Finite Group Databasebeta

← #15789482

Subgroups — #15789482

Order 3328.

1658 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#13113089C212yesmaximal, complemented
3#13113085C212yesmaximal, complemented
4#13113081C212yesmaximal, complemented
5#13113077C212yesmaximal
6#13113073C212yesmaximal, complemented
7#13113063C211yesmaximal, characteristic, complemented
8C4×#88071C211yesmaximal, characteristic, complemented
9C2×C13×#390C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C22⋊C4C2212yes—
13C22×C13×C22⋊C4C2212yes—
14C22×C42×C13C2211yescharacteristic
15C22×C22⋊Dic13C2212yes—
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C13×#390C418yescomplemented
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32#11718612—28no—
33C25×C13C2312yes—
34C22×D4×C13—24no—
35C22×D4×C13—41no—
36C22×D4×C13—41no—
37C22×D4×C13—42no—
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—42no—
48C2×C13×C4⋊C4C2×C414yes—
49C2×C13×C22⋊C4—24no—
50C2×C13×C22⋊C4—24no—
51C2×C13×C22⋊C4—42no—
52C2×C13×C22⋊C4—42no—
53C2×C13×C22⋊C4C2×C418yes—
54C2×C13×C22⋊C4C2×C418yes—
55C2×C42×C13—41no—
56C2×C42×C13—41no—
57C2×C42×C13C2×C414yes—
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×C22⋊Dic13—42no—
69C2×C22⋊Dic13—42no—
70C2×C4⋊Dic13—24no—
71C2×C4⋊Dic13—42no—
72C2×C4⋊Dic13—42no—
73C2×C4×Dic13—22no—
74C2×C4×Dic13—41no—
75C2×C4×Dic13—41no—
76C2×C4×Dic13—41no—
77C2×C4×Dic13—41no—
78C2×C4×Dic13D414yescomplemented
79#88071—24no—
80#88071—24no—
81#88071—24no—
82#88071—24no—
83#88071—24no—
84#88071—42no—
85#88071—42no—
86#88071—41no—
87#88071—41no—
88#14278—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—28no—
106C2×D4×C13—44no—
107C2×D4×C13—44no—
108C2×D4×C13—48no—
109C2×D4×C13—48no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
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—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C414yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C2×D412yes—
132C22×C4×C13#4114yes—
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×Dic13C2×D414yes—
161C22×Dic13#4114yes—
162C13×C4⋊C4—44no—
163C13×C22⋊C4—216no—
164C13×C22⋊C4—48no—
165C42×C13—44no—
166C22⋊Dic13—48no—
167C22⋊Dic13—48no—
168C22⋊Dic13—48no—
169C22⋊Dic13—48no—
170C4⋊Dic13—48no—
171C4×Dic13—44no—
172C4×Dic13—44no—
173C2×#390D1311yescharacteristic
174C2×#388—132no—
175#1441—132no—
176#1440—132no—
177#1439—132no—
178#1438—132no—
179#1437—132no—
180#1434—131no—
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×#4112yes—
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4112yes—
222C23×C13H(5,𝔽2)11yescharacteristic
223C23×C13H(5,𝔽2)12yes—
224C23×C13H(5,𝔽2)12yes—
225C23×C13H(5,𝔽2)11yescharacteristic
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—22no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13#11714yes—
252C2×C4×C13C4×D414yes—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—24no—
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—132no—
283C22×C4⋊C4C2×D1311yescharacteristic
284C22×C22⋊C4—132no—
285C22×C22⋊C4—132no—
286C22×C22⋊C4—132no—
287C22×C22⋊C4—132no—
288C22×C22⋊C4C2×D1312yes—
289C22×C22⋊C4C2×D1312yes—
290C22×C42—131no—
291C22×C42—131no—
292C22×C42C2×D1311yescharacteristic
293#390Dic1318yescomplemented
294#388—268no—
295C2×#95—132no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—131no—
301C2×#95—131no—
302C2×#95—132no—
303C2×#95—132no—
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×#11711yescharacteristic
320C22×C13C2×C4×D411yescharacteristic
321C22×C13C4×#4111yescharacteristic
322C22×C13#51811yescharacteristic
323C22×C13#51811yescharacteristic
324C22×C13#51811yescharacteristic
325C22×C13#52011yescharacteristic
326C22×C13#52912yes—
327C22×C13#53212yes—
328C22×C13#53411yescharacteristic
329C22×C13#53512yes—
330C22×C13#53711yescharacteristic
331C22×C13#53812yes—
332C22×C13#53812yes—
333C22×C13#53812yes—
334C22×C13#53811yescharacteristic
335C22×C13#53812yes—
336C22×C13#53911yescharacteristic
337C22×C13#54012yes—
338C22×C13#54012yes—
339C22×C13#54012yes—
340C22×C13#54212yes—
341C22×C13#54212yes—
342C4×C13—24no—
343C4×C13—24no—
344C4×C13—44no—
345C4×C13—42no—
346Dic13—44no—
347Dic13—44no—
348Dic13—82no—
349Dic13—82no—
350C25C22×D1312yes—
351C22×D4—24no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4—42no—
355C22×D4C2×Dic1314yes—
356C23×C4—132no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4—132no—
360C23×C4C22×D1312yes—
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1311yescharacteristic
363C23×C4C22×D1311yescharacteristic
364C2×C4⋊C4—42no—
365C2×C4⋊C4—264no—
366C2×C4⋊C4—522no—
367C2×C4⋊C4—522no—
368C2×C4⋊C4C2×Dic1314yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—264no—
374C2×C22⋊C4—264no—
375C2×C22⋊C4—264no—
376C2×C22⋊C4—264no—
377C2×C22⋊C4—522no—
378C2×C22⋊C4—522no—
379C2×C22⋊C4—522no—
380C2×C22⋊C4—522no—
381C2×C22⋊C4—522no—
382C2×C22⋊C4—522no—
383C2×C22⋊C4—522no—
384C2×C22⋊C4—522no—
385C2×C22⋊C4C2×Dic1318yes—
386C2×C22⋊C4C2×Dic1318yes—
387C2×C42—41no—
388C2×C42—41no—
389C2×C42—134no—
390C2×C42—262no—
391C2×C42—521no—
392C2×C42—521no—
393C2×C42—521no—
394C2×C42—521no—
395C2×C42C2×Dic1314yes—
396#95—264no—
397#95—264no—
398#95—264no—
399#95—264no—
400#95—264no—
401#95—521no—
402#95—521no—
403#95—522no—
404#95—522no—
405C2×C13—84no—
406C2×C13#229311yescharacteristic
407C2×C13#231211yescharacteristic
408C2×C13#231911yescharacteristic
409C2×C13#232511yescharacteristic
410C2×C13#232811yescharacteristic
411C2×C13#233311yescharacteristic
412C2×C13#233711yescharacteristic
413C2×C13#264812yes—
414C2×C13#265112yes—
415C2×C13#266112yes—
416C2×C13#266212yes—
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—28no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—48no—
437C2×D4—48no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—134no—
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#612714yes—
484C22×C4D4×D1312yes—
485C22×C4#612912yes—
486C22×C4C22×Dic1312yes—
487C22×C4C22×Dic1314yes—
488C22×C4C22×Dic1312yes—
489C22×C4C22×Dic1312yes—
490C4⋊C4—44no—
491C4⋊C4—528no—
492C22⋊C4—216no—
493C22⋊C4—48no—
494C22⋊C4—528no—
495C22⋊C4—528no—
496C22⋊C4—528no—
497C22⋊C4—528no—
498C42—44no—
499C42—524no—
500C42—524no—
501C13#1427811yescharacteristic, 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×#612712yes—
538C23C2×D4×D1311yescharacteristic
539C23C2×#612911yescharacteristic
540C23#8825112yes—
541C23#8825112yes—
542C23#8825111yescharacteristic
543C23#8825111yescharacteristic
544C23#41×D1312yes—
545C23#8825611yescharacteristic
546C23#8825711yescharacteristic
547C23C23×Dic1311yescharacteristic
548D4—416no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—264no—
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#8818014yes—
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#1171919912yes—
617C22#1171919912yes—
618C22#1171925312yes—
619C22#1171926212yes—
620C22#1171926612yes—
621C22#1171926712yes—
622C22#1171930211yescharacteristic
623C22#1171930711yescharacteristic
624C22#1171931011yescharacteristic
625C22#1171931812yes—
626C22#1171932012yes—
627C22#1171932211yescharacteristic
628C22#1171937412yes—
629C22#1171938312yes—
630C22#1171942012yes—
631C22#1171942412yes—
632C22C2×#8818011yescharacteristic
633C22C2×D4×Dic1311yescharacteristic
634C22#1171950311yescharacteristic
635C22#1171950311yescharacteristic
636C22#1171950311yescharacteristic
637C22#41×Dic1311yescharacteristic
638C22#1171953211yescharacteristic
639C4—24no—
640C4—24no—
641C4—44no—
642C4—42no—
643C4—524no—
644C4—524no—
645C4—1042no—
646C4—1042no—
647C2—84no—
648C2#1311730111yescharacteristic
649C2#1311743411yescharacteristic
650C2#1311747911yescharacteristic
651C2#1311754111yescharacteristic
652C2#1311756211yescharacteristic
653C2#1311760311yescharacteristic
654C2#1311765111yescharacteristic
655C2#1312082812yes—
656C2#1312087312yes—
657C2#1312096612yes—
658C2#1312097712yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#390C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#14278
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#11718612C2semidirect
2. #13113089C2semidirect
3. #13113085C2semidirect
4. #13113081C2semidirect
6. #13113073C2semidirect
7. #13113063C2semidirect
8. C4×#88071C2semidirect
22. C13×#390C4semidirect
78. C2×C4×Dic13D4semidirect
293. #390Dic13semidirect
501. C13#14278semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
#131130892
#131130852
#131130812
#131130772
#131130732
#131130632
C4×#880712
C2×C13×#3902
#1427813