Finite Group Databasebeta

← #16787041

Subgroups — #16787041

Order 3328.

446 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130087C212yesmaximal
2#13129780C214yesmaximal
3#13117320C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C2211yescharacteristic
6C22×C4×Dic13C411yescharacteristic
7#11719128—22no—
8#11718646—22no—
9#11718611C412yes—
10#11718611C2212yes—
11C4×C4⋊Dic13—22no—
12#11718305C2214yes—
13#11718285—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13C2×C412yes—
16C13×#117—24no—
17C2×C13×C4⋊C4—21no—
18C2×C13×C22⋊C4C2×C412yes—
19C2×C42×C13—21no—
20C2×C22⋊Dic13C2×C411yescharacteristic
21C2×C22⋊Dic13C2311yescharacteristic
22#88180—42no—
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13D412yes—
26C2×C4×Dic13—21no—
27C2×C4×Dic13—21no—
28C2×C4×Dic13—42no—
29C2×C4×Dic13D412yes—
30C22⋊#1057—24no—
31#88112—42no—
32#88110—42no—
33#88071—22no—
34#88071—22no—
35#11518—131nomaximal, Sylow
36C24×C13C22×C411yescharacteristic
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13C22⋊C411yescharacteristic
42C22×C4×C13C22⋊C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13—44no—
45C22×Dic13—42no—
46C22×Dic13C22⋊C412yes—
47C22×Dic13C2×D412yes—
48C2×#1057—44no—
49C13×C4⋊C4—24no—
50C13×C22⋊C4—22no—
51C13×C22⋊C4M1614yes—
52C42×C13—24no—
53C22⋊Dic13—41no—
54C22⋊Dic13—41no—
55C4⋊Dic13—42no—
56C4⋊Dic13—44no—
57C4⋊Dic13—44no—
58C4×Dic13—22no—
59C4×Dic13—22no—
60C4×Dic13—42no—
61C4×Dic13—42no—
62#2296—131no—
63#1464—132no—
64#1326—134no—
65C23×C13—21no—
66C23×C13—21no—
67C23×C13—42no—
68C23×C13C2×C22⋊C411yescharacteristic
69C23×C13C2×M1612yes—
70C2×C4×C13—28no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—24no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13#9912yes—
79C2×C4×C13#10112yes—
80C2×Dic13—24no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—42no—
84C2×Dic13—44no—
85C2×Dic13—42no—
86C2×Dic13—42no—
87C2×Dic13—42no—
88C2×Dic13—44no—
89#1057—84no—
90C2×#117—131no—
91C2×#117#26111yescharacteristic
92C22×C42—131no—
93#432—262no—
94#389—262no—
95#385—132no—
96#385—132no—
97C4×C4⋊C4—262no—
98#324—262no—
99#323—134no—
100C22×C13—22no—
101C22×C13—22no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13#40711yescharacteristic
106C22×C13C2×#9911yescharacteristic
107C22×C13C2×#10111yescharacteristic
108C4×C13—22no—
109C4×C13—22no—
110C4×C13—44no—
111Dic13—42no—
112Dic13—42no—
113Dic13—44no—
114C23×C4—132no—
115C23×C4C2×#26111yescharacteristic
116#117—24no—
117#117—522no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—262no—
121C2×C4⋊C4—262no—
122C2×C22⋊C4—131no—
123C2×C22⋊C4—131no—
124C2×C22⋊C4C2×#26112yes—
125C2×C42—21no—
126C2×C42—132no—
127C2×C42—261no—
128C2×C42—261no—
129C2×C42—522no—
130C4⋊C8—522no—
131C22⋊C8—264no—
132#97—522no—
133#95—262no—
134#95—262no—
135C2×C13—21no—
136C2×C13—21no—
137C2×C13—42no—
138C2×C13#146311yescharacteristic
139C2×C13#212012yes—
140C24C22×#26111yescharacteristic
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—132no—
146C22×C4—132no—
147C22×C4—262no—
148C22×C4—524no—
149C22×C4—522no—
150C22×C4C22⋊#26111yescharacteristic
151C22×C4C22⋊#26111yescharacteristic
152C2×C8—524no—
153C4⋊C4—24no—
154C4⋊C4—522no—
155C4⋊C4—524no—
156C4⋊C4—524no—
157C22⋊C4—22no—
158C22⋊C4—521no—
159C22⋊C4—521no—
160C22⋊C4#612214yes—
161C42—24no—
162C42—262no—
163C42—262no—
164C42—522no—
165C42—522no—
166C13#1151811yescharacteristic, complemented, Sylow
167C23—21no—
168C23—21no—
169C23—42no—
170C23C2×#612212yes—
171C23C2×C22⋊#26111yescharacteristic
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—24no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—264no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—522no—
184C2×C4—524no—
185C2×C4—522no—
186C2×C4—522no—
187C2×C4—522no—
188C2×C4—524no—
189C2×C4#8810712yes—
190C2×C4#8811312yes—
191C8—1044no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×#8810711yescharacteristic
198C22C2×#8811311yescharacteristic
199C22#1171916911yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—522no—
204C4—522no—
205C4—524no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2#1313008411yescharacteristic
210C2#1313108912yes—
subgroupG/H
centerC22C2×#88107
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
cosocleC2×C22⋊Dic13C23
hypercenterC2×#117#261
hypocenterC13#11518
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
166. C13#11518semidirect

Maximal subgroups

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

subgroupindex
#131300872
#131297802
#131173202
#1151813