Finite Group Databasebeta

← #16786554

Subgroups — #16786554

Order 3328.

1142 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 1142 conjugacy classes of subgroups — too many to draw. Only its 184 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×#11718291C214yesmaximal
2#13130499C212yesmaximal
3C22×#88142C211yesmaximal, characteristic
4C23×Dic26C412yes—
5C22×#6122C2214yes—
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C22×#6101C2212yes—
9C22×C4×Dic13C2211yescharacteristic
10C2×#88142—28no—
11C2×#88142—24no—
12#11718291—28no—
13#11718290—24no—
14C23×C4×C13C2×C412yes—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13C2×C411yescharacteristic
17C23×Dic13C2×C412yes—
18C23×Dic13C2311yescharacteristic
19C22×Dic26—24no—
20C22×Dic26—24no—
21C22×Dic26—24no—
22C22×Dic26—48no—
23C2×#6122—24no—
24C2×#6122—28no—
25C2×#6122—28no—
26C2×#6122Q818yescomplemented
27C22×#1057—24no—
28C2×C13×C4⋊C4—24no—
29C2×C13×C4⋊C4—22no—
30C2×C4⋊Dic13—22no—
31C2×C4⋊Dic13—24no—
32C2×#6101—24no—
33C2×#6101—24no—
34C2×#6101D418yes—
35C2×C4×Dic13—24no—
36C2×C4×Dic13D414yes—
37#88142—232no—
38#11382—131nomaximal, Sylow
39C24×C13C22×C411yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13—24no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—44no—
45C22×C4×C13C22⋊C412yes—
46C22×C4×C13C22⋊C414yes—
47C22×Dic13—22no—
48C22×Dic13—24no—
49C22×Dic13—22no—
50C22×Dic13—22no—
51C22×Dic13—44no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C22⋊C414yes—
54C22×Dic13C2×D414yes—
55C22×Dic13C2×D412yes—
56C22×Dic13C2×Q814yes—
57C22×Dic13#4114yes—
58C2×Dic26—216no—
59C2×Dic26—416no—
60C2×Dic26—416no—
61C2×Dic26—48no—
62C2×Dic26—48no—
63#6122—216no—
64#6122—48no—
65C2×#1057—28no—
66C2×#1057—44no—
67C2×#1057—44no—
68C13×C4⋊C4—28no—
69C4⋊Dic13—28no—
70#6101—216no—
71C4×Dic13—28no—
72C22×C4⋊Q8—131no—
73C2×#343—134no—
74#1728—132no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13C2×C22⋊C412yes—
78C23×C13C2×C22⋊C411yescharacteristic
79C23×C13C4×Q814yes—
80C2×C4×C13—28no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—24no—
84C2×C4×C13—44no—
85C2×C4×C13—44no—
86C2×C4×C13—44no—
87C2×C4×C13#10114yes—
88C2×Dic13—28no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—24no—
92C2×Dic13—44no—
93C2×Dic13—44no—
94C2×Dic13—44no—
95C2×Dic13#10014yes—
96C2×Dic13#12014yes—
97C2×Dic13C22⋊Q814yes—
98C2×Dic13C22⋊Q818yes—
99C2×Dic13#12412yes—
100C2×Dic13#12414yes—
101C2×Dic13C4⋊Q814yes—
102C2×Dic13C4⋊Q812yes—
103Dic26—432no—
104#1057—48no—
105C23×Q8—132no—
106C22×M16—134no—
107C2×C4⋊Q8—264no—
108C2×C4⋊Q8—268no—
109C22×C4⋊C4—132no—
110C22×C4⋊C4—131no—
111C22×C4⋊C4#26111yescharacteristic
112C22×C42—131no—
113#343—268no—
114#336—264no—
115C22×C13—28no—
116C22×C13—22no—
117C22×C13—22no—
118C22×C13#37911yescharacteristic
119C22×C13#39114yes—
120C22×C13#39112yes—
121C22×C13C2×#10012yes—
122C22×C13C2×#10112yes—
123C4×C13—24no—
124C4×C13—44no—
125Dic13—24no—
126Dic13—44no—
127Dic13#39314yes—
128Dic13#39514yes—
129C22×Q8—264no—
130C22×Q8—264no—
131C22×Q8—264no—
132C22×Q8—528no—
133C23×C4—131no—
134C23×C4—131no—
135C23×C4—132no—
136C23×C4C2×#26112yes—
137C23×C4C2×#26111yescharacteristic
138C2×M16—138no—
139C2×M16—264no—
140C2×M16—268no—
141C2×M16—268no—
142C22×C8—264no—
143C4⋊Q8—2632no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—138no—
147C2×C4⋊C4—264no—
148C2×C4⋊C4—264no—
149C2×C4⋊C4—264no—
150C2×C4⋊C4—262no—
151C2×C42—134no—
152C2×C42—264no—
153C2×C13—24no—
154C2×C13#144611yescharacteristic
155C2×C13#178311yescharacteristic
156C2×C13#178411yescharacteristic
157C2×C13#199714yes—
158C24C22×#26111yescharacteristic
159C2×Q8—2616no—
160C2×Q8—528no—
161C2×Q8—5216no—
162C2×Q8—528no—
163C2×Q8—5216no—
164C22×C4—22no—
165C22×C4—24no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—44no—
169C22×C4—134no—
170C22×C4—134no—
171C22×C4—134no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4—134no—
175C22×C4—264no—
176C22×C4—262no—
177C22×C4—262no—
178C22×C4—262no—
179C22×C4—524no—
180C22×C4C22⋊#26112yes—
181C22×C4C22⋊#26114yes—
182M16—2616no—
183M16—528no—
184C2×C8—268no—
185C2×C8—524no—
186C2×C8—524no—
187C4⋊C4—28no—
188C4⋊C4—2616no—
189C4⋊C4—268no—
190C42—268no—
191C13#1138211yescharacteristic, complemented, Sylow
192C23—22no—
193C23—22no—
194C23Q8×#26114yes—
195C23C2×C22⋊#26112yes—
196C23C2×C22⋊#26111yescharacteristic
197Q8—5232no—
198C2×C4—28no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—44no—
203C2×C4—44no—
204C2×C4—44no—
205C2×C4—134no—
206C2×C4—134no—
207C2×C4—132no—
208C2×C4—138no—
209C2×C4—134no—
210C2×C4—134no—
211C2×C4—132no—
212C2×C4—134no—
213C2×C4—268no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—264no—
217C2×C4—524no—
218C2×C4—524no—
219C2×C4—524no—
220C2×C4#8811314yes—
221C8—528no—
222C22—28no—
223C22—22no—
224C22—22no—
225C22C2×#8811312yes—
226C22D13⋊#10012yes—
227C22(C2×#261)⋊Q814yes—
228C22(C2×#261)⋊Q812yes—
229C22#1171917111yescharacteristic
230C4—24no—
231C4—44no—
232C4—134no—
233C4—134no—
234C4—264no—
235C4—524no—
236C2—24no—
237C2#1313002611yescharacteristic
238C2#1313066911yescharacteristic
239C2#1313067011yescharacteristic
240C2#1313102914yes—
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11382
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
26. C2×#6122Q8semidirect
191. C13#11382semidirect

Maximal subgroups

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

subgroupindex
C2×#117182912
#131304992
C22×#881422
#1138213