Finite Group Databasebeta

← C2×#13114586 #15860387

Subgroups — C2×#13114586 #15860387

Order 3328.

1134 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88055C211yesmaximal, characteristic
2C22×C8×Dic13C211yesmaximal, characteristic
3C2×#11718593C211yesmaximal, characteristic
4#13114586C218yesmaximal, direct product factor
5C2×#11718116C211yesmaximal, characteristic
6C2×#11718142C211yesmaximal, characteristic
7C2×#11718142C211yesmaximal, characteristic
8C2×C13×#336C211yesmaximal, characteristic
9C23×C8×C13C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C22×C4×Dic13C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C23×#1055C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16C2×#88071C412yes—
17C2×#88071C412yes—
18C2×#88055C418yescomplemented
19C2×#88055C2214yes—
20C2×C8×Dic13C418yescomplemented
21C2×C8×Dic13C2214yes—
22#11718593C414yes—
23#11718593C2214yes—
24C13×#336C2214yes—
25#11718142C2214yes—
26#11718142C2214yes—
27#11718116C2214yes—
28C23×C4×C13C2×C412yes—
29C23×C4×C13C2311yescharacteristic
30C23×Dic13C2×C412yes—
31C23×Dic13C2×C411yescharacteristic
32C23×Dic13C2×C411yescharacteristic
33C22×C8×C13—22no—
34C22×C8×C13—22no—
35C22×C8×C13—22no—
36C22×C8×C13—22no—
37C22×C8×C13C2×C414yes—
38C22×C8×C13C2×C414yes—
39C22×C8×C13C2312yes—
40C22×C8×C13C2312yes—
41C2×C42×C13—22no—
42C2×C42×C13—22no—
43C2×C42×C13C2×C412yes—
44C2×C42×C13C2312yes—
45C2×C4×Dic13—22no—
46C2×C4×Dic13—22no—
47C2×C4×Dic13C2×C412yes—
48C2×C4×Dic13C2×C412yes—
49C2×C4×Dic13C2×C414yes—
50C2×C4×Dic13C2×C414yes—
51C2×C4×Dic13C2312yes—
52C2×C4×Dic13C2312yes—
53C22×#1055—22no—
54C22×#1055—22no—
55C22×#1055—22no—
56C22×#1055—22no—
57C22×#1055C2×C414yes—
58C22×#1055C2×C414yes—
59C22×#1055C2312yes—
60C22×#1055C2312yes—
61#88071C2×C418yes—
62#88071C2×C418yes—
63#88055C2×C4116yescomplemented
64C8×Dic13C2×C4116yescomplemented
65C2×#1746—131nomaximal, Sylow
66C24×C13C22×C411yescharacteristic
67C22×C4×C13—24no—
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13C22×C414yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C22×C412yes—
73C22×C4×C13C22×C412yes—
74C22×C4×C13#4112yes—
75C22×C4×C13#4112yes—
76C22×C4×C13#4112yes—
77C22×C4×C13#4112yes—
78C22×C4×C13C2411yescharacteristic
79C22×Dic13—24no—
80C22×Dic13—24no—
81C22×Dic13—24no—
82C22×Dic13—24no—
83C22×Dic13—24no—
84C22×Dic13C4214yes—
85C22×Dic13C4214yes—
86C22×Dic13C22×C414yes—
87C22×Dic13C22×C412yes—
88C22×Dic13C22×C412yes—
89C2×C8×C13—28no—
90C2×C8×C13—28no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13C22×C414yes—
96C2×C8×C13C22×C414yes—
97C42×C13—24no—
98C42×C13—22no—
99C42×C13—22no—
100C4×Dic13—24no—
101C4×Dic13—22no—
102C4×Dic13—22no—
103C4×Dic13C4218yes—
104C4×Dic13C22×C414yes—
105C4×Dic13C22×C414yes—
106C2×#1055—28no—
107C2×#1055—28no—
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—22no—
112C2×#1055C22×C414yes—
113C2×#1055C22×C414yes—
114C22×#97—131no—
115C22×C4×C8—131no—
116C2×#376—131no—
117#1746—138no—
118C2×#336—131no—
119C2×#336—131no—
120C2×#336—131no—
121C2×#336D1311yescharacteristic
122C23×C13C2×C4212yes—
123C23×C13#11712yes—
124C23×C13#11712yes—
125C23×C13#13114yes—
126C23×C13#13114yes—
127C23×C13C23×C411yescharacteristic
128C2×C4×C13—24no—
129C2×C4×C13—24no—
130C2×C4×C13—24no—
131C2×C4×C13—48no—
132C2×C4×C13C2×C4212yes—
133C2×C4×C13#11714yes—
134C2×C4×C13#11714yes—
135C2×C4×C13#11714yes—
136C2×C4×C13#11714yes—
137C2×C4×C13#11712yes—
138C2×C4×C13#11712yes—
139C2×C4×C13C23×C411yescharacteristic
140C2×C4×C13C23×C411yescharacteristic
141C2×C4×C13C2×#4111yescharacteristic
142C2×C4×C13C2×#4111yescharacteristic
143C2×C4×C13C2×#4111yescharacteristic
144C2×C4×C13C2×#4111yescharacteristic
145C2×Dic13—24no—
146C2×Dic13—24no—
147C2×Dic13—28no—
148C2×Dic13—28no—
149C2×Dic13—24no—
150C2×Dic13—24no—
151C2×Dic13—24no—
152C2×Dic13—48no—
153C2×Dic13C2×C4214yes—
154C2×Dic13C2×C4214yes—
155C8×C13—24no—
156C8×C13—24no—
157#1055—24no—
158#1055—24no—
159C23×C8—131no—
160C23×C8—131no—
161C23×C8C2×D1311yescharacteristic
162C23×C8C2×D1311yescharacteristic
163C22×C42—131no—
164C22×C42—131no—
165C22×C42C2×D1311yescharacteristic
166C2×#97—138no—
167C2×#97—134no—
168C2×C4×C8—138no—
169C2×C4×C8—134no—
170#376—134no—
171#376—134no—
172C2×#95—132no—
173C2×#95—132no—
174#336—134no—
175#336—134no—
176#336—134no—
177#336C2×D1314yes—
178C22×C13#37614yes—
179C22×C13#40514yes—
180C22×C13#40514yes—
181C22×C13#43318yes—
182C22×C13#43318yes—
183C22×C13C22×C4211yescharacteristic
184C22×C13C2×#11711yescharacteristic
185C22×C13C2×#11711yescharacteristic
186C22×C13C2×#13112yes—
187C22×C13C2×#13112yes—
188C4×C13—44no—
189C4×C13#37614yes—
190C4×C13C2×#11711yescharacteristic
191C4×C13C2×#11711yescharacteristic
192C4×C13C2×#11711yescharacteristic
193C4×C13C2×#11711yescharacteristic
194Dic13—24no—
195Dic13—24no—
196Dic13—44no—
197C23×C4—131no—
198C23×C4—131no—
199C23×C4—132no—
200C23×C4C4×D1312yes—
201C23×C4C22×D1311yescharacteristic
202C22×C8—22no—
203C22×C8—22no—
204C22×C8—22no—
205C22×C8—22no—
206C22×C8—134no—
207C22×C8—134no—
208C22×C8—132no—
209C22×C8—132no—
210C22×C8—262no—
211C22×C8—262no—
212C22×C8—262no—
213C22×C8—262no—
214C22×C8C4×D1314yes—
215C22×C8C4×D1314yes—
216C22×C8C22×D1312yes—
217C22×C8C22×D1312yes—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—132no—
221C2×C42—134no—
222C2×C42—134no—
223C2×C42—132no—
224C2×C42—132no—
225C2×C42—132no—
226C2×C42—262no—
227C2×C42—262no—
228C2×C42C4×D1312yes—
229C2×C42C22×D1312yes—
230#97—1316no—
231C4×C8—1316no—
232#95—138no—
233#95—138no—
234C2×C13#174618yescomplemented
235C2×C13C2×#37611yescharacteristic
236C2×C13C2×#40511yescharacteristic
237C2×C13C2×#40511yescharacteristic
238C2×C13C2×#43312yes—
239C2×C13C2×#43312yes—
240C24C2×C4×D1311yescharacteristic
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—134no—
245C22×C4—134no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—134no—
249C22×C4—264no—
250C22×C4—264no—
251C22×C4—264no—
252C22×C4—264no—
253C22×C4—264no—
254C22×C4C2×C4×D1314yes—
255C22×C4C2×C4×D1311yescharacteristic
256C22×C4C2×C4×D1312yes—
257C22×C4C2×C4×D1312yes—
258C22×C4#612912yes—
259C22×C4#612912yes—
260C22×C4#612912yes—
261C22×C4#613112yes—
262C22×C4C23×D1311yescharacteristic
263C2×C8—28no—
264C2×C8—28no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—134no—
270C2×C8—134no—
271C2×C8—268no—
272C2×C8—268no—
273C2×C8—262no—
274C2×C8—262no—
275C2×C8—262no—
276C2×C8—262no—
277C2×C8C2×C4×D1314yes—
278C2×C8C2×C4×D1314yes—
279C42—24no—
280C42—22no—
281C42—22no—
282C42—138no—
283C42—134no—
284C42—134no—
285C42—264no—
286C42—262no—
287C42—262no—
288C13C2×#174611yescharacteristic, complemented, Sylow
289C23C42×D1312yes—
290C23#8813112yes—
291C23#8814612yes—
292C23#8815514yes—
293C23#8816114yes—
294C23C22×C4×D1311yescharacteristic
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—48no—
299C2×C4—134no—
300C2×C4—134no—
301C2×C4—264no—
302C2×C4—264no—
303C2×C4—268no—
304C2×C4—268no—
305C2×C4—264no—
306C2×C4—264no—
307C2×C4—264no—
308C2×C4—528no—
309C2×C4C42×D1312yes—
310C2×C4#8813114yes—
311C2×C4#8813114yes—
312C2×C4#8813112yes—
313C2×C4#8814614yes—
314C2×C4#8814614yes—
315C2×C4#8814612yes—
316C2×C4C22×C4×D1311yescharacteristic
317C2×C4C22×C4×D1311yescharacteristic
318C2×C4C2×#612911yescharacteristic
319C2×C4C2×#612911yescharacteristic
320C2×C4C2×#612911yescharacteristic
321C2×C4C2×#613111yescharacteristic
322C8—24no—
323C8—24no—
324C8—264no—
325C8—264no—
326C22#1171830914yes—
327C22#1171835014yes—
328C22#1171836914yes—
329C22#1171838118yes—
330C22#1171850118yes—
331C22C2×C42×D1311yescharacteristic
332C22C2×#8813111yescharacteristic
333C22C2×#8814611yescharacteristic
334C22C2×#8815512yes—
335C22C2×#8816112yes—
336C4—44no—
337C4—264no—
338C4—264no—
339C4—524no—
340C4#1171830914yes—
341C4C2×#8813111yescharacteristic
342C4C2×#8813111yescharacteristic
343C4C2×#8814611yescharacteristic
344C4C2×#8814611yescharacteristic
345C2#1311458618yesdirect product factor
346C2C2×#1171830911yescharacteristic
347C2C2×#1171835011yescharacteristic
348C2C2×#1171836911yescharacteristic
349C2C2×#1171838112yes—
350C2C2×#1171850112yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C13×#336C2
socle, prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC2×#336D13
hypocenterC13C2×#1746
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. #13114586C2direct (N × H)
18. C2×#88055C4semidirect
20. C2×C8×Dic13C4semidirect
63. #88055C2×C4semidirect
64. C8×Dic13C2×C4semidirect
234. C2×C13#1746semidirect
288. C13C2×#1746semidirect
345. C2#13114586direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880552
C22×C8×Dic132
C2×#117185932
#131145862
C2×#117181162
C2×#117181422
C2×C13×#3362
C2×#174613