Finite Group Databasebeta

← #16778560

Subgroups — #16778560

Order 3328.

624 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 114 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#13130752C212yesmaximal, complemented
2#13129653C214yesmaximal, complemented
3#13117398C211yesmaximal, characteristic
4C2×#88147—22no—
5C2×#88147C412yes—
6C2×#88128C411yescharacteristic
7C2×#88112—22no—
8C13×#384C411yescharacteristic
9#11718649—22no—
10#11718649C2212yes—
11C42×Dic13C2211yescharacteristic
12#11718290—22no—
13#11718290C2214yes—
14C22×D52—22no—
15C22×D52C2×C412yes—
16C22×C4×D13—22no—
17C22×#1057—24no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4C2×C412yes—
20C2×C42×C13C2×C411yescharacteristic
21C2×#6103—22no—
22C2×#6103—24no—
23C2×C4×Dic13C2×C411yescharacteristic
24C2×C4×Dic13D412yes—
25C2×C4×Dic13D412yes—
26C2×C4×Dic13C2311yescharacteristic
27#88147—44no—
28#88147—44no—
29#88147—44no—
30#88128—24no—
31#88112—44no—
32#7651—131nomaximal, Sylow
33C23×D13—22no—
34C22×C4×C13—22no—
35C22×C4×C13C22⋊C412yes—
36C22×C4×C13C22×C411yescharacteristic
37C22×Dic13C22⋊C411yescharacteristic
38C22×Dic13C22⋊C411yescharacteristic
39C22×Dic13C2×D412yes—
40C2×D52—28no—
41C2×D52—22no—
42C2×D52—42no—
43C2×D52—42no—
44C2×D52—44no—
45C2×D52—44no—
46C2×D52M1614yes—
47C2×C4×D13—44no—
48C2×C4×D13—48no—
49C2×#1057—44no—
50C2×#1057—44no—
51C2×#1057—44no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—44no—
54C42×C13—22no—
55#6103—44no—
56#6103—44no—
57#6103—44no—
58C4×Dic13—22no—
59C4×Dic13—42no—
60C4×Dic13—41no—
61C4×Dic13D814yes—
62C4×Dic13SD1614yes—
63C4×#127—131no—
64#1831—132no—
65#1270—134no—
66C23×C13C2×C22⋊C411yescharacteristic
67C22×D13—24no—
68C22×D13—42no—
69C22×D13—42no—
70C22×D13—44no—
71C22×D13—44no—
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—42no—
77C2×C4×C13—44no—
78C2×C4×C13#10214yes—
79C2×C4×C13C2×M1612yes—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—22no—
84C2×Dic13#10012yes—
85C2×Dic13#10214yes—
86C2×Dic13C2×D812yes—
87C2×Dic13C2×SD1612yes—
88D52—44no—
89D52—416no—
90D52—44no—
91C4×D13—88no—
92#1057—84no—
93C2×#127—131no—
94C2×C4×D4—132no—
95C2×C4×D4—262no—
96C2×C4⋊C8—262no—
97#390—132no—
98#390—262no—
99#384#26111yescharacteristic
100C43—131no—
101#336—134no—
102#336—262no—
103C22×C13#40711yescharacteristic
104C22×C13#41011yescharacteristic
105C22×C13C2×#10011yescharacteristic
106C22×C13C2×#10212yes—
107C22×C13#42112yes—
108C2×D13—44no—
109C2×D13—48no—
110C2×D13—82no—
111C2×D13—82no—
112C2×D13—84no—
113C4×C13—22no—
114C4×C13—24no—
115C4×C13—82no—
116Dic13—22no—
117Dic13—22no—
118Dic13—41no—
119Dic13#33114yes—
120C22×D4—132no—
121C22×D4—262no—
122C23×C4—262no—
123C22×C8—264no—
124#127—264no—
125C4×D4—524no—
126C4×D4—524no—
127C4×D4—524no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4C2×#26112yes—
130C2×C22⋊C4—262no—
131C2×C22⋊C4—264no—
132C2×C42—132no—
133C2×C42—131no—
134C2×C42—132no—
135C2×C42—131no—
136C2×C42C2×#26111yescharacteristic
137C4⋊C8—524no—
138C2×C13#146611yescharacteristic
139C2×C13#148612yes—
140C2×C13#151712yes—
141C2×C13#153611yescharacteristic
142C2×C13C2×#33111yescharacteristic
143D13—84no—
144C24—262no—
145C2×D4—134no—
146C2×D4—268no—
147C2×D4—262no—
148C2×D4—522no—
149C2×D4—522no—
150C2×D4—524no—
151C2×D4—524no—
152C22×C4—22no—
153C22×C4—131no—
154C22×C4—132no—
155C22×C4—131no—
156C22×C4—528no—
157C22×C4—524no—
158C22×C4C22⋊#26112yes—
159C22×C4C22×#26111yescharacteristic
160C2×C8—524no—
161C2×C8—524no—
162C2×C8—524no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C22⋊C4—524no—
166C22⋊C4—524no—
167C22⋊C4—524no—
168C42—22no—
169C42—134no—
170C42—134no—
171C42—262no—
172C42—522no—
173C42—521no—
174C13#765111yescharacteristic, complemented, Sylow
175C23—264no—
176C23—524no—
177C23—522no—
178C23—524no—
179C23—522no—
180C23C2×C22⋊#26111yescharacteristic
181D4—524no—
182D4—524no—
183D4—5216no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—44no—
189C2×C4—42no—
190C2×C4—134no—
191C2×C4—132no—
192C2×C4—132no—
193C2×C4—132no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—261no—
197C2×C4—262no—
198C2×C4—1048no—
199C2×C4#8811514yes—
200C2×C4D13⋊M1612yes—
201C8—1044no—
202C22—524no—
203C22—528no—
204C22—1044no—
205C22—1042no—
206C22—1042no—
207C22#1171912611yescharacteristic
208C22C2×#8811512yes—
209C22D13⋊#10011yescharacteristic
210C22#1171915512yes—
211C22#1171915611yescharacteristic
212C4—22no—
213C4—24no—
214C4—82no—
215C4—134no—
216C4—262no—
217C4—262no—
218C4—521no—
219C2—1044no—
220C2#1313009711yescharacteristic
221C2#1313016312yes—
222C2#1313026712yes—
223C2#1313032611yescharacteristic
224C2D13⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC2×#88128C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#7651
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #13130752C2semidirect
2. #13129653C2semidirect
174. C13#7651semidirect

Maximal subgroups

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

subgroupindex
#131307522
#131296532
#131173982
#765113