Finite Group Databasebeta

← C2×#13126023 #16735021

Subgroups — C2×#13126023 #16735021

Order 3328.

2050 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719301C211yesmaximal, characteristic
2C22×#88144C211yesmaximal, characteristic, complemented
3#13126023C2116yesmaximal, direct product factor
4C2×#11718537C212yesmaximal, complemented
5C2×#11718425C212yesmaximal, complemented
6C2×#11718396C211yesmaximal, characteristic, complemented
7C2×#11718695C211yesmaximal, characteristic, complemented
8C2×#11718628C211yesmaximal, characteristic, complemented
9C2×#11718552C212yesmaximal, complemented
10C2×#11718424C212yesmaximal, complemented
11C2×#11718380C211yesmaximal, characteristic, complemented
12C2×C13×#480C211yesmaximal, characteristic, complemented
13C22×#6129—21no—
14C2×C13×#121C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C2×#88194C2211yescharacteristic
17C2×#88193—21no—
18C2×D4×Dic13C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C22×C4⋊Dic13—21no—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101—21no—
23C22×C4×Dic13C2211yescharacteristic
24#11719301—24no—
25#11719301C2218yes—
26C2×#88147C2211yescharacteristic
27C2×#88144—24no—
28C2×#88144—21no—
29C2×#88144—21no—
30C2×#88144C2212yes—
31C2×#88144C2212yes—
32C2×#88144C2218yescomplemented
33C2×#88142C2211yescharacteristic
34C2×#88139—21no—
35C2×#88135—21no—
36C13×#480C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×#102C2212yes—
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×#88072C2212yes—
41C2×C22⋊#1055C2211yescharacteristic
42C2×#88061C2212yes—
43C2×#88057C2212yes—
44C2×#88055C2212yes—
45C2×#88054C2212yes—
46#11718695C2218yescomplemented
47#11718628C2218yescomplemented
48C2×#88049C2212yes—
49C2×#88048C2212yes—
50C2×#88047C2212yes—
51#11718552C22116yescomplemented
52#11718537C22116yescomplemented
53#11718425C22116yescomplemented
54#11718424C22116yescomplemented
55#11718396C2218yescomplemented
56#11718380C2218yescomplemented
57C22×D4×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—21no—
62C22×C22⋊D13—21no—
63C22×C22⋊D13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C23×Dic13D411yescharacteristic
67C23×Dic13D411yescharacteristic
68C2×#6129—28no—
69C2×#6129—48no—
70C22×D52C2311yescharacteristic
71C22×C4×D13—21no—
72C22×Dic26—21no—
73C22×C8×C13C2312yes—
74C13×#121—22no—
75C13×#121C2314yes—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2312yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C22⋊C4—21no—
82C2×C22⋊Dic13—21no—
83#88194—22no—
84#88194C2314yes—
85#88193—28no—
86D4×Dic13—22no—
87D4×Dic13C2314yes—
88#88184—22no—
89#88184C2314yes—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—28no—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2312yes—
99C2×C4⋊Dic13C2314yes—
100C2×#6101—21no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—28no—
104C2×C4×Dic13D411yescharacteristic
105C2×C4×Dic13D411yescharacteristic
106C2×C4×Dic13D414yes—
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2314yes—
110C22×#1055C2312yes—
111#88147—22no—
112#88147C2314yes—
113#88144—24no—
114#88144—24no—
115#88144—28no—
116#88144—28no—
117#88144C2318yes—
118#88144C2318yes—
119#88142—22no—
120#88142C2314yes—
121#88139—28no—
122#88135—28no—
123C13×#107C2318yes—
124C13×#102C2318yes—
125C13×C22⋊C8C2314yes—
126#88072C2318yes—
127C22⋊#1055C2314yes—
128#88061C2318yes—
129#88057C2318yes—
130#88055C2318yes—
131#88054C2318yes—
132#88049C2318yes—
133#88048C2318yes—
134#88047C2318yes—
135C2×#3234—131nomaximal, Sylow
136C24×C13—21no—
137C24×C13C2×D411yescharacteristic
138C23×D13—21no—
139C2×D4×C13—24no—
140C2×D4×C13—21no—
141C2×D4×C13—24no—
142C2×D4×C13—44no—
143C2×D4×C13C2412yes—
144C22×C4×C13—24no—
145C22×C4×C13—24no—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—44no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2412yes—
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—24no—
154C2×C22⋊D13—24no—
155C2×C22⋊D13—24no—
156C2×C22⋊D13—44no—
157C2×C22⋊D13—44no—
158C2×C22⋊D13—44no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—24no—
164C22×Dic13—42no—
165C22×Dic13—44no—
166C22×Dic13—44no—
167C22×Dic13C2×D411yescharacteristic
168C22×Dic13C2×D411yescharacteristic
169C22×Dic13C2×D414yes—
170C22×Dic13C2×D411yescharacteristic
171C22×Dic13C2×D411yescharacteristic
172C22×Dic13C2×D414yes—
173#6129—432no—
174C2×D52—24no—
175C2×D52—21no—
176C2×D52C2412yes—
177C2×C4×D13—24no—
178C2×C4×D13—44no—
179C2×Dic26—24no—
180C2×Dic26—44no—
181C2×C8×C13—24no—
182C2×C8×C13C2414yes—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4C2414yes—
187C13×C4⋊C4C2412yes—
188C13×C22⋊C4—24no—
189C22⋊Dic13—24no—
190#6103—24no—
191#6103—24no—
192C4⋊Dic13—21no—
193C4⋊Dic13—24no—
194C4⋊Dic13—22no—
195C4⋊Dic13—28no—
196C4⋊Dic13—28no—
197C4⋊Dic13C2414yes—
198C4⋊Dic13C2412yes—
199#6101—24no—
200#6101—28no—
201#6101—28no—
202C4×Dic13C2×D414yes—
203C4×Dic13C2×D414yes—
204C4×Dic13C2×D412yes—
205C4×Dic13C2×D412yes—
206C4×Dic13C2412yes—
207C4×Dic13C2412yes—
208C2×#1055—24no—
209C2×#1055C2414yes—
210C2×#532—131no—
211C22×#125—131no—
212#3234—1316no—
213C2×#501—132no—
214C2×#490—132no—
215C2×#481—131no—
216C2×#481—131no—
217C2×#480—131no—
218C2×#480D1311yescharacteristic, complemented
219C2×#478—132no—
220C2×#478—132no—
221C2×#432—131no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13—42no—
228C23×C13AGL(1,ℤ/8)14yes—
229C23×C13C22×D412yes—
230C23×C13C22×D411yescharacteristic
231C22×D13—22no—
232C22×D13—42no—
233C22×D13—42no—
234C22×D13—42no—
235D4×C13—24no—
236D4×C13—48no—
237D4×C13—42no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—42no—
244C2×C4×C13—48no—
245C2×C4×C13—44no—
246C2×C4×C13C22×D412yes—
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C132−1+414yes—
249C2×C4×C13C2511yescharacteristic
250C22⋊D13—48no—
251C22⋊D13—48no—
252C22⋊D13—48no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—28no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13—44no—
261C2×Dic13—48no—
262C2×Dic13—48no—
263C2×Dic13—42no—
264C2×Dic13—44no—
265C2×Dic13C22×D412yes—
266C2×Dic13C22×D412yes—
267C2×Dic13C22×D412yes—
268C2×Dic13C22×D412yes—
269D52—24no—
270D52—42no—
271C4×D13—48no—
272Dic26—48no—
273C8×C13—24no—
274#1055—24no—
275C22×#41—261no—
276#532—138no—
277#532—264no—
278C2×C4⋊Q8—131no—
279C2×#127—131no—
280C2×#125—132no—
281C2×#125—132no—
282C2×#125—138no—
283C2×#125—261no—
284C2×#125—261no—
285C2×#125—264no—
286C2×#124—261no—
287C2×#121—131no—
288C2×#121—261no—
289C2×#121C2×D1311yescharacteristic
290C2×C4×D4—131no—
291C2×C4×D4—131no—
292C2×C4×D4—261no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—261no—
295C22×C4⋊C4—261no—
296C22×C4⋊C4C2×D1311yescharacteristic
297C22×C42—131no—
298#501—1316no—
299#490—1316no—
300#481—138no—
301#481—138no—
302#480—138no—
303#480C2×D1318yescomplemented
304#478—1316no—
305#478—1316no—
306#432—138no—
307C2×#107—132no—
308C2×#107C2×D1312yes—
309C2×#106—132no—
310C2×#106—132no—
311C2×C4⋊C8—132no—
312C2×#102—132no—
313C2×#102—132no—
314C2×#102—132no—
315C2×#102C2×D1312yes—
316C2×C22⋊C8—131no—
317C2×C22⋊C8C2×D1311yescharacteristic
318C2×#97—132no—
319C22×C13—22no—
320C22×C13—28no—
321C22×C13—22no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—84no—
326C22×C13#53612yes—
327C22×C13C2×AGL(1,ℤ/8)14yes—
328C22×C13C2×AGL(1,ℤ/8)12yes—
329C22×C13#57512yes—
330C22×C13C23×D411yescharacteristic
331C2×D13—42no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—84no—
335C4×C13—22no—
336C4×C13—42no—
337C4×C13—44no—
338C4×C13#53612yes—
339C4×C13C2×2−1+412yes—
340Dic13—22no—
341Dic13—22no—
342Dic13—22no—
343Dic13—22no—
344Dic13—42no—
345Dic13—44no—
346C2×#41—268no—
347C2×#41—528no—
348C22×Q8—261no—
349C22×D4—21no—
350C22×D4—131no—
351C22×D4—261no—
352C22×D4—261no—
353C22×D4—261no—
354C22×D4C22×D1311yescharacteristic
355C23×C4—21no—
356C23×C4—131no—
357C23×C4—131no—
358C23×C4—261no—
359C23×C4—261no—
360C23×C4—261no—
361C23×C4C22×D1311yescharacteristic
362C22×C8—132no—
363C22×C8C22×D1312yes—
364C4⋊Q8—134no—
365C4⋊Q8—262no—
366#127—134no—
367#127—262no—
368#125—138no—
369#125—138no—
370#125—264no—
371#125—268no—
372#125—268no—
373#125—264no—
374#124—268no—
375#121—22no—
376#121—134no—
377#121—268no—
378#121—262no—
379#121C22×D1314yes—
380C4×D4—134no—
381C4×D4—134no—
382C4×D4—268no—
383C4×D4—262no—
384C4×D4—262no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—132no—
388C2×C4⋊C4—134no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—268no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—262no—
393C2×C4⋊C4—268no—
394C2×C4⋊C4—262no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4C22×D1312yes—
400C2×C4⋊C4C22×D1314yes—
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—261no—
405C2×C22⋊C4—261no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—134no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—134no—
412#107—138no—
413#107C22×D1318yes—
414#106—138no—
415#106—138no—
416C4⋊C8—138no—
417#102—138no—
418#102—138no—
419#102—138no—
420#102C22×D1318yes—
421C22⋊C8—134no—
422C22⋊C8C22×D1314yes—
423#97—138no—
424C2×C13—24no—
425C2×C13—82no—
426C2×C13#323414yescomplemented
427C2×C13C2×#53611yescharacteristic
428C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
429C2×C13C2×#57511yescharacteristic
430D13—82no—
431C24—21no—
432C24—261no—
433C24D4×D1311yescharacteristic
434#41—5232no—
435C2×Q8—264no—
436C2×Q8—524no—
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—24no—
440C2×D4—44no—
441C2×D4—132no—
442C2×D4—264no—
443C2×D4—264no—
444C2×D4—264no—
445C2×D4—261no—
446C2×D4—264no—
447C2×D4—524no—
448C2×D4—524no—
449C2×D4—524no—
450C2×D4C23×D1312yes—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—44no—
456C22×C4—134no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—134no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—264no—
465C22×C4—264no—
466C22×C4—261no—
467C22×C4—262no—
468C22×C4—524no—
469C22×C4—522no—
470C22×C4—524no—
471C22×C4—524no—
472C22×C4D4×D1312yes—
473C22×C4D4×D1311yescharacteristic
474C22×C4C23×D1312yes—
475C22×C4C23×D1311yescharacteristic
476C2×C8—24no—
477C2×C8—134no—
478C2×C8—264no—
479C2×C8C23×D1314yes—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—134no—
484C4⋊C4—132no—
485C4⋊C4—268no—
486C4⋊C4—268no—
487C4⋊C4—268no—
488C4⋊C4—268no—
489C4⋊C4—264no—
490C4⋊C4—264no—
491C4⋊C4—262no—
492C4⋊C4—261no—
493C4⋊C4C23×D1314yes—
494C4⋊C4C23×D1312yes—
495C22⋊C4—24no—
496C22⋊C4—264no—
497C22⋊C4—264no—
498C22⋊C4—264no—
499C42—132no—
500C42—134no—
501C42—134no—
502C42—132no—
503C42—132no—
504C42—132no—
505C13C2×#323411yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—262no—
513C23—522no—
514C23—522no—
515C23—522no—
516C23#8816514yes—
517C23C2×D4×D1312yes—
518C23C2×D4×D1311yescharacteristic
519Q8—528no—
520D4—24no—
521D4—48no—
522D4—42no—
523D4—264no—
524D4—528no—
525D4—528no—
526D4—528no—
527D4—522no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—48no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—132no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—268no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—264no—
547C2×C4—528no—
548C2×C4—524no—
549C2×C4—528no—
550C2×C4—528no—
551C2×C4—522no—
552C2×C4—524no—
553C2×C4C2×D4×D1312yes—
554C2×C4C2×D4×D1311yescharacteristic
555C2×C4#8825714yes—
556C2×C4C24×D1311yescharacteristic
557C8—24no—
558C8—264no—
559C22—22no—
560C22—28no—
561C22—22no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—522no—
567C22—522no—
568C22—522no—
569C22—1044no—
570C22#1171935312yes—
571C22C2×#8816514yes—
572C22C2×#8816512yes—
573C22#1171948212yes—
574C22C22×D4×D1311yescharacteristic
575C4—22no—
576C4—44no—
577C4—42no—
578C4—262no—
579C4—262no—
580C4—262no—
581C4—262no—
582C4—522no—
583C4—524no—
584C4#1171935312yes—
585C4C2×#8825712yes—
586C2—24no—
587C2—82no—
588C2—1042no—
589C2#1312602314yesdirect product factor
590C2C2×#1171935311yescharacteristic
591C2C22×#8816511yescharacteristic
592C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#480C2
socleC23×C13C22×D4
prime radicalC2×#11719301C2
hypercenterC2×#480D13
hypocenterC13C2×#3234
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#88144C2semidirect
3. #13126023C2direct (N × H)
4. C2×#11718537C2semidirect
5. C2×#11718425C2semidirect
6. C2×#11718396C2semidirect
7. C2×#11718695C2semidirect
8. C2×#11718628C2semidirect
9. C2×#11718552C2semidirect
10. C2×#11718424C2semidirect
11. C2×#11718380C2semidirect
12. C2×C13×#480C2semidirect
32. C2×#88144C22semidirect
36. C13×#480C22semidirect
46. #11718695C22semidirect
47. #11718628C22semidirect
51. #11718552C22semidirect
52. #11718537C22semidirect
53. #11718425C22semidirect
54. #11718424C22semidirect
55. #11718396C22semidirect
56. #11718380C22semidirect
218. C2×#480D13semidirect
303. #480C2×D13semidirect
426. C2×C13#3234semidirect
505. C13C2×#3234semidirect
589. C2#13126023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193012
C22×#881442
#131260232
C2×#117185372
C2×#117184252
C2×#117183962
C2×#117186952
C2×#117186282
C2×#117185522
C2×#117184242
C2×#117183802
C2×C13×#4802
C2×#323413