Finite Group Databasebeta

← #15777328

Subgroups — #15777328

Order 3328.

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

normal subgroups only

This group has 186 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
1#13117081C211yesmaximal, characteristic, complemented
2#13117013C211yesmaximal, characteristic
3#13116914C211yesmaximal, characteristic
4#13116677C211yesmaximal, characteristic
5#13112903C211yesmaximal, characteristic, complemented
6#13112898C211yesmaximal, characteristic, complemented
7C13×#1358C211yesmaximal, characteristic, complemented
8C13×#494C2211yescharacteristic
9#11718840—21no—
10#11718568—21no—
11#11718361C2211yescharacteristic
12#11718344C2211yescharacteristic
13C13×#364C2211yescharacteristic
14C13×#364C2211yescharacteristic
15#11718157—21no—
16#11718156—21no—
17#11718156—21no—
18#11718110—21no—
19#11718107—21no—
20#11718105—21no—
21#11718055C2211yescharacteristic
22#11718053C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26#88158D411yescharacteristic
27#88155—21no—
28#88124—21no—
29C13×M32—21no—
30C13×M32—21no—
31C4×C8×C13C2311yescharacteristic
32#88069—41no—
33#88068—41no—
34#88059D411yescharacteristic
35#88058—21no—
36#88057—21no—
37#88052—21no—
38C2×#6090D411yescharacteristic
39C2×#6090D411yescharacteristic
40#88045—21no—
41#88038—41no—
42C16×D13—41no—
43#12466—131nomaximal, Sylow
44C2×Q8×C13—41no—
45#6127—21no—
46C13×Q16—41no—
47C13×Q16—41no—
48C13×Q16—41no—
49C13×Q16—41no—
50C2×C8×C13C2×D411yescharacteristic
51C2×C8×C13C2×D411yescharacteristic
52C13×C4⋊C4—81no—
53C42×C13#4111yescharacteristic
54C4⋊Dic13—41no—
55#6101—81no—
56#6099—21no—
57Dic52SD1611yescharacteristic
58D104SD1611yescharacteristic
59#6095—21no—
60#6094—41no—
61C8×D13—41no—
62C13×C16—41no—
63C13×C16—41no—
64#6090—21no—
65#6090—21no—
66#6090—41no—
67#2245—131no—
68#2231—131no—
69#2214—131no—
70#2171—131no—
71#1369—131no—
72#1366—131no—
73#1358D1311yescharacteristic, complemented
74Q8×C13—81no—
75Q8×C13—81no—
76C2×C4×C13—21no—
77C2×C4×C13—81no—
78C2×C4×C13#12111yescharacteristic
79C22⋊D13—41no—
80C2×Dic13—81no—
81D52—21no—
82C4×D13—41no—
83Dic26—21no—
84C8×C13C2×SD1611yescharacteristic
85C8×C13#13511yescharacteristic
86C8×C13#13511yescharacteristic
87C8×C13AGL(1,ℤ/8)11yescharacteristic
88#1055—41no—
89#510—261no—
90#504—261no—
91#499—131no—
92#494C2×D1311yescharacteristic
93#443—131no—
94#365—261no—
95#364—131no—
96#364C2×D1311yescharacteristic
97#364C2×D1311yescharacteristic
98#362—261no—
99#360—261no—
100#358—261no—
101#358—261no—
102#350—261no—
103#346—131no—
104C22×C13#47211yescharacteristic
105C2×D13—41no—
106C4×C13—41no—
107C4×C13—161no—
108C4×C13#46311yescharacteristic
109C4×C13#46511yescharacteristic
110Dic13—41no—
111Dic13—161no—
112#135—131no—
113C2×Q16—21no—
114C2×Q16—21no—
115#131—261no—
116C4⋊Q8—21no—
117#125—261no—
118Q32—521no—
119SD32—521no—
120M32—21no—
121M32—21no—
122M32—261no—
123M32—521no—
124C2×C16—131no—
125C2×C16—131no—
126C2×C16—521no—
127#108—131no—
128#107—261no—
129#106—261no—
130#104—261no—
131C4×C8C22×D1311yescharacteristic
132C2×C13—21no—
133C2×C13#167711yescharacteristic
134D13—81no—
135#41—261no—
136C2×Q8—41no—
137Q16—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16—131no—
142SD16—261no—
143D8—131no—
144M16—261no—
145M16—521no—
146C2×C8—521no—
147C2×C8D4×D1311yescharacteristic
148C2×C8D4×D1311yescharacteristic
149C4⋊C4—81no—
150C4⋊C4—521no—
151C4⋊C4—1041no—
152C42#612711yescharacteristic
153C16—41no—
154C16—41no—
155C16—261no—
156C16—261no—
157C16—521no—
158C13#1246611yescharacteristic, complemented, Sylow
159Q8—81no—
160Q8—81no—
161Q8—261no—
162D4—261no—
163D4—521no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—521no—
167C2×C4—1041no—
168C2×C4#8813811yescharacteristic
169C8—521no—
170C8#8816511yescharacteristic
171C8#8816611yescharacteristic
172C8SD16×D1311yescharacteristic
173C8#8817011yescharacteristic
174C22—521no—
175C22#1171841011yescharacteristic
176C4—41no—
177C4—161no—
178C4—521no—
179C4—2081no—
180C4#1171843911yescharacteristic
181C4#1171844811yescharacteristic
182C2—21no—
183C2—1041no—
184C2#1311424411yescharacteristic
subgroupG/H
centerC2#13114244
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1358C2
socleC2×C13#1677
prime radical#88158D4
hypercenter#1358D13
hypocenterC13#12466
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #13117081C2semidirect
5. #13112903C2semidirect
6. #13112898C2semidirect
7. C13×#1358C2semidirect
73. #1358D13semidirect
158. C13#12466semidirect

Maximal subgroups

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

subgroupindex
#131170812
#131170132
#131169142
#131166772
#131129032
#131128982
C13×#13582
#1246613