Finite Group Databasebeta

← #15793201

Subgroups — #15793201

Order 3328.

1650 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#13113089C211yesmaximal, characteristic, complemented
3#13113081C212yesmaximal, complemented
4#13113077C212yesmaximal
5#13113073C212yesmaximal, complemented
6#13113073C212yesmaximal, complemented
7#13113065C211yesmaximal, 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⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C13×#394C418yescomplemented
23C2×C13×#95C2211yescharacteristic
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
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×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
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—24no—
59C2×C22⋊Dic13—24no—
60C2×C22⋊Dic13—24no—
61C2×C22⋊Dic13—24no—
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—41no—
69C2×C4⋊Dic13—41no—
70C2×C4⋊Dic13—42no—
71C2×C4⋊Dic13—41no—
72C2×C4⋊Dic13D414yescomplemented
73C2×C4×Dic13—22no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—42no—
77C2×C4×Dic13—41no—
78C2×C4×Dic13—41no—
79C13×#95C2×C414yes—
80#88071—24no—
81#88071—24no—
82#88071—24no—
83#88071—42no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071—41no—
88#14589—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—22no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
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×Dic13C2×D414yes—
160C22×Dic13#4114yes—
161C22×Dic13#4114yes—
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—44no—
170C4⋊Dic13—44no—
171C4×Dic13—48no—
172C4×Dic13—44no—
173C2×#394D1311yescharacteristic
174C2×#388—132no—
175#1441—131no—
176#1439—132no—
177#1438—132no—
178#1437—132no—
179#1437—132no—
180C4⋊#95—131no—
181#1434—132no—
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×C13C2×#4112yes—
221C23×C13C2×#4112yes—
222C23×C13H(5,𝔽2)11yescharacteristic
223C23×C13H(5,𝔽2)11yescharacteristic
224C23×C13H(5,𝔽2)12yes—
225C23×C13H(5,𝔽2)12yes—
226C23×C13H(5,𝔽2)11yescharacteristic
227C23×C132−1+411yescharacteristic
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—24no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
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—24no—
257C2×Dic13—24no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—24no—
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—131no—
284C22×C4⋊C4C2×D1311yescharacteristic
285C22×C22⋊C4—132no—
286C22×C22⋊C4—132no—
287C22×C22⋊C4—132no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4C2×D1312yes—
290C22×C22⋊C4C2×D1312yes—
291C22×C42—132no—
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—132no—
301C2×#95—132no—
302C2×#95—131no—
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×C13C4×#4112yes—
321C22×C13#51811yescharacteristic
322C22×C13#51812yes—
323C22×C13#52011yescharacteristic
324C22×C13#53411yescharacteristic
325C22×C13#53711yescharacteristic
326C22×C13#53811yescharacteristic
327C22×C13#53812yes—
328C22×C13#53911yescharacteristic
329C22×C13#53912yes—
330C22×C13#54012yes—
331C22×C13#54212yes—
332C22×C13#54612yes—
333C22×C13#55012yes—
334C22×C13#55112yes—
335C22×C13#55312yes—
336C22×C13#55512yes—
337C22×C13#55511yescharacteristic
338C22×C13#55511yescharacteristic
339C22×C13#56011yescharacteristic
340C22×C13#56012yes—
341C22×C13H(3,𝔽4)11yescharacteristic
342C4×C13—24no—
343C4×C13—44no—
344C4×C13—42no—
345C4×C13—42no—
346Dic13—44no—
347Dic13—44no—
348Dic13—44no—
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—134no—
367C2×C4⋊C4—521no—
368C2×C4⋊C4—521no—
369C2×C4⋊C4—522no—
370C2×C4⋊C4—521no—
371C2×C4⋊C4C2×Dic1314yes—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—264no—
377C2×C22⋊C4—264no—
378C2×C22⋊C4—264no—
379C2×C22⋊C4—264no—
380C2×C22⋊C4—264no—
381C2×C22⋊C4—264no—
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⋊C4C2×Dic1318yes—
389C2×C22⋊C4C2×Dic1318yes—
390C2×C42—264no—
391C2×C42—264no—
392C2×C42—262no—
393C2×C42—521no—
394C2×C42—521no—
395C2×C42—522no—
396#95—264no—
397#95—264no—
398#95—264no—
399#95—522no—
400#95—522no—
401#95—521no—
402#95—522no—
403#95—522no—
404#95C2×Dic1314yes—
405C2×C13—84no—
406C2×C13#232511yescharacteristic
407C2×C13#233512yes—
408C2×C13#236312yes—
409C2×C13#237211yescharacteristic
410C2×C13#237511yescharacteristic
411C2×C13#269911yescharacteristic
412C2×C13#270512yes—
413C2×C13#273311yescharacteristic
414C2×C13#275612yes—
415C2×C13#278511yescharacteristic
416C2×C13#279511yescharacteristic
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—134no—
458C22×C4—134no—
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—524no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—528no—
496C22⋊C4—528no—
497C22⋊C4—528no—
498C22⋊C4—528no—
499C42—524no—
500C42—528no—
501C13#1458911yescharacteristic, 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#8825112yes—
540C23#8825111yescharacteristic
541C23#8825111yescharacteristic
542C23#8825112yes—
543C23#41×D1312yes—
544C23#41×D1312yes—
545C23#8825611yescharacteristic
546C23#8825711yescharacteristic
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—264no—
576C2×C4—264no—
577C2×C4—264no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—264no—
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#1171930412yes—
621C22#1171930711yescharacteristic
622C22#1171931011yescharacteristic
623C22#1171931712yes—
624C22#1171931912yes—
625C22#1171932112yes—
626C22#1171932211yescharacteristic
627C22#1171936212yes—
628C22#1171936512yes—
629C22#1171936712yes—
630C22#1171936812yes—
631C22#1171937511yescharacteristic
632C22#1171937511yescharacteristic
633C22#1171938412yes—
634C22C2×D4×Dic1311yescharacteristic
635C22#1171950311yescharacteristic
636C22#1171950312yes—
637C22#41×Dic1312yes—
638C22#1171953211yescharacteristic
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—524no—
644C4—524no—
645C4—524no—
646C4—1042no—
647C2—84no—
648C2#1311754111yescharacteristic
649C2#1311763012yes—
650C2#1311787812yes—
651C2#1311794811yescharacteristic
652C2#1311797711yescharacteristic
653C2#1312141811yescharacteristic
654C2#1312150212yes—
655C2#1312185911yescharacteristic
656C2#1312215712yes—
657C2#1312254311yescharacteristic
658C2#1312266911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#394C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#394D13
hypocenterC13#14589
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. #13113089C2semidirect
3. #13113081C2semidirect
5. #13113073C2semidirect
6. #13113073C2semidirect
7. #13113065C2semidirect
8. #13113061C2semidirect
22. C13×#394C4semidirect
72. C2×C4⋊Dic13D4semidirect
293. #394Dic13semidirect
501. C13#14589semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
#131130892
#131130812
#131130772
#131130732
#131130652
#131130612
C2×C13×#3942
#1458913