Finite Group Databasebeta

← #15750500

Subgroups — #15750500

Order 3328.

214 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 37 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#13116003C211yesmaximal, characteristic
2#13112766C211yesmaximal, characteristic
3C13×#1306C211yesmaximal, characteristic
4#11719188C411yescharacteristic
5C13×#407—21no—
6C13×#381C2211yescharacteristic
7#11718872—21no—
8#11718119—21no—
9#11718118C411yescharacteristic
10#11718117—21no—
11C23×C4×C13D411yescharacteristic
12C2×C13×M16—41no—
13C2×C13×C22⋊C4C2×C411yescharacteristic
14C2×C13×C22⋊C4D411yescharacteristic
15C2×C22⋊Dic13—21no—
16C2×C22⋊Dic13—21no—
17#88178—41no—
18#88132—42no—
19C13×C22⋊C8—22no—
20C13×C22⋊C8—41no—
21C13×#95—41no—
22#88071—42no—
23C22⋊#1055—41no—
24#7427—131nomaximal, Sylow
25C24×C13C22⋊C411yescharacteristic
26C22×C4×C13—21no—
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13—41no—
31C22×C4×C13—41no—
32C22×C4×C13SD1611yescharacteristic
33C22×C4×C13Q1611yescharacteristic
34C22×Dic13—22no—
35C22×Dic13—41no—
36C2×Dic26—41no—
37C13×M16—81no—
38C13×M16—81no—
39C2×C8×C13—42no—
40C13×C22⋊C4—41no—
41C13×C22⋊C4—41no—
42C22⋊Dic13—41no—
43C22⋊Dic13—41no—
44C22⋊Dic13—41no—
45C22⋊Dic13—41no—
46C4⋊Dic13—41no—
47#6101—42no—
48C2×#1055—81no—
49#2030—131no—
50#1317—131no—
51#1306D1311yescharacteristic
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—81no—
55C23×C13#9911yescharacteristic
56C23×C13#10311yescharacteristic
57C23×C13#10411yescharacteristic
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—81no—
67C2×C4×C13—81no—
68C2×C4×C13—81no—
69C2×Dic13—42no—
70C2×Dic13—82no—
71C2×Dic13—81no—
72C2×Dic13—82no—
73Dic26—161no—
74C8×C13—82no—
75#1055—161no—
76#543—131no—
77#407—21no—
78#381—261no—
79#381C2×D1311yescharacteristic
80#342—131no—
81#342—261no—
82#323—261no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13—41no—
86C22×C13—41no—
87C22×C13—41no—
88C22×C13—42no—
89C22×C13—81no—
90C22×C13#32811yescharacteristic
91C22×C13AΣL(1,𝔽16)11yescharacteristic
92C22×C13#35411yescharacteristic
93C4×C13—41no—
94C4×C13—41no—
95C4×C13—81no—
96C4×C13—81no—
97Dic13—82no—
98Dic13—161no—
99C23×C4C22⋊D1311yescharacteristic
100C2×M16—41no—
101C22⋊Q8—522no—
102C22⋊Q8—521no—
103C2×C22⋊C4—261no—
104C2×C22⋊C4—261no—
105C2×C22⋊C4C4×D1311yescharacteristic
106C2×C22⋊C4D5211yescharacteristic
107C22⋊C8—22no—
108C22⋊C8—41no—
109C22⋊C8—521no—
110#95—41no—
111#95—522no—
112C2×C13—21no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13—41no—
116C2×C13—41no—
117C2×C13#135111yescharacteristic
118C24#610311yescharacteristic
119C2×Q8—521no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4—262no—
127C22×C4—521no—
128C22×C4#610511yescharacteristic
129C22×C4#610711yescharacteristic
130M16—81no—
131M16—81no—
132C2×C8—42no—
133C2×C8—1041no—
134C4⋊C4—522no—
135C4⋊C4—521no—
136C22⋊C4—41no—
137C22⋊C4—41no—
138C22⋊C4—521no—
139C22⋊C4—521no—
140C22⋊C4—521no—
141C22⋊C4—521no—
142C13#742711yescharacteristic, complemented, Sylow
143C23—21no—
144C23—21no—
145C23—81no—
146C23#8804511yescharacteristic
147C23#8804611yescharacteristic
148C23#8805011yescharacteristic
149Q8—2081no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—522no—
162C2×C4—1042no—
163C2×C4—1041no—
164C2×C4—1042no—
165C8—82no—
166C8—2081no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1171804411yescharacteristic
175C22#1171806311yescharacteristic
176C22#1171806511yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—1042no—
182C4—2081no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#1311285611yescharacteristic
subgroupG/H
centerC2#13112856
commutatorC2×C13×C22⋊C4C2×C4
Frattini#381C2×D13
FittingC13×#1306C2
socleC2×C13#1351
prime radicalC24×C13C22⋊C4
cosocleC13×#381C22
hypercenter#1306D13
hypocenterC13#7427
LCSG ▷ C2×C13×C22⋊C4 ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1306

Complements

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

NH ≅ G/Ntype
142. C13#7427semidirect

Maximal subgroups

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

subgroupindex
#131160032
#131127662
C13×#13062
#742713