Finite Group Databasebeta

← C2×#13116287 #15891838

Subgroups — C2×#13116287 #15891838

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×#11718666C211yesmaximal, characteristic
2C2×#11718774C211yesmaximal, characteristic
3C2×#11718793C211yesmaximal, characteristic
4#13116287C218yesmaximal, direct product factor
5C2×#11718151C211yesmaximal, characteristic, complemented
6C2×#11718144C211yesmaximal, characteristic, complemented
7C2×#11718123C211yesmaximal, characteristic, complemented
8C2×C13×#424C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16C13×#424—22no—
17C13×#424C2214yescomplemented
18C2×C13×C4⋊C8—22no—
19C2×#88064—21no—
20#11718793—22no—
21#11718793C2214yes—
22C2×#88063—21no—
23#11718774—22no—
24#11718774C2214yes—
25C2×#88061—21no—
26C2×#88056—21no—
27#11718666—22no—
28#11718666C2214yes—
29C2×#88045—22no—
30#11718151C2214yescomplemented
31#11718144C2214yescomplemented
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×M16C2312yes—
56C22×C8×C13—21no—
57C22×C8×C13—21no—
58C22×C8×C13—21no—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C22×C8×C13—21no—
62C22×C8×C13—21no—
63C22×C8×C13C2312yes—
64C13×#117—21no—
65C13×#117—21no—
66C13×#117D412yes—
67C13×#117C2312yes—
68C2×C13×C4⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C42×C13D412yes—
71C2×C22⋊Dic13—21no—
72#88180—21no—
73#88180—21no—
74#88180—21no—
75#88180C2312yes—
76C2×C4⋊Dic13—21no—
77C2×C4×Dic13—21no—
78C2×#6099—21no—
79C2×#6099—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099C2312yes—
89C2×#6099C2312yes—
90C22×#1055—21no—
91C22×#1055—21no—
92C13×C4⋊C8—28no—
93#88064—24no—
94#88063—24no—
95#88061—24no—
96#88056—24no—
97#88045—28no—
98C2×#2080—131nomaximal, Sylow
99C24×C13#4111yescharacteristic
100C23×D13—21no—
101C22×C4×C13—22no—
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—21no—
123C22×Dic13—41no—
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—41no—
161C13×M16—41no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C2×C8×C13—41no—
167C2×C8×C13—41no—
168C2×C8×C13—41no—
169C2×C8×C13—41no—
170C2×C8×C13—41no—
171C2×C8×C13—41no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C42×C13—22no—
177C42×C13C2×D414yes—
178C22⋊Dic13—22no—
179C22⋊Dic13—41no—
180C4⋊Dic13—22no—
181C4⋊Dic13—41no—
182C4×Dic13—22no—
183C4×Dic13—41no—
184#6099—22no—
185#6099—22no—
186#6099—22no—
187#6099—22no—
188#6099—41no—
189#6099—41no—
190#6099—41no—
191#6099—41no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—41no—
195C2×#1055—41no—
196C2×#1055—41no—
197C2×#1055—41no—
198C2×#424D1311yescharacteristic, complemented
199C2×#421—131no—
200C2×#416—131no—
201C2×#413—131no—
202#2080—138no—
203C2×#344—131no—
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—24no—
219C2×C4×C13—44no—
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—22no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—42no—
256C2×Dic13—82no—
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×M16—131no—
276C22×M16C2×D1311yescharacteristic
277C23×C8C2×D1311yescharacteristic
278C2×#117—131no—
279C2×#117C2×D1311yescharacteristic
280#424—22no—
281#424C2×D1314yescomplemented
282C2×C4⋊C8—22no—
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#344—134no—
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—44no—
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—42no—
325Dic13—82no—
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—132no—
349C2×M16—132no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16—261no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16—261no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16C22×D1312yes—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—261no—
369C22×C8—261no—
370C22×C8C22×D1312yes—
371#117—21no—
372#117—21no—
373#117—132no—
374#117—261no—
375#117—261no—
376#117—261no—
377#117C22⋊D1312yes—
378#117C22×D1312yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—261no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—261no—
383C2×C42—261no—
384C2×C42C22⋊D1312yes—
385C4⋊C8—28no—
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—22no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—521no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—521no—
444C22×C4—521no—
445C22×C4#612711yescharacteristic
446C22×C4#612711yescharacteristic
447C22×C4#612711yescharacteristic
448C22×C4D4×D1311yescharacteristic
449C22×C4D4×D1311yescharacteristic
450C22×C4#612911yescharacteristic
451C22×C4#612911yescharacteristic
452C22×C4#613111yescharacteristic
453C22×C4#613111yescharacteristic
454C22×C4#613111yescharacteristic
455C22×C4#613111yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459M16—22no—
460M16—22no—
461M16—41no—
462M16—41no—
463M16—262no—
464M16—262no—
465M16—262no—
466M16—262no—
467M16—521no—
468M16—521no—
469M16—521no—
470M16—521no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—521no—
484C2×C8—521no—
485C2×C8—521no—
486C2×C8—521no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—262no—
490C4⋊C4—521no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—262no—
494C22⋊C4—521no—
495C42—22no—
496C42—262no—
497C42—521no—
498C42C2×C22⋊D1314yes—
499C13C2×#208011yescharacteristic, complemented, Sylow
500C23—42no—
501C23—262no—
502C23—521no—
503C23—521no—
504C23—1042no—
505C23#8814811yescharacteristic
506C23#8814811yescharacteristic
507C23#8815211yescharacteristic
508C23#8815211yescharacteristic
509C23#8818311yescharacteristic
510C23#8818311yescharacteristic
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—24no—
525C2×C4—44no—
526C2×C4—262no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—1042no—
535C2×C4#8814811yescharacteristic
536C2×C4#8814811yescharacteristic
537C2×C4#8814811yescharacteristic
538C2×C4#8814811yescharacteristic
539C2×C4#8814811yescharacteristic
540C2×C4#8814811yescharacteristic
541C2×C4#8815211yescharacteristic
542C2×C4#8815211yescharacteristic
543C2×C4#8815211yescharacteristic
544C2×C4#8815211yescharacteristic
545C2×C4#8815211yescharacteristic
546C2×C4#8815211yescharacteristic
547C2×C4#8818311yescharacteristic
548C2×C4#8818311yescharacteristic
549C2×C4#8819211yescharacteristic
550C2×C4#8819211yescharacteristic
551C2×C4#8819211yescharacteristic
552C2×C4#8819211yescharacteristic
553C2×C4#8820111yescharacteristic
554C2×C4#8820111yescharacteristic
555C2×C4#8820111yescharacteristic
556C2×C4#8820111yescharacteristic
557C2×C4C2×#612711yescharacteristic
558C2×C4C2×D4×D1311yescharacteristic
559C2×C4C2×#612911yescharacteristic
560C2×C4C2×#613111yescharacteristic
561C2×C4C2×#613111yescharacteristic
562C2×C4C22×C22⋊D1311yescharacteristic
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#1171865411yescharacteristic
579C22#1171865411yescharacteristic
580C22#1171865411yescharacteristic
581C22#1171865411yescharacteristic
582C22C2×#8814811yescharacteristic
583C22C2×#8815211yescharacteristic
584C22C2×#8818311yescharacteristic
585C4—44no—
586C4—522no—
587C4—1042no—
588C4#1171865411yescharacteristic
589C4#1171865411yescharacteristic
590C4#1171865411yescharacteristic
591C4#1171865411yescharacteristic
592C4C2×#8814811yescharacteristic
593C4C2×#8815211yescharacteristic
594C4C2×#8819211yescharacteristic
595C4C2×#8820111yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—1042no—
603C2#1311628712yesdirect product factor
604C2C2×#1171865411yescharacteristic
subgroupG/H
centerC2×C4#88201
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#424C2
socleC22×C13#397
prime radicalC22×#6127C22
hypercenterC2×#424D13
hypocenterC13C2×#2080
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. #13116287C2direct (N × H)
5. C2×#11718151C2semidirect
6. C2×#11718144C2semidirect
7. C2×#11718123C2semidirect
8. C2×C13×#424C2semidirect
17. C13×#424C22semidirect
30. #11718151C22semidirect
31. #11718144C22semidirect
32. #11718123C22semidirect
198. C2×#424D13semidirect
281. #424C2×D13semidirect
397. C2×C13#2080semidirect
499. C13C2×#2080semidirect
603. C2#13116287direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186662
C2×#117187742
C2×#117187932
#131162872
C2×#117181512
C2×#117181442
C2×#117181232
C2×C13×#4242
C2×#208013