Finite Group Databasebeta

← #15864282

Subgroups — #15864282

Order 3328.

2234 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88203C211yesmaximal, characteristic
2C22×C4×D52C211yesmaximal, characteristic, complemented
3C2×#11718893C211yesmaximal, characteristic, complemented
4C2×#11718662C211yesmaximal, characteristic, complemented
5#13115187C214yesmaximal, complemented
6#13115173C214yesmaximal, complemented
7#13114557C211yesmaximal, characteristic, complemented
8#13114530C211yesmaximal, characteristic, complemented
9C13×#2297C211yesmaximal, characteristic, complemented
10C22×C13×#41C2211yescharacteristic
11C23×D52C2211yescharacteristic
12C23×C4×D13—21no—
13C2×C13×#117C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C2×#88203—24no—
16C2×#88203—24no—
17C2×#88203C418yescomplemented
18C22×#6106C2212yes—
19C22×#6104C2212yes—
20C22×#6103—21no—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24C2×C4×D52—24no—
25C2×C4×D52—22no—
26C2×C4×D52—24no—
27C2×C4×D52C2214yes—
28C13×#391C2212yescomplemented
29C13×#390C2212yescomplemented
30C13×#386—21no—
31C13×#386—21no—
32C4×C13×C22⋊C4—22no—
33#11718893—24no—
34C2×#88075C2212yescomplemented
35C2×#88072C2212yescomplemented
36#11718662—24no—
37C2×#88049C2214yes—
38#11718121C2214yescomplemented
39#11718116C2214yescomplemented
40C24×D13—21no—
41C2×C13×#41—22no—
42C2×C13×#41—22no—
43C2×C13×#41—22no—
44C2×C13×#41—22no—
45C2×C13×#41—22no—
46C2×C13×#41C2×C414yescomplemented
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13—21no—
49C22×D4×C13C2311yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13—21no—
55C22×D52—22no—
56C22×D52—21no—
57C22×D52—22no—
58C22×D52—22no—
59C22×D52C2×C414yes—
60C22×D52D414yes—
61C22×D52D414yes—
62C22×D52C2312yes—
63C22×C4×D13—28no—
64C22×C4×D13—24no—
65C22×C4×D13—48no—
66C13×#117—22no—
67C13×#117—22no—
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C42×C13—22no—
73C2×C42×C13—22no—
74C2×C42×C13—21no—
75C2×C42×C13D412yes—
76C2×C42×C13C2312yes—
77#88203—232no—
78C2×#6106—24no—
79C2×#6106—24no—
80C2×#6106C2×C418yescomplemented
81C2×#6104—24no—
82C2×#6104—24no—
83C2×#6104C2×C418yescomplemented
84C2×#6103—28no—
85C2×#6103—24no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13D414yes—
89C2×C4⋊Dic13C2312yes—
90C2×#6099—22no—
91C2×#6099—22no—
92C2×#6099—22no—
93C2×#6099—22no—
94C2×#6099—22no—
95C2×#6099C2×C414yescomplemented
96C22×#1055C2312yes—
97C22×#1055C2312yes—
98C4×D52—216no—
99C4×D52—28no—
100C4×D52—28no—
101C13×#95—22no—
102C13×#95—22no—
103#88075—24no—
104#88072—24no—
105#88049—28no—
106#20925—131nomaximal, Sylow
107C24×C13—21no—
108C24×C13C2×D411yescharacteristic
109C23×D13—24no—
110C23×D13—24no—
111C23×D13—24no—
112C23×D13—22no—
113C23×D13—44no—
114C23×D13—44no—
115C13×#41—28no—
116C13×#41—28no—
117C13×#41—44no—
118C13×#41—44no—
119C2×Q8×C13—21no—
120C2×Q8×C13—21no—
121C2×Q8×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13C22×C412yescomplemented
125C2×D4×C13—24no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—42no—
132C2×D4×C13—42no—
133C2×D4×C13C22×C412yescomplemented
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13C22×C412yes—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—24no—
154C22×Dic13—22no—
155C22×Dic13—44no—
156C2×D52—28no—
157C2×D52—24no—
158C2×D52—24no—
159C2×D52—28no—
160C2×D52—24no—
161C2×D52—28no—
162C2×D52—22no—
163C2×D52—22no—
164C2×D52—22no—
165C2×D52C22⋊C4116yescomplemented
166C2×D52C22×C414yes—
167C2×D52C2×D414yes—
168C2×D52C2×D414yes—
169C2×C4×D13—216no—
170C2×C4×D13—432no—
171C2×C4×D13—48no—
172C2×C4×D13—48no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C22⋊C4—44no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—44no—
178C42×C13—24no—
179C42×C13—22no—
180C42×C13—22no—
181C42×C13—42no—
182#6106—216no—
183#6104—216no—
184#6103—216no—
185C4⋊Dic13—24no—
186C4⋊Dic13—22no—
187C4⋊Dic13C2×D414yes—
188#6099—28no—
189#6099—44no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055C22×C414yescomplemented
196C22×AGL(1,ℤ/8)—131no—
197C22×C4×D4—131no—
198C2×#417—131no—
199C2×#418—131no—
200#2297D1311yescharacteristic, complemented
201#1879—134no—
202#1877—134no—
203#1736—131no—
204#1728—131no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13C4×D412yes—
213C23×C13#12012yes—
214C23×C13#12112yes—
215C23×C13C22×D411yescharacteristic
216C22×D13—24no—
217C22×D13—24no—
218C22×D13—24no—
219C22×D13—216no—
220C22×D13—48no—
221C22×D13—416no—
222C22×D13—48no—
223C22×D13—416no—
224C22×D13—44no—
225C22×D13—44no—
226Q8×C13—22no—
227Q8×C13—22no—
228Q8×C13—41no—
229Q8×C13—41no—
230D4×C13—22no—
231D4×C13—22no—
232D4×C13—48no—
233D4×C13—41no—
234D4×C13—41no—
235C2×C4×C13—28no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—44no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—48no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13C2×C22⋊C414yes—
250C2×C4×C13C4×D414yes—
251C2×C4×C13C4×D412yes—
252C2×C4×C13#12012yes—
253C2×C4×C13#12114yes—
254C2×C4×C13#12112yes—
255C2×C4×C13#12314yes—
256C2×C4×C13AGL(1,ℤ/8)14yescomplemented
257C2×C4×C13C23×C411yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×Dic13—24no—
264C2×Dic13—48no—
265C2×Dic13—44no—
266D52—24no—
267D52—24no—
268D52—24no—
269D52—216no—
270D52C2×C22⋊C418yes—
271C4×D13—432no—
272#1055—24no—
273#1055—42no—
274C22×#41C2×D1311yescharacteristic
275C23×D4—131no—
276C24×C4—261no—
277C2×AGL(1,ℤ/8)—138no—
278C2×AGL(1,ℤ/8)—264no—
279C2×AGL(1,ℤ/8)—264no—
280C22×SD16—132no—
281C22×D8—132no—
282C22×M16—131no—
283C22×M16—131no—
284C2×C4×D4—134no—
285C2×C4×D4—264no—
286C2×C4×D4—264no—
287C2×C4×D4—262no—
288C2×#117C2×D1311yescharacteristic
289C22×C4⋊C4—131no—
290C22×C22⋊C4—261no—
291C22×C42C2×D1311yescharacteristic
292#418—264no—
293#417—264no—
294C2×#103—132no—
295C2×#102—132no—
296C2×#102—134no—
297#391C2×D1312yescomplemented
298#390C2×D1312yescomplemented
299#386—21no—
300#386—21no—
301C4×C22⋊C4—22no—
302#340—134no—
303#336—134no—
304C22×C13—24no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—24no—
308C22×C13—44no—
309C22×C13—42no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13—82no—
313C22×C13#38614yes—
314C22×C13C2×C4×D411yescharacteristic
315C22×C13C2×#12011yescharacteristic
316C22×C13C2×#12111yescharacteristic
317C22×C13C2×AGL(1,ℤ/8)12yes—
318C22×C13#57512yes—
319C2×D13—28no—
320C2×D13—432no—
321C2×D13—48no—
322C2×D13—44no—
323C2×D13—44no—
324C2×D13—48no—
325C4×C13—24no—
326C4×C13—42no—
327C4×C13—42no—
328C4×C13—82no—
329C4×C13#38614yes—
330C4×C13C22×C22⋊C411yescharacteristic
331C4×C13C2×C4×D411yescharacteristic
332C4×C13C2×#12111yescharacteristic
333C4×C13C2×#12311yescharacteristic
334Dic13—44no—
335C25—261no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41C4×D1314yescomplemented
342C22×Q8C22×D1311yescharacteristic
343C22×D4—21no—
344C22×D4—134no—
345C22×D4—134no—
346C22×D4—134no—
347C22×D4—132no—
348C22×D4—262no—
349C22×D4—262no—
350C22×D4—262no—
351C22×D4—261no—
352C22×D4C22×D1311yescharacteristic
353C23×C4—21no—
354C23×C4—268no—
355C23×C4—261no—
356C23×C4—264no—
357C23×C4—528no—
358C23×C4C22⋊D1311yescharacteristic
359C23×C4C22⋊D1311yescharacteristic
360C23×C4C22×D1311yescharacteristic
361AGL(1,ℤ/8)—2632no—
362C2×SD16—138no—
363C2×SD16—264no—
364C2×SD16—264no—
365C2×D8—138no—
366C2×D8—264no—
367C2×D8—264no—
368C2×M16—134no—
369C2×M16—262no—
370C2×M16—262no—
371C2×M16—262no—
372C2×M16—262no—
373C2×M16—262no—
374C22×C8—132no—
375C22×C8—132no—
376C4×D4—268no—
377C4×D4—268no—
378C4×D4—2616no—
379#117—22no—
380#117—22no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—132no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4C22×D1312yes—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—268no—
390C2×C22⋊C4—264no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—21no—
394C2×C42C22⋊D1312yes—
395C2×C42C22×D1312yes—
396#103—264no—
397#102—268no—
398#102—264no—
399#95—22no—
400#95—22no—
401C2×C13—24no—
402C2×C13—82no—
403C2×C13C2×#38611yescharacteristic
404C2×C13C4×AGL(1,ℤ/8)12yes—
405C2×C13#300311yescharacteristic
406C2×C13#300511yescharacteristic
407C2×C13#303612yes—
408D13—48no—
409C24—21no—
410C24—264no—
411C24—264no—
412C24—264no—
413C24—262no—
414C24—524no—
415C24—524no—
416C24C2×C22⋊D1311yescharacteristic
417#41—28no—
418#41—28no—
419#41—44no—
420#41—44no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×C4×D1312yescomplemented
427C2×D4—24no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—1316no—
436C2×D4—134no—
437C2×D4—134no—
438C2×D4—134no—
439C2×D4—268no—
440C2×D4—268no—
441C2×D4—268no—
442C2×D4—264no—
443C2×D4—264no—
444C2×D4—264no—
445C2×D4—262no—
446C2×D4—262no—
447C2×D4—262no—
448C2×D4C2×C4×D1312yescomplemented
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—2616no—
459C22×C4—264no—
460C22×C4—262no—
461C22×C4—5232no—
462C22×C4—528no—
463C22×C4—524no—
464C22×C4—528no—
465C22×C4C2×C4×D1312yes—
466C22×C4#612712yes—
467C22×C4D4×D1312yes—
468C22×C4D4×D1312yes—
469C22×C4D4×D1312yes—
470C22×C4#612912yes—
471C22×C4C2×C22⋊D1312yes—
472C22×C4C2×C22⋊D1312yes—
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C23×D1311yescharacteristic
475SD16—2616no—
476D8—2616no—
477M16—268no—
478M16—524no—
479C2×C8—134no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—262no—
484C2×C8—262no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—134no—
488C4⋊C4—264no—
489C4⋊C4—262no—
490C22⋊C4—44no—
491C22⋊C4—42no—
492C22⋊C4—44no—
493C22⋊C4—2616no—
494C42—24no—
495C42—22no—
496C42—22no—
497C42—42no—
498C13#2092511yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—264no—
507C23—264no—
508C23—264no—
509C23—2616no—
510C23—528no—
511C23—5216no—
512C23—5216no—
513C23—528no—
514C23—524no—
515C23—524no—
516C23C4×C22⋊D1312yes—
517C23#8819112yes—
518C23#8819212yes—
519C23C22×C22⋊D1311yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524D4—22no—
525D4—22no—
526D4—48no—
527D4—41no—
528D4—41no—
529D4—138no—
530D4—264no—
531D4—264no—
532D4—264no—
533D4—2616no—
534C2×C4—28no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—44no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—48no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—264no—
549C2×C4—5232no—
550C2×C4—528no—
551C2×C4—524no—
552C2×C4C22⋊C4×D1314yes—
553C2×C4#8813514yes—
554C2×C4#8813714yes—
555C2×C4#8813814yes—
556C2×C4C4×C22⋊D1312yes—
557C2×C4#8819112yes—
558C2×C4#8819212yes—
559C2×C4#8820314yescomplemented
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C2×#612711yescharacteristic
562C2×C4C2×D4×D1311yescharacteristic
563C2×C4C2×D4×D1311yescharacteristic
564C2×C4C2×D4×D1311yescharacteristic
565C2×C4C2×#612911yescharacteristic
566C8—264no—
567C8—522no—
568C22—24no—
569C22—24no—
570C22—22no—
571C22—22no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—81no—
576C22—81no—
577C22—268no—
578C22—5232no—
579C22—528no—
580C22—528no—
581C22—524no—
582C22—524no—
583C22#1171861714yes—
584C22C2×C4×C22⋊D1311yescharacteristic
585C22C2×#8819111yescharacteristic
586C22C2×#8819211yescharacteristic
587C22C2×#8820312yes—
588C22#1171952712yes—
589C4—24no—
590C4—42no—
591C4—42no—
592C4—82no—
593C4—524no—
594C4#1171861714yes—
595C4C2×C22⋊C4×D1311yescharacteristic
596C4C2×#8813511yescharacteristic
597C4C2×#8813711yescharacteristic
598C4C2×#8813811yescharacteristic
599C2—24no—
600C2—82no—
601C2—528no—
602C2C2×#1171861711yescharacteristic
603C2C4×#8820312yes—
604C2#1312406211yescharacteristic
605C2#1312407611yescharacteristic
606C2#1312429612yes—
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2297C2
socleC23×C13C22×D4
prime radicalC22×#88203C2
cosocleC22×C4×C13C24
hypercenter#2297D13
hypocenterC13#20925
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C22×C4×D52C2semidirect
3. C2×#11718893C2semidirect
4. C2×#11718662C2semidirect
5. #13115187C2semidirect
6. #13115173C2semidirect
7. #13114557C2semidirect
8. #13114530C2semidirect
9. C13×#2297C2semidirect
17. C2×#88203C4semidirect
28. C13×#391C22semidirect
29. C13×#390C22semidirect
34. C2×#88075C22semidirect
35. C2×#88072C22semidirect
38. #11718121C22semidirect
39. #11718116C22semidirect
46. C2×C13×#41C2×C4semidirect
80. C2×#6106C2×C4semidirect
83. C2×#6104C2×C4semidirect
95. C2×#6099C2×C4semidirect
124. C2×Q8×C13C22×C4semidirect
133. C2×D4×C13C22×C4semidirect
165. C2×D52C22⋊C4semidirect
195. C2×#1055C22×C4semidirect
200. #2297D13semidirect
256. C2×C4×C13AGL(1,ℤ/8)semidirect
297. #391C2×D13semidirect
298. #390C2×D13semidirect
341. C2×#41C4×D13semidirect
426. C2×Q8C2×C4×D13semidirect
448. C2×D4C2×C4×D13semidirect
498. C13#20925semidirect
559. C2×C4#88203semidirect

Maximal subgroups

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

subgroupindex
C22×#882032
C22×C4×D522
C2×#117188932
C2×#117186622
#131151872
#131151732
#131145572
#131145302
C13×#22972
#2092513