Finite Group Databasebeta

← #15793980

Subgroups — #15793980

Order 3328.

1602 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13113098C212yesmaximal, complemented
2#13113093C212yesmaximal, complemented
3#13113085C212yesmaximal, complemented
4#13113081C212yesmaximal, complemented
5#13113081C212yesmaximal, complemented
6#13113077C211yesmaximal, characteristic
7#13113077C211yesmaximal, characteristic
8#13113059C212yesmaximal, complemented
9C2×C13×#386C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C22×C13×C22⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2212yes—
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2212yes—
20C13×#386C418yescomplemented
21C2×C13×#95C2212yes—
22C2×#88071C2211yescharacteristic
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C25×C13C2311yescharacteristic
33C25×C13C2311yescharacteristic
34C22×D4×C13—24no—
35C22×D4×C13—42no—
36C22×D4×C13—41no—
37C22×D4×C13—41no—
38C22×D4×C13C2×C414yes—
39C23×C4×C13—41no—
40C23×C4×C13—41no—
41C23×C4×C13—42no—
42C23×C4×C13—42no—
43C23×C4×C13C2×C414yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C2×C13×C22⋊C4—42no—
52C2×C13×C22⋊C4—42no—
53C2×C13×C22⋊C4—42no—
54C2×C13×C22⋊C4C2×C414yes—
55C2×C13×C22⋊C4C2×C418yes—
56C2×C22⋊Dic13—24no—
57C2×C22⋊Dic13—24no—
58C2×C22⋊Dic13—42no—
59C2×C22⋊Dic13—42no—
60C2×C22⋊Dic13—42no—
61C2×C22⋊Dic13—42no—
62C2×C22⋊Dic13—41no—
63C2×C22⋊Dic13—41no—
64C2×C22⋊Dic13—42no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13—42no—
67C2×C22⋊Dic13—42no—
68C2×C22⋊Dic13—42no—
69C2×C4⋊Dic13—42no—
70C2×C4⋊Dic13—42no—
71C2×C4⋊Dic13—42no—
72C13×#95C2×C418yes—
73#88071—41no—
74#88071—41no—
75#88071—42no—
76#88071—42no—
77#88071—42no—
78#88071—42no—
79#88071—42no—
80#88071—42no—
81#88071—42no—
82#88071—42no—
83#14666—131nomaximal, Sylow
84C24×C13—22no—
85C24×C13—22no—
86C24×C13—22no—
87C24×C13—22no—
88C24×C13—21no—
89C24×C13—21no—
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—21no—
96C24×C13—22no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13C22×C412yes—
100C24×C13C22×C412yes—
101C24×C13#4114yes—
102C24×C13C2411yescharacteristic
103C2×D4×C13—28no—
104C2×D4×C13—44no—
105C2×D4×C13—44no—
106C2×D4×C13—48no—
107C2×D4×C13—48no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—48no—
125C22×C4×C13—44no—
126C22×C4×C13—48no—
127C22×C4×C13—44no—
128C22×C4×C13—44no—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C414yes—
131C22×C4×C13C22×C414yes—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C13×C22⋊C4—48no—
161C13×C22⋊C4—44no—
162C22⋊Dic13—48no—
163C22⋊Dic13—48no—
164C22⋊Dic13—48no—
165C22⋊Dic13—44no—
166C22⋊Dic13—44no—
167C4⋊Dic13—48no—
168C2×#386D1311yescharacteristic
169#1443—132no—
170#1442—132no—
171#1440—132no—
172#1439—132no—
173#1439—132no—
174#1438—131no—
175#1438—131no—
176C22⋊#95—132no—
177C23×C13—22no—
178C23×C13—22no—
179C23×C13—24no—
180C23×C13—24no—
181C23×C13—24no—
182C23×C13—24no—
183C23×C13—24no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—22no—
188C23×C13—24no—
189C23×C13—22no—
190C23×C13—22no—
191C23×C13—24no—
192C23×C13—42no—
193C23×C13—41no—
194C23×C13—42no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—41no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—42no—
213C23×C13—41no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—41no—
218C23×C13#11714yes—
219C23×C13C23×C411yescharacteristic
220C23×C13C2×#4112yes—
221C23×C13H(5,𝔽2)11yescharacteristic
222C23×C13H(5,𝔽2)12yes—
223C23×C13H(5,𝔽2)11yescharacteristic
224C23×C13H(5,𝔽2)12yes—
225C23×C13H(5,𝔽2)12yes—
226C23×C13H(5,𝔽2)12yes—
227C23×C132−1+412yes—
228D4×C13—416no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—416no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C23×D4C2×D1311yescharacteristic
278C24×C4C2×D1311yescharacteristic
279C22×C4⋊C4—132no—
280C22×C22⋊C4—132no—
281C22×C22⋊C4—132no—
282C22×C22⋊C4—131no—
283C22×C22⋊C4—132no—
284C22×C22⋊C4—131no—
285C22×C22⋊C4C2×D1311yescharacteristic
286C22×C22⋊C4C2×D1312yes—
287#386Dic1318yescomplemented
288C2×#95—132no—
289C2×#95—132no—
290C2×#95—132no—
291C2×#95—132no—
292C2×#95—131no—
293C2×#95—132no—
294C2×#95—131no—
295C2×#95—132no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95C2×D1312yes—
299C22×C13—24no—
300C22×C13—28no—
301C22×C13—44no—
302C22×C13—44no—
303C22×C13—44no—
304C22×C13—44no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—44no—
308C22×C13—42no—
309C22×C13—44no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—44no—
313C22×C13—82no—
314C22×C13—82no—
315C22×C13—82no—
316C22×C13—82no—
317C22×C13C2×#11711yescharacteristic
318C22×C13#51811yescharacteristic
319C22×C13#51811yescharacteristic
320C22×C13#51812yes—
321C22×C13#52012yes—
322C22×C13#53812yes—
323C22×C13#53812yes—
324C22×C13#53812yes—
325C22×C13#53812yes—
326C22×C13#53912yes—
327C22×C13#53912yes—
328C22×C13#56012yes—
329C22×C13#56011yescharacteristic
330C22×C13#56012yes—
331C22×C13#56012yes—
332C22×C13#56011yescharacteristic
333C22×C13H(3,𝔽4)11yescharacteristic
334C22×C13#56212yes—
335C22×C13#56212yes—
336C22×C13#56212yes—
337C22×C13#56311yescharacteristic
338C4×C13—42no—
339C4×C13—44no—
340C4×C13—44no—
341Dic13—82no—
342Dic13—82no—
343Dic13—82no—
344Dic13—82no—
345C25C22×D1311yescharacteristic
346C25C22×D1311yescharacteristic
347C22×D4—24no—
348C22×D4—42no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4C2×Dic1314yes—
352C23×C4—41no—
353C23×C4—41no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—132no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4—132no—
360C23×C4C2×Dic1314yes—
361C23×C4C22×D1312yes—
362C23×C4C22×D1312yes—
363C23×C4C22×D1311yescharacteristic
364C2×C4⋊C4—522no—
365C2×C4⋊C4—522no—
366C2×C4⋊C4—522no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—264no—
371C2×C22⋊C4—264no—
372C2×C22⋊C4—522no—
373C2×C22⋊C4—522no—
374C2×C22⋊C4—522no—
375C2×C22⋊C4—522no—
376C2×C22⋊C4—521no—
377C2×C22⋊C4—521no—
378C2×C22⋊C4—522no—
379C2×C22⋊C4—522no—
380C2×C22⋊C4—522no—
381C2×C22⋊C4—522no—
382C2×C22⋊C4—522no—
383C2×C22⋊C4C2×Dic1314yes—
384C2×C22⋊C4C2×Dic1318yes—
385#95—522no—
386#95—522no—
387#95—522no—
388#95—522no—
389#95—522no—
390#95—522no—
391#95—521no—
392#95—521no—
393#95—522no—
394#95—522no—
395#95C2×Dic1318yes—
396C2×C13—44no—
397C2×C13—82no—
398C2×C13#231211yescharacteristic
399C2×C13#231812yes—
400C2×C13#237511yescharacteristic
401C2×C13#237611yescharacteristic
402C2×C13#237712yes—
403C2×C13#282412yes—
404C2×C13#282512yes—
405C2×C13#282612yes—
406C2×C13#282712yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24#612714yes—
423C24C22×Dic1312yes—
424C24C22×Dic1312yes—
425C24C23×D1311yescharacteristic
426C2×D4—28no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—48no—
430C2×D4—48no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—48no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—48no—
451C22×C4—44no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4C22×Dic1312yes—
481C22×C4C22×Dic1314yes—
482C22×C4C22×Dic1314yes—
483C4⋊C4—528no—
484C22⋊C4—48no—
485C22⋊C4—44no—
486C22⋊C4—528no—
487C22⋊C4—528no—
488C22⋊C4—524no—
489C22⋊C4—528no—
490C22⋊C4—524no—
491C13#1466611yescharacteristic, complemented, Sylow
492C23—24no—
493C23—24no—
494C23—22no—
495C23—22no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—24no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—41no—
508C23—42no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—42no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—41no—
531C23—41no—
532C23—42no—
533C23#8818014yes—
534C23C2×#612712yes—
535C23#8825111yescharacteristic
536C23#8825111yescharacteristic
537C23#8825112yes—
538C23#8825112yes—
539C23#8825112yes—
540C23#8825612yes—
541C23#8825712yes—
542C23C23×Dic1311yescharacteristic
543D4—416no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—416no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—522no—
575C2×C4—522no—
576C2×C4—522no—
577C2×C4—522no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4—522no—
587C2×C4—522no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C22—28no—
593C22—24no—
594C22—42no—
595C22—42no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—44no—
603C22—42no—
604C22—44no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22#1171919912yes—
611C22#1171919912yes—
612C22#1171926512yes—
613C22#1171926512yes—
614C22#1171926912yes—
615C22#1171926912yes—
616C22#1171929911yescharacteristic
617C22#1171930012yes—
618C22#1171930011yescharacteristic
619C22#1171932512yes—
620C22#1171932512yes—
621C22#1171932612yes—
622C22#1171932612yes—
623C22#1171935611yescharacteristic
624C22#1171937111yescharacteristic
625C22#1171937212yes—
626C22C2×#8818011yescharacteristic
627C22#1171950312yes—
628C22#1171950311yescharacteristic
629C22#1171950311yescharacteristic
630C22#1171953212yes—
631C4—44no—
632C4—44no—
633C4—42no—
634C4—1042no—
635C4—1042no—
636C4—1042no—
637C4—1042no—
638C2—44no—
639C2—82no—
640C2#1311743411yescharacteristic
641C2#1311746912yes—
642C2#1311797711yescharacteristic
643C2#1311798411yescharacteristic
644C2#1311799312yes—
645C2#1312291312yes—
646C2#1312292212yes—
647C2#1312293112yes—
648C2#1312294012yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#386C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#386D13
hypocenterC13#14666
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #13113098C2semidirect
2. #13113093C2semidirect
3. #13113085C2semidirect
4. #13113081C2semidirect
5. #13113081C2semidirect
8. #13113059C2semidirect
20. C13×#386C4semidirect
287. #386Dic13semidirect
491. C13#14666semidirect

Maximal subgroups

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

subgroupindex
#131130982
#131130932
#131130852
#131130812
#131130772
#131130592
C2×C13×#3862
#1466613