Finite Group Databasebeta

← #16778392

Subgroups — #16778392

Order 3328.

608 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 110 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#13130763C212yesmaximal, complemented
2#13129653C214yesmaximal, complemented
3#13117398C211yesmaximal, characteristic
4C2×#88147—22no—
5C2×#88147C412yes—
6C2×#88128C411yescharacteristic
7C13×#384C411yescharacteristic
8#11718649—22no—
9#11718649C2212yes—
10C42×Dic13C2211yescharacteristic
11#11718290—22no—
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—48no—
28#88147—44no—
29#88128—22no—
30#88128C814yescomplemented
31#7603—131nomaximal, Sylow
32C23×D13—22no—
33C22×C4×C13—22no—
34C22×C4×C13C22⋊C412yes—
35C22×C4×C13C22×C411yescharacteristic
36C22×Dic13C22⋊C411yescharacteristic
37C22×Dic13C22⋊C411yescharacteristic
38C22×Dic13C2×D412yes—
39C2×D52—28no—
40C2×D52—22no—
41C2×D52—42no—
42C2×D52—42no—
43C2×D52—44no—
44C2×D52—44no—
45C2×D52C2×C814yes—
46C2×C4×D13—48no—
47C2×C4×D13—44no—
48C2×#1057—44no—
49C2×#1057—44no—
50C2×#1057—44no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—44no—
53C42×C13C2×C812yes—
54C42×C13M1612yes—
55#6103—44no—
56#6103—48no—
57C4×Dic13—22no—
58C4×Dic13—24no—
59C4×Dic13—42no—
60C4×Dic13—41no—
61C4×#127—131no—
62#1839—132no—
63#1270—134no—
64C23×C13C2×C22⋊C411yescharacteristic
65C22×D13—24no—
66C22×D13—42no—
67C22×D13—42no—
68C22×D13—44no—
69C22×D13—44no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—42no—
75C2×C4×C13—44no—
76C2×C4×C13C22⋊C814yes—
77C2×C4×C13C22×C811yescharacteristic
78C2×C4×C13C2×M1611yescharacteristic
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—22no—
84C2×Dic13#10012yes—
85C2×Dic13AGL(1,ℤ/8)14yes—
86D52—44no—
87D52—416no—
88D52—44no—
89C4×D13—88no—
90#1057—84no—
91C2×#127—131no—
92C2×C4×D4—132no—
93C2×C4×D4—262no—
94#390—132no—
95#390—262no—
96#384#26111yescharacteristic
97C43—131no—
98#336—134no—
99#336—262no—
100#336—262no—
101C22×C13C2×C22⋊C811yescharacteristic
102C22×C13#41011yescharacteristic
103C22×C13C2×#10011yescharacteristic
104C22×C13#41812yes—
105C22×C13#42112yes—
106C2×D13—44no—
107C2×D13—48no—
108C2×D13—82no—
109C2×D13—82no—
110C2×D13—84no—
111C4×C13—21no—
112C4×C13—21no—
113C4×C13—24no—
114C4×C13—82no—
115Dic13—22no—
116Dic13—24no—
117Dic13—41no—
118C22×D4—132no—
119C22×D4—262no—
120C23×C4—262no—
121C22×C8—264no—
122#127—134no—
123#127—262no—
124C4×D4—528no—
125C4×D4—524no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4C2×#26112yes—
128C2×C22⋊C4—262no—
129C2×C22⋊C4—264no—
130C2×C42—132no—
131C2×C42—131no—
132C2×C42—132no—
133C2×C42—131no—
134C2×C42C2×#26111yescharacteristic
135C2×C13#146011yescharacteristic
136C2×C13#147812yes—
137C2×C13#151412yes—
138C2×C13#153611yescharacteristic
139C2×C13#155511yescharacteristic
140D13—84no—
141C24—262no—
142C2×D4—134no—
143C2×D4—268no—
144C2×D4—262no—
145C2×D4—522no—
146C2×D4—522no—
147C2×D4—524no—
148C2×D4—524no—
149C22×C4—22no—
150C22×C4—132no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—524no—
154C22×C4—528no—
155C22×C4C22⋊#26112yes—
156C22×C4C22×#26111yescharacteristic
157C2×C8—524no—
158C2×C8—524no—
159C2×C8—524no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C22⋊C4—528no—
163C22⋊C4—524no—
164C42—264no—
165C42—262no—
166C42—522no—
167C42—521no—
168C42D13⋊C812yes—
169C42#611812yes—
170C13#760311yescharacteristic, complemented, Sylow
171C23—264no—
172C23—524no—
173C23—522no—
174C23—524no—
175C23—522no—
176C23C2×C22⋊#26111yescharacteristic
177D4—524no—
178D4—524no—
179D4—5216no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—134no—
187C2×C4—132no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—261no—
192C2×C4—262no—
193C2×C4—1048no—
194C2×C4#8811114yes—
195C2×C4C2×D13⋊C811yescharacteristic
196C2×C4C2×#611811yescharacteristic
197C8—1044no—
198C22—524no—
199C22—528no—
200C22—1044no—
201C22—1042no—
202C22—1042no—
203C22C2×#8811111yescharacteristic
204C22#1171913812yes—
205C22D13⋊#10011yescharacteristic
206C22#1171915512yes—
207C22#1171915611yescharacteristic
208C4—21no—
209C4—21no—
210C4—24no—
211C4—82no—
212C4—264no—
213C4—262no—
214C4—521no—
215C2—1044no—
216C2#1313007711yescharacteristic
217C2#1313013712yes—
218C2#1313025712yes—
219C2#1313032611yescharacteristic
220C2#1313036411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC2×#88128C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#7603
LCSG ▷ C2×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. #13130763C2semidirect
2. #13129653C2semidirect
30. #88128C8semidirect
170. C13#7603semidirect

Maximal subgroups

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

subgroupindex
#131307632
#131296532
#131173982
#760313