Finite Group Databasebeta

← #16782173

Subgroups — #16782173

Order 3328.

554 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 112 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
3C2×#11718638C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88110C2214yes—
9C2×#88071—22no—
10#11718638—22no—
11#11718638C412yes—
12#11718638C2212yes—
13#11718290—22no—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C22×#1057—24no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—42no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C4⋊Dic13—21no—
23C2×C4⋊Dic13—42no—
24C2×C4⋊Dic13C2×C412yes—
25C2×C4×Dic13—24no—
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13D412yes—
28C2×C4×Dic13C2311yescharacteristic
29C22⋊#1057—28no—
30#88110—28no—
31#88071—24no—
32#88071—24no—
33#8718—131nomaximal, Sylow
34C24×C13C22⋊C411yescharacteristic
35C22×C4×C13—22no—
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—42no—
40C22×C4×C13—44no—
41C22×C4×C13C22⋊C411yescharacteristic
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—24no—
44C22×Dic13—24no—
45C22×Dic13—22no—
46C22×Dic13—42no—
47C22×Dic13—44no—
48C22×Dic13—42no—
49C22×Dic13C22⋊C412yes—
50C22×Dic13C2×D412yes—
51C2×#1057—28no—
52C2×#1057—44no—
53C2×#1057—44no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—42no—
56C4⋊Dic13—42no—
57C4⋊Dic13—42no—
58C4×Dic13—22no—
59C4×Dic13—24no—
60C4×Dic13#4114yes—
61C2×#382—131no—
62#1749—132no—
63#1295—134no—
64C23×C13—21no—
65C23×C13—21no—
66C23×C13—22no—
67C23×C13#10012yes—
68C23×C13#10414yes—
69C23×C13C2×C22⋊C411yescharacteristic
70C2×C4×C13—28no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—42no—
76C2×C4×C13—44no—
77C2×C4×C13—84no—
78C2×C4×C13#10112yes—
79C2×C4×C13#11712yes—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—48no—
86C2×Dic13—42no—
87C2×Dic13—44no—
88C2×Dic13—84no—
89C2×Dic13#12314yes—
90#1057—48no—
91C22×C4⋊C4—131no—
92C22×C4⋊C4#26111yescharacteristic
93C22×C42—131no—
94C2×C22⋊C8—262no—
95C2×#97—134no—
96#382—132no—
97#382—132no—
98#382—262no—
99C2×#95—262no—
100#336—262no—
101C22×C13—22no—
102C22×C13—24no—
103C22×C13—24no—
104C22×C13—22no—
105C22×C13#32914yes—
106C22×C13#38111yescharacteristic
107C22×C13C2×#10011yescharacteristic
108C22×C13C2×#10111yescharacteristic
109C22×C13C2×#10412yes—
110C22×C13#42112yes—
111C4×C13—22no—
112C4×C13—22no—
113C4×C13—82no—
114Dic13—24no—
115Dic13—42no—
116Dic13—82no—
117C23×C4—21no—
118C23×C4—132no—
119C23×C4—261no—
120C23×C4C2×#26111yescharacteristic
121C22×C8—264no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—261no—
126C2×C4⋊C4—522no—
127C2×C4⋊C4C2×#26112yes—
128C2×C42—131no—
129C2×C42—132no—
130C2×C42—131no—
131C2×C42—264no—
132C22⋊C8—268no—
133#97—268no—
134#95—264no—
135#95—264no—
136C2×C13—24no—
137C2×C13C2×#32911yescharacteristic
138C2×C13#152812yes—
139C2×C13#153311yescharacteristic
140C2×C13#182111yescharacteristic
141C2×C13#182612yes—
142C24C22⋊#26111yescharacteristic
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—44no—
148C22×C4—42no—
149C22×C4—132no—
150C22×C4—132no—
151C22×C4—264no—
152C22×C4—264no—
153C22×C4—262no—
154C22×C4—522no—
155C22×C4—524no—
156C22×C4—522no—
157C22×C4C22⋊#26111yescharacteristic
158C22×C4C22×#26111yescharacteristic
159C2×C8—268no—
160C2×C8—524no—
161C2×C8—524no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—522no—
165C4⋊C4—522no—
166C42—134no—
167C42—264no—
168C42—262no—
169C13#871811yescharacteristic, complemented, Sylow
170C23—21no—
171C23—21no—
172C23—22no—
173C23#8811614yes—
174C23#8812112yes—
175C23C2×C22⋊#26111yescharacteristic
176C2×C4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—44no—
183C2×C4—84no—
184C2×C4—134no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—528no—
191C2×C4—522no—
192C2×C4—524no—
193C2×C4—1044no—
194C2×C4#8811312yes—
195C2×C4#8823712yes—
196C8—528no—
197C22—24no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22#1171829314yes—
202C22C2×#8811311yescharacteristic
203C22#1171913511yescharacteristic
204C22C2×#8811612yes—
205C22#1171915512yes—
206C22C2×#8812111yescharacteristic
207C4—22no—
208C4—22no—
209C4—82no—
210C4—264no—
211C4—522no—
212C4—1042no—
213C2—24no—
214C2C2×#1171829311yescharacteristic
215C2#1313029812yes—
216C2#1313031711yescharacteristic
217C2#1313073511yescharacteristic
218C2#1313074212yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#8718
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129712C2semidirect
169. C13#8718semidirect

Maximal subgroups

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

subgroupindex
#131305622
#131297122
C2×#117186382
#871813