Finite Group Databasebeta

← #13113510

Subgroups — #13113510

Order 1664.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#11719421C211yesmaximal, characteristic
2#11718498C211yesmaximal, characteristic, complemented
3D13×C4⋊C8C211yesmaximal, characteristic, complemented
4C13×#331C211yesmaximal, characteristic, complemented
5#11718136C211yesmaximal, characteristic, complemented
6#11718078C211yesmaximal, characteristic, complemented
7#11718074C211yesmaximal, characteristic, complemented
8C2×#6129—21no—
9C13×#127C2211yescharacteristic
10#88192—21no—
11#88192C412yes—
12#88190—21no—
13D4×Dic13—21no—
14D4×Dic13C412yes—
15C2×#6094—21no—
16C2×C8×D13—21no—
17C42×D13C2211yescharacteristic
18#88123C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20C13×C4⋊C8C2211yescharacteristic
21#88054—21no—
22#88054—21no—
23C4⋊#1055C2211yescharacteristic
24C4⋊#1055C2211yescharacteristic
25C2×D4×C13—21no—
26C2×D4×C13—21no—
27C2×D4×C13C2×C412yes—
28C2×C22⋊D13—22no—
29C22×Dic13—22no—
30#6129—42no—
31#6129—42no—
32C2×C4×D13C2×C411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×Dic26—21no—
36C2×C8×C13—21no—
37C2×C8×C13—21no—
38C42×C13C2311yescharacteristic
39C22⋊Dic13—22no—
40C22⋊Dic13—22no—
41C4⋊Dic13—21no—
42C4⋊Dic13C2×C412yes—
43C4×Dic13C2×C411yescharacteristic
44C4×Dic13D411yescharacteristic
45C4×Dic13D411yescharacteristic
46C2×#1055—21no—
47C2×#1055—21no—
48#6094—42no—
49C8×D13—42no—
50#1547—131nomaximal, Sylow
51C23×C13—22no—
52C22×D13C22⋊C411yescharacteristic
53D4×C13—42no—
54D4×C13—41no—
55D4×C13—41no—
56D4×C13—41no—
57D4×C13—41no—
58C2×C4×C13C22×C411yescharacteristic
59C2×C4×C13C2×D411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C22⋊D13—44no—
62C2×Dic13—22no—
63C2×Dic13—44no—
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C22⋊C411yescharacteristic
67C4×D13—21no—
68C4×D13—21no—
69C4×D13—41no—
70C4×D13D812yes—
71C4×D13SD1612yes—
72Dic26—41no—
73Dic26—41no—
74C8×C13—41no—
75C8×C13—41no—
76#1055—41no—
77#1055—41no—
78#532—131no—
79#423—131no—
80C2×C4⋊C8—131no—
81#332—131no—
82#332—131no—
83#331—131no—
84#331D1311yescharacteristic, complemented
85C22×C13—42no—
86C22×C13—42no—
87C22×C13—42no—
88C22×C13C2×C22⋊C411yescharacteristic
89C2×D13—21no—
90C2×D13—21no—
91C2×D13#10212yes—
92C4×C13—21no—
93C4×C13C2×D811yescharacteristic
94C4×C13C2×SD1611yescharacteristic
95C4×C13AGL(1,ℤ/8)11yescharacteristic
96C4×C13#13711yescharacteristic
97Dic13—21no—
98Dic13—21no—
99Dic13—42no—
100Dic13#10212yes—
101C2×#41—261no—
102C2×M16—261no—
103C22×C8—261no—
104C4⋊Q8—131no—
105#127C2×D1311yescharacteristic
106#124—261no—
107#121—132no—
108#121—261no—
109C4×D4—132no—
110C4×D4—261no—
111C2×C42—131no—
112C4⋊C8—131no—
113C4⋊C8—131no—
114C4⋊C8—261no—
115C4⋊C8—261no—
116C4⋊C8C2×D1311yescharacteristic
117C4⋊C8C2×D1311yescharacteristic
118C2×C13—82no—
119C2×C13#41311yescharacteristic
120C2×C13C2×#10211yescharacteristic
121C2×C13#41711yescharacteristic
122D13—22no—
123#41—522no—
124#41—522no—
125C2×Q8—261no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—262no—
129C2×D4C4×D1312yes—
130C22×C4—131no—
131C22×C4—131no—
132C22×C4—131no—
133C22×C4—262no—
134M16—522no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—261no—
138C2×C8—261no—
139C2×C8—522no—
140C4⋊C4—132no—
141C4⋊C4—261no—
142C22⋊C4—262no—
143C22⋊C4—262no—
144C42—131no—
145C42—131no—
146C42—131no—
147C42C22×D1311yescharacteristic
148C13#154711yescharacteristic, complemented, Sylow
149C23—22no—
150C23—131no—
151Q8—521no—
152Q8—521no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—524no—
159C2×C4—131no—
160C2×C4—132no—
161C2×C4—132no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—261no—
165C2×C4—261no—
166C2×C4—262no—
167C2×C4—521no—
168C2×C4—524no—
169C2×C4C2×C4×D1311yescharacteristic
170C2×C4D4×D1311yescharacteristic
171C2×C4D4×D1311yescharacteristic
172C8—41no—
173C8—41no—
174C8—521no—
175C8—521no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—132no—
180C22—261no—
181C22—261no—
182C22C22⋊C4×D1311yescharacteristic
183C4—21no—
184C4—132no—
185C4—261no—
186C4—261no—
187C4—522no—
188C4D8×D1311yescharacteristic
189C4#8816511yescharacteristic
190C4SD16×D1311yescharacteristic
191C4#8816911yescharacteristic
192C2—82no—
193C2—262no—
194C2#1171840611yescharacteristic
195C2D13×#10211yescharacteristic
196C2#1171843211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#331C2
socleC22×C13C2×C22⋊C4
prime radical#11719421C2
cosocleC42×C13C23
hypercenter#331D13
hypocenterC13#1547
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #11718498C2semidirect
3. D13×C4⋊C8C2semidirect
4. C13×#331C2semidirect
5. #11718136C2semidirect
6. #11718078C2semidirect
7. #11718074C2semidirect
84. #331D13semidirect
148. C13#1547semidirect

Maximal subgroups

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

subgroupindex
#117194212
#117184982
D13×C4⋊C82
C13×#3312
#117181362
#117180782
#117180742
#154713