Finite Group Databasebeta

← #15901642

Subgroups — #15901642

Order 3328.

1188 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718707C211yesmaximal, characteristic
2C2×#11718587C211yesmaximal, characteristic, complemented
3C2×#11718600C211yesmaximal, characteristic
4#13116221C212yesmaximal, complemented
5#13116151C212yesmaximal, complemented
6#13115720C212yesmaximal, complemented
7#13115532C212yesmaximal, complemented
8#13115144C211yesmaximal, characteristic, complemented
9#13115023C211yesmaximal, characteristic, complemented
10#13114766C211yesmaximal, characteristic
11C13×#2855C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C2×C13×C22⋊Q8C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×#6106C2212yes—
16C22×#6103—21no—
17C22×#6103—21no—
18C22×C4⋊Dic13C2211yescharacteristic
19C13×#391C2211yescharacteristic, complemented
20C13×#391C2211yescharacteristic, complemented
21C13×#389C2211yescharacteristic, complemented
22C13×#389C2211yescharacteristic, complemented
23C13×#387—21no—
24C13×#387—21no—
25C13×#385—21no—
26C13×#381—21no—
27C13×#380C2211yescharacteristic
28C2×#88075C2212yescomplemented
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31#11718707—24no—
32C2×#88049C2212yes—
33C2×#88049C2212yes—
34C2×#88049C2212yes—
35C2×#88047C2212yescomplemented
36#11718600—21no—
37#11718600—21no—
38#11718600C2212yes—
39#11718600C2212yes—
40#11718587—24no—
41C2×C4⋊#1055C2212yescomplemented
42C2×#88043C2212yescomplemented
43#11718121C2212yescomplemented
44#11718121C2212yescomplemented
45C24×D13—21no—
46C22×Q8×C13C2311yescharacteristic
47C23×C4×C13D411yescharacteristic
48C23×C4×C13D411yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×Dic13—21no—
51C22×D52—21no—
52C22×D52—24no—
53C22×D52—22no—
54C22×D52—22no—
55C22×D52—42no—
56C22×D52C2312yes—
57C13×C22⋊Q8—22no—
58C13×C22⋊Q8—22no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4C2311yescharacteristic
63C2×C13×C4⋊C4C2311yescharacteristic
64C2×C13×C4⋊C4C2311yescharacteristic
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13D411yescharacteristic
70C2×C42×C13D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×#6106—24no—
74C2×#6106—24no—
75C2×#6106—42no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—44no—
81C2×#6103—44no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—42no—
84C2×C4⋊Dic13C2312yes—
85C22×#1055C2312yes—
86C22×#1055C2312yes—
87C13×#95—21no—
88C13×#95—21no—
89C13×#95—21no—
90C13×#95—21no—
91C13×#95—21no—
92C13×#95—21no—
93C13×#95—21no—
94#88075—42no—
95C22⋊#1055—22no—
96C22⋊#1055D414yes—
97#88049—24no—
98#88049—24no—
99#88049—42no—
100#88047—42no—
101C4⋊#1055—24no—
102#88043—24no—
103#24507—131nomaximal, Sylow
104C24×C13C2×D411yescharacteristic
105C23×D13—24no—
106C23×D13—22no—
107C23×D13—42no—
108C23×D13—42no—
109C23×D13—42no—
110C23×D13—42no—
111C23×D13—42no—
112C23×D13—42no—
113C2×Q8×C13—21no—
114C2×Q8×C13—22no—
115C2×Q8×C13—21no—
116C2×Q8×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—41no—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13#4112yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—22no—
138C22×Dic13—42no—
139C22×Dic13—42no—
140C22×Dic13—42no—
141C2×D52—22no—
142C2×D52—22no—
143C2×D52—22no—
144C2×D52—22no—
145C2×D52—24no—
146C2×D52—22no—
147C2×D52—48no—
148C2×D52—48no—
149C2×D52—42no—
150C2×D52—42no—
151C2×D52#4114yes—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—42no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4—42no—
159C13×C22⋊C4—42no—
160C13×C22⋊C4—42no—
161C42×C13—22no—
162C42×C13—22no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167#6106—48no—
168#6103—44no—
169#6103—44no—
170#6103—44no—
171#6103—44no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—42no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055C2×D414yes—
181C2×#450—131no—
182C2×#432—131no—
183#2855D1311yescharacteristic, complemented
184C2×#390—131no—
185#2067—132no—
186#2055—132no—
187#1973—132no—
188#1936—132no—
189#1872—131no—
190#1852—131no—
191#1786—131no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13—21no—
196C23×C13#12112yes—
197C23×C13AGL(1,ℤ/8)12yes—
198C23×C13#13712yes—
199C23×C13C22×D411yescharacteristic
200C22×D13—24no—
201C22×D13—48no—
202C22×D13—48no—
203C22×D13—48no—
204C22×D13—42no—
205C22×D13—42no—
206C22×D13—42no—
207C22×D13—42no—
208C22×D13—42no—
209C22×D13—42no—
210C22×D13—84no—
211C22×D13—84no—
212C22×D13—84no—
213C22×D13—84no—
214Q8×C13—42no—
215Q8×C13—42no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—44no—
232C2×C4×C13—44no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13#12112yes—
246C2×C4×C13AGL(1,ℤ/8)12yes—
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4112yes—
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13H(5,𝔽2)12yes—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—84no—
255D52—24no—
256D52—24no—
257D52—48no—
258D52—42no—
259D52—42no—
260#1055—24no—
261#1055—42no—
262C23×D4—131no—
263C22×SD16—132no—
264C2×C22⋊Q8C2×D1311yescharacteristic
265C22×C4⋊C4—131no—
266C22×C22⋊C4—261no—
267C22×C22⋊C4—261no—
268C22×C42C2×D1311yescharacteristic
269#450—264no—
270#432—264no—
271C2×#107—132no—
272C2×C4⋊C8—132no—
273C2×#103—132no—
274C2×#102—132no—
275C2×#102—132no—
276C2×#102—132no—
277C2×C22⋊C8—131no—
278C2×C22⋊C8—131no—
279C2×#97—132no—
280#391C2×D1311yescharacteristic, complemented
281#391C2×D1311yescharacteristic, complemented
282#390—132no—
283#390—132no—
284#390—261no—
285#390—261no—
286#389C2×D1311yescharacteristic, complemented
287#389C2×D1311yescharacteristic, complemented
288#387—21no—
289#387—21no—
290#385—21no—
291#381—21no—
292#380C2×D1311yescharacteristic
293#340—132no—
294#340—132no—
295C22×C13—22no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13#46814yes—
302C22×C13C2×#12111yescharacteristic
303C22×C13#52511yescharacteristic
304C22×C13#53511yescharacteristic
305C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C13C2×#13711yescharacteristic
308C22×C13#57511yescharacteristic
309C2×D13—44no—
310C2×D13—44no—
311C2×D13—44no—
312C2×D13—816no—
313C2×D13—82no—
314C2×D13—82no—
315C2×D13—82no—
316C2×D13—82no—
317C4×C13—22no—
318C4×C13—22no—
319C4×C13—41no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—81no—
323C4×C13—81no—
324C4×C13—81no—
325C4×C13—81no—
326C4×C13#54612yes—
327C4×C13#55112yes—
328Dic13—82no—
329C25—261no—
330C22×Q8C22×D1311yescharacteristic
331C22×D4—132no—
332C22×D4—264no—
333C22×D4—262no—
334C22×D4—262no—
335C22×D4—261no—
336C22×D4—522no—
337C23×C4—261no—
338C23×C4C22⋊D1311yescharacteristic
339C23×C4C22⋊D1311yescharacteristic
340C23×C4C22×D1311yescharacteristic
341C2×SD16—264no—
342C2×SD16—264no—
343C2×SD16—522no—
344C22×C8—132no—
345C22×C8—132no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—132no—
352C2×C4⋊C4—261no—
353C2×C4⋊C4—522no—
354C2×C4⋊C4C22×D1311yescharacteristic
355C2×C4⋊C4C22×D1311yescharacteristic
356C2×C4⋊C4C22×D1311yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—262no—
360C2×C22⋊C4—262no—
361C2×C22⋊C4—262no—
362C2×C22⋊C4—262no—
363C2×C22⋊C4—524no—
364C2×C22⋊C4—524no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42C22⋊D1311yescharacteristic
368C2×C42C22⋊D1311yescharacteristic
369C2×C42C22×D1311yescharacteristic
370C2×C42C22×D1311yescharacteristic
371#107—522no—
372C4⋊C8—264no—
373#103—522no—
374#102—264no—
375#102—264no—
376#102—522no—
377C22⋊C8—134no—
378C22⋊C8—262no—
379#97—264no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387C2×C13—24no—
388C2×C13#241111yescharacteristic
389C2×C13C2×#46811yescharacteristic
390C2×C13#305511yescharacteristic
391C2×C13#311011yescharacteristic
392C2×C13#311411yescharacteristic
393C2×C13#321511yescharacteristic
394C2×C13#321711yescharacteristic
395D13—84no—
396C24—264no—
397C24—262no—
398C24—522no—
399C24—522no—
400C24—522no—
401C24—522no—
402C24—522no—
403C24—522no—
404C24C2×C22⋊D1311yescharacteristic
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×D4—134no—
410C2×D4—264no—
411C2×D4—262no—
412C2×D4—262no—
413C2×D4—262no—
414C2×D4—262no—
415C2×D4—262no—
416C2×D4—528no—
417C2×D4—528no—
418C2×D4—522no—
419C2×D4—522no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—262no—
433C22×C4—522no—
434C22×C4—522no—
435C22×C4—522no—
436C22×C4D4×D1312yes—
437C22×C4#612912yes—
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C23×D1311yescharacteristic
444SD16—528no—
445C2×C8—134no—
446C2×C8—262no—
447C2×C8—262no—
448C2×C8—262no—
449C2×C8—262no—
450C2×C8—262no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—262no—
459C4⋊C4—262no—
460C4⋊C4—522no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—524no—
464C22⋊C4—524no—
465C22⋊C4—524no—
466C22⋊C4—524no—
467C42—22no—
468C42—22no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C13#2450711yescharacteristic, complemented, Sylow
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—264no—
479C23—528no—
480C23—528no—
481C23—528no—
482C23—522no—
483C23—522no—
484C23—522no—
485C23—522no—
486C23—522no—
487C23—522no—
488C23—1044no—
489C23—1044no—
490C23—1044no—
491C23—1044no—
492C23#8819312yes—
493C23#8819612yes—
494C23#8820312yes—
495C23C22×C22⋊D1311yescharacteristic
496Q8—42no—
497Q8—42no—
498D4—264no—
499D4—264no—
500D4—528no—
501D4—522no—
502D4—522no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—1044no—
536C2×C4#8819312yes—
537C2×C4#8820312yes—
538C2×C4C2×D4×D1311yescharacteristic
539C2×C4C2×#612911yescharacteristic
540C2×C4#41×D1312yes—
541C2×C4#8825612yes—
542C8—264no—
543C8—522no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—524no—
551C22—524no—
552C22—524no—
553C22—10416no—
554C22—1042no—
555C22—1042no—
556C22—1042no—
557C22—1042no—
558C22#1171871014yes—
559C22C2×#8819311yescharacteristic
560C22C2×#8819611yescharacteristic
561C22C2×#8820311yescharacteristic
562C22C2×#8820311yescharacteristic
563C22#1171952711yescharacteristic
564C22#1171953311yescharacteristic
565C22#1171953511yescharacteristic
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—1042no—
576C4#1171935912yes—
577C4#1171936312yes—
578C2—24no—
579C2—1044no—
580C2#1311822211yescharacteristic
581C2C2×#1171871011yescharacteristic
582C2#1312445711yescharacteristic
583C2#1312493111yescharacteristic
584C2#1312497011yescharacteristic
585C2#1312583511yescharacteristic
586C2#1312585111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2855C2
socleC23×C13C22×D4
prime radicalC23×D52C22
hypercenter#2855D13
hypocenterC13#24507
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
2. C2×#11718587C2semidirect
4. #13116221C2semidirect
5. #13116151C2semidirect
6. #13115720C2semidirect
7. #13115532C2semidirect
8. #13115144C2semidirect
9. #13115023C2semidirect
11. C13×#2855C2semidirect
19. C13×#391C22semidirect
20. C13×#391C22semidirect
21. C13×#389C22semidirect
22. C13×#389C22semidirect
28. C2×#88075C22semidirect
35. C2×#88047C22semidirect
41. C2×C4⋊#1055C22semidirect
42. C2×#88043C22semidirect
43. #11718121C22semidirect
44. #11718121C22semidirect
183. #2855D13semidirect
280. #391C2×D13semidirect
281. #391C2×D13semidirect
286. #389C2×D13semidirect
287. #389C2×D13semidirect
473. C13#24507semidirect

Maximal subgroups

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

subgroupindex
C2×#117187072
C2×#117185872
C2×#117186002
#131162212
#131161512
#131157202
#131155322
#131151442
#131150232
#131147662
C13×#28552
#2450713