Finite Group Databasebeta

← #16776983

Subgroups — #16776983

Order 3328.

264 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 40 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#13129757C211yesmaximal, characteristic
2#13129708C211yesmaximal, characteristic
3#13115843C211yesmaximal, characteristic
4C22×C13×Q16C411yescharacteristic
5C2×#88200—21no—
6#11719127—21no—
7C2×#88075—21no—
8C2×#88060C2211yescharacteristic
9C22⋊#6092—21no—
10#11718143C411yescharacteristic
11C22×Q8×C13—21no—
12C22×C4×D13D411yescharacteristic
13C2×#6118—41no—
14C2×C13×Q16—41no—
15C2×C13×Q16—42no—
16C22×C8×C13C2×C411yescharacteristic
17#88200—42no—
18#88200—42no—
19C2×#6103—41no—
20C2×C4⋊Dic13—21no—
21C2×#6101—41no—
22C22×#1055D411yescharacteristic
23C22⋊#1057—41no—
24#88111—22no—
25C2×#6092—41no—
26#88075—42no—
27#88060—41no—
28#7086—131nomaximal, Sylow
29C23×D13SD1611yescharacteristic
30C2×Q8×C13—22no—
31C2×Q8×C13—41no—
32C2×Q8×C13—41no—
33C2×Q8×C13—41no—
34C2×Q8×C13—41no—
35C2×Q8×C13—41no—
36C22×C4×C13—41no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×Dic13—41no—
39C22×Dic13D811yescharacteristic
40C2×C4×D13—21no—
41C2×C4×D13—21no—
42C2×C4×D13—41no—
43C2×C4×D13—41no—
44C2×#1057—42no—
45#6118—81no—
46#6118—81no—
47C13×Q16—42no—
48C13×Q16—42no—
49C2×C8×C13—21no—
50C2×C8×C13—41no—
51#6103—44no—
52C4⋊Dic13—22no—
53C4⋊Dic13—41no—
54#6101—44no—
55C2×#1055—21no—
56C2×#1055—41no—
57#6092—81no—
58#2001—131no—
59#1314—131no—
60#1293—131no—
61C23×C13#10211yescharacteristic
62C22×D13—21no—
63C22×D13—21no—
64C22×D13—21no—
65C22×D13—41no—
66C22×D13—41no—
67Q8×C13—42no—
68Q8×C13—42no—
69Q8×C13—81no—
70Q8×C13—81no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—42no—
74C2×C4×C13—81no—
75C2×C4×C13—81no—
76C2×C4×C13#9911yescharacteristic
77C2×C4×C13#10411yescharacteristic
78C2×Dic13—21no—
79C2×Dic13—41no—
80C2×Dic13—42no—
81C2×Dic13—81no—
82C2×Dic13—81no—
83C4×D13—41no—
84C4×D13—41no—
85C4×D13—81no—
86#1057—82no—
87C8×C13—41no—
88#1055—41no—
89C22×Q16#26111yescharacteristic
90C2×C22⋊Q8—261no—
91C2×#103—261no—
92#407—261no—
93C2×C22⋊C8—131no—
94C22⋊C16—261no—
95#340—131no—
96C22×C13—21no—
97C22×C13—21no—
98C22×C13#32711yescharacteristic
99C22×C13#35911yescharacteristic
100C22×C13#36211yescharacteristic
101C2×D13—42no—
102C2×D13—41no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13—81no—
106C4×C13—21no—
107C4×C13—82no—
108C4×C13AΣL(1,𝔽16)11yescharacteristic
109C4×C13#35311yescharacteristic
110Dic13—41no—
111Dic13—82no—
112C22×Q8—21no—
113C23×C4—131no—
114C2×Q16—41no—
115C2×Q16—42no—
116C2×M16—521no—
117C22×C8—131no—
118C22×C8C2×#26111yescharacteristic
119C22⋊Q8—522no—
120C22⋊Q8—522no—
121C2×C4⋊C4—261no—
122C2×C4⋊C4—521no—
123C2×C22⋊C4—521no—
124C2×C16—521no—
125#103—522no—
126C22⋊C8—262no—
127C22⋊C8—521no—
128C22⋊C8—521no—
129C2×C13—21no—
130C2×C13—21no—
131C2×C13#134211yescharacteristic
132C2×C13#134311yescharacteristic
133C2×C13#135011yescharacteristic
134D13—81no—
135C24—131no—
136C2×Q8—22no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C22×C4—41no—
143C22×C4—131no—
144C22×C4—261no—
145C22×C4—261no—
146C22×C4—521no—
147C22×C4—521no—
148C22×C4—521no—
149C22×C4C22⋊#26111yescharacteristic
150Q16—42no—
151Q16—42no—
152M16—1041no—
153M16—1041no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—261no—
157C2×C8—521no—
158C2×C8—522no—
159C4⋊C4—262no—
160C4⋊C4—521no—
161C4⋊C4—524no—
162C22⋊C4—524no—
163C16—1041no—
164C13#708611yescharacteristic, complemented, Sylow
165C23—261no—
166C23—261no—
167C23—261no—
168C23—521no—
169C23—521no—
170C23#8811511yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—81no—
174Q8—81no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—261no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4—521no—
184C2×C4—522no—
185C2×C4—1041no—
186C2×C4—1041no—
187C2×C4—1041no—
188C2×C4#8811611yescharacteristic
189C2×C4#8811911yescharacteristic
190C8—41no—
191C8—521no—
192C8—1042no—
193C22—21no—
194C22—21no—
195C22—522no—
196C22—521no—
197C22—521no—
198C22—521no—
199C22—1041no—
200C22#1171828111yescharacteristic
201C22#1171828211yescharacteristic
202C22#1171829211yescharacteristic
203C4—21no—
204C4—82no—
205C4—521no—
206C4—1042no—
207C4#1171829411yescharacteristic
208C4#1171830611yescharacteristic
209C2—21no—
210C2—21no—
211C2—1041no—
212C2#1312981211yescharacteristic
213C2#1312981411yescharacteristic
214C2#1312982811yescharacteristic
subgroupG/H
centerC22#11718292
commutatorC22×C8×C13C2×C4
FrattiniC22×C8C2×#261
FittingC22×C13×Q16C4
socleC22×C13#327
prime radicalC23×D13SD16
cosocleC2×#88060C22
hypercenterC22×Q16#261
hypocenterC13#7086
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
164. C13#7086semidirect

Maximal subgroups

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

subgroupindex
#131297572
#131297082
#131158432
#708613