Finite Group Databasebeta

← C2×#13124687 #16730500

Subgroups — C2×#13124687 #16730500

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719224C211yesmaximal, characteristic, complemented
2#13124687C2116yesmaximal, direct product factor
3C2×#11718683C212yesmaximal, complemented
4C2×#11718682C212yesmaximal, complemented
5C2×#11718670C212yesmaximal, complemented
6C2×#11718668C212yesmaximal, complemented
7C2×#11718625C211yesmaximal, characteristic, complemented
8C22×#88047C211yesmaximal, characteristic, complemented
9C2×#11718660C211yesmaximal, characteristic, complemented
10C2×#11718893C211yesmaximal, characteristic
11C2×#11718894C211yesmaximal, characteristic
12C2×C13×#520C211yesmaximal, characteristic
13C22×C13×#41C2211yescharacteristic
14C13×#520—24no—
15C13×#520C2218yes—
16C2×C4×Q8×C13C2212yes—
17C2×C4×D4×C13—22no—
18C2×C4×D4×C13C2212yes—
19C2×C13×#117—21no—
20C2×C13×#117C2211yescharacteristic
21C22×C13×C4⋊C4—21no—
22C22×C13×C4⋊C4C2211yescharacteristic
23C2×#88180C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C23×#1055C2211yescharacteristic
27#11719224—24no—
28#11719224C2218yescomplemented
29C2×#88144—21no—
30C2×#88142—21no—
31C2×#88132—22no—
32C2×#88124C2212yes—
33C2×#88123C2212yes—
34#11718894C2218yes—
35#11718893C2218yes—
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2212yes—
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41C2×#88072C2212yes—
42#11718683C22116yescomplemented
43#11718682C22116yescomplemented
44#11718670C22116yescomplemented
45#11718668C22116yescomplemented
46#11718660C2218yescomplemented
47#11718625C2218yescomplemented
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×#88047C2212yes—
51C2×#88047C2212yes—
52C2×#88047C2218yescomplemented
53C2×C4⋊#1055C2212yes—
54C2×C4⋊#1055C2212yes—
55C2×C13×#41—22no—
56C2×C13×#41—24no—
57C2×C13×#41Q818yescomplemented
58C2×C13×#41C2314yes—
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13—22no—
65C23×C4×C13C2311yescharacteristic
66C23×Dic13—21no—
67C22×Dic26—22no—
68C4×Q8×C13—24no—
69C4×Q8×C13C2318yes—
70C4×D4×C13—216no—
71C4×D4×C13—24no—
72C4×D4×C13C2318yes—
73C13×#117—28no—
74C13×#117D414yes—
75C13×#117C2314yes—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—28no—
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4D411yescharacteristic
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C4⋊C4C2314yes—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4D412yes—
86C2×C42×C13—22no—
87C2×C42×C13C2312yes—
88C2×C22⋊Dic13—21no—
89#88180—22no—
90#88180C2314yes—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2312yes—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2314yes—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×C4×Dic13—21no—
101C2×#6099—24no—
102C2×#6099C2314yes—
103C22×#1055—24no—
104C22×#1055C2314yes—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2312yes—
108#88144—28no—
109#88142—28no—
110#88132—216no—
111#88124—24no—
112#88124C2318yes—
113#88123—24no—
114#88123C2318yes—
115#88075C2314yes—
116#88075C2318yes—
117#88075C2314yes—
118#88072C2314yes—
119#88072C2318yes—
120#88072C2314yes—
121#88048C2318yes—
122#88047C2318yes—
123#88047C2318yes—
124#88047C2318yes—
125C4⋊#1055C2318yes—
126C4⋊#1055C2318yes—
127C2×#3083—131nomaximal, Sylow
128C24×C13—21no—
129C24×C13C2×D411yescharacteristic
130C13×#41—216no—
131C13×#41—28no—
132C13×#41C2×Q8116yescomplemented
133C2×Q8×C13—21no—
134C2×Q8×C13—22no—
135C2×Q8×C13C2×Q814yes—
136C2×Q8×C13C2412yes—
137C2×D4×C13—28no—
138C2×D4×C13—24no—
139C2×D4×C13—21no—
140C2×D4×C13—22no—
141C2×D4×C13C2×Q814yes—
142C2×D4×C13C2412yes—
143C22×C4×C13—21no—
144C22×C4×C13—28no—
145C22×C4×C13—24no—
146C22×C4×C13—22no—
147C22×C4×C13—24no—
148C22×C4×C13—28no—
149C22×C4×C13—84no—
150C22×C4×C13—82no—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×Q814yes—
156C22×C4×C13#4114yes—
157C22×C4×C13C2411yescharacteristic
158C22×C4×C13C2412yes—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—24no—
163C22×Dic13—82no—
164C2×Dic26—28no—
165C2×Dic26—84no—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—28no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4C2×D414yes—
170C13×C4⋊C4C2×D414yes—
171C13×C4⋊C4C2414yes—
172C13×C22⋊C4—28no—
173C13×C22⋊C4C2×D418yes—
174C42×C13—28no—
175C42×C13C2×D414yes—
176C42×C13C2414yes—
177C22⋊Dic13—24no—
178C4⋊Dic13—21no—
179C4⋊Dic13—22no—
180C4⋊Dic13—28no—
181C4⋊Dic13—21no—
182C4⋊Dic13—24no—
183C4⋊Dic13C2412yes—
184C4⋊Dic13C2414yes—
185C4⋊Dic13C2412yes—
186#6101—28no—
187#6101—28no—
188C4×Dic13—24no—
189#6099—28no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—28no—
193C2×#1055—24no—
194C2×#1055C2412yes—
195C2×#1055C2412yes—
196C2×#1055C2414yes—
197C2×#544—131no—
198C2×#520D1311yescharacteristic
199#3083—1316no—
200C2×#479—132no—
201C2×#477—132no—
202C2×#478—132no—
203C2×#474—132no—
204C2×#428—131no—
205C22×#107—131no—
206C2×#424—131no—
207C2×#417—131no—
208C2×#416—131no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—24no—
212C23×C13—22no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13C22⋊Q814yes—
216C23×C13C22×D412yes—
217C23×C13C22×D411yescharacteristic
218Q8×C13—24no—
219Q8×C13—22no—
220Q8×C13C22×Q814yes—
221D4×C13—216no—
222D4×C13—24no—
223D4×C13—22no—
224D4×C13C22×Q814yes—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—22no—
229C2×C4×C13—216no—
230C2×C4×C13—24no—
231C2×C4×C13—44no—
232C2×C4×C13—88no—
233C2×C4×C13—84no—
234C2×C4×C13C22⋊Q814yes—
235C2×C4×C13C22⋊Q818yes—
236C2×C4×C13C22×D414yes—
237C2×C4×C13C22×D414yes—
238C2×C4×C13C22×D412yes—
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C13C22×Q812yes—
241C2×C4×C13C22×Q814yes—
242C2×C4×C13C2×#4112yes—
243C2×C4×C13C2×#4114yes—
244C2×C4×C13C2511yescharacteristic
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—24no—
248C2×Dic13—42no—
249C2×Dic13—44no—
250C2×Dic13—42no—
251C2×Dic13—84no—
252Dic26—88no—
253#1055—22no—
254#1055—22no—
255#1055—24no—
256C22×#41C2×D1311yescharacteristic
257C22×M16—131no—
258C23×C8—131no—
259#544—138no—
260#544—264no—
261C2×C4⋊Q8—132no—
262C2×C4⋊Q8—261no—
263C2×#125—132no—
264C2×#125—261no—
265C2×C22⋊Q8—262no—
266#520—24no—
267#520C2×D1318yes—
268C2×C4×Q8C2×D1312yes—
269C2×C4×D4—22no—
270C2×C4×D4C2×D1312yes—
271C2×#117—21no—
272C2×#117—131no—
273C2×#117C2×D1311yescharacteristic
274C22×C4⋊C4—21no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4C2×D1311yescharacteristic
277#479—1316no—
278#478—1316no—
279#477—1316no—
280#474—1316no—
281#428—138no—
282C2×#107—132no—
283C2×#107—132no—
284C2×#107—132no—
285C2×#107—138no—
286C2×#106—132no—
287#424—138no—
288C2×C4⋊C8—132no—
289C2×C4⋊C8—132no—
290#417—138no—
291#416—138no—
292C2×#103—131no—
293C2×#103—132no—
294C2×#103—131no—
295C2×#102—131no—
296C2×#102—132no—
297C2×#102—131no—
298C22×C13—28no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13—24no—
302C22×C13—48no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13C2×C22⋊Q814yes—
306C22×C13C2×C22⋊Q812yes—
307C22×C13#57612yes—
308C22×C13#57812yes—
309C22×C13C23×D411yescharacteristic
310C4×C13—24no—
311C4×C13—24no—
312C4×C13—24no—
313C4×C13—44no—
314C4×C13C2×C22⋊Q814yes—
315C4×C13C2×C22⋊Q812yes—
316C4×C13C23×Q811yescharacteristic
317C4×C13C22×#4111yescharacteristic
318Dic13—42no—
319Dic13—44no—
320Dic13—42no—
321C2×#41—24no—
322C2×#41—22no—
323C2×#41Dic2618yescomplemented
324C2×#41C22×D1314yes—
325C22×Q8—262no—
326C22×Q8C22×D1311yescharacteristic
327C22×D4—21no—
328C22×D4C22×D1311yescharacteristic
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—22no—
332C23×C4—261no—
333C23×C4C22×D1311yescharacteristic
334C2×M16—134no—
335C2×M16—264no—
336C22×C8—131no—
337C22×C8—131no—
338C22×C8—134no—
339C22×C8—132no—
340C22×C8—264no—
341C4⋊Q8—138no—
342C4⋊Q8—268no—
343C4⋊Q8—264no—
344#125—138no—
345#125—268no—
346#125—264no—
347C22⋊Q8—2616no—
348C4×Q8—24no—
349C4×Q8C22×D1318yes—
350C4×D4—216no—
351C4×D4—24no—
352C4×D4C22×D1318yes—
353#117—28no—
354#117—134no—
355#117—262no—
356#117C22⋊D1314yes—
357#117C22×D1314yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—132no—
363C2×C4⋊C4—134no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4C22⋊D1311yescharacteristic
372C2×C4⋊C4C22⋊D1311yescharacteristic
373C2×C4⋊C4C22×D1312yes—
374C2×C4⋊C4C22×D1314yes—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4C22⋊D1312yes—
378C2×C42—22no—
379C2×C42—261no—
380C2×C42C22×D1312yes—
381#107—138no—
382#107—138no—
383#107—138no—
384#106—138no—
385C4⋊C8—138no—
386C4⋊C8—138no—
387#103—134no—
388#103—134no—
389#103—138no—
390#102—134no—
391#102—134no—
392#102—138no—
393C2×C13—24no—
394C2×C13—44no—
395C2×C13#308314yescomplemented
396C2×C13C22×C22⋊Q811yescharacteristic
397C2×C13C2×#57611yescharacteristic
398C2×C13C2×#57811yescharacteristic
399C24—21no—
400C24C2×C22⋊D1311yescharacteristic
401#41—216no—
402#41—28no—
403#41C2×Dic26116yescomplemented
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—268no—
407C2×Q8—1044no—
408C2×Q8C2×Dic2614yes—
409C2×Q8C23×D1312yes—
410C2×D4—28no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4C2×Dic2614yes—
415C2×D4C23×D1312yes—
416C22×C4—21no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—28no—
422C22×C4—84no—
423C22×C4—82no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—262no—
427C22×C4—264no—
428C22×C4—1042no—
429C22×C4C2×Dic2614yes—
430C22×C4#612714yes—
431C22×C4C2×C22⋊D1312yes—
432C22×C4C2×C22⋊D1312yes—
433C22×C4C2×C22⋊D1312yes—
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C23×D1312yes—
436C22×C4C23×D1311yescharacteristic
437M16—268no—
438C2×C8—134no—
439C2×C8—132no—
440C2×C8—132no—
441C2×C8—262no—
442C2×C8—262no—
443C2×C8—268no—
444C2×C8—264no—
445C4⋊C4—24no—
446C4⋊C4—28no—
447C4⋊C4—22no—
448C4⋊C4—132no—
449C4⋊C4—134no—
450C4⋊C4—132no—
451C4⋊C4—264no—
452C4⋊C4—262no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—268no—
456C4⋊C4—268no—
457C4⋊C4—268no—
458C4⋊C4C2×C22⋊D1314yes—
459C4⋊C4C2×C22⋊D1314yes—
460C4⋊C4C23×D1314yes—
461C22⋊C4—28no—
462C22⋊C4—264no—
463C22⋊C4C2×C22⋊D1318yes—
464C42—28no—
465C42—264no—
466C42C2×C22⋊D1314yes—
467C42C23×D1314yes—
468C13C2×#308311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—24no—
472C23—22no—
473C23—42no—
474C23—42no—
475C23#8817814yes—
476C23C22×C22⋊D1312yes—
477C23C22×C22⋊D1311yescharacteristic
478Q8—24no—
479Q8—22no—
480Q8—1048no—
481Q8C22×Dic2614yes—
482D4—216no—
483D4—24no—
484D4—22no—
485D4C22×Dic2614yes—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—216no—
491C2×C4—24no—
492C2×C4—44no—
493C2×C4—88no—
494C2×C4—84no—
495C2×C4—262no—
496C2×C4—262no—
497C2×C4—264no—
498C2×C4—524no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—1044no—
502C2×C4#8817814yes—
503C2×C4#8817818yes—
504C2×C4C22×Dic2612yes—
505C2×C4C22×Dic2614yes—
506C2×C4C2×#612712yes—
507C2×C4C2×#612714yes—
508C2×C4C22×C22⋊D1314yes—
509C2×C4C22×C22⋊D1314yes—
510C2×C4C22×C22⋊D1312yes—
511C2×C4C22×C22⋊D1311yescharacteristic
512C2×C4C24×D1311yescharacteristic
513C8—262no—
514C8—262no—
515C8—264no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—48no—
521C22—42no—
522C22—42no—
523C22C2×#8817814yes—
524C22C2×#8817812yes—
525C22#1171954012yes—
526C22#1171954312yes—
527C22C23×C22⋊D1311yescharacteristic
528C4—24no—
529C4—24no—
530C4—24no—
531C4—44no—
532C4—524no—
533C4—522no—
534C4—522no—
535C4C2×#8817814yes—
536C4C2×#8817812yes—
537C4C23×Dic2611yescharacteristic
538C4C22×#612711yescharacteristic
539C2—24no—
540C2—44no—
541C2#1312468714yesdirect product factor
542C2C22×#8817811yescharacteristic
543C2C2×#1171954011yescharacteristic
544C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#520C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenterC2×#520D13
hypocenterC13C2×#3083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#11719224C2semidirect
2. #13124687C2direct (N × H)
3. C2×#11718683C2semidirect
4. C2×#11718682C2semidirect
5. C2×#11718670C2semidirect
6. C2×#11718668C2semidirect
7. C2×#11718625C2semidirect
8. C22×#88047C2semidirect
9. C2×#11718660C2semidirect
28. #11719224C22semidirect
42. #11718683C22semidirect
43. #11718682C22semidirect
44. #11718670C22semidirect
45. #11718668C22semidirect
46. #11718660C22semidirect
47. #11718625C22semidirect
52. C2×#88047C22semidirect
57. C2×C13×#41Q8semidirect
132. C13×#41C2×Q8semidirect
323. C2×#41Dic26semidirect
395. C2×C13#3083semidirect
403. #41C2×Dic26semidirect
468. C13C2×#3083semidirect
541. C2#13124687direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192242
#131246872
C2×#117186832
C2×#117186822
C2×#117186702
C2×#117186682
C2×#117186252
C22×#880472
C2×#117186602
C2×#117188932
C2×#117188942
C2×C13×#5202
C2×#308313