Finite Group Databasebeta

← #15777204

Subgroups — #15777204

Order 3328.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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#13117092C211yesmaximal, characteristic
2#13116744C211yesmaximal, characteristic, complemented
3#13114207C211yesmaximal, characteristic, complemented
4#13114197C211yesmaximal, characteristic
5#13112884C211yesmaximal, characteristic, complemented
6#13112881C211yesmaximal, characteristic
7C13×#1371C211yesmaximal, characteristic, complemented
8C2×#88040—21no—
9C2×#88040—21no—
10#11718512—21no—
11#11718509—21no—
12#11718360C2211yescharacteristic
13#11718356C2211yescharacteristic
14C8×Dic26C2211yescharacteristic
15C4×C13×C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17C13×#335C2211yescharacteristic
18#11718094—21no—
19#11718093—21no—
20#11718078—21no—
21#11718077—21no—
22C4⋊#6090C2211yescharacteristic
23C2×Dic52—21no—
24C2×Dic52—21no—
25C2×D104—21no—
26C2×D104—21no—
27C2×#6095—41no—
28#88128—21no—
29#88123—21no—
30C4×Dic26D411yescharacteristic
31C2×C13×C16D411yescharacteristic
32C2×C13×C16D411yescharacteristic
33C13×C4⋊C8—21no—
34C13×C4⋊C8—21no—
35C4×C8×C13C2311yescharacteristic
36#88061—41no—
37#88057—41no—
38#88056—41no—
39#88054—21no—
40C8×Dic13—21no—
41C2×#6090—21no—
42C4⋊#1055D411yescharacteristic
43#88040—42no—
44#88040—42no—
45#12444—131nomaximal, Sylow
46C2×D52—41no—
47C2×D52—41no—
48C2×D52—41no—
49C2×Dic26—41no—
50C2×Dic26D811yescharacteristic
51C2×C8×C13—41no—
52C2×C8×C13—41no—
53C2×C8×C13C2×D411yescharacteristic
54C2×C8×C13#4111yescharacteristic
55C42×C13C2×D411yescharacteristic
56C4⋊Dic13—41no—
57C4⋊Dic13—41no—
58C4⋊Dic13D811yescharacteristic
59#6101—21no—
60C4×Dic13—21no—
61C2×#1055—21no—
62Dic52—41no—
63Dic52—41no—
64Dic52—81no—
65D104—41no—
66D104—41no—
67D104—81no—
68#6095—82no—
69C13×C16—21no—
70C13×C16SD1612yescomplemented
71#6090—41no—
72#2248—131no—
73#2183—131no—
74#1670—131no—
75#1668—131no—
76#1371D1311yescharacteristic, complemented
77#1362—131no—
78#1361—131no—
79C22×D13—81no—
80C2×C4×C13#12111yescharacteristic
81C2×C4×C13C2×D811yescharacteristic
82C2×C4×C13#13511yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—81no—
86D52—81no—
87D52—81no—
88D52—81no—
89D52—81no—
90D52—161no—
91Dic26—21no—
92Dic26—21no—
93Dic26—81no—
94Dic26—81no—
95C8×C13—21no—
96C8×C13—81no—
97C8×C13—81no—
98C8×C13C2×SD1611yescharacteristic
99C8×C13AGL(1,ℤ/8)11yescharacteristic
100#1055—41no—
101C2×SD32—261no—
102C2×SD32—261no—
103#494—131no—
104#493—131no—
105#475—261no—
106#460—261no—
107C8×Q8—131no—
108C4⋊C16—131no—
109C4⋊C16—261no—
110#346—261no—
111C4×C16C2×D1311yescharacteristic
112#335C2×D1311yescharacteristic
113#335C2×D1311yescharacteristic
114#332—261no—
115#331—261no—
116C22×C13#46611yescharacteristic
117C2×D13—161no—
118C2×D13—161no—
119C2×D13—161no—
120C4×C13—21no—
121C4×C13#46011yescharacteristic
122C4×C13#47211yescharacteristic
123C4×C13#50911yescharacteristic
124C4×C13#51011yescharacteristic
125Dic13—41no—
126Dic13—41no—
127Dic13—161no—
128C2×Q16—261no—
129C2×Q16—261no—
130C2×SD16—521no—
131C2×D8—261no—
132C2×D8—261no—
133C4⋊Q8—261no—
134#127—261no—
135C4×Q8—131no—
136SD32—522no—
137SD32—522no—
138C2×C16—261no—
139C2×C16D5211yescharacteristic
140C2×C16D5211yescharacteristic
141#106—521no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—131no—
145C4⋊C8—261no—
146#103—521no—
147#102—521no—
148C4×C8—261no—
149C4×C8C22×D1311yescharacteristic
150C2×C13#166811yescharacteristic
151C2×C13#222011yescharacteristic
152C2×C13#222311yescharacteristic
153D13—321no—
154C2×Q8—131no—
155C2×Q8—521no—
156C2×D4—521no—
157C2×D4—521no—
158C2×D4—521no—
159Q16—521no—
160Q16—521no—
161Q16—1041no—
162SD16—1042no—
163D8—521no—
164D8—521no—
165D8—1041no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—261no—
169C2×C8C2×D5211yescharacteristic
170C2×C8#613111yescharacteristic
171C4⋊C4—131no—
172C4⋊C4—261no—
173C4⋊C4—521no—
174C4⋊C4—521no—
175C42—261no—
176C42D4×D1311yescharacteristic
177C16—21no—
178C16—521no—
179C16#609512yescomplemented
180C13#1244411yescharacteristic, complemented, Sylow
181C23—1041no—
182Q8—261no—
183Q8—261no—
184Q8—1041no—
185Q8—1041no—
186D4—1041no—
187D4—1041no—
188D4—1041no—
189D4—1041no—
190D4—2081no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—1041no—
194C2×C4#8814911yescharacteristic
195C2×C4D8×D1311yescharacteristic
196C2×C4#8817311yescharacteristic
197C8—21no—
198C8—81no—
199C8—81no—
200C8—521no—
201C8C2×#609511yescharacteristic
202C8#8816211yescharacteristic
203C22—2081no—
204C22—2081no—
205C22—2081no—
206C22#1171854411yescharacteristic
207C4—21no—
208C4—521no—
209C4—521no—
210C4—2081no—
211C4#1171850911yescharacteristic
212C4#1171855811yescharacteristic
213C4#1171857211yescharacteristic
214C4#1171857911yescharacteristic
215C2—4161no—
216C2#1311419711yescharacteristic
217C2#1311695011yescharacteristic
218C2#1311696711yescharacteristic
subgroupG/H
centerC22#11718544
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1371C2
socleC22×C13#466
prime radical#11718356C22
hypercenter#1371D13
hypocenterC13#12444
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1371

Complements

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

NH ≅ G/Ntype
2. #13116744C2semidirect
3. #13114207C2semidirect
5. #13112884C2semidirect
7. C13×#1371C2semidirect
70. C13×C16SD16semidirect
76. #1371D13semidirect
179. C16#6095semidirect
180. C13#12444semidirect

Maximal subgroups

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

subgroupindex
#131170922
#131167442
#131142072
#131141972
#131128842
#131128812
C13×#13712
#1244413