Finite Group Databasebeta

← C22×#11719062 #16808004

Subgroups — C22×#11719062 #16808004

Order 3328.

3518 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6122C211yesmaximal, characteristic
2C24×#1057C211yesmaximal, characteristic
3C2×#11719062C2124yesmaximal, direct product factor
4C22×#88110C212yesmaximal, complemented
5C22×C4×#1057C212yesmaximal, complemented
6C22×#88131C211yesmaximal, characteristic
7C24×Dic13C2211yescharacteristic
8C22×#6122C4116yescomplemented
9C22×#6122C22112yes—
10C23×#1057C4116yescomplemented
11C23×#1057C2211yescharacteristic
12C23×#1057C2211yescharacteristic
13C23×#1057C2212yes—
14C23×#1057C22112yes—
15C22×C13×C22⋊C4C411yescharacteristic
16C22×C22⋊Dic13C411yescharacteristic
17C22×#6101C412yes—
18C22×C4×Dic13C2212yes—
19C2×#88131C4112yes—
20C2×#88131C22112yes—
21C2×#88110C22124yescomplemented
22C2×C4×#1057C22124yescomplemented
23#11719062C22164yesdirect product factor
24C25×C13C2×C411yescharacteristic
25C23×C4×C13C2×C412yes—
26C23×Dic13C2×C412yes—
27C23×Dic13C2×C416yes—
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C418yes—
30C23×Dic13C2×C418yes—
31C23×Dic13C2316yes—
32C23×Dic13C2311yescharacteristic
33C2×#6122C2×C4196yescomplemented
34C2×#6122C23116yes—
35C22×#1057C2×C418yes—
36C22×#1057C2×C418yes—
37C22×#1057C2×C4116yes—
38C22×#1057C2×C4196yescomplemented
39C22×#1057C2316yes—
40C22×#1057C23112yes—
41C22×#1057C2316yes—
42C22×#1057C23116yes—
43C2×C13×C22⋊C4C2×C4112yes—
44C2×C22⋊Dic13C2×C4112yes—
45C2×#6101C2×C4124yes—
46C2×C4×Dic13C2×C4112yes—
47C2×C4×Dic13C23112yes—
48#88131C2×C4148yes—
49#88131C23116yes—
50#88110C23132yescomplemented
51C4×#1057C23132yescomplemented
52C22×#405—131nomaximal, Sylow
53C24×C13—28no—
54C24×C13C4218yes—
55C24×C13C22×C416yes—
56C24×C13C22×C411yescharacteristic
57C22×C4×C13—28no—
58C22×C4×C13C22×C4112yes—
59C22×Dic13—28no—
60C22×Dic13C42148yes—
61C22×Dic13C4218yes—
62C22×Dic13C22×C4112yes—
63C22×Dic13C22×C4112yes—
64C22×Dic13C22×C413yes—
65C22×Dic13C22×C416yes—
66C22×Dic13C22×C414yes—
67C22×Dic13C22×C414yes—
68C22×Dic13C22×C4124yes—
69C22×Dic13C22×C4124yes—
70C22×Dic13C2414yes—
71C22×Dic13C2413yes—
72#6122C22×C4164yescomplemented
73C2×#1057C22×C4124yes—
74C2×#1057C22×C4124yes—
75C2×#1057C22×C4148yes—
76C2×#1057C22×C4164yescomplemented
77C2×#1057C2414yes—
78C2×#1057C2418yes—
79C2×#1057C2414yes—
80C13×C22⋊C4C22×C4116yes—
81C22⋊Dic13C22×C4116yes—
82#6101C22×C4132yes—
83C4×Dic13C22×C4124yes—
84C4×Dic13C2418yes—
85C23×M16—131no—
86C24×C8—131no—
87C22×#117—131no—
88C2×#405—1324no—
89C22×#97—132no—
90C22×C4×C8—132no—
91C23×C13—224no—
92C23×C13—232no—
93C23×C13C2×C42124yes—
94C23×C13C2×C4214yes—
95C23×C13#13118yes—
96C23×C13C23×C414yes—
97C23×C13C23×C413yes—
98C2×C4×C13—224no—
99C2×C4×C13C23×C418yes—
100C2×Dic13—224no—
101C2×Dic13C2×C42148yes—
102C2×Dic13C2×C42112yes—
103C2×Dic13C2×C42124yes—
104C2×Dic13C23×C418yes—
105C2×Dic13C23×C416yes—
106C2×Dic13C23×C416yes—
107C2×Dic13C23×C418yes—
108C2×Dic13C23×C418yes—
109C2×Dic13C23×C413yes—
110C2×Dic13C23×C414yes—
111C2×Dic13C2511yescharacteristic
112#1057C23×C418yes—
113#1057C23×C418yes—
114#1057C23×C4116yes—
115C24×C4—131no—
116C22×M16—1312no—
117C22×M16—1316no—
118C23×C8—131no—
119C23×C8—132no—
120C23×C8—131no—
121C23×C8—1312no—
122C23×C8—1316no—
123C2×#117—1312no—
124C2×#117—1312no—
125C22×C4⋊C4—132no—
126C22×C22⋊C4—131no—
127C22×C22⋊C4#26111yescharacteristic
128C22×C42—132no—
129#405—1364no—
130C2×#97—1324no—
131C2×C4×C8—1324no—
132C22×C13—248no—
133C22×C13—28no—
134C22×C13#405116yescomplemented
135C22×C13C22×C4218yes—
136C22×C13C22×C4216yes—
137C22×C13C2×#131112yes—
138C22×C13C24×C411yescharacteristic
139C4×C13—28no—
140Dic13—28no—
141Dic13C22×C4216yes—
142Dic13C22×C4218yes—
143Dic13C24×C411yescharacteristic
144Dic13C24×C411yescharacteristic
145C25C2×#26111yescharacteristic
146C23×C4—138no—
147C23×C4—138no—
148C23×C4—136no—
149C23×C4—136no—
150C23×C4—131no—
151C23×C4—131no—
152C23×C4—132no—
153C23×C4C2×#26112yes—
154C2×M16—1316no—
155C2×M16—1396no—
156C22×C8—136no—
157C22×C8—136no—
158C22×C8—1316no—
159C22×C8—138no—
160C22×C8—138no—
161C22×C8—1396no—
162C22×C8—1312no—
163C22×C8—1316no—
164#117—1348no—
165#117—1316no—
166C2×C4⋊C4—1324no—
167C2×C22⋊C4—1312no—
168C2×C22⋊C4C2×#261112yes—
169C2×C42—1312no—
170C2×C42—1312no—
171#97—1332no—
172C4×C8—1332no—
173C2×C13—28no—
174C2×C13C2×#405112yescomplemented
175C2×C13C23×C4211yescharacteristic
176C2×C13C22×#13112yes—
177C24—28no—
178C24C4×#26118yes—
179C24C22×#26116yes—
180C24C22×#26111yescharacteristic
181C22×C4—28no—
182C22×C4—1324no—
183C22×C4—134no—
184C22×C4—134no—
185C22×C4—1324no—
186C22×C4—1348no—
187C22×C4—138no—
188C22×C4—133no—
189C22×C4—133no—
190C22×C4—136no—
191C22×C4—134no—
192C22×C4—1312no—
193C22×C4—1312no—
194C22×C4—268no—
195C22×C4C22×#261112yes—
196M16—1364no—
197C2×C8—134no—
198C2×C8—138no—
199C2×C8—134no—
200C2×C8—1324no—
201C2×C8—1324no—
202C2×C8—1364no—
203C2×C8—1348no—
204C4⋊C4—1332no—
205C22⋊C4—1316no—
206C22⋊C4C22×#261116yes—
207C42—138no—
208C42—1324no—
209C13C22×#40511yescharacteristic, complemented, Sylow
210C23—232no—
211C23—224no—
212C23C2×C4×#261124yes—
213C23C2×C4×#26114yes—
214C23#8823818yes—
215C23C23×#26114yes—
216C23C23×#26113yes—
217C2×C4—224no—
218C2×C4—138no—
219C2×C4—136no—
220C2×C4—136no—
221C2×C4—138no—
222C2×C4—1348no—
223C2×C4—1312no—
224C2×C4—1324no—
225C2×C4—131no—
226C2×C4—133no—
227C2×C4—134no—
228C2×C4—138no—
229C2×C4—2624no—
230C2×C4C23×#26118yes—
231C8—138no—
232C8—138no—
233C8—1316no—
234C22—28no—
235C22—248no—
236C22#11719062116yesdirect product factor
237C22C22×C4×#26118yes—
238C22C22×C4×#26116yes—
239C22C2×#88238112yes—
240C22C24×#26111yescharacteristic
241C4—28no—
242C4—131no—
243C4—131no—
244C4—136no—
245C4—138no—
246C4—268no—
247C2—28no—
248C2C2×#11719062112yesdirect product factor
249C2C23×C4×#26111yescharacteristic
250C2C22×#8823812yes—
subgroupG/H
centerC24C22×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC22×C13×C22⋊C4C4
socleC24×C13C22×C4
prime radicalC25×C13C2×C4
cosocleC2×Dic13C25
hypercenterC22×C22⋊C4#261
hypocenterC13C22×#405
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#11719062C2direct (N × H)
4. C22×#88110C2semidirect
5. C22×C4×#1057C2semidirect
8. C22×#6122C4semidirect
10. C23×#1057C4semidirect
21. C2×#88110C22semidirect
22. C2×C4×#1057C22semidirect
23. #11719062C22direct (N × H)
33. C2×#6122C2×C4semidirect
38. C22×#1057C2×C4semidirect
50. #88110C23semidirect
51. C4×#1057C23semidirect
72. #6122C22×C4semidirect
76. C2×#1057C22×C4semidirect
134. C22×C13#405semidirect
174. C2×C13C2×#405semidirect
209. C13C22×#405semidirect
236. C22#11719062direct (N × H)
248. C2C2×#11719062direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#61222
C24×#10572
C2×#117190622
C22×#881102
C22×C4×#10572
C22×#881312
C22×#40513