Finite Group Databasebeta

← C22×#11719119 #16808162

Subgroups — C22×#11719119 #16808162

Order 3328.

3086 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719119C2124yesmaximal, direct product factor
2C22×C4⋊#1057C212yesmaximal, complemented
3C22×C22⋊#1057C212yesmaximal
4C22×C4×#1057C212yesmaximal, complemented
5C23×C4×Dic13C211yesmaximal, characteristic
6C24×C4×C13C411yescharacteristic
7C24×Dic13C411yescharacteristic
8C24×Dic13C2211yescharacteristic
9C23×#1057C2214yes—
10C22×C4×Dic13C4112yes—
11C22×C4×Dic13C411yescharacteristic
12C22×C4×Dic13C411yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C22×C4×Dic13C2211yescharacteristic
15C22×C4×Dic13C22112yes—
16C2×C22⋊#1057C22124yes—
17#11719119C22164yesdirect product factor
18C2×C4⋊#1057C22124yescomplemented
19C2×C4×#1057C22124yescomplemented
20C25×C13C2×C411yescharacteristic
21C23×C4×C13C8116yescomplemented
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13C2×C4112yes—
24C23×C4×C13C2×C411yescharacteristic
25C23×Dic13—28no—
26C23×Dic13—28no—
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C416yes—
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2×C4112yes—
31C23×Dic13C2×C411yescharacteristic
32C23×Dic13C2316yes—
33C23×Dic13C2311yescharacteristic
34C22×#1057—216no—
35C22×#1057C23124yes—
36C2×C4×Dic13C2×C4112yes—
37C2×C4×Dic13C2×C4148yes—
38C2×C4×Dic13C2×C4112yes—
39C2×C4×Dic13C2×C416yes—
40C2×C4×Dic13C2×C416yes—
41C2×C4×Dic13C2316yes—
42C2×C4×Dic13C2316yes—
43C2×C4×Dic13C23116yes—
44C22⋊#1057C23132yes—
45C4⋊#1057C23132yescomplemented
46C4×#1057C23132yescomplemented
47C22×#431—131nomaximal, Sylow
48C24×C13—24no—
49C24×C13—24no—
50C24×C13C2×C818yes—
51C24×C13C22×C416yes—
52C24×C13C22×C411yescharacteristic
53C22×C4×C13C2×C818yes—
54C22×C4×C13C2×C818yes—
55C22×C4×C13C2×C8196yescomplemented
56C22×C4×C13C22×C416yes—
57C22×C4×C13C22×C416yes—
58C22×C4×C13C22×C4116yes—
59C22×Dic13—24no—
60C22×Dic13—24no—
61C22×Dic13—224no—
62C22×Dic13—248no—
63C22×Dic13—224no—
64C22×Dic13M1618yes—
65C22×Dic13C22×C416yes—
66C22×Dic13C22×C4112yes—
67C22×Dic13C22×C416yes—
68C22×Dic13C22×C4116yes—
69C22×Dic13C22×C413yes—
70C22×Dic13C22×C416yes—
71C22×Dic13#4118yes—
72C22×Dic13C2414yes—
73C22×Dic13C2413yes—
74C2×#1057—248no—
75C2×#1057C24116yes—
76C4×Dic13C22×C4116yes—
77C4×Dic13C22×C4116yes—
78C4×Dic13C22×C4112yes—
79C4×Dic13C22×C4112yes—
80C4×Dic13C2414yes—
81C4×Dic13C2414yes—
82C23×C42—131no—
83C2×#431—1324no—
84C22×C4⋊C8—132no—
85C22×C22⋊C8—132no—
86C22×C4×C8—132no—
87C23×C13—212no—
88C23×C13—212no—
89C23×C13—232no—
90C23×C13#11714yes—
91C23×C13C22×C8124yes—
92C23×C13C22×C814yes—
93C23×C13C2×M1614yes—
94C23×C13C23×C414yes—
95C23×C13C23×C413yes—
96C2×C4×C13C22×C8124yes—
97C2×C4×C13C22×C8124yes—
98C2×C4×C13C22×C8164yescomplemented
99C2×C4×C13C23×C414yes—
100C2×C4×C13C23×C414yes—
101C2×Dic13—212no—
102C2×Dic13—212no—
103C2×Dic13—224no—
104C2×Dic13—232no—
105C2×Dic13—28no—
106C2×Dic13#117112yes—
107C2×Dic13C2×M16124yes—
108C2×Dic13C23×C414yes—
109C2×Dic13C23×C414yes—
110C2×Dic13C23×C413yes—
111C2×Dic13C23×C414yes—
112C2×Dic13C2×#41112yes—
113C2×Dic13C2511yescharacteristic
114#1057—216no—
115C24×C4—131no—
116C24×C4—131no—
117C24×C4#26111yescharacteristic
118C23×C8—134no—
119C22×C42—131no—
120C22×C42—1312no—
121C22×C42—131no—
122C22×C42—1312no—
123C22×C42—131no—
124C22×C42—131no—
125#431—1364no—
126C2×C4⋊C8—1324no—
127C2×C22⋊C8—1324no—
128C2×C4×C8—1324no—
129C22×C13—24no—
130C22×C13—248no—
131C22×C13—24no—
132C22×C13#431116yescomplemented
133C22×C13C2×#11716yes—
134C22×C13C23×C818yes—
135C22×C13C23×C816yes—
136C22×C13C22×M1616yes—
137C22×C13C24×C411yescharacteristic
138C4×C13C23×C818yes—
139C4×C13C23×C818yes—
140Dic13—24no—
141Dic13—24no—
142Dic13C2×#11716yes—
143Dic13C22×M1618yes—
144Dic13C22×#4112yes—
145C25C2×#26111yescharacteristic
146C23×C4—131no—
147C23×C4—131no—
148C23×C4—136no—
149C23×C4—136no—
150C23×C4—1312no—
151C23×C4—131no—
152C23×C4—131no—
153C23×C4—268no—
154C23×C4—268no—
155C23×C4#1057116yescomplemented
156C23×C4C2×#26111yescharacteristic
157C23×C4C2×#261112yes—
158C23×C4C2×#26111yescharacteristic
159C22×C8—1324no—
160C22×C8—2616no—
161C2×C42—136no—
162C2×C42—136no—
163C2×C42—1312no—
164C2×C42—1312no—
165C2×C42—1348no—
166C2×C42—136no—
167C2×C42—136no—
168C2×C42—1316no—
169C4⋊C8—1332no—
170C22⋊C8—1332no—
171C4×C8—1332no—
172C2×C13—28no—
173C2×C13C2×#431112yescomplemented
174C2×C13C22×#11711yescharacteristic
175C2×C13C24×C811yescharacteristic
176C2×C13C23×M1611yescharacteristic
177C24—24no—
178C24—24no—
179C24C2×#105718yes—
180C24C22×#26116yes—
181C24C22×#26111yescharacteristic
182C22×C4—138no—
183C22×C4—138no—
184C22×C4—133no—
185C22×C4—136no—
186C22×C4—133no—
187C22×C4—134no—
188C22×C4—1312no—
189C22×C4—1316no—
190C22×C4—136no—
191C22×C4—136no—
192C22×C4—2648no—
193C22×C4—2624no—
194C22×C4—2624no—
195C22×C4—264no—
196C22×C4—264no—
197C22×C4C2×#105718yes—
198C22×C4C2×#105718yes—
199C22×C4C2×#1057196yescomplemented
200C22×C4C22×#26116yes—
201C22×C4C22×#26116yes—
202C22×C4C22×#261116yes—
203C2×C8—1316no—
204C2×C8—2648no—
205C42—134no—
206C42—134no—
207C42—1312no—
208C42—1312no—
209C42—1316no—
210C42—1316no—
211C13C22×#43111yescharacteristic, complemented, Sylow
212C23—212no—
213C23—212no—
214C23—232no—
215C23D13⋊M1614yes—
216C23#8823714yes—
217C23C22×#1057124yes—
218C23C22×#105714yes—
219C23C23×#26114yes—
220C23C23×#26113yes—
221C2×C4—1324no—
222C2×C4—1312no—
223C2×C4—1312no—
224C2×C4—131no—
225C2×C4—133no—
226C2×C4—134no—
227C2×C4—134no—
228C2×C4—134no—
229C2×C4—2624no—
230C2×C4—268no—
231C2×C4—2632no—
232C2×C4—2612no—
233C2×C4—2612no—
234C2×C4C22×#1057124yes—
235C2×C4C22×#1057124yes—
236C2×C4C22×#1057164yescomplemented
237C2×C4C23×#26114yes—
238C2×C4C23×#26114yes—
239C8—2616no—
240C22—24no—
241C22—24no—
242C22—248no—
243C22#11719119116yesdirect product factor
244C22C2×D13⋊M1616yes—
245C22C2×#8823716yes—
246C22C23×#105718yes—
247C22C23×#105716yes—
248C22C24×#26111yescharacteristic
249C4—136no—
250C4—132no—
251C4—138no—
252C4—264no—
253C4—264no—
254C4C23×#105718yes—
255C4C23×#105718yes—
256C2—28no—
257C2C2×#11719119112yesdirect product factor
258C2C22×#8823711yescharacteristic
259C2C24×#105711yescharacteristic
260C2C22×D13⋊M1611yescharacteristic
subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C24×C8
FrattiniC22C24×#261
FittingC24×C4×C13C4
socleC24×C13C22×C4
prime radicalC25×C13C2×C4
cosocleC2×Dic13C25
hypercenterC24×C4#261
hypocenterC13C22×#431
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C2×#11719119C2direct (N × H)
2. C22×C4⋊#1057C2semidirect
4. C22×C4×#1057C2semidirect
17. #11719119C22direct (N × H)
18. C2×C4⋊#1057C22semidirect
19. C2×C4×#1057C22semidirect
21. C23×C4×C13C8semidirect
45. C4⋊#1057C23semidirect
46. C4×#1057C23semidirect
55. C22×C4×C13C2×C8semidirect
98. C2×C4×C13C22×C8semidirect
132. C22×C13#431semidirect
155. C23×C4#1057semidirect
173. C2×C13C2×#431semidirect
199. C22×C4C2×#1057semidirect
211. C13C22×#431semidirect
236. C2×C4C22×#1057semidirect
243. C22#11719119direct (N × H)
257. C2C2×#11719119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191192
C22×C4⋊#10572
C22×C22⋊#10572
C22×C4×#10572
C23×C4×Dic132
C22×#43113