Finite Group Databasebeta

← #16800775

Subgroups — #16800775

Order 3328.

1242 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 1242 conjugacy classes of subgroups — too many to draw. Only its 264 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×#11719128C212yesmaximal
2#13131008C218yesmaximal, complemented
3#13130727C214yesmaximal
4C22×#88141C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C22×#6101C412yes—
8C22×C4×Dic13C2212yes—
9C22×C4×Dic13C2211yescharacteristic
10C2×#88141—28no—
11C2×#88141C414yes—
12C2×#88141C2214yes—
13C2×C22⋊#1057C2214yes—
14#11719128—28no—
15C2×#88112C2214yes—
16C2×#88110C2214yes—
17#11718290C22116yes—
18C23×C4×C13C2×C411yescharacteristic
19C23×C4×C13C2×C412yes—
20C23×Dic13C2×C412yes—
21C23×Dic13C2×C411yescharacteristic
22C23×Dic13C2311yescharacteristic
23C22×Dic26—24no—
24C22×Dic26—28no—
25C22×Dic26C2×C414yes—
26C22×#1057C2318yes—
27C2×C13×C4⋊C4—24no—
28C2×C13×C4⋊C4C2×C414yes—
29C2×#6101—28no—
30C2×#6101C2×C418yes—
31C2×C4×Dic13—28no—
32C2×C4×Dic13C2×C414yes—
33C2×C4×Dic13C2×C412yes—
34C2×C4×Dic13D418yes—
35C2×C4×Dic13C2314yes—
36C2×C4×Dic13C2312yes—
37#88141—216no—
38#88141—28no—
39#88141—28no—
40C22⋊#1057—28no—
41#88112—28no—
42#88110—28no—
43#21822—131nomaximal, Sylow
44C24×C13C22×C411yescharacteristic
45C22×C4×C13—24no—
46C22×C4×C13—24no—
47C22×C4×C13—44no—
48C22×C4×C13C22⋊C414yes—
49C22×C4×C13C22×C414yes—
50C22×C4×C13C22×C412yes—
51C22×Dic13—24no—
52C22×Dic13—24no—
53C22×Dic13—24no—
54C22×Dic13—42no—
55C22×Dic13C22⋊C414yes—
56C22×Dic13M1618yes—
57C22×Dic13C22×C411yescharacteristic
58C22×Dic13C22×C412yes—
59C22×Dic13C22×C414yes—
60C22×Dic13C2×D414yes—
61C22×Dic13C2411yescharacteristic
62C2×Dic26—232no—
63C2×Dic26—28no—
64C2×Dic26—216no—
65C2×#1057—28no—
66C2×#1057—216no—
67C13×C4⋊C4—28no—
68#6101—216no—
69C4×Dic13—28no—
70C4×Dic13—28no—
71C4×Dic13C22⋊C418yes—
72C4×Dic13C2×D414yes—
73C4×Dic13C2×D414yes—
74C22×C4×Q8—131no—
75C2×#432—132no—
76#1985—138no—
77#1817—134no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13C2×C22⋊C412yes—
81C23×C13C2×M1614yes—
82C23×C13C23×C411yescharacteristic
83C2×C4×C13—24no—
84C2×C4×C13—28no—
85C2×C4×C13—24no—
86C2×C4×C13—28no—
87C2×C4×C13—48no—
88C2×C4×C13C2×C22⋊C414yes—
89C2×Dic13—24no—
90C2×Dic13—22no—
91C2×Dic13—24no—
92C2×Dic13—24no—
93C2×Dic13—216no—
94C2×Dic13—28no—
95C2×Dic13—44no—
96C2×Dic13C2×C22⋊C412yes—
97C2×Dic13C2×C22⋊C414yes—
98C2×Dic13C2×M1618yes—
99C2×Dic13C22×D412yes—
100C2×Dic132−1+414yes—
101Dic26—232no—
102#1057—48no—
103C23×Q8—131no—
104C2×C4×Q8—134no—
105C2×C4×Q8—134no—
106C2×C4×Q8—268no—
107C22×C4⋊C4—132no—
108C22×C4⋊C4#26111yescharacteristic
109C22×C42—131no—
110C22×C42—132no—
111#432—268no—
112C2×C4⋊C8—134no—
113C2×C22⋊C8—134no—
114C2×#97—134no—
115#336—1316no—
116C22×C13—22no—
117C22×C13—22no—
118C22×C13—28no—
119C22×C13#40714yes—
120C22×C13C22×C22⋊C411yescharacteristic
121C22×C13#51912yes—
122C22×C13C22×M1612yes—
123C22×C13#56812yes—
124C4×C13—24no—
125C4×C13—44no—
126Dic13—22no—
127Dic13—28no—
128Dic13—24no—
129Dic13#53614yes—
130C22×Q8—134no—
131C22×Q8—268no—
132C22×Q8—264no—
133C23×C4—132no—
134C23×C4—131no—
135C23×C4—131no—
136C23×C4C2×#26111yescharacteristic
137C23×C4C2×#26112yes—
138C22×C8—138no—
139C4×Q8—268no—
140C4×Q8—268no—
141C4×Q8—2616no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4—138no—
144C2×C4⋊C4—268no—
145C2×C4⋊C4C2×#26114yes—
146C2×C42—138no—
147C2×C42—132no—
148C2×C42—132no—
149C2×C42—134no—
150C2×C42—134no—
151C2×C42—268no—
152C4⋊C8—268no—
153C22⋊C8—268no—
154#97—268no—
155C2×C13—24no—
156C2×C13#231011yescharacteristic
157C2×C13C2×#40711yescharacteristic
158C2×C13#287911yescharacteristic
159C2×C13#298314yes—
160C24C22×#26111yescharacteristic
161C2×Q8—2616no—
162C2×Q8—2632no—
163C2×Q8—268no—
164C22×C4—24no—
165C22×C4—24no—
166C22×C4—44no—
167C22×C4—131no—
168C22×C4—138no—
169C22×C4—134no—
170C22×C4—131no—
171C22×C4—132no—
172C22×C4—134no—
173C22×C4—134no—
174C22×C4—264no—
175C22×C4—264no—
176C22×C4—264no—
177C22×C4—522no—
178C22×C4C22⋊#26114yes—
179C22×C4C22×#26114yes—
180C22×C4C22×#26112yes—
181C2×C8—268no—
182C2×C8—2616no—
183C4⋊C4—28no—
184C4⋊C4—2616no—
185C42—134no—
186C42—134no—
187C42—138no—
188C42—268no—
189C42—268no—
190C13#2182211yescharacteristic, complemented, Sylow
191C23—22no—
192C23—22no—
193C23D13⋊M1614yes—
194C23C2×C22⋊#26112yes—
195C23C23×#26111yescharacteristic
196Q8—2632no—
197C2×C4—24no—
198C2×C4—28no—
199C2×C4—28no—
200C2×C4—24no—
201C2×C4—48no—
202C2×C4—134no—
203C2×C4—132no—
204C2×C4—138no—
205C2×C4—132no—
206C2×C4—134no—
207C2×C4—268no—
208C2×C4—264no—
209C2×C4—264no—
210C2×C4—262no—
211C2×C4—264no—
212C2×C4—2616no—
213C2×C4—524no—
214C2×C4C2×C22⋊#26114yes—
215C8—528no—
216C22—22no—
217C22—22no—
218C22—28no—
219C22#1171912614yes—
220C22C2×D13⋊M1612yes—
221C22#1171962112yes—
222C22#1171962712yes—
223C22C22×C22⋊#26111yescharacteristic
224C4—24no—
225C4—44no—
226C4—134no—
227C4—262no—
228C4—268no—
229C4—264no—
230C2—24no—
231C2#1313131011yescharacteristic
232C2C2×#1171912611yescharacteristic
233C2#1313142211yescharacteristic
234C2#1313173514yes—
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC22×C13×C4⋊C4C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13#21822
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13131008C2semidirect
190. C13#21822semidirect

Maximal subgroups

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

subgroupindex
C2×#117191282
#131310082
#131307272
C22×#881412
#2182213