Finite Group Databasebeta

← C2×#13123400 #16726541

Subgroups — C2×#13123400 #16726541

Order 3328.

2830 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6099C212yesmaximal
2#13123400C2116yesmaximal, direct product factor
3C2×#11718660C218yesmaximal, complemented
4C2×#11718585C214yesmaximal, complemented
5C22×C13×#117C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C2×C13×#117C414yes—
8C2×C13×#117C418yes—
9C2×C13×#117C2214yes—
10C2×C13×#117C2218yes—
11C22×C13×C4⋊C4C412yes—
12C22×C13×C22⋊C4C412yes—
13C22×C42×C13C2212yes—
14C22×#6099—216no—
15C22×#6099C2214yes—
16C22×#6099C2214yes—
17C22×#6099C22116yes—
18C23×#1055C2214yes—
19#11718660C22164yescomplemented
20#11718585C22132yescomplemented
21C2×C4⋊#1055C22116yescomplemented
22C25×C13C2×C411yescharacteristic
23C23×C4×C13C2×C414yes—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C412yes—
26C23×C4×C13C2×C414yes—
27C23×C4×C13D418yes—
28C23×C4×C13Q818yes—
29C23×C4×C13C2312yes—
30C23×C4×C13C2311yescharacteristic
31C23×C4×C13C2314yes—
32C13×#117C2×C4116yes—
33C13×#117C2×C4132yes—
34C13×#117C23116yes—
35C2×C13×C4⋊C4C2×C418yes—
36C2×C13×C4⋊C4C2×C4116yes—
37C2×C13×C22⋊C4C2×C418yes—
38C2×C13×C22⋊C4C2×C4116yes—
39C2×C42×C13C2×C414yes—
40C2×C42×C13C2×C418yes—
41C2×C42×C13C2314yes—
42C2×C42×C13C2318yes—
43C2×#6099—216no—
44C2×#6099—216no—
45C2×#6099—264no—
46C2×#6099C23116yes—
47C2×#6099C23116yes—
48C22×#1055—216no—
49C22×#1055C23116yes—
50C22×#1055C2318yes—
51C4⋊#1055C23164yescomplemented
52C2×#2905—131nomaximal, Sylow
53C24×C13—44no—
54C24×C13C4⋊C418yes—
55C24×C13C22×C412yes—
56C24×C13C22×C411yescharacteristic
57C24×C13C22×C414yes—
58C22×C4×C13—48no—
59C22×C4×C13C4⋊C418yes—
60C22×C4×C13C4⋊C4116yes—
61C22×C4×C13C4⋊C4132yes—
62C22×C4×C13C22×C418yes—
63C22×C4×C13C22×C4116yes—
64C22×C4×C13C22×C412yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C22×C414yes—
67C22×C4×C13C22×C412yes—
68C22×C4×C13C22×C414yes—
69C22×C4×C13C22×C418yes—
70C22×C4×C13C2×D418yes—
71C22×C4×C13C2×D414yes—
72C22×C4×C13C2×D4116yes—
73C22×C4×C13C2×Q818yes—
74C22×C4×C13C2×Q814yes—
75C22×C4×C13C2×Q8116yes—
76C22×C4×C13C2414yes—
77C22×C4×C13C2412yes—
78C22×C4×C13C2411yescharacteristic
79C13×C4⋊C4C22×C4132yes—
80C13×C22⋊C4C22×C4132yes—
81C42×C13C22×C418yes—
82C42×C13C22×C4116yes—
83C42×C13C2418yes—
84#6099—232no—
85#6099—232no—
86C2×#1055—216no—
87C2×#1055—232no—
88C2×#1055C24116yes—
89C23×M16—132no—
90C22×#117D1311yescharacteristic
91#2905—1316no—
92C2×#424—138no—
93C2×#423—134no—
94C23×C13—24no—
95C23×C13—28no—
96C23×C13—416no—
97C23×C13—48no—
98C23×C13C2×C4⋊C418yes—
99C23×C13C2×C4⋊C414yes—
100C23×C13C2×C4⋊C4116yes—
101C23×C13C23×C414yes—
102C23×C13C23×C412yes—
103C23×C13C23×C411yescharacteristic
104C2×C4×C13—216no—
105C2×C4×C13—416no—
106C2×C4×C13C2×C4⋊C418yes—
107C2×C4×C13C2×C4⋊C4116yes—
108C2×C4×C13C2×C4⋊C4116yes—
109C2×C4×C13C2×C4⋊C4132yes—
110C2×C4×C13C2×C4⋊C414yes—
111C2×C4×C13C2×C4⋊C418yes—
112C2×C4×C13C23×C4116yes—
113C2×C4×C13C23×C412yes—
114C2×C4×C13C23×C411yescharacteristic
115C2×C4×C13C23×C414yes—
116C2×C4×C13C22×D412yes—
117C2×C4×C13C22×D418yes—
118C2×C4×C13C22×D414yes—
119C2×C4×C13C22×Q818yes—
120C2×C4×C13C22×Q814yes—
121C2×C4×C13C22×Q812yes—
122C2×C4×C13C2511yescharacteristic
123#1055—216no—
124C24×C4C2×D1311yescharacteristic
125C22×M16—134no—
126C22×M16—134no—
127C22×M16—1316no—
128C22×M16—2616no—
129C23×C8—134no—
130C2×#117Dic1314yes—
131C2×#117Dic1318yes—
132C2×#117C2×D1314yes—
133C2×#117C2×D1318yes—
134C22×C4⋊C4Dic1312yes—
135C22×C22⋊C4Dic1312yes—
136C22×C42C2×D1312yes—
137#424—1364no—
138#423—1332no—
139C2×C4⋊C8—1316no—
140C22×C13—28no—
141C22×C13—216no—
142C22×C13—24no—
143C22×C13—28no—
144C22×C13—416no—
145C22×C13C22×C4⋊C418yes—
146C22×C13C22×C4⋊C414yes—
147C22×C13C22×C4⋊C412yes—
148C22×C13#56814yes—
149C22×C13C24×C411yescharacteristic
150C4×C13—216no—
151C4×C13C22×C4⋊C412yes—
152C4×C13C22×C4⋊C414yes—
153C4×C13C22×C4⋊C418yes—
154C4×C13C23×D411yescharacteristic
155C4×C13C23×Q811yescharacteristic
156C25C2×Dic1311yescharacteristic
157C23×C4Dic2618yes—
158C23×C4D5218yes—
159C23×C4C2×Dic1314yes—
160C23×C4C2×Dic1311yescharacteristic
161C23×C4C2×Dic1312yes—
162C23×C4C2×Dic1314yes—
163C23×C4C22×D1314yes—
164C23×C4C22×D1312yes—
165C23×C4C22×D1311yescharacteristic
166C2×M16—1316no—
167C2×M16—1316no—
168C2×M16—2616no—
169C2×M16—2616no—
170C2×M16—2664no—
171C22×C8—1316no—
172C22×C8—138no—
173C22×C8—2616no—
174#117C2×Dic13116yes—
175#117C2×Dic13132yes—
176#117C22×D13116yes—
177C2×C4⋊C4C2×Dic1318yes—
178C2×C4⋊C4C2×Dic13116yes—
179C2×C22⋊C4C2×Dic1318yes—
180C2×C22⋊C4C2×Dic13116yes—
181C2×C42C2×Dic1314yes—
182C2×C42C2×Dic1318yes—
183C2×C42C22×D1318yes—
184C2×C42C22×D1314yes—
185C4⋊C8—1364no—
186C2×C13—24no—
187C2×C13—28no—
188C2×C13#290514yescomplemented
189C2×C13C23×C4⋊C411yescharacteristic
190C2×C13C2×#56812yes—
191C24—44no—
192C24C4⋊Dic1318yes—
193C24C22×Dic1312yes—
194C24C22×Dic1311yescharacteristic
195C24C22×Dic1314yes—
196C22×C4—48no—
197C22×C4C4⋊Dic1318yes—
198C22×C4C4⋊Dic13116yes—
199C22×C4C4⋊Dic13132yes—
200C22×C4C2×Dic26116yes—
201C22×C4C2×Dic2618yes—
202C22×C4C2×Dic2614yes—
203C22×C4C2×D5218yes—
204C22×C4C2×D5214yes—
205C22×C4C2×D52116yes—
206C22×C4C22×Dic1318yes—
207C22×C4C22×Dic13116yes—
208C22×C4C22×Dic1311yescharacteristic
209C22×C4C22×Dic1312yes—
210C22×C4C22×Dic1314yes—
211C22×C4C22×Dic1312yes—
212C22×C4C22×Dic1318yes—
213C22×C4C22×Dic1314yes—
214C22×C4C23×D1312yes—
215C22×C4C23×D1314yes—
216C22×C4C23×D1311yescharacteristic
217M16—2632no—
218M16—2632no—
219C2×C8—1316no—
220C2×C8—2616no—
221C2×C8—2632no—
222C4⋊C4C22×Dic13132yes—
223C22⋊C4C22×Dic13132yes—
224C42C22×Dic13116yes—
225C42C22×Dic1318yes—
226C42C23×D1318yes—
227C13C2×#290511yescharacteristic, complemented, Sylow
228C23—24no—
229C23—28no—
230C23—416no—
231C23—48no—
232C23C2×C4⋊Dic1318yes—
233C23C2×C4⋊Dic1314yes—
234C23C2×C4⋊Dic13116yes—
235C23C23×Dic1314yes—
236C23C23×Dic1312yes—
237C23C23×Dic1311yescharacteristic
238C2×C4—216no—
239C2×C4—416no—
240C2×C4C2×C4⋊Dic13116yes—
241C2×C4C2×C4⋊Dic1318yes—
242C2×C4C2×C4⋊Dic13116yes—
243C2×C4C2×C4⋊Dic13132yes—
244C2×C4C2×C4⋊Dic1318yes—
245C2×C4C2×C4⋊Dic1314yes—
246C2×C4C22×Dic2614yes—
247C2×C4C22×Dic2618yes—
248C2×C4C22×Dic2612yes—
249C2×C4C22×D5212yes—
250C2×C4C22×D5218yes—
251C2×C4C22×D5214yes—
252C2×C4C23×Dic13116yes—
253C2×C4C23×Dic1312yes—
254C2×C4C23×Dic1311yescharacteristic
255C2×C4C23×Dic1314yes—
256C2×C4C24×D1311yescharacteristic
257C8—2616no—
258C22—28no—
259C22—216no—
260C22—24no—
261C22—28no—
262C22—416no—
263C22C22×C4⋊Dic1318yes—
264C22C22×C4⋊Dic1314yes—
265C22C22×C4⋊Dic1312yes—
266C22#1171952414yes—
267C22C24×Dic1311yescharacteristic
268C4—216no—
269C4C22×C4⋊Dic1318yes—
270C4C22×C4⋊Dic1314yes—
271C4C22×C4⋊Dic1312yes—
272C4C23×Dic2611yescharacteristic
273C4C23×D5211yescharacteristic
274C2—24no—
275C2—28no—
276C2#1312340014yesdirect product factor
277C2C23×C4⋊Dic1311yescharacteristic
278C2C2×#1171952412yes—
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#117C2
socleC23×C13C23×C4
prime radicalC25×C13C2×C4
cosocleC2×C4×C13C25
hypercenterC22×#117D13
hypocenterC13C2×#2905
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #13123400C2direct (N × H)
3. C2×#11718660C2semidirect
4. C2×#11718585C2semidirect
19. #11718660C22semidirect
20. #11718585C22semidirect
21. C2×C4⋊#1055C22semidirect
51. C4⋊#1055C23semidirect
188. C2×C13#2905semidirect
227. C13C2×#2905semidirect
276. C2#13123400direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#60992
#131234002
C2×#117186602
C2×#117185852
C22×C13×#1172
C2×#290513