Finite Group Databasebeta

← #16781149

Subgroups — #16781149

Order 3328.

814 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 120 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#13130562C212yesmaximal
2C2×#11718242C214yesmaximal, complemented
3C2×#11719222C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7#11719222—28no—
8C2×#88144C2212yes—
9C2×#88142C412yes—
10C2×#88132—22no—
11C2×C4×Dic26—22no—
12C2×C22⋊#1057—22no—
13C2×#88110C2214yes—
14#11718290—22no—
15#11718242—28no—
16C23×C4×C13C2×C411yescharacteristic
17C23×Dic13D412yes—
18C22×Dic26—22no—
19C22×#1057—24no—
20C13×#117—24no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C13×C22⋊C4—21no—
23C2×C42×C13—21no—
24C2×C22⋊Dic13—21no—
25#88180—24no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13C2×C412yes—
28C2×#6101—22no—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13—24no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13C2311yescharacteristic
35#88144—24no—
36#88144D418yes—
37#88142—24no—
38#88142—24no—
39#88132—216no—
40C4×Dic26—216no—
41C22⋊#1057—28no—
42#88110—28no—
43#8338—131nomaximal, Sylow
44C24×C13C22⋊C411yescharacteristic
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—22no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—24no—
53C22×Dic13—24no—
54C22×Dic13—42no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C2×D412yes—
57C2×Dic26—28no—
58C2×Dic26—44no—
59C2×Dic26—44no—
60C2×#1057—28no—
61C2×#1057—44no—
62C2×#1057—44no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4C22⋊C414yes—
65C13×C22⋊C4—24no—
66C42×C13—24no—
67C22⋊Dic13—24no—
68C4⋊Dic13—22no—
69C4⋊Dic13—28no—
70C4⋊Dic13C22⋊C414yes—
71#6101—28no—
72#6101—28no—
73C4×Dic13—24no—
74C4×Dic13—22no—
75C4×Dic13—24no—
76C4×Dic13C2×D414yes—
77C2×#533—131no—
78#1749—132no—
79C2×#330—134no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—22no—
83C23×C13—22no—
84C23×C13#10112yes—
85C23×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13—28no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—24no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13#10112yes—
95C2×C4×C13C2×C22⋊C412yes—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—24no—
101C2×Dic13—48no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13#10414yes—
105C2×Dic13#12014yes—
106Dic26—416no—
107#1057—48no—
108#533—268no—
109C2×C4⋊Q8—132no—
110C2×#125—132no—
111C2×C22⋊Q8—262no—
112C2×C4×Q8—262no—
113C2×#117—131no—
114C2×#117#26111yescharacteristic
115C22×C42—131no—
116C2×C22⋊C8—262no—
117C2×#97—134no—
118#336—262no—
119#330—268no—
120C22×C13—22no—
121C22×C13—24no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—42no—
125C22×C13#37911yescharacteristic
126C22×C13C2×#10111yescharacteristic
127C22×C13C2×#10111yescharacteristic
128C22×C13C2×#10412yes—
129C22×C13#42112yes—
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—44no—
133Dic13—24no—
134Dic13—24no—
135Dic13—44no—
136C22×Q8—262no—
137C23×C4—132no—
138C23×C4C2×#26111yescharacteristic
139C22×C8—264no—
140C4⋊Q8—264no—
141C4⋊Q8—264no—
142#125—138no—
143#125—264no—
144C22⋊Q8—2616no—
145C4×Q8—2616no—
146#117—24no—
147#117—264no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—262no—
151C2×C4⋊C4—262no—
152C2×C4⋊C4C2×#26112yes—
153C2×C22⋊C4—21no—
154C2×C22⋊C4—261no—
155C2×C42—21no—
156C2×C42—131no—
157C2×C42—132no—
158C2×C42—131no—
159C2×C42—264no—
160C2×C42—261no—
161C22⋊C8—268no—
162#97—268no—
163C2×C13—42no—
164C2×C13#152611yescharacteristic
165C2×C13#153112yes—
166C2×C13#153711yescharacteristic
167C2×C13#178411yescharacteristic
168C2×C13#178912yes—
169C24C22⋊#26111yescharacteristic
170C2×Q8—268no—
171C2×Q8—524no—
172C2×Q8—524no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—132no—
178C22×C4—132no—
179C22×C4—264no—
180C22×C4—264no—
181C22×C4—262no—
182C22×C4—522no—
183C22×C4C22⋊#26111yescharacteristic
184C22×C4C22×#26111yescharacteristic
185C2×C8—268no—
186C2×C8—524no—
187C2×C8—524no—
188C4⋊C4—22no—
189C4⋊C4—134no—
190C4⋊C4—268no—
191C4⋊C4—268no—
192C4⋊C4—268no—
193C4⋊C4—262no—
194C4⋊C4C22⋊#26114yes—
195C22⋊C4—24no—
196C22⋊C4—264no—
197C42—24no—
198C42—134no—
199C42—264no—
200C42—264no—
201C42—262no—
202C13#833811yescharacteristic, complemented, Sylow
203C23—21no—
204C23—21no—
205C23—22no—
206C23—22no—
207C23#8811312yes—
208C23C2×C22⋊#26111yescharacteristic
209Q8—5216no—
210C2×C4—28no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—24no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—134no—
219C2×C4—134no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—264no—
225C2×C4—528no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4#8811312yes—
229C2×C4C2×C22⋊#26112yes—
230C8—528no—
231C22—24no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22C2×#8811311yescharacteristic
237C22C2×#8811311yescharacteristic
238C22D13⋊#10412yes—
239C22#1171916612yes—
240C22#1171917111yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—264no—
245C4—264no—
246C4—524no—
247C2—42no—
248C2#1313029311yescharacteristic
249C2#1313030812yes—
250C2#1313032711yescharacteristic
251C2#1313067011yescharacteristic
252C2#1313067812yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8338
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11718242C2semidirect
202. C13#8338semidirect

Maximal subgroups

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

subgroupindex
#131305622
C2×#117182422
C2×#117192222
#833813