2×C13#1393
prime radical, cosocle#11719182C22
hypercenter#423#261
hypocenterC13#7500
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
5. C13×#423C4semidirect
7. C42×Dic13C4semidirect
8. #11718226C4semidirect
72. #423#261semidirect
133. C13#7500semidirect

Maximal subgroups

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

subgroupindex
#131311092
#131156632
#750013