Finite Group Databasebeta

← #15793677

Subgroups — #15793677

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×#11718652C211yesmaximal, characteristic
2C2×#11718601C212yesmaximal, complemented
3#13113091C212yesmaximal, complemented
4#13113089C211yesmaximal, characteristic, complemented
5#13113082C212yesmaximal, complemented
6#13113080C212yesmaximal, complemented
7#13113078C212yesmaximal, complemented
8#13113076C212yesmaximal
9C13×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D52C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×#6103C2212yes—
15C22×#6103C2212yes—
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C2×C13×#95C2212yes—
23C2×C13×#95C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31#11718652C418yescomplemented
32#11718601—28no—
33C24×D13C2312yes—
34C23×C4×C13C2312yes—
35C23×C4×C13C2311yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2312yes—
38C23×C4×C13C2311yescharacteristic
39C23×Dic13C2312yes—
40C23×Dic13C2312yes—
41C23×Dic13C2312yes—
42C22×D52—42no—
43C22×D52—42no—
44C22×D52—41no—
45C22×D52—41no—
46C22×D52C2×C414yes—
47C2×C13×C4⋊C4—22no—
48C2×C13×C4⋊C4—41no—
49C2×C13×C4⋊C4—41no—
50C2×C13×C4⋊C4—41no—
51C2×C13×C4⋊C4—41no—
52C2×C13×C4⋊C4C2×C414yes—
53C2×C42×C13—41no—
54C2×C42×C13—41no—
55C2×C42×C13D414yescomplemented
56C2×#6103—24no—
57C2×#6103—24no—
58C2×#6103—24no—
59C2×#6103—24no—
60C2×#6103—42no—
61C2×#6103—42no—
62C2×#6103—42no—
63C2×#6103—42no—
64C2×#6103—42no—
65C2×#6103—42no—
66C2×#6103—42no—
67C2×#6103—42no—
68C2×#6103—42no—
69C2×#6103—42no—
70C2×#6103—42no—
71C2×#6103—42no—
72C2×#6103C2×C418yes—
73C2×#6103C2×C418yes—
74C2×C4⋊Dic13—42no—
75C2×C4⋊Dic13—41no—
76C2×#6101—24no—
77C2×#6101—42no—
78C2×#6101—42no—
79C13×#95—42no—
80C13×#95—42no—
81#88071—24no—
82#88071—24no—
83#88071—42no—
84#88071—42no—
85#88071—42no—
86#88071—41no—
87#88071C2×C414yes—
88#14632—131nomaximal, Sylow
89C24×C13C2411yescharacteristic
90C23×D13—22no—
91C23×D13—22no—
92C23×D13—22no—
93C23×D13—22no—
94C23×D13—22no—
95C23×D13—22no—
96C23×D13—22no—
97C23×D13—22no—
98C23×D13—22no—
99C23×D13—22no—
100C23×D13—22no—
101C23×D13—22no—
102C23×D13—22no—
103C23×D13—22no—
104C23×D13C22×C414yes—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
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×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C2×D414yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13#4112yes—
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×Dic13C22×C414yes—
157C2×D52—44no—
158C2×D52—48no—
159C2×D52—44no—
160C2×D52—48no—
161C2×D52—44no—
162C13×C4⋊C4—44no—
163C13×C4⋊C4—44no—
164C42×C13—44no—
165#6103—216no—
166#6103—48no—
167#6103—48no—
168#6103—48no—
169#6103—48no—
170#6103—48no—
171C4⋊Dic13—44no—
172#6101—48no—
173C2×#394—131no—
174C2×#388—132no—
175#1442—132no—
176#1441—131no—
177#1439—132no—
178#1439—132no—
179#1439—132no—
180#1438—132no—
181C4⋊#95D1311yescharacteristic, complemented
182C23×C13C23×C411yescharacteristic
183C23×C13C22×D411yescharacteristic
184C23×C13C2×#4111yescharacteristic
185C23×C13H(5,𝔽2)11yescharacteristic
186C23×C13H(5,𝔽2)12yes—
187C23×C13H(5,𝔽2)11yescharacteristic
188C23×C13H(5,𝔽2)12yes—
189C23×C13H(5,𝔽2)11yescharacteristic
190C23×C13H(5,𝔽2)12yes—
191C23×C132−1+411yescharacteristic
192C23×C132−1+412yes—
193C22×D13—24no—
194C22×D13—24no—
195C22×D13—24no—
196C22×D13—24no—
197C22×D13—24no—
198C22×D13—24no—
199C22×D13—24no—
200C22×D13—42no—
201C22×D13—42no—
202C22×D13—42no—
203C22×D13—42no—
204C22×D13—42no—
205C22×D13—42no—
206C22×D13—42no—
207C22×D13—42no—
208C22×D13—42no—
209C22×D13—42no—
210C22×D13—42no—
211C22×D13—42no—
212C22×D13—42no—
213C22×D13—42no—
214C22×D13—42no—
215C22×D13—42no—
216C22×D13—42no—
217C22×D13—42no—
218C22×D13—42no—
219C22×D13—42no—
220C22×D13—42no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13—42no—
227C22×D13—42no—
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—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—41no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
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×C13C4×D414yes—
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—
280D52—416no—
281C23×D4—131no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—131no—
284C22×C4⋊C4C2×D1311yescharacteristic
285C22×C4⋊C4C2×D1311yescharacteristic
286C22×C22⋊C4—132no—
287C22×C22⋊C4—132no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—132no—
290C22×C22⋊C4—132no—
291C22×C22⋊C4—132no—
292C22×C42C2×D1311yescharacteristic
293#394—138no—
294#388—268no—
295C2×#95—131no—
296C2×#95—132no—
297C2×#95—132no—
298C2×#95—132no—
299C2×#95—131no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95C2×D1312yes—
303C2×#95C2×D1312yes—
304C22×C13C2×C4×D411yescharacteristic
305C22×C13#51811yescharacteristic
306C22×C13#51812yes—
307C22×C13#52011yescharacteristic
308C22×C13#52012yes—
309C22×C13#53411yescharacteristic
310C22×C13#53512yes—
311C22×C13#53711yescharacteristic
312C22×C13#53712yes—
313C22×C13#53811yescharacteristic
314C22×C13#53911yescharacteristic
315C22×C13#54012yes—
316C22×C13#54212yes—
317C22×C13#56011yescharacteristic
318C22×C13#56012yes—
319C22×C13#56012yes—
320C22×C13H(3,𝔽4)11yescharacteristic
321C22×C13H(3,𝔽4)11yescharacteristic
322C22×C13#56212yes—
323C22×C13#56212yes—
324C22×C13#56212yes—
325C22×C13#56311yescharacteristic
326C22×C13#56312yes—
327C2×D13—44no—
328C2×D13—44no—
329C2×D13—44no—
330C2×D13—44no—
331C2×D13—44no—
332C2×D13—44no—
333C2×D13—44no—
334C2×D13—82no—
335C2×D13—82no—
336C2×D13—82no—
337C2×D13—82no—
338C2×D13—82no—
339C2×D13—82no—
340C2×D13—82no—
341C2×D13—82no—
342C4×C13—24no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—44no—
346C4×C13—82no—
347Dic13—44no—
348Dic13—82no—
349Dic13—82no—
350C25—132no—
351C22×D4—134no—
352C22×D4—522no—
353C22×D4—521no—
354C22×D4—521no—
355C22×D4—522no—
356C23×C4—132no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4C22×D1312yes—
360C23×C4C22×D1311yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1312yes—
363C23×C4C22×D1311yescharacteristic
364C2×C4⋊C4—22no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—264no—
370C2×C4⋊C4—522no—
371C2×C4⋊C4—522no—
372C2×C4⋊C4—521no—
373C2×C4⋊C4—522no—
374C2×C4⋊C4C4×D1314yes—
375C2×C22⋊C4—138no—
376C2×C22⋊C4—138no—
377C2×C22⋊C4—264no—
378C2×C22⋊C4—264no—
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⋊C4—522no—
392C2×C22⋊C4—522no—
393C2×C42—41no—
394C2×C42—41no—
395C2×C42D5214yescomplemented
396#95—42no—
397#95—42no—
398#95—134no—
399#95—264no—
400#95—264no—
401#95—521no—
402#95—522no—
403#95—522no—
404#95—522no—
405C2×C13#232412yes—
406C2×C13#232511yescharacteristic
407C2×C13#237511yescharacteristic
408C2×C13#237612yes—
409C2×C13#237911yescharacteristic
410C2×C13#281312yes—
411C2×C13#281911yescharacteristic
412C2×C13#282311yescharacteristic
413C2×C13#282811yescharacteristic
414C2×C13#283211yescharacteristic
415C2×C13#283712yes—
416D13—84no—
417C24—134no—
418C24—262no—
419C24—262no—
420C24—262no—
421C24—262no—
422C24—262no—
423C24—262no—
424C24—262no—
425C24—262no—
426C24—262no—
427C24—262no—
428C24—262no—
429C24—262no—
430C24—262no—
431C24—262no—
432C24C23×D1311yescharacteristic
433C2×D4—524no—
434C2×D4—528no—
435C2×D4—524no—
436C2×D4—528no—
437C2×D4—524no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
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—134no—
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×C4C2×C4×D1312yes—
485C22×C4C2×C4×D1312yes—
486C22×C4C2×C4×D1312yes—
487C22×C4C2×D5214yes—
488C22×C4C2×D5212yes—
489C22×C4#612712yes—
490C4⋊C4—44no—
491C4⋊C4—44no—
492C4⋊C4—528no—
493C4⋊C4—524no—
494C22⋊C4—2616no—
495C22⋊C4—528no—
496C22⋊C4—528no—
497C22⋊C4—528no—
498C22⋊C4—528no—
499C22⋊C4—528no—
500C42—44no—
501C13#1463211yescharacteristic, complemented, Sylow
502C23—264no—
503C23—264no—
504C23—264no—
505C23—264no—
506C23—264no—
507C23—264no—
508C23—264no—
509C23—522no—
510C23—522no—
511C23—522no—
512C23—522no—
513C23—522no—
514C23—522no—
515C23—522no—
516C23—522no—
517C23—522no—
518C23—522no—
519C23—522no—
520C23—522no—
521C23—522no—
522C23—522no—
523C23—522no—
524C23—522no—
525C23—522no—
526C23—522no—
527C23—522no—
528C23—522no—
529C23—522no—
530C23—522no—
531C23—522no—
532C23—522no—
533C23—522no—
534C23—522no—
535C23—522no—
536C23—522no—
537C23C22×C4×D1311yescharacteristic
538C23C22×D5211yescharacteristic
539C23C2×#612711yescharacteristic
540C23#8825111yescharacteristic
541C23#8825112yes—
542C23#8825111yescharacteristic
543C23#8825111yescharacteristic
544C23#8825411yescharacteristic
545C23#8825412yes—
546C23#8825612yes—
547C23#8825612yes—
548D4—5216no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—264no—
580C2×C4—264no—
581C2×C4—264no—
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×C4C4×D5214yes—
601C22—524no—
602C22—524no—
603C22—524no—
604C22—524no—
605C22—524no—
606C22—524no—
607C22—524no—
608C22—1042no—
609C22—1042no—
610C22—1042no—
611C22—1042no—
612C22—1042no—
613C22—1042no—
614C22—1042no—
615C22—1042no—
616C22C2×C4×D5211yescharacteristic
617C22#1171919111yescharacteristic
618C22#1171919811yescharacteristic
619C22#1171919911yescharacteristic
620C22#1171920911yescharacteristic
621C22#1171921512yes—
622C22#1171921511yescharacteristic
623C22#1171922011yescharacteristic
624C22#1171923012yes—
625C22#1171925012yes—
626C22#1171926712yes—
627C22#1171927912yes—
628C22#1171928712yes—
629C22#1171932512yes—
630C22#1171932512yes—
631C22#1171935212yes—
632C22#1171935212yes—
633C22#1171938811yescharacteristic
634C22#1171938811yescharacteristic
635C22#1171940512yes—
636C22#1171942511yescharacteristic
637C22#1171944012yes—
638C22#1171944011yescharacteristic
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—82no—
644C4—524no—
645C4—1042no—
646C4—1042no—
647C2—1044no—
648C2#1311753012yes—
649C2#1311753911yescharacteristic
650C2#1311797311yescharacteristic
651C2#1311798112yes—
652C2#1311800811yescharacteristic
653C2#1312284012yes—
654C2#1312288211yescharacteristic
655C2#1312291011yescharacteristic
656C2#1312295511yescharacteristic
657C2#1312300311yescharacteristic
658C2#1312304612yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC4⋊#95D13
hypocenterC13#14632
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718601C2semidirect
3. #13113091C2semidirect
4. #13113089C2semidirect
5. #13113082C2semidirect
6. #13113080C2semidirect
7. #13113078C2semidirect
9. C13×C4⋊#95C2semidirect
31. #11718652C4semidirect
55. C2×C42×C13D4semidirect
181. C4⋊#95D13semidirect
395. C2×C42D52semidirect
501. C13#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#117186522
C2×#117186012
#131130912
#131130892
#131130822
#131130802
#131130782
#131130762
C13×C4⋊#952
#1463213