Finite Group Databasebeta

← #13131016

Subgroups — #13131016

Order 1664.

260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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×#125C211yesmaximal, characteristic
2C4×C4⋊#261C211yesmaximal, characteristic
3D13⋊(C4⋊C8)C211yesmaximal, characteristic
4#11718246C212yesmaximal
5#11718246C212yesmaximal
6C2×C4⋊#261C2212yes—
7C2×C4×#261—21no—
8C2×D13⋊C8C2212yes—
9C13×#125C411yescharacteristic, complemented
10C4⋊C4×D13—21no—
11C4⋊C4×D13—21no—
12C4⋊C4×D13C2211yescharacteristic
13C4⋊C4×D13C2211yescharacteristic
14#88144C411yescharacteristic, complemented
15#88144C411yescharacteristic, complemented
16#88143—21no—
17#88143—21no—
18C42×D13C2211yescharacteristic
19#88124C411yescharacteristic, complemented
20(C2×#261)⋊C4—21no—
21#88112—21no—
22C4⋊#1057—21no—
23C22×#261—22no—
24C2×C4×D13—21no—
25C2×C4×D13—21no—
26C2×C4×D13D411yescharacteristic
27C2×C4×D13D411yescharacteristic
28C2×C4×D13C2311yescharacteristic
29C2×#1057—22no—
30C4⋊#261—22no—
31C4⋊#261Q814yes—
32C4×#261—42no—
33D13⋊C8—24no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4C2×C411yescharacteristic
37C13×C4⋊C4C2×C411yescharacteristic
38C42×C13C2×C411yescharacteristic
39C4⋊Dic13—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13C2×C411yescharacteristic
42C4⋊Dic13C2×C411yescharacteristic
43#6101—21no—
44#6101—21no—
45#6101—21no—
46#6101—21no—
47#6101—21no—
48#6101—21no—
49C4×Dic13C2×C411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13D411yescharacteristic
52#1989—131nomaximal, Sylow
53C22×D13C2×D411yescharacteristic
54C2×#261—24no—
55C2×#261—42no—
56C2×#261—42no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C2×Dic13—21no—
63C2×Dic13—21no—
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67C4×D13—22no—
68C4×D13—21no—
69C4×D13—21no—
70C4×D13—42no—
71C4×D13—41no—
72C4×D13—41no—
73C4×D13C2×Q812yes—
74C4×D13#4112yes—
75#1057—42no—
76C2×#125—131no—
77C2×C4⋊C8—131no—
78C4×C4⋊C4—131no—
79#340—132no—
80#340—132no—
81C22×C13C2×C22⋊C411yescharacteristic
82C2×D13C22⋊Q812yes—
83C2×D13#13512yes—
84C2×D13AGL(1,ℤ/8)11yescharacteristic
85C2×D13#13711yescharacteristic
86#261—44no—
87C4×C13—21no—
88C4×C13—21no—
89C4×C13—41no—
90C4×C13—41no—
91C4×C13C4×Q812yes—
92Dic13—21no—
93Dic13—21no—
94Dic13—41no—
95Dic13—41no—
96Dic13#12411yescharacteristic
97Dic13C4⋊Q811yescharacteristic
98C22×C8—132no—
99#125—131no—
100#125—131no—
101#125—131no—
102#125—261no—
103#125—261no—
104#125#26111yescharacteristic, complemented
105C2×C4⋊C4—132no—
106C2×C4⋊C4—131no—
107C2×C4⋊C4—131no—
108C2×C4⋊C4—261no—
109C2×C4⋊C4—261no—
110C2×C42—131no—
111C2×C42—261no—
112C4⋊C8—261no—
113C4⋊C8—261no—
114#95—261no—
115C2×C13#39111yescharacteristic
116C2×C13#41611yescharacteristic
117C2×C13#41711yescharacteristic
118D13#47812yes—
119D13#47912yes—
120C22×C4—131no—
121C22×C4—131no—
122C22×C4—131no—
123C22×C4—261no—
124C22×C4—261no—
125C22×C4—262no—
126C2×C8—262no—
127C2×C8—264no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—134no—
131C4⋊C4—131no—
132C4⋊C4—131no—
133C4⋊C4—261no—
134C4⋊C4—261no—
135C4⋊C4—261no—
136C4⋊C4—261no—
137C4⋊C4—261no—
138C4⋊C4—261no—
139C4⋊C4—262no—
140C4⋊C4—261no—
141C4⋊C4—261no—
142C4⋊C4C2×#26111yescharacteristic
143C4⋊C4C2×#26111yescharacteristic
144C42—131no—
145C42—131no—
146C42—131no—
147C42—522no—
148C42C2×#26111yescharacteristic
149C13#198911yescharacteristic, complemented, Sylow
150C23—131no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—131no—
154C2×C4—132no—
155C2×C4—132no—
156C2×C4—131no—
157C2×C4—131no—
158C2×C4—261no—
159C2×C4—261no—
160C2×C4—262no—
161C2×C4—264no—
162C2×C4—261no—
163C2×C4—261no—
164C2×C4—521no—
165C2×C4—521no—
166C2×C4—522no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22⋊#26111yescharacteristic
171C2×C4C22×#26111yescharacteristic
172C8—522no—
173C22—132no—
174C22—131no—
175C22—131no—
176C22—132no—
177C22C2×C22⋊#26111yescharacteristic
178C4—21no—
179C4—21no—
180C4—41no—
181C4—41no—
182C4—131no—
183C4—131no—
184C4—261no—
185C4—261no—
186C4—524no—
187C4—521no—
188C4—521no—
189C4Q8×#26112yes—
190C2—132no—
191C2—132no—
192C2(C2×#261)⋊Q811yescharacteristic
193C2#1171916411yescharacteristic
194C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#125C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenter#125#261
hypocenterC13#1989
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C13×#125C4semidirect
14. #88144C4semidirect
15. #88144C4semidirect
19. #88124C4semidirect
104. #125#261semidirect
149. C13#1989semidirect

Maximal subgroups

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

subgroupindex
D13×#1252
C4×C4⋊#2612
D13⋊(C4⋊C8)2
#117182462
#198913