Finite Group Databasebeta

← C2×#13116260 #15891739

Subgroups — C2×#13116260 #15891739

Order 3328.

1270 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88060C211yesmaximal, characteristic
2C2×#11718648C212yesmaximal
3#13116260C218yesmaximal, direct product factor
4C2×#11718143C211yesmaximal, characteristic, complemented
5C2×#11718121C212yesmaximal, complemented
6C22×C13×#107C211yesmaximal, characteristic, complemented
7C23×C4×D13C2211yescharacteristic
8C23×C8×C13C2211yescharacteristic
9C22×C13×C4⋊C4C2212yes—
10C22×#6103—22no—
11C22×C4⋊Dic13C2212yes—
12C23×#1055C2211yescharacteristic
13C2×C13×#107—24no—
14C2×C13×#107C2214yescomplemented
15C2×#88071—22no—
16C2×#88060—24no—
17C2×#88060C2214yes—
18#11718648—24no—
19#11718648C2218yes—
20#11718143C2214yescomplemented
21#11718121C2218yescomplemented
22C24×D13D411yescharacteristic
23C23×C4×C13—22no—
24C23×C4×C13C2311yescharacteristic
25C23×Dic13—22no—
26C23×Dic13D411yescharacteristic
27C22×C4×D13—22no—
28C22×C4×D13—24no—
29C22×C4×D13—22no—
30C22×C4×D13—24no—
31C22×C4×D13D412yes—
32C22×C4×D13C2312yes—
33C22×C8×C13—24no—
34C22×C8×C13D414yes—
35C22×C8×C13C2312yes—
36C2×C13×C4⋊C4—24no—
37C2×C13×C4⋊C4—24no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4C2314yes—
40C2×#6103—28no—
41C2×#6103—48no—
42C2×C4⋊Dic13—24no—
43C2×C4⋊Dic13—24no—
44C2×C4⋊Dic13—22no—
45C2×C4⋊Dic13C2314yes—
46C22×#1055—22no—
47C22×#1055—24no—
48C22×#1055C2312yes—
49C13×#107—28no—
50#88071—28no—
51#88060—28no—
52C2×#2075—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C23×D13—22no—
55C23×D13—24no—
56C23×D13—22no—
57C23×D13—24no—
58C23×D13D814yes—
59C23×D13C2×D412yes—
60C22×C4×C13—24no—
61C22×C4×C13—44no—
62C22×C4×C13—44no—
63C22×C4×C13—44no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D412yes—
66C22×C4×C13#4114yes—
67C22×C4×C13#4112yes—
68C22×C4×C13#4114yes—
69C22×C4×C13C2411yescharacteristic
70C22×Dic13—22no—
71C22×Dic13—24no—
72C22×Dic13—24no—
73C22×Dic13—44no—
74C22×Dic13—44no—
75C22×Dic13—44no—
76C22×Dic13C2×D412yes—
77C2×C4×D13—24no—
78C2×C4×D13—28no—
79C2×C4×D13—22no—
80C2×C4×D13—24no—
81C2×C4×D13—24no—
82C2×C4×D13—22no—
83C2×C4×D13—44no—
84C2×C4×D13—44no—
85C2×C4×D13—48no—
86C2×C8×C13—28no—
87C2×C8×C13—24no—
88C2×C8×C13C2×D414yes—
89C13×C4⋊C4—24no—
90C13×C4⋊C4—24no—
91C13×C4⋊C4—44no—
92#6103—416no—
93C4⋊Dic13—24no—
94C4⋊Dic13—24no—
95C4⋊Dic13—44no—
96C2×#1055—22no—
97C2×#1055—24no—
98C2×#1055—44no—
99C22×#107D1311yescharacteristic, complemented
100C22×C22⋊C8—131no—
101C2×#380—132no—
102#2075—138no—
103C2×#340—131no—
104C2×#340—132no—
105C23×C13#12112yes—
106C23×C13#12314yes—
107C23×C13C2×D812yes—
108C23×C13#13512yes—
109C23×C13#13714yes—
110C23×C13C22×D411yescharacteristic
111C22×D13—22no—
112C22×D13—24no—
113C22×D13—22no—
114C22×D13—24no—
115C22×D13—28no—
116C22×D13—216no—
117C22×D13—44no—
118C22×D13—44no—
119C22×D13—48no—
120C22×D13C2×D814yes—
121C2×C4×C13—44no—
122C2×C4×C13—44no—
123C2×C4×C13—44no—
124C2×C4×C13—88no—
125C2×C4×C13#12112yes—
126C2×C4×C13#12314yes—
127C2×C4×C13#12314yes—
128C2×C4×C13#12414yes—
129C2×C4×C13#12618yes—
130C2×C4×C13C22×D411yescharacteristic
131C2×C4×C13C2×#4112yes—
132C2×C4×C13C2×#4112yes—
133C2×C4×C13C2×#4111yescharacteristic
134C2×Dic13—22no—
135C2×Dic13—24no—
136C2×Dic13—44no—
137C2×Dic13—44no—
138C2×Dic13—44no—
139C2×Dic13—44no—
140C2×Dic13—88no—
141C4×D13—42no—
142C4×D13—42no—
143C4×D13—44no—
144C4×D13—48no—
145C8×C13—24no—
146#1055—42no—
147C24×C4—131no—
148C23×C8—131no—
149C23×C8C2×D1311yescharacteristic
150C22×C4⋊C4—132no—
151C22×C4⋊C4C2×D1312yes—
152C22×C22⋊C4—262no—
153C2×#107—24no—
154C2×#107C2×D1314yescomplemented
155C2×C22⋊C8—134no—
156C2×C22⋊C8—264no—
157#380—138no—
158#380—264no—
159C2×#95—262no—
160#340—134no—
161#340—138no—
162C22×C13#39714yes—
163C22×C13#46614yes—
164C22×C13#47014yes—
165C22×C13#48018yes—
166C22×C13#48518yes—
167C22×C13C2×#12111yescharacteristic
168C22×C13C2×#12312yes—
169C22×C13C22×D811yescharacteristic
170C22×C13C2×#13511yescharacteristic
171C22×C13C2×#13712yes—
172C2×D13—28no—
173C2×D13—24no—
174C2×D13—44no—
175C2×D13—416no—
176C2×D13—42no—
177C2×D13—42no—
178C4×C13—84no—
179C4×C13#39714yes—
180C4×C13C2×#12311yescharacteristic
181C4×C13C2×#12411yescharacteristic
182C4×C13C2×#12612yes—
183Dic13—42no—
184Dic13—84no—
185C25—131no—
186C23×C4—22no—
187C23×C4—131no—
188C23×C4—132no—
189C23×C4—132no—
190C23×C4—264no—
191C23×C4—262no—
192C23×C4—264no—
193C23×C4—262no—
194C23×C4—262no—
195C23×C4C22×D1311yescharacteristic
196C22×C8—24no—
197C22×C8—132no—
198C22×C8—264no—
199C22×C8—262no—
200C22×C8C22⋊D1314yes—
201C22×C8C22×D1312yes—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—134no—
206C2×C4⋊C4—264no—
207C2×C4⋊C4—264no—
208C2×C4⋊C4—262no—
209C2×C4⋊C4C22×D1314yes—
210C2×C22⋊C4—268no—
211C2×C22⋊C4—528no—
212#107—28no—
213C22⋊C8—268no—
214#95—268no—
215C2×C13#207518yescomplemented
216C2×C13C2×#39711yescharacteristic
217C2×C13C2×#46611yescharacteristic
218C2×C13C2×#47011yescharacteristic
219C2×C13C2×#48012yes—
220C2×C13C2×#48512yes—
221D13—44no—
222C24—134no—
223C24—132no—
224C24—264no—
225C24—262no—
226C24—264no—
227C24—262no—
228C24D4×D1311yescharacteristic
229C22×C4—24no—
230C22×C4—44no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—132no—
234C22×C4—264no—
235C22×C4—262no—
236C22×C4—268no—
237C22×C4—264no—
238C22×C4—264no—
239C22×C4—262no—
240C22×C4—264no—
241C22×C4—262no—
242C22×C4—264no—
243C22×C4—528no—
244C22×C4—524no—
245C22×C4—524no—
246C22×C4—524no—
247C22×C4—524no—
248C22×C4—524no—
249C22×C4#612714yes—
250C22×C4D4×D1311yescharacteristic
251C22×C4#612912yes—
252C22×C4#613114yes—
253C22×C4C2×C22⋊D1312yes—
254C22×C4C23×D1311yescharacteristic
255C2×C8—28no—
256C2×C8—24no—
257C2×C8—264no—
258C2×C8—262no—
259C2×C8—524no—
260C2×C8C2×C22⋊D1314yes—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—44no—
264C4⋊C4—264no—
265C4⋊C4—264no—
266C4⋊C4—524no—
267C22⋊C4—5216no—
268C13C2×#207511yescharacteristic, complemented, Sylow
269C23—134no—
270C23—262no—
271C23—264no—
272C23—264no—
273C23—262no—
274C23—2616no—
275C23—268no—
276C23—528no—
277C23—524no—
278C23—524no—
279C23#8814814yes—
280C23D8×D1312yes—
281C23#8816612yes—
282C23#8817214yes—
283C23#8819212yes—
284C23C2×D4×D1311yescharacteristic
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—88no—
289C2×C4—264no—
290C2×C4—262no—
291C2×C4—524no—
292C2×C4—524no—
293C2×C4—522no—
294C2×C4—522no—
295C2×C4—528no—
296C2×C4—524no—
297C2×C4—524no—
298C2×C4—524no—
299C2×C4—1048no—
300C2×C4#8814814yes—
301C2×C4#8815218yes—
302C2×C4#8818314yes—
303C2×C4#8819212yes—
304C2×C4#8820114yes—
305C2×C4C2×#612712yes—
306C2×C4C2×#612911yescharacteristic
307C2×C4C2×#613112yes—
308C2×C4C22×C22⋊D1311yescharacteristic
309C8—24no—
310C8—522no—
311C22—264no—
312C22—268no—
313C22—522no—
314C22—5216no—
315C22—522no—
316C22—524no—
317C22#1171854318yes—
318C22#1171854918yes—
319C22#1171865414yes—
320C22#1171881814yes—
321C22#1171885014yes—
322C22C2×#8814812yes—
323C22C2×D8×D1311yescharacteristic
324C22C2×#8816611yescharacteristic
325C22C2×#8817212yes—
326C22C2×#8819211yescharacteristic
327C4—84no—
328C4—522no—
329C4—1044no—
330C4#1171865414yes—
331C4C2×#8815212yes—
332C4C2×#8818311yescharacteristic
333C4C2×#8820111yescharacteristic
334C2—524no—
335C2#1311626018yesdirect product factor
336C2C2×#1171865411yescharacteristic
337C2C2×#1171881811yescharacteristic
338C2C2×#1171885011yescharacteristic
339C2C2×#1171854312yes—
340C2C2×#1171854912yes—
subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#107C2
socleC24×C13C2×D4
prime radicalC24×D13D4
hypercenterC22×#107D13
hypocenterC13C2×#2075
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
3. #13116260C2direct (N × H)
4. C2×#11718143C2semidirect
5. C2×#11718121C2semidirect
6. C22×C13×#107C2semidirect
14. C2×C13×#107C22semidirect
20. #11718143C22semidirect
21. #11718121C22semidirect
99. C22×#107D13semidirect
154. C2×#107C2×D13semidirect
215. C2×C13#2075semidirect
268. C13C2×#2075semidirect
335. C2#13116260direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880602
C2×#117186482
#131162602
C2×#117181432
C2×#117181212
C22×C13×#1072
C2×#207513