Finite Group Databasebeta

← #15793523

Subgroups — #15793523

Order 3328.

1550 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13113104C211yesmaximal, characteristic, complemented
2#13113085C212yesmaximal, complemented
3#13113077C212yesmaximal
4#13113073C212yesmaximal, complemented
5#13113073C212yesmaximal, complemented
6#13113073C212yesmaximal, complemented
7#13113068C211yesmaximal, characteristic, complemented
8#13113061C212yesmaximal, complemented
9C2×C13×#394C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C22⋊C4C2212yes—
13C22×C13×C22⋊C4C2212yes—
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2212yes—
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2212yes—
18C22×C4×Dic13C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C13×#394C418yescomplemented
21C2×C13×#95C2211yescharacteristic
22C2×#88071C2212yes—
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C25×C13C2312yes—
33C22×D4×C13—42no—
34C22×D4×C13—42no—
35C22×D4×C13—41no—
36C22×D4×C13—41no—
37C22×D4×C13C2×C414yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C2×C13×C4⋊C4—41no—
47C2×C13×C4⋊C4—41no—
48C2×C13×C4⋊C4C2×C414yes—
49C2×C13×C22⋊C4—42no—
50C2×C13×C22⋊C4—42no—
51C2×C13×C22⋊C4—42no—
52C2×C13×C22⋊C4—42no—
53C2×C13×C22⋊C4C2×C418yes—
54C2×C13×C22⋊C4C2×C418yes—
55C2×C22⋊Dic13—24no—
56C2×C22⋊Dic13—24no—
57C2×C22⋊Dic13—24no—
58C2×C22⋊Dic13—24no—
59C2×C22⋊Dic13—24no—
60C2×C22⋊Dic13—24no—
61C2×C22⋊Dic13—42no—
62C2×C22⋊Dic13—42no—
63C2×C22⋊Dic13—42no—
64C2×C22⋊Dic13—42no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13—42no—
67C2×C4×Dic13—24no—
68C2×C4×Dic13—42no—
69C2×C4×Dic13—42no—
70C2×C4×Dic13—42no—
71C2×C4×Dic13—41no—
72C13×#95C2×C414yes—
73#88071—24no—
74#88071—24no—
75#88071—42no—
76#88071—42no—
77#88071—42no—
78#88071—42no—
79#88071—41no—
80#88071—41no—
81#88071—42no—
82#88071—41no—
83#14617—131nomaximal, Sylow
84C24×C13—22no—
85C24×C13—22no—
86C24×C13—22no—
87C24×C13—22no—
88C24×C13—22no—
89C24×C13—22no—
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13C22×C414yes—
99C24×C13C2411yescharacteristic
100C2×D4×C13—44no—
101C2×D4×C13—48no—
102C2×D4×C13—44no—
103C2×D4×C13—48no—
104C2×D4×C13—44no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13C22×C414yes—
124C22×C4×C13C22×C412yes—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C22×C412yes—
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—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#4114yes—
153C22×Dic13#4114yes—
154C22×Dic13#4114yes—
155C13×C4⋊C4—44no—
156C13×C22⋊C4—48no—
157C13×C22⋊C4—48no—
158C22⋊Dic13—48no—
159C22⋊Dic13—48no—
160C22⋊Dic13—48no—
161C22⋊Dic13—48no—
162C4×Dic13—48no—
163C4×Dic13—44no—
164C2×#394D1311yescharacteristic
165#1445—131no—
166#1440—132no—
167#1438—132no—
168#1437—132no—
169#1437—132no—
170#1437—132no—
171#1436—131no—
172#1434—132no—
173C23×C13—24no—
174C23×C13—24no—
175C23×C13—24no—
176C23×C13—24no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—24no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—42no—
195C23×C13—42no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13C23×C411yescharacteristic
209C23×C13C2×#4112yes—
210C23×C13C2×#4112yes—
211C23×C13C2×#4112yes—
212C23×C13H(5,𝔽2)12yes—
213C23×C13H(5,𝔽2)11yescharacteristic
214C23×C13H(5,𝔽2)12yes—
215C23×C13H(5,𝔽2)12yes—
216C23×C13H(5,𝔽2)11yescharacteristic
217D4×C13—416no—
218C2×C4×C13—24no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—41no—
235C2×C4×C13—42no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×Dic13—24no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—24no—
248C2×Dic13—24no—
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—
268C23×D4C2×D1311yescharacteristic
269C22×C4⋊C4C2×D1311yescharacteristic
270C22×C22⋊C4—132no—
271C22×C22⋊C4—132no—
272C22×C22⋊C4—132no—
273C22×C22⋊C4—132no—
274C22×C22⋊C4C2×D1312yes—
275C22×C22⋊C4C2×D1312yes—
276C22×C42—132no—
277C22×C42—131no—
278#394Dic1318yescomplemented
279C2×#95—132no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—131no—
286C2×#95—131no—
287C2×#95—132no—
288C2×#95—131no—
289C2×#95C2×D1311yescharacteristic
290C22×C13—44no—
291C22×C13—44no—
292C22×C13—44no—
293C22×C13—44no—
294C22×C13—44no—
295C22×C13—44no—
296C22×C13—44no—
297C22×C13—82no—
298C22×C13—82no—
299C22×C13—82no—
300C22×C13—82no—
301C22×C13—82no—
302C22×C13—82no—
303C22×C13—82no—
304C22×C13—82no—
305C22×C13C4×#4112yes—
306C22×C13C4×#4111yescharacteristic
307C22×C13#51811yescharacteristic
308C22×C13#51811yescharacteristic
309C22×C13#51812yes—
310C22×C13#53812yes—
311C22×C13#53812yes—
312C22×C13#53812yes—
313C22×C13#54012yes—
314C22×C13#54012yes—
315C22×C13#54012yes—
316C22×C13#55112yes—
317C22×C13#55112yes—
318C22×C13#55312yes—
319C22×C13#55312yes—
320C22×C13#55511yescharacteristic
321C22×C13#55511yescharacteristic
322C22×C13#55912yes—
323C22×C13#56011yescharacteristic
324C22×C13#56012yes—
325C22×C13H(3,𝔽4)11yescharacteristic
326C4×C13—42no—
327C4×C13—44no—
328C4×C13—42no—
329C4×C13—42no—
330Dic13—44no—
331Dic13—44no—
332Dic13—44no—
333Dic13—82no—
334C25C22×D1312yes—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4C2×Dic1314yes—
340C23×C4—132no—
341C23×C4—132no—
342C23×C4—132no—
343C23×C4—132no—
344C23×C4C22×D1311yescharacteristic
345C23×C4C22×D1311yescharacteristic
346C23×C4C22×D1312yes—
347C23×C4C22×D1311yescharacteristic
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4C2×Dic1314yes—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—264no—
356C2×C22⋊C4—264no—
357C2×C22⋊C4—264no—
358C2×C22⋊C4—264no—
359C2×C22⋊C4—264no—
360C2×C22⋊C4—264no—
361C2×C22⋊C4—522no—
362C2×C22⋊C4—522no—
363C2×C22⋊C4—522no—
364C2×C22⋊C4—522no—
365C2×C22⋊C4—522no—
366C2×C22⋊C4—522no—
367C2×C22⋊C4C2×Dic1318yes—
368C2×C22⋊C4C2×Dic1318yes—
369C2×C42—264no—
370C2×C42—522no—
371C2×C42—522no—
372C2×C42—522no—
373C2×C42—521no—
374#95—264no—
375#95—264no—
376#95—522no—
377#95—522no—
378#95—522no—
379#95—521no—
380#95—521no—
381#95—521no—
382#95—522no—
383#95—522no—
384#95C2×Dic1314yes—
385C2×C13—84no—
386C2×C13#233312yes—
387C2×C13#233311yescharacteristic
388C2×C13#237211yescharacteristic
389C2×C13#237412yes—
390C2×C13#237511yescharacteristic
391C2×C13#275212yes—
392C2×C13#275312yes—
393C2×C13#275612yes—
394C2×C13#280312yes—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C22×Dic1314yes—
410C24C23×D1311yescharacteristic
411C2×D4—44no—
412C2×D4—48no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—48no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—134no—
435C22×C4—134no—
436C22×C4—134no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
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×C4C22×Dic1314yes—
463C22×C4C22×Dic1312yes—
464C22×C4C22×Dic1312yes—
465C22×C4C22×Dic1312yes—
466C4⋊C4—44no—
467C22⋊C4—48no—
468C22⋊C4—48no—
469C22⋊C4—528no—
470C22⋊C4—528no—
471C22⋊C4—528no—
472C22⋊C4—528no—
473C42—528no—
474C42—524no—
475C13#1461711yescharacteristic, complemented, Sylow
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#8825112yes—
512C23#8825111yescharacteristic
513C23#8825111yescharacteristic
514C23#8825112yes—
515C23#8825112yes—
516C23#41×D1312yes—
517C23#41×D1312yes—
518C23#41×D1312yes—
519C23C23×Dic1311yescharacteristic
520D4—416no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—264no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—264no—
549C2×C4—264no—
550C2×C4—264no—
551C2×C4—264no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22#1171929911yescharacteristic
587C22#1171930011yescharacteristic
588C22#1171930012yes—
589C22#1171931812yes—
590C22#1171931812yes—
591C22#1171931812yes—
592C22#1171932012yes—
593C22#1171932012yes—
594C22#1171932012yes—
595C22#1171936412yes—
596C22#1171936612yes—
597C22#1171936612yes—
598C22#1171936912yes—
599C22#1171937511yescharacteristic
600C22#1171937511yescharacteristic
601C22#1171938412yes—
602C22#1171950312yes—
603C22#1171950311yescharacteristic
604C22#1171950311yescharacteristic
605C22#41×Dic1311yescharacteristic
606C22#41×Dic1312yes—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—44no—
611C4—524no—
612C4—524no—
613C4—524no—
614C4—1042no—
615C2—84no—
616C2#1311760312yes—
617C2#1311760311yescharacteristic
618C2#1311794811yescharacteristic
619C2#1311797212yes—
620C2#1311797711yescharacteristic
621C2#1312210212yes—
622C2#1312211212yes—
623C2#1312216312yes—
624C2#1312277612yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#394C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#394D13
hypocenterC13#14617
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13113104C2semidirect
2. #13113085C2semidirect
4. #13113073C2semidirect
5. #13113073C2semidirect
6. #13113073C2semidirect
7. #13113068C2semidirect
8. #13113061C2semidirect
20. C13×#394C4semidirect
278. #394Dic13semidirect
475. C13#14617semidirect

Maximal subgroups

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

subgroupindex
#131131042
#131130852
#131130772
#131130732
#131130682
#131130612
C2×C13×#3942
#1461713