Finite Group Databasebeta

← #16778551

Subgroups — #16778551

Order 3328.

468 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130764C212yesmaximal, complemented
2#13129657C212yesmaximal, complemented
3#13129652C212yesmaximal
4C4×#88190C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88190C411yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8#11718882C2211yescharacteristic
9C4×C22⋊Dic13—22no—
10#11718638C411yescharacteristic
11#11718635C2211yescharacteristic
12#11718606—22no—
13C42×Dic13C2211yescharacteristic
14#11718290—22no—
15#11718290—22no—
16#11718290C2214yes—
17C22×D4×C13C2×C411yescharacteristic
18C23×C4×C13—21no—
19C22×Dic26C2×C411yescharacteristic
20C22×#1057—24no—
21C4×D4×C13—42no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4—21no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—22no—
26C2×C22⋊Dic13—22no—
27#88190—22no—
28#88190—22no—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×#6101—21no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13D412yes—
35C2×C4×Dic13C2311yescharacteristic
36C4×Dic26—42no—
37#88071—22no—
38#88071—22no—
39#7649—131nomaximal, Sylow
40C24×C13—21no—
41C2×D4×C13—21no—
42C2×D4×C13—41no—
43C2×D4×C13—41no—
44C2×D4×C13M1612yes—
45C22×C4×C13—21no—
46C22×C4×C13—44no—
47C22×C4×C13—42no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—21no—
52C22×Dic13—21no—
53C22×Dic13C22⋊C412yes—
54C22×Dic13C2×D412yes—
55C2×Dic26—21no—
56C2×Dic26—41no—
57C2×Dic26—41no—
58C2×Dic26M1612yes—
59C2×#1057—44no—
60C2×#1057—44no—
61C2×#1057—44no—
62C13×C4⋊C4—41no—
63C13×C22⋊C4—42no—
64C42×C13—22no—
65C22⋊Dic13—28no—
66C22⋊Dic13—44no—
67C4⋊Dic13—41no—
68#6101—42no—
69C4×Dic13—21no—
70C4×Dic13—21no—
71C4×Dic13—24no—
72C4×Dic13—42no—
73C4×Dic13—41no—
74C4×Dic13—42no—
75C4×#124—131no—
76#1839—132no—
77#1272—132no—
78#1270—132no—
79C23×C13—22no—
80C23×C13—41no—
81C23×C13—41no—
82C23×C13—42no—
83C23×C13—42no—
84C23×C13C2×C22⋊C411yescharacteristic
85D4×C13—42no—
86D4×C13—42no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13—84no—
95C2×C4×C13#10012yes—
96C2×C4×C13C2×M1611yescharacteristic
97C2×C4×C13C2×M1611yescharacteristic
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—41no—
105C2×Dic13—41no—
106C2×Dic13—41no—
107C2×Dic13—42no—
108C2×Dic13#13514yes—
109Dic26—42no—
110Dic26—42no—
111#1057—84no—
112C2×#124—131no—
113C2×C4×Q8—131no—
114C2×C4×D4#26111yescharacteristic
115#391—131no—
116#390—131no—
117#388—262no—
118#382—131no—
119C4×C22⋊C4—262no—
120C43—131no—
121#336—134no—
122#336—262no—
123#336—262no—
124C22×C13—42no—
125C22×C13—44no—
126C22×C13—81no—
127C22×C13—82no—
128C22×C13—81no—
129C22×C13#40711yescharacteristic
130C22×C13#41011yescharacteristic
131C22×C13C2×#10011yescharacteristic
132C22×C13#41612yes—
133C22×C13#42112yes—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—41no—
138C4×C13—81no—
139Dic13—24no—
140Dic13—42no—
141Dic13—42no—
142Dic13—81no—
143C22×Q8—131no—
144C22×D4C2×#26111yescharacteristic
145C23×C4—21no—
146C22×C8—264no—
147#124—262no—
148#124—262no—
149C4×Q8—522no—
150C4×D4—42no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—261no—
153C2×C4⋊C4C2×#26111yescharacteristic
154C2×C22⋊C4—21no—
155C2×C22⋊C4—262no—
156C2×C22⋊C4—262no—
157C2×C42—132no—
158C2×C42—131no—
159C2×C42—132no—
160C2×C42—131no—
161C2×C42—261no—
162C2×C42C2×#26111yescharacteristic
163#95—262no—
164#95—262no—
165C2×C13—82no—
166C2×C13#146611yescharacteristic
167C2×C13#148812yes—
168C2×C13#152112yes—
169C2×C13#153311yescharacteristic
170C2×C13#154311yescharacteristic
171C24—21no—
172C2×Q8—132no—
173C2×Q8—261no—
174C2×Q8—521no—
175C2×Q8—521no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4#611812yes—
180C22×C4—21no—
181C22×C4—44no—
182C22×C4—42no—
183C22×C4—132no—
184C22×C4—132no—
185C22×C4—261no—
186C22×C4—261no—
187C22×C4C22⋊#26111yescharacteristic
188C22×C4C22⋊#26111yescharacteristic
189C22×C4C22×#26111yescharacteristic
190C2×C8—524no—
191C2×C8—524no—
192C2×C8—524no—
193C4⋊C4—41no—
194C4⋊C4—521no—
195C4⋊C4—522no—
196C22⋊C4—42no—
197C22⋊C4—268no—
198C22⋊C4—524no—
199C42—22no—
200C42—264no—
201C42—261no—
202C42—261no—
203C42—521no—
204C42—522no—
205C42—522no—
206C13#764911yescharacteristic, complemented, Sylow
207C23—22no—
208C23—41no—
209C23—41no—
210C23—42no—
211C23—42no—
212C23C2×C22⋊#26111yescharacteristic
213Q8—522no—
214Q8—522no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—84no—
225C2×C4—134no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—521no—
233C2×C4—521no—
234C2×C4—521no—
235C2×C4—522no—
236C2×C4#8812112yes—
237C2×C4C2×#611811yescharacteristic
238C2×C4D13⋊M1611yescharacteristic
239C8—1044no—
240C22—42no—
241C22—44no—
242C22—82no—
243C22—81no—
244C22—81no—
245C22#1171911611yescharacteristic
246C22#1171912711yescharacteristic
247C22#1171914012yes—
248C22#1171916512yes—
249C22C2×#8812111yescharacteristic
250C4—22no—
251C4—21no—
252C4—21no—
253C4—41no—
254C4—81no—
255C4—264no—
256C4—522no—
257C4—522no—
258C4—1041no—
259C2—82no—
260C2#1313009511yescharacteristic
261C2#1313016812yes—
262C2#1313027812yes—
263C2#1313031511yescharacteristic
264C2#1313033911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#7649
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13130764C2semidirect
2. #13129657C2semidirect
206. C13#7649semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131296572
#131296522
C4×#881902
#764913