Finite Group Databasebeta

← #16782177

Subgroups — #16782177

Order 3328.

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

normal subgroups only

This group has 554 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#13130563C212yesmaximal
2#13129712C214yesmaximal, complemented
3D13×#382C211yesmaximal, characteristic
4C2×C4⋊C4×D13C412yes—
5C2×C42×D13C2211yescharacteristic
6C2×#88111—22no—
7C2×#88110C2214yes—
8C13×#382C411yescharacteristic
9#11718638C2212yes—
10#11718597C411yescharacteristic
11D13×#95—22no—
12#11718311—22no—
13#11718290—22no—
14C22×C4×D13—22no—
15C22×C4×D13C2×C411yescharacteristic
16C22×C4×D13D412yes—
17C22×#1057—24no—
18C2×C13×C4⋊C4C2×C412yes—
19C2×C42×C13C2×C411yescharacteristic
20C2×C4⋊Dic13C2×C412yes—
21C2×#6101—22no—
22C2×C4×Dic13D412yes—
23C2×C4×Dic13C2311yescharacteristic
24C4⋊C4×D13—44no—
25C42×D13—24no—
26#88111—28no—
27#88110—28no—
28C13×#95—22no—
29#88071—22no—
30#88071—24no—
31#8719—131nomaximal, Sylow
32C23×D13C22⋊C411yescharacteristic
33C22×C4×C13—22no—
34C22×C4×C13C22⋊C412yes—
35C22×C4×C13C22×C411yescharacteristic
36C22×Dic13—22no—
37C22×Dic13C22⋊C411yescharacteristic
38C22×Dic13C2×D412yes—
39C2×C4×D13—22no—
40C2×C4×D13—22no—
41C2×C4×D13—22no—
42C2×C4×D13—24no—
43C2×C4×D13—24no—
44C2×C4×D13—42no—
45C2×C4×D13—44no—
46C2×C4×D13—44no—
47C2×C4×D13—44no—
48C2×#1057—28no—
49C2×#1057—44no—
50C2×#1057—44no—
51C13×C4⋊C4—42no—
52C42×C13—22no—
53C4⋊Dic13—42no—
54#6101—44no—
55C4×Dic13—24no—
56C4×Dic13#4114yes—
57C2×#382—131no—
58#1749—132no—
59#1295—134no—
60C23×C13C2×C22⋊C411yescharacteristic
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—22no—
64C22×D13#10112yes—
65C22×D13#10414yes—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—42no—
72C2×C4×C13—42no—
73C2×C4×C13—42no—
74C2×C4×C13#11712yes—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—42no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C2×Dic13#10012yes—
83C2×Dic13#12314yes—
84C4×D13—28no—
85C4×D13—48no—
86C4×D13—88no—
87#1057—48no—
88C22×C4⋊C4—132no—
89C22×C42—131no—
90C2×C22⋊C8—262no—
91C2×#97—134no—
92#382—132no—
93#382—131no—
94#382—262no—
95#382#26111yescharacteristic
96C2×#95—262no—
97#336—262no—
98C22×C13#38111yescharacteristic
99C22×C13C2×#10011yescharacteristic
100C22×C13C2×#10111yescharacteristic
101C22×C13C2×#10412yes—
102C22×C13#42112yes—
103C2×D13—22no—
104C2×D13—24no—
105C2×D13—24no—
106C2×D13—22no—
107C2×D13#33014yes—
108C4×C13—22no—
109C4×C13—42no—
110C4×C13—82no—
111Dic13—22no—
112Dic13—24no—
113Dic13—82no—
114C23×C4—131no—
115C23×C4—132no—
116C23×C4—262no—
117C22×C8—264no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—262no—
120C2×C4⋊C4—524no—
121C2×C4⋊C4C2×#26112yes—
122C2×C42—131no—
123C2×C42—132no—
124C2×C42—264no—
125C2×C42C2×#26111yescharacteristic
126C22⋊C8—268no—
127#97—268no—
128#95—22no—
129#95—264no—
130#95—262no—
131C2×C13C2×#33011yescharacteristic
132C2×C13#152712yes—
133C2×C13#153411yescharacteristic
134C2×C13#182111yescharacteristic
135C2×C13#182612yes—
136D13—24no—
137C24—131no—
138C22×C4—22no—
139C22×C4—132no—
140C22×C4—131no—
141C22×C4—262no—
142C22×C4—264no—
143C22×C4—262no—
144C22×C4—264no—
145C22×C4—262no—
146C22×C4—262no—
147C22×C4—522no—
148C22×C4—524no—
149C22×C4—524no—
150C22×C4—524no—
151C22×C4C22⋊#26112yes—
152C22×C4C22×#26111yescharacteristic
153C2×C8—268no—
154C2×C8—524no—
155C2×C8—524no—
156C4⋊C4—42no—
157C4⋊C4—522no—
158C4⋊C4—524no—
159C42—22no—
160C42—134no—
161C42—264no—
162C13#871911yescharacteristic, complemented, Sylow
163C23—132no—
164C23—134no—
165C23—261no—
166C23—261no—
167C23—262no—
168C23C2×C22⋊#26111yescharacteristic
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—134no—
178C2×C4—132no—
179C2×C4—268no—
180C2×C4—261no—
181C2×C4—261no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—528no—
185C2×C4—522no—
186C2×C4—522no—
187C2×C4—522no—
188C2×C4—1048no—
189C2×C4#8823712yes—
190C8—528no—
191C22—134no—
192C22—264no—
193C22—262no—
194C22—262no—
195C22—264no—
196C22#1171913511yescharacteristic
197C22D13⋊#10011yescharacteristic
198C22D13⋊#10111yescharacteristic
199C22D13⋊#10412yes—
200C22#1171916612yes—
201C4—22no—
202C4—42no—
203C4—82no—
204C4—262no—
205C4—264no—
206C4—1042no—
207C2—264no—
208C2D13⋊#33011yescharacteristic
209C2#1313029612yes—
210C2#1313031911yescharacteristic
211C2#1313073611yescharacteristic
212C2#1313074412yes—
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#8719
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. #13129712C2semidirect
162. C13#8719semidirect

Maximal subgroups

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

subgroupindex
#131305632
#131297122
D13×#3822
#871913