Finite Group Databasebeta

← #15790160

Subgroups — #15790160

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic13C211yesmaximal, characteristic
2#13113096C212yesmaximal, complemented
3#13113094C212yesmaximal, complemented
4#13113083C212yesmaximal
5#13113079C212yesmaximal
6#13113064C211yesmaximal, characteristic, complemented
7#13113062C211yesmaximal, characteristic, complemented
8#13113061C211yesmaximal, characteristic, complemented
9#13113061C211yesmaximal, characteristic, complemented
10#13113059C211yesmaximal, characteristic
11C13×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C22⋊Dic13C2211yescharacteristic
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2212yes—
17C22×#6101C2212yes—
18C22×C4×Dic13C2211yescharacteristic
19C22×C4×Dic13C2211yescharacteristic
20C2×C13×#95C2211yescharacteristic
21C2×C13×#95C2211yescharacteristic
22C2×C13×#95C2212yes—
23C4×C22⋊Dic13C418yescomplemented
24C2×#88071C2212yes—
25C2×#88071C2211yescharacteristic
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C25×C13C2311yescharacteristic
37C23×C4×C13—22no—
38C23×C4×C13—22no—
39C23×C4×C13—42no—
40C23×C4×C13—42no—
41C23×C4×C13C2×C414yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C2×C13×C22⋊C4—24no—
53C2×C13×C22⋊C4—42no—
54C2×C13×C22⋊C4—42no—
55C2×C22⋊Dic13—24no—
56C2×C22⋊Dic13—24no—
57C2×C22⋊Dic13—24no—
58C2×C22⋊Dic13—42no—
59C2×C22⋊Dic13—42no—
60C2×C22⋊Dic13C2×C414yes—
61C2×C22⋊Dic13C2×C414yes—
62C2×#6101—24no—
63C2×#6101—42no—
64C2×#6101—42no—
65C2×C4×Dic13—42no—
66C2×C4×Dic13—42no—
67C2×C4×Dic13C2×C414yes—
68C2×C4×Dic13C2×C414yes—
69C13×#95—22no—
70C13×#95—22no—
71C13×#95—42no—
72#88071—22no—
73#88071—22no—
74#88071—24no—
75#88071—42no—
76#88071—42no—
77#88071—42no—
78#88071—42no—
79#88071—42no—
80#88071—42no—
81#88071—42no—
82#88071C2×C414yes—
83#88071C2×C414yes—
84#14351—131nomaximal, Sylow
85C24×C13—22no—
86C24×C13—21no—
87C24×C13—21no—
88C24×C13—21no—
89C24×C13—22no—
90C24×C13—21no—
91C24×C13—22no—
92C24×C13—21no—
93C24×C13—21no—
94C24×C13C22×C412yes—
95C24×C13#4114yes—
96C24×C13C2411yescharacteristic
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—28no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
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—22no—
118C22×C4×C13—44no—
119C22×C4×C13—44no—
120C22×C4×C13—48no—
121C22×C4×C13—48no—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C22×C412yes—
124C22×C4×C13#4112yes—
125C22×C4×C13#4112yes—
126C22×Dic13—22no—
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
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×Dic13C22×C412yes—
156C22×Dic13C22×C412yes—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13#4114yes—
160C13×C22⋊C4—48no—
161C22⋊Dic13—28no—
162C22⋊Dic13—28no—
163C22⋊Dic13—48no—
164#6101—48no—
165C4×Dic13—44no—
166C4×Dic13—44no—
167C2×C4×C22⋊C4—131no—
168#1443—132no—
169#1442—132no—
170#1440—132no—
171#1439—132no—
172C4⋊#95—131no—
173#1434—131no—
174#1434—131no—
175#1434—131no—
176C22⋊#95—131no—
177C22⋊#95D1311yescharacteristic
178C23×C13—22no—
179C23×C13—22no—
180C23×C13—22no—
181C23×C13—22no—
182C23×C13—22no—
183C23×C13—22no—
184C23×C13—24no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—24no—
188C23×C13—24no—
189C23×C13—24no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—41no—
195C23×C13—42no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13—42no—
200C23×C13#11714yes—
201C23×C13C23×C411yescharacteristic
202C23×C13C2×#4112yes—
203C23×C13C2×#4111yescharacteristic
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4112yes—
206C23×C13H(5,𝔽2)12yes—
207C23×C13H(5,𝔽2)12yes—
208C23×C13H(5,𝔽2)11yescharacteristic
209C23×C13H(5,𝔽2)11yescharacteristic
210C23×C132−1+411yescharacteristic
211C23×C132−1+411yescharacteristic
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—416no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13#11714yes—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
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#11714yes—
271C24×C4C2×D1311yescharacteristic
272C22×C4⋊C4—132no—
273C22×C22⋊C4—131no—
274C22×C22⋊C4—131no—
275C22×C22⋊C4—132no—
276C22×C22⋊C4C2×D1312yes—
277C22×C42—131no—
278C22×C42—131no—
279C4×C22⋊C4—138no—
280C2×#95—131no—
281C2×#95—131no—
282C2×#95—131no—
283C2×#95—131no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95—132no—
288C2×#95—132no—
289C2×#95—132no—
290C2×#95—132no—
291C2×#95—132no—
292C2×#95C2×D1311yescharacteristic
293C2×#95C2×D1311yescharacteristic
294C2×#95C2×D1312yes—
295C22×C13—24no—
296C22×C13—24no—
297C22×C13—24no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—44no—
303C22×C13—44no—
304C22×C13—44no—
305C22×C13—44no—
306C22×C13C2×#11711yescharacteristic
307C22×C13C2×#11711yescharacteristic
308C22×C13C2×#11711yescharacteristic
309C22×C13#51811yescharacteristic
310C22×C13#51811yescharacteristic
311C22×C13#52011yescharacteristic
312C22×C13#52011yescharacteristic
313C22×C13#52912yes—
314C22×C13#52912yes—
315C22×C13#53812yes—
316C22×C13#53812yes—
317C22×C13#53812yes—
318C22×C13#53812yes—
319C22×C13#53812yes—
320C22×C13#53912yes—
321C22×C13#53912yes—
322C22×C13#53912yes—
323C22×C13#54011yescharacteristic
324C22×C13#54012yes—
325C22×C13#54111yescharacteristic
326C22×C13#54211yescharacteristic
327C22×C13#54211yescharacteristic
328C22×C13#54212yes—
329C4×C13—24no—
330C4×C13—42no—
331C4×C13—82no—
332C4×C13—82no—
333Dic13—24no—
334Dic13—42no—
335Dic13—42no—
336Dic13—42no—
337Dic13—82no—
338Dic13—82no—
339C25C22×D1311yescharacteristic
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4—131no—
348C23×C4—132no—
349C23×C4—132no—
350C23×C4C4×D1314yes—
351C23×C4C22×D1312yes—
352C23×C4C22×D1312yes—
353C23×C4C22×D1311yescharacteristic
354C23×C4C22×D1311yescharacteristic
355C2×C4⋊C4—264no—
356C2×C4⋊C4—522no—
357C2×C4⋊C4—522no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—134no—
362C2×C22⋊C4—134no—
363C2×C22⋊C4—264no—
364C2×C22⋊C4—264no—
365C2×C22⋊C4—264no—
366C2×C22⋊C4—522no—
367C2×C22⋊C4—522no—
368C2×C42—134no—
369C2×C42—134no—
370C2×C42—522no—
371C2×C42—522no—
372#95—22no—
373#95—22no—
374#95—42no—
375#95—134no—
376#95—134no—
377#95—264no—
378#95—262no—
379#95—262no—
380#95—522no—
381#95—522no—
382#95—522no—
383#95—522no—
384#95—522no—
385#95—522no—
386#95—522no—
387C2×C13—44no—
388C2×C13#228311yescharacteristic
389C2×C13#231211yescharacteristic
390C2×C13#231411yescharacteristic
391C2×C13#231811yescharacteristic
392C2×C13#231811yescharacteristic
393C2×C13#231811yescharacteristic
394C2×C13#231911yescharacteristic
395C2×C13#264812yes—
396C2×C13#264912yes—
397C2×C13#265212yes—
398C2×C13#265312yes—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—22no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—21no—
408C24C2×C4×D1312yes—
409C24#612714yes—
410C24C23×D1311yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—28no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—132no—
437C22×C4—134no—
438C22×C4—132no—
439C22×C4—132no—
440C22×C4—132no—
441C22×C4—262no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—261no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—261no—
451C22×C4—262no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—262no—
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×C4C2×C4×D1312yes—
471C22×C4C2×C4×D1312yes—
472C22×C4#612912yes—
473C22×C4#612912yes—
474C4⋊C4—528no—
475C22⋊C4—48no—
476C22⋊C4—268no—
477C22⋊C4—268no—
478C22⋊C4—528no—
479C42—524no—
480C42—524no—
481C13#1435111yescharacteristic, complemented, Sylow
482C23—22no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—22no—
487C23—24no—
488C23—22no—
489C23—22no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—42no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—41no—
502C23—42no—
503C23—42no—
504C23#8812614yes—
505C23C22×C4×D1311yescharacteristic
506C23C2×#612712yes—
507C23C2×#612911yescharacteristic
508C23C2×#612911yescharacteristic
509C23#8825112yes—
510C23#8825112yes—
511C23#8825111yescharacteristic
512C23#8825411yescharacteristic
513C23#41×D1312yes—
514C23#8825611yescharacteristic
515C23#8825711yescharacteristic
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—416no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—134no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4#8813114yes—
575C22—24no—
576C22—24no—
577C22—24no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—42no—
586C22C2×#8812611yescharacteristic
587C22C2×#8813111yescharacteristic
588C22#1171919111yescharacteristic
589C22#1171919111yescharacteristic
590C22#1171919912yes—
591C22#1171920911yescharacteristic
592C22#1171922012yes—
593C22D13×#11711yescharacteristic
594C22#1171922811yescharacteristic
595C22#1171924312yes—
596C22#1171924312yes—
597C22#1171926512yes—
598C22#1171926912yes—
599C22#1171929812yes—
600C22#1171929812yes—
601C22#1171930811yescharacteristic
602C22#1171931812yes—
603C22#1171932411yescharacteristic
604C22#1171933011yescharacteristic
605C22#1171934312yes—
606C22#1171934811yescharacteristic
607C22#1171936712yes—
608C22#1171936812yes—
609C4—24no—
610C4—42no—
611C4—82no—
612C4—82no—
613C4—264no—
614C4—522no—
615C4—522no—
616C4—522no—
617C4—1042no—
618C4—1042no—
619C2—44no—
620C2#1311723011yescharacteristic
621C2#1311743211yescharacteristic
622C2#1311744311yescharacteristic
623C2#1311746311yescharacteristic
624C2#1311747011yescharacteristic
625C2#1311747111yescharacteristic
626C2#1311747611yescharacteristic
627C2#1312082412yes—
628C2#1312084112yes—
629C2#1312088412yes—
630C2#1312090112yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#14351
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #13113096C2semidirect
3. #13113094C2semidirect
6. #13113064C2semidirect
7. #13113062C2semidirect
8. #13113061C2semidirect
9. #13113061C2semidirect
23. C4×C22⋊Dic13C4semidirect
481. C13#14351semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic132
#131130962
#131130942
#131130832
#131130792
#131130642
#131130622
#131130612
#131130592
C13×C22⋊#952
#1435113