Finite Group Databasebeta

← C2×#13113850 #15835161

Subgroups — C2×#13113850 #15835161

Order 3328.

1156 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718704C211yesmaximal, characteristic, complemented
2C2×#11718694C211yesmaximal, characteristic, complemented
3C2×#11718614C211yesmaximal, characteristic, complemented
4#13113850C218yesmaximal, direct product factor
5C2×#11718130C211yesmaximal, characteristic, complemented
6C2×#11718129C211yesmaximal, characteristic, complemented
7C2×#11718117C211yesmaximal, characteristic, complemented
8C2×C13×#538C211yesmaximal, characteristic
9C13×#538—22no—
10C13×#538—22no—
11C13×#538—22no—
12C13×#538C2214yes—
13C2×C13×#126—21no—
14C2×C13×#124—21no—
15C2×C13×#123—21no—
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C13×#121—21no—
18C2×C13×#121C2211yescharacteristic
19C2×C13×#120—21no—
20C2×C4×D4×C13—21no—
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic13—21no—
23C22×C4⋊Dic13C2211yescharacteristic
24C2×#88075—21no—
25C2×#88072—21no—
26C2×#88071—21no—
27C2×#88071C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30#11718704—22no—
31#11718704C2214yescomplemented
32#11718694—22no—
33#11718694C2214yescomplemented
34C2×#88048—21no—
35C2×#88047—21no—
36#11718614—22no—
37#11718614C2214yescomplemented
38#11718130C2214yescomplemented
39#11718129C2214yescomplemented
40#11718117C2214yescomplemented
41C25×C13D411yescharacteristic
42C22×Q8×C13D411yescharacteristic
43C22×D4×C13—21no—
44C22×D4×C13—21no—
45C22×D4×C13—21no—
46C22×D4×C13D411yescharacteristic
47C23×C4×C13—21no—
48C23×C4×C13D411yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×Dic13—21no—
51C23×Dic13—21no—
52C13×#126—24no—
53C13×#126—24no—
54C13×#124—24no—
55C13×#124—24no—
56C13×#123—24no—
57C13×#123—24no—
58C13×C22⋊Q8—21no—
59C13×C22⋊Q8—21no—
60C13×C22⋊Q8D412yes—
61C13×C22⋊Q8C2312yes—
62C13×#121—24no—
63C13×#121—24no—
64C13×#121—21no—
65C13×#121—21no—
66C13×#121D412yes—
67C13×#121C2312yes—
68C13×#120—24no—
69C13×#120—24no—
70C4×D4×C13—24no—
71C4×D4×C13—24no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4D412yes—
86C2×C13×C22⋊C4C2312yes—
87C2×C42×C13—21no—
88C2×C22⋊Dic13—24no—
89C2×C22⋊Dic13—44no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13C2312yes—
96C22×#1055—21no—
97C22×#1055—21no—
98#88075—24no—
99#88072—24no—
100#88071—24no—
101#88071—21no—
102#88071C2312yes—
103C22⋊#1055—21no—
104C22⋊#1055—21no—
105C22⋊#1055C2312yes—
106C22⋊#1055C2312yes—
107#88048—24no—
108#88047—24no—
109C2×#1612—131nomaximal, Sylow
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—22no—
113C24×C13—21no—
114C24×C13—22no—
115C24×C13—42no—
116C24×C13—42no—
117C24×C13C2×D411yescharacteristic
118C24×C13C2×D412yes—
119C2×Q8×C13—21no—
120C2×Q8×C13—42no—
121C2×Q8×C13C2×D412yes—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—24no—
125C2×D4×C13—24no—
126C2×D4×C13—21no—
127C2×D4×C13—42no—
128C2×D4×C13—42no—
129C2×D4×C13—42no—
130C2×D4×C13—82no—
131C2×D4×C13—82no—
132C2×D4×C13C2×D412yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—24no—
138C22×C4×C13—21no—
139C22×C4×C13—42no—
140C22×C4×C13—42no—
141C22×C4×C13—82no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—42no—
152C22×Dic13—42no—
153C22×Dic13—41no—
154C22×Dic13—41no—
155C22×Dic13—42no—
156C22×Dic13—42no—
157C22×Dic13—42no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4C2×D412yes—
164C13×C4⋊C4C2×D412yes—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C42×C13—24no—
177C22⋊Dic13—48no—
178C4⋊Dic13—22no—
179C4⋊Dic13—22no—
180C4⋊Dic13—41no—
181C4⋊Dic13—41no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—42no—
185C2×#1055—42no—
186C2×#538D1311yescharacteristic
187C2×#483—131no—
188C2×#480—131no—
189C2×#397—131no—
190#1612—138no—
191C2×#328—131no—
192C2×#327—131no—
193C2×#323—131no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—48no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—81no—
211C23×C13—81no—
212C23×C13—84no—
213C23×C13#12011yescharacteristic
214C23×C13#12011yescharacteristic
215C23×C13#13512yes—
216C23×C13AGL(1,ℤ/8)12yes—
217C23×C13C22×D411yescharacteristic
218Q8×C13—42no—
219Q8×C13—81no—
220D4×C13—42no—
221D4×C13—42no—
222D4×C13—42no—
223D4×C13—44no—
224D4×C13—81no—
225D4×C13—84no—
226D4×C13—84no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—81no—
243C2×C4×C13—84no—
244C2×C4×C13#12011yescharacteristic
245C2×C4×C13#12011yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—84no—
255C2×Dic13—82no—
256C2×Dic13—82no—
257#1055—42no—
258#1055—42no—
259#538—22no—
260#538—22no—
261#538—22no—
262#538C2×D1314yes—
263C2×#126—21no—
264C2×#124—21no—
265C2×#123—21no—
266C2×C22⋊Q8C2×D1311yescharacteristic
267C2×#121—21no—
268C2×#121C2×D1311yescharacteristic
269C2×#120—21no—
270C2×C4×D4—21no—
271C22×C4⋊C4—131no—
272C22×C22⋊C4—261no—
273C22×C22⋊C4C2×D1311yescharacteristic
274#483—134no—
275#483—262no—
276#480—134no—
277#480—262no—
278C2×#107—261no—
279C2×#106—261no—
280C2×#103—261no—
281C2×#102—261no—
282C2×C22⋊C8—131no—
283C2×C22⋊C8—131no—
284#397—134no—
285#397—262no—
286C2×#95—131no—
287C2×#95—261no—
288#328—134no—
289#327—134no—
290#323—134no—
291C22×C13—24no—
292C22×C13—24no—
293C22×C13—21no—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—44no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—82no—
305C22×C13—84no—
306C22×C13—84no—
307C22×C13—84no—
308C22×C13#44912yes—
309C22×C13#44912yes—
310C22×C13#45512yes—
311C22×C13#45812yes—
312C22×C13C2×#12011yescharacteristic
313C22×C13C2×#13511yescharacteristic
314C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
315C4×C13—21no—
316C4×C13—21no—
317C4×C13—21no—
318C4×C13—21no—
319C4×C13—42no—
320C4×C13—42no—
321C4×C13—42no—
322C4×C13—42no—
323Dic13—82no—
324Dic13—82no—
325C25C22⋊D1311yescharacteristic
326C22×Q8C22⋊D1311yescharacteristic
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C22⋊D1311yescharacteristic
331C23×C4—21no—
332C23×C4—261no—
333C23×C4—261no—
334C23×C4C22⋊D1311yescharacteristic
335C23×C4C22×D1311yescharacteristic
336C22×C8—261no—
337C22×C8—261no—
338#126—24no—
339#126—24no—
340#124—24no—
341#124—24no—
342#123—24no—
343#123—24no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8C22⋊D1312yes—
347C22⋊Q8C22×D1312yes—
348#121—24no—
349#121—24no—
350#121—21no—
351#121—21no—
352#121C22⋊D1312yes—
353#121C22×D1312yes—
354#120—24no—
355#120—24no—
356C4×D4—24no—
357C4×D4—24no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—132no—
361C2×C4⋊C4—261no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4C22⋊D1311yescharacteristic
367C2×C4⋊C4C22⋊D1311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—264no—
378C2×C22⋊C4—524no—
379C2×C22⋊C4C22⋊D1312yes—
380C2×C22⋊C4C22×D1312yes—
381C2×C42—21no—
382#107—264no—
383#106—264no—
384#103—264no—
385#102—264no—
386C22⋊C8—132no—
387C22⋊C8—132no—
388C22⋊C8—261no—
389C22⋊C8—261no—
390#95—132no—
391#95—261no—
392#95—264no—
393C2×C13—21no—
394C2×C13—21no—
395C2×C13—22no—
396C2×C13—82no—
397C2×C13—82no—
398C2×C13#161214yescomplemented
399C2×C13C2×#44911yescharacteristic
400C2×C13C2×#45511yescharacteristic
401C2×C13C2×#45811yescharacteristic
402C24—22no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—42no—
408C24—42no—
409C24C2×C22⋊D1311yescharacteristic
410C24C2×C22⋊D1312yes—
411C2×Q8—21no—
412C2×Q8—42no—
413C2×Q8C2×C22⋊D1312yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—21no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C2×C22⋊D1312yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—82no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—522no—
437C22×C4—522no—
438C22×C4—522no—
439C22×C4—522no—
440C22×C4—522no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1312yes—
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C23×D1311yescharacteristic
450C2×C8—262no—
451C2×C8—262no—
452C2×C8—522no—
453C2×C8—522no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—262no—
460C4⋊C4—262no—
461C4⋊C4—521no—
462C4⋊C4—521no—
463C4⋊C4C2×C22⋊D1312yes—
464C4⋊C4C2×C22⋊D1312yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—528no—
477C42—24no—
478C13C2×#161211yescharacteristic, complemented, Sylow
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—48no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23#8820312yes—
499C23#8820412yes—
500C23#8820711yescharacteristic
501C23#8820711yescharacteristic
502C23C22×C22⋊D1311yescharacteristic
503Q8—42no—
504Q8—81no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—81no—
510D4—84no—
511D4—84no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—84no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—1044no—
536C2×C4—1042no—
537C2×C4—1042no—
538C2×C4#8820711yescharacteristic
539C2×C4#8820711yescharacteristic
540C2×C4C22×C22⋊D1311yescharacteristic
541C2×C4C22×C22⋊D1311yescharacteristic
542C8—522no—
543C8—522no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—24no—
549C22—24no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—82no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22#1171889912yes—
562C22#1171889912yes—
563C22#1171890312yes—
564C22#1171890412yes—
565C22C2×#8820311yescharacteristic
566C22C2×#8820411yescharacteristic
567C22C2×#8820711yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—1042no—
577C4—1042no—
578C2—21no—
579C2—21no—
580C2—22no—
581C2—82no—
582C2—82no—
583C2#1311385014yesdirect product factor
584C2C2×#1171889911yescharacteristic
585C2C2×#1171890311yescharacteristic
586C2C2×#1171890411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#538C2
socleC23×C13#120
hypercenterC2×#538D13
hypocenterC13C2×#1612
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. C2×#11718704C2semidirect
2. C2×#11718694C2semidirect
3. C2×#11718614C2semidirect
4. #13113850C2direct (N × H)
5. C2×#11718130C2semidirect
6. C2×#11718129C2semidirect
7. C2×#11718117C2semidirect
31. #11718704C22semidirect
33. #11718694C22semidirect
37. #11718614C22semidirect
38. #11718130C22semidirect
39. #11718129C22semidirect
40. #11718117C22semidirect
398. C2×C13#1612semidirect
478. C13C2×#1612semidirect
583. C2#13113850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117186942
C2×#117186142
#131138502
C2×#117181302
C2×#117181292
C2×#117181172
C2×C13×#5382
C2×#161213