Finite Group Databasebeta

← #16782200

Subgroups — #16782200

Order 3328.

514 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#13130693C212yesmaximal
2#13129714C214yesmaximal, complemented
3#13117242C211yesmaximal, characteristic
4C2×#88146C412yes—
5C2×C42×D13C2211yescharacteristic
6C2×#88112C2214yes—
7C2×#88111—22no—
8C13×#382C411yescharacteristic
9#11718637C2212yes—
10#11718597C411yescharacteristic
11#11718328—22no—
12#11718310—22no—
13#11718290—22no—
14C22×C4×D13C2×C411yescharacteristic
15C22×C4×D13D412yes—
16C22×#1057—24no—
17C2×C13×C4⋊C4C2×C412yes—
18C2×C42×C13C2×C411yescharacteristic
19C2×#6103—22no—
20C2×C4⋊Dic13C2×C412yes—
21C2×#6101—22no—
22C2×#6101—22no—
23C2×C4×Dic13—22no—
24C2×C4×Dic13D412yes—
25C2×C4×Dic13C2311yescharacteristic
26#88146—44no—
27C42×D13—24no—
28#88112—28no—
29#88111—44no—
30C13×#95—22no—
31#88071—22no—
32#8729—131nomaximal, Sylow
33C23×D13C22⋊C411yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13C22⋊C412yes—
36C22×C4×C13C22×C411yescharacteristic
37C22×Dic13—22no—
38C22×Dic13C22⋊C411yescharacteristic
39C22×Dic13C2×D412yes—
40C2×C4×D13—22no—
41C2×C4×D13—22no—
42C2×C4×D13—22no—
43C2×C4×D13—24no—
44C2×C4×D13—24no—
45C2×C4×D13—22no—
46C2×C4×D13—22no—
47C2×#1057—44no—
48C2×#1057—44no—
49C2×#1057—44no—
50C13×C4⋊C4—42no—
51C42×C13—22no—
52#6103—44no—
53C4⋊Dic13—42no—
54#6101—44no—
55#6101—42no—
56#6101—42no—
57C4×Dic13—24no—
58C4×Dic13—44no—
59C4×Dic13#4114yes—
60#2285—131no—
61#1797—132no—
62#1296—134no—
63C23×C13C2×C22⋊C411yescharacteristic
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—22no—
67C22×D13—22no—
68C22×D13#10012yes—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—42no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13#11712yes—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C2×Dic13—42no—
83C2×Dic13#10112yes—
84C2×Dic13#12314yes—
85C2×Dic13#13514yes—
86C2×Dic13AGL(1,ℤ/8)12yes—
87C2×Dic13#13712yes—
88C4×D13—28no—
89C4×D13—44no—
90C4×D13—44no—
91#1057—84no—
92C2×#117—132no—
93C22×C42—131no—
94C2×C4⋊C8—134no—
95C2×C22⋊C8—262no—
96#384—132no—
97#382—131no—
98#382#26111yescharacteristic
99#380—262no—
100C4×C4⋊C4—262no—
101#336—262no—
102C22×C13#38111yescharacteristic
103C22×C13C2×#10011yescharacteristic
104C22×C13C2×#10111yescharacteristic
105C22×C13#41612yes—
106C22×C13#41712yes—
107C2×D13—24no—
108C2×D13—22no—
109C2×D13—41no—
110C2×D13—41no—
111C2×D13—42no—
112C4×C13—22no—
113C4×C13—42no—
114C4×C13—82no—
115Dic13—22no—
116Dic13—82no—
117Dic13#48214yes—
118Dic13#48514yes—
119C23×C4—132no—
120C23×C4—131no—
121C22×C8—264no—
122#117—524no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—262no—
125C2×C4⋊C4—262no—
126C2×C4⋊C4C2×#26112yes—
127C2×C22⋊C4—262no—
128C2×C42—131no—
129C2×C42—132no—
130C2×C42—264no—
131C2×C42—262no—
132C2×C42C2×#26111yescharacteristic
133C4⋊C8—268no—
134C22⋊C8—524no—
135#95—22no—
136#95—262no—
137C2×C13#154411yescharacteristic
138C2×C13#155112yes—
139C2×C13#156111yescharacteristic
140C2×C13#182111yescharacteristic
141C2×C13#182512yes—
142D13—42no—
143C24—131no—
144C22×C4—22no—
145C22×C4—132no—
146C22×C4—131no—
147C22×C4—262no—
148C22×C4—262no—
149C22×C4—264no—
150C22×C4—262no—
151C22×C4—264no—
152C22×C4—262no—
153C22×C4—262no—
154C22×C4—262no—
155C22×C4C22⋊#26112yes—
156C22×C4C22×#26111yescharacteristic
157C2×C8—524no—
158C2×C8—524no—
159C2×C8—524no—
160C4⋊C4—42no—
161C4⋊C4—522no—
162C4⋊C4—522no—
163C4⋊C4—522no—
164C4⋊C4—524no—
165C22⋊C4—524no—
166C42—22no—
167C42—134no—
168C42—264no—
169C42—524no—
170C13#872911yescharacteristic, complemented, Sylow
171C23—132no—
172C23—261no—
173C23—261no—
174C23—262no—
175C23—262no—
176C23C2×C22⋊#26111yescharacteristic
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—134no—
186C2×C4—132no—
187C2×C4—132no—
188C2×C4—134no—
189C2×C4—132no—
190C2×C4—268no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—524no—
194C2×C4—524no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4#8823712yes—
199C8—1044no—
200C22—264no—
201C22—262no—
202C22—521no—
203C22—521no—
204C22—522no—
205C22#1171913511yescharacteristic
206C22D13⋊#10011yescharacteristic
207C22D13⋊#10111yescharacteristic
208C22#1171916412yes—
209C22#1171916512yes—
210C4—22no—
211C4—42no—
212C4—82no—
213C4—134no—
214C4—134no—
215C4—262no—
216C4—1042no—
217C2—522no—
218C2#1313034211yescharacteristic
219C2#1313035612yes—
220C2#1313037611yescharacteristic
221C2#1313073611yescharacteristic
222C2#1313074112yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#382#261
hypocenterC13#8729
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #13129714C2semidirect
170. C13#8729semidirect

Maximal subgroups

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

subgroupindex
#131306932
#131297142
#131172422
#872913