Finite Group Databasebeta

← #15799686

Subgroups — #15799686

Order 3328.

1710 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×#11718613C214yesmaximal
2C2×#11718637C211yesmaximal, characteristic, complemented
3C2×#11718873C211yesmaximal, characteristic
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113102C214yesmaximal, complemented
6#13113065C211yesmaximal, characteristic, complemented
7#13113065C211yesmaximal, characteristic, complemented
8#13113065C211yesmaximal, characteristic, complemented
9C2×C13×#380C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2212yes—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×#6101C2214yes—
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C13×#380—24no—
22C2×C13×#95C2212yes—
23#11718873—24no—
24C4×C22⋊Dic13—24no—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2214yes—
28C2×#88071C2214yes—
29C2×#88071C2214yes—
30#11718637—24no—
31#11718613—216no—
32C25×C13C2311yescharacteristic
33C23×C4×C13—22no—
34C23×C4×C13—22no—
35C23×C4×C13—22no—
36C23×C4×C13—22no—
37C23×C4×C13—22no—
38C23×C4×C13—22no—
39C23×C4×C13D414yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C22⋊C4—24no—
55C2×C13×C22⋊C4—28no—
56C2×C22⋊Dic13—24no—
57C2×C22⋊Dic13—24no—
58C2×C22⋊Dic13—28no—
59C2×C22⋊Dic13—24no—
60C2×C22⋊Dic13D418yes—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13—22no—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—22no—
67C2×#6101—28no—
68C2×#6101—28no—
69C2×#6101—28no—
70C2×C4×Dic13—22no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—22no—
73C2×C4×Dic13—22no—
74C2×C4×Dic13—22no—
75C2×C4×Dic13D414yes—
76C13×#95—24no—
77#88071—24no—
78#88071—28no—
79#88071—28no—
80#88071—28no—
81#88071—24no—
82#15150—131nomaximal, Sylow
83C24×C13—21no—
84C24×C13—22no—
85C24×C13—21no—
86C24×C13—21no—
87C24×C13—21no—
88C24×C13—21no—
89C24×C13—21no—
90C24×C13—22no—
91C24×C13—22no—
92C24×C13C2×D414yes—
93C24×C13C2×D412yes—
94C24×C13C2411yescharacteristic
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—28no—
102C22×C4×C13—28no—
103C22×C4×C13—28no—
104C22×C4×C13—24no—
105C22×C4×C13—24no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—24no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—24no—
114C22×C4×C13—44no—
115C22×C4×C13—44no—
116C22×C4×C13—44no—
117C22×C4×C13—44no—
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×D412yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13#4112yes—
122C22×C4×C13#4112yes—
123C22×C4×C13#4112yes—
124C22×C4×C13#4112yes—
125C22×C4×C13#4112yes—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—24no—
137C22×Dic13—24no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—24no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—24no—
146C22×Dic13C2×D414yes—
147C22×Dic13C2×D414yes—
148C22×Dic13C2×D414yes—
149C22×Dic13#4114yes—
150C13×C4⋊C4—44no—
151C13×C4⋊C4—44no—
152C13×C22⋊C4—48no—
153C22⋊Dic13—216no—
154C22⋊Dic13—48no—
155C4⋊Dic13—44no—
156C4⋊Dic13—44no—
157#6101—416no—
158C4×Dic13—28no—
159C4×Dic13—44no—
160C2×#397—134no—
161C2×#384—131no—
162C2×#380—131no—
163C2×#380D1311yescharacteristic
164C2×C4×C22⋊C4—131no—
165#1445—134no—
166C4⋊#95—131no—
167C4⋊#95—131no—
168C4⋊#95—131no—
169C23×C13—24no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—24no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—24no—
180C23×C13—24no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13#12714yes—
192C23×C13C22×D411yescharacteristic
193C23×C13C22×D411yescharacteristic
194C23×C13C22×D412yes—
195C23×C13C2×#4111yescharacteristic
196C23×C13C2×#4112yes—
197C23×C13C2×#4111yescharacteristic
198C23×C13C2×#4111yescharacteristic
199C23×C13C2×#4111yescharacteristic
200C23×C13C2×#4111yescharacteristic
201C23×C132−1+412yes—
202C23×C132−1+412yes—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—416no—
211C2×C4×C13—44no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—44no—
218C2×C4×C13—42no—
219C2×C4×C13—44no—
220C2×C4×C13—44no—
221C2×C4×C13#12114yes—
222C2×C4×C13#12314yes—
223C2×C4×C13#12314yes—
224C2×C4×C13#12314yes—
225C2×C4×C13#12414yes—
226C2×C4×C13#12614yes—
227C2×C4×C13#12614yes—
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—44no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—44no—
248C2×Dic13—42no—
249C2×Dic13—44no—
250C2×Dic13—44no—
251C2×Dic13#12118yes—
252C24×C4C2×D1311yescharacteristic
253C22×C4⋊C4—134no—
254C22×C4⋊C4—131no—
255C22×C4⋊C4—131no—
256C22×C4⋊C4C2×D1311yescharacteristic
257C22×C4⋊C4C2×D1311yescharacteristic
258C22×C22⋊C4—132no—
259C22×C22⋊C4—132no—
260C22×C22⋊C4C2×D1312yes—
261C22×C42—131no—
262C22×C42—131no—
263#397—2616no—
264#384—264no—
265#380—24no—
266#380—264no—
267C4×C22⋊C4—264no—
268C2×#95—134no—
269C2×#95—134no—
270C2×#95—134no—
271C2×#95—132no—
272C2×#95—132no—
273C2×#95C2×D1312yes—
274C22×C13—24no—
275C22×C13—24no—
276C22×C13—24no—
277C22×C13—42no—
278C22×C13—42no—
279C22×C13—44no—
280C22×C13—44no—
281C22×C13—44no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—44no—
285C22×C13C2×#12111yescharacteristic
286C22×C13C2×#12112yes—
287C22×C13C2×#12311yescharacteristic
288C22×C13C2×#12311yescharacteristic
289C22×C13C2×#12311yescharacteristic
290C22×C13C2×#12411yescharacteristic
291C22×C13C2×#12611yescharacteristic
292C22×C13C2×#12611yescharacteristic
293C22×C13C2×#12711yescharacteristic
294C22×C13#53211yescharacteristic
295C22×C13#53212yes—
296C22×C13#53611yescharacteristic
297C22×C13#53611yescharacteristic
298C22×C13#53612yes—
299C22×C13#54112yes—
300C22×C13#54712yes—
301C22×C13#54712yes—
302C22×C13#54712yes—
303C22×C13#54712yes—
304C22×C13#55212yes—
305C22×C13#55212yes—
306C22×C13#55612yes—
307C22×C13#55612yes—
308C4×C13—42no—
309C4×C13—82no—
310C4×C13—82no—
311C4×C13#39718yescomplemented
312Dic13—28no—
313Dic13—44no—
314Dic13—82no—
315Dic13—82no—
316C25C22×D1311yescharacteristic
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—132no—
324C23×C4—132no—
325C23×C4—132no—
326C23×C4—132no—
327C23×C4C22⋊D1314yes—
328C23×C4C22×D1312yes—
329C23×C4C22×D1312yes—
330C23×C4C22×D1311yescharacteristic
331C23×C4C22×D1311yescharacteristic
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—268no—
339C2×C4⋊C4—268no—
340C2×C4⋊C4—268no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—262no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4—262no—
346C2×C4⋊C4—262no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—138no—
350C2×C22⋊C4—264no—
351C2×C22⋊C4—264no—
352C2×C22⋊C4—268no—
353C2×C22⋊C4—264no—
354C2×C42—134no—
355C2×C42—262no—
356C2×C42—262no—
357C2×C42—262no—
358C2×C42—262no—
359C2×C42—262no—
360#95—24no—
361#95—264no—
362#95—268no—
363#95—268no—
364#95—268no—
365#95—264no—
366C2×C13—44no—
367C2×C13C2×#39711yescharacteristic
368C2×C13#248612yes—
369C2×C13#249612yes—
370C2×C13#249612yes—
371C2×C13#249911yescharacteristic
372C2×C13#249911yescharacteristic
373C2×C13#250111yescharacteristic
374C2×C13#250111yescharacteristic
375C2×C13#254712yes—
376C2×C13#262111yescharacteristic
377C2×C13#285611yescharacteristic
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24D4×D1314yes—
388C24C2×C22⋊D1312yes—
389C24C23×D1311yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—28no—
397C22×C4—28no—
398C22×C4—28no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—44no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—134no—
414C22×C4—134no—
415C22×C4—134no—
416C22×C4—134no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—264no—
430C22×C4—264no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—264no—
434C22×C4—264no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4#612712yes—
438C22×C4#612712yes—
439C22×C4D4×D1312yes—
440C22×C4#612912yes—
441C22×C4#612912yes—
442C22×C4#612912yes—
443C22×C4C2×C22⋊D1312yes—
444C22×C4C2×C22⋊D1312yes—
445C4⋊C4—44no—
446C4⋊C4—44no—
447C4⋊C4—5216no—
448C4⋊C4—524no—
449C4⋊C4—524no—
450C22⋊C4—48no—
451C22⋊C4—2616no—
452C22⋊C4—528no—
453C42—268no—
454C42—524no—
455C13#1515011yescharacteristic, complemented, Sylow
456C23—24no—
457C23—24no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23#8819414yes—
479C23C2×#612711yescharacteristic
480C23C2×#612711yescharacteristic
481C23C2×D4×D1311yescharacteristic
482C23C2×D4×D1312yes—
483C23C2×#612911yescharacteristic
484C23C2×#612911yescharacteristic
485C23C2×#612911yescharacteristic
486C23#8825412yes—
487C23#41×D1312yes—
488C23#8825712yes—
489C23C22×C22⋊D1311yescharacteristic
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—416no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—138no—
509C2×C4—264no—
510C2×C4—264no—
511C2×C4—264no—
512C2×C4—264no—
513C2×C4—264no—
514C2×C4—264no—
515C2×C4—264no—
516C2×C4—264no—
517C2×C4—264no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—524no—
523C2×C4—524no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—524no—
531C2×C4—524no—
532C2×C4#8813314yes—
533C2×C4#8813314yes—
534C2×C4#8813714yes—
535C2×C4#8813914yes—
536C2×C4#8818314yes—
537C2×C4#8818914yes—
538C2×C4#8819314yes—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—44no—
543C22—44no—
544C22—42no—
545C22—42no—
546C22—44no—
547C22—42no—
548C22—42no—
549C22—44no—
550C22C2×#8813311yescharacteristic
551C22C2×#8813311yescharacteristic
552C22C2×#8813711yescharacteristic
553C22C2×#8813911yescharacteristic
554C22#1171921212yes—
555C22#1171921212yes—
556C22#1171923412yes—
557C22#1171923812yes—
558C22#1171930112yes—
559C22D13×#12112yes—
560C22#1171931612yes—
561C22#1171931612yes—
562C22#1171933012yes—
563C22#1171933312yes—
564C22#1171934412yes—
565C22#1171934612yes—
566C22C2×#8818311yescharacteristic
567C22C2×#8818911yescharacteristic
568C22C2×#8819311yescharacteristic
569C22C2×#8819411yescharacteristic
570C22#1171952111yescharacteristic
571C22#1171953011yescharacteristic
572C22#1171953711yescharacteristic
573C4—42no—
574C4—82no—
575C4—82no—
576C4—268no—
577C4—524no—
578C4—1042no—
579C4—1042no—
580C4#1171861318yescomplemented
581C2—44no—
582C2C2×#1171861311yescharacteristic
583C2#1311914012yes—
584C2#1311925412yes—
585C2#1311926012yes—
586C2#1311928511yescharacteristic
587C2#1311929011yescharacteristic
588C2#1311930311yescharacteristic
589C2#1311930811yescharacteristic
590C2#1311983012yes—
591C2#1312060611yescharacteristic
592C2#1312317911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#380C2
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#15150
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#11718637C2semidirect
5. #13113102C2semidirect
6. #13113065C2semidirect
7. #13113065C2semidirect
8. #13113065C2semidirect
311. C4×C13#397semidirect
455. C13#15150semidirect
580. C4#11718613semidirect

Maximal subgroups

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

subgroupindex
C2×#117186132
C2×#117186372
C2×#117188732
C2×C4×C22⋊Dic132
#131131022
#131130652
C2×C13×#3802
#1515013