Finite Group Databasebeta

← #15777157

Subgroups — #15777157

Order 3328.

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

normal subgroups only

This group has 234 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#13117085C211yesmaximal, characteristic, complemented
2#13116912C211yesmaximal, characteristic, complemented
3#13116673C211yesmaximal, characteristic, complemented
4#13112911C211yesmaximal, characteristic, complemented
5#13112873C211yesmaximal, characteristic, complemented
6#13112872C211yesmaximal, characteristic, complemented
7C13×#2213C211yesmaximal, characteristic, complemented
8C13×#509—21no—
9C13×#493C2211yescharacteristic
10C13×#443C2211yescharacteristic
11#11718854—21no—
12C2×#88066—21no—
13C2×#88066—21no—
14#11718801—21no—
15#11718356C2211yescharacteristic
16C13×#364C2211yescharacteristic
17C13×#361—21no—
18#11718153—21no—
19#11718087—21no—
20#11718055C2211yescharacteristic
21#11718055C2211yescharacteristic
22C4×#6090C2211yescharacteristic
23C13×#135D411yescharacteristic
24C2×C13×D8—21no—
25C2×C13×D8—21no—
26C13×#131—21no—
27C13×#127—21no—
28C2×D104—21no—
29C2×D104—21no—
30#88128—21no—
31C13×SD32—41no—
32C13×D16—41no—
33C13×M32—21no—
34C13×#108D411yescharacteristic
35C13×#104—21no—
36C4×C8×C13C2311yescharacteristic
37#88068—41no—
38#88066—42no—
39#88066—41no—
40#88066—41no—
41#88066—41no—
42#88052—21no—
43#88052—21no—
44#88052—41no—
45C2×#6090—41no—
46C2×#6090D411yescharacteristic
47C2×#6090D411yescharacteristic
48#12436—131nomaximal, Sylow
49C13×#41—21no—
50C2×D4×C13—41no—
51C2×D4×C13—81no—
52C2×D52—41no—
53C2×D52—81no—
54C13×Q16D811yescharacteristic
55C13×SD16—21no—
56C13×D8—41no—
57C13×D8—41no—
58C13×D8—41no—
59C13×D8—41no—
60C13×D8D811yescharacteristic
61C13×M16—21no—
62C13×M16—41no—
63C2×C8×C13—41no—
64C2×C8×C13C2×D411yescharacteristic
65C2×C8×C13C2×D411yescharacteristic
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#2246—131no—
78#2213—131no—
79#2213D1311yescharacteristic, complemented
80#2170—131no—
81#1373—131no—
82#1357—131no—
83#1357—131no—
84C23×C13—81no—
85C22×D13—81no—
86Q8×C13—21no—
87D4×C13—21no—
88D4×C13—41no—
89D4×C13—81no—
90D4×C13—81no—
91D4×C13—162no—
92C2×C4×C13—21no—
93C2×C4×C13—41no—
94C2×C4×C13#12111yescharacteristic
95D52—81no—
96D52—81no—
97D52—162no—
98C8×C13—41no—
99C8×C13C2×D811yescharacteristic
100C8×C13C2×D811yescharacteristic
101C8×C13#13511yescharacteristic
102C8×C13AGL(1,ℤ/8)11yescharacteristic
103#509—21no—
104#509—261no—
105C2×D16—261no—
106C2×D16—261no—
107#504—261no—
108#493—131no—
109#493C2×D1311yescharacteristic
110#443C2×D1311yescharacteristic
111#364—131no—
112#364—131no—
113#364C2×D1311yescharacteristic
114#361—21no—
115#361—261no—
116#350—261no—
117C4×C16—131no—
118C22×C13—41no—
119C22×C13—162no—
120C22×C13—161no—
121C22×C13#47211yescharacteristic
122C2×D13—162no—
123C2×D13—161no—
124C4×C13—22no—
125C4×C13—41no—
126C4×C13#45911yescharacteristic
127C4×C13#46611yescharacteristic
128#135C22⋊D1311yescharacteristic
129C2×D8—21no—
130C2×D8—21no—
131C2×D8—261no—
132C2×D8—261no—
133#131—21no—
134#127—21no—
135#127—261no—
136SD32—41no—
137SD32—521no—
138D16—41no—
139D16—521no—
140D16—521no—
141D16—522no—
142D16—521no—
143M32—21no—
144M32—261no—
145M32—261no—
146M32—521no—
147C2×C16—131no—
148C2×C16—131no—
149C2×C16—521no—
150#108C22⋊D1311yescharacteristic
151#104—21no—
152C4×C8C22×D1311yescharacteristic
153C2×C13—21no—
154C2×C13—81no—
155C2×C13—321no—
156C2×C13#166711yescharacteristic
157D13—321no—
158#41—21no—
159C2×D4—41no—
160C2×D4—81no—
161C2×D4—521no—
162C2×D4—1041no—
163Q16#610411yescharacteristic
164SD16—21no—
165D8—41no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—521no—
170D8—521no—
171D8—521no—
172D8—521no—
173D8#610411yescharacteristic
174M16—21no—
175M16—41no—
176C2×C8—41no—
177C2×C8D4×D1311yescharacteristic
178C2×C8C2×C22⋊D1311yescharacteristic
179C42#612911yescharacteristic
180C16—41no—
181C16—131no—
182C16—131no—
183C16—261no—
184C16—521no—
185C16—521no—
186C13#1243611yescharacteristic, complemented, Sylow
187C23—81no—
188C23—1041no—
189Q8—21no—
190D4—21no—
191D4—41no—
192D4—81no—
193D4—81no—
194D4—162no—
195D4—1041no—
196D4—1041no—
197D4—2082no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4#8819311yescharacteristic
201C8—41no—
202C8D8×D1311yescharacteristic
203C8#8816511yescharacteristic
204C8C2×#610411yescharacteristic
205C8#8820411yescharacteristic
206C22—41no—
207C22—162no—
208C22—161no—
209C22—2082no—
210C22—2081no—
211C22#1171886011yescharacteristic
212C4—22no—
213C4—41no—
214C4#1171869911yescharacteristic
215C4#1171881111yescharacteristic
216C2—21no—
217C2—81no—
218C2—321no—
219C2—4161no—
220C2#1311418911yescharacteristic
subgroupG/H
centerC2#13114189
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2213C2
socleC2×C13#1667
hypercenter#2213D13
hypocenterC13#12436
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #13117085C2semidirect
2. #13116912C2semidirect
3. #13116673C2semidirect
4. #13112911C2semidirect
5. #13112873C2semidirect
6. #13112872C2semidirect
7. C13×#2213C2semidirect
79. #2213D13semidirect
186. C13#12436semidirect

Maximal subgroups

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

subgroupindex
#131170852
#131169122
#131166732
#131129112
#131128732
#131128722
C13×#22132
#1243613