Finite Group Databasebeta

← C2×#13116291 #15891842

Subgroups — C2×#13116291 #15891842

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718780C211yesmaximal, characteristic, complemented
2C2×#11718800C211yesmaximal, characteristic
3C2×#11718663C211yesmaximal, characteristic
4C2×#11718793C211yesmaximal, characteristic
5#13116291C218yesmaximal, direct product factor
6C2×#11718150C211yesmaximal, characteristic, complemented
7C2×#11718123C211yesmaximal, characteristic, complemented
8C2×C13×#344C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16#11718800—22no—
17#11718800C2214yes—
18C2×#88065—22no—
19C2×#88064—21no—
20#11718793—22no—
21#11718793C2214yes—
22C2×#88063—21no—
23#11718780—22no—
24#11718780C2214yescomplemented
25C2×#88054—22no—
26#11718663—22no—
27#11718663C2214yes—
28C2×#88050—21no—
29C2×#88049—21no—
30C13×#344C2214yescomplemented
31#11718150C2214yescomplemented
32#11718123C2214yescomplemented
33C23×C4×C13C2311yescharacteristic
34C22×C22⋊D13—21no—
35C2×#6127—21no—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127D412yes—
46C2×#6127C2312yes—
47C22×D52D411yescharacteristic
48C22×C4×D13—21no—
49C22×Dic26D411yescharacteristic
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C2×C13×M16C2312yes—
61C2×C13×M16C2312yes—
62C22×C8×C13—21no—
63C22×C8×C13—21no—
64C13×#117—21no—
65C13×#117—21no—
66C13×#117—21no—
67C13×#117C2312yes—
68C2×C13×C4⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C42×C13—21no—
71C2×C22⋊Dic13—21no—
72#88180—21no—
73#88180—21no—
74#88180D412yes—
75#88180C2312yes—
76C2×C4⋊Dic13—21no—
77C2×C4×Dic13D412yes—
78C2×#6099—21no—
79C2×#6099—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099C2312yes—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055—21no—
89C22×#1055—21no—
90C22×#1055—21no—
91C22×#1055C2312yes—
92#88065—28no—
93#88064—24no—
94#88063—24no—
95#88054—28no—
96#88050—24no—
97#88049—24no—
98C2×#2080—131nomaximal, Sylow
99C24×C13#4111yescharacteristic
100C23×D13—21no—
101C22×C4×C13—41no—
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13C2411yescharacteristic
116C2×C22⋊D13—22no—
117C2×C22⋊D13—22no—
118C2×C22⋊D13—41no—
119C2×C22⋊D13—41no—
120C2×C22⋊D13—41no—
121C2×C22⋊D13—41no—
122C22×Dic13—22no—
123C22×Dic13—21no—
124#6127—22no—
125#6127—22no—
126#6127—22no—
127#6127—22no—
128#6127—22no—
129#6127—22no—
130#6127—22no—
131#6127—22no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135#6127—41no—
136#6127—41no—
137#6127—41no—
138#6127—41no—
139#6127—41no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52C2×D412yes—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—41no—
149C2×C4×D13—41no—
150C2×C4×D13—41no—
151C2×C4×D13—41no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26C2×D412yes—
158C13×M16—22no—
159C13×M16—22no—
160C13×M16—22no—
161C13×M16—22no—
162C13×M16—41no—
163C13×M16—41no—
164C13×M16—41no—
165C13×M16—41no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C2×C8×C13—41no—
169C2×C8×C13—41no—
170C2×C8×C13—41no—
171C2×C8×C13—41no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—41no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—41no—
176C42×C13—22no—
177C42×C13—41no—
178C22⋊Dic13—22no—
179C22⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13—22no—
182C4×Dic13—22no—
183C4×Dic13C2×D414yes—
184#6099—22no—
185#6099—22no—
186#6099—41no—
187#6099—41no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#1055—41no—
195C2×#1055—41no—
196C2×#1055—41no—
197C2×#1055—41no—
198C2×#424—131no—
199C2×#421—131no—
200C2×#416—131no—
201C2×#413—131no—
202#2080—138no—
203C2×#344D1311yescharacteristic, complemented
204C2×#341—131no—
205C2×H(3,ℤ/4)—131no—
206C23×C13—42no—
207C23×C13#12311yescharacteristic
208C23×C13#12311yescharacteristic
209C23×C13#12311yescharacteristic
210C23×C13#12311yescharacteristic
211C23×C13#12611yescharacteristic
212C23×C13#12611yescharacteristic
213C23×C13C2×#4111yescharacteristic
214C22×D13—22no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—82no—
218C2×C4×C13—42no—
219C2×C4×C13—82no—
220C2×C4×C13#12111yescharacteristic
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13#12111yescharacteristic
223C2×C4×C13#12111yescharacteristic
224C2×C4×C13#12311yescharacteristic
225C2×C4×C13#12311yescharacteristic
226C2×C4×C13#12311yescharacteristic
227C2×C4×C13#12311yescharacteristic
228C2×C4×C13#12311yescharacteristic
229C2×C4×C13#12311yescharacteristic
230C2×C4×C13#12311yescharacteristic
231C2×C4×C13#12311yescharacteristic
232C2×C4×C13#12411yescharacteristic
233C2×C4×C13#12411yescharacteristic
234C2×C4×C13#12411yescharacteristic
235C2×C4×C13#12411yescharacteristic
236C2×C4×C13#12611yescharacteristic
237C2×C4×C13#12611yescharacteristic
238C2×C4×C13#12611yescharacteristic
239C2×C4×C13#12611yescharacteristic
240C2×C4×C13#12611yescharacteristic
241C2×C4×C13#12611yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C22⋊D13—42no—
249C22⋊D13—42no—
250C22⋊D13—42no—
251C22⋊D13—42no—
252C2×Dic13—24no—
253C2×Dic13—22no—
254C2×Dic13—44no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257D52—22no—
258D52—22no—
259D52—41no—
260D52—41no—
261C4×D13—42no—
262C4×D13—42no—
263C4×D13—42no—
264C4×D13—42no—
265Dic26—22no—
266Dic26—22no—
267Dic26—41no—
268Dic26—41no—
269C8×C13—42no—
270C8×C13—42no—
271#1055—42no—
272#1055—42no—
273C22×#41—131no—
274C22×M16—131no—
275C22×M16C2×D1311yescharacteristic
276C22×M16C2×D1311yescharacteristic
277C23×C8—131no—
278C2×#117—131no—
279C2×#117C2×D1311yescharacteristic
280#424—134no—
281#424—262no—
282C2×C4⋊C8—262no—
283#421—134no—
284#421—262no—
285C2×#104—262no—
286#416—134no—
287#416—262no—
288C2×#103—261no—
289C2×#102—261no—
290#413—134no—
291#413—262no—
292C2×#101—261no—
293C2×#100—261no—
294#344C2×D1314yescomplemented
295#341—134no—
296H(3,ℤ/4)—134no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—22no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13#39711yescharacteristic
305C22×C13#39711yescharacteristic
306C22×C13#39711yescharacteristic
307C22×C13#39711yescharacteristic
308C22×C13C2×#12311yescharacteristic
309C22×C13C2×#12311yescharacteristic
310C22×C13C2×#12611yescharacteristic
311C2×D13—42no—
312C2×D13—82no—
313C2×D13—82no—
314C2×D13—82no—
315C4×C13—82no—
316C4×C13#39711yescharacteristic
317C4×C13#39711yescharacteristic
318C4×C13#39711yescharacteristic
319C4×C13#39711yescharacteristic
320C4×C13C2×#12111yescharacteristic
321C4×C13C2×#12311yescharacteristic
322C4×C13C2×#12411yescharacteristic
323C4×C13C2×#12611yescharacteristic
324Dic13—44no—
325Dic13—42no—
326C2×#41—132no—
327C2×#41—132no—
328C2×#41—261no—
329C2×#41—261no—
330C2×#41—261no—
331C2×#41—261no—
332C2×#41—261no—
333C2×#41—261no—
334C2×#41—261no—
335C2×#41—261no—
336C2×#41—261no—
337C2×#41—261no—
338C22×Q8—131no—
339C22×D4—131no—
340C22×D4—261no—
341C23×C4—261no—
342C23×C4C22×D1311yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—132no—
354C2×M16—261no—
355C2×M16—261no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16C22×D1312yes—
360C2×M16C22×D1312yes—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—132no—
364C22×C8—261no—
365C22×C8—261no—
366C22×C8—261no—
367C22×C8—261no—
368C22×C8—261no—
369C22×C8—261no—
370C22×C8—261no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—132no—
375#117—132no—
376#117—261no—
377#117—261no—
378#117C22×D1312yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—261no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—261no—
383C2×C42—21no—
384C2×C42—132no—
385C4⋊C8—268no—
386#104—268no—
387#103—264no—
388#102—264no—
389#101—264no—
390#100—264no—
391C2×C13—21no—
392C2×C13—21no—
393C2×C13—21no—
394C2×C13—21no—
395C2×C13—21no—
396C2×C13—21no—
397C2×C13#208012yescomplemented
398C2×C13C2×#39711yescharacteristic
399D13—82no—
400C24—261no—
401C24#612711yescharacteristic
402#41—262no—
403#41—262no—
404#41—262no—
405#41—262no—
406#41—262no—
407#41—262no—
408#41—262no—
409#41—262no—
410#41—521no—
411#41—521no—
412#41—521no—
413#41—521no—
414#41—521no—
415#41—521no—
416#41—521no—
417#41—521no—
418C2×Q8—132no—
419C2×Q8—261no—
420C2×Q8—261no—
421C2×Q8—261no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×D4—132no—
425C2×D4—262no—
426C2×D4—262no—
427C2×D4—261no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C2×D4—521no—
433C2×D4—521no—
434C2×D4—521no—
435C2×D4—521no—
436C22×C4—41no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—521no—
444C22×C4—521no—
445C22×C4#612711yescharacteristic
446C22×C4#612711yescharacteristic
447C22×C4#612711yescharacteristic
448C22×C4#612711yescharacteristic
449C22×C4#612711yescharacteristic
450C22×C4D4×D1311yescharacteristic
451C22×C4D4×D1311yescharacteristic
452C22×C4D4×D1311yescharacteristic
453C22×C4D4×D1311yescharacteristic
454C22×C4#612911yescharacteristic
455C22×C4#612911yescharacteristic
456C22×C4#613111yescharacteristic
457C22×C4#613111yescharacteristic
458C22×C4C23×D1311yescharacteristic
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—262no—
468M16—262no—
469M16—521no—
470M16—521no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—262no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—521no—
482C2×C8—521no—
483C2×C8—521no—
484C2×C8—521no—
485C2×C8—521no—
486C2×C8—521no—
487C4⋊C4—22no—
488C4⋊C4—41no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C22⋊C4—22no—
492C22⋊C4—41no—
493C22⋊C4—262no—
494C22⋊C4—262no—
495C42—22no—
496C42—41no—
497C42—134no—
498C42—262no—
499C13C2×#208011yescharacteristic, complemented, Sylow
500C23—42no—
501C23—262no—
502C23—521no—
503C23—521no—
504C23—1042no—
505C23#8813011yescharacteristic
506C23#8813011yescharacteristic
507C23#8813711yescharacteristic
508C23#8813711yescharacteristic
509C23#8814811yescharacteristic
510C23#8814811yescharacteristic
511C23C2×#612711yescharacteristic
512Q8—262no—
513Q8—262no—
514Q8—521no—
515Q8—521no—
516D4—262no—
517D4—262no—
518D4—522no—
519D4—522no—
520D4—522no—
521D4—522no—
522D4—521no—
523D4—521no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—524no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4#8813011yescharacteristic
536C2×C4#8813011yescharacteristic
537C2×C4#8813711yescharacteristic
538C2×C4#8813711yescharacteristic
539C2×C4#8813811yescharacteristic
540C2×C4#8813811yescharacteristic
541C2×C4#8813811yescharacteristic
542C2×C4#8813811yescharacteristic
543C2×C4#8813911yescharacteristic
544C2×C4#8813911yescharacteristic
545C2×C4#8813911yescharacteristic
546C2×C4#8813911yescharacteristic
547C2×C4#8814811yescharacteristic
548C2×C4#8814811yescharacteristic
549C2×C4#8814811yescharacteristic
550C2×C4#8814811yescharacteristic
551C2×C4#8814811yescharacteristic
552C2×C4#8814811yescharacteristic
553C2×C4#8815211yescharacteristic
554C2×C4#8815211yescharacteristic
555C2×C4#8815211yescharacteristic
556C2×C4#8815211yescharacteristic
557C2×C4C2×#612711yescharacteristic
558C2×C4C2×#612711yescharacteristic
559C2×C4C2×D4×D1311yescharacteristic
560C2×C4C2×D4×D1311yescharacteristic
561C2×C4C2×#612911yescharacteristic
562C2×C4C2×#613111yescharacteristic
563C8—42no—
564C8—42no—
565C8—522no—
566C8—522no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—522no—
575C22—1042no—
576C22—1042no—
577C22—1042no—
578C22#1171833611yescharacteristic
579C22#1171833611yescharacteristic
580C22#1171833611yescharacteristic
581C22#1171833611yescharacteristic
582C22C2×#8813011yescharacteristic
583C22C2×#8813711yescharacteristic
584C22C2×#8814811yescharacteristic
585C4—82no—
586C4—524no—
587C4—522no—
588C4#1171833611yescharacteristic
589C4#1171833611yescharacteristic
590C4#1171833611yescharacteristic
591C4#1171833611yescharacteristic
592C4C2×#8813811yescharacteristic
593C4C2×#8813911yescharacteristic
594C4C2×#8814811yescharacteristic
595C4C2×#8815211yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—1042no—
603C2#1311629112yesdirect product factor
604C2C2×#1171833611yescharacteristic
subgroupG/H
centerC2×C4#88139
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#344C2
socleC22×C13#397
prime radicalC22×#6127C22
hypercenterC2×#344D13
hypocenterC13C2×#2080
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#11718780C2semidirect
5. #13116291C2direct (N × H)
6. C2×#11718150C2semidirect
7. C2×#11718123C2semidirect
8. C2×C13×#344C2semidirect
24. #11718780C22semidirect
30. C13×#344C22semidirect
31. #11718150C22semidirect
32. #11718123C22semidirect
203. C2×#344D13semidirect
294. #344C2×D13semidirect
397. C2×C13#2080semidirect
499. C13C2×#2080semidirect
603. C2#13116291direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187802
C2×#117188002
C2×#117186632
C2×#117187932
#131162912
C2×#117181502
C2×#117181232
C2×C13×#3442
C2×#208013