Finite Group Databasebeta

← #15785245

Subgroups — #15785245

Order 3328.

1730 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C212yesmaximal
2C2×#11718597C211yesmaximal, characteristic, complemented
3C2×#11718873C211yesmaximal, characteristic
4#13113101C212yesmaximal, complemented
5#13113081C212yesmaximal
6#13113070C212yesmaximal, complemented
7#13113066C211yesmaximal, characteristic, complemented
8#13113063C211yesmaximal, characteristic, complemented
9#13113059C211yesmaximal, characteristic
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2212yes—
20C22×C4⋊Dic13C2212yes—
21C22×C4⋊Dic13C2212yes—
22C22×C4×Dic13C2212yes—
23C4×C13×C22⋊C4C418yescomplemented
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2211yescharacteristic
26#11718873—24no—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37#11718612—28no—
38#11718597—24no—
39C25×C13C2311yescharacteristic
40C23×C4×C13—22no—
41C23×C4×C13—24no—
42C23×C4×C13—22no—
43C23×C4×C13—42no—
44C23×C4×C13C2×C414yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2312yes—
53C23×Dic13C2312yes—
54C23×Dic13C2312yes—
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4C2×C414yes—
57C2×C13×C22⋊C4C2×C414yes—
58C2×C13×C22⋊C4D414yes—
59C2×C13×C22⋊C4Q814yes—
60C2×C42×C13—22no—
61C2×C42×C13—22no—
62C2×C42×C13—42no—
63C2×C42×C13C2×C414yes—
64C2×C42×C13C2×C414yes—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13—24no—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—24no—
69C2×C22⋊Dic13—42no—
70C2×C22⋊Dic13—42no—
71C2×C4⋊Dic13—24no—
72C2×C4⋊Dic13—24no—
73C2×C4⋊Dic13—24no—
74C2×C4⋊Dic13—24no—
75C2×C4⋊Dic13—24no—
76C2×C4⋊Dic13—42no—
77C2×C4⋊Dic13—42no—
78C2×C4⋊Dic13—42no—
79C2×C4⋊Dic13—42no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—42no—
83C13×#95C2×C414yes—
84C13×#95C2×C414yes—
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—22no—
92#88071—24no—
93#88071—24no—
94#88071D414yes—
95#13915—131nomaximal, Sylow
96C24×C13—21no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—21no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13C22×C412yes—
105C24×C13C2×D412yes—
106C24×C13C2×Q812yes—
107C24×C13C2411yescharacteristic
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—28no—
127C22×C4×C13—28no—
128C22×C4×C13—44no—
129C22×C4×C13—48no—
130C22×C4×C13—48no—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×Q812yes—
141C22×C4×C13C2×Q812yes—
142C22×C4×C13#4114yes—
143C22×C4×C13#4114yes—
144C22×C4×C13#4112yes—
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×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13C2×D414yes—
172C22×Dic13#4114yes—
173C13×C22⋊C4—28no—
174C13×C22⋊C4C4⋊C4116yescomplemented
175C42×C13—28no—
176C42×C13—44no—
177C22⋊Dic13—48no—
178C22⋊Dic13—48no—
179C4⋊Dic13—48no—
180C4⋊Dic13—48no—
181C4⋊Dic13—48no—
182C4×Dic13—48no—
183C2×#388—132no—
184C2×#382—131no—
185C2×#380—131no—
186C2×C4×C22⋊C4D1311yescharacteristic
187#1444—132no—
188#1439—132no—
189#1436—132no—
190C4⋊#95—131no—
191#1434—131no—
192C22⋊#95—131no—
193C4×#95—131no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—22no—
203C23×C13—24no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—24no—
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×C13C2×C4⋊C414yes—
217C23×C13C23×C411yescharacteristic
218C23×C13C22×D411yescharacteristic
219C23×C13C22×D411yescharacteristic
220C23×C13C22×Q811yescharacteristic
221C23×C13C2×#4112yes—
222C23×C13C2×#4112yes—
223C23×C13C2×#4111yescharacteristic
224C23×C13C2×#4112yes—
225C23×C13H(5,𝔽2)12yes—
226C23×C13H(5,𝔽2)11yescharacteristic
227C23×C132−1+411yescharacteristic
228C2×C4×C13—22no—
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—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—24no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—416no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13C2×C4⋊C414yes—
257C2×C4×C13C2×C4⋊C414yes—
258C2×C4×C13#11714yes—
259C2×C4×C13#11714yes—
260C2×C4×C13C4×D414yes—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
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—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C24×C4C2×D1311yescharacteristic
290C22×C4⋊C4—132no—
291C22×C4⋊C4—132no—
292C22×C4⋊C4—132no—
293C22×C22⋊C4—132no—
294C22×C22⋊C4—132no—
295C22×C22⋊C4C2×D1311yescharacteristic
296C22×C22⋊C4C2×D1311yescharacteristic
297C22×C42—132no—
298C22×C42C2×D1311yescharacteristic
299C22×C42C2×D1311yescharacteristic
300#388—268no—
301#382—264no—
302#380—264no—
303C4×C22⋊C4Dic1318yescomplemented
304C2×#95—131no—
305C2×#95—131no—
306C2×#95—132no—
307C2×#95—131no—
308C2×#95—132no—
309C2×#95—131no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95C2×D1311yescharacteristic
315C2×#95C2×D1311yescharacteristic
316C22×C13—24no—
317C22×C13—24no—
318C22×C13—24no—
319C22×C13—42no—
320C22×C13—44no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—44no—
325C22×C13—44no—
326C22×C13—44no—
327C22×C13C22×C4⋊C411yescharacteristic
328C22×C13C2×#11711yescharacteristic
329C22×C13C2×#11711yescharacteristic
330C22×C13C2×C4×D411yescharacteristic
331C22×C13C4×#4111yescharacteristic
332C22×C13#51811yescharacteristic
333C22×C13#52011yescharacteristic
334C22×C13#52912yes—
335C22×C13#53212yes—
336C22×C13#53212yes—
337C22×C13#53312yes—
338C22×C13#53812yes—
339C22×C13#53912yes—
340C22×C13D4211yescharacteristic
341C22×C13#54612yes—
342C22×C13#54612yes—
343C22×C13#54711yescharacteristic
344C22×C13D4×Q811yescharacteristic
345C22×C13#55112yes—
346C22×C13#55212yes—
347C22×C13#55412yes—
348C22×C13#55411yescharacteristic
349C22×C13#55512yes—
350C4×C13—24no—
351C4×C13—24no—
352C4×C13—24no—
353C4×C13—24no—
354C4×C13—24no—
355C4×C13—42no—
356Dic13—44no—
357Dic13—44no—
358Dic13—82no—
359Dic13—82no—
360C25C22×D1311yescharacteristic
361C23×C4—24no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—42no—
365C23×C4—132no—
366C23×C4—132no—
367C23×C4—132no—
368C23×C4—132no—
369C23×C4C2×Dic1314yes—
370C23×C4C22×D1311yescharacteristic
371C23×C4C22×D1311yescharacteristic
372C23×C4C22×D1311yescharacteristic
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C2×C4⋊C4—264no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4—522no—
382C2×C4⋊C4—522no—
383C2×C4⋊C4—522no—
384C2×C4⋊C4—522no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4—264no—
388C2×C22⋊C4—264no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—522no—
391C2×C22⋊C4—522no—
392C2×C22⋊C4Dic2614yes—
393C2×C22⋊C4D5214yes—
394C2×C22⋊C4C2×Dic1314yes—
395C2×C22⋊C4C2×Dic1314yes—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—42no—
399C2×C42—264no—
400C2×C42—264no—
401C2×C42—522no—
402C2×C42C2×Dic1314yes—
403C2×C42C2×Dic1314yes—
404#95—134no—
405#95—264no—
406#95—264no—
407#95—264no—
408#95—264no—
409#95—264no—
410#95—264no—
411#95—262no—
412#95—262no—
413#95—262no—
414#95C2×Dic1314yes—
415#95C2×Dic1314yes—
416C2×C13—44no—
417C2×C13#228511yescharacteristic
418C2×C13#229311yescharacteristic
419C2×C13#231811yescharacteristic
420C2×C13#234211yescharacteristic
421C2×C13#234611yescharacteristic
422C2×C13D4×C4⋊C411yescharacteristic
423C2×C13#234911yescharacteristic
424C2×C13#255312yes—
425C2×C13#255512yes—
426C2×C13#255612yes—
427C2×C13#257412yes—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24C2×Dic2612yes—
437C24C2×D5212yes—
438C24C22×Dic1312yes—
439C24C23×D1311yescharacteristic
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—44no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—134no—
464C22×C4—134no—
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×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4C2×Dic2612yes—
492C22×C4C2×Dic2612yes—
493C22×C4C2×D5212yes—
494C22×C4C2×D5212yes—
495C22×C4#612714yes—
496C22×C4#612714yes—
497C22×C4D4×D1312yes—
498C22×C4#612912yes—
499C22×C4C22×Dic1312yes—
500C22×C4C22×Dic1312yes—
501C22×C4C22×Dic1312yes—
502C22×C4C22×Dic1312yes—
503C22×C4C22×Dic1312yes—
504C22×C4C22×Dic1312yes—
505C4⋊C4—528no—
506C4⋊C4—528no—
507C4⋊C4—528no—
508C22⋊C4—28no—
509C22⋊C4—528no—
510C22⋊C4—528no—
511C22⋊C4C4⋊Dic13116yescomplemented
512C42—28no—
513C42—44no—
514C42—528no—
515C13#1391511yescharacteristic, complemented, Sylow
516C23—24no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—24no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23C2×C4⋊Dic1314yes—
539C23C22×Dic2611yescharacteristic
540C23C22×D5211yescharacteristic
541C23C2×#612712yes—
542C23C2×#612712yes—
543C23C2×D4×D1311yescharacteristic
544C23C2×#612911yescharacteristic
545C23#8825112yes—
546C23#41×D1312yes—
547C23#8825611yescharacteristic
548C23#8825711yescharacteristic
549C23C23×Dic1311yescharacteristic
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—416no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—264no—
581C2×C4—264no—
582C2×C4—264no—
583C2×C4—264no—
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×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4C2×C4⋊Dic1314yes—
607C2×C4C2×C4⋊Dic1314yes—
608C2×C4#8818014yes—
609C2×C4#8818014yes—
610C2×C4D4×Dic1314yes—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—42no—
615C22—42no—
616C22—44no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22#1171917512yes—
623C22#1171918212yes—
624C22#1171919512yes—
625C22#1171920012yes—
626C22#1171923412yes—
627C22#1171923712yes—
628C22D4×Dic2611yescharacteristic
629C22#1171924412yes—
630C22#1171924811yescharacteristic
631C22#1171925312yes—
632C22D4×D5211yescharacteristic
633C22#1171925912yes—
634C22#1171926011yescharacteristic
635C22#1171926212yes—
636C22#1171926512yes—
637C22#1171926912yes—
638C22C22×C4⋊Dic1311yescharacteristic
639C22C2×#8818011yescharacteristic
640C22C2×#8818011yescharacteristic
641C22C2×D4×Dic1311yescharacteristic
642C22#1171950311yescharacteristic
643C22#41×Dic1311yescharacteristic
644C22#1171953211yescharacteristic
645C4—24no—
646C4—24no—
647C4—24no—
648C4—24no—
649C4—24no—
650C4—42no—
651C4—524no—
652C4—524no—
653C4—1042no—
654C4—1042no—
655C2—44no—
656C2#1311724311yescharacteristic
657C2#1311730111yescharacteristic
658C2#1311746911yescharacteristic
659C2#1311768511yescharacteristic
660C2#1311772111yescharacteristic
661C2D4×C4⋊Dic1311yescharacteristic
662C2#1311774611yescharacteristic
663C2#1311987512yes—
664C2#1311990512yes—
665C2#1311992012yes—
666C2#1312011012yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13915
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718597C2semidirect
4. #13113101C2semidirect
6. #13113070C2semidirect
7. #13113066C2semidirect
8. #13113063C2semidirect
10. C4×#88071C2semidirect
23. C4×C13×C22⋊C4C4semidirect
174. C13×C22⋊C4C4⋊C4semidirect
303. C4×C22⋊C4Dic13semidirect
511. C22⋊C4C4⋊Dic13semidirect
515. C13#13915semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117185972
C2×#117188732
#131131012
#131130812
#131130702
#131130662
#131130632
#131130592
C4×#880712
C2×C4×C13×C22⋊C42
#1391513