Finite Group Databasebeta

← #15777166

Subgroups — #15777166

Order 3328.

224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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#13116914C211yesmaximal, characteristic, complemented
2#13116909C211yesmaximal, characteristic
3#13116674C211yesmaximal, characteristic, complemented
4#13112912C211yesmaximal, characteristic, complemented
5#13112875C211yesmaximal, characteristic, complemented
6#13112873C211yesmaximal, characteristic, complemented
7C13×#2248C211yesmaximal, characteristic, complemented
8C2×C13×SD32—21no—
9C2×C13×SD32—21no—
10C13×#494C2211yescharacteristic
11C13×#493C2211yescharacteristic
12#11718840—21no—
13#11718808—21no—
14#11718562—21no—
15#11718361C2211yescharacteristic
16C4×C13×C16C2211yescharacteristic
17#11718157—21no—
18#11718155—21no—
19#11718100—21no—
20#11718055C2211yescharacteristic
21#11718055C2211yescharacteristic
22#11718055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C2×C13×D8—21no—
26C2×C13×D8—21no—
27C13×C4⋊Q8—21no—
28C13×#127—21no—
29#88158D411yescharacteristic
30#88155—21no—
31C13×SD32—42no—
32C13×SD32—41no—
33C13×SD32—41no—
34C2×C13×C16D411yescharacteristic
35C2×C13×C16D411yescharacteristic
36C4×C8×C13C2311yescharacteristic
37#88069—41no—
38#88068—41no—
39#88067—41no—
40#88066—41no—
41#88059D411yescharacteristic
42#88052—21no—
43#88052—21no—
44#88052—21no—
45#88045—21no—
46#88038—41no—
47C16×D13—41no—
48#12438—131nomaximal, Sylow
49C2×Q8×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13—81no—
52#6127—21no—
53C13×Q16—41no—
54C13×Q16—41no—
55C13×Q16—41no—
56C13×Q16—41no—
57C13×D8—41no—
58C13×D8—41no—
59C13×D8—41no—
60C13×D8—41no—
61C2×C8×C13C2×D411yescharacteristic
62C2×C8×C13C2×D411yescharacteristic
63C13×C4⋊C4—81no—
64C42×C13#4111yescharacteristic
65#6099—21no—
66Dic52D811yescharacteristic
67D104D811yescharacteristic
68#6095—21no—
69#6094—41no—
70C8×D13—41no—
71C13×C16—21no—
72C13×C16D811yescharacteristic
73C13×C16D811yescharacteristic
74#6090—41no—
75#6090—41no—
76#6090—41no—
77#2248D1311yescharacteristic, complemented
78#2214—131no—
79#2213—131no—
80#2170—131no—
81#1373—131no—
82#1358—131no—
83#1357—131no—
84C23×C13—81no—
85Q8×C13—81no—
86Q8×C13—81no—
87D4×C13—81no—
88D4×C13—81no—
89D4×C13—162no—
90C2×C4×C13—21no—
91C2×C4×C13—81no—
92C2×C4×C13#12111yescharacteristic
93C22⋊D13—41no—
94D52—21no—
95C4×D13—41no—
96Dic26—21no—
97C8×C13C2×D811yescharacteristic
98C8×C13C2×D811yescharacteristic
99C8×C13#13511yescharacteristic
100C8×C13AGL(1,ℤ/8)11yescharacteristic
101#1055—41no—
102#510—261no—
103#509—261no—
104C2×SD32—21no—
105C2×SD32—21no—
106#504—261no—
107#494C2×D1311yescharacteristic
108#493C2×D1311yescharacteristic
109#443—131no—
110#364—131no—
111#364—131no—
112#364—131no—
113#362—261no—
114#361—261no—
115#350—261no—
116C4×C16C2×D1311yescharacteristic
117C22×C13—162no—
118C22×C13—161no—
119C22×C13#47211yescharacteristic
120C2×D13—41no—
121C4×C13—22no—
122C4×C13—161no—
123C4×C13#45911yescharacteristic
124C4×C13#46611yescharacteristic
125Dic13—41no—
126#135—131no—
127C2×Q16—21no—
128C2×Q16—21no—
129C2×D8—21no—
130C2×D8—21no—
131#131—261no—
132C4⋊Q8—21no—
133#127—21no—
134Q32—521no—
135SD32—42no—
136SD32—41no—
137SD32—41no—
138SD32—521no—
139SD32—521no—
140D16—521no—
141M32—261no—
142M32—261no—
143M32—261no—
144M32—521no—
145C2×C16—521no—
146C2×C16C22⋊D1311yescharacteristic
147C2×C16C22⋊D1311yescharacteristic
148#108—131no—
149#104—261no—
150C4×C8C22×D1311yescharacteristic
151C2×C13—21no—
152C2×C13—321no—
153C2×C13#166711yescharacteristic
154D13—81no—
155#41—261no—
156C2×Q8—41no—
157C2×D4—41no—
158C2×D4—81no—
159Q16—41no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—131no—
164SD16—261no—
165D8—41no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—131no—
170M16—261no—
171M16—521no—
172C2×C8—521no—
173C2×C8D4×D1311yescharacteristic
174C2×C8C2×C22⋊D1311yescharacteristic
175C4⋊C4—81no—
176C42#612911yescharacteristic
177C16—21no—
178C16—521no—
179C16—521no—
180C16—521no—
181C16#610411yescharacteristic
182C16#610411yescharacteristic
183C13#1243811yescharacteristic, complemented, Sylow
184C23—81no—
185Q8—81no—
186Q8—81no—
187Q8—261no—
188D4—81no—
189D4—81no—
190D4—162no—
191D4—261no—
192D4—521no—
193C2×C4—21no—
194C2×C4—81no—
195C2×C4—521no—
196C2×C4#8819211yescharacteristic
197C8—521no—
198C8D8×D1311yescharacteristic
199C8#8816611yescharacteristic
200C8C2×#610411yescharacteristic
201C8#8818611yescharacteristic
202C22—162no—
203C22—161no—
204C22—521no—
205C22#1171882111yescharacteristic
206C4—22no—
207C4—161no—
208C4—521no—
209C4#1171873311yescharacteristic
210C4#1171881811yescharacteristic
211C2—21no—
212C2—321no—
213C2—1041no—
214C2#1311418811yescharacteristic
subgroupG/H
centerC2#13114188
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2248C2
socleC2×C13#1667
prime radical#13116909C2
hypercenter#2248D13
hypocenterC13#12438
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #13116914C2semidirect
3. #13116674C2semidirect
4. #13112912C2semidirect
5. #13112875C2semidirect
6. #13112873C2semidirect
7. C13×#2248C2semidirect
77. #2248D13semidirect
183. C13#12438semidirect

Maximal subgroups

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

subgroupindex
#131169142
#131169092
#131166742
#131129122
#131128752
#131128732
C13×#22482
#1243813