Finite Group Databasebeta

← #13113921

Subgroups — #13113921

Order 1664.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#11719268C211yesmaximal, characteristic, complemented
2#11718676C211yesmaximal, characteristic, complemented
3#11718504C211yesmaximal, characteristic, complemented
4#11718354C211yesmaximal, characteristic, complemented
5C13×D4⋊C8C211yesmaximal, characteristic, complemented
6#11718073C211yesmaximal, characteristic, complemented
7#11718051C211yesmaximal, characteristic, complemented
8C4×D4×C13C2211yescharacteristic
9#88192—21no—
10C2×#6104—21no—
11#88184—21no—
12#88180—21no—
13C2×D104—21no—
14C2×#6095—22no—
15#88146—21no—
16#88139—22no—
17#88128C2211yescharacteristic
18C4×D52C2211yescharacteristic
19#88123C2211yescharacteristic
20C13×C4⋊C8C2211yescharacteristic
21C4×C8×C13C2211yescharacteristic
22#88061—21no—
23#88049—21no—
24C4⋊#1055C2211yescharacteristic
25C2×D4×C13D411yescharacteristic
26C22×C4×C13—21no—
27C2×C22⋊D13—22no—
28C2×D52—21no—
29C2×D52—21no—
30C2×D52—21no—
31C2×D52D411yescharacteristic
32C2×C4×D13—21no—
33C2×Dic26D412yes—
34C2×C8×C13—21no—
35C2×C8×C13—21no—
36C13×C4⋊C4D411yescharacteristic
37C13×C22⋊C4—21no—
38C42×C13C2311yescharacteristic
39C22⋊Dic13—22no—
40#6104—42no—
41#6103—22no—
42#6103—21no—
43C4⋊Dic13—21no—
44C4⋊Dic13—21no—
45C4⋊Dic13D411yescharacteristic
46C4×Dic13—22no—
47C2×#1055—21no—
48D104—42no—
49#6095—44no—
50#1624—131nomaximal, Sylow
51C23×C13—21no—
52C22×D13—21no—
53C22×D13—41no—
54D4×C13—21no—
55D4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×C4×C13C2×D411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C2×C4×C13C2×D411yescharacteristic
62C22⋊D13—82no—
63C2×Dic13—21no—
64C2×Dic13—22no—
65D52—21no—
66D52—21no—
67D52—42no—
68D52—41no—
69D52—41no—
70D52—41no—
71D52—41no—
72C4×D13—41no—
73C4×D13—41no—
74Dic26—42no—
75C8×C13—22no—
76C8×C13—41no—
77#1055—41no—
78#555—131no—
79#492—131no—
80#459—131no—
81#459—131no—
82#333—131no—
83D4⋊C8—131no—
84D4⋊C8D1311yescharacteristic, complemented
85C22×C13—41no—
86C22×C13—41no—
87C22×C13—41no—
88C22×C13#12011yescharacteristic
89C2×D13—41no—
90C2×D13—41no—
91C2×D13—41no—
92C2×D13—81no—
93C2×D13—81no—
94C2×D13—81no—
95C4×C13—21no—
96C4×C13—41no—
97C4×C13#13511yescharacteristic
98C4×C13#13511yescharacteristic
99C4×C13AGL(1,ℤ/8)11yescharacteristic
100C4×C13AGL(1,ℤ/8)11yescharacteristic
101Dic13—41no—
102Dic13—42no—
103C2×SD16—262no—
104C2×D8—261no—
105C2×D8—261no—
106C4⋊Q8—131no—
107#127—131no—
108#124—262no—
109#121—261no—
110#121—261no—
111C4×D4—131no—
112C4×D4C2×D1311yescharacteristic
113#117—261no—
114#117—261no—
115C4⋊C8—131no—
116C4⋊C8C2×D1311yescharacteristic
117#102—261no—
118#102—261no—
119C4×C8C2×D1311yescharacteristic
120C2×C13—81no—
121C2×C13#44911yescharacteristic
122C2×C13#44911yescharacteristic
123C2×C13#45311yescharacteristic
124D13—81no—
125D13—161no—
126C2×Q8—132no—
127C2×D4—131no—
128C2×D4—262no—
129C2×D4—261no—
130C2×D4—261no—
131C2×D4—261no—
132C2×D4D5211yescharacteristic
133C22×C4—21no—
134C22×C4—261no—
135SD16—524no—
136D8—522no—
137D8—522no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—261no—
141C4⋊C4—131no—
142C4⋊C4—261no—
143C4⋊C4—261no—
144C4⋊C4D5211yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—262no—
147C22⋊C4—262no—
148C22⋊C4—261no—
149C42—262no—
150C42C22×D1311yescharacteristic
151C13#162411yescharacteristic, complemented, Sylow
152C23—21no—
153C23—261no—
154C23—521no—
155Q8—522no—
156D4—21no—
157D4—21no—
158D4—261no—
159D4—261no—
160D4—522no—
161D4—521no—
162D4—521no—
163D4—521no—
164D4—521no—
165D4—1042no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—261no—
170C2×C4—262no—
171C2×C4—521no—
172C2×C4—521no—
173C2×C4C2×D5211yescharacteristic
174C2×C4D4×D1311yescharacteristic
175C2×C4D4×D1311yescharacteristic
176C8—22no—
177C8—41no—
178C8—521no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—521no—
183C22—521no—
184C22—521no—
185C22—1041no—
186C22—1041no—
187C22—1041no—
188C22#8813611yescharacteristic
189C4—21no—
190C4—41no—
191C4—522no—
192C4—521no—
193C4#8815811yescharacteristic
194C4#8816211yescharacteristic
195C4#8816511yescharacteristic
196C4#8817011yescharacteristic
197C2—81no—
198C2—1041no—
199C2—2081no—
200C2#1171839511yescharacteristic
201C2#1171844211yescharacteristic
202C2#1171848311yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×D4⋊C8C2
socleC22×C13#120
hypercenterD4⋊C8D13
hypocenterC13#1624
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
1. #11719268C2semidirect
2. #11718676C2semidirect
3. #11718504C2semidirect
4. #11718354C2semidirect
5. C13×D4⋊C8C2semidirect
6. #11718073C2semidirect
7. #11718051C2semidirect
84. D4⋊C8D13semidirect
151. C13#1624semidirect

Maximal subgroups

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

subgroupindex
#117192682
#117186762
#117185042
#117183542
C13×D4⋊C82
#117180732
#117180512
#162413