Finite Group Databasebeta

← #16790160

Subgroups — #16790160

Order 3328.

642 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130665C212yesmaximal
2#13129930C214yesmaximal, complemented
3#13117424C211yesmaximal, characteristic
4C22×#6127C2211yescharacteristic
5C2×C13×#117C411yescharacteristic, complemented
6C22×C4⋊Dic13C411yescharacteristic, complemented
7C2×#88119—22no—
8#11719135—22no—
9C2×#88107C2214yes—
10#11718648—22no—
11#11718619—22no—
12#11718600C2212yes—
13#11718590C412yescomplemented
14C23×C4×C13C2×C411yescharacteristic
15C22×C22⋊D13D412yes—
16C23×Dic13—21no—
17C2×#6127—24no—
18C2×#6127—42no—
19C2×#6127—42no—
20C22×D52C2311yescharacteristic
21C22×C4×D13D412yes—
22C22×Dic26C2×C411yescharacteristic
23C2×C22⋊#261—24no—
24C13×#117—42no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C22⋊C4—21no—
27C2×C42×C13C2×C412yes—
28C2×#6103—24no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—42no—
31C2×C4⋊Dic13C2×C412yes—
32#88119—44no—
33(C2×#261)⋊C4—44no—
34#88107—28no—
35#88071—24no—
36#12859—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C23×D13C2×D412yes—
39C22×#261—44no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13C22⋊C411yescharacteristic
45C22×C4×C13C22×C411yescharacteristic
46C2×C22⋊D13—24no—
47C2×C22⋊D13—24no—
48C2×C22⋊D13—42no—
49C22×Dic13—22no—
50C22×Dic13—42no—
51C22×Dic13—82no—
52C22×Dic13C22⋊C412yes—
53#6127—416no—
54C2×D52—41no—
55C2×D52—41no—
56C2×D52#4114yes—
57C2×C4×D13—24no—
58C2×C4×D13—24no—
59C2×C4×D13—42no—
60C2×Dic26—22no—
61C2×Dic26—41no—
62C2×Dic26—41no—
63C22⋊#261—44no—
64C22⋊#261—44no—
65C13×C4⋊C4—42no—
66C13×C22⋊C4—42no—
67C42×C13—42no—
68#6103—84no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71#2311—131no—
72#1782—132no—
73#1393—134no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—41no—
77C23×C13—41no—
78C23×C13#9912yes—
79C23×C13C2×C22⋊C411yescharacteristic
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—42no—
83C22×D13—42no—
84C22×D13#12314yes—
85C2×#261—84no—
86C2×#261—84no—
87C2×#261—84no—
88C2×C4×C13—28no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13#9912yes—
97C2×C4×C13#11712yes—
98C22⋊D13—48no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—44no—
103C2×Dic13—42no—
104C2×Dic13—84no—
105D52—44no—
106C4×D13—48no—
107Dic26—44no—
108C22×#41—131no—
109C2×#117#26111yescharacteristic, complemented
110C22×C4⋊C4—131no—
111C2×#99—134no—
112C2×#99—262no—
113#391—132no—
114#390—132no—
115#386—262no—
116#381—262no—
117#380—262no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13—22no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13#38111yescharacteristic
126C22×C13C2×#9911yescharacteristic
127C22×C13C2×#9911yescharacteristic
128C2×D13—24no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—44no—
132C2×D13—82no—
133#261—164no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—82no—
137Dic13—42no—
138Dic13—82no—
139C2×#41—264no—
140C2×#41—522no—
141C2×#41—522no—
142C22×Q8—131no—
143C22×D4—132no—
144C22×D4—131no—
145C23×C4—132no—
146C23×C4—261no—
147C23×C4C2×#26111yescharacteristic
148#117—42no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4—522no—
153C2×C22⋊C4—21no—
154C2×C22⋊C4—264no—
155C2×C22⋊C4—264no—
156C2×C42C2×#26112yes—
157#99—268no—
158#99—524no—
159#95—264no—
160#95—524no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13—42no—
164C2×C13#181911yescharacteristic
165C2×C13#212811yescharacteristic
166C2×C13#212911yescharacteristic
167D13—44no—
168C24—132no—
169C24C22⋊#26111yescharacteristic
170#41—5216no—
171C2×Q8—262no—
172C2×Q8—521no—
173C2×Q8—521no—
174C2×D4—134no—
175C2×D4—264no—
176C2×D4—264no—
177C2×D4—521no—
178C2×D4—521no—
179C2×D4—522no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—132no—
185C22×C4—264no—
186C22×C4—264no—
187C22×C4—262no—
188C22×C4—522no—
189C22×C4—522no—
190C22×C4—524no—
191C22×C4—1042no—
192C22×C4C22⋊#26111yescharacteristic
193C22×C4C22×#26111yescharacteristic
194C4⋊C4—42no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C22⋊C4—42no—
198C22⋊C4—524no—
199C22⋊C4—524no—
200C22⋊C4—1044no—
201C42—42no—
202C13#1285911yescharacteristic, complemented, Sylow
203C23—21no—
204C23—21no—
205C23—41no—
206C23—41no—
207C23—134no—
208C23—262no—
209C23—262no—
210C23—522no—
211C23—522no—
212C23#8811912yes—
213C23C2×C22⋊#26111yescharacteristic
214Q8—524no—
215D4—524no—
216D4—528no—
217C2×C4—28no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—528no—
229C2×C4—524no—
230C2×C4—522no—
231C2×C4—1044no—
232C2×C4—1044no—
233C2×C4—1044no—
234C2×C4—1044no—
235C2×C4#8810712yes—
236C2×C4#8823712yes—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—264no—
245C22—524no—
246C22—522no—
247C22—522no—
248C22—1042no—
249C22C2×#8810711yescharacteristic
250C22#1171913511yescharacteristic
251C22C2×#8811911yescharacteristic
252C4—22no—
253C4—22no—
254C4—82no—
255C4—522no—
256C4—1042no—
257C4—2084no—
258C2—21no—
259C2—21no—
260C2—42no—
261C2—524no—
262C2#1313073111yescharacteristic
263C2#1313111711yescharacteristic
264C2#1313112011yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC22×#6127C22
cosocleC22×D52C23
hypercenterC2×#117#261
hypocenterC13#12859
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129930C2semidirect
5. C2×C13×#117C4semidirect
6. C22×C4⋊Dic13C4semidirect
13. #11718590C4semidirect
109. C2×#117#261semidirect
202. C13#12859semidirect

Maximal subgroups

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

subgroupindex
#131306652
#131299302
#131174242
#1285913