Finite Group Databasebeta

← #16778127

Subgroups — #16778127

Order 3328.

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

normal subgroups only

This group has 274 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#13115667C211yesmaximal, characteristic
3#11719182C2211yescharacteristic
4#11719116—22no—
5C13×#423C411yescharacteristic, complemented
6C2×#88065—22no—
7#11718593C411yescharacteristic, 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—
16#88129C2×C412yes—
17#88128D411yescharacteristic
18C4×D52—41no—
19#88123Q811yescharacteristic
20#88119—42no—
21#88107—24no—
22C13×C4⋊C8—41no—
23#88071—41no—
24#88065—44no—
25#7506—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—
48#2126—132no—
49#1963—131no—
50C23×C13#9911yescharacteristic
51C22×D13—22no—
52C2×#261—84no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—81no—
58C2×C4×C13#9511yescharacteristic
59C2×C4×C13#9911yescharacteristic
60C22⋊D13—82no—
61C2×Dic13—22no—
62C2×Dic13—42no—
63C2×Dic13—82no—
64D52—42no—
65D52—82no—
66C4×D13—42no—
67C4×D13—42no—
68Dic26—42no—
69C8×C13—81no—
70#532—131no—
71#423#26111yescharacteristic, complemented
72C2×#104—262no—
73#410—262no—
74#376—131no—
75#354—134no—
76#353—262no—
77C22×C13—21no—
78C22×C13—41no—
79C22×C13#34211yescharacteristic
80C2×D13—42no—
81C2×D13—82no—
82#261—164no—
83C4×C13—21no—
84C4×C13—41no—
85C4×C13—41no—
86C4×C13#35311yescharacteristic
87C4×C13#35411yescharacteristic
88Dic13—42no—
89Dic13—82no—
90C2×#41—132no—
91C2×M16—21no—
92C4⋊Q8—131no—
93#127—131no—
94#124—132no—
95#121—521no—
96C4×D4—521no—
97#117—522no—
98C2×C42—261no—
99C2×C42C2×#26111yescharacteristic
100C4⋊C8—41no—
101#104—524no—
102#99—264no—
103#99—522no—
104#95—521no—
105C2×C13—21no—
106C2×C13—41no—
107C2×C13#139311yescharacteristic
108D13—82no—
109#41—522no—
110#41—522no—
111C2×Q8—132no—
112C2×D4—132no—
113C2×D4—262no—
114C2×D4—521no—
115C22×C4—21no—
116C22×C4—262no—
117C22×C4—521no—
118C22×C4C22⋊#26111yescharacteristic
119M16—42no—
120C2×C8—41no—
121C4⋊C4—521no—
122C4⋊C4—1042no—
123C22⋊C4—522no—
124C22⋊C4—524no—
125C42—21no—
126C42—262no—
127C42—521no—
128C42—1042no—
129C42C4×#26111yescharacteristic
130C42C4⋊#26111yescharacteristic
131C13#750611yescharacteristic, complemented, Sylow
132C23—262no—
133C23#8810711yescharacteristic
134Q8—522no—
135D4—522no—
136D4—1042no—
137D4—1042no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—81no—
143C2×C4—262no—
144C2×C4—522no—
145C2×C4—522no—
146C2×C4—522no—
147C2×C4—1042no—
148C2×C4—1044no—
149C2×C4(C2×#261)⋊C411yescharacteristic
150C2×C4#8811911yescharacteristic
151C8—81no—
152C22—21no—
153C22—41no—
154C22—522no—
155C22—1042no—
156C22#1171828911yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—522no—
161C4—1042no—
162C4—2084no—
163C4#1171829411yescharacteristic
164C4#1171830011yescharacteristic
165C2—21no—
166C2—41no—
167C2—1042no—
168C2#1312993111yescharacteristic
subgroupG/H
centerC4#11718294
commutatorC42×C13C42
FrattiniC2×C42C2×#261
FittingC13×#423C4
socleC2×C13#1393
prime radical, cosocle#11719182C22
hypercenter#423#261
hypocenterC13#7506
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. #11718593C4semidirect
8. #11718226C4semidirect
71. #423#261semidirect
131. C13#7506semidirect

Maximal subgroups

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

subgroupindex
#131311092
#131156672
#750613