Finite Group Databasebeta

← #16777126

Subgroups — #16777126

Order 3328.

262 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 102 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⋊(C4⋊C16)C211yesmaximal, characteristic
2C8×D13⋊C8C211yesmaximal, characteristic
3D13×C4⋊C16C211yesmaximal, characteristic
4C2×D13⋊C16—21no—
5C4×D13⋊C8C411yescharacteristic
6C4×D13⋊C8C411yescharacteristic
7C2×C16×D13—21no—
8C4×C8×D13C2211yescharacteristic
9#11718260—21no—
10C8×#1057—21no—
11C8×#1057—21no—
12C4⋊#6092C412yes—
13C13×C4⋊C16C411yescharacteristic
14#11718093—21no—
15C4⋊#6090C411yescharacteristic
16C2×D13⋊C8—21no—
17C2×D13⋊C8C812yes—
18C2×C8×D13D411yescharacteristic
19C2×C8×D13Q811yescharacteristic
20C42×D13C2×C411yescharacteristic
21C4×#1057—21no—
22C4×#1057—21no—
23C4×#1057—21no—
24C4×#1057C812yes—
25C2×#6092—22no—
26D13⋊C16—41no—
27D13⋊C16—41no—
28C2×C13×C16—21no—
29C4×C8×C13C2×C411yescharacteristic
30C8×Dic13D411yescharacteristic
31C8×Dic13D411yescharacteristic
32C2×#6090—21no—
33C4×#1055C2×C411yescharacteristic
34C16×D13—41no—
35C16×D13—41no—
36#7151—131nomaximal, Sylow
37C2×C4×D13C4⋊C411yescharacteristic
38C2×C4×D13C2×C811yescharacteristic
39C2×C4×D13M1611yescharacteristic
40C2×#1057—22no—
41C2×#1057—22no—
42D13⋊C8—24no—
43D13⋊C8—22no—
44D13⋊C8C1614yescomplemented
45C2×C8×C13C22⋊C411yescharacteristic
46C2×C8×C13C4⋊C411yescharacteristic
47C42×C13C4211yescharacteristic
48C4×Dic13C22⋊C411yescharacteristic
49C4×Dic13C2×C811yescharacteristic
50C4×Dic13M1611yescharacteristic
51C2×#1055C22⋊C411yescharacteristic
52C2×#1055C4⋊C411yescharacteristic
53C8×D13—21no—
54C8×D13—21no—
55C8×D13D811yescharacteristic
56C8×D13SD1611yescharacteristic
57C8×D13SD1611yescharacteristic
58C8×D13Q1611yescharacteristic
59#6092—42no—
60C13×C16—41no—
61#6090—41no—
62C2×C4⋊C16—131no—
63C2×C4⋊C16—131no—
64C2×C82—131no—
65C22×D13C4⋊C811yescharacteristic
66C2×C4×C13#9511yescharacteristic
67C2×C4×C13C4×C811yescharacteristic
68C2×C4×C13#9711yescharacteristic
69C2×Dic13C22⋊C811yescharacteristic
70C2×Dic13C22⋊C811yescharacteristic
71C2×Dic13C4⋊C811yescharacteristic
72C4×D13—22no—
73C4×D13#10611yescharacteristic
74C4×D13#10711yescharacteristic
75C4×D13#10811yescharacteristic
76C4×D13#10811yescharacteristic
77C4×D13C2×C1612yes—
78C4×D13M3212yes—
79#1057—24no—
80#1057—24no—
81C8×C13—21no—
82C8×C13#10211yescharacteristic
83C8×C13#10311yescharacteristic
84#1055—21no—
85#1055#10211yescharacteristic
86#1055#10311yescharacteristic
87C22×C16—261no—
88C22×C16—261no—
89C2×C4×C8—131no—
90C2×C4×C8—131no—
91C2×C4×C8—131no—
92C4⋊C16—132no—
93C4⋊C16—131no—
94C4⋊C16—261no—
95C4⋊C16—261no—
96C4⋊C16#26111yescharacteristic
97C82—261no—
98C82—261no—
99C22×C13#33611yescharacteristic
100C2×D13#33411yescharacteristic
101C2×D13#33511yescharacteristic
102C2×D13C4⋊C1612yes—
103C2×D13#36412yes—
104C4×C13—21no—
105C4×C13#34011yescharacteristic
106C4×C13#34111yescharacteristic
107C4×C13C4×C1611yescharacteristic
108C4×C13#34611yescharacteristic
109Dic13—21no—
110Dic13#33411yescharacteristic
111Dic13#33511yescharacteristic
112Dic13C22⋊C1612yes—
113C22×C8—131no—
114C22×C8—132no—
115C22×C8—131no—
116C22×C8—261no—
117C2×C42—131no—
118C2×C16—21no—
119C2×C16—262no—
120C2×C16—261no—
121C2×C16—521no—
122C2×C16—521no—
123C2×C16—521no—
124C2×C16—521no—
125C4×C8—131no—
126C4×C8—131no—
127C4×C8—132no—
128C4×C8—131no—
129C4×C8—261no—
130C4×C8—261no—
131C4×C8—261no—
132C4×C8C2×#26111yescharacteristic
133C2×C13#127711yescharacteristic
134C2×C13#137411yescharacteristic
135C2×C13#137611yescharacteristic
136D13#136712yes—
137D13#137012yes—
138C22×C4—131no—
139C22×C4—131no—
140C22×C4—131no—
141C2×C8—131no—
142C2×C8—131no—
143C2×C8—131no—
144C2×C8—131no—
145C2×C8—131no—
146C2×C8—134no—
147C2×C8—131no—
148C2×C8—261no—
149C2×C8—261no—
150C2×C8—262no—
151C2×C8—262no—
152C2×C8—262no—
153C2×C8—264no—
154C2×C8C4⋊#26111yescharacteristic
155C2×C8C22⋊#26111yescharacteristic
156C42—131no—
157C42—131no—
158C42—131no—
159C42C4×#26111yescharacteristic
160C16—41no—
161C16—522no—
162C16—521no—
163C13#715111yescharacteristic, complemented, Sylow
164C23—131no—
165C2×C4—131no—
166C2×C4—131no—
167C2×C4—132no—
168C2×C4—132no—
169C2×C4—131no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—262no—
175C2×C4C8×#26111yescharacteristic
176C2×C4#8810011yescharacteristic
177C2×C4(C2×#261)⋊C411yescharacteristic
178C8—21no—
179C8—131no—
180C8—131no—
181C8—264no—
182C8—264no—
183C8—261no—
184C8#8811511yescharacteristic
185C8#8811711yescharacteristic
186C22—132no—
187C22—132no—
188C22—131no—
189C22—131no—
190C22(C2×#261)⋊C811yescharacteristic
191C4—21no—
192C4—132no—
193C4—131no—
194C4—131no—
195C4—261no—
196C4C16×#26111yescharacteristic
197C4#1171821611yescharacteristic
198C4#1171824611yescharacteristic
199C4#1171827311yescharacteristic
200C2—132no—
201C2—132no—
202C2#1312966511yescharacteristic
203C2(C2×#261)⋊C1611yescharacteristic
204C2#1312987911yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC4×C13C4×C16
FrattiniC4×C8C2×#261
FittingC13×C4⋊C16C4
socleC22×C13#336
prime radicalC22×D13C4⋊C8
cosocleC4×C8×D13C22
hypercenterC4⋊C16#261
hypocenterC13#7151
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
44. D13⋊C8C16semidirect
163. C13#7151semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C4⋊C16)2
C8×D13⋊C82
D13×C4⋊C162
#715113