Finite Group Databasebeta

← C2×#13116017 #15890366

Subgroups — C2×#13116017 #15890366

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88192C211yesmaximal, characteristic
2C22×#88058C211yesmaximal, characteristic, complemented
3C22×#88072C211yesmaximal, characteristic, complemented
4C22×#88060C211yesmaximal, characteristic, complemented
5C2×#11718648C211yesmaximal, characteristic, complemented
6#13116017C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C22×C13×#102C211yesmaximal, characteristic, complemented
9C23×D4×C13C2211yescharacteristic
10C23×C22⋊D13—21no—
11C23×C4×D13C2211yescharacteristic
12C23×C8×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C22⋊Dic13—21no—
15C2×#88192—24no—
16C2×#88192—22no—
17C2×#88192—24no—
18C2×#88192C2214yes—
19C22×#6103—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C13×#102—24no—
24C2×C13×#102C2214yescomplemented
25C2×#88072—24no—
26C2×#88072C2214yescomplemented
27C2×#88071—21no—
28C2×#88060—24no—
29C2×#88060C2214yescomplemented
30C2×#88058—24no—
31C2×#88058C2214yescomplemented
32#11718648—22no—
33#11718648C2214yescomplemented
34#11718121C2214yescomplemented
35C25×C13—21no—
36C24×D13D411yescharacteristic
37C22×D4×C13—22no—
38C22×D4×C13—21no—
39C22×D4×C13—22no—
40C22×D4×C13—22no—
41C22×D4×C13—22no—
42C22×D4×C13—22no—
43C22×D4×C13D414yes—
44C22×D4×C13C2312yes—
45C23×C4×C13—21no—
46C23×C4×C13C2311yescharacteristic
47C22×C22⋊D13—28no—
48C22×C22⋊D13—24no—
49C22×C22⋊D13—44no—
50C22×C22⋊D13—44no—
51C23×Dic13—21no—
52C23×Dic13—21no—
53C23×Dic13D411yescharacteristic
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13D412yes—
61C22×C4×D13C2312yes—
62C22×C8×C13—22no—
63C22×C8×C13—22no—
64C22×C8×C13D414yescomplemented
65C22×C8×C13C2312yes—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4C2312yes—
70C2×C22⋊Dic13—28no—
71C2×C22⋊Dic13—24no—
72#88192—216no—
73#88192—28no—
74#88192—28no—
75C2×#6103—24no—
76C2×#6103—44no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13D414yes—
83C2×C4⋊Dic13C2312yes—
84C2×C4⋊Dic13C2312yes—
85C22×#1055—22no—
86C22×#1055—22no—
87C22×#1055—22no—
88C22×#1055C2312yes—
89C13×#102—28no—
90#88072—28no—
91#88071—24no—
92#88060—28no—
93#88058—28no—
94C2×#2033—131nomaximal, Sylow
95C24×C13—24no—
96C24×C13—22no—
97C24×C13—42no—
98C24×C13—42no—
99C24×C13—42no—
100C24×C13—42no—
101C24×C13—42no—
102C24×C13—42no—
103C24×C13C2×D411yescharacteristic
104C23×D13—22no—
105C23×D13—22no—
106C23×D13—22no—
107C23×D13—22no—
108C23×D13—22no—
109C23×D13—22no—
110C23×D13D814yes—
111C23×D13C2×D412yes—
112C2×D4×C13—24no—
113C2×D4×C13—28no—
114C2×D4×C13—28no—
115C2×D4×C13—22no—
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—42no—
121C2×D4×C13—44no—
122C2×D4×C13—42no—
123C2×D4×C13—44no—
124C2×D4×C13C2×D414yes—
125C22×C4×C13—22no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13#4112yes—
134C22×C4×C13#4112yes—
135C22×C4×C13#4112yes—
136C22×C4×C13C2411yescharacteristic
137C2×C22⋊D13—216no—
138C2×C22⋊D13—48no—
139C2×C22⋊D13—432no—
140C2×C22⋊D13—48no—
141C22×Dic13—24no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—42no—
151C22×Dic13—42no—
152C22×Dic13C2×D412yes—
153C2×C4×D13—24no—
154C2×C4×D13—24no—
155C2×C4×D13—24no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—44no—
163C2×C4×D13—44no—
164C2×C4×D13—44no—
165C2×C4×D13—44no—
166C2×C8×C13—28no—
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13C2×D414yescomplemented
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—42no—
173C22⋊Dic13—216no—
174#6103—48no—
175C4⋊Dic13—24no—
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13—22no—
179C4⋊Dic13—42no—
180C4⋊Dic13C2×D414yes—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—44no—
185C22×#121—131no—
186C22×#107—131no—
187C22×#102—131no—
188C22×#102D1311yescharacteristic, complemented
189C22×C22⋊C8—131no—
190C2×#380—131no—
191#2033—138no—
192C2×#340—131no—
193C23×C13—24no—
194C23×C13—42no—
195C23×C13—42no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—48no—
201C23×C13—48no—
202C23×C13—48no—
203C23×C13—84no—
204C23×C13—84no—
205C23×C13—84no—
206C23×C13—84no—
207C23×C13#12012yes—
208C23×C13#12112yes—
209C23×C13#12312yes—
210C23×C13C2×D812yes—
211C23×C13#13512yes—
212C23×C13AGL(1,ℤ/8)12yes—
213C23×C13#13712yes—
214C23×C13C22×D411yescharacteristic
215C22×D13—22no—
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—28no—
222C22×D13—28no—
223C22×D13—28no—
224C22×D13—44no—
225C22×D13—44no—
226C22×D13—44no—
227C22×D13—44no—
228C22×D13C2×D814yes—
229D4×C13—24no—
230D4×C13—24no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—48no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—84no—
238C2×C4×C13#12012yes—
239C2×C4×C13#12114yes—
240C2×C4×C13#12114yes—
241C2×C4×C13#12112yes—
242C2×C4×C13#12314yes—
243C2×C4×C13#12312yes—
244C2×C4×C13#12414yes—
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C22⋊D13—432no—
252C2×Dic13—24no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—44no—
259C2×Dic13—48no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—84no—
264C4×D13—42no—
265C4×D13—42no—
266C4×D13—42no—
267C4×D13—42no—
268C4×D13—48no—
269C8×C13—24no—
270#1055—42no—
271C23×D4—261no—
272C23×D4C2×D1311yescharacteristic
273C24×C4—131no—
274C23×C8—131no—
275C23×C8C2×D1311yescharacteristic
276C2×#121—134no—
277C2×#121—264no—
278C2×#121—262no—
279C2×#121—264no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C22⋊C4—261no—
284C22×C22⋊C4—261no—
285C2×#107—134no—
286C2×#107—264no—
287C2×#102—24no—
288C2×#102—134no—
289C2×#102—264no—
290C2×#102C2×D1314yescomplemented
291C2×C22⋊C8—134no—
292C2×C22⋊C8—264no—
293#380—134no—
294#380—262no—
295C2×#95—261no—
296#340—134no—
297C22×C13—44no—
298C22×C13—44no—
299C22×C13—44no—
300C22×C13—82no—
301C22×C13—82no—
302C22×C13—82no—
303C22×C13—82no—
304C22×C13—816no—
305C22×C13#39414yes—
306C22×C13#44714yes—
307C22×C13#45214yes—
308C22×C13#46614yes—
309C22×C13#46814yes—
310C22×C13#48014yes—
311C22×C13#48214yes—
312C22×C13C2×#12011yescharacteristic
313C22×C13C2×#12111yescharacteristic
314C22×C13C2×#12311yescharacteristic
315C22×C13C22×D811yescharacteristic
316C22×C13C2×#13511yescharacteristic
317C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C13C2×#13711yescharacteristic
319C2×D13—24no—
320C2×D13—24no—
321C2×D13—24no—
322C2×D13—42no—
323C2×D13—42no—
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—416no—
327C4×C13—82no—
328C4×C13#39414yes—
329C4×C13C2×#12111yescharacteristic
330C4×C13C2×#12111yescharacteristic
331C4×C13C2×#12311yescharacteristic
332C4×C13C2×#12411yescharacteristic
333Dic13—42no—
334Dic13—44no—
335Dic13—82no—
336C25—21no—
337C25—131no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—264no—
345C22×D4—268no—
346C22×D4—524no—
347C22×D4—524no—
348C22×D4D5214yes—
349C22×D4C22×D1312yes—
350C23×C4—21no—
351C23×C4—131no—
352C23×C4—132no—
353C23×C4—132no—
354C23×C4—261no—
355C23×C4—262no—
356C23×C4—262no—
357C23×C4—262no—
358C23×C4—262no—
359C23×C4—262no—
360C23×C4—262no—
361C23×C4—261no—
362C23×C4C22×D1311yescharacteristic
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—132no—
366C22×C8—262no—
367C22×C8—262no—
368C22×C8—262no—
369C22×C8C22⋊D1314yescomplemented
370C22×C8C22×D1312yes—
371#121—268no—
372#121—2616no—
373#121—268no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—134no—
378C2×C4⋊C4—132no—
379C2×C4⋊C4—132no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4C22×D1312yes—
386C2×C22⋊C4—264no—
387C2×C22⋊C4—268no—
388C2×C22⋊C4—264no—
389C2×C22⋊C4—524no—
390#107—268no—
391#102—28no—
392#102—268no—
393C22⋊C8—268no—
394#95—264no—
395C2×C13—84no—
396C2×C13#203318yescomplemented
397C2×C13C2×#39411yescharacteristic
398C2×C13C2×#44711yescharacteristic
399C2×C13C2×#45211yescharacteristic
400C2×C13C2×#46611yescharacteristic
401C2×C13C2×#46811yescharacteristic
402C2×C13C2×#48011yescharacteristic
403C2×C13C2×#48211yescharacteristic
404D13—44no—
405C24—24no—
406C24—22no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—134no—
414C24—132no—
415C24—262no—
416C24—262no—
417C24—262no—
418C24—262no—
419C24—262no—
420C24—262no—
421C24D4×D1311yescharacteristic
422C2×D4—24no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—42no—
431C2×D4—44no—
432C2×D4—42no—
433C2×D4—44no—
434C2×D4—2616no—
435C2×D4—528no—
436C2×D4—5232no—
437C2×D4—528no—
438C2×D4C2×D5214yes—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—132no—
444C22×C4—262no—
445C22×C4—264no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—264no—
450C22×C4—264no—
451C22×C4—264no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—522no—
460C22×C4—522no—
461C22×C4—524no—
462C22×C4—524no—
463C22×C4—524no—
464C22×C4—524no—
465C22×C4—522no—
466C22×C4—522no—
467C22×C4—522no—
468C22×C4C2×D5212yes—
469C22×C4#612712yes—
470C22×C4D4×D1311yescharacteristic
471C22×C4D4×D1312yes—
472C22×C4#612912yes—
473C22×C4#612912yes—
474C22×C4C2×C22⋊D1312yes—
475C22×C4C23×D1311yescharacteristic
476C2×C8—28no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—524no—
483C2×C8C2×C22⋊D1314yescomplemented
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C4⋊C4—134no—
488C4⋊C4—264no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4—522no—
493C22⋊C4—2616no—
494C22⋊C4—528no—
495C13C2×#203311yescharacteristic, complemented, Sylow
496C23—24no—
497C23—42no—
498C23—48no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—48no—
504C23—42no—
505C23—48no—
506C23—84no—
507C23—84no—
508C23—84no—
509C23—84no—
510C23—134no—
511C23—262no—
512C23—262no—
513C23—268no—
514C23—268no—
515C23—262no—
516C23—262no—
517C23—262no—
518C23—262no—
519C23—268no—
520C23—524no—
521C23—524no—
522C23—524no—
523C23—524no—
524C23#8813612yes—
525C23#8813712yes—
526C23D8×D1312yes—
527C23#8816612yes—
528C23#8816812yes—
529C23#8816912yes—
530C23#8819212yes—
531C23C2×D4×D1311yescharacteristic
532D4—24no—
533D4—24no—
534D4—42no—
535D4—42no—
536D4—48no—
537D4—5232no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—262no—
543C2×C4—264no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—528no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—524no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—528no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—1044no—
559C2×C4#8813612yes—
560C2×C4#8813712yes—
561C2×C4#8813914yes—
562C2×C4#8814014yes—
563C2×C4#8818414yes—
564C2×C4#8819212yes—
565C2×C4#8819314yes—
566C2×C4C22×D5211yescharacteristic
567C2×C4C2×#612711yescharacteristic
568C2×C4C2×D4×D1311yescharacteristic
569C2×C4C2×#612911yescharacteristic
570C2×C4C2×#612911yescharacteristic
571C2×C4C22×C22⋊D1311yescharacteristic
572C8—24no—
573C8—522no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—816no—
582C22—264no—
583C22—264no—
584C22—264no—
585C22—522no—
586C22—522no—
587C22—522no—
588C22—5216no—
589C22—522no—
590C22#1171843414yes—
591C22#1171843514yes—
592C22#1171844414yes—
593C22#1171844514yes—
594C22#1171862214yes—
595C22#1171881814yes—
596C22#1171883514yes—
597C22C2×#8813611yescharacteristic
598C22C2×#8813711yescharacteristic
599C22C2×D8×D1311yescharacteristic
600C22C2×#8816611yescharacteristic
601C22C2×#8816811yescharacteristic
602C22C2×#8816911yescharacteristic
603C22C2×#8819211yescharacteristic
604C4—82no—
605C4—522no—
606C4—524no—
607C4—1042no—
608C4#1171862214yes—
609C4C2×#8813911yescharacteristic
610C4C2×#8814011yescharacteristic
611C4C2×#8818411yescharacteristic
612C4C2×#8819311yescharacteristic
613C2—84no—
614C2—524no—
615C2#1311601718yesdirect product factor
616C2C2×#1171862211yescharacteristic
617C2C2×#1171843411yescharacteristic
618C2C2×#1171844411yescharacteristic
619C2C2×#1171881811yescharacteristic
620C2C2×#1171883511yescharacteristic
621C2C2×#1171843511yescharacteristic
622C2C2×#1171844511yescharacteristic
subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#102C2
socleC24×C13C2×D4
prime radicalC22×#88192C2
hypercenterC22×#102D13
hypocenterC13C2×#2033
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#88058C2semidirect
3. C22×#88072C2semidirect
4. C22×#88060C2semidirect
5. C2×#11718648C2semidirect
6. #13116017C2direct (N × H)
7. C2×#11718121C2semidirect
8. C22×C13×#102C2semidirect
24. C2×C13×#102C22semidirect
26. C2×#88072C22semidirect
29. C2×#88060C22semidirect
31. C2×#88058C22semidirect
33. #11718648C22semidirect
34. #11718121C22semidirect
64. C22×C8×C13D4semidirect
169. C2×C8×C13C2×D4semidirect
188. C22×#102D13semidirect
290. C2×#102C2×D13semidirect
369. C22×C8C22⋊D13semidirect
396. C2×C13#2033semidirect
483. C2×C8C2×C22⋊D13semidirect
495. C13C2×#2033semidirect
615. C2#13116017direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881922
C22×#880582
C22×#880722
C22×#880602
C2×#117186482
#131160172
C2×#117181212
C22×C13×#1022
C2×#203313