Finite Group Databasebeta

← #13130742

Subgroups — #13130742

Order 1664.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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×#88146C211yesmaximal, characteristic
2C4×C22⋊#261C211yesmaximal, characteristic
3#11719127C211yesmaximal, characteristic
4#11718247C214yesmaximal, complemented
5C22×C4×D13C2211yescharacteristic
6C2×C22⋊#261—21no—
7C2×C4×#261C2212yes—
8C2×#6118C2212yes—
9C2×C13×C4⋊C4C411yescharacteristic, complemented
10C2×#6103—21no—
11C2×C4⋊Dic13C411yescharacteristic, complemented
12C2×C4×Dic13—21no—
13#88146—21no—
14#88146—21no—
15#88146C412yescomplemented
16#88146C2212yes—
17C22⋊#1057—21no—
18(C2×#261)⋊C4—21no—
19#88111—21no—
20C23×D13D411yescharacteristic
21C22×#261—22no—
22C22×C4×C13—21no—
23C22×C4×C13C2×C411yescharacteristic
24C22×Dic13—21no—
25C22×Dic13D411yescharacteristic
26C2×C4×D13—24no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13C2311yescharacteristic
31C22⋊#261—24no—
32C2×#1057—22no—
33C4×#261—24no—
34#6118—24no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4C2×C412yes—
37#6103—22no—
38#6103—22no—
39C4⋊Dic13—21no—
40C4⋊Dic13C2×C412yes—
41C4×Dic13—22no—
42C4×Dic13—22no—
43#1826—131nomaximal, Sylow
44C23×C13C22⋊C411yescharacteristic
45C22×D13—22no—
46C22×D13—22no—
47C22×D13—41no—
48C22×D13C22⋊C411yescharacteristic
49C22×D13C2×D411yescharacteristic
50C2×#261—24no—
51C2×#261—42no—
52C2×#261—42no—
53C2×C4×C13—22no—
54C2×C4×C13—22no—
55C2×C4×C13—42no—
56C2×C4×C13C22⋊C411yescharacteristic
57C2×C4×C13C22×C411yescharacteristic
58C2×Dic13—22no—
59C2×Dic13—22no—
60C2×Dic13—42no—
61C2×Dic13C22⋊C411yescharacteristic
62C2×Dic13C2×D411yescharacteristic
63C4×D13—22no—
64C4×D13—22no—
65C4×D13—22no—
66C4×D13#4114yes—
67#1057—42no—
68C2×#117—131no—
69#407—131no—
70C4×C22⋊C4—131no—
71#339—134no—
72C22×C13—21no—
73C22×C13—21no—
74C22×C13#10412yes—
75C22×C13C2×C22⋊C411yescharacteristic
76C2×D13—21no—
77C2×D13—21no—
78C2×D13—21no—
79C2×D13—21no—
80C2×D13—21no—
81C2×D13—44no—
82C2×D13#12312yes—
83#261—44no—
84C4×C13—21no—
85C4×C13—42no—
86C4×C13#11712yes—
87Dic13—21no—
88Dic13—42no—
89Dic13#12312yes—
90C23×C4—131no—
91C2×M16—132no—
92#117—132no—
93#117—132no—
94#117—261no—
95#117—261no—
96C2×C4⋊C4—131no—
97C2×C4⋊C4#26111yescharacteristic, complemented
98C2×C22⋊C4—261no—
99C2×C22⋊C4—261no—
100C2×C42—132no—
101C2×C42—261no—
102C22⋊C8—261no—
103C22⋊C8—261no—
104#95—261no—
105C2×C13—22no—
106C2×C13#38111yescharacteristic
107C2×C13C2×#10411yescharacteristic
108C2×C13#42111yescharacteristic
109D13—22no—
110D13—41no—
111C24—131no—
112C22×C4—21no—
113C22×C4—131no—
114C22×C4—131no—
115C22×C4—131no—
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—264no—
119C22×C4—262no—
120C22×C4—261no—
121C22×C4C2×#26111yescharacteristic
122M16—264no—
123C2×C8—262no—
124C4⋊C4—21no—
125C4⋊C4—132no—
126C4⋊C4—261no—
127C4⋊C4C2×#26112yes—
128C22⋊C4—262no—
129C22⋊C4—262no—
130C22⋊C4—264no—
131C42—262no—
132C42—262no—
133C42—264no—
134C13#182611yescharacteristic, complemented, Sylow
135C23—131no—
136C23—131no—
137C23—262no—
138C23—262no—
139C23—521no—
140C23C22⋊#26111yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—131no—
145C2×C4—134no—
146C2×C4—131no—
147C2×C4—262no—
148C2×C4—262no—
149C2×C4—262no—
150C2×C4—262no—
151C2×C4—264no—
152C2×C4—262no—
153C2×C4—522no—
154C2×C4—522no—
155C2×C4—522no—
156C2×C4C22⋊#26111yescharacteristic
157C2×C4C22×#26111yescharacteristic
158C8—522no—
159C22—21no—
160C22—21no—
161C22—132no—
162C22—261no—
163C22—261no—
164C22—261no—
165C22—261no—
166C22—261no—
167C22—524no—
168C22#8811612yes—
169C22C2×C22⋊#26111yescharacteristic
170C4—21no—
171C4—42no—
172C4—132no—
173C4—261no—
174C4—524no—
175C4—522no—
176C4#8823712yes—
177C2—22no—
178C2—262no—
179C2—521no—
180C2#1171913511yescharacteristic
181C2C2×#8811611yescharacteristic
182C2#1171915511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1826
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11718247C2semidirect
9. C2×C13×C4⋊C4C4semidirect
11. C2×C4⋊Dic13C4semidirect
15. #88146C4semidirect
97. C2×C4⋊C4#261semidirect
134. C13#1826semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C4×C22⋊#2612
#117191272
#117182472
#182613