Finite Group Databasebeta

← C2×#13114924 #15862703

Subgroups — C2×#13114924 #15862703

Order 3328.

1878 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic13C211yesmaximal, characteristic
2C22×C22⋊#1055C211yesmaximal, characteristic
3#13114924C218yesmaximal, direct product factor
4C2×#11718121C214yesmaximal, complemented
5C2×C13×#380C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C24×Dic13—21no—
8C22×C13×C4⋊C4C2212yes—
9C22×C13×C22⋊C4—21no—
10C22×C4⋊Dic13—24no—
11C22×C4⋊Dic13—22no—
12C22×C4⋊Dic13—21no—
13C22×C4⋊Dic13C418yescomplemented
14C22×C4⋊Dic13C2212yes—
15C22×C4⋊Dic13C2214yes—
16C23×#1055C2212yes—
17C13×#380—22no—
18C13×#380C2214yes—
19C2×C13×#95—21no—
20C2×C22⋊#1055—24no—
21C2×C22⋊#1055C2214yes—
22#11718121C22116yescomplemented
23C25×C13D411yescharacteristic
24C23×C4×C13—28no—
25C23×C4×C13—22no—
26C23×C4×C13C2×C414yes—
27C23×C4×C13D414yes—
28C23×C4×C13D412yes—
29C23×C4×C13D411yescharacteristic
30C23×C4×C13C2312yes—
31C23×C4×C13C2311yescharacteristic
32C23×Dic13—28no—
33C23×Dic13—24no—
34C23×Dic13—22no—
35C23×Dic13—48no—
36C2×C13×C4⋊C4—28no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4C2314yes—
39C2×C13×C22⋊C4—24no—
40C2×C13×C22⋊C4—44no—
41C2×C4⋊Dic13—216no—
42C2×C4⋊Dic13—28no—
43C2×C4⋊Dic13—24no—
44C2×C4⋊Dic13—28no—
45C2×C4⋊Dic13—22no—
46C2×C4⋊Dic13—24no—
47C2×C4⋊Dic13C2×C418yes—
48C2×C4⋊Dic13C2×C4116yescomplemented
49C2×C4⋊Dic13C2314yes—
50C22×#1055—24no—
51C22×#1055—28no—
52C22×#1055C2314yes—
53C13×#95—24no—
54C22⋊#1055—28no—
55C2×#1824—131nomaximal, Sylow
56C24×C13—24no—
57C24×C13—24no—
58C24×C13C22⋊C414yes—
59C24×C13SD1614yes—
60C24×C13Q1614yes—
61C24×C13C2×D412yes—
62C24×C13C2×D411yescharacteristic
63C22×C4×C13—24no—
64C22×C4×C13—216no—
65C22×C4×C13—216no—
66C22×C4×C13—28no—
67C22×C4×C13—28no—
68C22×C4×C13—24no—
69C22×C4×C13—44no—
70C22×C4×C13—44no—
71C22×C4×C13—44no—
72C22×C4×C13C22⋊C414yes—
73C22×C4×C13C22⋊C418yes—
74C22×C4×C13C22×C414yes—
75C22×C4×C13C22×C412yes—
76C22×C4×C13C2×D414yes—
77C22×C4×C13C2×D412yes—
78C22×C4×C13C2×D412yes—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4118yes—
81C22×C4×C13C2411yescharacteristic
82C22×Dic13—28no—
83C22×Dic13—216no—
84C22×Dic13—24no—
85C22×Dic13—416no—
86C22×Dic13—432no—
87C22×Dic13—48no—
88C13×C4⋊C4—28no—
89C13×C4⋊C4—44no—
90C13×C22⋊C4—48no—
91C4⋊Dic13—28no—
92C4⋊Dic13—216no—
93C4⋊Dic13—24no—
94C4⋊Dic13C22×C418yes—
95C2×#1055—24no—
96C2×#1055—28no—
97C2×#1055—48no—
98C23×C4⋊C4—131no—
99C22×C22⋊C8—131no—
100C2×#380D1311yescharacteristic
101#1824—138no—
102C2×#340—134no—
103C23×C13—24no—
104C23×C13—24no—
105C23×C13—28no—
106C23×C13—28no—
107C23×C13—216no—
108C23×C13—216no—
109C23×C13#103116yes—
110C23×C13C2×C22⋊C414yes—
111C23×C13C2×C22⋊C412yes—
112C23×C13#12314yes—
113C23×C13C2×SD1614yes—
114C23×C13C2×SD1612yes—
115C23×C13C2×Q1614yes—
116C23×C13C2×Q1612yes—
117C23×C13AGL(1,ℤ/8)14yes—
118C23×C13C22×D411yescharacteristic
119C2×C4×C13—24no—
120C2×C4×C13—28no—
121C2×C4×C13—28no—
122C2×C4×C13—28no—
123C2×C4×C13—216no—
124C2×C4×C13—44no—
125C2×C4×C13—44no—
126C2×C4×C13—44no—
127C2×C4×C13—88no—
128C2×C4×C13C2×C22⋊C414yes—
129C2×C4×C13C2×C22⋊C412yes—
130C2×C4×C13#11718yes—
131C2×C4×C13#12318yes—
132C2×C4×C13#12314yes—
133C2×C4×C13C23×C411yescharacteristic
134C2×C4×C13C22×D411yescharacteristic
135C2×C4×C13C2×#4114yes—
136C2×Dic13—28no—
137C2×Dic13—432no—
138C2×Dic13—48no—
139C2×Dic13—416no—
140#1055—44no—
141C24×C4—261no—
142C24×C4C2×D1311yescharacteristic
143C23×C8—132no—
144C22×C4⋊C4—138no—
145C22×C4⋊C4—134no—
146C22×C4⋊C4—132no—
147C22×C4⋊C4—264no—
148C22×C4⋊C4—262no—
149C22×C4⋊C4—261no—
150C22×C4⋊C4C2×D1312yes—
151C22×C22⋊C4—21no—
152C2×C22⋊C8—134no—
153C2×C22⋊C8—264no—
154#380—22no—
155#380C2×D1314yes—
156C2×#95—21no—
157#340—1316no—
158C22×C13—28no—
159C22×C13—28no—
160C22×C13—232no—
161C22×C13—24no—
162C22×C13—24no—
163C22×C13#38114yes—
164C22×C13C2×#10318yes—
165C22×C13C2×#10314yes—
166C22×C13#41814yes—
167C22×C13#48118yes—
168C22×C13#48418yes—
169C22×C13C22×C22⋊C411yescharacteristic
170C22×C13C2×#12312yes—
171C22×C13C22×SD1611yescharacteristic
172C22×C13C22×Q1611yescharacteristic
173C22×C13C2×AGL(1,ℤ/8)12yes—
174C4×C13—24no—
175C4×C13—84no—
176C4×C13#38114yes—
177C4×C13C2×#11712yes—
178C4×C13C2×#12312yes—
179Dic13—48no—
180C25C22⋊D1311yescharacteristic
181C23×C4—28no—
182C23×C4—22no—
183C23×C4—268no—
184C23×C4—264no—
185C23×C4—262no—
186C23×C4—528no—
187C23×C4C4×D1314yes—
188C23×C4D5214yes—
189C23×C4C22⋊D1312yes—
190C23×C4C22⋊D1311yescharacteristic
191C23×C4C22×D1312yes—
192C23×C4C22×D1311yescharacteristic
193C22×C8—134no—
194C22×C8—264no—
195C22×C8—268no—
196C2×C4⋊C4—28no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—138no—
199C2×C4⋊C4—1316no—
200C2×C4⋊C4—134no—
201C2×C4⋊C4—268no—
202C2×C4⋊C4—2616no—
203C2×C4⋊C4—268no—
204C2×C4⋊C4—264no—
205C2×C4⋊C4—264no—
206C2×C4⋊C4—262no—
207C2×C4⋊C4C22×D1314yes—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—44no—
210C22⋊C8—268no—
211#95—24no—
212C2×C13—28no—
213C2×C13#182418yescomplemented
214C2×C13C2×#38111yescharacteristic
215C2×C13C22×#10311yescharacteristic
216C2×C13C2×#41811yescharacteristic
217C2×C13C2×#48112yes—
218C2×C13C2×#48412yes—
219C24—24no—
220C24—24no—
221C24#610314yes—
222C24#610514yes—
223C24#610714yes—
224C24C2×C22⋊D1312yes—
225C24C2×C22⋊D1311yescharacteristic
226C22×C4—24no—
227C22×C4—216no—
228C22×C4—216no—
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—24no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—2616no—
236C22×C4—268no—
237C22×C4—264no—
238C22×C4—5232no—
239C22×C4—5216no—
240C22×C4—528no—
241C22×C4#610314yes—
242C22×C4#610318yes—
243C22×C4C2×C4×D1314yes—
244C22×C4C2×C4×D1312yes—
245C22×C4C2×D5214yes—
246C22×C4C2×D5212yes—
247C22×C4#612918yes—
248C22×C4C2×C22⋊D1312yes—
249C22×C4C2×C22⋊D1311yescharacteristic
250C22×C4C23×D1311yescharacteristic
251C2×C8—264no—
252C2×C8—268no—
253C2×C8—528no—
254C4⋊C4—28no—
255C4⋊C4—44no—
256C4⋊C4—138no—
257C4⋊C4—2616no—
258C4⋊C4—268no—
259C4⋊C4—264no—
260C22⋊C4—48no—
261C13C2×#182411yescharacteristic, complemented, Sylow
262C23—28no—
263C23—216no—
264C23—216no—
265C23—24no—
266C23—24no—
267C23—28no—
268C23#88050116yes—
269C23C2×#610314yes—
270C23C2×#610312yes—
271C23C2×#610514yes—
272C23C2×#610512yes—
273C23#8818914yes—
274C23C2×#610714yes—
275C23C2×#610712yes—
276C23#8820314yes—
277C23C22×C22⋊D1311yescharacteristic
278C2×C4—24no—
279C2×C4—28no—
280C2×C4—28no—
281C2×C4—28no—
282C2×C4—216no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—88no—
287C2×C4—268no—
288C2×C4—5232no—
289C2×C4—5216no—
290C2×C4—528no—
291C2×C4#8813118yes—
292C2×C4#8814018yes—
293C2×C4C2×#610314yes—
294C2×C4C2×#610312yes—
295C2×C4#8818914yes—
296C2×C4C22×C4×D1311yescharacteristic
297C2×C4C22×D5211yescharacteristic
298C2×C4C2×#612914yes—
299C8—524no—
300C22—24no—
301C22—24no—
302C22—232no—
303C22—28no—
304C22—28no—
305C22#1171860414yes—
306C22C2×#8805018yes—
307C22C2×#8805014yes—
308C22#1171866214yes—
309C22#1171869518yes—
310C22#1171870518yes—
311C22C22×#610311yescharacteristic
312C22C22×#610511yescharacteristic
313C22C2×#8818912yes—
314C22C22×#610711yescharacteristic
315C22C2×#8820312yes—
316C4—24no—
317C4—84no—
318C4—528no—
319C4#1171860414yes—
320C4C2×#8813112yes—
321C4C2×#8814012yes—
322C2—28no—
323C2#1311492418yesdirect product factor
324C2C2×#1171860411yescharacteristic
325C2C22×#8805011yescharacteristic
326C2C2×#1171866211yescharacteristic
327C2C2×#1171869512yes—
328C2C2×#1171870512yes—
subgroupG/H
centerC24C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#380C2
socleC24×C13C2×D4
prime radicalC25×C13D4
cosocleC22×C4×C13C24
hypercenterC2×#380D13
hypocenterC13C2×#1824
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. #13114924C2direct (N × H)
4. C2×#11718121C2semidirect
13. C22×C4⋊Dic13C4semidirect
22. #11718121C22semidirect
48. C2×C4⋊Dic13C2×C4semidirect
213. C2×C13#1824semidirect
261. C13C2×#1824semidirect
323. C2#13114924direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic132
C22×C22⋊#10552
#131149242
C2×#117181212
C2×C13×#3802
C2×#182413