Finite Group Databasebeta

← #13130741

Subgroups — #13130741

Order 1664.

300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D13×#117C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic
3D13⋊(C22⋊C8)C211yesmaximal, characteristic
4#11718246C212yesmaximal, complemented
5#11718246C212yesmaximal, complemented
6C22×C4×D13C2211yescharacteristic
7C2×C22⋊#261—21no—
8C2×C4⋊#261C2212yes—
9C2×D13⋊C8C2212yes—
10C13×#117C411yescharacteristic, complemented
11#88180C411yescharacteristic, complemented
12#88146C411yescharacteristic, complemented
13#88146C411yescharacteristic, complemented
14C4⋊C4×D13C2211yescharacteristic
15C4⋊C4×D13C2211yescharacteristic
16C22⋊C4×D13—21no—
17#88131—21no—
18#88126—21no—
19C42×D13—21no—
20C22⋊#1057—21no—
21(C2×#261)⋊C4—21no—
22#88111—21no—
23C23×D13D411yescharacteristic
24C22×#261—22no—
25C22×C4×C13C2×C411yescharacteristic
26C22×Dic13D411yescharacteristic
27C2×C4×D13—24no—
28C2×C4×D13—21no—
29C2×C4×D13—21no—
30C2×C4×D13C2×C411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×C4×D13C2311yescharacteristic
34C22⋊#261—42no—
35C2×#1057—22no—
36C4⋊#261—24no—
37D13⋊C8—24no—
38C13×C4⋊C4C2×C411yescharacteristic
39C13×C4⋊C4C2×C411yescharacteristic
40C13×C22⋊C4—21no—
41C42×C13—21no—
42C22⋊Dic13—21no—
43#6103—21no—
44#6103—21no—
45C4⋊Dic13C2×C411yescharacteristic
46C4⋊Dic13C2×C411yescharacteristic
47#6101—21no—
48#6101—21no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51C4×Dic13—21no—
52#1825—131nomaximal, Sylow
53C23×C13C22⋊C411yescharacteristic
54C22×D13—22no—
55C22×D13—22no—
56C22×D13—21no—
57C22×D13—21no—
58C22×D13C22⋊C411yescharacteristic
59C22×D13C2×D411yescharacteristic
60C2×#261—42no—
61C2×#261—42no—
62C2×#261—42no—
63C2×C4×C13—22no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13C22⋊C411yescharacteristic
67C2×C4×C13C22×C411yescharacteristic
68C2×Dic13—22no—
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13C22⋊C411yescharacteristic
72C2×Dic13C2×D411yescharacteristic
73C4×D13—22no—
74C4×D13—22no—
75C4×D13—22no—
76C4×D13—42no—
77C4×D13—41no—
78C4×D13—41no—
79C4×D13#4114yes—
80#1057—42no—
81C2×#117—131no—
82C2×C22⋊C8—131no—
83#380—131no—
84#340—132no—
85#340—132no—
86C22×C13—21no—
87C22×C13—21no—
88C22×C13—21no—
89C22×C13C2×C22⋊C411yescharacteristic
90C2×D13—21no—
91C2×D13—21no—
92C2×D13—21no—
93C2×D13—42no—
94C2×D13—42no—
95C2×D13#12312yes—
96C2×D13#13512yes—
97C2×D13AGL(1,ℤ/8)11yescharacteristic
98C2×D13#13711yescharacteristic
99#261—82no—
100C4×C13—21no—
101C4×C13—41no—
102C4×C13—41no—
103C4×C13#11712yes—
104Dic13—21no—
105Dic13—41no—
106Dic13—41no—
107Dic13#12312yes—
108C23×C4—131no—
109C22×C8—132no—
110#117—131no—
111#117—131no—
112#117—131no—
113#117—261no—
114#117—261no—
115#117#26111yescharacteristic, complemented
116C2×C4⋊C4—131no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—132no—
119C2×C22⋊C4—261no—
120C2×C22⋊C4—261no—
121C2×C42—261no—
122C22⋊C8—261no—
123C22⋊C8—261no—
124#95—261no—
125C2×C13—41no—
126C2×C13#38111yescharacteristic
127C2×C13#41611yescharacteristic
128C2×C13#41711yescharacteristic
129D13—41no—
130D13#48212yes—
131D13#48512yes—
132C24—131no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—131no—
138C22×C4—264no—
139C22×C4—261no—
140C22×C4—261no—
141C22×C4—262no—
142C22×C4C2×#26111yescharacteristic
143C2×C8—262no—
144C2×C8—264no—
145C4⋊C4—131no—
146C4⋊C4—131no—
147C4⋊C4—261no—
148C4⋊C4—261no—
149C4⋊C4—264no—
150C4⋊C4C2×#26111yescharacteristic
151C4⋊C4C2×#26111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—261no—
154C22⋊C4—261no—
155C22⋊C4—261no—
156C22⋊C4—522no—
157C42—21no—
158C42—261no—
159C42—261no—
160C42—261no—
161C13#182511yescharacteristic, complemented, Sylow
162C23—131no—
163C23—131no—
164C23—261no—
165C23—262no—
166C23—261no—
167C23—262no—
168C23C22⋊#26111yescharacteristic
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—131no—
173C2×C4—134no—
174C2×C4—131no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—261no—
180C2×C4—261no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4—522no—
184C2×C4—522no—
185C2×C4—522no—
186C2×C4—522no—
187C2×C4C22⋊#26111yescharacteristic
188C2×C4C22×#26111yescharacteristic
189C8—522no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—132no—
194C22—131no—
195C22—131no—
196C22—132no—
197C22—261no—
198C22—261no—
199C22—261no—
200C22—522no—
201C22—522no—
202C22C2×C22⋊#26111yescharacteristic
203C4—21no—
204C4—41no—
205C4—41no—
206C4—132no—
207C4—261no—
208C4—521no—
209C4—521no—
210C4—1042no—
211C4#8823712yes—
212C2—41no—
213C2—132no—
214C2—132no—
215C2—521no—
216C2#1171913511yescharacteristic
217C2#1171916411yescharacteristic
218C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#117C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenter#117#261
hypocenterC13#1825
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11718246C2semidirect
5. #11718246C2semidirect
10. C13×#117C4semidirect
11. #88180C4semidirect
12. #88146C4semidirect
13. #88146C4semidirect
115. #117#261semidirect
161. C13#1825semidirect

Maximal subgroups

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

subgroupindex
D13×#1172
#117191362
D13⋊(C22⋊C8)2
#117182462
#182513