Finite Group Databasebeta

← C2×#13114381 #15845474

Subgroups — C2×#13114381 #15845474

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718742C211yesmaximal, characteristic, complemented
2C2×#11718680C211yesmaximal, characteristic
3C2×#11718673C211yesmaximal, characteristic
4#13114381C218yesmaximal, direct product factor
5C2×#11718071C211yesmaximal, characteristic, complemented
6C2×#11718074C211yesmaximal, characteristic, complemented
7C2×#11718139C211yesmaximal, characteristic, complemented
8C2×C13×#474C211yesmaximal, characteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C22×#6105—21no—
12C22×#6099—21no—
13C2×#88123C2211yescharacteristic
14C13×#474—22no—
15C13×#474C2214yes—
16C2×C13×#107—21no—
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#102—21no—
19C2×#88075—21no—
20C2×#88075—21no—
21C2×C22⋊#1055—21no—
22#11718742—22no—
23#11718742C2214yescomplemented
24#11718680—22no—
25#11718680C2214yes—
26#11718673—22no—
27#11718673C2214yes—
28C2×#88050—21no—
29C2×C4⋊#1055C2211yescharacteristic
30C2×C4⋊#1055C2211yescharacteristic
31C2×C4×#1055C2211yescharacteristic
32#11718139C2214yescomplemented
33#11718074C2214yescomplemented
34#11718071C2214yescomplemented
35C22×Q8×C13—21no—
36C22×D4×C13D411yescharacteristic
37C23×C4×C13—21no—
38C22×Dic26—21no—
39C22×C8×C13—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8C2312yes—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13D412yes—
47C4×D4×C13C2312yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4D411yescharacteristic
51C2×C13×C22⋊C4—21no—
52C2×C42×C13C2311yescharacteristic
53C2×#6105—24no—
54C2×#6105—44no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×#6099—24no—
58C2×#6099—44no—
59C22×#1055—21no—
60C22×#1055—21no—
61C22×#1055D411yescharacteristic
62C22×#1055D411yescharacteristic
63#88123—21no—
64#88123—21no—
65#88123—21no—
66#88123C2312yes—
67C13×#107—24no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8C2312yes—
70C13×#102—24no—
71#88075—24no—
72#88075—24no—
73C22⋊#1055—24no—
74#88050—24no—
75C4⋊#1055—21no—
76C4⋊#1055—21no—
77C4⋊#1055C2312yes—
78C4⋊#1055C2312yes—
79C4×#1055D412yes—
80C4×#1055C2312yes—
81C2×#1699—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×C13—22no—
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—42no—
103C2×Dic26—42no—
104C2×Dic26—41no—
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
119#6105—48no—
120C4⋊Dic13—22no—
121C4⋊Dic13—22no—
122C4⋊Dic13—41no—
123C4⋊Dic13—41no—
124#6099—48no—
125C2×#1055—22no—
126C2×#1055—22no—
127C2×#1055—22no—
128C2×#1055—22no—
129C2×#1055—42no—
130C2×#1055—42no—
131C2×#1055C2×D412yes—
132C2×#1055C2×D412yes—
133C2×#487—131no—
134C2×#474D1311yescharacteristic
135C2×#461—131no—
136C2×#436—131no—
137#1699—138no—
138C2×#335—131no—
139C2×#332—131no—
140C2×#332—131no—
141C23×C13—22no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13#12111yescharacteristic
146Q8×C13—42no—
147Q8×C13—42no—
148Q8×C13—82no—
149D4×C13—22no—
150D4×C13—22no—
151D4×C13—42no—
152C2×C4×C13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—44no—
158C2×C4×C13—42no—
159C2×C4×C13—82no—
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#13512yes—
164C2×C4×C13AGL(1,ℤ/8)12yes—
165C2×C4×C13AGL(1,ℤ/8)12yes—
166C2×C4×C13#13712yes—
167C2×C4×C13C22×D411yescharacteristic
168C2×C4×C13C22×D411yescharacteristic
169C2×C4×C13C2×#4111yescharacteristic
170C2×Dic13—42no—
171C2×Dic13—82no—
172Dic26—42no—
173Dic26—42no—
174Dic26—82no—
175C8×C13—42no—
176#1055—22no—
177#1055—22no—
178#1055—42no—
179#1055—42no—
180C22×SD16—261no—
181C22×M16—261no—
182C2×C4⋊Q8—131no—
183C2×C4⋊Q8C2×D1311yescharacteristic
184C2×C4×D4C2×D1311yescharacteristic
185#487—134no—
186#487—262no—
187#474—22no—
188#474C2×D1314yes—
189#461—134no—
190#461—262no—
191#436—134no—
192#436—262no—
193C2×#107—21no—
194C2×C4⋊C8—131no—
195C2×C4⋊C8—131no—
196C2×C4⋊C8C2×D1311yescharacteristic
197C2×#103—261no—
198C2×#103—261no—
199C2×#103—261no—
200C2×#102—21no—
201C2×C22⋊C8—261no—
202C2×C4×C8—131no—
203#335—134no—
204#332—134no—
205#332—134no—
206C22×C13—42no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—84no—
210C22×C13#46312yes—
211C22×C13#46812yes—
212C22×C13#47312yes—
213C22×C13C2×#12111yescharacteristic
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—42no—
217C4×C13—82no—
218C4×C13#46312yes—
219C4×C13#46812yes—
220C4×C13C2×#13511yescharacteristic
221C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C13C2×#13711yescharacteristic
224Dic13—82no—
225C22×Q8—21no—
226C22×Q8—261no—
227C22×D4C22⋊D1311yescharacteristic
228C23×C4—21no—
229C2×SD16—264no—
230C2×SD16—524no—
231C2×M16—264no—
232C2×M16—524no—
233C22×C8—21no—
234C22×C8—131no—
235C22×C8—131no—
236C22×C8—261no—
237C22×C8—261no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—132no—
242C4⋊Q8—261no—
243C4⋊Q8—261no—
244C4⋊Q8—261no—
245C4⋊Q8C22×D1312yes—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4C22⋊D1312yes—
249C4×D4C22×D1312yes—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—261no—
253C2×C4⋊C4—261no—
254C2×C4⋊C4C22⋊D1311yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C22×D1311yescharacteristic
257#107—24no—
258C4⋊C8—21no—
259C4⋊C8—132no—
260C4⋊C8—132no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C4⋊C8C22×D1312yes—
264#103—264no—
265#103—264no—
266#103—264no—
267#102—24no—
268C22⋊C8—264no—
269C4×C8—132no—
270C4×C8—132no—
271C2×C13—82no—
272C2×C13#169914yescomplemented
273C2×C13C2×#46311yescharacteristic
274C2×C13C2×#46811yescharacteristic
275C2×C13C2×#47311yescharacteristic
276C24—21no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—262no—
282C2×Q8—521no—
283C2×Q8—522no—
284C2×Q8—522no—
285C2×D4—21no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4C2×C22⋊D1312yes—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—41no—
295C22×C4—521no—
296C22×C4D4×D1311yescharacteristic
297C22×C4#612911yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299SD16—528no—
300M16—528no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—132no—
304C2×C8—132no—
305C2×C8—262no—
306C2×C8—262no—
307C2×C8—262no—
308C2×C8—262no—
309C2×C8—522no—
310C2×C8—522no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—262no—
317C4⋊C4—262no—
318C4⋊C4—521no—
319C4⋊C4—521no—
320C4⋊C4C2×C22⋊D1312yes—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C42D4×D1311yescharacteristic
324C42#612911yescharacteristic
325C42C2×C22⋊D1311yescharacteristic
326C42C23×D1311yescharacteristic
327C13C2×#169911yescharacteristic, complemented, Sylow
328C23—22no—
329C23—42no—
330C23—42no—
331C23—42no—
332C23#8819311yescharacteristic
333Q8—42no—
334Q8—42no—
335Q8—82no—
336Q8—522no—
337Q8—522no—
338Q8—1042no—
339D4—22no—
340D4—22no—
341D4—42no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—522no—
351C2×C4—1042no—
352C2×C4#8816512yes—
353C2×C4#8816612yes—
354C2×C4#8819311yescharacteristic
355C2×C4#8819311yescharacteristic
356C2×C4#8819311yescharacteristic
357C2×C4#8819612yes—
358C2×C4#8820312yes—
359C2×C4C2×D4×D1311yescharacteristic
360C2×C4C2×#612911yescharacteristic
361C2×C4C22×C22⋊D1311yescharacteristic
362C8—42no—
363C8—262no—
364C8—262no—
365C8—522no—
366C8—522no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—84no—
371C22#1171871012yes—
372C22#1171881412yes—
373C22#1171886512yes—
374C22C2×#8819311yescharacteristic
375C4—21no—
376C4—21no—
377C4—42no—
378C4—82no—
379C4—1042no—
380C4#1171871012yes—
381C4#1171881412yes—
382C4C2×#8816511yescharacteristic
383C4C2×#8816611yescharacteristic
384C4C2×#8819611yescharacteristic
385C4C2×#8820311yescharacteristic
386C2—82no—
387C2#1311438114yesdirect product factor
388C2C2×#1171881411yescharacteristic
389C2C2×#1171871011yescharacteristic
390C2C2×#1171886511yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#474C2
socleC23×C13#121
prime radicalC22×D4×C13D4
hypercenterC2×#474D13
hypocenterC13C2×#1699
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#11718742C2semidirect
4. #13114381C2direct (N × H)
5. C2×#11718071C2semidirect
6. C2×#11718074C2semidirect
7. C2×#11718139C2semidirect
23. #11718742C22semidirect
32. #11718139C22semidirect
33. #11718074C22semidirect
34. #11718071C22semidirect
272. C2×C13#1699semidirect
327. C13C2×#1699semidirect
387. C2#13114381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187422
C2×#117186802
C2×#117186732
#131143812
C2×#117180712
C2×#117180742
C2×#117181392
C2×C13×#4742
C2×#169913