Finite Group Databasebeta

← C2×#13113360 #15830045

Subgroups — C2×#13113360 #15830045

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×#11719329C211yesmaximal, characteristic
2C2×#11718380C211yesmaximal, characteristic, complemented
3C2×#11718310C211yesmaximal, characteristic, complemented
4#13113360C218yesmaximal, direct product factor
5C2×#11718130C211yesmaximal, characteristic, complemented
6C2×#11718062C211yesmaximal, characteristic
7C2×#11718043C211yesmaximal, characteristic
8C2×C13×#328C211yesmaximal, characteristic, complemented
9C2×C13×C22⋊Q8C2211yescharacteristic
10C2×#88201C411yescharacteristic, complemented
11C2×Q8×Dic13C411yescharacteristic, complemented
12C2×#88184C2211yescharacteristic
13C22×#6101—21no—
14C22×C4×Dic13—21no—
15C22×C4×Dic13C2211yescharacteristic
16#11719329—22no—
17#11719329—22no—
18#11719329C414yescomplemented
19#11719329C2214yes—
20C2×#88152—21no—
21C2×#88147C411yescharacteristic, complemented
22C2×#88146—21no—
23C2×#88144C411yescharacteristic, complemented
24C2×#88140—21no—
25C2×#88135—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×#328C2214yescomplemented
37#11718130C2214yescomplemented
38#11718062C2214yes—
39#11718043C2214yes—
40C22×Q8×C13C2×C411yescharacteristic
41C23×C4×C13—21no—
42C23×C4×C13C2311yescharacteristic
43C22×C22⋊D13—21no—
44C23×Dic13—21no—
45C23×Dic13D411yescharacteristic
46C23×Dic13D411yescharacteristic
47C22×D52C2×C411yescharacteristic
48C22×C4×D13—21no—
49C22×C8×C13—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C13×C22⋊Q8C2×C412yes—
53C13×C22⋊Q8C2312yes—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C13×C22⋊C4—21no—
57#88201—22no—
58#88201C2×C414yescomplemented
59Q8×Dic13—22no—
60Q8×Dic13C2×C414yescomplemented
61#88184—21no—
62#88184—21no—
63#88184C2×C412yes—
64#88184C2312yes—
65C2×#6103—21no—
66C2×#6103—21no—
67C2×#6103—21no—
68C2×#6103—21no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13C2×C411yescharacteristic
72C2×#6101—28no—
73C2×#6101—21no—
74C2×#6101—24no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—44no—
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C412yes—
81C2×C4×Dic13D412yes—
82C2×C4×Dic13D411yescharacteristic
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13D412yes—
85C2×C4×Dic13C2312yes—
86C22×#1055—21no—
87#88152—24no—
88#88152—24no—
89#88147—22no—
90#88147C2×C414yescomplemented
91#88146—24no—
92#88146—24no—
93#88144—22no—
94#88144C2×C414yescomplemented
95#88140—24no—
96#88140—24no—
97#88135—24no—
98#88135—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×C13C2×D411yescharacteristic
111C23×D13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—42no—
114C2×Q8×C13C22×C412yes—
115C22×C4×C13—24no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—42no—
120C22×C4×C13—42no—
121C22×C4×C13—42no—
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2411yescharacteristic
128C2×C22⋊D13—22no—
129C2×C22⋊D13—22no—
130C2×C22⋊D13—42no—
131C2×C22⋊D13—42no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—24no—
135C22×Dic13—24no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—42no—
139C22×Dic13—42no—
140C22×Dic13C22⋊C412yes—
141C22×Dic13C22⋊C412yes—
142C22×Dic13C22⋊C411yescharacteristic
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C22⋊C411yescharacteristic
145C22×Dic13C22⋊C411yescharacteristic
146C22×Dic13C2×D412yes—
147C22×Dic13C2×D412yes—
148C2×D52—21no—
149C2×D52—42no—
150C2×D52C22×C412yes—
151C2×C4×D13—24no—
152C2×C4×D13—44no—
153C2×C8×C13—22no—
154C2×C8×C13—42no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4C22×C412yes—
159C13×C22⋊C4—22no—
160C13×C22⋊C4—22no—
161#6103—22no—
162#6103—22no—
163#6103—24no—
164#6103—24no—
165#6103—24no—
166C4⋊Dic13—21no—
167C4⋊Dic13—24no—
168C4⋊Dic13—24no—
169C4⋊Dic13C22×C412yes—
170#6101—216no—
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×#328D1311yescharacteristic, complemented
190C2×#327—131no—
191C2×#327—131no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13C2×C22⋊C411yescharacteristic
195C23×C13C2×C22⋊C411yescharacteristic
196C23×C13AGL(1,ℤ/8)12yes—
197C23×C13#13712yes—
198C23×C13C22×D411yescharacteristic
199C22×D13—22no—
200C22×D13—42no—
201C22×D13—42no—
202C22×D13—42no—
203Q8×C13—42no—
204Q8×C13—42no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—48no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13C2×C22⋊C411yescharacteristic
220C2×C4×C13C2×C22⋊C411yescharacteristic
221C2×C4×C13C23×C411yescharacteristic
222C2×C4×C13C22×D411yescharacteristic
223C22⋊D13—42no—
224C22⋊D13—42no—
225C22⋊D13—44no—
226C2×Dic13—22no—
227C2×Dic13—22no—
228C2×Dic13—24no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—22no—
236C2×Dic13—42no—
237C2×Dic13—48no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13#10414yes—
241C2×Dic13C2×C22⋊C412yes—
242C2×Dic13C2×C22⋊C412yes—
243C2×Dic13C2×C22⋊C412yes—
244C2×Dic13C2×C22⋊C412yes—
245D52—42no—
246D52—42no—
247C4×D13—48no—
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⋊Q8C2×D1311yescharacteristic
259C2×#121—131no—
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#328C2×D1314yescomplemented
279#327—134no—
280#327—134no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—24no—
286C22×C13—24no—
287C22×C13#41012yes—
288C22×C13#41712yes—
289C22×C13#41712yes—
290C22×C13C2×#10412yes—
291C22×C13C22×C22⋊C411yescharacteristic
292C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C13C2×#13711yescharacteristic
294C2×D13—42no—
295C2×D13—42no—
296C2×D13—42no—
297C2×D13—84no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—44no—
303C4×C13—42no—
304C4×C13—42no—
305Dic13—22no—
306Dic13—22no—
307Dic13—22no—
308Dic13—44no—
309Dic13—42no—
310Dic13C2×#10414yes—
311C22×Q8C4×D1311yescharacteristic
312C22×D4—131no—
313C22×D4—261no—
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—21no—
331C22⋊Q8—21no—
332C22⋊Q8C4×D1312yes—
333C22⋊Q8C22×D1312yes—
334#121—132no—
335#121—132no—
336#121—261no—
337#121—261no—
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—21no—
347C2×C4⋊C4—131no—
348C2×C4⋊C4—264no—
349C2×C4⋊C4—261no—
350C2×C4⋊C4—261no—
351C2×C4⋊C4—261no—
352C2×C4⋊C4—268no—
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#150914yescomplemented
384C2×C13C2×#41011yescharacteristic
385C2×C13C2×#41711yescharacteristic
386C2×C13C22×#10411yescharacteristic
387D13—82no—
388C24—261no—
389C24D4×D1311yescharacteristic
390C2×Q8—21no—
391C2×Q8—42no—
392C2×Q8C2×C4×D1312yes—
393C2×D4—132no—
394C2×D4—262no—
395C2×D4—262no—
396C2×D4—261no—
397C2×D4—522no—
398C2×D4—522no—
399C2×D4—522no—
400C22×C4—24no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—131no—
408C22×C4—132no—
409C22×C4—132no—
410C22×C4—131no—
411C22×C4—131no—
412C22×C4—131no—
413C22×C4—132no—
414C22×C4—132no—
415C22×C4—264no—
416C22×C4—264no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—264no—
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—22no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—132no—
439C4⋊C4—264no—
440C4⋊C4—264no—
441C4⋊C4—264no—
442C4⋊C4—2616no—
443C4⋊C4—261no—
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—262no—
466C23—522no—
467C23—522no—
468C23—522no—
469C23C22⋊C4×D1311yescharacteristic
470C23C22⋊C4×D1311yescharacteristic
471C23#8816812yes—
472C23#8817212yes—
473C23C2×D4×D1311yescharacteristic
474Q8—42no—
475Q8—42no—
476D4—522no—
477D4—522no—
478D4—522no—
479D4—522no—
480D4—524no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—48no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—132no—
496C2×C4—134no—
497C2×C4—132no—
498C2×C4—132no—
499C2×C4—132no—
500C2×C4—264no—
501C2×C4—264no—
502C2×C4—262no—
503C2×C4—262no—
504C2×C4—264no—
505C2×C4—262no—
506C2×C4—262no—
507C2×C4—262no—
508C2×C4—264no—
509C2×C4—262no—
510C2×C4—528no—
511C2×C4—528no—
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—522no—
528C22—522no—
529C22—522no—
530C22—1044no—
531C22#1171840112yes—
532C22#1171846412yes—
533C22#1171846412yes—
534C22D13×#10412yes—
535C22C2×C22⋊C4×D1311yescharacteristic
536C22C2×#8816811yescharacteristic
537C22C2×#8817211yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—42no—
544C4—42no—
545C4—134no—
546C4—262no—
547C4—262no—
548C4—262no—
549C4—524no—
550C4—522no—
551C2—21no—
552C2—21no—
553C2—22no—
554C2—1042no—
555C2#1311336014yesdirect product factor
556C2C2×#1171840111yescharacteristic
557C2C2×#1171846411yescharacteristic
558C2C2×D13×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#328C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenterC2×#328D13
hypocenterC13C2×#1509
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#11718380C2semidirect
3. C2×#11718310C2semidirect
4. #13113360C2direct (N × H)
5. C2×#11718130C2semidirect
8. C2×C13×#328C2semidirect
10. C2×#88201C4semidirect
11. C2×Q8×Dic13C4semidirect
18. #11719329C4semidirect
21. C2×#88147C4semidirect
23. C2×#88144C4semidirect
33. #11718380C22semidirect
35. #11718310C22semidirect
36. C13×#328C22semidirect
37. #11718130C22semidirect
58. #88201C2×C4semidirect
60. Q8×Dic13C2×C4semidirect
90. #88147C2×C4semidirect
94. #88144C2×C4semidirect
189. C2×#328D13semidirect
278. #328C2×D13semidirect
383. C2×C13#1509semidirect
462. C13C2×#1509semidirect
555. C2#13113360direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193292
C2×#117183802
C2×#117183102
#131133602
C2×#117181302
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C2×#117180432
C2×C13×#3282
C2×#150913