Finite Group Databasebeta

← C2×#13116398 #15892826

Subgroups — C2×#13116398 #15892826

Order 3328.

998 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
1C2×#11718589C211yesmaximal, characteristic
2#13116398C218yesmaximal, direct product factor
3C2×#11718121C212yesmaximal
4C2×#11718121C212yesmaximal
5C2×#11718116C211yesmaximal, characteristic
6C2×C13×#384C211yesmaximal, characteristic
7C22×C13×C4⋊C4—21no—
8C22×C13×C4⋊C4—21no—
9C22×C13×C4⋊C4C2212yes—
10C22×C42×C13C2211yescharacteristic
11C22×C4⋊Dic13C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C22×#6101—21no—
14C23×#1055C2212yes—
15C13×#384—22no—
16C13×#384C2214yes—
17C2×#88071—21no—
18#11718589—22no—
19#11718589C2214yes—
20#11718121C2218yes—
21#11718121C2218yes—
22#11718116C2214yes—
23C23×C4×C13—22no—
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C23×Dic13—21no—
28C23×Dic13—21no—
29C2×C13×C4⋊C4—28no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—24no—
32C2×C13×C4⋊C4—24no—
33C2×C13×C4⋊C4—44no—
34C2×C13×C4⋊C4—44no—
35C2×C13×C4⋊C4C2314yes—
36C2×C42×C13—24no—
37C2×C42×C13D412yes—
38C2×C42×C13C2312yes—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—22no—
41C2×C4⋊Dic13—24no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13Q814yes—
44C2×C4⋊Dic13C2312yes—
45C2×C4⋊Dic13C2312yes—
46C2×#6101—24no—
47C2×#6101—44no—
48C22×#1055—24no—
49C22×#1055—24no—
50C22×#1055—24no—
51C22×#1055C2314yes—
52#88071—24no—
53C2×#2100—131nomaximal, Sylow
54C24×C13C2×D411yescharacteristic
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—24no—
60C22×C4×C13—44no—
61C22×C4×C13—44no—
62C22×C4×C13—44no—
63C22×C4×C13SD1614yes—
64C22×C4×C13Q1614yes—
65C22×C4×C13C2×D412yes—
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×Q812yes—
69C22×C4×C13#4114yes—
70C22×C4×C13#4114yes—
71C22×C4×C13#4112yes—
72C22×C4×C13C2411yescharacteristic
73C22×Dic13—24no—
74C22×Dic13—22no—
75C22×Dic13—22no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C22×Dic13—42no—
81C13×C4⋊C4—28no—
82C13×C4⋊C4—48no—
83C13×C4⋊C4—48no—
84C13×C4⋊C4—44no—
85C42×C13—24no—
86C42×C13—24no—
87C4⋊Dic13—24no—
88C4⋊Dic13—22no—
89C4⋊Dic13—24no—
90C4⋊Dic13—42no—
91C4⋊Dic13C2×Q814yes—
92#6101—48no—
93C2×#1055—24no—
94C2×#1055—24no—
95C2×#1055—24no—
96C2×#1055—48no—
97C2×#389—131no—
98C2×#384D1311yescharacteristic
99#2100—138no—
100C2×#340—132no—
101C2×#340—132no—
102C2×#336—131no—
103C23×C13C22⋊Q812yes—
104C23×C13#12312yes—
105C23×C13#12412yes—
106C23×C13C2×SD1612yes—
107C23×C13C2×Q1612yes—
108C23×C13AGL(1,ℤ/8)12yes—
109C23×C13AGL(1,ℤ/8)12yes—
110C23×C13C22×D411yescharacteristic
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—28no—
116C2×C4×C13—28no—
117C2×C4×C13—44no—
118C2×C4×C13—44no—
119C2×C4×C13—44no—
120C2×C4×C13—88no—
121C2×C4×C13C22⋊Q812yes—
122C2×C4×C13#12312yes—
123C2×C4×C13#12412yes—
124C2×C4×C13#12518yes—
125C2×C4×C13#12618yes—
126C2×C4×C13C2×SD1614yes—
127C2×C4×C13C2×Q1614yes—
128C2×C4×C13C22×Q811yescharacteristic
129C2×C4×C13C2×#4112yes—
130C2×C4×C13C2×#4112yes—
131C2×C4×C13C2×#4111yescharacteristic
132C2×Dic13—24no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—48no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—84no—
140#1055—44no—
141C23×C8—132no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—131no—
145C22×C4⋊C4—131no—
146C22×C4⋊C4—261no—
147C22×C4⋊C4C2×D1312yes—
148C22×C42C2×D1311yescharacteristic
149#389—134no—
150#389—262no—
151#384—22no—
152#384C2×D1314yes—
153C2×#95—261no—
154#340—138no—
155#340—138no—
156#336—134no—
157C22×C13#40014yes—
158C22×C13#47614yes—
159C22×C13#47714yes—
160C22×C13#48114yes—
161C22×C13#48414yes—
162C22×C13#48714yes—
163C22×C13#49014yes—
164C22×C13C2×C22⋊Q811yescharacteristic
165C22×C13C2×#12311yescharacteristic
166C22×C13C2×#12411yescharacteristic
167C22×C13C22×SD1611yescharacteristic
168C22×C13C22×Q1611yescharacteristic
169C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
170C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
171C4×C13—24no—
172C4×C13—24no—
173C4×C13—84no—
174C4×C13#40014yes—
175C4×C13C2×#12512yes—
176C4×C13C2×#12612yes—
177Dic13—44no—
178Dic13—82no—
179C23×C4—22no—
180C23×C4—261no—
181C23×C4—261no—
182C23×C4C22⋊D1311yescharacteristic
183C23×C4C22⋊D1311yescharacteristic
184C23×C4C22×D1311yescharacteristic
185C22×C8—134no—
186C22×C8—264no—
187C22×C8—264no—
188C22×C8—264no—
189C2×C4⋊C4—28no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—134no—
196C2×C4⋊C4—132no—
197C2×C4⋊C4—132no—
198C2×C4⋊C4—262no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—264no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—264no—
203C2×C4⋊C4—524no—
204C2×C4⋊C4C22×D1314yes—
205C2×C42—24no—
206C2×C42C22⋊D1312yes—
207C2×C42C22×D1312yes—
208#95—264no—
209C2×C13#210018yescomplemented
210C2×C13C2×#40011yescharacteristic
211C2×C13C2×#47611yescharacteristic
212C2×C13C2×#47711yescharacteristic
213C2×C13C2×#48111yescharacteristic
214C2×C13C2×#48411yescharacteristic
215C2×C13C2×#48711yescharacteristic
216C2×C13C2×#49011yescharacteristic
217C24C2×C22⋊D1311yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—44no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4—264no—
227C22×C4—262no—
228C22×C4—262no—
229C22×C4—522no—
230C22×C4—522no—
231C22×C4—522no—
232C22×C4—522no—
233C22×C4—522no—
234C22×C4#610614yes—
235C22×C4#610714yes—
236C22×C4#612714yes—
237C22×C4#612914yes—
238C22×C4Q8×D1312yes—
239C22×C4#613112yes—
240C22×C4C2×C22⋊D1312yes—
241C22×C4C2×C22⋊D1312yes—
242C22×C4C2×C22⋊D1311yescharacteristic
243C22×C4C23×D1311yescharacteristic
244C2×C8—264no—
245C2×C8—264no—
246C2×C8—264no—
247C2×C8—528no—
248C4⋊C4—28no—
249C4⋊C4—48no—
250C4⋊C4—48no—
251C4⋊C4—44no—
252C4⋊C4—134no—
253C4⋊C4—264no—
254C4⋊C4—262no—
255C4⋊C4—264no—
256C4⋊C4—522no—
257C4⋊C4—528no—
258C42—24no—
259C42—24no—
260C13C2×#210011yescharacteristic, complemented, Sylow
261C23#8818312yes—
262C23#8818612yes—
263C23#8818612yes—
264C23#8819012yes—
265C23C2×#610612yes—
266C23C2×#610712yes—
267C23#8820012yes—
268C23C22×C22⋊D1311yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—88no—
279C2×C4—264no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—528no—
283C2×C4—522no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4—1044no—
287C2×C4#8814318yes—
288C2×C4#8815218yes—
289C2×C4#8818312yes—
290C2×C4#8819012yes—
291C2×C4C2×#610614yes—
292C2×C4C2×#610714yes—
293C2×C4#8820012yes—
294C2×C4C2×#612712yes—
295C2×C4C2×#612912yes—
296C2×C4C2×Q8×D1311yescharacteristic
297C2×C4C2×#613111yescharacteristic
298C8—524no—
299C22#1171862914yes—
300C22#1171863114yes—
301C22#1171864314yes—
302C22#1171873214yes—
303C22#1171874214yes—
304C22#1171874514yes—
305C22#1171875214yes—
306C22C2×#8818311yescharacteristic
307C22C2×#8818611yescharacteristic
308C22C2×#8818611yescharacteristic
309C22C2×#8819011yescharacteristic
310C22C22×#610611yescharacteristic
311C22C22×#610711yescharacteristic
312C22C2×#8820011yescharacteristic
313C4—24no—
314C4—24no—
315C4—84no—
316C4—524no—
317C4—1042no—
318C4#1171864314yes—
319C4C2×#8814312yes—
320C4C2×#8815212yes—
321C2#1311639818yesdirect product factor
322C2C2×#1171864311yescharacteristic
323C2C2×#1171874511yescharacteristic
324C2C2×#1171875211yescharacteristic
325C2C2×#1171862911yescharacteristic
326C2C2×#1171863111yescharacteristic
327C2C2×#1171874211yescharacteristic
328C2C2×#1171873211yescharacteristic
subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#384C2
socle, prime radicalC24×C13C2×D4
hypercenterC2×#384D13
hypocenterC13C2×#2100
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. #13116398C2direct (N × H)
209. C2×C13#2100semidirect
260. C13C2×#2100semidirect
321. C2#13116398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117185892
#131163982
C2×#117181212
C2×#117181162
C2×C13×#3842
C2×#210013