Finite Group Databasebeta

← #15783880

Subgroups — #15783880

Order 3328.

170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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#13116940C211yesmaximal, characteristic
2#13116629C211yesmaximal, characteristic, complemented
3#13113041C211yesmaximal, characteristic, complemented
4#13113027C211yesmaximal, characteristic, complemented
5#13113025C211yesmaximal, characteristic, complemented
6#13112975C211yesmaximal, characteristic, complemented
7C13×#1426C211yesmaximal, characteristic, complemented
8C2×D208C2211yescharacteristic
9C2×#88038C2211yescharacteristic
10D13×#108—21no—
11#11718544—21no—
12C13×M64C2211yescharacteristic
13C13×#368C2211yescharacteristic
14C13×#367C2211yescharacteristic
15#11718098C2211yescharacteristic
16#11718091C2211yescharacteristic
17#11718085—21no—
18#11718083—21no—
19M16×D13—41no—
20C2×D104—21no—
21C2×C8×D13D411yescharacteristic
22#88149—41no—
23C2×C13×C16C2311yescharacteristic
24C13×#108—21no—
25C13×#107—21no—
26#88062—41no—
27#88059—21no—
28C2×#6090D411yescharacteristic
29#88049—41no—
30D208—21no—
31D208—21no—
32#88038—21no—
33#88038—21no—
34C13×C32—21no—
35#88034—21no—
36#13717—131nomaximal, Sylow
37C2×D52—41no—
38C2×D52—81no—
39C2×C4×D13D811yescharacteristic
40C13×M16—41no—
41C2×C8×C13C2×D411yescharacteristic
42C13×C4⋊C4—41no—
43#6103—81no—
44#6099—41no—
45C2×#1055D811yescharacteristic
46D104—41no—
47D104—41no—
48#6094—81no—
49C8×D13—21no—
50C8×D13—21no—
51C8×D13—81no—
52C13×C16#4111yescharacteristic
53C13×C16#4111yescharacteristic
54#6090—21no—
55#2218—131no—
56#2161—131no—
57#1426—131no—
58#1426D1311yescharacteristic, complemented
59#1419—131no—
60#1419—131no—
61#1400—131no—
62C22×D13—81no—
63C22×D13SD3211yescharacteristic
64C2×C4×C13—81no—
65C2×C4×C13C2×D811yescharacteristic
66C2×Dic13SD3211yescharacteristic
67D52—81no—
68D52—81no—
69D52—162no—
70C4×D13—21no—
71C4×D13—21no—
72C8×C13—81no—
73C8×C13#12311yescharacteristic
74C8×C13#13711yescharacteristic
75#1055—21no—
76#1055—81no—
77C2×D16—131no—
78C2×M32—131no—
79#466—261no—
80C2×#108—261no—
81M64—131no—
82M64C2×D1311yescharacteristic
83#368—131no—
84#368—261no—
85#368C2×D1311yescharacteristic
86#367C2×D1311yescharacteristic
87#357—261no—
88C22×C13C2×SD3211yescharacteristic
89C2×D13—21no—
90C2×D13—41no—
91C2×D13—161no—
92C2×D13—161no—
93C2×D13—161no—
94C4×C13—161no—
95C4×C13#48011yescharacteristic
96C4×C13#50911yescharacteristic
97Dic13—21no—
98C2×D8—261no—
99C2×M16—521no—
100C22×C8—131no—
101#121—521no—
102D16—261no—
103D16—261no—
104M32—261no—
105M32—261no—
106C2×C16—131no—
107C2×C16C22×D1311yescharacteristic
108#108—21no—
109#108—261no—
110#108—521no—
111#107—21no—
112#102—521no—
113C32—21no—
114C32—261no—
115C2×C13—21no—
116C2×C13#223311yescharacteristic
117D13—41no—
118D13—321no—
119C2×D4—521no—
120C2×D4—1041no—
121C22×C4—131no—
122D8—521no—
123D8—521no—
124M16—41no—
125M16—521no—
126M16—1041no—
127C2×C8—131no—
128C2×C8—261no—
129C2×C8—261no—
130C2×C8—1041no—
131C2×C8D4×D1311yescharacteristic
132C4⋊C4—41no—
133C22⋊C4—1041no—
134C16—261no—
135C16#612711yescharacteristic
136C16#613111yescharacteristic
137C13#1371711yescharacteristic, complemented, Sylow
138C23—131no—
139C23—1041no—
140D4—1041no—
141D4—1041no—
142D4—2082no—
143C2×C4—81no—
144C2×C4—131no—
145C2×C4—261no—
146C2×C4—261no—
147C2×C4D8×D1311yescharacteristic
148C8—81no—
149C8—261no—
150C8—1041no—
151C8#8814811yescharacteristic
152C8#8817211yescharacteristic
153C22—261no—
154C22—521no—
155C22—2081no—
156C22—2081no—
157C22—2081no—
158C22D13×SD3211yescharacteristic
159C4—161no—
160C4—261no—
161C4#1171854311yescharacteristic
162C4#1171857511yescharacteristic
163C2—21no—
164C2—521no—
165C2—4161no—
166C2#1311702311yescharacteristic
subgroupG/H
centerC2#13117023
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1426C2
socleC2×C13#2233
prime radical#13116940C2
hypercenter#1426D13
hypocenterC13#13717
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

Complements

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

NH ≅ G/Ntype
2. #13116629C2semidirect
3. #13113041C2semidirect
4. #13113027C2semidirect
5. #13113025C2semidirect
6. #13112975C2semidirect
7. C13×#1426C2semidirect
58. #1426D13semidirect
137. C13#13717semidirect

Maximal subgroups

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

subgroupindex
#131169402
#131166292
#131130412
#131130272
#131130252
#131129752
C13×#14262
#1371713