Finite Group Databasebeta

← #15750469

Subgroups — #15750469

Order 3328.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#13116065C211yesmaximal, characteristic
2#13112717C211yesmaximal, characteristic, complemented
3C13×#1324C211yesmaximal, characteristic, complemented
4#11719215C411yescharacteristic
5C13×#382C2211yescharacteristic
6#11718627—21no—
7C2×#88045—21no—
8C2×#88043—21no—
9C13×#324—21no—
10#11718122C411yescharacteristic
11C2×#6127—21no—
12C2×C13×C4⋊C4C2×C411yescharacteristic
13C2×C13×C4⋊C4D411yescharacteristic
14C2×C42×C13D411yescharacteristic
15#88184—41no—
16C2×#6099—21no—
17C22×#1055—41no—
18#88151—41no—
19#88149—41no—
20C13×C22⋊C8—41no—
21C13×#95—41no—
22#88050—41no—
23#88049—41no—
24#88045—41no—
25#88045—41no—
26#88043—22no—
27#88043—41no—
28#7416—131nomaximal, Sylow
29C22×C4×C13—21no—
30C22×C4×C13—21no—
31C22×C4×C13—21no—
32C22×C4×C13C22⋊C411yescharacteristic
33C2×C22⋊D13—41no—
34#6127—41no—
35#6127—41no—
36#6127—41no—
37#6127—41no—
38C2×D52—21no—
39C2×D52—41no—
40C2×C4×D13—41no—
41C2×Dic26—21no—
42C2×C8×C13—81no—
43C13×C4⋊C4—41no—
44C13×C4⋊C4—41no—
45C42×C13—21no—
46C42×C13D811yescharacteristic
47C42×C13SD1611yescharacteristic
48#6103—42no—
49C4⋊Dic13—41no—
50#6099—41no—
51#6099—41no—
52C2×#1055—42no—
53C2×#1055—42no—
54C2×#1055—42no—
55C2×#1055—41no—
56#2040—131no—
57#1324D1311yescharacteristic, complemented
58#1295—131no—
59C23×C13#9911yescharacteristic
60C22×D13—41no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—81no—
70C2×C4×C13—81no—
71C2×C4×C13#10211yescharacteristic
72C2×C4×C13#10411yescharacteristic
73C22⋊D13—81no—
74C22⋊D13—81no—
75C2×Dic13—41no—
76D52—41no—
77D52—41no—
78D52—161no—
79C4×D13—81no—
80C4×D13—81no—
81Dic26—41no—
82Dic26—41no—
83C8×C13—161no—
84#1055—44no—
85#1055—81no—
86#537—131no—
87C2×#104—261no—
88#417—261no—
89C2×#97—261no—
90#382C2×D1311yescharacteristic
91#343—131no—
92#324—21no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13#32711yescharacteristic
96C22×C13AΣL(1,𝔽16)11yescharacteristic
97C22×C13#35511yescharacteristic
98C2×D13—81no—
99C2×D13—81no—
100C2×D13—81no—
101C4×C13—21no—
102C4×C13—21no—
103C4×C13—41no—
104C4×C13—41no—
105C4×C13—81no—
106C4×C13—81no—
107Dic13—81no—
108C2×#41—261no—
109C2×M16—261no—
110C22×C8—521no—
111C22⋊Q8—521no—
112#121—521no—
113#121—521no—
114C2×C4⋊C4C4×D1311yescharacteristic
115C2×C4⋊C4C22⋊D1311yescharacteristic
116C2×C42D5211yescharacteristic
117#104—521no—
118#104—521no—
119#103—521no—
120#102—521no—
121C22⋊C8—41no—
122#97—262no—
123#97—521no—
124#95—41no—
125C2×C13—21no—
126C2×C13—21no—
127C2×C13#134511yescharacteristic
128C2×C13#140311yescharacteristic
129C2×C13#140411yescharacteristic
130D13—161no—
131#41—521no—
132#41—521no—
133#41—521no—
134#41—521no—
135C2×Q8—261no—
136C2×D4—261no—
137C2×D4—521no—
138C2×D4—521no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—521no—
143C22×C4#610311yescharacteristic
144M16—521no—
145M16—521no—
146C2×C8—81no—
147C2×C8—522no—
148C2×C8—522no—
149C2×C8—522no—
150C2×C8—521no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—521no—
154C22⋊C4—522no—
155C42—21no—
156C42#609511yescharacteristic
157C42D10411yescharacteristic
158C13#741611yescharacteristic, complemented, Sylow
159C23—521no—
160C23#8804611yescharacteristic
161Q8—521no—
162Q8—521no—
163D4—521no—
164D4—521no—
165D4—1041no—
166D4—1041no—
167D4—2081no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—521no—
179C2×C4—1041no—
180C2×C4—1041no—
181C2×C4#8806111yescharacteristic
182C2×C4#8806511yescharacteristic
183C8—161no—
184C8—524no—
185C8—1041no—
186C22—21no—
187C22—21no—
188C22—1041no—
189C22—1041no—
190C22—1041no—
191C22#1171806211yescharacteristic
192C22#1171806311yescharacteristic
193C22#1171806911yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—81no—
200C4—1041no—
201C2—21no—
202C2—21no—
203C2—2081no—
204C2#1311284011yescharacteristic
205C2#1311298311yescharacteristic
206C2#1311298611yescharacteristic
subgroupG/H
centerC22#11718063
commutatorC2×C13×C4⋊C4C2×C4
Frattini#382C2×D13
FittingC13×#1324C2
socleC22×C13AΣL(1,𝔽16)
prime radical#11719215C4
cosocleC13×#382C22
hypercenter#1324D13
hypocenterC13#7416
LCSG ▷ C2×C13×C4⋊C4 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #13112717C2semidirect
3. C13×#1324C2semidirect
57. #1324D13semidirect
158. C13#7416semidirect

Maximal subgroups

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

subgroupindex
#131160652
#131127172
C13×#13242
#741613