Finite Group Databasebeta

← #16791303

Subgroups — #16791303

Order 3328.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#13129977C214yesmaximal, complemented
3#13125237C211yesmaximal, characteristic
4#11719182C2211yescharacteristic
5C2×#88124C411yescharacteristic, complemented
6#11719116—22no—
7C4×C13×M16C411yescharacteristic, complemented
8#11718794—22no—
9#11718374C2212yes—
10#11718364C412yescomplemented
11#11718358—22no—
12#11718226—22no—
13#11718225C2214yes—
14C2×#6127D412yes—
15#88237—42no—
16C2×C13×M16—21no—
17C2×C42×C13C2×C411yescharacteristic
18#88184—41no—
19C2×C4⋊Dic13—21no—
20C2×#6101—41no—
21#88129D412yes—
22#88128C2311yescharacteristic
23C4×D52—41no—
24#88124—21no—
25#88124—41no—
26#88124C2×C412yes—
27#88123C2×C411yescharacteristic
28#88119—42no—
29#88107—24no—
30C13×#97C2×C412yes—
31C4×C8×C13—21no—
32#88061—24no—
33#88056—24no—
34#13596—131nomaximal, Sylow
35C22×C4×C13—21no—
36C22×C4×C13C22⋊C411yescharacteristic
37C2×C22⋊D13—22no—
38C22×Dic13—41no—
39#6127—42no—
40#6127—42no—
41C2×D52—41no—
42C2×D52C2×D412yes—
43C2×C4×D13—22no—
44C2×Dic26C22⋊C412yes—
45C22⋊#261—44no—
46C4⋊#261—82no—
47C4×#261—82no—
48C13×M16—42no—
49C2×C8×C13—22no—
50C42×C13—21no—
51C42×C13C22⋊C411yescharacteristic
52C42×C13C22×C411yescharacteristic
53#6103—42no—
54C4⋊Dic13—22no—
55C4⋊Dic13—41no—
56C4⋊Dic13—41no—
57#6101—42no—
58#6101—42no—
59#3142—131no—
60#2126—132no—
61#1412—134no—
62C23×C13#9911yescharacteristic
63C22×D13—22no—
64C2×#261—84no—
65C2×C4×C13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—81no—
69C2×C4×C13#9911yescharacteristic
70C2×C4×C13C2×C22⋊C411yescharacteristic
71C22⋊D13—82no—
72C2×Dic13—22no—
73C2×Dic13—42no—
74C2×Dic13—82no—
75D52—42no—
76D52—82no—
77C4×D13—42no—
78C4×D13—42no—
79Dic26—42no—
80C8×C13—42no—
81#532—131no—
82C2×#125—131no—
83#491—132no—
84#490—132no—
85#488—262no—
86#417—262no—
87#410—262no—
88C4×M16#26111yescharacteristic, complemented
89#354—262no—
90#353—134no—
91C22×C13—21no—
92C22×C13—41no—
93C22×C13C2×#9911yescharacteristic
94C2×D13—42no—
95C2×D13—82no—
96#261—164no—
97C4×C13—21no—
98C4×C13—41no—
99C4×C13—41no—
100C4×C13#35412yes—
101Dic13—42no—
102Dic13—82no—
103C2×#41—132no—
104C2×M16—21no—
105C4⋊Q8—131no—
106#127—131no—
107#125—132no—
108#125—261no—
109#125—521no—
110#124—132no—
111#121—521no—
112C4×D4—521no—
113#117—522no—
114C2×C4⋊C4—261no—
115C2×C4⋊C4—521no—
116C2×C42C2×#26111yescharacteristic
117#103—264no—
118#102—264no—
119#99—264no—
120#99—522no—
121#97C2×#26112yes—
122C4×C8—21no—
123C2×C13—21no—
124C2×C13—41no—
125C2×C13C2×#35411yescharacteristic
126D13—82no—
127#41—522no—
128#41—522no—
129C2×Q8—132no—
130C2×D4—132no—
131C2×D4—262no—
132C2×D4—521no—
133C22×C4—21no—
134C22×C4—262no—
135C22×C4—521no—
136C22×C4C22⋊#26111yescharacteristic
137M16—42no—
138C2×C8—22no—
139C4⋊C4—262no—
140C4⋊C4—521no—
141C4⋊C4—522no—
142C4⋊C4—522no—
143C4⋊C4—521no—
144C4⋊C4—1042no—
145C22⋊C4—522no—
146C22⋊C4—524no—
147C42—21no—
148C42—1042no—
149C42C22⋊#26111yescharacteristic
150C42C22×#26111yescharacteristic
151C13#1359611yescharacteristic, complemented, Sylow
152C23—262no—
153C23#8810711yescharacteristic
154Q8—522no—
155D4—522no—
156D4—1042no—
157D4—1042no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—81no—
162C2×C4—262no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4—1042no—
167C2×C4—1044no—
168C2×C4#8810711yescharacteristic
169C2×C4C2×C22⋊#26111yescharacteristic
170C8—42no—
171C22—21no—
172C22—41no—
173C22—522no—
174C22—1042no—
175C22C2×#8810711yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—522no—
180C4—1042no—
181C4—2084no—
182C4#1171822612yes—
183C2—21no—
184C2—41no—
185C2—1042no—
186C2C2×#1171822611yescharacteristic
subgroupG/H
centerC2C2×#11718226
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC4×C13×M16C4
socleC2×C13C2×#354
prime radical#11719182C22
cosocle#88128C23
hypercenterC4×M16#261
hypocenterC13#13596
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #13129977C2semidirect
5. C2×#88124C4semidirect
7. C4×C13×M16C4semidirect
10. #11718364C4semidirect
88. C4×M16#261semidirect
151. C13#13596semidirect

Maximal subgroups

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

subgroupindex
#131311092
#131299772
#131252372
#1359613