Finite Group Databasebeta

← #15750501

Subgroups — #15750501

Order 3328.

214 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 39 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#13112766C211yesmaximal, characteristic
2#13112744C211yesmaximal, characteristic
3C13×#2030C211yesmaximal, characteristic
4C13×#543C411yescharacteristic
5C13×#381—21no—
6C13×#381C2211yescharacteristic
7#11718868—21no—
8C13×#342—21no—
9C13×#342C411yescharacteristic
10#11718117—21no—
11C23×C4×C13D411yescharacteristic
12C13×C22⋊Q8—42no—
13C13×C22⋊Q8—41no—
14C2×C13×C22⋊C4—21no—
15C2×C13×C22⋊C4—21no—
16C2×C13×C22⋊C4C2×C411yescharacteristic
17C2×C13×C22⋊C4D411yescharacteristic
18C2×#6099—41no—
19C13×#95—41no—
20C13×#95—42no—
21C22⋊#1055—22no—
22C22⋊#1055—41no—
23C22⋊#1055—41no—
24#7427—131nomaximal, Sylow
25C24×C13C22⋊C411yescharacteristic
26C2×Q8×C13—41no—
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—22no—
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13—41no—
33C22×C4×C13—41no—
34C22×C4×C13—41no—
35C22×C4×C13SD1611yescharacteristic
36C22×C4×C13Q1611yescharacteristic
37C13×C4⋊C4—42no—
38C13×C4⋊C4—41no—
39C13×C22⋊C4—41no—
40C13×C22⋊C4—41no—
41C13×C22⋊C4—41no—
42C13×C22⋊C4—41no—
43C13×C22⋊C4—41no—
44C13×C22⋊C4—41no—
45#6099—81no—
46#6099—81no—
47C2×#1055—42no—
48C2×#1055—81no—
49#2030D1311yescharacteristic
50#1317—131no—
51#1306—131no—
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—81no—
55C23×C13#9911yescharacteristic
56C23×C13#10311yescharacteristic
57C23×C13#10411yescharacteristic
58Q8×C13—161no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—42no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—81no—
69C2×C4×C13—81no—
70C2×C4×C13—81no—
71C2×C4×C13—82no—
72C2×C4×C13—81no—
73C2×C4×C13—82no—
74#1055—82no—
75#1055—161no—
76#543Dic1311yescharacteristic
77#407—261no—
78#381—21no—
79#381C2×D1311yescharacteristic
80#342—21no—
81#342Dic1311yescharacteristic
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—82no—
97C4×C13—81no—
98C4×C13—161no—
99C23×C4C22⋊D1311yescharacteristic
100C2×M16—521no—
101C22⋊Q8—42no—
102C22⋊Q8—41no—
103C2×C22⋊C4—21no—
104C2×C22⋊C4—21no—
105C2×C22⋊C4C2×Dic1311yescharacteristic
106C2×C22⋊C4C22⋊D1311yescharacteristic
107C22⋊C8—262no—
108C22⋊C8—521no—
109C22⋊C8—521no—
110#95—41no—
111#95—42no—
112C2×C13—21no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13—41no—
116C2×C13—41no—
117C2×C13#135111yescharacteristic
118C24C22⋊Dic1311yescharacteristic
119C2×Q8—41no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—22no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4#610611yescharacteristic
129C22×C4#610711yescharacteristic
130M16—1041no—
131M16—1041no—
132C2×C8—522no—
133C2×C8—1041no—
134C4⋊C4—42no—
135C4⋊C4—41no—
136C22⋊C4—41no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—41no—
140C22⋊C4—41no—
141C22⋊C4—41no—
142C13#742711yescharacteristic, complemented, Sylow
143C23—21no—
144C23—21no—
145C23—81no—
146C23#8807411yescharacteristic
147C23#8807511yescharacteristic
148C23#8807711yescharacteristic
149Q8—161no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—82no—
165C8—1042no—
166C8—2081no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1171812811yescharacteristic
175C22#1171813011yescharacteristic
176C22#1171813311yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—82no—
181C4—81no—
182C4—161no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#1311285711yescharacteristic
subgroupG/H
centerC2#13112857
commutatorC2×C13×C22⋊C4C2×C4
Frattini#381C2×D13
FittingC13×#2030C2
socleC2×C13#1351
prime radicalC24×C13C22⋊C4
cosocleC13×#381C22
hypercenter#2030D13
hypocenterC13#7427
LCSG ▷ C2×C13×C22⋊C4 ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #2030

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
#131127662
#131127442
C13×#20302
#742713