Finite Group Databasebeta

← #15890407

Subgroups — #15890407

Order 3328.

1902 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×#11718625C211yesmaximal, characteristic, complemented
2C2×#11718876C211yesmaximal, characteristic, complemented
3C2×#11718876C211yesmaximal, characteristic, complemented
4C2×#11718868C211yesmaximal, characteristic, complemented
5#13117219C211yesmaximal, characteristic, complemented
6#13116022C214yesmaximal, complemented
7#13116015C214yesmaximal, complemented
8#13114555C211yesmaximal, characteristic, complemented
9C22×C13×#121C211yesmaximal, characteristic
10C23×D4×C13—21no—
11C23×D4×C13C2211yescharacteristic
12C24×C4×C13C2211yescharacteristic
13C2×C13×#121—24no—
14C2×C13×#121—22no—
15C2×C13×#121—24no—
16C2×C13×#121C2214yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4—21no—
19C2×#88180C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23#11718908—21no—
24#11718876—24no—
25#11718876—24no—
26C2×#88072C2212yescomplemented
27C2×#88072C2214yescomplemented
28C2×#88072C2212yescomplemented
29#11718873C2212yescomplemented
30#11718873C2212yescomplemented
31#11718872—21no—
32C4×C22⋊Dic13—22no—
33#11718868—24no—
34C2×C22⋊#1055C2214yescomplemented
35#11718625—24no—
36C2×#88048C2212yescomplemented
37C2×#88047C2212yescomplemented
38#11718121C2214yescomplemented
39C25×C13—21no—
40C25×C13D411yescharacteristic
41C22×D4×C13—28no—
42C22×D4×C13—24no—
43C22×D4×C13—22no—
44C22×D4×C13—21no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13—48no—
50C22×D4×C13D414yes—
51C22×D4×C13C2312yes—
52C23×C4×C13—21no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13D411yescharacteristic
60C23×C4×C13D412yes—
61C23×C4×C13C2312yes—
62C23×C4×C13C2311yescharacteristic
63C13×#121—216no—
64C13×#121—28no—
65C13×#121—28no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4D414yes—
69C2×C13×C4⋊C4C2312yes—
70C2×C13×C22⋊C4—28no—
71C2×C13×C22⋊C4—24no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—22no—
75C2×C22⋊Dic13—22no—
76#88180—22no—
77#88180—22no—
78#88180—22no—
79#88180—22no—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2312yes—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×#6099—22no—
86C2×#6099—22no—
87C2×#6099—22no—
88C2×#6099—22no—
89C2×#6099—22no—
90C2×#6099D414yescomplemented
91C22×#1055C2312yes—
92C22×#1055C2312yes—
93#88072—24no—
94#88072—24no—
95#88072—28no—
96#88071—22no—
97#88071—22no—
98C22⋊#1055—28no—
99#88048—24no—
100#88047—24no—
101#23480—131nomaximal, Sylow
102C24×C13—22no—
103C24×C13—24no—
104C24×C13—24no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—42no—
109C24×C13—44no—
110C24×C13—44no—
111C24×C13—42no—
112C24×C13—42no—
113C24×C13C2×D412yes—
114C24×C13C2×D411yescharacteristic
115C2×D4×C13—216no—
116C2×D4×C13—24no—
117C2×D4×C13—28no—
118C2×D4×C13—28no—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—432no—
125C2×D4×C13—48no—
126C2×D4×C13—48no—
127C2×D4×C13—44no—
128C2×D4×C13—42no—
129C2×D4×C13—42no—
130C2×D4×C13—44no—
131C2×D4×C13C2×D414yes—
132C22×C4×C13—22no—
133C22×C4×C13—24no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—44no—
147C22×C4×C13—44no—
148C22×C4×C13—44no—
149C22×C4×C13—44no—
150C22×C4×C13—44no—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×C4×C13C2411yescharacteristic
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—22no—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4C2×D414yes—
166C13×C22⋊C4—216no—
167C22⋊Dic13—44no—
168C22⋊Dic13—42no—
169C22⋊Dic13—42no—
170C22⋊Dic13—44no—
171C4⋊Dic13—22no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—22no—
177C4×Dic13—42no—
178C4×Dic13—42no—
179#6099—28no—
180#6099—44no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055C2×D414yescomplemented
187C22×#121D1311yescharacteristic
188C2×#428—131no—
189C2×#418—131no—
190C2×#418—131no—
191C2×#407—131no—
192#2280—131no—
193#2034—134no—
194#2033—134no—
195#1736—131no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—28no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—24no—
206C23×C13—48no—
207C23×C13—48no—
208C23×C13—44no—
209C23×C13—48no—
210C23×C13—48no—
211C23×C13—44no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—44no—
215C23×C13—44no—
216C23×C13—48no—
217C23×C13—88no—
218C23×C13—88no—
219C23×C13#12012yes—
220C23×C13#12112yes—
221C23×C13#12312yes—
222C23×C13AGL(1,ℤ/8)14yes—
223C23×C13C22×D411yescharacteristic
224D4×C13—24no—
225D4×C13—24no—
226D4×C13—432no—
227D4×C13—42no—
228D4×C13—42no—
229D4×C13—48no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—48no—
235C2×C4×C13—44no—
236C2×C4×C13—44no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—48no—
242C2×C4×C13#12012yes—
243C2×C4×C13#12114yes—
244C2×C4×C13#12114yes—
245C2×C4×C13#12112yes—
246C2×C4×C13#12314yes—
247C2×C4×C13#12312yes—
248C2×C4×C13#12414yes—
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262#1055—24no—
263#1055—42no—
264C23×D4—21no—
265C23×D4C2×D1311yescharacteristic
266C24×C4C2×D1311yescharacteristic
267C22×M16—131no—
268C22×M16—131no—
269C2×#121—24no—
270C2×#121—22no—
271C2×#121—24no—
272C2×#121C2×D1314yes—
273C2×#117—131no—
274C2×#117—131no—
275C22×C4⋊C4C2×D1311yescharacteristic
276C22×C22⋊C4—21no—
277#428—264no—
278C2×#107—132no—
279C2×#106—132no—
280#418—264no—
281#418—264no—
282C2×#102—132no—
283C2×#102—134no—
284C2×#102—132no—
285#407—264no—
286C2×C22⋊C8—134no—
287#381—261no—
288#380—132no—
289#380—132no—
290#379—261no—
291C4×C22⋊C4—262no—
292#340—134no—
293C22×C13—24no—
294C22×C13—22no—
295C22×C13—22no—
296C22×C13—24no—
297C22×C13—24no—
298C22×C13—24no—
299C22×C13—24no—
300C22×C13—416no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—816no—
309C22×C13—84no—
310C22×C13—84no—
311C22×C13#39414yes—
312C22×C13C2×#12011yescharacteristic
313C22×C13C2×#12111yescharacteristic
314C22×C13C2×#12311yescharacteristic
315C22×C13C2×AGL(1,ℤ/8)12yes—
316C22×C13#57512yes—
317C4×C13—42no—
318C4×C13—44no—
319C4×C13#39414yes—
320C4×C13C2×#12111yescharacteristic
321C4×C13C2×#12111yescharacteristic
322C4×C13C2×#12311yescharacteristic
323C4×C13C2×#12411yescharacteristic
324Dic13—81no—
325Dic13—81no—
326Dic13—82no—
327C25—21no—
328C25C22⋊D1311yescharacteristic
329C22×D4—28no—
330C22×D4—24no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—48no—
338C22×D4C22⋊D1314yes—
339C22×D4C22×D1312yes—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4C22⋊D1311yescharacteristic
348C23×C4C22⋊D1312yes—
349C23×C4C22×D1312yes—
350C23×C4C22×D1311yescharacteristic
351C2×M16—134no—
352C2×M16—262no—
353C2×M16—262no—
354C2×M16—262no—
355C2×M16—262no—
356C2×M16—262no—
357C22×C8—132no—
358C22×C8—132no—
359#121—216no—
360#121—28no—
361#121—28no—
362#117—262no—
363#117—262no—
364#117—262no—
365#117—262no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—132no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4C22⋊D1314yes—
372C2×C4⋊C4C22×D1312yes—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—262no—
378C2×C22⋊C4—262no—
379C2×C42—261no—
380C2×C42—261no—
381#107—264no—
382#106—264no—
383#102—268no—
384#102—264no—
385#102—264no—
386C22⋊C8—268no—
387#95—262no—
388#95—262no—
389C2×C13—24no—
390C2×C13—44no—
391C2×C13—84no—
392C2×C13C2×#39411yescharacteristic
393C2×C13#300311yescharacteristic
394C2×C13#300511yescharacteristic
395C2×C13#305512yes—
396C2×C13#309412yes—
397C24—24no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—24no—
402C24—22no—
403C24—42no—
404C24—44no—
405C24—44no—
406C24—42no—
407C24—42no—
408C24C2×C22⋊D1312yes—
409C24C2×C22⋊D1311yescharacteristic
410C2×D4—216no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—24no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—432no—
420C2×D4—48no—
421C2×D4—48no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4C2×C22⋊D1314yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—261no—
447C22×C4—262no—
448C22×C4—261no—
449C22×C4D4×D1312yes—
450C22×C4#612912yes—
451C22×C4#612912yes—
452C22×C4#612912yes—
453C22×C4C2×C22⋊D1312yes—
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1312yes—
456C22×C4C2×C22⋊D1312yes—
457C22×C4C23×D1311yescharacteristic
458M16—268no—
459M16—524no—
460C2×C8—134no—
461C2×C8—262no—
462C2×C8—262no—
463C2×C8—262no—
464C2×C8—262no—
465C2×C8—262no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4C2×C22⋊D1314yes—
475C22⋊C4—216no—
476C22⋊C4—524no—
477C22⋊C4—524no—
478C22⋊C4—522no—
479C22⋊C4—522no—
480C42—522no—
481C42—522no—
482C13#2348011yescharacteristic, complemented, Sylow
483C23—22no—
484C23—22no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—48no—
494C23—48no—
495C23—44no—
496C23—48no—
497C23—48no—
498C23—44no—
499C23—44no—
500C23—42no—
501C23—42no—
502C23—44no—
503C23—48no—
504C23—88no—
505C23—88no—
506C23#8818614yes—
507C23#8818912yes—
508C23#8819312yes—
509C23#8820712yes—
510C23C22×C22⋊D1311yescharacteristic
511D4—24no—
512D4—24no—
513D4—432no—
514D4—42no—
515D4—42no—
516D4—48no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—48no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4#8818914yes—
537C2×C4#8818912yes—
538C2×C4#8819014yes—
539C2×C4#8819214yes—
540C2×C4#8819314yes—
541C2×C4#8819312yes—
542C2×C4#8820712yes—
543C2×C4C2×D4×D1311yescharacteristic
544C2×C4C2×#612911yescharacteristic
545C2×C4C2×#612911yescharacteristic
546C2×C4C2×#612911yescharacteristic
547C2×C4C22×C22⋊D1311yescharacteristic
548C2×C4C22×C22⋊D1311yescharacteristic
549C8—264no—
550C8—522no—
551C22—24no—
552C22—24no—
553C22—22no—
554C22—22no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—416no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—816no—
567C22—84no—
568C22—84no—
569C22#1171888314yes—
570C22C2×#8818612yes—
571C22C2×#8818911yescharacteristic
572C22C2×#8819311yescharacteristic
573C22#1171952712yes—
574C22C2×#8820711yescharacteristic
575C4—42no—
576C4—44no—
577C4—1042no—
578C4—1041no—
579C4—1041no—
580C4#1171888314yes—
581C4C2×#8818911yescharacteristic
582C4C2×#8819011yescharacteristic
583C4C2×#8819211yescharacteristic
584C4C2×#8819311yescharacteristic
585C2—24no—
586C2—44no—
587C2—84no—
588C2C2×#1171888311yescharacteristic
589C2#1312406311yescharacteristic
590C2#1312407811yescharacteristic
591C2#1312445112yes—
592C2#1312477212yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC22×C13×#121C2
socleC23×C13C22×D4
hypercenterC22×#121D13
hypocenterC13#23480
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11718625C2semidirect
2. C2×#11718876C2semidirect
3. C2×#11718876C2semidirect
4. C2×#11718868C2semidirect
5. #13117219C2semidirect
6. #13116022C2semidirect
7. #13116015C2semidirect
8. #13114555C2semidirect
26. C2×#88072C22semidirect
27. C2×#88072C22semidirect
28. C2×#88072C22semidirect
29. #11718873C22semidirect
30. #11718873C22semidirect
34. C2×C22⋊#1055C22semidirect
36. C2×#88048C22semidirect
37. C2×#88047C22semidirect
38. #11718121C22semidirect
90. C2×#6099D4semidirect
186. C2×#1055C2×D4semidirect
482. C13#23480semidirect

Maximal subgroups

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

subgroupindex
C2×#117186252
C2×#117188762
C2×#117188682
#131172192
#131160222
#131160152
#131145552
C22×C13×#1212
#2348013