Finite Group Databasebeta

← #15793679

Subgroups — #15793679

Order 3328.

1586 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C212yesmaximal, complemented
2#13113093C212yesmaximal, complemented
3#13113089C211yesmaximal, characteristic, complemented
4#13113081C212yesmaximal, complemented
5#13113081C212yesmaximal, complemented
6#13113081C212yesmaximal, complemented
7#13113077C212yesmaximal
8#13113065C211yesmaximal, characteristic, 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
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C13×#394C418yescomplemented
23C2×C13×#95C2211yescharacteristic
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32#11718612—28no—
33C25×C13C2312yes—
34C22×D4×C13—42no—
35C22×D4×C13—42no—
36C22×D4×C13—41no—
37C22×D4×C13—41no—
38C22×D4×C13C2×C414yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C2×C13×C4⋊C4—41no—
48C2×C13×C4⋊C4—41no—
49C2×C13×C4⋊C4C2×C414yes—
50C2×C13×C22⋊C4—24no—
51C2×C13×C22⋊C4—24no—
52C2×C13×C22⋊C4—42no—
53C2×C13×C22⋊C4—42no—
54C2×C13×C22⋊C4C2×C418yes—
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—42no—
63C2×C22⋊Dic13—42no—
64C2×C22⋊Dic13—42no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13—42no—
67C2×C22⋊Dic13—42no—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—24no—
70C2×C4⋊Dic13—42no—
71C2×C4⋊Dic13—42no—
72C2×C4⋊Dic13—41no—
73C2×C4⋊Dic13—41no—
74C2×C4⋊Dic13—42no—
75C2×C4⋊Dic13—41no—
76C2×C4×Dic13—41no—
77C2×C4×Dic13—41no—
78C2×C4×Dic13D414yescomplemented
79C13×#95C2×C414yes—
80#88071—24no—
81#88071—24no—
82#88071—42no—
83#88071—42no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071—41no—
88#14632—131nomaximal, Sylow
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×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13C22×C414yes—
104C24×C13C2411yescharacteristic
105C2×D4×C13—44no—
106C2×D4×C13—48no—
107C2×D4×C13—44no—
108C2×D4×C13—48no—
109C2×D4×C13—44no—
110C22×C4×C13—21no—
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—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13C22×C414yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13#4112yes—
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—
160C22×Dic13—22no—
161C22×Dic13C2×D414yes—
162C13×C4⋊C4—44no—
163C13×C22⋊C4—216no—
164C13×C22⋊C4—48no—
165C22⋊Dic13—48no—
166C22⋊Dic13—48no—
167C22⋊Dic13—48no—
168C22⋊Dic13—48no—
169C4⋊Dic13—48no—
170C4⋊Dic13—44no—
171C4⋊Dic13—44no—
172C4×Dic13—44no—
173C2×#394D1311yescharacteristic
174C2×#388—132no—
175#1442—132no—
176#1441—131no—
177#1439—132no—
178#1439—132no—
179#1439—132no—
180#1438—132no—
181C4⋊#95—131no—
182C23×C13—24no—
183C23×C13—24no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—24no—
188C23×C13—24no—
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×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13C23×C411yescharacteristic
218C23×C13C22×D411yescharacteristic
219C23×C13C2×#4111yescharacteristic
220C23×C13H(5,𝔽2)11yescharacteristic
221C23×C13H(5,𝔽2)12yes—
222C23×C13H(5,𝔽2)11yescharacteristic
223C23×C13H(5,𝔽2)12yes—
224C23×C13H(5,𝔽2)11yescharacteristic
225C23×C13H(5,𝔽2)12yes—
226C23×C132−1+411yescharacteristic
227C23×C132−1+412yes—
228D4×C13—416no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—41no—
247C2×C4×C13—42no—
248C2×C4×C13—41no—
249C2×C4×C13—42no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13C4×D414yes—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
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—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C23×D4C2×D1311yescharacteristic
282C22×C4⋊C4—131no—
283C22×C4⋊C4—132no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4C2×D1311yescharacteristic
286C22×C22⋊C4—132no—
287C22×C22⋊C4—132no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—132no—
290C22×C22⋊C4C2×D1312yes—
291C22×C22⋊C4C2×D1312yes—
292C22×C42—131no—
293#394Dic1318yescomplemented
294#388—268no—
295C2×#95—132no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—131no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95C2×D1311yescharacteristic
304C22×C13—44no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—44no—
309C22×C13—44no—
310C22×C13—44no—
311C22×C13—82no—
312C22×C13—82no—
313C22×C13—82no—
314C22×C13—82no—
315C22×C13—82no—
316C22×C13—82no—
317C22×C13—82no—
318C22×C13—82no—
319C22×C13C2×C4×D411yescharacteristic
320C22×C13#51812yes—
321C22×C13#51811yescharacteristic
322C22×C13#52012yes—
323C22×C13#52011yescharacteristic
324C22×C13#53411yescharacteristic
325C22×C13#53512yes—
326C22×C13#53711yescharacteristic
327C22×C13#53712yes—
328C22×C13#53811yescharacteristic
329C22×C13#53911yescharacteristic
330C22×C13#54012yes—
331C22×C13#54212yes—
332C22×C13#56011yescharacteristic
333C22×C13#56012yes—
334C22×C13#56012yes—
335C22×C13H(3,𝔽4)11yescharacteristic
336C22×C13H(3,𝔽4)11yescharacteristic
337C22×C13#56212yes—
338C22×C13#56212yes—
339C22×C13#56212yes—
340C22×C13#56312yes—
341C22×C13#56311yescharacteristic
342C4×C13—24no—
343C4×C13—44no—
344C4×C13—42no—
345C4×C13—42no—
346Dic13—44no—
347Dic13—82no—
348Dic13—82no—
349Dic13—82no—
350C25C22×D1312yes—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—41no—
354C22×D4—41no—
355C22×D4C2×Dic1314yes—
356C23×C4—132no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4—132no—
360C23×C4C22×D1311yescharacteristic
361C23×C4C22×D1312yes—
362C23×C4C22×D1311yescharacteristic
363C23×C4C22×D1311yescharacteristic
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—521no—
369C2×C4⋊C4—521no—
370C2×C4⋊C4—522no—
371C2×C4⋊C4—522no—
372C2×C4⋊C4—522no—
373C2×C4⋊C4—521no—
374C2×C4⋊C4C2×Dic1314yes—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—264no—
380C2×C22⋊C4—264no—
381C2×C22⋊C4—522no—
382C2×C22⋊C4—522no—
383C2×C22⋊C4—522no—
384C2×C22⋊C4—522no—
385C2×C22⋊C4—522no—
386C2×C22⋊C4—522no—
387C2×C22⋊C4—522no—
388C2×C22⋊C4—522no—
389C2×C22⋊C4—522no—
390C2×C22⋊C4—522no—
391C2×C22⋊C4C2×Dic1318yes—
392C2×C22⋊C4C2×Dic1318yes—
393C2×C42—134no—
394C2×C42—521no—
395C2×C42—521no—
396#95—264no—
397#95—264no—
398#95—522no—
399#95—522no—
400#95—521no—
401#95—522no—
402#95—522no—
403#95—522no—
404#95C2×Dic1314yes—
405C2×C13—84no—
406C2×C13#232412yes—
407C2×C13#232511yescharacteristic
408C2×C13#237511yescharacteristic
409C2×C13#237612yes—
410C2×C13#237911yescharacteristic
411C2×C13#281312yes—
412C2×C13#281911yescharacteristic
413C2×C13#282311yescharacteristic
414C2×C13#282811yescharacteristic
415C2×C13#283211yescharacteristic
416C2×C13#283712yes—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24C22×Dic1314yes—
432C24C23×D1311yescharacteristic
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—48no—
437C2×D4—44no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—134no—
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×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4D4×D1312yes—
485C22×C4#612912yes—
486C22×C4C22×Dic1314yes—
487C22×C4C22×Dic1312yes—
488C22×C4C22×Dic1312yes—
489C22×C4C22×Dic1312yes—
490C4⋊C4—44no—
491C4⋊C4—524no—
492C4⋊C4—528no—
493C4⋊C4—524no—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C22⋊C4—528no—
497C22⋊C4—528no—
498C22⋊C4—528no—
499C22⋊C4—528no—
500C42—524no—
501C13#1463211yescharacteristic, complemented, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C2×D4×D1311yescharacteristic
538C23C2×#612911yescharacteristic
539C23#8825111yescharacteristic
540C23#8825112yes—
541C23#8825111yescharacteristic
542C23#8825112yes—
543C23#8825611yescharacteristic
544C23#8825612yes—
545C23#8825711yescharacteristic
546C23#8825712yes—
547C23C23×Dic1311yescharacteristic
548D4—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
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—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4D4×Dic1314yes—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22#1171929911yescharacteristic
617C22#1171930012yes—
618C22#1171930011yescharacteristic
619C22#1171930211yescharacteristic
620C22#1171930711yescharacteristic
621C22#1171930812yes—
622C22#1171931011yescharacteristic
623C22#1171931212yes—
624C22#1171931312yes—
625C22#1171932211yescharacteristic
626C22#1171932412yes—
627C22#1171935612yes—
628C22#1171937112yes—
629C22#1171937212yes—
630C22#1171937212yes—
631C22#1171937711yescharacteristic
632C22#1171938811yescharacteristic
633C22#1171938912yes—
634C22C2×D4×Dic1311yescharacteristic
635C22#1171950312yes—
636C22#1171950311yescharacteristic
637C22#1171953211yescharacteristic
638C22#1171953212yes—
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—524no—
644C4—1042no—
645C4—1042no—
646C4—1042no—
647C2—84no—
648C2#1311753112yes—
649C2#1311754111yescharacteristic
650C2#1311797711yescharacteristic
651C2#1311798412yes—
652C2#1311801011yescharacteristic
653C2#1312284312yes—
654C2#1312288011yescharacteristic
655C2#1312290711yescharacteristic
656C2#1312295911yescharacteristic
657C2#1312300711yescharacteristic
658C2#1312305212yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#394C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#394D13
hypocenterC13#14632
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#11718612C2semidirect
2. #13113093C2semidirect
3. #13113089C2semidirect
4. #13113081C2semidirect
5. #13113081C2semidirect
6. #13113081C2semidirect
8. #13113065C2semidirect
22. C13×#394C4semidirect
78. C2×C4×Dic13D4semidirect
293. #394Dic13semidirect
501. C13#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
#131130932
#131130892
#131130812
#131130772
#131130652
C2×C13×#3942
#1463213