Finite Group Databasebeta

← C4×#91312 #14416734

Subgroups — C4×#91312 #14416734

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
1C4×#6817C211yesmaximal, characteristic, complemented
2C2×C3×C4×D20C211yesmaximal, characteristic, complemented
3C2×#91312C211yesmaximal, characteristic
4C4×C5×#208C211yesmaximal, characteristic, complemented
5#11748453C211yesmaximal, characteristic, complemented
6#11748413C211yesmaximal, characteristic, complemented
7#11748367C211yesmaximal, characteristic, complemented
8#11747052C212yesmaximal, complemented
9C4×#6657C212yesmaximal, complemented
10#11747023C212yesmaximal, complemented
11C4×#6653C212yesmaximal, complemented
12C4×#4054—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5—21no—
16C2×C3×C42×C5C2211yescharacteristic
17C4×#1220—21no—
18C4×#1220—21no—
19#91815C2211yescharacteristic
20C4×D60C2211yescharacteristic, complemented
21C4×D60C2211yescharacteristic, complemented
22#91761—21no—
23C42×D15—21no—
24C4×Dic30C2211yescharacteristic, complemented
25C4×Dic30C2211yescharacteristic, complemented
26C2×C5×#208C2211yescharacteristic
27C2×C5×#208C2211yescharacteristic
28C2×C3×#685—21no—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C3×C4×D20—21no—
31C3×C4×D20—21no—
32C3×C4×D20C2212yes—
33C3×C4×D20C2212yes—
34#91312C418yesdirect product factor
35C2×#6657C2212yes—
36C2×#6653C2212yes—
37C5×#803C2212yescomplemented
38C4×C5×C3⋊C8C2212yescomplemented
39#90990C2212yescomplemented
40#90987C2212yescomplemented
41#90974C2212yescomplemented
42#90968C2212yescomplemented
43#90965C2212yes—
44#90965C2212yes—
45C4×#932—51nomaximal, Hall
46C2×#4054—31no—
47C4×#709—31no—
48C2×C4×D20D311yescharacteristic, complemented
49C4×C5×M16—31no—
50#65422—31no—
51#65420—31no—
52#65410—31no—
53#65000—32no—
54#64999—32no—
55C4×D40—32no—
56C4×#677—32no—
57C23×C3×D5—21no—
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5D411yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C2×#1220—21no—
62#6817—22no—
63#6817C2×C414yescomplemented
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×C4×D15—21no—
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C22×C3×Dic5—21no—
70C2×C3×D20—21no—
71C2×C3×D20—22no—
72C2×C3×D20C2×C414yescomplemented
73C2×C3×D20C2312yes—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—44no—
77C3×C42×C5D411yescharacteristic
78C3×C42×C5D411yescharacteristic
79C3×C42×C5C2311yescharacteristic
80C3×C42×C5C2311yescharacteristic
81#6719—21no—
82#6714—21no—
83#6714—21no—
84C4⋊Dic15C2311yescharacteristic
85C4⋊Dic15C2311yescharacteristic
86#6712—21no—
87#6712—21no—
88C4×Dic15—21no—
89C4×Dic15—21no—
90C4×Dic15—21no—
91C5×#208—22no—
92C5×#208C2×C414yescomplemented
93C2×C5×C3⋊C8C2312yes—
94C2×C5×C3⋊C8C2312yes—
95C3×#685—22no—
96C3×#685—22no—
97C3×C4⋊Dic5—21no—
98C3×C4⋊Dic5C2312yes—
99#6657C2×C418yescomplemented
100#6653C2×C418yescomplemented
101C2×C3×C4×D4—51no—
102C2×#932—51no—
103C4×#235—51no—
104#5215—51no—
105#5018—52no—
106C4×#214—52no—
107#5014—52no—
108C4×#213—52no—
109#4966—51no—
110#4964—51no—
111C4×#208D511yescharacteristic, complemented
112C2×#709—31no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—21no—
115C2×C5×M16—31no—
116C2×C5×M16—31no—
117C2×C42×C5C2×D311yescharacteristic
118C4×C22⋊D5—61no—
119C4×C22⋊D5—61no—
120C2×#685—21no—
121#4072—31no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123#4054—38no—
124C2×D40—32no—
125C2×#677—32no—
126C4×D20—21no—
127C4×D20—21no—
128C4×D20—31no—
129C4×D20—31no—
130C4×D20C2×D312yes—
131C4×D20C2×D312yes—
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#3953—32no—
141#3950—32no—
142#3949—32no—
143#3948—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C3×D5—24no—
148C22×C3×D5—22no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—41no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D411yescharacteristic
159C2×C3×C4×C5#4112yes—
160C2×C3×C4×C5C2411yescharacteristic
161#1220—24no—
162C2×Dic15—21no—
163C2×Dic15—21no—
164C2×Dic15—21no—
165D60—21no—
166D60C22×C412yescomplemented
167C4×D15—24no—
168C4×D15—42no—
169C4×D15—42no—
170Dic30—21no—
171Dic30C22×C412yescomplemented
172C2×C3×Dic5—22no—
173C2×C3×Dic5—42no—
174C3×D20—24no—
175C3×D20—22no—
176C3×D20C22×C414yes—
177C3×C4×D5—44no—
178C3×C4×D5—44no—
179C5×C3⋊C8—22no—
180C5×C3⋊C8C22×C414yescomplemented
181C22×C3×D4—51no—
182C23×C3×C4—101no—
183C2×#235—51no—
184C3×C4×D4—52no—
185C3×C4×D4—52no—
186C3×C4×D4—101no—
187C3×C4×D4—101no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C22⋊C4—101no—
190C2×C3×C42C2×D511yescharacteristic
191C2×#214—52no—
192#932—58no—
193C2×#213—52no—
194C4×#67—101no—
195C4×#67—101no—
196#926—51no—
197C2×#208C2×D511yescharacteristic
198C2×#208C2×D511yescharacteristic
199C4×D12—51no—
200C4×D12—51no—
201#872—101no—
202C42×D3—101no—
203C4×Dic6—51no—
204C4×Dic6—51no—
205#832—52no—
206#832—52no—
207#810—52no—
208#809—52no—
209#808—52no—
210#807—52no—
211#803C2×D512yescomplemented
212C4×C3⋊C8C2×D512yescomplemented
213C23×D5—21no—
214C22×C4×C5#6711yescharacteristic
215C22×C4×C5#6711yescharacteristic
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—61no—
218C22×Dic5—21no—
219#709—34no—
220#709—62no—
221C2×D20—22no—
222C2×D20—21no—
223C2×D20—31no—
224C2×D20C4×D314yescomplemented
225C2×D20C22×D312yes—
226C2×C4×D5—22no—
227C2×C4×D5—22no—
228C2×C4×D5—44no—
229C2×C4×D5—61no—
230C2×C4×D5—61no—
231C2×C4×D5—61no—
232C2×Dic10—31no—
233C5×M16—34no—
234C5×M16—62no—
235C2×C5×C8—32no—
236C2×C5×C8—32no—
237C42×C5#6711yescharacteristic
238C42×C5#6711yescharacteristic
239C42×C5C22×D311yescharacteristic
240C42×C5C22×D311yescharacteristic
241C22⋊Dic5—61no—
242#685—22no—
243#685—22no—
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—51no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—151no—
266#417—151no—
267C4×M16—31no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—22no—
273C2×D15—41no—
274C2×D15—41no—
275C2×C3×D5—24no—
276C2×C3×D5—48no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C3×C4×C5—21no—
280C3×C4×C5—21no—
281C3×C4×C5—21no—
282C3×C4×C5C4×D412yes—
283C3×C4×C5AGL(1,ℤ/8)12yescomplemented
284C3×C4×C5C23×C411yescharacteristic
285C3×C4×C5C2×#4111yescharacteristic
286Dic15—22no—
287Dic15—41no—
288Dic15—41no—
289C3×Dic5—42no—
290C24×C3—101no—
291C2×C3×D4—54no—
292C2×C3×D4—52no—
293C2×C3×D4—101no—
294C2×C3×D4—102no—
295C22×C3×C4—101no—
296C22×C3×C4—102no—
297C22×C3×C4—102no—
298C22×C3×C4—204no—
299C22×C3×C4D2011yescharacteristic
300C22×C3×C4D2011yescharacteristic
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—101no—
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×C4⋊C4—52no—
311C3×C4⋊C4—101no—
312C3×C22⋊C4—102no—
313C3×C22⋊C4—102no—
314C3×C42D2011yescharacteristic
315C3×C42D2011yescharacteristic
316C3×C42C22×D511yescharacteristic
317C3×C42C22×D511yescharacteristic
318#217—101no—
319#214—58no—
320#213—58no—
321(C2×D3)⋊C4—101no—
322(C2×D3)⋊C4—101no—
323C4⋊Dic3—51no—
324C4⋊Dic3—51no—
325Dic3⋊C4—101no—
326Dic3⋊C4—101no—
327C4×Dic3—101no—
328C4×Dic3—101no—
329C4×Dic3—101no—
330#208—22no—
331#208C4×D514yescomplemented
332C2×C3⋊C8C22×D512yes—
333C2×C3⋊C8C22×D512yes—
334C23×C5C2×#6711yescharacteristic
335C22×D5—24no—
336C22×D5—22no—
337C22×D5—42no—
338C22×D5—42no—
339C22×D5—61no—
340C2×C4×C5—22no—
341C2×C4×C5—41no—
342C2×C4×C5C2×C4×D312yes—
343C2×C4×C5#23512yes—
344C2×C4×C5C2×#6711yescharacteristic
345C2×C4×C5C2×#6711yescharacteristic
346C2×C4×C5C2×#6711yescharacteristic
347C2×C4×C5C2×#6711yescharacteristic
348C2×C4×C5C2×#6711yescharacteristic
349C2×C4×C5C23×D311yescharacteristic
350C22⋊D5—64no—
351C2×Dic5—22no—
352C2×Dic5—42no—
353C2×Dic5—61no—
354C2×Dic5—61no—
355C2×Dic5—61no—
356D20—24no—
357D20—22no—
358D20—32no—
359D20—61no—
360D20C2×C4×D314yes—
361C4×D5—44no—
362C4×D5—44no—
363C4×D5—64no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—32no—
367Dic10—61no—
368C5×C8—34no—
369C5×C8—62no—
370C2×#41—151no—
371C22×D4—51no—
372C23×C4—101no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—31no—
377C2×M16—31no—
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—52no—
381C4×D4—52no—
382C4×D4—101no—
383C4×D4—101no—
384C4×D4—151no—
385C4×D4—151no—
386C4×D4—301no—
387C4×D4—301no—
388#117—151no—
389#117—301no—
390C2×C4⋊C4—51no—
391C2×C22⋊C4—101no—
392C2×C42—301no—
393C2×C42D3×D511yescharacteristic
394#107—152no—
395#106—152no—
396#103—152no—
397#102—152no—
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—42no—
407C3×D5—44no—
408C23×C3—102no—
409C23×C3—104no—
410C23×C3—202no—
411C23×C3—202no—
412C23×C3C2×D2011yescharacteristic
413C22×D3—101no—
414C3×D4—54no—
415C3×D4—102no—
416C3×D4—104no—
417C2×C3×C4—22no—
418C2×C3×C4—41no—
419C2×C3×C4—102no—
420C2×C3×C4—204no—
421C2×C3×C4—202no—
422C2×C3×C4—204no—
423C2×C3×C4C2×C4×D512yes—
424C2×C3×C4C2×D2011yescharacteristic
425C2×C3×C4C2×D2011yescharacteristic
426C2×C3×C4C2×D2011yescharacteristic
427C2×C3×C4C2×D2011yescharacteristic
428C2×C3×C4C2×D2011yescharacteristic
429C2×C3×C4#70912yes—
430C2×C3×C4C23×D511yescharacteristic
431#67—104no—
432C2×Dic3—101no—
433C2×Dic3—101no—
434C2×Dic3—101no—
435D12—52no—
436D12—101no—
437C4×D3—104no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—52no—
441Dic6—101no—
442C3⋊C8—22no—
443C3⋊C8C2×C4×D514yescomplemented
444C22×C5—21no—
445C22×C5—21no—
446C22×C5C4×#6712yes—
447C22×C5C22×#6711yescharacteristic
448C2×D5—24no—
449C2×D5—48no—
450C2×D5—42no—
451C2×D5—42no—
452C2×D5—62no—
453C2×D5—121no—
454C2×D5—121no—
455C4×C5—21no—
456C4×C5—21no—
457C4×C5—21no—
458C4×C5C4×#6712yes—
459C4×C5#93212yescomplemented
460C4×C5C22×C4×D311yescharacteristic
461C4×C5C2×#23511yescharacteristic
462Dic5—42no—
463Dic5—62no—
464Dic5—121no—
465Dic5—121no—
466C24—101no—
467#41—154no—
468#41—302no—
469C2×Q8—151no—
470C2×D4—54no—
471C2×D4—52no—
472C2×D4—102no—
473C2×D4—101no—
474C2×D4—151no—
475C2×D4—301no—
476C22×C4—101no—
477C22×C4—102no—
478C22×C4—102no—
479C22×C4—204no—
480C22×C4—301no—
481C22×C4—301no—
482C22×C4—301no—
483C22×C4#120211yescharacteristic
484C22×C4#120211yescharacteristic
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—34no—
489M16—62no—
490C2×C8—32no—
491C2×C8—32no—
492C4⋊C4—52no—
493C4⋊C4—101no—
494C4⋊C4—151no—
495C4⋊C4—151no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—102no—
499C22⋊C4—102no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—301no—
504C42—301no—
505C42—301no—
506C42#120211yescharacteristic
507C42#120211yescharacteristic
508C42C2×D3×D511yescharacteristic
509C42C2×D3×D511yescharacteristic
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—104no—
514C22×C3—208no—
515C22×C3—202no—
516C22×C3—202no—
517C22×C3C4×D2012yes—
518C22×C3C22×D2011yescharacteristic
519C2×D3—102no—
520C2×D3—201no—
521C2×D3—201no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—202no—
526C3×C4C4×D2012yes—
527C3×C4#405412yescomplemented
528C3×C4C22×C4×D511yescharacteristic
529C3×C4C2×#70911yescharacteristic
530Dic3—102no—
531Dic3—201no—
532Dic3—201no—
533C2×C5—22no—
534C2×C5C2×C4×#6711yescharacteristic
535C2×C5C2×#93211yescharacteristic
536C2×C5#582211yescharacteristic
537D5—44no—
538D5—122no—
539C23—104no—
540C23—102no—
541C23—202no—
542C23—202no—
543C23—301no—
544C23C2×#120211yescharacteristic
545Q8—152no—
546Q8—301no—
547D4—54no—
548D4—104no—
549D4—102no—
550D4—152no—
551D4—304no—
552D4—301no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—102no—
556C2×C4—204no—
557C2×C4—202no—
558C2×C4—204no—
559C2×C4—301no—
560C2×C4—304no—
561C2×C4—301no—
562C2×C4—301no—
563C2×C4—602no—
564C2×C4—602no—
565C2×C4#677112yes—
566C2×C4C4×D3×D512yes—
567C2×C4C2×#120211yescharacteristic
568C2×C4C2×#120211yescharacteristic
569C2×C4C2×#120211yescharacteristic
570C2×C4C2×#120211yescharacteristic
571C2×C4C2×#120211yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—34no—
574C8—62no—
575C2×C3—22no—
576C2×C3—204no—
577C2×C3C2×C4×D2011yescharacteristic
578C2×C3C2×#405411yescharacteristic
579C2×C3#6608211yescharacteristic
580D3—202no—
581C5C4×#93211yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—104no—
585C22—208no—
586C22—202no—
587C22—202no—
588C22—302no—
589C22—601no—
590C22—601no—
591C22C4×#120212yes—
592C22C22×#120211yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—202no—
597C4—302no—
598C4—601no—
599C4—601no—
600C4#9131212yesdirect product factor
601C4C4×#120212yes—
602C4C2×#677111yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3C4×#405411yescharacteristic, complemented, Sylow
605C2—22no—
606C2—204no—
607C2—602no—
608C2C2×#9131211yescharacteristic
609C2#1175415411yescharacteristic
610C2C2×C4×#120211yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
prime radicalC2×#91312C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×#6817C2semidirect
2. C2×C3×C4×D20C2semidirect
4. C4×C5×#208C2semidirect
5. #11748453C2semidirect
6. #11748413C2semidirect
7. #11748367C2semidirect
8. #11747052C2semidirect
9. C4×#6657C2semidirect
10. #11747023C2semidirect
11. C4×#6653C2semidirect
20. C4×D60C22semidirect
21. C4×D60C22semidirect
24. C4×Dic30C22semidirect
25. C4×Dic30C22semidirect
34. #91312C4direct (N × H)
37. C5×#803C22semidirect
38. C4×C5×C3⋊C8C22semidirect
39. #90990C22semidirect
40. #90987C22semidirect
41. #90974C22semidirect
42. #90968C22semidirect
48. C2×C4×D20D3semidirect
63. #6817C2×C4semidirect
72. C2×C3×D20C2×C4semidirect
92. C5×#208C2×C4semidirect
99. #6657C2×C4semidirect
100. #6653C2×C4semidirect
111. C4×#208D5semidirect
166. D60C22×C4semidirect
171. Dic30C22×C4semidirect
180. C5×C3⋊C8C22×C4semidirect
211. #803C2×D5semidirect
212. C4×C3⋊C8C2×D5semidirect
224. C2×D20C4×D3semidirect
283. C3×C4×C5AGL(1,ℤ/8)semidirect
331. #208C4×D5semidirect
443. C3⋊C8C2×C4×D5semidirect
459. C4×C5#932semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
527. C3×C4#4054semidirect
581. C5C4×#932semidirect
600. C4#91312direct (N × H)
604. C3C4×#4054semidirect

Maximal subgroups

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

subgroupindex
C4×#68172
C2×C3×C4×D202
C2×#913122
C4×C5×#2082
#117484532
#117484132
#117483672
#117470522
C4×#66572
#117470232
C4×#66532
C4×#40543
C4×#9325