Finite Group Databasebeta

← #14416725

Subgroups — #14416725

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
1C2×#91821C211yesmaximal, characteristic
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3#11754436C211yesmaximal, characteristic, complemented
4C3×#65504C211yesmaximal, characteristic, complemented
5#11749014C212yesmaximal, complemented
6#11749011C212yesmaximal, complemented
7#11748989C212yesmaximal, complemented
8#11748986C212yesmaximal, complemented
9#11748472C211yesmaximal, characteristic, complemented
10#11748394C211yesmaximal, characteristic, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12C4×#4078—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C23×C5×Dic3—21no—
16C2×#6716C2212yes—
17#91821C418yescomplemented
18C2×#6715C2212yes—
19C2×#6710C2211yescharacteristic
20C2×C5×#217—21no—
21C5×D4×Dic3—21no—
22C5×D4×Dic3—21no—
23C5×D4×Dic3C2212yes—
24C5×D4×Dic3C2212yes—
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C3×#4072C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29#91556—21no—
30#91556—21no—
31#91428C2211yescharacteristic, complemented
32#91428C2211yescharacteristic, complemented
33C4×#1200—21no—
34#91386—21no—
35#91340C2211yescharacteristic, complemented
36#91340C2211yescharacteristic, complemented
37C3×#3964C2212yes—
38C3×#3964C2212yes—
39#90989C2212yescomplemented
40#90986C2212yescomplemented
41#90975C2212yescomplemented
42#90969C2212yescomplemented
43#90953C2212yescomplemented
44Dic3×#168C2212yescomplemented
45#78914—51nomaximal, Hall
46C2×C4×C5×D4—31no—
47C2×#4078—31no—
48C4×#709—31no—
49#65504D311yescharacteristic, complemented
50#65307—32no—
51C4×#687—32no—
52#65303—32no—
53C4×#686—32no—
54#65255—31no—
55#65253—31no—
56C4×#681—31no—
57C24×C3×C5—21no—
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4C2×C414yescomplemented
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817C2×C414yescomplemented
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C22×C5×Dic3—21no—
70C22×C5×Dic3—22no—
71C22×C5×Dic3—22no—
72C22×C5×Dic3—44no—
73C22×C5×Dic3D411yescharacteristic
74C22×C5×Dic3D411yescharacteristic
75C2×#1200—21no—
76C2×#1200—21no—
77#6716C2×C418yescomplemented
78#6715C2×C418yescomplemented
79#6710C2×C414yescomplemented
80C2×C3⋊#168C2312yes—
81C5×#217—22no—
82C5×#217—22no—
83C5×C4⋊Dic3—21no—
84C5×C4⋊Dic3C2312yes—
85C4×C5×Dic3D411yescharacteristic
86C4×C5×Dic3D411yescharacteristic
87C4×C5×Dic3C2311yescharacteristic
88C4×C5×Dic3C2311yescharacteristic
89C3×C22⋊Dic5—21no—
90C3×C4⋊Dic5C2311yescharacteristic
91C3×C4⋊Dic5C2311yescharacteristic
92C3×C4×Dic5—21no—
93C3×#681—22no—
94C2×C3×#168C2312yes—
95#6669—21no—
96#6669—21no—
97#6667—21no—
98#6667—21no—
99Dic3×Dic5—21no—
100Dic3×Dic5—21no—
101C2×D4×Dic3D511yescharacteristic, complemented
102C2×#932—51no—
103#5522—51no—
104C3×#418—51no—
105#5133—51no—
106Dic3×M16—51no—
107#4995—51no—
108#4785—52no—
109#4758—52no—
110#4757—52no—
111#4756—52no—
112C22×C5×D4C2×D311yescharacteristic
113C23×C4×C5—61no—
114C2×#709—31no—
115C4×C5×D4—32no—
116C4×C5×D4—32no—
117C4×C5×D4—61no—
118C4×C5×D4—61no—
119C2×C5×C4⋊C4—31no—
120C2×C5×C22⋊C4—61no—
121C2×C42×C5—31no—
122C2×#687—32no—
123#4078—38no—
124C2×#686—32no—
125C4×C22⋊D5—61no—
126C4×C22⋊D5—61no—
127#4072C2×D311yescharacteristic
128C2×#681—31no—
129C2×#681C2×D311yescharacteristic
130C4×D20—31no—
131C4×D20—31no—
132#4018—61no—
133C42×D5—61no—
134C4×Dic10—31no—
135C4×Dic10—31no—
136#3964C2×D312yes—
137#3964C2×D312yes—
138#3942—32no—
139#3941—32no—
140#3940—32no—
141#3939—32no—
142#3935—32no—
143C4×#168—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5—24no—
146C23×C3×C5—22no—
147C23×C3×C5—42no—
148C23×C3×C5—42no—
149C23×C3×C5C2×D411yescharacteristic
150C22×D15—21no—
151C3×C5×D4—24no—
152C3×C5×D4—22no—
153C3×C5×D4C22×C414yes—
154C2×C3×C4×C5C22×C412yes—
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5C2411yescharacteristic
158#1220—24no—
159C2×Dic15—21no—
160D60—21no—
161D60C22×C412yescomplemented
162C4×D15—24no—
163Dic30—21no—
164Dic30C22×C412yescomplemented
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—41no—
168C2×C5×Dic3—44no—
169C2×C5×Dic3—42no—
170C2×C5×Dic3—44no—
171C2×C5×Dic3C2×D411yescharacteristic
172C2×C5×Dic3C2×D411yescharacteristic
173C2×C5×Dic3C2×D411yescharacteristic
174C2×C5×Dic3C2×D411yescharacteristic
175C2×C3×Dic5—21no—
176C2×C3×Dic5—21no—
177#1200—42no—
178#1200—42no—
179C3⋊#168C22×C414yescomplemented
180C3×#168—22no—
181C22×C3×D4C2×D511yescharacteristic
182C23×Dic3—21no—
183C2×#235—51no—
184C2×C3×M16—51no—
185C3×#117—51no—
186C2×#217—21no—
187D4×Dic3—21no—
188D4×Dic3—21no—
189D4×Dic3C2×D512yes—
190D4×Dic3C2×D512yes—
191C2×#214—52no—
192#932—58no—
193C2×#213—52no—
194C2×C4⋊Dic3C2×D511yescharacteristic
195C2×C4×Dic3C2×D511yescharacteristic
196C2×#208—51no—
197#893—51no—
198#893—51no—
199#887—51no—
200#887—51no—
201#67⋊C4—101no—
202#67⋊C4—101no—
203#872—101no—
204C42×D3—101no—
205C3×#102—52no—
206C3×#102—52no—
207#821—52no—
208#816—52no—
209#815—52no—
210C8×Dic3—52no—
211#808—52no—
212#807—52no—
213C24×C5—21no—
214C2×C5×D4—21no—
215C2×C5×D4—22no—
216C2×C5×D4C4×D314yescomplemented
217C2×C5×D4C22×D312yes—
218C22×C4×C5—31no—
219C22×C4×C5—31no—
220C22×C4×C5—62no—
221C22×C4×C5—62no—
222C22×C4×C5—61no—
223C22×C4×C5—124no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—61no—
226#709—34no—
227#709—62no—
228C2×D20—31no—
229C2×C4×D5—61no—
230C2×C4×D5—61no—
231C2×C4×D5—61no—
232C2×Dic10—31no—
233C5×C4⋊C4—32no—
234C5×C4⋊C4—61no—
235C5×C22⋊C4—62no—
236C5×C22⋊C4—62no—
237C42×C5—31no—
238C42×C5—31no—
239C42×C5—31no—
240C42×C5—31no—
241C22⋊Dic5—21no—
242#687—38no—
243#686—38no—
244#685—61no—
245#685—61no—
246C4⋊Dic5C22×D311yescharacteristic
247C4⋊Dic5C22×D311yescharacteristic
248#683—61no—
249#683—61no—
250C4×Dic5—21no—
251C4×Dic5—61no—
252C4×Dic5—61no—
253#681—22no—
254#681—34no—
255C2×#168—32no—
256C2×#168C22×D312yes—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—151no—
259C2×C4×D4—31no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—51no—
266#417—151no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5—24no—
271C22×C3×C5—48no—
272C22×C3×C5—42no—
273C22×C3×C5—42no—
274C22×C3×C5C4×D412yes—
275C22×C3×C5C22×D411yescharacteristic
276C2×D15—22no—
277C2×D15—41no—
278C2×D15—41no—
279C3×C4×C5C4×D412yes—
280C3×C4×C5C23×C411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282Dic15—22no—
283C3×Dic5—41no—
284C3×Dic5—41no—
285C5×Dic3—21no—
286C5×Dic3—21no—
287C5×Dic3—21no—
288C5×Dic3—42no—
289C5×Dic3AGL(1,ℤ/8)12yescomplemented
290C24×C3—21no—
291C2×C3×D4—22no—
292C2×C3×D4—21no—
293C2×C3×D4C4×D514yescomplemented
294C2×C3×D4C22×D512yes—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—101no—
297C22×Dic3—21no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—44no—
301C22×Dic3C22⋊D511yescharacteristic
302C22×Dic3C22⋊D511yescharacteristic
303#235—54no—
304#235—102no—
305C2×D12—51no—
306C2×C4×D3—101no—
307C2×C4×D3—101no—
308C2×C4×D3—101no—
309C2×Dic6—51no—
310C3×M16—102no—
311C2×C3×C8—52no—
312C3×C4⋊C4—51no—
313C3×C4⋊C4—51no—
314C3×C22⋊C4—101no—
315C3×C42—101no—
316#217—22no—
317#217—22no—
318#214—58no—
319#213—58no—
320(C2×D3)⋊C4—101no—
321(C2×D3)⋊C4—101no—
322C4⋊Dic3—21no—
323C4⋊Dic3C22×D512yes—
324Dic3⋊C4—101no—
325Dic3⋊C4—101no—
326C4×Dic3—101no—
327C4×Dic3—101no—
328C4×Dic3C22⋊D511yescharacteristic
329C4×Dic3C22⋊D511yescharacteristic
330C4×Dic3C22×D511yescharacteristic
331C4×Dic3C22×D511yescharacteristic
332#208—54no—
333C2×C3⋊C8—52no—
334C23×C5—24no—
335C23×C5—22no—
336C23×C5—42no—
337C23×C5—42no—
338C23×C5D3×D411yescharacteristic
339C22×D5—61no—
340C5×D4—24no—
341C5×D4—22no—
342C5×D4C2×C4×D314yes—
343C2×C4×C5—31no—
344C2×C4×C5—31no—
345C2×C4×C5—31no—
346C2×C4×C5—31no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—124no—
350C2×C4×C5—121no—
351C2×C4×C5—124no—
352C2×C4×C5—122no—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5#23712yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—64no—
358C2×Dic5—21no—
359C2×Dic5—21no—
360C2×Dic5—61no—
361D20—32no—
362D20—61no—
363C4×D5—64no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—32no—
367Dic10—61no—
368#168—22no—
369#168—34no—
370C2×#41—151no—
371C22×D4D3×D511yescharacteristic
372C23×C4—61no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—51no—
377C2×M16—151no—
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—32no—
381C4×D4—32no—
382C4×D4—61no—
383C4×D4—61no—
384C4×D4—151no—
385C4×D4—151no—
386C4×D4—301no—
387C4×D4—301no—
388#117—51no—
389#117—301no—
390C2×C4⋊C4—31no—
391C2×C22⋊C4—61no—
392C2×C42—31no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—152no—
397#102—52no—
398#102—52no—
399#102—152no—
400#97—152no—
401C4×C8—152no—
402C2×C3×C5—22no—
403C2×C3×C5—44no—
404C2×C3×C5C2×C4×D411yescharacteristic
405C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C3×C5#57511yescharacteristic
407D15—42no—
408C23×C3—22no—
409C23×C3—24no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3C2×C22⋊D511yescharacteristic
413C22×D3—101no—
414C3×D4—22no—
415C3×D4—24no—
416C3×D4C2×C4×D514yes—
417C2×C3×C4—101no—
418C2×C3×C4—101no—
419C2×C3×C4C2×C4×D512yes—
420C2×C3×C4#70912yes—
421C2×C3×C4C2×C22⋊D511yescharacteristic
422C2×C3×C4C23×D511yescharacteristic
423#67—104no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—41no—
427C2×Dic3—44no—
428C2×Dic3—42no—
429C2×Dic3—44no—
430C2×Dic3—101no—
431C2×Dic3C2×C22⋊D511yescharacteristic
432C2×Dic3C2×C22⋊D511yescharacteristic
433C2×Dic3C2×C22⋊D511yescharacteristic
434C2×Dic3C2×C22⋊D511yescharacteristic
435D12—52no—
436D12—101no—
437C4×D3—104no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—52no—
441Dic6—101no—
442C3×C8—102no—
443C3⋊C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—24no—
447C22×C5—48no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5#67⋊C412yes—
451C22×C5C2×D3×D411yescharacteristic
452C2×D5—62no—
453C2×D5—121no—
454C2×D5—121no—
455C4×C5—32no—
456C4×C5—61no—
457C4×C5—61no—
458C4×C5—61no—
459C4×C5—122no—
460C4×C5#67⋊C412yes—
461C4×C5C22×C4×D311yescharacteristic
462C4×C5C2×#23711yescharacteristic
463Dic5—41no—
464Dic5—41no—
465Dic5—62no—
466C24—21no—
467#41—154no—
468#41—302no—
469C2×Q8—151no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—151no—
473C2×D4—301no—
474C2×D4#120014yescomplemented
475C2×D4C2×D3×D512yes—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—62no—
479C22×C4—62no—
480C22×C4—61no—
481C22×C4—124no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—301no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—102no—
489M16—154no—
490C2×C8—52no—
491C2×C8—152no—
492C4⋊C4—32no—
493C4⋊C4—51no—
494C4⋊C4—51no—
495C4⋊C4—61no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—62no—
499C22⋊C4—62no—
500C22⋊C4—101no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—31no—
504C42—31no—
505C42—31no—
506C42—31no—
507C42—101no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—24no—
514C22×C3—48no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3C4×C22⋊D512yes—
518C22×C3C22×C22⋊D511yescharacteristic
519C2×D3—102no—
520C2×D3—201no—
521C2×D3—201no—
522C3×C4—201no—
523C3×C4—201no—
524C3×C4C4×C22⋊D512yes—
525C3×C4C22×C4×D511yescharacteristic
526C3×C4C2×#70911yescharacteristic
527Dic3—21no—
528Dic3—21no—
529Dic3—21no—
530Dic3—42no—
531Dic3—102no—
532Dic3#407812yescomplemented
533C2×C5—22no—
534C2×C5—44no—
535C2×C5C2×#67⋊C411yescharacteristic
536C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
537C2×C5#577311yescharacteristic
538D5—122no—
539C23—22no—
540C23—24no—
541C23—42no—
542C23—42no—
543C23—301no—
544C23D3×C22⋊D511yescharacteristic
545Q8—152no—
546Q8—301no—
547D4—22no—
548D4—24no—
549D4—152no—
550D4—304no—
551D4—301no—
552D4C2×#120014yes—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—124no—
562C2×C4—121no—
563C2×C4—124no—
564C2×C4—122no—
565C2×C4—301no—
566C2×C4—304no—
567C2×C4—602no—
568C2×C4—602no—
569C2×C4#677912yes—
570C2×C4C2×#120012yes—
571C2×C4D3×C22⋊D511yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—102no—
574C8—154no—
575C2×C3—22no—
576C2×C3—44no—
577C2×C3C2×C4×C22⋊D511yescharacteristic
578C2×C3C2×#407811yescharacteristic
579C2×C3#6615611yescharacteristic
580D3—202no—
581C5#7891411yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—24no—
585C22—48no—
586C22—42no—
587C22—42no—
588C22—302no—
589C22—601no—
590C22—601no—
591C22#9155612yes—
592C22C2×D3×C22⋊D511yescharacteristic
593C4—32no—
594C4—61no—
595C4—61no—
596C4—61no—
597C4—122no—
598C4—201no—
599C4—201no—
600C4—302no—
601C4#9155612yes—
602C4C2×#677911yescharacteristic
603C4C22×#120011yescharacteristic
604C3C4×#407811yescharacteristic, complemented, Sylow
605C2—22no—
606C2—44no—
607C2—602no—
608C2D3×#407811yescharacteristic
609C2#1175469611yescharacteristic
610C2C2×#9155611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91821C2
cosocleC2×C3×C4×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×D4×Dic3C2semidirect
3. #11754436C2semidirect
4. C3×#65504C2semidirect
5. #11749014C2semidirect
6. #11749011C2semidirect
7. #11748989C2semidirect
8. #11748986C2semidirect
9. #11748472C2semidirect
10. #11748394C2semidirect
11. Dic3×#681C2semidirect
17. #91821C4semidirect
31. #91428C22semidirect
32. #91428C22semidirect
35. #91340C22semidirect
36. #91340C22semidirect
39. #90989C22semidirect
40. #90986C22semidirect
41. #90975C22semidirect
42. #90969C22semidirect
43. #90953C22semidirect
44. Dic3×#168C22semidirect
49. #65504D3semidirect
60. C2×C3×C5×D4C2×C4semidirect
65. #6817C2×C4semidirect
77. #6716C2×C4semidirect
78. #6715C2×C4semidirect
79. #6710C2×C4semidirect
101. C2×D4×Dic3D5semidirect
161. D60C22×C4semidirect
164. Dic30C22×C4semidirect
179. C3⋊#168C22×C4semidirect
216. C2×C5×D4C4×D3semidirect
289. C5×Dic3AGL(1,ℤ/8)semidirect
293. C2×C3×D4C4×D5semidirect
474. C2×D4#1200semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
532. Dic3#4078semidirect
581. C5#78914semidirect
604. C3C4×#4078semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C2×C5×D4×Dic32
#117544362
C3×#655042
#117490142
#117490112
#117489892
#117489862
#117484722
#117483942
Dic3×#6812
C4×#40783
#789145