Finite Group Databasebeta

← C2×#13114209 #15845166

Subgroups — C2×#13114209 #15845166

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718740C211yesmaximal, characteristic, complemented
2C2×#11718669C211yesmaximal, characteristic
3C2×D4×#1055C211yesmaximal, characteristic
4#13114209C218yesmaximal, direct product factor
5C2×#11718072C211yesmaximal, characteristic, complemented
6C2×#11718073C211yesmaximal, characteristic, complemented
7C2×#11718139C211yesmaximal, characteristic, complemented
8C2×C13×#461C211yesmaximal, characteristic
9C22×C13×SD16—21no—
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C23×#1055—21no—
13C2×#88123C2211yescharacteristic
14C13×#461—22no—
15C13×#461C2214yes—
16C2×C13×C4⋊C8C2211yescharacteristic
17C2×C13×#103—21no—
18C2×#88072—21no—
19C2×C22⋊#1055—21no—
20#11718740—22no—
21#11718740C2214yescomplemented
22D4×#1055—22no—
23D4×#1055C2214yes—
24#11718669—22no—
25#11718669C2214yes—
26C2×#88048—21no—
27C2×#88048—21no—
28C2×#88048—21no—
29C2×C4⋊#1055C2211yescharacteristic
30C2×C4⋊#1055C2211yescharacteristic
31C2×C4×#1055C2211yescharacteristic
32#11718139C2214yescomplemented
33#11718073C2214yescomplemented
34#11718072C2214yescomplemented
35C22×Q8×C13—21no—
36C22×D4×C13D411yescharacteristic
37C23×C4×C13—21no—
38C22×Dic26—21no—
39C2×C13×SD16—24no—
40C2×C13×SD16—44no—
41C22×C8×C13—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8—21no—
45C13×C4⋊Q8C2312yes—
46C4×D4×C13—21no—
47C4×D4×C13—21no—
48C4×D4×C13D412yes—
49C4×D4×C13C2312yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C22⋊C4—21no—
54C2×C42×C13C2311yescharacteristic
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C22×#1055—21no—
58C22×#1055—21no—
59C22×#1055—24no—
60C22×#1055—44no—
61C22×#1055D411yescharacteristic
62C22×#1055D411yescharacteristic
63#88123—21no—
64#88123—21no—
65#88123—21no—
66#88123C2312yes—
67C13×C4⋊C8—21no—
68C13×C4⋊C8C2312yes—
69C13×#103—24no—
70#88072—24no—
71C22⋊#1055—24no—
72#88048—24no—
73#88048—24no—
74#88048—24no—
75C4⋊#1055—21no—
76C4⋊#1055—21no—
77C4⋊#1055C2312yes—
78C4⋊#1055C2312yes—
79C4×#1055D412yes—
80C4×#1055C2312yes—
81C2×#1671—131nomaximal, Sylow
82C24×C13—21no—
83C2×Q8×C13—22no—
84C2×Q8×C13—41no—
85C2×Q8×C13—42no—
86C2×Q8×C13—42no—
87C2×D4×C13—21no—
88C2×D4×C13—22no—
89C2×D4×C13SD1614yes—
90C2×D4×C13C2×D412yes—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13—41no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13#4111yescharacteristic
100C22×Dic13—41no—
101C2×Dic26—22no—
102C2×Dic26—41no—
103C2×Dic26—82no—
104C13×SD16—48no—
105C2×C8×C13—22no—
106C2×C8×C13—42no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4C2×D412yes—
113C13×C22⋊C4—22no—
114C13×C22⋊C4—22no—
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13#4111yescharacteristic
118C42×C13C2411yescharacteristic
119C4⋊Dic13—22no—
120C4⋊Dic13—22no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C2×#1055—22no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055—42no—
127C2×#1055—42no—
128C2×#1055—48no—
129C2×#1055SD1614yescomplemented
130C2×#1055C2×D412yes—
131C2×#1055C2×D412yes—
132C2×#498—131no—
133C2×#476—131no—
134C2×#461D1311yescharacteristic
135C2×C8×D4—131no—
136#1671—138no—
137C2×#334—131no—
138C2×#333—131no—
139C2×#332—131no—
140C23×C13—22no—
141C23×C13—24no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13#12111yescharacteristic
145Q8×C13—42no—
146Q8×C13—42no—
147Q8×C13—82no—
148D4×C13—22no—
149D4×C13—24no—
150D4×C13C2×SD1614yes—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—44no—
157C2×C4×C13—42no—
158C2×C4×C13—82no—
159C2×C4×C13#12111yescharacteristic
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13C2×SD1612yes—
163C2×C4×C13C2×SD1612yes—
164C2×C4×C13#13512yes—
165C2×C4×C13#13712yes—
166C2×C4×C13C22×D411yescharacteristic
167C2×C4×C13C22×D411yescharacteristic
168C2×C4×C13C2×#4111yescharacteristic
169C2×Dic13—42no—
170C2×Dic13—82no—
171Dic26—82no—
172Dic26—82no—
173C8×C13—42no—
174#1055—22no—
175#1055—42no—
176#1055—42no—
177#1055C2×SD1614yescomplemented
178C22×SD16—21no—
179C23×C8—261no—
180C2×C4⋊Q8—131no—
181C2×C4⋊Q8C2×D1311yescharacteristic
182C2×C4×D4C2×D1311yescharacteristic
183#498—134no—
184#498—262no—
185#476—134no—
186#476—262no—
187#461—22no—
188#461C2×D1314yes—
189C8×D4—134no—
190C8×D4—262no—
191C2×#106—261no—
192C2×#106—261no—
193C2×#106—261no—
194C2×C4⋊C8—131no—
195C2×C4⋊C8—131no—
196C2×C4⋊C8C2×D1311yescharacteristic
197C2×#103—21no—
198C2×#102—261no—
199C2×C22⋊C8—261no—
200C2×C4×C8—131no—
201#334—134no—
202#333—134no—
203#332—134no—
204C22×C13—24no—
205C22×C13—48no—
206C22×C13—42no—
207C22×C13—42no—
208C22×C13#46112yes—
209C22×C13#46512yes—
210C22×C13#47112yes—
211C22×C13C2×#12111yescharacteristic
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—42no—
215C4×C13—82no—
216C4×C13#46112yes—
217C4×C13#46512yes—
218C4×C13C22×SD1611yescharacteristic
219C4×C13C22×SD1611yescharacteristic
220C4×C13C2×#13511yescharacteristic
221C4×C13C2×#13711yescharacteristic
222Dic13—82no—
223C22×Q8—21no—
224C22×Q8—261no—
225C22×D4C22⋊D1311yescharacteristic
226C23×C4—21no—
227C2×SD16—24no—
228C2×SD16—44no—
229C22×C8—21no—
230C22×C8—131no—
231C22×C8—131no—
232C22×C8—264no—
233C22×C8—261no—
234C22×C8—261no—
235C22×C8—524no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—132no—
240C4⋊Q8—261no—
241C4⋊Q8—261no—
242C4⋊Q8—261no—
243C4⋊Q8C22×D1312yes—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4C22⋊D1312yes—
247C4×D4C22×D1312yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—261no—
251C2×C4⋊C4—261no—
252C2×C4⋊C4C22⋊D1311yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C22×D1311yescharacteristic
255#106—264no—
256#106—264no—
257#106—264no—
258C4⋊C8—21no—
259C4⋊C8—132no—
260C4⋊C8—132no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C4⋊C8C22×D1312yes—
264#103—24no—
265#102—264no—
266C22⋊C8—264no—
267C4×C8—132no—
268C4×C8—132no—
269C2×C13—44no—
270C2×C13#167114yescomplemented
271C2×C13C2×#46111yescharacteristic
272C2×C13C2×#46511yescharacteristic
273C2×C13C2×#47111yescharacteristic
274C24—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—262no—
280C2×Q8—521no—
281C2×Q8—1042no—
282C2×D4—21no—
283C2×D4—22no—
284C2×D4#610514yes—
285C2×D4C2×C22⋊D1312yes—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—521no—
293C22×C4D4×D1311yescharacteristic
294C22×C4#612911yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296SD16—48no—
297C2×C8—22no—
298C2×C8—42no—
299C2×C8—134no—
300C2×C8—132no—
301C2×C8—132no—
302C2×C8—262no—
303C2×C8—262no—
304C2×C8—262no—
305C2×C8—528no—
306C2×C8—522no—
307C2×C8—522no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—262no—
314C4⋊C4—262no—
315C4⋊C4—521no—
316C4⋊C4—521no—
317C4⋊C4C2×C22⋊D1312yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C42D4×D1311yescharacteristic
321C42#612911yescharacteristic
322C42C2×C22⋊D1311yescharacteristic
323C42C23×D1311yescharacteristic
324C13C2×#167111yescharacteristic, complemented, Sylow
325C23—24no—
326C23—22no—
327C23—42no—
328C23—42no—
329C23#8819311yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—1042no—
334Q8—1042no—
335D4—24no—
336D4—22no—
337D4C2×#610514yes—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—522no—
347C2×C4—1042no—
348C2×C4SD16×D1312yes—
349C2×C4#8816912yes—
350C2×C4C2×#610512yes—
351C2×C4#8819311yescharacteristic
352C2×C4#8819311yescharacteristic
353C2×C4#8819311yescharacteristic
354C2×C4#8820412yes—
355C2×C4C2×D4×D1311yescharacteristic
356C2×C4C2×#612911yescharacteristic
357C2×C4C22×C22⋊D1311yescharacteristic
358C8—42no—
359C8—134no—
360C8—262no—
361C8—522no—
362C8—522no—
363C22—24no—
364C22—48no—
365C22—42no—
366C22—42no—
367C22#1171870212yes—
368C22#1171882312yes—
369C22#1171886412yes—
370C22C2×#8819311yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—82no—
375C4—1042no—
376C4#1171870212yes—
377C4#1171882312yes—
378C4C2×SD16×D1311yescharacteristic
379C4C2×#8816911yescharacteristic
380C4C22×#610511yescharacteristic
381C4C2×#8820411yescharacteristic
382C2—44no—
383C2#1311420914yesdirect product factor
384C2C2×#1171882311yescharacteristic
385C2C2×#1171870211yescharacteristic
386C2C2×#1171886411yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#461C2
socleC23×C13#121
prime radicalC22×D4×C13D4
hypercenterC2×#461D13
hypocenterC13C2×#1671
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#11718740C2semidirect
4. #13114209C2direct (N × H)
5. C2×#11718072C2semidirect
6. C2×#11718073C2semidirect
7. C2×#11718139C2semidirect
21. #11718740C22semidirect
32. #11718139C22semidirect
33. #11718073C22semidirect
34. #11718072C22semidirect
129. C2×#1055SD16semidirect
177. #1055C2×SD16semidirect
270. C2×C13#1671semidirect
324. C13C2×#1671semidirect
383. C2#13114209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187402
C2×#117186692
C2×D4×#10552
#131142092
C2×#117180722
C2×#117180732
C2×#117181392
C2×C13×#4612
C2×#167113