Finite Group Databasebeta

← #16791317

Subgroups — #16791317

Order 3328.

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

normal subgroups only

This group has 318 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#13131129C212yesmaximal
2#13129980C214yesmaximal, complemented
3#13125237C211yesmaximal, characteristic
4#11719182C2211yescharacteristic
5C2×#88124C411yescharacteristic
6#11719132—22no—
7C4×C13×M16C411yescharacteristic
8#11718794—22no—
9#11718374C412yes—
10#11718364C2212yes—
11#11718358—22no—
12#11718228—22no—
13#11718227C2214yes—
14C2×#6127D412yes—
15D13⋊M16—42no—
16C2×C13×M16—21no—
17C2×C42×C13C2×C411yescharacteristic
18#88184—41no—
19C2×C4⋊Dic13—21no—
20C2×#6101—41no—
21#88129D412yes—
22#88128C2×C411yescharacteristic
23C4×D52—41no—
24#88124—21no—
25#88124—41no—
26#88124C2×C412yes—
27#88123C2311yescharacteristic
28#88121—42no—
29#88113—24no—
30C13×#97C2×C412yes—
31C4×C8×C13—21no—
32#88061—24no—
33#88056—24no—
34#13600—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×D52C22⋊C412yes—
43C2×C4×D13—22no—
44C2×Dic26C2×D412yes—
45#6122—44no—
46#6118—82no—
47D13⋊C8—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#2132—132no—
61#1413—134no—
62C23×C13#9911yescharacteristic
63C22×D13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—81no—
68C2×C4×C13#9911yescharacteristic
69C2×C4×C13C2×C22⋊C411yescharacteristic
70C22⋊D13—82no—
71C2×Dic13—22no—
72C2×Dic13—42no—
73C2×Dic13—82no—
74D52—42no—
75D52—82no—
76C4×D13—42no—
77C4×D13—42no—
78Dic26—42no—
79#1057—84no—
80C8×C13—42no—
81#532—131no—
82C2×#125—131no—
83#491—132no—
84#490—132no—
85#488—262no—
86#417—262no—
87#413—262no—
88C4×M16#26111yescharacteristic
89#356—134no—
90#355—262no—
91C22×C13—21no—
92C22×C13—41no—
93C22×C13C2×#9911yescharacteristic
94C2×D13—42no—
95C2×D13—82no—
96C4×C13—21no—
97C4×C13—41no—
98C4×C13—41no—
99C4×C13#35412yes—
100Dic13—42no—
101Dic13—82no—
102C2×#41—132no—
103C2×M16—21no—
104C2×M16—522no—
105C4⋊Q8—131no—
106#127—131no—
107#125—132no—
108#125—261no—
109#125—521no—
110#124—132no—
111#121—521no—
112C4×D4—521no—
113C2×C4⋊C4—261no—
114C2×C4⋊C4—521no—
115C2×C42C2×#26111yescharacteristic
116#103—264no—
117#102—264no—
118#101—264no—
119#100—522no—
120#97C2×#26112yes—
121C4×C8—21no—
122C2×C13—21no—
123C2×C13—41no—
124C2×C13C2×#35411yescharacteristic
125D13—82no—
126#41—522no—
127#41—522no—
128C2×Q8—132no—
129C2×D4—132no—
130C2×D4—262no—
131C2×D4—521no—
132C22×C4—21no—
133C22×C4—262no—
134C22×C4—521no—
135C22×C4C22⋊#26111yescharacteristic
136M16—42no—
137M16—524no—
138M16—1042no—
139C2×C8—22no—
140C2×C8—1042no—
141C4⋊C4—262no—
142C4⋊C4—521no—
143C4⋊C4—522no—
144C4⋊C4—522no—
145C4⋊C4—521no—
146C22⋊C4—522no—
147C42—21no—
148C42C22⋊#26111yescharacteristic
149C42C22×#26111yescharacteristic
150C13#1360011yescharacteristic, complemented, Sylow
151C23—262no—
152C23#8810711yescharacteristic
153Q8—522no—
154D4—522no—
155D4—1042no—
156D4—1042no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—81no—
161C2×C4—262no—
162C2×C4—522no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4—1042no—
166C2×C4#8810711yescharacteristic
167C2×C4C2×C22⋊#26111yescharacteristic
168C8—42no—
169C8—1044no—
170C22—21no—
171C22—41no—
172C22—522no—
173C22—1042no—
174C22C2×#8810711yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—522no—
179C4—1042no—
180C4#1171822612yes—
181C2—21no—
182C2—41no—
183C2—1042no—
184C2C2×#1171822611yescharacteristic
subgroupG/H
centerC2C2×#11718226
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC4×C13×M16C4
socleC2×C13C2×#354
prime radical#11719182C22
cosocle#88123C23
hypercenterC4×M16#261
hypocenterC13#13600
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. #13129980C2semidirect
150. C13#13600semidirect

Maximal subgroups

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

subgroupindex
#131311292
#131299802
#131252372
#1360013