Finite Group Databasebeta

← #14416738

Subgroups — #14416738

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#709C211yesmaximal, characteristic, complemented
2C2×#91428C211yesmaximal, characteristic, complemented
3C2×#91301C211yesmaximal, characteristic
4#11751232C211yesmaximal, characteristic, complemented
5C5×Dic3×M16C211yesmaximal, characteristic, complemented
6C3×#65422C211yesmaximal, characteristic, complemented
7#11748453C211yesmaximal, characteristic, complemented
8#11747830C212yesmaximal, complemented
9#11747743C212yesmaximal, complemented
10#11747741C212yesmaximal, complemented
11#11747740C212yesmaximal, complemented
12C4×#4054—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×#1200—21no—
16C2×C3×C5×M16C2211yescharacteristic
17#91815C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×C4⋊Dic5C2211yescharacteristic
21Dic3×C22⋊D5—21no—
22Dic3×C22⋊D5—21no—
23C2×#6667—21no—
24#91428—21no—
25#91428—21no—
26#91428C2212yes—
27#91428C2212yes—
28Dic3×D20C2211yescharacteristic, complemented
29Dic3×D20C2211yescharacteristic, complemented
30C4×D5×Dic3—21no—
31#91357—21no—
32Dic3×Dic10C2211yescharacteristic, complemented
33Dic3×Dic10C2211yescharacteristic, complemented
34C2×#6658C2212yes—
35#91301C418yescomplemented
36C2×#6653C2212yes—
37#91105C2212yes—
38#91105C2212yes—
39C5×#815C2212yescomplemented
40C5×C8×Dic3C2212yescomplemented
41C3×#3953C2212yescomplemented
42C3×#3948C2212yescomplemented
43#90990C2212yescomplemented
44#90987C2212yescomplemented
45#78866—51nomaximal, Hall
46C2×#4054—31no—
47C4×#709—31no—
48C2×C4×D20—31no—
49C4×C5×M16—31no—
50#65422D311yescharacteristic, complemented
51#65420—31no—
52#65410—31no—
53#65000—32no—
54#64999—32no—
55C4×D40—32no—
56C4×#677—32no—
57C23×D15—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×D60—21no—
60C2×D60—22no—
61C2×D60C2×C414yescomplemented
62C2×D60C2312yes—
63C22×C5×Dic3D411yescharacteristic
64C22×C5×Dic3D411yescharacteristic
65C2×C3×C22⋊D5—21no—
66C22×C3×Dic5—21no—
67C3×#709—22no—
68C3×#709C2×C414yescomplemented
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×Dic10C2311yescharacteristic
72C2×#1200—22no—
73C2×#1200—22no—
74C2×#1200—44no—
75C2×D5×Dic3—21no—
76C2×D5×Dic3—21no—
77C3×C5×M16—22no—
78C2×C3×C5×C8C2312yes—
79#6719—21no—
80C4⋊Dic15C2311yescharacteristic
81C4⋊Dic15C2311yescharacteristic
82C4×Dic15—21no—
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3C2311yescharacteristic
86C4×C5×Dic3C2311yescharacteristic
87C5×#208C2×C414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×C4⋊Dic5—21no—
90C3×C4⋊Dic5C2312yes—
91#6668—21no—
92#6668—21no—
93#6667—22no—
94#6667—22no—
95#6665—21no—
96#6665—21no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6658C2×C418yescomplemented
100#6653C2×C418yescomplemented
101Dic3×#41—51no—
102C2×#949—51no—
103C2×#893—51no—
104C3×#417—51no—
105#5131—51no—
106Dic3×M16D511yescharacteristic, complemented
107#4964—51no—
108#4817—52no—
109#4788—52no—
110#4785—52no—
111#4756—52no—
112C2×#709C2×D311yescharacteristic
113C22×D20—31no—
114C22×C4×D5—61no—
115C2×C5×M16—31no—
116C2×C5×M16C2×D311yescharacteristic
117C2×C42×C5—31no—
118C4×C22⋊D5—61no—
119C4×C22⋊D5—61no—
120C2×#685—61no—
121#4072—31no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123#4054—38no—
124C2×D40—32no—
125C2×#677—32no—
126C4×D20—31no—
127C4×D20—31no—
128C4×D20—32no—
129C4×D20—32no—
130C4×D20—61no—
131C4×D20—61no—
132#4018—61no—
133C42×D5—61no—
134C4×Dic10—31no—
135C4×Dic10—31no—
136C5×#97—32no—
137C4×C5×C8—32no—
138#3953—32no—
139#3953—32no—
140#3953C2×D312yescomplemented
141#3950—32no—
142#3949—32no—
143#3948C2×D312yescomplemented
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—24no—
147C22×D15—22no—
148C22×D15—42no—
149C22×D15—42no—
150C22×C3×D5—21no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5#4112yes—
154C2×C3×C4×C5C2411yescharacteristic
155C2×Dic15—21no—
156C2×Dic15—21no—
157D60—24no—
158D60—22no—
159D60C22×C414yes—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—41no—
162C2×C5×Dic3C2×D411yescharacteristic
163C2×C5×Dic3C2×D411yescharacteristic
164C2×C5×Dic3C2×D411yescharacteristic
165C2×C5×Dic3C2×D411yescharacteristic
166C3×C22⋊D5—24no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—42no—
170C3×D20—21no—
171C3×D20C22×C412yescomplemented
172C3×C4×D5—24no—
173C3×Dic10—21no—
174C3×Dic10C22×C412yescomplemented
175#1200—44no—
176#1200—44no—
177D5×Dic3—42no—
178D5×Dic3—42no—
179C3×C5×C8—22no—
180C5×C3⋊C8C22×C414yescomplemented
181C2×C3×#41—51no—
182C22×D12—51no—
183C22×C4×D3—101no—
184C2×C3×M16C2×D511yescharacteristic
185C2×C3×C4⋊C4—51no—
186#949—58no—
187Q8×Dic3—51no—
188Q8×Dic3—51no—
189C2×#215—52no—
190D4×Dic3—51no—
191D4×Dic3—51no—
192D4×Dic3—101no—
193D4×Dic3—101no—
194C2×#213—52no—
195C2×(C2×D3)⋊C4—101no—
196#926—51no—
197#926—101no—
198C2×C4×Dic3—101no—
199C2×C4×Dic3C2×D511yescharacteristic
200C2×#208C2×D511yescharacteristic
201#893—52no—
202#893—52no—
203#893—101no—
204#893—101no—
205C3×#103—52no—
206C3×#102—52no—
207#821—52no—
208#821—52no—
209#815C2×D512yescomplemented
210C8×Dic3C2×D512yescomplemented
211#808—52no—
212#807—52no—
213C23×D5—61no—
214C22×C4×C5—31no—
215C22×C4×C5—31no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—21no—
218C22×Dic5—21no—
219#709—22no—
220#709C4×D314yescomplemented
221C2×D20—34no—
222C2×D20—32no—
223C2×D20—61no—
224C2×D20—62no—
225C2×D20C22×D311yescharacteristic
226C2×C4×D5—21no—
227C2×C4×D5—62no—
228C2×C4×D5—62no—
229C2×C4×D5—61no—
230C2×C4×D5—61no—
231C2×C4×D5—124no—
232C2×Dic10C22×D311yescharacteristic
233C5×M16—22no—
234C5×M16—34no—
235C2×C5×C8—32no—
236C2×C5×C8C22×D312yes—
237C42×C5—31no—
238C42×C5—31no—
239C42×C5—31no—
240C42×C5—31no—
241C22⋊Dic5—61no—
242#685—62no—
243#685—62no—
244#685—61no—
245#685—61no—
246C4⋊Dic5—21no—
247C4⋊Dic5—31no—
248C4⋊Dic5—31no—
249C4⋊Dic5C22×D312yes—
250#683—61no—
251#683—61no—
252C4×Dic5—61no—
253C4×Dic5—61no—
254C4×Dic5—61no—
255D40—38no—
256#677—38no—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—151no—
259C2×C4×D4—151no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—151no—
266#417—51no—
267C4×M16—31no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—24no—
273C2×D15—48no—
274C2×D15—42no—
275C2×D15—42no—
276C2×C3×D5—22no—
277C2×C3×D5—41no—
278C2×C3×D5—41no—
279C3×C4×C5C4×D412yes—
280C3×C4×C5C23×C411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282Dic15—41no—
283Dic15—41no—
284C3×Dic5—22no—
285C3×Dic5—42no—
286C5×Dic3—21no—
287C5×Dic3—21no—
288C5×Dic3—21no—
289C5×Dic3AGL(1,ℤ/8)12yescomplemented
290C23×D3—101no—
291C3×#41—54no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—51no—
295C2×C3×D4—101no—
296C22×C3×C4—101no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C22×Dic3—101no—
300C22×Dic3—101no—
301C22×Dic3D2011yescharacteristic
302C22×Dic3D2011yescharacteristic
303C2×D12—54no—
304C2×D12—52no—
305C2×D12—101no—
306C2×D12—102no—
307C2×C4×D3—102no—
308C2×C4×D3—102no—
309C2×C4×D3—204no—
310C3×M16—22no—
311C2×C3×C8C22×D512yes—
312C3×C4⋊C4—52no—
313C3×C4⋊C4—101no—
314#217—101no—
315#217—101no—
316#217—101no—
317#215—58no—
318#213—58no—
319(C2×D3)⋊C4—102no—
320(C2×D3)⋊C4—102no—
321C4⋊Dic3—51no—
322C4⋊Dic3—51no—
323C4⋊Dic3—101no—
324C4⋊Dic3—101no—
325C4×Dic3—101no—
326C4×Dic3—101no—
327C4×Dic3—101no—
328C4×Dic3D2011yescharacteristic
329C4×Dic3D2011yescharacteristic
330C4×Dic3C22×D511yescharacteristic
331C4×Dic3C22×D511yescharacteristic
332#208C4×D514yescomplemented
333C2×C3⋊C8C22×D512yes—
334C23×C5D3×D411yescharacteristic
335C22×D5—21no—
336C22×D5—64no—
337C22×D5—62no—
338C22×D5—122no—
339C22×D5—122no—
340C2×C4×C5—31no—
341C2×C4×C5—31no—
342C2×C4×C5—31no—
343C2×C4×C5—31no—
344C2×C4×C5—62no—
345C2×C4×C5—121no—
346C2×C4×C5C2×C4×D312yes—
347C2×C4×C5D3×D411yescharacteristic
348C2×C4×C5#23712yes—
349C2×C4×C5C23×D311yescharacteristic
350C22⋊D5—24no—
351C2×Dic5—21no—
352C2×Dic5—22no—
353C2×Dic5—42no—
354C2×Dic5—61no—
355C2×Dic5—61no—
356D20—21no—
357D20—34no—
358D20—64no—
359D20—62no—
360D20C2×C4×D312yescomplemented
361C4×D5—24no—
362C4×D5—124no—
363C4×D5—124no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—21no—
367Dic10C2×C4×D312yescomplemented
368C5×C8—22no—
369C5×C8—34no—
370C2×#41—51no—
371C22×D4—151no—
372C23×C4—301no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—31no—
377C2×M16D3×D511yescharacteristic
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—152no—
381C4×D4—152no—
382C4×D4—151no—
383C4×D4—151no—
384C4×D4—301no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4—301no—
388#117—151no—
389#117—301no—
390C2×C4⋊C4—51no—
391C2×C22⋊C4—301no—
392C2×C42—31no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—52no—
397#102—52no—
398#102—152no—
399#102—152no—
400#97—32no—
401C4×C8—32no—
402C2×C3×C5—22no—
403C2×C3×C5C2×C4×D411yescharacteristic
404C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C3×C5#57511yescharacteristic
406D15—44no—
407C3×D5—42no—
408C23×C3—101no—
409C23×C3C2×D2011yescharacteristic
410C22×D3—102no—
411C22×D3—104no—
412C22×D3—202no—
413C22×D3—202no—
414C3×Q8—52no—
415C3×Q8—101no—
416C3×D4—52no—
417C3×D4—104no—
418C3×D4—101no—
419C2×C3×C4—101no—
420C2×C3×C4—104no—
421C2×C3×C4—102no—
422C2×C3×C4—202no—
423C2×C3×C4C2×C4×D512yes—
424C2×C3×C4C2×D2011yescharacteristic
425C2×C3×C4#70912yes—
426C2×C3×C4C23×D511yescharacteristic
427C2×Dic3—22no—
428C2×Dic3—41no—
429C2×Dic3—101no—
430C2×Dic3—101no—
431C2×Dic3—202no—
432C2×Dic3—202no—
433C2×Dic3C2×D2011yescharacteristic
434C2×Dic3C2×D2011yescharacteristic
435C2×Dic3C2×D2011yescharacteristic
436C2×Dic3C2×D2011yescharacteristic
437D12—54no—
438D12—102no—
439D12—104no—
440C4×D3—204no—
441C4×D3—204no—
442C3×C8—22no—
443C3⋊C8C2×C4×D514yescomplemented
444C22×C5—21no—
445C22×C5—21no—
446C22×C5#67⋊C412yes—
447C22×C5C2×D3×D411yescharacteristic
448C2×D5—22no—
449C2×D5—41no—
450C2×D5—41no—
451C2×D5—64no—
452C2×D5—128no—
453C2×D5—122no—
454C2×D5—122no—
455C4×C5—32no—
456C4×C5—61no—
457C4×C5—61no—
458C4×C5—61no—
459C4×C5#67⋊C412yes—
460C4×C5C22×C4×D311yescharacteristic
461C4×C5C2×#23711yescharacteristic
462Dic5—22no—
463Dic5—42no—
464Dic5—121no—
465Dic5—121no—
466C24—301no—
467#41—54no—
468#41—102no—
469C2×Q8—51no—
470C2×D4—51no—
471C2×D4—101no—
472C2×D4—154no—
473C2×D4—152no—
474C2×D4—301no—
475C2×D4—302no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—302no—
481C22×C4—302no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—604no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—22no—
489M16—34no—
490C2×C8—32no—
491C2×C8C2×D3×D512yes—
492C4⋊C4—52no—
493C4⋊C4—101no—
494C4⋊C4—151no—
495C4⋊C4—151no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—302no—
499C22⋊C4—302no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—31no—
504C42—31no—
505C42—31no—
506C42—31no—
507C42—301no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—102no—
514C22×C3—201no—
515C22×C3—201no—
516C22×C3C4×D2012yes—
517C22×C3C22×D2011yescharacteristic
518C2×D3—104no—
519C2×D3—208no—
520C2×D3—202no—
521C2×D3—202no—
522C3×C4—102no—
523C3×C4—202no—
524C3×C4C4×D2012yes—
525C3×C4C22×C4×D511yescharacteristic
526C3×C4C2×#70911yescharacteristic
527Dic3—21no—
528Dic3—21no—
529Dic3—21no—
530Dic3—201no—
531Dic3—201no—
532Dic3#405412yescomplemented
533C2×C5—22no—
534C2×C5C2×#67⋊C411yescharacteristic
535C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
536C2×C5#577711yescharacteristic
537D5—42no—
538D5—124no—
539C23—101no—
540C23—304no—
541C23—302no—
542C23—602no—
543C23—602no—
544C23D3×D2011yescharacteristic
545Q8—52no—
546Q8—101no—
547D4—52no—
548D4—104no—
549D4—101no—
550D4—154no—
551D4—304no—
552D4—302no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—62no—
558C2×C4—101no—
559C2×C4—104no—
560C2×C4—102no—
561C2×C4—121no—
562C2×C4—202no—
563C2×C4—301no—
564C2×C4—301no—
565C2×C4—604no—
566C2×C4—602no—
567C2×C4—604no—
568C2×C4—602no—
569C2×C4C4×D3×D512yes—
570C2×C4D3×D2011yescharacteristic
571C2×C4#677912yes—
572C2×C4C22×D3×D511yescharacteristic
573C8—22no—
574C8—34no—
575C2×C3—22no—
576C2×C3—202no—
577C2×C3C2×C4×D2011yescharacteristic
578C2×C3C2×#405411yescharacteristic
579C2×C3#6608211yescharacteristic
580D3—204no—
581C5#7886611yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—102no—
585C22—201no—
586C22—201no—
587C22—304no—
588C22—608no—
589C22—602no—
590C22—602no—
591C22#9139512yes—
592C22C2×D3×D2011yescharacteristic
593C4—32no—
594C4—61no—
595C4—61no—
596C4—61no—
597C4—102no—
598C4—202no—
599C4—601no—
600C4—601no—
601C4#9139512yes—
602C4C2×C4×D3×D511yescharacteristic
603C4C2×#677911yescharacteristic
604C3C4×#405411yescharacteristic, complemented, Sylow
605C2—22no—
606C2—202no—
607C2—604no—
608C2D3×#405411yescharacteristic
609C2#1175402811yescharacteristic
610C2C2×#9139511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#91301C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. Dic3×#709C2semidirect
2. C2×#91428C2semidirect
4. #11751232C2semidirect
5. C5×Dic3×M16C2semidirect
6. C3×#65422C2semidirect
7. #11748453C2semidirect
8. #11747830C2semidirect
9. #11747743C2semidirect
10. #11747741C2semidirect
11. #11747740C2semidirect
28. Dic3×D20C22semidirect
29. Dic3×D20C22semidirect
32. Dic3×Dic10C22semidirect
33. Dic3×Dic10C22semidirect
35. #91301C4semidirect
39. C5×#815C22semidirect
40. C5×C8×Dic3C22semidirect
41. C3×#3953C22semidirect
42. C3×#3948C22semidirect
43. #90990C22semidirect
44. #90987C22semidirect
50. #65422D3semidirect
61. C2×D60C2×C4semidirect
68. C3×#709C2×C4semidirect
87. C5×#208C2×C4semidirect
99. #6658C2×C4semidirect
100. #6653C2×C4semidirect
106. Dic3×M16D5semidirect
140. #3953C2×D3semidirect
143. #3948C2×D3semidirect
171. C3×D20C22×C4semidirect
174. C3×Dic10C22×C4semidirect
180. C5×C3⋊C8C22×C4semidirect
209. #815C2×D5semidirect
210. C8×Dic3C2×D5semidirect
220. #709C4×D3semidirect
289. C5×Dic3AGL(1,ℤ/8)semidirect
332. #208C4×D5semidirect
360. D20C2×C4×D3semidirect
367. Dic10C2×C4×D3semidirect
443. C3⋊C8C2×C4×D5semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
532. Dic3#4054semidirect
581. C5#78866semidirect
604. C3C4×#4054semidirect

Maximal subgroups

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

subgroupindex
Dic3×#7092
C2×#914282
C2×#913012
#117512322
C5×Dic3×M162
C3×#654222
#117484532
#117478302
#117477432
#117477412
#117477402
C4×#40543
#788665