Finite Group Databasebeta

← #15786591

Subgroups — #15786591

Order 3328.

1862 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×Dic13C211yesmaximal, characteristic
2C22×#88071C211yesmaximal, characteristic
3#13113104C212yesmaximal, complemented
4#13113098C212yesmaximal, complemented
5#13113068C212yesmaximal, complemented
6#13113061C212yesmaximal, complemented
7#13113059C211yesmaximal, characteristic
8#13113058C211yesmaximal, characteristic
9#13113058C211yesmaximal, characteristic
10#13113058C211yesmaximal, characteristic
11C2×C13×#385C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C24×Dic13C2211yescharacteristic
14C24×Dic13C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic13C2211yescharacteristic
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C13×#385C418yescomplemented
23C2×C13×#95C2212yes—
24C2×#88071—24no—
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C22⋊C4×Dic13—24no—
38C25×C13C2311yescharacteristic
39C23×C4×C13—22no—
40C23×C4×C13—22no—
41C23×C4×C13—42no—
42C23×C4×C13—42no—
43C23×C4×C13C2×C414yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2312yes—
48C23×Dic13—22no—
49C23×Dic13—22no—
50C23×Dic13—22no—
51C23×Dic13—24no—
52C23×Dic13—24no—
53C23×Dic13—22no—
54C23×Dic13—22no—
55C23×Dic13—42no—
56C23×Dic13—42no—
57C23×Dic13D414yes—
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2312yes—
63C23×Dic13C2311yescharacteristic
64C2×C13×C4⋊C4—42no—
65C2×C13×C4⋊C4—42no—
66C2×C13×C4⋊C4C2×C418yescomplemented
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4C2×C414yes—
72C2×C13×C22⋊C4C2×C414yes—
73C2×C22⋊Dic13—22no—
74C2×C22⋊Dic13—22no—
75C2×C22⋊Dic13—22no—
76C2×C22⋊Dic13—22no—
77C2×C22⋊Dic13—22no—
78C2×C22⋊Dic13Q814yes—
79C2×C4×Dic13—22no—
80C2×C4×Dic13—22no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—42no—
83C13×#95C2×C418yescomplemented
84#88071—22no—
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—24no—
89#88071—24no—
90#88071—24no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#88071—42no—
95#88071—42no—
96#14040—131nomaximal, Sylow
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13C22×C412yes—
102C24×C13C2×D412yes—
103C24×C13C2×Q812yes—
104C24×C13#4112yes—
105C24×C13#4112yes—
106C24×C13#4112yes—
107C24×C13#4112yes—
108C24×C13C2411yescharacteristic
109C22×C4×C13—28no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
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—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—48no—
131C22×C4×C13—44no—
132C22×C4×C13—44no—
133C22×C4×C13—48no—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C22×C414yes—
136C22×C4×C13C22×C414yes—
137C22×C4×C13C22×C412yes—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—28no—
142C22×Dic13—28no—
143C22×Dic13—22no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
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×Dic13—28no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—44no—
170C22×Dic13—48no—
171C22×Dic13—48no—
172C22×Dic13—48no—
173C22×Dic13—48no—
174C22×Dic13—44no—
175C22×Dic13—44no—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D412yes—
178C22×Dic13C2×Q812yes—
179C22×Dic13C2×Q812yes—
180C22×Dic13#4114yes—
181C22×Dic13#4114yes—
182C13×C4⋊C4—48no—
183C13×C22⋊C4—28no—
184C13×C22⋊C4—28no—
185C22⋊Dic13—28no—
186C22⋊Dic13—44no—
187C4×Dic13—44no—
188C4×Dic13—44no—
189C2×#385D1311yescharacteristic
190C2×C4×C22⋊C4—131no—
191C22×#95—131no—
192#1445—132no—
193#1443—132no—
194#1436—132no—
195#1434—132no—
196C22⋊#95—131no—
197C22⋊#95—131no—
198C22⋊#95—131no—
199C22⋊#95—131no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—24no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—24no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—24no—
213C23×C13—24no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13#11714yes—
217C23×C13C4×D414yes—
218C23×C13C4×Q814yes—
219C23×C13C22⋊Q814yes—
220C23×C13#12314yes—
221C23×C13#12514yes—
222C23×C13#12614yes—
223C23×C13C23×C411yescharacteristic
224C23×C13C22×D411yescharacteristic
225C23×C13C22×Q811yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13C2×#4111yescharacteristic
230C23×C13C2×#4112yes—
231C23×C13C2×#4112yes—
232C23×C13H(5,𝔽2)12yes—
233C23×C13H(5,𝔽2)12yes—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—416no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—42no—
248C2×C4×C13—41no—
249C2×C4×C13—42no—
250C2×C4×C13—41no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—24no—
268C2×Dic13—22no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—416no—
274C2×Dic13—416no—
275C2×Dic13—41no—
276C2×Dic13—42no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13#12314yes—
295C24×C4—131no—
296C24×C4—131no—
297C24×C4C2×D1311yescharacteristic
298C22×C4⋊C4C2×D1312yes—
299C22×C22⋊C4—131no—
300C22×C22⋊C4—131no—
301C22×C22⋊C4C2×D1311yescharacteristic
302C22×C22⋊C4C2×D1311yescharacteristic
303C22×C42—131no—
304C22×C42—131no—
305#385Dic1318yescomplemented
306C4×C22⋊C4—264no—
307C2×#95—132no—
308C2×#95—132no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—131no—
312C2×#95—132no—
313C2×#95—131no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95—132no—
317C2×#95—132no—
318C2×#95—132no—
319C2×#95—264no—
320C2×#95C2×D1312yes—
321C22×C13—24no—
322C22×C13—24no—
323C22×C13—28no—
324C22×C13—28no—
325C22×C13—24no—
326C22×C13—24no—
327C22×C13—24no—
328C22×C13—28no—
329C22×C13—28no—
330C22×C13—24no—
331C22×C13#38718yes—
332C22×C13C2×#11711yescharacteristic
333C22×C13C2×C4×D411yescharacteristic
334C22×C13C2×C4×Q811yescharacteristic
335C22×C13C4×#4112yes—
336C22×C13#51812yes—
337C22×C13C2×C22⋊Q811yescharacteristic
338C22×C13C2×#12311yescharacteristic
339C22×C13C2×#12311yescharacteristic
340C22×C13#52511yescharacteristic
341C22×C13C2×#12511yescharacteristic
342C22×C13C2×#12611yescharacteristic
343C22×C13#52912yes—
344C22×C13#53411yescharacteristic
345C22×C13#53511yescharacteristic
346C22×C13#53812yes—
347C22×C13#55112yes—
348C22×C13#55112yes—
349C22×C13#55112yes—
350C22×C13#55112yes—
351C22×C13#55312yes—
352C22×C13#55312yes—
353C22×C13#55412yes—
354C22×C13#55412yes—
355C4×C13—42no—
356C4×C13—44no—
357C4×C13—44no—
358C4×C13—42no—
359Dic13—24no—
360Dic13—42no—
361Dic13—44no—
362Dic13—42no—
363Dic13—42no—
364Dic13—82no—
365C25C22×D1311yescharacteristic
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—131no—
373C23×C4—131no—
374C23×C4—132no—
375C23×C4—134no—
376C23×C4—132no—
377C23×C4—264no—
378C23×C4—264no—
379C23×C4—262no—
380C23×C4—262no—
381C23×C4—262no—
382C23×C4—262no—
383C23×C4—262no—
384C23×C4—522no—
385C23×C4—522no—
386C23×C4C2×Dic1314yes—
387C23×C4C22×D1311yescharacteristic
388C23×C4C22×D1312yes—
389C23×C4C22×D1311yescharacteristic
390C23×C4C22×D1312yes—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×Dic1318yescomplemented
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—134no—
399C2×C22⋊C4—262no—
400C2×C22⋊C4—262no—
401C2×C22⋊C4—262no—
402C2×C22⋊C4—262no—
403C2×C22⋊C4—262no—
404C2×C22⋊C4C2×Dic1314yes—
405C2×C22⋊C4C2×Dic1314yes—
406C2×C42—262no—
407C2×C42—262no—
408C2×C42—264no—
409C2×C42—522no—
410#95—264no—
411#95—264no—
412#95—264no—
413#95—264no—
414#95—264no—
415#95—262no—
416#95—262no—
417#95—522no—
418#95—522no—
419#95—522no—
420#95—522no—
421#95—522no—
422#95C2×Dic1318yescomplemented
423C2×C13—28no—
424C2×C13C2×#38711yescharacteristic
425C2×C13C4×#12311yescharacteristic
426C2×C13#232111yescharacteristic
427C2×C13#235312yes—
428C2×C13#236812yes—
429C2×C13#248211yescharacteristic
430C2×C13#248311yescharacteristic
431C2×C13#248711yescharacteristic
432C2×C13#250512yes—
433C2×C13#251012yes—
434C2×C13#257911yescharacteristic
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24#612712yes—
440C24#612712yes—
441C24D4×D1312yes—
442C24#612912yes—
443C24Q8×D1312yes—
444C24#613112yes—
445C24C22×Dic1312yes—
446C24C23×D1311yescharacteristic
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—48no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—48no—
472C22×C4—132no—
473C22×C4—134no—
474C22×C4—132no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—134no—
478C22×C4—268no—
479C22×C4—261no—
480C22×C4—262no—
481C22×C4—261no—
482C22×C4—268no—
483C22×C4—268no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—261no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—524no—
510C22×C4—528no—
511C22×C4—528no—
512C22×C4—528no—
513C22×C4—528no—
514C22×C4—524no—
515C22×C4—524no—
516C22×C4C22×Dic1312yes—
517C22×C4C22×Dic1314yes—
518C22×C4C22×Dic1314yes—
519C22×C4C22×Dic1312yes—
520C4⋊C4—48no—
521C22⋊C4—28no—
522C22⋊C4—28no—
523C22⋊C4—268no—
524C22⋊C4—524no—
525C42—524no—
526C42—524no—
527C13#1404011yescharacteristic, complemented, Sylow
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—22no—
535C23—22no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—22no—
543C23—22no—
544C23#8814314yes—
545C23#8814814yes—
546C23#8815014yes—
547C23#8815214yes—
548C23#8818014yes—
549C23D4×Dic1314yes—
550C23Q8×Dic1314yes—
551C23C2×#612711yescharacteristic
552C23C2×#612711yescharacteristic
553C23C2×D4×D1311yescharacteristic
554C23C2×#612911yescharacteristic
555C23#8825112yes—
556C23#8825112yes—
557C23C2×Q8×D1311yescharacteristic
558C23C2×#613111yescharacteristic
559C23#41×D1312yes—
560C23#41×D1312yes—
561C23C23×Dic1311yescharacteristic
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—416no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—134no—
588C2×C4—262no—
589C2×C4—264no—
590C2×C4—262no—
591C2×C4—264no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—264no—
596C2×C4—262no—
597C2×C4—264no—
598C2×C4—264no—
599C2×C4—264no—
600C2×C4—262no—
601C2×C4—264no—
602C2×C4—5216no—
603C2×C4—5216no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—522no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—522no—
612C2×C4—522no—
613C2×C4—522no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4—522no—
621C2×C4—522no—
622C2×C4—522no—
623C22—24no—
624C22—28no—
625C22—28no—
626C22—24no—
627C22—24no—
628C22—28no—
629C22—24no—
630C22—24no—
631C22—24no—
632C22—28no—
633C22#1171864218yes—
634C22C2×#8814311yescharacteristic
635C22C2×#8814811yescharacteristic
636C22C2×#8815011yescharacteristic
637C22C2×#8815211yescharacteristic
638C22#1171924512yes—
639C22#1171924512yes—
640C22#1171926112yes—
641C22#1171926112yes—
642C22#1171929411yescharacteristic
643C22#1171929711yescharacteristic
644C22#1171929812yes—
645C22#1171934112yes—
646C22#1171934112yes—
647C22#1171934212yes—
648C22#1171934212yes—
649C22#1171935412yes—
650C22D13×#12311yescharacteristic
651C22#1171936111yescharacteristic
652C22C2×#8818011yescharacteristic
653C22C2×D4×Dic1311yescharacteristic
654C22#1171950312yes—
655C22C2×Q8×Dic1311yescharacteristic
656C22#41×Dic1312yes—
657C4—42no—
658C4—44no—
659C4—44no—
660C4—42no—
661C4—264no—
662C4—524no—
663C4—522no—
664C4—522no—
665C4—522no—
666C4—1042no—
667C2—28no—
668C2C2×#1171864211yescharacteristic
669C2#123×Dic1311yescharacteristic
670C2#1311749711yescharacteristic
671C2#1311777612yes—
672C2#1311792112yes—
673C2#1311910911yescharacteristic
674C2#1311911611yescharacteristic
675C2#1311915211yescharacteristic
676C2#1311933512yes—
677C2#1311940212yes—
678C2#1312018811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14040
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #13113104C2semidirect
4. #13113098C2semidirect
5. #13113068C2semidirect
6. #13113061C2semidirect
22. C13×#385C4semidirect
66. C2×C13×C4⋊C4C2×C4semidirect
83. C13×#95C2×C4semidirect
305. #385Dic13semidirect
393. C2×C4⋊C4C2×Dic13semidirect
422. #95C2×Dic13semidirect
527. C13#14040semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×Dic132
C22×#880712
#131131042
#131130982
#131130682
#131130612
#131130592
#131130582
C2×C13×#3852
#1404013