Finite Group Databasebeta

← #15777171

Subgroups — #15777171

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#13117093C211yesmaximal, characteristic, complemented
2#13116912C211yesmaximal, characteristic
3#13116673C211yesmaximal, characteristic, complemented
4#13112911C211yesmaximal, characteristic, complemented
5#13112875C211yesmaximal, characteristic, complemented
6#13112872C211yesmaximal, characteristic, complemented
7C13×#2214C211yesmaximal, characteristic, complemented
8C13×#510—21no—
9C13×#494C2211yescharacteristic
10C13×#443C2211yescharacteristic
11#11718854—21no—
12C2×#88068—21no—
13C2×#88068—21no—
14#11718801—21no—
15#11718356C2211yescharacteristic
16C13×#364C2211yescharacteristic
17C13×#362—21no—
18#11718153—21no—
19#11718087—21no—
20#11718055C2211yescharacteristic
21#11718055C2211yescharacteristic
22C4×#6090C2211yescharacteristic
23C13×#135D411yescharacteristic
24C2×C13×Q16—21no—
25C2×C13×Q16—21no—
26C13×#131—21no—
27C13×C4⋊Q8—21no—
28C2×D104—21no—
29C2×D104—21no—
30#88128—21no—
31C13×Q32—41no—
32C13×SD32—41no—
33C13×M32—21no—
34C13×#108D411yescharacteristic
35C13×#104—21no—
36C4×C8×C13C2311yescharacteristic
37#88068—42no—
38#88068—41no—
39#88068—41no—
40#88068—41no—
41#88066—41no—
42#88052—21no—
43#88052—21no—
44#88052—41no—
45C2×#6090—41no—
46C2×#6090D411yescharacteristic
47C2×#6090D411yescharacteristic
48#12438—131nomaximal, Sylow
49C13×#41—21no—
50C2×Q8×C13—41no—
51C2×D52—41no—
52C2×D52—81no—
53C13×Q16—41no—
54C13×Q16—41no—
55C13×Q16—41no—
56C13×Q16—41no—
57C13×Q16D811yescharacteristic
58C13×SD16—21no—
59C13×D8D811yescharacteristic
60C13×M16—21no—
61C13×M16—41no—
62C2×C8×C13—41no—
63C2×C8×C13C2×D411yescharacteristic
64C2×C8×C13C2×D411yescharacteristic
65C13×C4⋊C4—81no—
66C42×C13#4111yescharacteristic
67D104—41no—
68D104—41no—
69D104—41no—
70D104—41no—
71C13×C16—41no—
72#6090—21no—
73#6090—41no—
74#6090—41no—
75#6090D811yescharacteristic
76#6090D811yescharacteristic
77#2248—131no—
78#2214D1311yescharacteristic, complemented
79#2213—131no—
80#2170—131no—
81#1373—131no—
82#1358—131no—
83#1357—131no—
84C22×D13—81no—
85Q8×C13—21no—
86Q8×C13—81no—
87Q8×C13—81no—
88D4×C13—21no—
89D4×C13—41no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—81no—
93C2×C4×C13#12111yescharacteristic
94D52—81no—
95D52—81no—
96D52—162no—
97C8×C13—41no—
98C8×C13C2×D811yescharacteristic
99C8×C13C2×D811yescharacteristic
100C8×C13#13511yescharacteristic
101C8×C13AGL(1,ℤ/8)11yescharacteristic
102#510—21no—
103#509—261no—
104C2×SD32—261no—
105C2×SD32—261no—
106#504—261no—
107#494C2×D1311yescharacteristic
108#493—131no—
109#443C2×D1311yescharacteristic
110#364—131no—
111#364—131no—
112#364C2×D1311yescharacteristic
113#362—21no—
114#361—261no—
115#350—261no—
116C4×C16—131no—
117C22×C13—41no—
118C22×C13#47211yescharacteristic
119C2×D13—162no—
120C2×D13—161no—
121C4×C13—22no—
122C4×C13—41no—
123C4×C13—161no—
124C4×C13#45911yescharacteristic
125C4×C13#46611yescharacteristic
126#135C22⋊D1311yescharacteristic
127C2×Q16—21no—
128C2×Q16—21no—
129C2×D8—261no—
130C2×D8—261no—
131#131—21no—
132C4⋊Q8—21no—
133#127—261no—
134Q32—41no—
135SD32—41no—
136SD32—521no—
137SD32—521no—
138SD32—522no—
139SD32—521no—
140D16—521no—
141M32—21no—
142M32—261no—
143M32—261no—
144M32—521no—
145C2×C16—131no—
146C2×C16—131no—
147C2×C16—521no—
148#108C22⋊D1311yescharacteristic
149#104—21no—
150C4×C8C22×D1311yescharacteristic
151C2×C13—21no—
152C2×C13—81no—
153C2×C13#166711yescharacteristic
154D13—321no—
155#41—21no—
156C2×Q8—41no—
157C2×D4—521no—
158C2×D4—1041no—
159Q16—41no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16#610411yescharacteristic
164SD16—21no—
165D8—521no—
166D8—521no—
167D8—521no—
168D8—521no—
169D8#610411yescharacteristic
170M16—21no—
171M16—41no—
172C2×C8—41no—
173C2×C8D4×D1311yescharacteristic
174C2×C8C2×C22⋊D1311yescharacteristic
175C4⋊C4—81no—
176C42#612911yescharacteristic
177C16—41no—
178C16—131no—
179C16—131no—
180C16—261no—
181C16—521no—
182C16—521no—
183C13#1243811yescharacteristic, complemented, Sylow
184C23—1041no—
185Q8—21no—
186Q8—81no—
187Q8—81no—
188D4—21no—
189D4—41no—
190D4—1041no—
191D4—1041no—
192D4—2082no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—81no—
196C2×C4#8819311yescharacteristic
197C8—41no—
198C8D8×D1311yescharacteristic
199C8#8816511yescharacteristic
200C8C2×#610411yescharacteristic
201C8#8820411yescharacteristic
202C22—41no—
203C22—2082no—
204C22—2081no—
205C22#1171886011yescharacteristic
206C4—22no—
207C4—41no—
208C4—161no—
209C4#1171869911yescharacteristic
210C4#1171881111yescharacteristic
211C2—21no—
212C2—81no—
213C2—4161no—
214C2#1311418911yescharacteristic
subgroupG/H
centerC2#13114189
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2214C2
socleC2×C13#1667
prime radical#13116912C2
hypercenter#2214D13
hypocenterC13#12438
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #13117093C2semidirect
3. #13116673C2semidirect
4. #13112911C2semidirect
5. #13112875C2semidirect
6. #13112872C2semidirect
7. C13×#2214C2semidirect
78. #2214D13semidirect
183. C13#12438semidirect

Maximal subgroups

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

subgroupindex
#131170932
#131169122
#131166732
#131129112
#131128752
#131128722
C13×#22142
#1243813