Finite Group Databasebeta

← #16782185

Subgroups — #16782185

Order 3328.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130562C212yesmaximal
2#13129712C214yesmaximal, complemented
3#13117239C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88110C2214yes—
9#11718638C2212yes—
10#11718637C412yes—
11#11718603—22no—
12C4×#6101—22no—
13#11718290—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13D412yes—
16C22×#1057—24no—
17C13×#117—42no—
18C2×C13×C4⋊C4C2×C412yes—
19C2×C13×C22⋊C4—21no—
20C2×C42×C13—21no—
21C2×C22⋊Dic13—21no—
22#88180—42no—
23C2×C4⋊Dic13C2×C412yes—
24C2×#6101—22no—
25C2×#6101—22no—
26C2×C4×Dic13—24no—
27C2×C4×Dic13—21no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13D412yes—
30C2×C4×Dic13C2311yescharacteristic
31C22⋊#1057—28no—
32#88110—28no—
33#88071—24no—
34#8722—131nomaximal, Sylow
35C24×C13C22⋊C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13C22⋊C411yescharacteristic
41C22×C4×C13C22×C411yescharacteristic
42C22×Dic13—24no—
43C22×Dic13—24no—
44C22×Dic13—22no—
45C22×Dic13—42no—
46C22×Dic13C22⋊C412yes—
47C22×Dic13C2×D412yes—
48C2×#1057—28no—
49C2×#1057—44no—
50C2×#1057—44no—
51C13×C4⋊C4—42no—
52C13×C22⋊C4—42no—
53C42×C13—42no—
54C22⋊Dic13—42no—
55C4⋊Dic13—42no—
56#6101—44no—
57#6101—44no—
58C4×Dic13—22no—
59C4×Dic13—24no—
60C4×Dic13—42no—
61C4×Dic13#4114yes—
62#2285—131no—
63#1749—132no—
64#1295—134no—
65C23×C13—21no—
66C23×C13—21no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13#10012yes—
70C23×C13C2×C22⋊C411yescharacteristic
71C2×C4×C13—28no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13#10112yes—
80C2×C4×C13#11712yes—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—48no—
86C2×Dic13—42no—
87C2×Dic13—42no—
88C2×Dic13—42no—
89C2×Dic13#10414yes—
90C2×Dic13#12314yes—
91#1057—48no—
92C2×#117—131no—
93C2×#117#26111yescharacteristic
94C22×C42—131no—
95C2×C22⋊C8—262no—
96C2×#97—134no—
97#384—132no—
98#382—132no—
99#380—262no—
100C4×C4⋊C4—262no—
101#336—262no—
102C22×C13—22no—
103C22×C13—24no—
104C22×C13—41no—
105C22×C13—42no—
106C22×C13—41no—
107C22×C13#38111yescharacteristic
108C22×C13C2×#10011yescharacteristic
109C22×C13C2×#10111yescharacteristic
110C22×C13C2×#10412yes—
111C22×C13#42112yes—
112C4×C13—22no—
113C4×C13—22no—
114C4×C13—82no—
115Dic13—24no—
116Dic13—24no—
117Dic13—82no—
118C23×C4—132no—
119C23×C4C2×#26111yescharacteristic
120C22×C8—264no—
121#117—42no—
122#117—522no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—262no—
125C2×C4⋊C4—262no—
126C2×C4⋊C4C2×#26112yes—
127C2×C22⋊C4—21no—
128C2×C22⋊C4—261no—
129C2×C42—21no—
130C2×C42—131no—
131C2×C42—132no—
132C2×C42—131no—
133C2×C42—264no—
134C2×C42—261no—
135C22⋊C8—268no—
136#97—268no—
137#95—264no—
138C2×C13—42no—
139C2×C13#152611yescharacteristic
140C2×C13#153012yes—
141C2×C13#153711yescharacteristic
142C2×C13#182111yescharacteristic
143C2×C13#182612yes—
144C24C22⋊#26111yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—132no—
150C22×C4—132no—
151C22×C4—264no—
152C22×C4—264no—
153C22×C4—262no—
154C22×C4—522no—
155C22×C4C22⋊#26111yescharacteristic
156C22×C4C22×#26111yescharacteristic
157C2×C8—268no—
158C2×C8—524no—
159C2×C8—524no—
160C4⋊C4—42no—
161C4⋊C4—522no—
162C4⋊C4—524no—
163C4⋊C4—524no—
164C22⋊C4—42no—
165C22⋊C4—522no—
166C42—42no—
167C42—134no—
168C42—264no—
169C42—262no—
170C42—522no—
171C13#872211yescharacteristic, complemented, Sylow
172C23—21no—
173C23—21no—
174C23—22no—
175C23—22no—
176C23#8812112yes—
177C23C2×C22⋊#26111yescharacteristic
178C2×C4—28no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—134no—
187C2×C4—134no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—528no—
193C2×C4—522no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4#8811312yes—
197C2×C4#8823712yes—
198C8—528no—
199C22—24no—
200C22—22no—
201C22—41no—
202C22—41no—
203C22—42no—
204C22C2×#8811311yescharacteristic
205C22#1171913511yescharacteristic
206C22D13⋊#10412yes—
207C22#1171916612yes—
208C22C2×#8812111yescharacteristic
209C4—22no—
210C4—22no—
211C4—82no—
212C4—264no—
213C4—264no—
214C4—1042no—
215C2—42no—
216C2#1313029311yescharacteristic
217C2#1313030512yes—
218C2#1313032711yescharacteristic
219C2#1313073511yescharacteristic
220C2#1313074412yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8722
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129712C2semidirect
171. C13#8722semidirect

Maximal subgroups

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

subgroupindex
#131305622
#131297122
#131172392
#872213