Finite Group Databasebeta

← #16790163

Subgroups — #16790163

Order 3328.

638 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130670C212yesmaximal
2#13129933C214yesmaximal, complemented
3C2×#11718590C211yesmaximal, characteristic
4C23×Dic26C2211yescharacteristic
5C22×C42×C13C411yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7#11719169—22no—
8C2×#88113—22no—
9C2×#88113C2214yes—
10C2×#88071—22no—
11#11718590—22no—
12#11718590C412yes—
13#11718590C2212yes—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C22×Dic26—24no—
19C22×Dic26—42no—
20C22×Dic26—41no—
21C22×Dic26—41no—
22C22×Dic26C2×C411yescharacteristic
23C22×Dic26D412yes—
24C22×Dic26C2311yescharacteristic
25C2×#6122—24no—
26C2×C42×C13—21no—
27C2×C42×C13—42no—
28C2×C42×C13C2×C412yes—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—41no—
31C2×C4⋊Dic13—41no—
32C2×C4⋊Dic13C2×C412yes—
33C22⋊#1057—42no—
34C22⋊#1057—42no—
35#88113—28no—
36#88113—44no—
37#88071—24no—
38#88071—24no—
39#12860—131nomaximal, Sylow
40C24×C13C22⋊C411yescharacteristic
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—24no—
46C22×C4×C13—22no—
47C22×C4×C13—42no—
48C22×C4×C13—42no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—24no—
54C22×Dic13—22no—
55C22×Dic13—42no—
56C22×Dic13—44no—
57C22×Dic13—41no—
58C22×Dic13—41no—
59C22×Dic13C22⋊C412yes—
60C22×Dic13C2×D412yes—
61C2×Dic26—24no—
62C2×Dic26—22no—
63C2×Dic26—24no—
64C2×Dic26—41no—
65C2×Dic26—41no—
66C2×Dic26—42no—
67C2×Dic26—41no—
68C2×Dic26—41no—
69C2×Dic26—48no—
70C2×Dic26—48no—
71C2×Dic26#4114yes—
72#6122—44no—
73#6122—44no—
74C2×#1057—44no—
75C42×C13—42no—
76C42×C13—42no—
77C4⋊Dic13—42no—
78C4⋊Dic13—42no—
79C2×#391—131no—
80#1784—132no—
81#1394—134no—
82C23×C13—22no—
83C23×C13—22no—
84C23×C13—21no—
85C23×C13—21no—
86C23×C13#9911yescharacteristic
87C23×C13#9911yescharacteristic
88C23×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13—24no—
90C2×C4×C13—24no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—24no—
96C2×C4×C13—48no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13#9912yes—
100C2×C4×C13#11712yes—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—44no—
107C2×Dic13—44no—
108C2×Dic13—44no—
109C2×Dic13—42no—
110C2×Dic13—82no—
111C2×Dic13—82no—
112C2×Dic13#12314yes—
113Dic26—44no—
114Dic26—48no—
115Dic26—44no—
116#1057—84no—
117C23×Q8—131no—
118C22×C4⋊C4—131no—
119C22×C42#26111yescharacteristic
120C2×#101—134no—
121C2×#101—262no—
122#407—262no—
123#391—132no—
124#391—132no—
125#391—262no—
126C2×#95—262no—
127C22×C13—24no—
128C22×C13—24no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13#35512yes—
136C22×C13#35612yes—
137C22×C13#38111yescharacteristic
138C22×C13C2×#9911yescharacteristic
139C22×C13C2×#9911yescharacteristic
140C4×C13—22no—
141C4×C13—22no—
142C4×C13—44no—
143Dic13—24no—
144Dic13—42no—
145Dic13—82no—
146C22×Q8—132no—
147C22×Q8—131no—
148C22×Q8—131no—
149C22×Q8—264no—
150C22×Q8—521no—
151C22×Q8—521no—
152C22×Q8—522no—
153C23×C4—21no—
154C23×C4—132no—
155C23×C4—261no—
156C23×C4C2×#26111yescharacteristic
157C2×M16—264no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4—521no—
161C2×C4⋊C4—521no—
162C2×C42—21no—
163C2×C42—42no—
164C2×C42C2×#26112yes—
165#101—268no—
166#101—524no—
167C22⋊C8—522no—
168C22⋊C8—522no—
169#95—264no—
170#95—264no—
171C2×C13—21no—
172C2×C13—22no—
173C2×C13—22no—
174C2×C13—21no—
175C2×C13#181911yescharacteristic
176C2×C13C2×#35511yescharacteristic
177C2×C13C2×#35611yescharacteristic
178C24C22⋊#26111yescharacteristic
179C2×Q8—134no—
180C2×Q8—264no—
181C2×Q8—264no—
182C2×Q8—262no—
183C2×Q8—522no—
184C2×Q8—521no—
185C2×Q8—521no—
186C2×Q8—521no—
187C2×Q8—521no—
188C2×Q8—528no—
189C2×Q8—528no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—132no—
199C22×C4—132no—
200C22×C4—264no—
201C22×C4—262no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4—522no—
205C22×C4—524no—
206C22×C4—521no—
207C22×C4—521no—
208C22×C4C22⋊#26111yescharacteristic
209C22×C4C22×#26111yescharacteristic
210M16—524no—
211M16—524no—
212C2×C8—524no—
213C4⋊C4—522no—
214C4⋊C4—522no—
215C42—42no—
216C42—42no—
217C13#1286011yescharacteristic, complemented, Sylow
218C23—22no—
219C23—22no—
220C23—21no—
221C23—21no—
222C23#8810711yescharacteristic
223C23#8810711yescharacteristic
224C23C2×C22⋊#26111yescharacteristic
225Q8—524no—
226Q8—528no—
227Q8—524no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—24no—
235C2×C4—48no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—134no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—524no—
245C2×C4—524no—
246C2×C4—524no—
247C2×C4—522no—
248C2×C4—1042no—
249C2×C4—1042no—
250C2×C4#8811912yes—
251C2×C4#8823712yes—
252C8—1044no—
253C22—24no—
254C22—24no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22#1171822712yes—
262C22#1171822812yes—
263C22C2×#8810711yescharacteristic
264C22#1171913511yescharacteristic
265C22C2×#8811911yescharacteristic
266C4—22no—
267C4—22no—
268C4—44no—
269C4—264no—
270C4—522no—
271C4—1042no—
272C2—21no—
273C2—22no—
274C2—22no—
275C2—21no—
276C2#1313073111yescharacteristic
277C2C2×#1171822811yescharacteristic
278C2C2×#1171822711yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C42×C13C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC22×Dic26C23
hypercenterC22×C42#261
hypocenterC13#12860
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #13129933C2semidirect
217. C13#12860semidirect

Maximal subgroups

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

subgroupindex
#131306702
#131299332
C2×#117185902
#1286013