Finite Group Databasebeta

← #16777909

Subgroups — #16777909

Order 3328.

214 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 32 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#13129763C211yesmaximal, characteristic
2#13129739C211yesmaximal, characteristic
3#13116002C211yesmaximal, characteristic
4C13×#543C411yescharacteristic
5#11719169—21no—
6#11718604—21no—
7#11718604C2211yescharacteristic
8#11718305—21no—
9#11718118—21no—
10#11718118C411yescharacteristic
11C23×Dic13D411yescharacteristic
12C2×#6122—41no—
13C13×C22⋊Q8—42no—
14C13×C22⋊Q8—41no—
15C2×C13×C22⋊C4—21no—
16C2×C13×C22⋊C4C2×C411yescharacteristic
17C2×C22⋊Dic13—21no—
18C2×C22⋊Dic13D411yescharacteristic
19C22⋊#1057—22no—
20C22⋊#1057—41no—
21C22⋊#1057—41no—
22#88071—41no—
23#88071—42no—
24#7427—131nomaximal, Sylow
25C24×C13C22⋊C411yescharacteristic
26C2×Q8×C13—41no—
27C22×C4×C13—22no—
28C22×C4×C13—21no—
29C22×Dic13—21no—
30C22×Dic13—21no—
31C22×Dic13—21no—
32C22×Dic13—41no—
33C22×Dic13—41no—
34C22×Dic13—41no—
35C22×Dic13SD1611yescharacteristic
36C22×Dic13Q1611yescharacteristic
37#6122—81no—
38#6122—81no—
39C2×#1057—42no—
40C2×#1057—81no—
41C13×C4⋊C4—42no—
42C13×C4⋊C4—41no—
43C13×C22⋊C4—41no—
44C13×C22⋊C4—41no—
45C13×C22⋊C4—41no—
46C22⋊Dic13—41no—
47C22⋊Dic13—41no—
48C22⋊Dic13—41no—
49#2030—131no—
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—42no—
60C2×C4×C13—41no—
61C2×C4×C13—81no—
62C2×C4×C13—82no—
63C2×Dic13—21no—
64C2×Dic13—21no—
65C2×Dic13—41no—
66C2×Dic13—41no—
67C2×Dic13—41no—
68C2×Dic13—41no—
69C2×Dic13—41no—
70C2×Dic13—81no—
71C2×Dic13—81no—
72C2×Dic13—81no—
73C2×Dic13—82no—
74#1057—82no—
75#1057—161no—
76#543#26111yescharacteristic
77#407—261no—
78#381—131no—
79#381—261no—
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—82no—
94C4×C13—81no—
95Dic13—41no—
96Dic13—41no—
97Dic13—81no—
98Dic13—161no—
99C23×C4—131no—
100C2×M16—521no—
101C22⋊Q8—42no—
102C22⋊Q8—41no—
103C2×C22⋊C4—21no—
104C2×C22⋊C4—131no—
105C2×C22⋊C4—261no—
106C2×C22⋊C4C2×#26111yescharacteristic
107C22⋊C8—262no—
108C22⋊C8—521no—
109C22⋊C8—521no—
110#95—521no—
111#95—522no—
112C2×C13—21no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13—41no—
116C2×C13—41no—
117C2×C13#135111yescharacteristic
118C24C22⋊#26111yescharacteristic
119C2×Q8—41no—
120C22×C4—22no—
121C22×C4—21no—
122C22×C4—131no—
123C22×C4—131no—
124C22×C4—261no—
125C22×C4—261no—
126C22×C4—261no—
127C22×C4—521no—
128C22×C4—521no—
129C22×C4—521no—
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—521no—
140C22⋊C4—521no—
141C22⋊C4—521no—
142C13#742711yescharacteristic, complemented, Sylow
143C23—21no—
144C23—21no—
145C23—81no—
146C23#8811711yescharacteristic
147C23#8811811yescharacteristic
148C23#8811911yescharacteristic
149Q8—161no—
150C2×C4—42no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—82no—
154C2×C4—261no—
155C2×C4—261no—
156C2×C4—521no—
157C2×C4—521no—
158C2×C4—521no—
159C2×C4—521no—
160C2×C4—521no—
161C2×C4—1041no—
162C2×C4—1041no—
163C2×C4—1041no—
164C2×C4—1042no—
165C8—1042no—
166C8—2081no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1171829811yescharacteristic
175C22#1171830011yescharacteristic
176C22#1171830611yescharacteristic
177C4—82no—
178C4—81no—
179C4—521no—
180C4—521no—
181C4—1041no—
182C4—2081no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#1312983111yescharacteristic
subgroupG/H
centerC2#13129831
commutatorC2×C13×C22⋊C4C2×C4
FrattiniC2×C22⋊C4C2×#261
FittingC13×#543C4
socleC2×C13#1351
prime radicalC24×C13C22⋊C4
cosocle#11718604C22
hypercenter#543#261
hypocenterC13#7427
LCSG ▷ C2×C13×C22⋊C4 ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C2×C22⋊C4 ◁ #543

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
#131297632
#131297392
#131160022
#742713