Finite Group Databasebeta

← #13113965

Subgroups — #13113965

Order 1664.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#11719282C211yesmaximal, characteristic
2#11718682C211yesmaximal, characteristic, complemented
3#11718503C211yesmaximal, characteristic, complemented
4#11718354C211yesmaximal, characteristic, complemented
5C13×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11718077C211yesmaximal, characteristic, complemented
7#11718051C211yesmaximal, characteristic, complemented
8C2×#6131—21no—
9C4×Q8×C13C2211yescharacteristic
10C2×#6095—22no—
11#88149—22no—
12#88149—21no—
13#88128—21no—
14#88128C2211yescharacteristic
15C4×D52—21no—
16C4×D52C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C4×C8×C13C2211yescharacteristic
20#88075—21no—
21#88061—21no—
22#88057—21no—
23#88047—21no—
24C4⋊#1055C2211yescharacteristic
25C2×Q8×C13D411yescharacteristic
26#6131—42no—
27#6131—42no—
28C2×D52—22no—
29C2×D52—21no—
30C2×D52—21no—
31C2×D52—22no—
32C2×D52D411yescharacteristic
33C2×D52D412yes—
34C2×C4×D13—22no—
35C2×C4×D13—21no—
36C2×Dic26—21no—
37C2×C8×C13—21no—
38C2×C8×C13—21no—
39C13×C4⋊C4—21no—
40C13×C4⋊C4D411yescharacteristic
41C42×C13—21no—
42C42×C13C2311yescharacteristic
43#6103—22no—
44#6103—21no—
45C4⋊Dic13—21no—
46C4⋊Dic13—21no—
47C4⋊Dic13D411yescharacteristic
48C2×#1055—21no—
49#6095—44no—
50#1631—131nomaximal, Sylow
51C22×D13—21no—
52C22×D13—22no—
53Q8×C13—21no—
54Q8×C13SD1612yescomplemented
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13C2×D411yescharacteristic
58C2×C4×C13C2×D411yescharacteristic
59C2×C4×C13C2×D411yescharacteristic
60C2×Dic13—21no—
61C2×Dic13—41no—
62D52—21no—
63D52—21no—
64D52—44no—
65D52—42no—
66D52—41no—
67D52—41no—
68D52—41no—
69D52—41no—
70D52—82no—
71C4×D13—44no—
72C4×D13—41no—
73C4×D13—41no—
74Dic26—42no—
75C8×C13—22no—
76C8×C13—41no—
77#1055—41no—
78#550—131no—
79#492—131no—
80#477—131no—
81#476—131no—
82#331—131no—
83Q8⋊C8D1311yescharacteristic, complemented
84D4⋊C8—131no—
85C22×C13#12011yescharacteristic
86C2×D13—42no—
87C2×D13—41no—
88C2×D13—41no—
89C2×D13—42no—
90C2×D13—42no—
91C2×D13—41no—
92C4×C13—22no—
93C4×C13—21no—
94C4×C13—41no—
95C4×C13C2×SD1611yescharacteristic
96C4×C13#13511yescharacteristic
97C4×C13AGL(1,ℤ/8)11yescharacteristic
98C4×C13#13711yescharacteristic
99Dic13—41no—
100Dic13—81no—
101C2×#41—261no—
102C2×SD16—262no—
103C4⋊Q8—131no—
104#127—131no—
105#127—261no—
106#121—262no—
107#121—261no—
108C4×Q8C2×D1311yescharacteristic
109C4×D4—131no—
110C4×D4—261no—
111#107—261no—
112#106—261no—
113C4⋊C8—131no—
114C4⋊C8C2×D1311yescharacteristic
115#103—261no—
116#102—261no—
117C4×C8C2×D1311yescharacteristic
118C2×C13#45011yescharacteristic
119C2×C13#45211yescharacteristic
120C2×C13#45311yescharacteristic
121D13—81no—
122D13—82no—
123#41—522no—
124#41—522no—
125C2×Q8—261no—
126C2×Q8D5211yescharacteristic
127C2×D4—131no—
128C2×D4—132no—
129C2×D4—262no—
130C2×D4—262no—
131C2×D4—261no—
132C2×D4—261no—
133C22×C4—262no—
134C22×C4—261no—
135SD16—524no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—261no—
139C4⋊C4—21no—
140C4⋊C4—131no—
141C4⋊C4—261no—
142C4⋊C4—261no—
143C4⋊C4D5211yescharacteristic
144C22⋊C4—262no—
145C22⋊C4—261no—
146C42—21no—
147C42C22×D1311yescharacteristic
148C13#163111yescharacteristic, complemented, Sylow
149C23—261no—
150C23—262no—
151Q8—21no—
152Q8—522no—
153Q8#609512yescomplemented
154D4—261no—
155D4—261no—
156D4—522no—
157D4—524no—
158D4—521no—
159D4—521no—
160D4—521no—
161D4—521no—
162D4—1042no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—261no—
166C2×C4—524no—
167C2×C4—521no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4C2×D5211yescharacteristic
171C2×C4D4×D1311yescharacteristic
172C2×C4D4×D1311yescharacteristic
173C8—22no—
174C8—41no—
175C8—521no—
176C22—521no—
177C22—522no—
178C22—522no—
179C22—521no—
180C22—522no—
181C22—521no—
182C22#8813611yescharacteristic
183C4—21no—
184C4—22no—
185C4—41no—
186C4—521no—
187C4—1041no—
188C4C2×#609511yescharacteristic
189C4#8816211yescharacteristic
190C4#8817011yescharacteristic
191C4#8817211yescharacteristic
192C2—1041no—
193C2—1042no—
194C2#1171839211yescharacteristic
195C2#1171847111yescharacteristic
196C2#1171848311yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×Q8⋊C8C2
socleC22×C13#120
prime radical#11719282C2
hypercenterQ8⋊C8D13
hypocenterC13#1631
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #11718682C2semidirect
3. #11718503C2semidirect
4. #11718354C2semidirect
5. C13×Q8⋊C8C2semidirect
6. #11718077C2semidirect
7. #11718051C2semidirect
54. Q8×C13SD16semidirect
83. Q8⋊C8D13semidirect
148. C13#1631semidirect
153. Q8#6095semidirect

Maximal subgroups

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

subgroupindex
#117192822
#117186822
#117185032
#117183542
C13×Q8⋊C82
#117180772
#117180512
#163113