Finite Group Databasebeta

← #15783783

Subgroups — #15783783

Order 3328.

188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#11718111C211yesmaximal, characteristic, complemented
2#13117131C211yesmaximal, characteristic, complemented
3#13116957C211yesmaximal, characteristic, complemented
4#13116953C211yesmaximal, characteristic, complemented
5#13113039C211yesmaximal, characteristic, complemented
6#13113027C211yesmaximal, characteristic, complemented
7C13×#1419C211yesmaximal, characteristic, complemented
8C2×C13×D16C2211yescharacteristic
9#11718821—21no—
10C2×D208C2211yescharacteristic
11#11718562C2211yescharacteristic
12#11718558—21no—
13C13×M64C2211yescharacteristic
14C13×#368C2211yescharacteristic
15#11718155—21no—
16#11718111—21no—
17#11718111—21no—
18#11718098C2211yescharacteristic
19C2×#88034C2211yescharacteristic
20#11718087—21no—
21#11718039—21no—
22D13×C32—21no—
23C2×C13×D8—21no—
24#88186—41no—
25#88162—41no—
26C2×D104—21no—
27#88155D411yescharacteristic
28C13×D16—21no—
29C13×D16—21no—
30C2×C13×C16C2311yescharacteristic
31C13×#108—21no—
32#88073—41no—
33#88063—41no—
34#88059—21no—
35#88052D411yescharacteristic
36D208—21no—
37D208—21no—
38#88038—21no—
39C16×D13—21no—
40C13×C32—21no—
41#88034D411yescharacteristic
42#88034D411yescharacteristic
43#13700—131nomaximal, Sylow
44C2×D4×C13—41no—
45#6127D811yescharacteristic
46C2×D52—41no—
47C13×D8—41no—
48C13×D8—41no—
49C13×M16—41no—
50C2×C8×C13C2×D411yescharacteristic
51#6105—81no—
52#6104—81no—
53#6099—41no—
54#6099D811yescharacteristic
55D104—41no—
56D104—41no—
57D104—81no—
58#6095—81no—
59#6094—21no—
60C8×D13—21no—
61C13×C16C2×D411yescharacteristic
62C13×C16#4111yescharacteristic
63#6090—21no—
64C2×D32—131no—
65#2258—131no—
66#2221—131no—
67#2221—131no—
68#1425—131no—
69#1419—131no—
70#1419D1311yescharacteristic, complemented
71C23×C13—81no—
72C22×D13—81no—
73D4×C13—81no—
74D4×C13—81no—
75C2×C4×C13C2×D811yescharacteristic
76C22⋊D13—21no—
77D52—81no—
78D52—81no—
79D52D1611yescharacteristic
80C4×D13—21no—
81Dic26D1611yescharacteristic
82C8×C13—81no—
83C8×C13#12111yescharacteristic
84C8×C13#13511yescharacteristic
85#1055—21no—
86#1055—81no—
87C2×D16—131no—
88C2×D16C2×D1311yescharacteristic
89#504—131no—
90#472—261no—
91#472—261no—
92D32—261no—
93D32—261no—
94M64—261no—
95M64C2×D1311yescharacteristic
96C2×C32—131no—
97C2×C32—261no—
98#368—131no—
99#368C2×D1311yescharacteristic
100#361—261no—
101#361—261no—
102C22×C13—161no—
103C22×C13—321no—
104C22×C13#50811yescharacteristic
105C2×D13—21no—
106C2×D13—161no—
107C2×D13—321no—
108C4×C13#46611yescharacteristic
109C4×C13C2×D1611yescharacteristic
110Dic13—21no—
111AGL(1,ℤ/8)—521no—
112AGL(1,ℤ/8)—521no—
113C2×D8—21no—
114C2×D8—261no—
115#131—131no—
116D16—21no—
117D16—21no—
118D16—261no—
119D16—261no—
120M32—131no—
121M32—261no—
122C2×C16—261no—
123C2×C16C22×D1311yescharacteristic
124#108—21no—
125#108—261no—
126#100—521no—
127#100—521no—
128C32—21no—
129C32—131no—
130C32—131no—
131C2×C13—21no—
132C2×C13—321no—
133C2×C13#221511yescharacteristic
134D13—41no—
135D13—321no—
136#41—131no—
137C2×D4—41no—
138C2×D4—521no—
139SD16—1041no—
140SD16—1041no—
141D8—41no—
142D8—41no—
143D8—521no—
144D8—521no—
145D8—1041no—
146D8—1041no—
147M16—41no—
148M16—131no—
149M16—261no—
150M16—521no—
151C2×C8—261no—
152C2×C8D4×D1311yescharacteristic
153C16—261no—
154C16#612711yescharacteristic
155C16D4×D1311yescharacteristic
156C13#1370011yescharacteristic, complemented, Sylow
157C23—81no—
158C23—1041no—
159Q8—131no—
160D4—81no—
161D4—81no—
162D4—131no—
163D4—261no—
164D4—1041no—
165D4—1041no—
166C2×C4—261no—
167C2×C4D8×D1311yescharacteristic
168C8—81no—
169C8—261no—
170C8—1041no—
171C8#8813811yescharacteristic
172C8#8817011yescharacteristic
173C22—161no—
174C22—261no—
175C22—321no—
176C22—4161no—
177C22—2081no—
178C22#1171857711yescharacteristic
179C4—261no—
180C4#1171843611yescharacteristic
181C4D13×D1611yescharacteristic
182C2—21no—
183C2—321no—
184C2—521no—
185C2—4161no—
186C2#1311692111yescharacteristic
subgroupG/H
centerC2#13116921
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1419C2
socleC2×C13#2215
hypercenter#1419D13
hypocenterC13#13700
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. C2×#11718111C2semidirect
2. #13117131C2semidirect
3. #13116957C2semidirect
4. #13116953C2semidirect
5. #13113039C2semidirect
6. #13113027C2semidirect
7. C13×#1419C2semidirect
70. #1419D13semidirect
156. C13#13700semidirect

Maximal subgroups

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

subgroupindex
C2×#117181112
#131171312
#131169572
#131169532
#131130392
#131130272
C13×#14192
#1370013