Finite Group Databasebeta

← #13114122

Subgroups — #13114122

Order 1664.

240 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 55 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#11719256C211yesmaximal, characteristic
2#11718680C211yesmaximal, characteristic, complemented
3#11718507C211yesmaximal, characteristic, complemented
4#11718341C211yesmaximal, characteristic, complemented
5C13×D4⋊C8C211yesmaximal, characteristic, complemented
6#11718074C211yesmaximal, characteristic, complemented
7#11718051C211yesmaximal, characteristic, complemented
8C2×#6127—21no—
9C4×D4×C13C2211yescharacteristic
10#88192—21no—
11C2×#6105—21no—
12#88178—21no—
13C4⋊C4×D13—21no—
14#88137—22no—
15C4×D52C2211yescharacteristic
16#88123C2211yescharacteristic
17#88123C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C4×C8×C13C2211yescharacteristic
20#88061—21no—
21#88058—21no—
22#88057—22no—
23#88050—21no—
24C4⋊#1055C2211yescharacteristic
25C2×D4×C13D411yescharacteristic
26C22×C4×C13—21no—
27C2×C22⋊D13—22no—
28#6127—42no—
29#6127—42no—
30C2×D52D411yescharacteristic
31C2×C4×D13—22no—
32C2×C4×D13—21no—
33C2×Dic26—21no—
34C2×Dic26—21no—
35C2×C8×C13—21no—
36C2×C8×C13—21no—
37C13×C4⋊C4D411yescharacteristic
38C13×C22⋊C4—21no—
39C42×C13C2311yescharacteristic
40C22⋊Dic13—22no—
41#6105—42no—
42#6103—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13—21no—
45C4⋊Dic13—21no—
46C4⋊Dic13D412yes—
47C4⋊Dic13D411yescharacteristic
48#6101—22no—
49C2×#1055—21no—
50#1654—131nomaximal, Sylow
51C23×C13—21no—
52C22×D13—21no—
53D4×C13—21no—
54D4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13—41no—
57C2×C4×C13—41no—
58C2×C4×C13C2×D411yescharacteristic
59C2×C4×C13C2×D411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C22⋊D13—44no—
62C2×Dic13—21no—
63C2×Dic13—22no—
64C2×Dic13—41no—
65D52—21no—
66D52SD1612yescomplemented
67C4×D13—44no—
68C4×D13—41no—
69C4×D13—41no—
70Dic26—41no—
71Dic26—41no—
72Dic26—41no—
73Dic26—41no—
74C8×C13—22no—
75C8×C13—41no—
76#1055—41no—
77#547—131no—
78#498—131no—
79#474—131no—
80#461—131no—
81#332—131no—
82D4⋊C8—131no—
83D4⋊C8D1311yescharacteristic, complemented
84C22×C13—41no—
85C22×C13—41no—
86C22×C13—41no—
87C22×C13#12011yescharacteristic
88C2×D13—22no—
89C2×D13—41no—
90C2×D13—41no—
91C4×C13—21no—
92C4×C13—41no—
93C4×C13C2×SD1611yescharacteristic
94C4×C13#13511yescharacteristic
95C4×C13AGL(1,ℤ/8)11yescharacteristic
96C4×C13AGL(1,ℤ/8)11yescharacteristic
97Dic13—41no—
98Dic13—42no—
99Dic13—81no—
100C2×#41—261no—
101C2×SD16—261no—
102C4⋊Q8—131no—
103C4⋊Q8—131no—
104#123—262no—
105C22⋊Q8—261no—
106#121—261no—
107C4×D4—131no—
108C4×D4C2×D1311yescharacteristic
109C2×C4⋊C4—261no—
110#107—261no—
111#106—262no—
112C4⋊C8—131no—
113C4⋊C8C2×D1311yescharacteristic
114#103—261no—
115#102—261no—
116C4×C8C2×D1311yescharacteristic
117C2×C13—81no—
118C2×C13#44911yescharacteristic
119C2×C13#45011yescharacteristic
120C2×C13#45611yescharacteristic
121D13—42no—
122#41—522no—
123#41—522no—
124C2×Q8—261no—
125C2×Q8—261no—
126C2×D4—131no—
127C2×D4—262no—
128C2×D4D5211yescharacteristic
129C22×C4—21no—
130C22×C4—262no—
131C22×C4—261no—
132SD16—522no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—261no—
136C4⋊C4—132no—
137C4⋊C4—131no—
138C4⋊C4—262no—
139C4⋊C4—261no—
140C4⋊C4—261no—
141C4⋊C4—261no—
142C4⋊C4D5211yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—262no—
145C22⋊C4—261no—
146C42C22×D1311yescharacteristic
147C13#165411yescharacteristic, complemented, Sylow
148C23—21no—
149C23—261no—
150Q8—521no—
151Q8—521no—
152Q8—521no—
153Q8—521no—
154D4—21no—
155D4—21no—
156D4—132no—
157D4—261no—
158D4—524no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—261no—
163C2×C4—262no—
164C2×C4—524no—
165C2×C4—521no—
166C2×C4—521no—
167C2×C4—521no—
168C2×C4C2×D5211yescharacteristic
169C2×C4D4×D1311yescharacteristic
170C2×C4D4×D1311yescharacteristic
171C8—22no—
172C8—41no—
173C8—521no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—262no—
178C22—521no—
179C22—521no—
180C22#8813611yescharacteristic
181C4—21no—
182C4—41no—
183C4—522no—
184C4—521no—
185C4—1041no—
186C4#8815811yescharacteristic
187C4#8816211yescharacteristic
188C4#8816511yescharacteristic
189C4SD16×D1311yescharacteristic
190C2—81no—
191C2—522no—
192C2#1171839511yescharacteristic
193C2#1171843711yescharacteristic
194C2#1171848711yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×D4⋊C8C2
socleC22×C13#120
prime radical#11719256C2
hypercenterD4⋊C8D13
hypocenterC13#1654
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11718680C2semidirect
3. #11718507C2semidirect
4. #11718341C2semidirect
5. C13×D4⋊C8C2semidirect
6. #11718074C2semidirect
7. #11718051C2semidirect
66. D52SD16semidirect
83. D4⋊C8D13semidirect
147. C13#1654semidirect

Maximal subgroups

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

subgroupindex
#117192562
#117186802
#117185072
#117183412
C13×D4⋊C82
#117180742
#117180512
#165413