Finite Group Databasebeta

← C2×#13114931 #15862700

Subgroups — C2×#13114931 #15862700

Order 3328.

1574 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊#1055C211yesmaximal, characteristic
2C2×#11718873C211yesmaximal, characteristic
3#13114931C218yesmaximal, direct product factor
4C2×#11718121C212yesmaximal, complemented
5C2×#11718121C212yesmaximal, complemented
6C22×C13×#117C211yesmaximal, characteristic
7C24×C4×C13C2211yescharacteristic
8C2×C13×#117—24no—
9C2×C13×#117—22no—
10C2×C13×#117C418yescomplemented
11C2×C13×#117C2214yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4—21no—
15C22×C42×C13—21no—
16C22×C22⋊Dic13—21no—
17C22×C4⋊Dic13C2212yes—
18C23×#1055C2212yes—
19#11718873—22no—
20#11718873C2214yes—
21C2×#88071—21no—
22C2×C22⋊#1055—24no—
23C2×C22⋊#1055C2214yes—
24#11718121C2218yescomplemented
25#11718121C2218yescomplemented
26C25×C13D411yescharacteristic
27C23×C4×C13—28no—
28C23×C4×C13—21no—
29C23×C4×C13—21no—
30C23×C4×C13C2×C414yes—
31C23×C4×C13D411yescharacteristic
32C23×C4×C13D412yes—
33C23×C4×C13D414yes—
34C23×C4×C13C2312yes—
35C23×C4×C13C2311yescharacteristic
36C23×Dic13—22no—
37C13×#117—216no—
38C13×#117—28no—
39C13×#117C2×C4116yescomplemented
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4C2×C414yes—
45C2×C13×C4⋊C4C2×C414yes—
46C2×C13×C4⋊C4C2312yes—
47C2×C13×C4⋊C4C2312yes—
48C2×C13×C22⋊C4—28no—
49C2×C13×C22⋊C4—24no—
50C2×C42×C13—28no—
51C2×C42×C13—24no—
52C2×C22⋊Dic13—24no—
53C2×C22⋊Dic13—44no—
54C2×C4⋊Dic13—28no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13C2314yes—
57C22×#1055—24no—
58C22×#1055—28no—
59C22×#1055C2314yes—
60#88071—24no—
61C22⋊#1055—28no—
62C2×#1825—131nomaximal, Sylow
63C24×C13—24no—
64C24×C13—24no—
65C24×C13—22no—
66C24×C13—22no—
67C24×C13C22⋊C414yes—
68C24×C13C2×D412yes—
69C24×C13C2×D411yescharacteristic
70C22×C4×C13—24no—
71C22×C4×C13—216no—
72C22×C4×C13—28no—
73C22×C4×C13—216no—
74C22×C4×C13—28no—
75C22×C4×C13—24no—
76C22×C4×C13—24no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—44no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13C22⋊C414yes—
83C22×C4×C13C22⋊C418yes—
84C22×C4×C13C22×C414yes—
85C22×C4×C13C22×C412yes—
86C22×C4×C13C2×D412yes—
87C22×C4×C13C2×D414yes—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D412yes—
90C22×C4×C13#4118yes—
91C22×C4×C13C2411yescharacteristic
92C22×Dic13—24no—
93C22×Dic13—44no—
94C22×Dic13—44no—
95C22×Dic13—44no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4C22×C414yes—
101C13×C4⋊C4C22×C414yes—
102C13×C22⋊C4—216no—
103C42×C13—216no—
104C22⋊Dic13—48no—
105C4⋊Dic13—28no—
106C4⋊Dic13—44no—
107C2×#1055—24no—
108C2×#1055—28no—
109C2×#1055—48no—
110C22×#117D1311yescharacteristic
111C22×C22⋊C8—131no—
112C2×#380—131no—
113#1825—138no—
114C2×#340—132no—
115C2×#340—132no—
116C23×C13—24no—
117C23×C13—24no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—28no—
121C23×C13—28no—
122C23×C13—28no—
123C23×C13—48no—
124C23×C13—48no—
125C23×C13C2×C22⋊C414yes—
126C23×C13C2×C22⋊C412yes—
127C23×C13#12314yes—
128C23×C13#13514yes—
129C23×C13AGL(1,ℤ/8)12yes—
130C23×C13#13712yes—
131C23×C13C22×D411yescharacteristic
132C2×C4×C13—24no—
133C2×C4×C13—28no—
134C2×C4×C13—28no—
135C2×C4×C13—28no—
136C2×C4×C13—216no—
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13—44no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—48no—
143C2×C4×C13—48no—
144C2×C4×C13C2×C22⋊C414yes—
145C2×C4×C13C2×C22⋊C412yes—
146C2×C4×C13#11718yes—
147C2×C4×C13#12318yes—
148C2×C4×C13#12314yes—
149C2×C4×C13C23×C411yescharacteristic
150C2×C4×C13C22×D411yescharacteristic
151C2×C4×C13C2×#4114yes—
152C2×Dic13—44no—
153C2×Dic13—44no—
154C2×Dic13—44no—
155C2×Dic13—88no—
156#1055—44no—
157C24×C4C2×D1311yescharacteristic
158C23×C8—132no—
159C2×#117—24no—
160C2×#117—22no—
161C2×#117Dic1318yescomplemented
162C2×#117C2×D1314yes—
163C22×C4⋊C4—132no—
164C22×C4⋊C4C2×D1311yescharacteristic
165C22×C4⋊C4C2×D1311yescharacteristic
166C22×C22⋊C4—21no—
167C22×C22⋊C4—261no—
168C22×C42—21no—
169C2×C22⋊C8—134no—
170C2×C22⋊C8—264no—
171#380—134no—
172#380—262no—
173C2×#95—261no—
174#340—138no—
175#340—138no—
176C22×C13—24no—
177C22×C13—24no—
178C22×C13—24no—
179C22×C13—44no—
180C22×C13—44no—
181C22×C13—416no—
182C22×C13#38114yes—
183C22×C13#41614yes—
184C22×C13#41714yes—
185C22×C13#48218yes—
186C22×C13#48518yes—
187C22×C13C22×C22⋊C411yescharacteristic
188C22×C13C2×#12312yes—
189C22×C13C2×#13512yes—
190C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
191C22×C13C2×#13711yescharacteristic
192C4×C13—24no—
193C4×C13—44no—
194C4×C13—44no—
195C4×C13#38114yes—
196C4×C13C2×#11712yes—
197C4×C13C2×#12312yes—
198Dic13—84no—
199C25C22⋊D1311yescharacteristic
200C23×C4—28no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—262no—
204C23×C4C2×Dic1314yes—
205C23×C4C22⋊D1312yes—
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22⋊D1314yes—
208C23×C4C22×D1312yes—
209C23×C4C22×D1311yescharacteristic
210C22×C8—134no—
211C22×C8—268no—
212C22×C8—264no—
213#117—216no—
214#117—28no—
215#117C2×Dic13116yescomplemented
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—134no—
221C2×C4⋊C4—268no—
222C2×C4⋊C4—262no—
223C2×C4⋊C4C2×Dic1314yes—
224C2×C4⋊C4C2×Dic1314yes—
225C2×C4⋊C4C22×D1312yes—
226C2×C4⋊C4C22×D1312yes—
227C2×C22⋊C4—28no—
228C2×C22⋊C4—24no—
229C2×C22⋊C4—264no—
230C2×C22⋊C4—524no—
231C2×C42—28no—
232C2×C42—24no—
233C22⋊C8—268no—
234#95—264no—
235C2×C13—44no—
236C2×C13#182518yescomplemented
237C2×C13C2×#38111yescharacteristic
238C2×C13C2×#41611yescharacteristic
239C2×C13C2×#41711yescharacteristic
240C2×C13C2×#48212yes—
241C2×C13C2×#48512yes—
242C24—24no—
243C24—22no—
244C24—24no—
245C24—22no—
246C24C22⋊Dic1314yes—
247C24C2×C22⋊D1312yes—
248C24C2×C22⋊D1311yescharacteristic
249C22×C4—24no—
250C22×C4—216no—
251C22×C4—28no—
252C22×C4—216no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—42no—
259C22×C4—44no—
260C22×C4—42no—
261C22×C4—264no—
262C22×C4—524no—
263C22×C4—524no—
264C22×C4—524no—
265C22×C4C22⋊Dic1314yes—
266C22×C4C22⋊Dic1318yes—
267C22×C4#612718yes—
268C22×C4C22×Dic1314yes—
269C22×C4C22×Dic1312yes—
270C22×C4C2×C22⋊D1312yes—
271C22×C4C2×C22⋊D1314yes—
272C22×C4C2×C22⋊D1311yescharacteristic
273C22×C4C2×C22⋊D1312yes—
274C22×C4C23×D1311yescharacteristic
275C2×C8—268no—
276C2×C8—264no—
277C2×C8—528no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—268no—
283C4⋊C4—524no—
284C4⋊C4C22×Dic1314yes—
285C4⋊C4C22×Dic1314yes—
286C22⋊C4—216no—
287C22⋊C4—528no—
288C42—216no—
289C13C2×#182511yescharacteristic, complemented, Sylow
290C23—24no—
291C23—22no—
292C23—24no—
293C23—22no—
294C23—28no—
295C23—28no—
296C23—28no—
297C23—48no—
298C23—48no—
299C23#8818314yes—
300C23#8820312yes—
301C23#8820414yes—
302C23#8820512yes—
303C23C2×C22⋊Dic1314yes—
304C23C2×C22⋊Dic1312yes—
305C23C22×C22⋊D1311yescharacteristic
306C2×C4—24no—
307C2×C4—28no—
308C2×C4—28no—
309C2×C4—28no—
310C2×C4—216no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—48no—
317C2×C4—48no—
318C2×C4—524no—
319C2×C4—524no—
320C2×C4—524no—
321C2×C4—1048no—
322C2×C4#8818018yes—
323C2×C4#8818318yes—
324C2×C4#8818314yes—
325C2×C4C2×C22⋊Dic1314yes—
326C2×C4C2×C22⋊Dic1312yes—
327C2×C4C2×#612714yes—
328C2×C4C23×Dic1311yescharacteristic
329C2×C4C22×C22⋊D1311yescharacteristic
330C8—524no—
331C22—24no—
332C22—24no—
333C22—24no—
334C22—416no—
335C22—44no—
336C22—44no—
337C22#1171865718yes—
338C22#1171866418yes—
339C22#1171887214yes—
340C22#1171889314yes—
341C22#1171889414yes—
342C22C2×#8818312yes—
343C22C2×#8820311yescharacteristic
344C22C2×#8820412yes—
345C22C2×#8820511yescharacteristic
346C22C22×C22⋊Dic1311yescharacteristic
347C4—24no—
348C4—44no—
349C4—44no—
350C4—1044no—
351C4#1171887214yes—
352C4C2×#8818012yes—
353C4C2×#8818312yes—
354C2—44no—
355C2#1311493118yesdirect product factor
356C2C2×#1171887211yescharacteristic
357C2C2×#1171889411yescharacteristic
358C2C2×#1171889311yescharacteristic
359C2C2×#1171866412yes—
360C2C2×#1171865712yes—
subgroupG/H
centerC24C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#117C2
socleC24×C13C2×D4
prime radicalC25×C13D4
cosocleC22×C4×C13C24
hypercenterC22×#117D13
hypocenterC13C2×#1825
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. #13114931C2direct (N × H)
4. C2×#11718121C2semidirect
5. C2×#11718121C2semidirect
10. C2×C13×#117C4semidirect
24. #11718121C22semidirect
25. #11718121C22semidirect
39. C13×#117C2×C4semidirect
161. C2×#117Dic13semidirect
215. #117C2×Dic13semidirect
236. C2×C13#1825semidirect
289. C13C2×#1825semidirect
355. C2#13114931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#10552
C2×#117188732
#131149312
C2×#117181212
C22×C13×#1172
C2×#182513