Finite Group Databasebeta

← #15783795

Subgroups — #15783795

Order 3328.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×#11718041C211yesmaximal, characteristic, complemented
2#13117129C211yesmaximal, characteristic, complemented
3#13116962C211yesmaximal, characteristic, complemented
4#13116957C211yesmaximal, characteristic
5#13113028C211yesmaximal, characteristic, complemented
6#13113025C211yesmaximal, characteristic, complemented
7C13×#1425C211yesmaximal, characteristic, complemented
8C2×Dic104C2211yescharacteristic
9C2×D208C2211yescharacteristic
10#11718562C2211yescharacteristic
11#11718558—21no—
12#11718557—21no—
13C2×C13×C32C2211yescharacteristic
14C13×#368C2211yescharacteristic
15C13×#368C2211yescharacteristic
16#11718091C2211yescharacteristic
17#11718088—21no—
18#11718087—21no—
19#11718041—21no—
20#11718041—21no—
21#11718039—21no—
22D13×C32—21no—
23#88163—41no—
24#88162—41no—
25C2×Dic52—21no—
26C2×D104—21no—
27#88155D411yescharacteristic
28C2×C13×C16C2311yescharacteristic
29C13×#108—21no—
30C13×#108—21no—
31#88064—41no—
32#88063—41no—
33#88052D411yescharacteristic
34Dic104—21no—
35Dic104—21no—
36D208—21no—
37D208—21no—
38#88038—21no—
39C16×D13—21no—
40C13×C32D411yescharacteristic
41C13×C32D411yescharacteristic
42#88034—21no—
43#13702—131nomaximal, Sylow
44#6127D811yescharacteristic
45C2×D52—41no—
46C2×Dic26—41no—
47C13×M16—41no—
48C13×M16—41no—
49C2×C8×C13C2×D411yescharacteristic
50#6099D811yescharacteristic
51Dic52—41no—
52Dic52—41no—
53Dic52—81no—
54D104—41no—
55D104—41no—
56D104—81no—
57#6095—81no—
58#6095—81no—
59#6094—21no—
60C8×D13—21no—
61C13×C16C2×D411yescharacteristic
62C13×C16#4111yescharacteristic
63#6090—21no—
64C2×SD64—131no—
65#2258—131no—
66#2222—131no—
67#2221—131no—
68#1425D1311yescharacteristic, complemented
69#1420—131no—
70#1419—131no—
71C22×D13—81no—
72C2×C4×C13C2×D811yescharacteristic
73C22⋊D13—21no—
74C2×Dic13—81no—
75D52—81no—
76D52—81no—
77D52D1611yescharacteristic
78C4×D13—21no—
79Dic26—81no—
80Dic26—81no—
81Dic26D1611yescharacteristic
82C8×C13—81no—
83C8×C13—81no—
84C8×C13#12111yescharacteristic
85C8×C13#13511yescharacteristic
86#1055—21no—
87C2×Q32—131no—
88C2×D16—131no—
89#504—131no—
90#473—261no—
91#472—261no—
92SD64—261no—
93SD64—261no—
94M64—131no—
95M64—261no—
96C2×C32—261no—
97C2×C32C2×D1311yescharacteristic
98#368C2×D1311yescharacteristic
99#368C2×D1311yescharacteristic
100#362—261no—
101#361—261no—
102C22×C13#50811yescharacteristic
103C2×D13—21no—
104C2×D13—161no—
105C2×D13—321no—
106C4×C13#46611yescharacteristic
107C4×C13C2×D1611yescharacteristic
108Dic13—21no—
109Dic13—161no—
110#137—521no—
111AGL(1,ℤ/8)—521no—
112C2×Q16—261no—
113C2×D8—261no—
114#131—131no—
115Q32—261no—
116Q32—261no—
117D16—261no—
118D16—261no—
119M32—131no—
120M32—261no—
121C2×C16—261no—
122C2×C16C22×D1311yescharacteristic
123#108—21no—
124#108—21no—
125#101—521no—
126#100—521no—
127C32—261no—
128C32D5211yescharacteristic
129C32D5211yescharacteristic
130C2×C13—21no—
131C2×C13#221511yescharacteristic
132D13—41no—
133D13—321no—
134#41—131no—
135C2×Q8—521no—
136C2×D4—521no—
137Q16—521no—
138Q16—521no—
139Q16—1041no—
140SD16—1041no—
141SD16—1041no—
142D8—521no—
143D8—521no—
144D8—1041no—
145M16—41no—
146M16—41no—
147M16—131no—
148M16—261no—
149C2×C8—261no—
150C2×C8D4×D1311yescharacteristic
151C16—261no—
152C16C2×D5211yescharacteristic
153C16#613111yescharacteristic
154C13#1370211yescharacteristic, complemented, Sylow
155C23—1041no—
156Q8—131no—
157Q8—1041no—
158Q8—1041no—
159D4—131no—
160D4—261no—
161D4—1041no—
162D4—1041no—
163C2×C4—261no—
164C2×C4—1041no—
165C2×C4D8×D1311yescharacteristic
166C8—81no—
167C8—81no—
168C8—261no—
169C8#8814911yescharacteristic
170C8#8817311yescharacteristic
171C22—261no—
172C22—4161no—
173C22—2081no—
174C22#1171858011yescharacteristic
175C4—261no—
176C4—2081no—
177C4#1171854411yescharacteristic
178C4D13×D1611yescharacteristic
179C2—21no—
180C2—521no—
181C2—4161no—
182C2#1311692311yescharacteristic
subgroupG/H
centerC2#13116923
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1425C2
socleC2×C13#2215
prime radical#13116957C2
hypercenter#1425D13
hypocenterC13#13702
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1425

Complements

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

NH ≅ G/Ntype
1. C2×#11718041C2semidirect
2. #13117129C2semidirect
3. #13116962C2semidirect
5. #13113028C2semidirect
6. #13113025C2semidirect
7. C13×#1425C2semidirect
68. #1425D13semidirect
154. C13#13702semidirect

Maximal subgroups

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

subgroupindex
C2×#117180412
#131171292
#131169622
#131169572
#131130282
#131130252
C13×#14252
#1370213