Finite Group Databasebeta

← #15901641

Subgroups — #15901641

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×#11718879C211yesmaximal, characteristic
2C2×#11718587C211yesmaximal, characteristic, complemented
3#13123175C211yesmaximal, characteristic, complemented
4#13116224C212yesmaximal, complemented
5#13116153C212yesmaximal, complemented
6#13115716C212yesmaximal, complemented
7#13115536C212yesmaximal, complemented
8#13115143C211yesmaximal, characteristic, complemented
9#13115024C211yesmaximal, characteristic, complemented
10#13114767C211yesmaximal, characteristic
11C2×C13×#390C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4—21no—
15C22×C13×C22⋊C4—21no—
16C22×C42×C13C2211yescharacteristic
17C22×#6105C2212yes—
18C2×#88178C2211yescharacteristic
19C13×#390—21no—
20C13×#390—21no—
21C13×#390C2212yes—
22C13×#390C2212yes—
23#11718879—24no—
24C2×#88072C2212yes—
25C2×#88072C2212yes—
26C2×#88072C2212yes—
27#11718873C2211yescharacteristic
28#11718872—21no—
29#11718871—21no—
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88050C2212yescomplemented
33C2×#88047C2212yescomplemented
34#11718594—21no—
35#11718594—21no—
36#11718590C2211yescharacteristic, complemented
37#11718590C2211yescharacteristic, complemented
38#11718589C2211yescharacteristic, complemented
39#11718589C2211yescharacteristic, complemented
40#11718587—24no—
41C2×C4⋊#1055C2212yescomplemented
42C2×#88043C2212yescomplemented
43#11718121C2212yescomplemented
44#11718121C2212yescomplemented
45C25×C13—21no—
46C22×D4×C13—24no—
47C22×D4×C13—21no—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13—42no—
51C22×D4×C13C2312yes—
52C23×C4×C13—21no—
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C22×Dic26C2311yescharacteristic
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—42no—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—44no—
65C2×C13×C22⋊C4—44no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13D411yescharacteristic
69C2×C42×C13D411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×#6105—24no—
75C2×#6105—24no—
76C2×#6105—42no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80#88178—22no—
81#88178—22no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C22×#1055C2312yes—
86C22×#1055C2312yes—
87#88072—24no—
88#88072—24no—
89#88072—42no—
90#88071—21no—
91#88071—21no—
92#88071—21no—
93#88071—21no—
94#88071—21no—
95#88071—21no—
96#88071—21no—
97C22⋊#1055—22no—
98C22⋊#1055D414yes—
99#88050—42no—
100#88047—42no—
101C4⋊#1055—24no—
102#88043—24no—
103#24507—131nomaximal, Sylow
104C24×C13—24no—
105C24×C13—22no—
106C24×C13—42no—
107C24×C13—42no—
108C24×C13—42no—
109C24×C13—42no—
110C24×C13—42no—
111C24×C13—42no—
112C24×C13C2×D411yescharacteristic
113C2×D4×C13—24no—
114C2×D4×C13—22no—
115C2×D4×C13—22no—
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—48no—
120C2×D4×C13—48no—
121C2×D4×C13—42no—
122C2×D4×C13—42no—
123C2×D4×C13#4114yes—
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×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—41no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13#4112yes—
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—22no—
151C2×Dic26—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—42no—
155C13×C22⋊C4—44no—
156C13×C22⋊C4—44no—
157C13×C22⋊C4—44no—
158C13×C22⋊C4—44no—
159C42×C13—22no—
160C42×C13—22no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C22⋊Dic13—42no—
166C22⋊Dic13—42no—
167#6105—48no—
168C4⋊Dic13—21no—
169C4⋊Dic13—22no—
170C4⋊Dic13—21no—
171C4⋊Dic13—22no—
172#6101—42no—
173#6101—42no—
174#6101—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#2855—131no—
184C2×#390D1311yescharacteristic
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—24no—
197C23×C13—48no—
198C23×C13—48no—
199C23×C13—48no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—84no—
207C23×C13—84no—
208C23×C13—84no—
209C23×C13—84no—
210C23×C13#12112yes—
211C23×C13AGL(1,ℤ/8)12yes—
212C23×C13#13712yes—
213C23×C13C22×D411yescharacteristic
214D4×C13—24no—
215D4×C13—24no—
216D4×C13—48no—
217D4×C13—42no—
218D4×C13—42no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
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—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—44no—
235C2×C4×C13—44no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—84no—
240C2×C4×C13#12112yes—
241C2×C4×C13AGL(1,ℤ/8)12yes—
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C2×#4112yes—
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13H(5,𝔽2)12yes—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258Dic26—42no—
259Dic26—42no—
260#1055—24no—
261#1055—42no—
262C23×D4C2×D1311yescharacteristic
263C22×SD16—132no—
264C2×C22⋊Q8—131no—
265C22×C4⋊C4C2×D1311yescharacteristic
266C22×C22⋊C4—21no—
267C22×C22⋊C4—21no—
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#391—131no—
281#391—131no—
282#390—21no—
283#390—21no—
284#390C2×D1312yes—
285#390C2×D1312yes—
286#389—131no—
287#389—131no—
288#387—261no—
289#387—261no—
290#385—261no—
291#381—261no—
292#380—131no—
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—44no—
302C22×C13—44no—
303C22×C13—44no—
304C22×C13—816no—
305C22×C13—82no—
306C22×C13—82no—
307C22×C13—82no—
308C22×C13—82no—
309C22×C13#46814yes—
310C22×C13C2×#12111yescharacteristic
311C22×C13#52511yescharacteristic
312C22×C13#53511yescharacteristic
313C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C13C2×#13711yescharacteristic
316C22×C13#57511yescharacteristic
317C4×C13—22no—
318C4×C13—22no—
319C4×C13—41no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—82no—
323C4×C13#54612yes—
324C4×C13#55112yes—
325Dic13—81no—
326Dic13—81no—
327Dic13—81no—
328Dic13—81no—
329C25—21no—
330C22×Q8—131no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—42no—
336C22×D4C22×D1312yes—
337C23×C4—21no—
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—262no—
347C22⋊Q8—262no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—131no—
351C2×C4⋊C4—131no—
352C2×C4⋊C4—131no—
353C2×C4⋊C4—261no—
354C2×C4⋊C4—261no—
355C2×C4⋊C4—261no—
356C2×C4⋊C4C22×D1312yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—261no—
364C2×C22⋊C4—261no—
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—261no—
381#95—261no—
382#95—261no—
383#95—261no—
384#95—261no—
385#95—261no—
386#95—261no—
387C2×C13—24no—
388C2×C13—84no—
389C2×C13#241111yescharacteristic
390C2×C13C2×#46811yescharacteristic
391C2×C13#305511yescharacteristic
392C2×C13#311011yescharacteristic
393C2×C13#311411yescharacteristic
394C2×C13#321511yescharacteristic
395C2×C13#321711yescharacteristic
396C24—24no—
397C24—22no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24C2×C22⋊D1311yescharacteristic
405C2×Q8—262no—
406C2×Q8—261no—
407C2×Q8—261no—
408C2×Q8—262no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4#612714yes—
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—41no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
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—22no—
452C4⋊C4—22no—
453C4⋊C4—42no—
454C4⋊C4—262no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—262no—
458C4⋊C4—522no—
459C4⋊C4—522no—
460C4⋊C4—522no—
461C22⋊C4—44no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C22⋊C4—522no—
466C22⋊C4—522no—
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—24no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23#8818612yes—
493C23#8819312yes—
494C23#8820512yes—
495C23C22×C22⋊D1311yescharacteristic
496Q8—522no—
497Q8—522no—
498D4—24no—
499D4—24no—
500D4—48no—
501D4—42no—
502D4—42no—
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—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—84no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4#8818612yes—
537C2×C4#8819312yes—
538C2×C4C2×#612712yes—
539C2×C4C2×D4×D1311yescharacteristic
540C2×C4C2×#612911yescharacteristic
541C2×C4#8825112yes—
542C8—264no—
543C8—522no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—816no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22#1171870314yes—
559C22#1171949611yescharacteristic
560C22C2×#8818611yescharacteristic
561C22C2×#8818611yescharacteristic
562C22C2×#8819311yescharacteristic
563C22#1171951011yescharacteristic
564C22#1171952711yescharacteristic
565C22C2×#8820511yescharacteristic
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—82no—
572C4—1041no—
573C4—1041no—
574C4—1041no—
575C4—1041no—
576C4#1171919512yes—
577C4#1171920012yes—
578C2—24no—
579C2—84no—
580C2#1311822111yescharacteristic
581C2C2×#1171870311yescharacteristic
582C2#1312445111yescharacteristic
583C2#1312493511yescharacteristic
584C2#1312497411yescharacteristic
585C2#1312583911yescharacteristic
586C2#1312585411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#390C2
socleC23×C13C22×D4
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#24507
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#11718587C2semidirect
3. #13123175C2semidirect
4. #13116224C2semidirect
5. #13116153C2semidirect
6. #13115716C2semidirect
7. #13115536C2semidirect
8. #13115143C2semidirect
9. #13115024C2semidirect
32. C2×#88050C22semidirect
33. C2×#88047C22semidirect
36. #11718590C22semidirect
37. #11718590C22semidirect
38. #11718589C22semidirect
39. #11718589C22semidirect
41. C2×C4⋊#1055C22semidirect
42. C2×#88043C22semidirect
43. #11718121C22semidirect
44. #11718121C22semidirect
473. C13#24507semidirect

Maximal subgroups

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

subgroupindex
C2×#117188792
C2×#117185872
#131231752
#131162242
#131161532
#131157162
#131155362
#131151432
#131150242
#131147672
C2×C13×#3902
#2450713