Finite Group Databasebeta

← C2×#13114551 #15860317

Subgroups — C2×#13114551 #15860317

Order 3328.

2398 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D13C211yesmaximal, characteristic
2C22×#88146C212yesmaximal
3#13114551C218yesmaximal, direct product factor
4C2×#11718143C211yesmaximal, characteristic, complemented
5C2×#11718121C212yesmaximal, complemented
6C2×C13×#340C211yesmaximal, characteristic, complemented
7C23×C4×D13C2211yescharacteristic
8C23×C8×C13C2211yescharacteristic
9C22×C13×C4⋊C4C2212yes—
10C22×#6103—22no—
11C22×C4⋊Dic13C2212yes—
12C22×C4×Dic13—22no—
13C23×#1055C2211yescharacteristic
14C22×C8×D13—28no—
15C22×C8×D13C418yescomplemented
16C22×C8×D13C2214yes—
17C2×#88146—24no—
18C2×#88146—28no—
19C2×#88146C4116yescomplemented
20C2×#88146C2218yes—
21C13×#340C2214yescomplemented
22#11718143C2214yescomplemented
23#11718121C2218yescomplemented
24C24×D13D411yescharacteristic
25C23×C4×C13—22no—
26C23×C4×C13C2311yescharacteristic
27C23×Dic13—22no—
28C23×Dic13D411yescharacteristic
29C22×C4×D13C2×C414yes—
30C22×C4×D13C2×C418yes—
31C22×C4×D13D412yes—
32C22×C4×D13D418yes—
33C22×C4×D13Q814yes—
34C22×C4×D13C2312yes—
35C22×C8×C13—24no—
36C22×C8×C13C2×C414yes—
37C22×C8×C13C2312yes—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—24no—
40C2×C13×C4⋊C4C2×C418yes—
41C2×C13×C4⋊C4C2314yes—
42C2×#6103—216no—
43C2×#6103—28no—
44C2×C4⋊Dic13—22no—
45C2×C4⋊Dic13—24no—
46C2×C4⋊Dic13C2×C418yes—
47C2×C4⋊Dic13C2314yes—
48C2×C4×Dic13—216no—
49C2×C4×Dic13—28no—
50C22×#1055—24no—
51C22×#1055C2×C414yes—
52C22×#1055C2312yes—
53C2×C8×D13—232no—
54C2×C8×D13—216no—
55C2×C8×D13C2×C4116yescomplemented
56#88146—232no—
57#88146—216no—
58#88146C2×C4132yescomplemented
59C2×#1735—131nomaximal, Sylow
60C24×C13C2×D411yescharacteristic
61C23×D13—22no—
62C23×D13—24no—
63C23×D13—22no—
64C23×D13C22⋊C418yes—
65C23×D13C4⋊C414yes—
66C23×D13C2×D412yes—
67C22×C4×C13—28no—
68C22×C4×C13—24no—
69C22×C4×C13—44no—
70C22×C4×C13—44no—
71C22×C4×C13C22×C412yes—
72C22×C4×C13C22×C414yes—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D414yes—
75C22×C4×C13C2×Q812yes—
76C22×C4×C13C2411yescharacteristic
77C22×Dic13—28no—
78C22×Dic13—24no—
79C22×Dic13—44no—
80C22×Dic13—44no—
81C22×Dic13C22⋊C418yes—
82C22×Dic13C4⋊C414yes—
83C22×Dic13C2×D412yes—
84C2×C4×D13C42116yes—
85C2×C4×D13C22⋊C4116yes—
86C2×C4×D13C22⋊C4116yes—
87C2×C4×D13C4⋊C418yes—
88C2×C4×D13C4⋊C4132yes—
89C2×C4×D13C22×C414yes—
90C2×C4×D13C22×C418yes—
91C2×C4×D13C2×D418yes—
92C2×C4×D13C2×Q814yes—
93C2×C8×C13—28no—
94C2×C8×C13—24no—
95C2×C8×C13C22×C414yes—
96C13×C4⋊C4—28no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4C22×C418yes—
99#6103—232no—
100C4⋊Dic13—28no—
101C4⋊Dic13—24no—
102C4⋊Dic13C22×C418yes—
103C4×Dic13—232no—
104C2×#1055—28no—
105C2×#1055—24no—
106C2×#1055C22×C414yes—
107C8×D13—232no—
108C24×C8—131no—
109C22×#117—132no—
110#1735—138no—
111C2×#340—131no—
112C2×#340—132no—
113C2×#340D1311yescharacteristic, complemented
114C23×C13C2×C22⋊C414yes—
115C23×C13C2×C4⋊C412yes—
116C23×C13#13512yes—
117C23×C13#13514yes—
118C23×C13#13512yes—
119C23×C13C22×D411yescharacteristic
120C22×D13—22no—
121C22×D13—24no—
122C22×D13—22no—
123C22×D13—216no—
124C22×D13—216no—
125C22×D13—28no—
126C22×D13—28no—
127C22×D13#95116yes—
128C22×D13C2×C22⋊C418yes—
129C22×D13C2×C4⋊C414yes—
130C2×C4×C13—28no—
131C2×C4×C13—44no—
132C2×C4×C13—44no—
133C2×C4×C13—416no—
134C2×C4×C13C2×C4214yes—
135C2×C4×C13C2×C22⋊C414yes—
136C2×C4×C13C2×C22⋊C414yes—
137C2×C4×C13C2×C4⋊C418yes—
138C2×C4×C13C2×C4⋊C412yes—
139C2×C4×C13C23×C411yescharacteristic
140C2×C4×C13C23×C412yes—
141C2×C4×C13C22×D412yes—
142C2×C4×C13C22×Q811yescharacteristic
143C2×Dic13—28no—
144C2×Dic13—44no—
145C2×Dic13—44no—
146C2×Dic13—416no—
147C2×Dic13#95116yes—
148C2×Dic13C2×C22⋊C418yes—
149C2×Dic13C2×C4⋊C414yes—
150C4×D13#95132yes—
151C4×D13C2×C4218yes—
152C4×D13C2×C22⋊C418yes—
153C4×D13C2×C4⋊C4116yes—
154C8×C13—24no—
155#1055—24no—
156C24×C4—131no—
157C23×C8—131no—
158C23×C8—138no—
159C23×C8—134no—
160C23×C8—268no—
161C23×C8C2×D1311yescharacteristic
162C2×#117—1316no—
163C2×#117—138no—
164C2×#117—264no—
165C2×#117—268no—
166C22×C4⋊C4—132no—
167C22×C4⋊C4C2×D1312yes—
168C22×C22⋊C4—262no—
169C22×C42—262no—
170#340—134no—
171#340—138no—
172#340C2×D1314yescomplemented
173C22×C13C2×#9514yes—
174C22×C13#41618yes—
175C22×C13#41618yes—
176C22×C13#42714yes—
177C22×C13#42714yes—
178C22×C13C22×C22⋊C412yes—
179C22×C13C22×C4⋊C411yescharacteristic
180C22×C13C2×#13511yescharacteristic
181C22×C13C2×#13512yes—
182C22×C13C2×#13511yescharacteristic
183C2×D13—28no—
184C2×D13—28no—
185C2×D13—24no—
186C2×D13—24no—
187C2×D13—232no—
188C2×D13C2×#9518yes—
189C4×C13—48no—
190C4×C13C2×#9514yes—
191C4×C13C22×C4211yescharacteristic
192C4×C13C22×C22⋊C411yescharacteristic
193C4×C13C22×C4⋊C412yes—
194Dic13—48no—
195Dic13C2×#9518yes—
196C25—131no—
197C23×C4—22no—
198C23×C4—131no—
199C23×C4—138no—
200C23×C4—134no—
201C23×C4—132no—
202C23×C4—138no—
203C23×C4—134no—
204C23×C4—132no—
205C23×C4—262no—
206C23×C4C22×D1311yescharacteristic
207C22×C8—24no—
208C22×C8—134no—
209C22×C8—132no—
210C22×C8—1316no—
211C22×C8—2632no—
212C22×C8—2616no—
213C22×C8—264no—
214C22×C8C4×D1314yes—
215C22×C8C22×D1312yes—
216#117—1332no—
217#117—2632no—
218#117—2616no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—138no—
222C2×C4⋊C4—134no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4—264no—
225C2×C4⋊C4C4×D1318yes—
226C2×C4⋊C4C22×D1314yes—
227C2×C22⋊C4—2616no—
228C2×C22⋊C4—268no—
229C2×C42—2616no—
230C2×C42—268no—
231C2×C13#173518yescomplemented
232C2×C13C22×#9511yescharacteristic
233C2×C13C2×#41612yes—
234C2×C13C2×#41612yes—
235C2×C13C2×#42711yescharacteristic
236C2×C13C2×#42711yescharacteristic
237D13—28no—
238C24—138no—
239C24—134no—
240C24—132no—
241C24—262no—
242C24—264no—
243C24—262no—
244C24D4×D1311yescharacteristic
245C22×C4—28no—
246C22×C4—24no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—138no—
250C22×C4—134no—
251C22×C4—132no—
252C22×C4—1316no—
253C22×C4—1316no—
254C22×C4—1316no—
255C22×C4—138no—
256C22×C4—1332no—
257C22×C4—138no—
258C22×C4—134no—
259C22×C4—138no—
260C22×C4—134no—
261C22×C4—268no—
262C22×C4—264no—
263C22×C4—524no—
264C22×C4—524no—
265C22×C4C2×C4×D1312yes—
266C22×C4C2×C4×D1314yes—
267C22×C4D4×D1311yescharacteristic
268C22×C4D4×D1314yes—
269C22×C4Q8×D1312yes—
270C22×C4C23×D1311yescharacteristic
271C2×C8—28no—
272C2×C8—24no—
273C2×C8—134no—
274C2×C8—2632no—
275C2×C8—268no—
276C2×C8—264no—
277C2×C8C2×C4×D1314yes—
278C4⋊C4—28no—
279C4⋊C4—24no—
280C4⋊C4—138no—
281C4⋊C4—268no—
282C4⋊C4—264no—
283C4⋊C4C2×C4×D1318yes—
284C22⋊C4—2632no—
285C42—2632no—
286C13C2×#173511yescharacteristic, complemented, Sylow
287C23—138no—
288C23—134no—
289C23—1316no—
290C23—2616no—
291C23—262no—
292C23—264no—
293C23—262no—
294C23—2616no—
295C23—268no—
296C23—268no—
297C23C22⋊C4×D1314yes—
298C23C4⋊C4×D1312yes—
299C23#8816612yes—
300C23#8817014yes—
301C23#8817312yes—
302C23C2×D4×D1311yescharacteristic
303C2×C4—28no—
304C2×C4—416no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—138no—
308C2×C4—134no—
309C2×C4—1316no—
310C2×C4—138no—
311C2×C4—138no—
312C2×C4—1316no—
313C2×C4—1332no—
314C2×C4—268no—
315C2×C4—524no—
316C2×C4—524no—
317C2×C4—5216no—
318C2×C4C42×D1314yes—
319C2×C4C22⋊C4×D1314yes—
320C2×C4C22⋊C4×D1314yes—
321C2×C4C4⋊C4×D1318yes—
322C2×C4C4⋊C4×D1312yes—
323C2×C4C22×C4×D1311yescharacteristic
324C2×C4C22×C4×D1312yes—
325C2×C4C2×D4×D1312yes—
326C2×C4C2×Q8×D1311yescharacteristic
327C8—24no—
328C8—264no—
329C22—138no—
330C22—268no—
331C22—268no—
332C22—264no—
333C22—264no—
334C22—2632no—
335C22D13×#9514yes—
336C22#1171843318yes—
337C22#1171846518yes—
338C22#1171852114yes—
339C22#1171854114yes—
340C22C2×C22⋊C4×D1312yes—
341C22C2×C4⋊C4×D1311yescharacteristic
342C22C2×#8816611yescharacteristic
343C22C2×#8817012yes—
344C22C2×#8817311yescharacteristic
345C4—48no—
346C4—138no—
347C4—528no—
348C4D13×#9514yes—
349C4C2×C42×D1311yescharacteristic
350C4C2×C22⋊C4×D1311yescharacteristic
351C4C2×C4⋊C4×D1312yes—
352C2—268no—
353C2#1311455118yesdirect product factor
354C2C2×D13×#9511yescharacteristic
355C2C2×#1171843312yes—
356C2C2×#1171846512yes—
357C2C2×#1171852111yescharacteristic
358C2C2×#1171854111yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenterC2×#340D13
hypocenterC13C2×#1735
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #13114551C2direct (N × H)
4. C2×#11718143C2semidirect
5. C2×#11718121C2semidirect
6. C2×C13×#340C2semidirect
15. C22×C8×D13C4semidirect
19. C2×#88146C4semidirect
21. C13×#340C22semidirect
22. #11718143C22semidirect
23. #11718121C22semidirect
55. C2×C8×D13C2×C4semidirect
58. #88146C2×C4semidirect
113. C2×#340D13semidirect
172. #340C2×D13semidirect
231. C2×C13#1735semidirect
286. C13C2×#1735semidirect
353. C2#13114551direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D132
C22×#881462
#131145512
C2×#117181432
C2×#117181212
C2×C13×#3402
C2×#173513