Finite Group Databasebeta

← #15763614

Subgroups — #15763614

Order 3328.

698 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#11718711C212yesmaximal
2#13114759C211yesmaximal, characteristic
3#13113200C212yesmaximal
4#13112723C211yesmaximal, characteristic
5C13×#3195C211yesmaximal, characteristic
6C23×Dic26C2211yescharacteristic
7C2×C13×C22⋊Q8C2212yes—
8C22×#6107—22no—
9C13×#483—22no—
10C13×#470—22no—
11C13×#451—22no—
12C13×#407C2211yescharacteristic
13#11718868C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15C2×#88064—22no—
16#11718711—24no—
17#11718711—24no—
18C2×#88050—22no—
19#11718120—24no—
20C22×Q8×C13D412yes—
21C23×C4×C13C2311yescharacteristic
22C23×Dic13—21no—
23C22×Dic26—22no—
24C22×Dic26—21no—
25C22×Dic26—22no—
26C22×Dic26—44no—
27C22×Dic26D412yes—
28C2×C13×Q16—22no—
29C2×C13×M16D412yes—
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—22no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4D412yes—
36C2×C13×C22⋊C4—22no—
37C2×#6107—28no—
38C2×#6107—48no—
39C2×#6099—21no—
40C22×#1055—22no—
41C13×#106—22no—
42C13×#103—24no—
43C13×C22⋊C8—22no—
44C22⋊#1055—22no—
45C22⋊#1055—22no—
46C22⋊#1055D414yes—
47#88064—44no—
48#88050—28no—
49#9991—131nomaximal, Sylow
50C24×C13#4111yescharacteristic
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13—44no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D412yes—
59C22×C4×C13C2×D412yes—
60C22×C4×C13C2×D411yescharacteristic
61C22×Dic13—22no—
62C22×Dic13—44no—
63C22×Dic13—42no—
64C2×Dic26—28no—
65C2×Dic26—24no—
66C2×Dic26—24no—
67C2×Dic26—44no—
68C2×Dic26—48no—
69C2×Dic26—44no—
70C2×Dic26—42no—
71C2×Dic26—41no—
72C2×Dic26—41no—
73C13×Q16—82no—
74C13×M16—42no—
75C2×C8×C13—22no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82#6107—416no—
83#6099—42no—
84C2×#1055—24no—
85C2×#1055—44no—
86C2×#1055—41no—
87#3195D1311yescharacteristic
88C2×#451—132no—
89#1784—131no—
90#1472—132no—
91#1298—131no—
92C23×C13—24no—
93C23×C13—41no—
94C23×C13#12111yescharacteristic
95C23×C13#12112yes—
96Q8×C13—44no—
97Q8×C13—44no—
98C2×C4×C13—24no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—44no—
105C2×C4×C13—82no—
106C2×C4×C13#12012yes—
107C2×C4×C13#12011yescharacteristic
108C2×C4×C13#12711yescharacteristic
109C2×Dic13—24no—
110C2×Dic13—48no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113Dic26—28no—
114Dic26—44no—
115Dic26—44no—
116Dic26—44no—
117C8×C13—42no—
118#1055—44no—
119#1055—81no—
120C23×Q8—131no—
121C22×Q16—262no—
122C2×C22⋊Q8C2×D1312yes—
123#483—22no—
124#470—22no—
125#451—22no—
126#451—264no—
127#451—264no—
128C2×#103—262no—
129C2×#101—262no—
130#407—131no—
131#407C2×D1311yescharacteristic
132C2×C22⋊C8—132no—
133#324—264no—
134C22×C13—22no—
135C22×C13—22no—
136C22×C13—22no—
137C22×C13—21no—
138C22×C13—44no—
139C22×C13#39211yescharacteristic
140C22×C13#47314yes—
141C4×C13—22no—
142C4×C13—21no—
143C4×C13—82no—
144C4×C13—82no—
145C4×C13B(4,𝔽2)12yes—
146Dic13—44no—
147C22×Q8—132no—
148C22×Q8—261no—
149C22×Q8—262no—
150C22×Q8—262no—
151C22×Q8—524no—
152C22×Q8C22⋊D1312yes—
153C23×C4—261no—
154C23×C4C22×D1311yescharacteristic
155C2×Q16—22no—
156C2×Q16—268no—
157C2×Q16—528no—
158C2×M16—261no—
159C2×M16C22⋊D1312yes—
160C22×C8—262no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C22⋊D1312yes—
167C2×C22⋊C4—22no—
168#106—22no—
169#103—24no—
170#103—268no—
171#101—524no—
172C22⋊C8—22no—
173C22⋊C8—134no—
174C22⋊C8—262no—
175C22⋊C8—262no—
176C2×C13—24no—
177C2×C13—41no—
178C2×C13#202012yes—
179C2×C13#202111yescharacteristic
180C24#612911yescharacteristic
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—44no—
184C2×Q8—264no—
185C2×Q8—268no—
186C2×Q8—264no—
187C2×Q8—524no—
188C2×Q8—522no—
189C2×Q8—524no—
190C2×Q8—528no—
191C2×Q8—521no—
192C2×Q8—521no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—42no—
196C22×C4—262no—
197C22×C4—524no—
198C22×C4—522no—
199C22×C4D4×D1311yescharacteristic
200C22×C4D4×D1312yes—
201C22×C4C2×C22⋊D1312yes—
202C22×C4C2×C22⋊D1311yescharacteristic
203Q16—82no—
204Q16—5216no—
205M16—42no—
206M16—522no—
207C2×C8—22no—
208C2×C8—264no—
209C2×C8—524no—
210C2×C8—521no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C13#999111yescharacteristic, complemented, Sylow
218C23—24no—
219C23—41no—
220C23#8819211yescharacteristic
221C23#8819312yes—
222Q8—44no—
223Q8—44no—
224Q8—268no—
225Q8—524no—
226Q8—524no—
227Q8—524no—
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—264no—
237C2×C4—522no—
238C2×C4—528no—
239C2×C4—522no—
240C2×C4#8819112yes—
241C2×C4#8819411yescharacteristic
242C2×C4#8820711yescharacteristic
243C8—42no—
244C8—524no—
245C8—1041no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—21no—
250C22—44no—
251C22#1171886514yes—
252C22#1171888411yescharacteristic
253C4—22no—
254C4—21no—
255C4—82no—
256C4—82no—
257C4—524no—
258C4#1171890512yes—
259C2—24no—
260C2—41no—
261C2#1311595412yes—
262C2#1311596011yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#3195C2
socleC22×C13#392
prime radicalC24×C13#41
hypercenter#3195D13
hypocenterC13#9991
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
217. C13#9991semidirect

Maximal subgroups

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

subgroupindex
C2×#117187112
#131147592
#131132002
#131127232
C13×#31952
#999113