Finite Group Databasebeta

← #13113369

Subgroups — #13113369

Order 1664.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C13×C22⋊Q8C211yesmaximal, characteristic
2#11718872C211yesmaximal, characteristic
3#11718868C211yesmaximal, characteristic
4#11718130C214yesmaximal, complemented
5C22×Q8×C13C411yescharacteristic, complemented
6C23×C4×C13C2211yescharacteristic
7C13×C22⋊Q8—21no—
8C13×C22⋊Q8—21no—
9C13×C22⋊Q8C412yescomplemented
10C13×C22⋊Q8C2212yes—
11C2×C13×C4⋊C4—21no—
12C2×C13×C4⋊C4C411yescharacteristic, complemented
13C2×C13×C22⋊C4—21no—
14C2×C22⋊Dic13—21no—
15C2×#6099—21no—
16#88071—21no—
17#88071C2212yes—
18C22⋊#1055—21no—
19C22⋊#1055C2212yes—
20C24×C13D411yescharacteristic
21C2×Q8×C13—21no—
22C2×Q8×C13—42no—
23C2×Q8×C13C2×C412yes—
24C22×C4×C13—21no—
25C22×C4×C13—21no—
26C22×C4×C13—42no—
27C22×C4×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C22×C4×C13D411yescharacteristic
30C22×C4×C13D411yescharacteristic
31C22×C4×C13D411yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×Dic13—22no—
34C13×C4⋊C4—22no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4—22no—
37C13×C4⋊C4C2×C412yes—
38C13×C22⋊C4—22no—
39C13×C22⋊C4—22no—
40C22⋊Dic13—42no—
41#6099—42no—
42C2×#1055—22no—
43#1511—131nomaximal, Sylow
44C23×C13—22no—
45C23×C13—22no—
46C23×C13—41no—
47C23×C13C22⋊C411yescharacteristic
48C23×C13C22⋊C411yescharacteristic
49C23×C13C2×D411yescharacteristic
50Q8×C13—42no—
51Q8×C13—42no—
52C2×C4×C13—22no—
53C2×C4×C13—22no—
54C2×C4×C13—22no—
55C2×C4×C13—22no—
56C2×C4×C13—41no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13—42no—
61C2×C4×C13—42no—
62C2×C4×C13C22⋊C411yescharacteristic
63C2×C4×C13C22⋊C411yescharacteristic
64C2×C4×C13C22×C411yescharacteristic
65C2×C4×C13C2×D411yescharacteristic
66C2×Dic13—42no—
67C2×Dic13—42no—
68C2×Dic13—42no—
69#1055—42no—
70C2×C22⋊Q8D1311yescharacteristic
71#407—131no—
72#381—131no—
73#328—134no—
74C22×C13—21no—
75C22×C13—21no—
76C22×C13—21no—
77C22×C13—21no—
78C22×C13—21no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13—44no—
82C22×C13#9912yes—
83C22×C13C2×C22⋊C411yescharacteristic
84C22×C13#13712yes—
85C4×C13—21no—
86C4×C13—21no—
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—42no—
90C4×C13—42no—
91Dic13—82no—
92C22×Q8Dic1311yescharacteristic, complemented
93C23×C4C2×D1311yescharacteristic
94C2×M16—261no—
95C22⋊Q8—21no—
96C22⋊Q8—21no—
97C22⋊Q8Dic1312yescomplemented
98C22⋊Q8C2×D1312yes—
99C2×C4⋊C4—21no—
100C2×C4⋊C4Dic1311yescharacteristic, complemented
101C2×C22⋊C4—21no—
102C2×C22⋊C4—261no—
103C22⋊C8—132no—
104C22⋊C8—261no—
105#95—132no—
106#95—261no—
107C2×C13—22no—
108C2×C13—22no—
109C2×C13—41no—
110C2×C13C2×#9911yescharacteristic
111C2×C13#41911yescharacteristic
112C2×C13#42111yescharacteristic
113C24C22⋊D1311yescharacteristic
114C2×Q8—21no—
115C2×Q8—42no—
116C2×Q8C2×Dic1312yes—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—42no—
120C22×C4—262no—
121C22×C4C2×Dic1311yescharacteristic
122C22×C4C2×Dic1311yescharacteristic
123C22×C4C22⋊D1311yescharacteristic
124C22×C4C22⋊D1311yescharacteristic
125C22×C4C22⋊D1311yescharacteristic
126C22×C4C22×D1311yescharacteristic
127M16—522no—
128C2×C8—262no—
129C4⋊C4—22no—
130C4⋊C4—21no—
131C4⋊C4—22no—
132C4⋊C4C2×Dic1312yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—522no—
136C13#151111yescharacteristic, complemented, Sylow
137C23—22no—
138C23—22no—
139C23—41no—
140C23C22⋊Dic1311yescharacteristic
141C23C22⋊Dic1311yescharacteristic
142C23C2×C22⋊D1311yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—522no—
156C2×C4—522no—
157C2×C4—522no—
158C2×C4C22⋊Dic1311yescharacteristic
159C2×C4C22⋊Dic1311yescharacteristic
160C2×C4C22×Dic1311yescharacteristic
161C2×C4C2×C22⋊D1311yescharacteristic
162C8—522no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#8807412yes—
172C22#8819612yes—
173C22C2×C22⋊Dic1311yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—42no—
179C4—42no—
180C4—1042no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#8807411yescharacteristic
185C2#1171888611yescharacteristic
186C2#1171889711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC2×C13×C22⋊Q8C2
socleC22×C13C2×C22⋊C4
prime radicalC24×C13D4
cosocleC22×C4×C13C23
hypercenterC2×C22⋊Q8D13
hypocenterC13#1511
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11718130C2semidirect
5. C22×Q8×C13C4semidirect
9. C13×C22⋊Q8C4semidirect
12. C2×C13×C4⋊C4C4semidirect
92. C22×Q8Dic13semidirect
97. C22⋊Q8Dic13semidirect
100. C2×C4⋊C4Dic13semidirect
136. C13#1511semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
#117188722
#117188682
#117181302
#151113