Finite Group Databasebeta

← C2×#13113358 #15830043

Subgroups — C2×#13113358 #15830043

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719305C211yesmaximal, characteristic
2C2×#11718380C211yesmaximal, characteristic, complemented
3C2×#11718310C211yesmaximal, characteristic, complemented
4#13113358C218yesmaximal, direct product factor
5C2×#11718059C211yesmaximal, characteristic, complemented
6C2×#11718044C211yesmaximal, characteristic, complemented
7C2×#11718129C211yesmaximal, characteristic
8C2×C13×#327C211yesmaximal, characteristic
9C2×C13×#121C2211yescharacteristic
10C2×#88190C411yescharacteristic, complemented
11C2×#88189—21no—
12C2×D4×Dic13—21no—
13C2×D4×Dic13C411yescharacteristic, complemented
14C2×#88178C2211yescharacteristic
15C22×#6101—21no—
16C22×C4×Dic13—21no—
17C22×C4×Dic13C2211yescharacteristic
18#11719305—22no—
19#11719305—22no—
20#11719305C414yescomplemented
21#11719305C2214yes—
22C2×#88144C411yescharacteristic, complemented
23C2×#88141C411yescharacteristic, complemented
24C2×#88133—21no—
25C2×#88131—21no—
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×#88071C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×#88055—21no—
31C2×#88054—21no—
32#11718380—22no—
33#11718380C2214yescomplemented
34#11718310—22no—
35#11718310C2214yescomplemented
36C13×#327C2214yes—
37#11718129C2214yes—
38#11718059C2214yescomplemented
39#11718044C2214yescomplemented
40C22×D4×C13—21no—
41C22×D4×C13C2×C411yescharacteristic
42C23×C4×C13—21no—
43C23×C4×C13C2311yescharacteristic
44C23×Dic13—21no—
45C23×Dic13—21no—
46C23×Dic13D411yescharacteristic
47C23×Dic13D411yescharacteristic
48C22×Dic26C2×C411yescharacteristic
49C22×C8×C13—21no—
50C13×#121—21no—
51C13×#121—21no—
52C13×#121C2×C412yes—
53C13×#121C2312yes—
54C2×C13×C4⋊C4C2×C411yescharacteristic
55C2×C13×C22⋊C4—21no—
56C2×C22⋊Dic13—21no—
57C2×C22⋊Dic13—21no—
58C2×C22⋊Dic13—21no—
59C2×C22⋊Dic13—21no—
60#88190—22no—
61#88190C2×C414yescomplemented
62#88189—24no—
63#88189—24no—
64D4×Dic13—24no—
65D4×Dic13—24no—
66D4×Dic13—22no—
67D4×Dic13C2×C414yescomplemented
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13C2×C411yescharacteristic
70#88178—21no—
71#88178—21no—
72#88178C2×C412yes—
73#88178C2312yes—
74C2×#6101—28no—
75C2×#6101—21no—
76C2×#6101—21no—
77C2×#6101—21no—
78C2×#6101—24no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—44no—
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C412yes—
85C2×C4×Dic13D412yes—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13D412yes—
89C2×C4×Dic13C2312yes—
90C22×#1055—21no—
91#88144—22no—
92#88144C2×C414yescomplemented
93#88141—22no—
94#88141C2×C414yescomplemented
95#88133—24no—
96#88133—24no—
97#88131—24no—
98#88131—24no—
99C13×C22⋊C8—21no—
100C13×C22⋊C8C2312yes—
101C13×#95—21no—
102C13×#95C2312yes—
103#88071—21no—
104#88071C2312yes—
105C22⋊#1055—21no—
106C22⋊#1055C2312yes—
107#88055—24no—
108#88054—24no—
109C2×#1509—131nomaximal, Sylow
110C24×C13—21no—
111C24×C13C2×D411yescharacteristic
112C2×D4×C13—22no—
113C2×D4×C13—22no—
114C2×D4×C13—21no—
115C2×D4×C13—42no—
116C2×D4×C13—42no—
117C2×D4×C13—42no—
118C2×D4×C13C22×C412yes—
119C22×C4×C13—24no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—42no—
123C22×C4×C13—42no—
124C22×C4×C13—42no—
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2411yescharacteristic
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—24no—
134C22×Dic13—24no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—24no—
139C22×Dic13—42no—
140C22×Dic13—42no—
141C22×Dic13—44no—
142C22×Dic13C22⋊C411yescharacteristic
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C22⋊C411yescharacteristic
145C22×Dic13C22⋊C412yes—
146C22×Dic13C22⋊C412yes—
147C22×Dic13C22⋊C411yescharacteristic
148C22×Dic13C2×D412yes—
149C22×Dic13C2×D412yes—
150C2×Dic26—21no—
151C2×Dic26—42no—
152C2×Dic26C22×C412yes—
153C2×C8×C13—22no—
154C2×C8×C13—42no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4C22×C412yes—
157C13×C22⋊C4—22no—
158C13×C22⋊C4—22no—
159C22⋊Dic13—22no—
160C22⋊Dic13—22no—
161C22⋊Dic13—24no—
162C22⋊Dic13—24no—
163C22⋊Dic13—24no—
164C4⋊Dic13—21no—
165C4⋊Dic13—24no—
166C4⋊Dic13C22×C412yes—
167#6101—216no—
168#6101—22no—
169#6101—22no—
170#6101—24no—
171#6101—24no—
172C4×Dic13—24no—
173C4×Dic13—48no—
174C4×Dic13C22⋊C412yes—
175C4×Dic13C22⋊C412yes—
176C4×Dic13C22⋊C412yes—
177C4×Dic13C22⋊C412yes—
178C4×Dic13C22×C412yes—
179C4×Dic13C22×C412yes—
180C4×Dic13C2×D412yes—
181C4×Dic13C2×D412yes—
182C2×#1055—22no—
183C2×#1055—42no—
184C2×#529—131no—
185C2×#432—131no—
186C2×C4×C4⋊C4—131no—
187#1509—138no—
188C2×#328—131no—
189C2×#328—131no—
190C2×#327—131no—
191C2×#327D1311yescharacteristic
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—42no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13C2×C22⋊C411yescharacteristic
199C23×C13C2×C22⋊C411yescharacteristic
200C23×C13AGL(1,ℤ/8)12yes—
201C23×C13#13712yes—
202C23×C13C22×D411yescharacteristic
203D4×C13—42no—
204D4×C13—42no—
205D4×C13—42no—
206D4×C13—42no—
207D4×C13—44no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—22no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—42no—
217C2×C4×C13—48no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13C2×C22⋊C411yescharacteristic
221C2×C4×C13C2×C22⋊C411yescharacteristic
222C2×C4×C13C23×C411yescharacteristic
223C2×C4×C13C22×D411yescharacteristic
224C2×Dic13—22no—
225C2×Dic13—22no—
226C2×Dic13—24no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—42no—
236C2×Dic13—48no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—48no—
241C2×Dic13#10414yes—
242C2×Dic13C2×C22⋊C412yes—
243C2×Dic13C2×C22⋊C412yes—
244C2×Dic13C2×C22⋊C412yes—
245C2×Dic13C2×C22⋊C412yes—
246Dic26—42no—
247Dic26—42no—
248C8×C13—42no—
249#1055—42no—
250#529—134no—
251#529—134no—
252#529—262no—
253#529—262no—
254C2×#126—261no—
255C2×#125—131no—
256C2×#124—131no—
257C2×#123—261no—
258C2×C22⋊Q8—131no—
259C2×#121C2×D1311yescharacteristic
260C2×C4×Q8—131no—
261C2×C4×D4—131no—
262C2×C4×D4—261no—
263C2×#117—261no—
264C22×C4⋊C4—261no—
265C22×C42—131no—
266C22×C42—261no—
267#432—134no—
268#432—262no—
269C2×C4⋊C8—261no—
270C2×C22⋊C8—131no—
271C2×C22⋊C8C2×D1311yescharacteristic
272C2×#97—261no—
273C4×C4⋊C4—134no—
274C4×C4⋊C4—262no—
275C2×#95—131no—
276C2×#95C2×D1311yescharacteristic
277#328—134no—
278#328—134no—
279#327—134no—
280#327C2×D1314yes—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—24no—
286C22×C13—24no—
287C22×C13—42no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—84no—
291C22×C13#41012yes—
292C22×C13#41712yes—
293C22×C13#41712yes—
294C22×C13C2×#10412yes—
295C22×C13C22×C22⋊C411yescharacteristic
296C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C13C2×#13711yescharacteristic
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—44no—
303C4×C13—42no—
304Dic13—22no—
305Dic13—22no—
306Dic13—22no—
307Dic13—44no—
308Dic13—42no—
309Dic13—42no—
310Dic13C2×#10414yes—
311C22×Q8—131no—
312C22×D4—21no—
313C22×D4C4×D1311yescharacteristic
314C23×C4—21no—
315C23×C4—131no—
316C23×C4—131no—
317C23×C4—261no—
318C23×C4—261no—
319C23×C4C22×D1311yescharacteristic
320C22×C8—21no—
321C22×C8—261no—
322#126—264no—
323#126—264no—
324#125—134no—
325#125—262no—
326#124—134no—
327#124—262no—
328#123—264no—
329#123—264no—
330C22⋊Q8—132no—
331C22⋊Q8—132no—
332C22⋊Q8—261no—
333C22⋊Q8—261no—
334#121—21no—
335#121—21no—
336#121C4×D1312yes—
337#121C22×D1312yes—
338C4×Q8—134no—
339C4×Q8—262no—
340C4×D4—134no—
341C4×D4—262no—
342C4×D4—264no—
343C4×D4—264no—
344#117—264no—
345#117—264no—
346C2×C4⋊C4—131no—
347C2×C4⋊C4—264no—
348C2×C4⋊C4—261no—
349C2×C4⋊C4—261no—
350C2×C4⋊C4—261no—
351C2×C4⋊C4—268no—
352C2×C4⋊C4—261no—
353C2×C4⋊C4C4×D1311yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—261no—
356C2×C22⋊C4—261no—
357C2×C22⋊C4—261no—
358C2×C22⋊C4—261no—
359C2×C42—131no—
360C2×C42—131no—
361C2×C42—132no—
362C2×C42—131no—
363C2×C42—131no—
364C2×C42—132no—
365C2×C42—132no—
366C2×C42—132no—
367C2×C42—261no—
368C2×C42—264no—
369C2×C42—524no—
370C4⋊C8—264no—
371C22⋊C8—21no—
372C22⋊C8—132no—
373C22⋊C8—261no—
374C22⋊C8C22×D1312yes—
375#97—264no—
376#95—21no—
377#95—132no—
378#95—261no—
379#95C22×D1312yes—
380C2×C13—21no—
381C2×C13—21no—
382C2×C13—22no—
383C2×C13—82no—
384C2×C13#150914yescomplemented
385C2×C13C2×#41011yescharacteristic
386C2×C13C2×#41711yescharacteristic
387C2×C13C22×#10411yescharacteristic
388C24—21no—
389C24D4×D1311yescharacteristic
390C2×Q8—132no—
391C2×Q8—261no—
392C2×Q8—522no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4C2×C4×D1312yes—
400C22×C4—24no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—131no—
407C22×C4—132no—
408C22×C4—132no—
409C22×C4—131no—
410C22×C4—131no—
411C22×C4—131no—
412C22×C4—132no—
413C22×C4—132no—
414C22×C4—264no—
415C22×C4—264no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—264no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—262no—
422C22×C4—524no—
423C22×C4—522no—
424C22×C4—522no—
425C22×C4C2×C4×D1311yescharacteristic
426C22×C4C2×C4×D1311yescharacteristic
427C22×C4D4×D1311yescharacteristic
428C22×C4D4×D1311yescharacteristic
429C22×C4D4×D1311yescharacteristic
430C22×C4C23×D1311yescharacteristic
431C2×C8—22no—
432C2×C8—42no—
433C2×C8—262no—
434C2×C8—522no—
435C4⋊C4—21no—
436C4⋊C4—132no—
437C4⋊C4—264no—
438C4⋊C4—264no—
439C4⋊C4—264no—
440C4⋊C4—2616no—
441C4⋊C4—261no—
442C4⋊C4—262no—
443C4⋊C4—262no—
444C4⋊C4C2×C4×D1312yes—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—264no—
448C22⋊C4—264no—
449C22⋊C4—264no—
450C22⋊C4—262no—
451C22⋊C4—262no—
452C42—132no—
453C42—132no—
454C42—132no—
455C42—132no—
456C42—132no—
457C42—132no—
458C42—132no—
459C42—132no—
460C42—264no—
461C42—528no—
462C13C2×#150911yescharacteristic, complemented, Sylow
463C23—22no—
464C23—22no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23C22⋊C4×D1311yescharacteristic
470C23C22⋊C4×D1311yescharacteristic
471C23#8816512yes—
472C23#8816912yes—
473C23C2×D4×D1311yescharacteristic
474Q8—522no—
475Q8—522no—
476D4—42no—
477D4—42no—
478D4—44no—
479D4—42no—
480D4—42no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—48no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—132no—
494C2×C4—134no—
495C2×C4—132no—
496C2×C4—132no—
497C2×C4—132no—
498C2×C4—264no—
499C2×C4—264no—
500C2×C4—264no—
501C2×C4—262no—
502C2×C4—262no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—262no—
506C2×C4—264no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—528no—
510C2×C4—528no—
511C2×C4—522no—
512C2×C4—522no—
513C2×C4—522no—
514C2×C4—522no—
515C2×C4C22⋊C4×D1311yescharacteristic
516C2×C4C22⋊C4×D1311yescharacteristic
517C2×C4C22×C4×D1311yescharacteristic
518C2×C4C2×D4×D1311yescharacteristic
519C8—42no—
520C8—522no—
521C22—24no—
522C22—24no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22#1171840112yes—
532C22#1171843212yes—
533C22#1171843212yes—
534C22D13×#10412yes—
535C22C2×C22⋊C4×D1311yescharacteristic
536C22C2×#8816511yescharacteristic
537C22C2×#8816911yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—42no—
544C4—134no—
545C4—262no—
546C4—262no—
547C4—262no—
548C4—524no—
549C4—522no—
550C4—522no—
551C2—21no—
552C2—22no—
553C2—21no—
554C2—82no—
555C2#1311335814yesdirect product factor
556C2C2×#1171840111yescharacteristic
557C2C2×#1171843211yescharacteristic
558C2C2×D13×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#327C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenterC2×#327D13
hypocenterC13C2×#1509
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#11718380C2semidirect
3. C2×#11718310C2semidirect
4. #13113358C2direct (N × H)
5. C2×#11718059C2semidirect
6. C2×#11718044C2semidirect
10. C2×#88190C4semidirect
13. C2×D4×Dic13C4semidirect
20. #11719305C4semidirect
22. C2×#88144C4semidirect
23. C2×#88141C4semidirect
33. #11718380C22semidirect
35. #11718310C22semidirect
38. #11718059C22semidirect
39. #11718044C22semidirect
61. #88190C2×C4semidirect
67. D4×Dic13C2×C4semidirect
92. #88144C2×C4semidirect
94. #88141C2×C4semidirect
384. C2×C13#1509semidirect
462. C13C2×#1509semidirect
555. C2#13113358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193052
C2×#117183802
C2×#117183102
#131133582
C2×#117180592
C2×#117180442
C2×#117181292
C2×C13×#3272
C2×#150913