Finite Group Databasebeta

← #16791301

Subgroups — #16791301

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#13129976C214yesmaximal, complemented
3#13125239C211yesmaximal, characteristic
4C2×C13×#125C411yescharacteristic, complemented
5#11719182C2211yescharacteristic
6#11719116—22no—
7#11718730C412yescomplemented
8#11718729—22no—
9#11718728C2212yes—
10#11718627—22no—
11C4×#6099C411yescharacteristic, complemented
12#11718226—22no—
13#11718225C2214yes—
14C2×#6127D412yes—
15#88237—42no—
16C13×#125—21no—
17C13×#125—41no—
18C13×#125C2×C412yes—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—41no—
21C2×C42×C13C2×C411yescharacteristic
22#88184—41no—
23C2×#6099—21no—
24#88129D412yes—
25#88128C2311yescharacteristic
26C4×D52—41no—
27#88123C2×C411yescharacteristic
28#88119—42no—
29#88107—24no—
30#88050—24no—
31#88049—24no—
32#88043C2×C412yes—
33C4×#1055—21no—
34#13596—131nomaximal, Sylow
35C22×C4×C13—21no—
36C22×C4×C13—41no—
37C22×C4×C13C22⋊C411yescharacteristic
38C2×C22⋊D13—22no—
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×C4⋊C4—22no—
49C13×C4⋊C4—42no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—41no—
52C42×C13—21no—
53C42×C13C22⋊C411yescharacteristic
54C42×C13C22×C411yescharacteristic
55#6103—42no—
56C4⋊Dic13—41no—
57#6099—42no—
58C2×#1055—22no—
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—42no—
69C2×C4×C13—81no—
70C2×C4×C13—82no—
71C2×C4×C13#9911yescharacteristic
72C2×C4×C13C2×C22⋊C411yescharacteristic
73C22⋊D13—82no—
74C2×Dic13—22no—
75D52—42no—
76D52—82no—
77C4×D13—42no—
78C4×D13—42no—
79Dic26—42no—
80#1055—42no—
81#532—131no—
82C2×#125#26111yescharacteristic, complemented
83#491—132no—
84#490—132no—
85#488—262no—
86#417—262no—
87#410—262no—
88C4×M16—131no—
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—82no—
101C4×C13#35412yes—
102Dic13—42no—
103C2×#41—132no—
104C2×M16—261no—
105C4⋊Q8—131no—
106#127—131no—
107#125—21no—
108#125—41no—
109#125C2×#26112yes—
110#124—132no—
111#121—521no—
112C4×D4—521no—
113#117—522no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—41no—
116C2×C42C2×#26111yescharacteristic
117#103—264no—
118#102—264no—
119#99—264no—
120#99—522no—
121#97—132no—
122C4×C8—261no—
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—41no—
135C22×C4—262no—
136C22×C4C22⋊#26111yescharacteristic
137M16—522no—
138C2×C8—262no—
139C4⋊C4—22no—
140C4⋊C4—42no—
141C4⋊C4—42no—
142C4⋊C4—41no—
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#8811911yescharacteristic
154Q8—522no—
155D4—522no—
156D4—1042no—
157D4—1042no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—262no—
165C2×C4—522no—
166C2×C4—522no—
167C2×C4—1044no—
168C2×C4#8811911yescharacteristic
169C2×C4C2×C22⋊#26111yescharacteristic
170C8—522no—
171C22—21no—
172C22—41no—
173C22—522no—
174C22—1042no—
175C22C2×#8811911yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—82no—
180C4—522no—
181C4—2084no—
182C4#1171830012yes—
183C2—21no—
184C2—41no—
185C2—1042no—
186C2C2×#1171830011yescharacteristic
subgroupG/H
centerC2C2×#11718300
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×#125C4
socleC2×C13C2×#354
prime radical#11719182C22
cosocle#88128C23
hypercenterC2×#125#261
hypocenterC13#13596
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #13129976C2semidirect
4. C2×C13×#125C4semidirect
7. #11718730C4semidirect
11. C4×#6099C4semidirect
82. C2×#125#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
#131299762
#131252392
#1359613