Finite Group Databasebeta

← C2×#11749461 #14425105

Subgroups — C2×#11749461 #14425105

Order 1920.

1456 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3C2×#91373C211yesmaximal, characteristic, complemented
4C2×#91304C211yesmaximal, characteristic, complemented
5C2×C3×#3969C211yesmaximal, characteristic, complemented
6#11749461C218yesmaximal, direct product factor
7C2×#90981C211yesmaximal, characteristic, complemented
8C2×#90963C211yesmaximal, characteristic, complemented
9C2×#65490—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11#92101—22no—
12#92101—22no—
13#92101—22no—
14#92101C2214yescomplemented
15C2×Q8×D15—21no—
16C2×#6819—21no—
17C2×#6819—22no—
18C2×#6817—21no—
19C2×#6817C2211yescharacteristic
20C22×Dic30—21no—
21C22×Dic30C2211yescharacteristic
22C22×C5×D12C2211yescharacteristic
23C5×#949—22no—
24C5×#949C2214yescomplemented
25C2×C5×#215—21no—
26C2×C5×#213—21no—
27C2×C5×#208C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×#681C2211yescharacteristic
30C2×(C2×D3)⋊Dic5—22no—
31#91373—22no—
32#91373C2214yescomplemented
33C2×#6659—21no—
34#91304—22no—
35#91304C2214yescomplemented
36C2×#6654—21no—
37C3×#3969C2214yescomplemented
38#90981C2214yescomplemented
39#90963C2214yescomplemented
40C2×#4827—51nomaximal, Hall
41C2×#4150—31no—
42C2×C5×AGL(1,ℤ/8)—31no—
43C2×#4082—31no—
44C2×#4078—31no—
45C2×#3969D311yescharacteristic, complemented
46#65490—38no—
47C2×#3957—31no—
48C2×#3956—31no—
49C23×C5×D3—21no—
50C3×C5×#41—21no—
51C3×C5×#41—21no—
52C3×C5×#41D412yes—
53C3×C5×#41C2312yes—
54C2×C3×C5×Q8D411yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4D411yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—22no—
60C2×#1220—21no—
61C22×Dic15—22no—
62C22×Dic15D412yes—
63Q8×D15—24no—
64Q8×D15—24no—
65#6819—28no—
66#6819—24no—
67#6819—24no—
68#6819—28no—
69#6817—24no—
70#6817—21no—
71#6817—21no—
72#6817—24no—
73#6817D412yes—
74#6817C2312yes—
75C2×D60D411yescharacteristic
76C2×C4×D15—22no—
77C2×C4×D15—21no—
78C2×Dic30—22no—
79C2×Dic30—24no—
80C2×Dic30—21no—
81C2×Dic30—21no—
82C2×Dic30—21no—
83C2×Dic30—21no—
84C2×Dic30—24no—
85C2×Dic30D412yes—
86C2×Dic30D411yescharacteristic
87C2×Dic30C2312yes—
88C2×C5×D12—21no—
89C2×C5×D12—21no—
90C2×C5×D12—21no—
91C2×C5×D12—21no—
92C2×C5×D12—21no—
93C2×C5×D12C2312yes—
94C22×C3×Dic5—21no—
95C5×#215—24no—
96C5×#213—24no—
97C5×#208—21no—
98C5×#208C2312yes—
99C2×C5×C3⋊C8—21no—
100C3×C4×Dic5—21no—
101C3×C4×Dic5C2312yes—
102C3×#681—21no—
103C3×#681C2312yes—
104C2×C3×#168—21no—
105(C2×D3)⋊Dic5—28no—
106#6659—24no—
107#6654—24no—
108C2×#1010—51no—
109C2×#949D511yescharacteristic, complemented
110C2×#908—51no—
111C2×#875—51no—
112C2×C3×#104—51no—
113C2×#824—51no—
114C2×#805—51no—
115#4827—58no—
116C2×C5×#41C2×D311yescharacteristic
117C22×C5×D4—31no—
118#4150—34no—
119#4150—62no—
120#4150—62no—
121#4150—62no—
122C2×Q8×D5—61no—
123C2×#711—62no—
124C2×#711—61no—
125C2×#709—31no—
126C2×#709—61no—
127C22×Dic10—31no—
128C22×Dic10—61no—
129C5×AGL(1,ℤ/8)—34no—
130C5×AGL(1,ℤ/8)—62no—
131C2×C5×SD16—61no—
132C2×C5×D8—61no—
133C2×C5×M16—31no—
134C2×C22⋊Dic5—62no—
135#4082—34no—
136#4082—62no—
137C2×#687—61no—
138#4078—34no—
139#4078—62no—
140C2×#686—61no—
141C2×C4×Dic5C2×D311yescharacteristic
142C2×#681C2×D311yescharacteristic
143#3969C2×D314yescomplemented
144#3957—34no—
145#3956—34no—
146C2×#454—151noSylow
147C23×C3×C5—21no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C22×C5×D3—22no—
151C22×C5×D3—44no—
152C22×C5×D3—41no—
153C22×C5×D3—41no—
154C3×C5×Q8—21no—
155C3×C5×Q8C2×D412yes—
156C3×C5×D4—22no—
157C3×C5×D4—22no—
158C3×C5×D4—21no—
159C3×C5×D4C2×D412yes—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5C2×D411yescharacteristic
164C2×C3×C4×C5C2×D411yescharacteristic
165C2×C3×C4×C5C2×D411yescharacteristic
166C2×C3×C4×C5C2×D411yescharacteristic
167C2×C3×C4×C5C2×D411yescharacteristic
168C2×C3×C4×C5C2411yescharacteristic
169#1220—28no—
170#1220—22no—
171#1220—22no—
172C2×Dic15—28no—
173C2×Dic15—22no—
174C2×Dic15—21no—
175C2×Dic15—22no—
176C2×Dic15C2×D414yes—
177D60—21no—
178D60C2×D412yes—
179C4×D15—28no—
180C4×D15—22no—
181C4×D15—22no—
182Dic30—28no—
183Dic30—22no—
184Dic30—21no—
185Dic30—22no—
186Dic30—22no—
187Dic30—22no—
188Dic30C2×D412yes—
189C5×D12—22no—
190C5×D12—22no—
191C5×D12—41no—
192C5×D12—41no—
193C2×C3×Dic5—22no—
194C2×C3×Dic5—42no—
195C3×#168—22no—
196C5×C3⋊C8—22no—
197C2×C3×#41C2×D511yescharacteristic
198#1010—54no—
199#1010—102no—
200#1010—102no—
201#1010—102no—
202C2×D3×Q8—101no—
203C2×#237—102no—
204C2×#237—101no—
205C2×#235—51no—
206C2×#235—101no—
207C22×D12C2×D511yescharacteristic
208C22×Dic6—51no—
209C22×Dic6—101no—
210C2×C3×M16—51no—
211C2×C3×C42—51no—
212#949—22no—
213#949C2×D514yescomplemented
214C2×#215—21no—
215C2×#213—21no—
216C2×(C2×D3)⋊C4—102no—
217C2×#208C2×D511yescharacteristic
218#908—54no—
219#908—102no—
220C2×D24—101no—
221C2×#204—101no—
222#875—54no—
223#875—102no—
224C3×#104—54no—
225#824—54no—
226#805—54no—
227C24×C5—61no—
228C5×#41—21no—
229C5×#41—21no—
230C5×#41D1212yes—
231C5×#41C22×D312yes—
232C2×C5×Q8D1211yescharacteristic
233C2×C5×D4—21no—
234C2×C5×D4—32no—
235C2×C5×D4—61no—
236C2×C5×D4—61no—
237C2×C5×D4—61no—
238C2×C5×D4—61no—
239C2×C5×D4—61no—
240C2×C5×D4D1211yescharacteristic
241C22×C4×C5—21no—
242C22×C4×C5C22×D311yescharacteristic
243C2×C22⋊D5—62no—
244C2×C22⋊D5—61no—
245C22×Dic5—21no—
246C22×Dic5—32no—
247C22×Dic5—62no—
248Q8×D5—64no—
249Q8×D5—64no—
250#711—68no—
251#711—68no—
252#711—64no—
253#711—64no—
254#709—32no—
255#709—32no—
256#709—64no—
257#709—64no—
258#709—61no—
259#709—61no—
260C2×D20—31no—
261C2×C4×D5—62no—
262C2×C4×D5—61no—
263C2×Dic10—31no—
264C2×Dic10—32no—
265C2×Dic10—32no—
266C2×Dic10—64no—
267C2×Dic10—62no—
268C2×Dic10—64no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271C2×Dic10—61no—
272C2×Dic10—61no—
273C5×SD16—64no—
274C5×D8—64no—
275C5×M16—32no—
276C5×M16—61no—
277C2×C5×C8—61no—
278C22⋊Dic5—68no—
279#687—64no—
280#686—64no—
281C4×Dic5—21no—
282C4×Dic5C22×D312yes—
283#681—21no—
284#681C22×D312yes—
285C2×#168—21no—
286C2×2−1+4—151no—
287C2×AGL(1,ℤ/8)—31no—
288C2×AGL(1,ℤ/8)—151no—
289C2×#124—151no—
290#454—158no—
291C2×#104—51no—
292C2×#104—151no—
293C2×#101—151no—
294C22×C3×C5—22no—
295C22×C3×C5—22no—
296C22×C3×C5—42no—
297C22×C3×C5#12011yescharacteristic
298C22×C3×C5#12011yescharacteristic
299C22×C3×C5C22×D411yescharacteristic
300C2×D15—22no—
301C2×D15—42no—
302C2×C5×D3—44no—
303C2×C5×D3—42no—
304C2×C5×D3—82no—
305C2×C5×D3—82no—
306C3×C4×C5—22no—
307C3×C4×C5#12011yescharacteristic
308C3×C4×C5#12011yescharacteristic
309C3×C4×C5C22×D411yescharacteristic
310C3×C4×C5C22×D411yescharacteristic
311Dic15—24no—
312Dic15—22no—
313C3×Dic5—42no—
314C23×D3—21no—
315C3×#41—21no—
316C3×#41—21no—
317C3×#41C22⋊D512yes—
318C3×#41C22×D512yes—
319C2×C3×Q8C22⋊D511yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4C22⋊D511yescharacteristic
322C22×C3×C4—21no—
323C22×C3×C4—101no—
324C22×C3×C4C22×D511yescharacteristic
325C2×#67—102no—
326C2×#67—101no—
327C22×Dic3—52no—
328C22×Dic3—102no—
329D3×Q8—104no—
330D3×Q8—104no—
331#237—108no—
332#237—108no—
333#237—104no—
334#237—104no—
335#235—52no—
336#235—52no—
337#235—104no—
338#235—104no—
339#235—101no—
340#235—101no—
341C2×D12—21no—
342C2×D12—21no—
343C2×D12—21no—
344C2×D12—21no—
345C2×D12—21no—
346C2×D12—51no—
347C2×D12C22×D512yes—
348C2×C4×D3—102no—
349C2×C4×D3—101no—
350C2×Dic6—51no—
351C2×Dic6—52no—
352C2×Dic6—52no—
353C2×Dic6—104no—
354C2×Dic6—102no—
355C2×Dic6—104no—
356C2×Dic6—101no—
357C2×Dic6—101no—
358C2×Dic6—101no—
359C2×Dic6—101no—
360C3×M16—52no—
361C3×M16—101no—
362C2×C3×C8—101no—
363C3×C42—52no—
364C3×C42—101no—
365#215—24no—
366#213—24no—
367(C2×D3)⋊C4—108no—
368#208—21no—
369#208C22×D512yes—
370C2×C3⋊C8—21no—
371D24—104no—
372#204—104no—
373C23×C5—21no—
374C23×C5—62no—
375C23×C5—124no—
376C23×C5—121no—
377C23×C5—121no—
378C23×C5D3×D411yescharacteristic
379C22×D5—61no—
380C5×Q8—21no—
381C5×Q8C2×D1212yes—
382C5×D4—22no—
383C5×D4—22no—
384C5×D4—21no—
385C5×D4—62no—
386C5×D4—62no—
387C5×D4—121no—
388C5×D4—121no—
389C5×D4C2×D1212yes—
390C2×C4×C5—21no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5C2×D1211yescharacteristic
394C2×C4×C5C2×D1211yescharacteristic
395C2×C4×C5D3×D411yescharacteristic
396C2×C4×C5D3×D411yescharacteristic
397C2×C4×C5D3×D411yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—68no—
400C22⋊D5—62no—
401C22⋊D5—62no—
402C2×Dic5—22no—
403C2×Dic5—34no—
404C2×Dic5—42no—
405C2×Dic5—68no—
406C2×Dic5—61no—
407C2×Dic5—62no—
408C2×Dic5—62no—
409D20—32no—
410D20—61no—
411C4×D5—68no—
412C4×D5—62no—
413C4×D5—62no—
414Dic10—32no—
415Dic10—68no—
416Dic10—61no—
417Dic10—62no—
418Dic10—62no—
419Dic10—62no—
420Dic10—62no—
421C5×C8—62no—
422#168—22no—
4232−1+4—154no—
4242−1+4—302no—
4252−1+4—302no—
4262−1+4—302no—
427C2×#41—151no—
428C2×#41—301no—
429C2×#41—302no—
430C2×#41—301no—
431C2×#41D3×D511yescharacteristic
432C22×Q8—151no—
433C22×Q8—301no—
434C22×Q8—301no—
435C22×D4—31no—
436AGL(1,ℤ/8)—34no—
437AGL(1,ℤ/8)—62no—
438AGL(1,ℤ/8)—154no—
439AGL(1,ℤ/8)—302no—
440C2×SD16—61no—
441C2×SD16—301no—
442C2×D8—61no—
443C2×D8—301no—
444C2×M16—31no—
445C2×M16—51no—
446#124—154no—
447#124—302no—
448C2×C22⋊C4—302no—
449C2×C42—51no—
450#104—54no—
451#104—154no—
452#101—154no—
453C2×C3×C5—21no—
454C2×C3×C5—21no—
455C2×C3×C5—42no—
456C2×C3×C5#45412yescomplemented
457C2×C3×C5C2×#12011yescharacteristic
458D15—42no—
459C5×D3—82no—
460C23×C3—21no—
461C23×C3D4×D511yescharacteristic
462C22×D3—22no—
463C22×D3—44no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—101no—
467C3×Q8—21no—
468C3×Q8C2×C22⋊D512yes—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4—21no—
472C3×D4C2×C22⋊D512yes—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—102no—
477C2×C3×C4—202no—
478C2×C3×C4D4×D511yescharacteristic
479C2×C3×C4D4×D511yescharacteristic
480C2×C3×C4D4×D511yescharacteristic
481C2×C3×C4C2×C22⋊D511yescharacteristic
482C2×C3×C4C2×C22⋊D511yescharacteristic
483C2×C3×C4C23×D511yescharacteristic
484#67—108no—
485#67—102no—
486#67—102no—
487C2×Dic3—54no—
488C2×Dic3—108no—
489C2×Dic3—101no—
490C2×Dic3—102no—
491C2×Dic3—102no—
492D12—22no—
493D12—22no—
494D12—41no—
495D12—41no—
496D12—52no—
497D12—101no—
498C4×D3—108no—
499C4×D3—102no—
500C4×D3—102no—
501Dic6—52no—
502Dic6—108no—
503Dic6—102no—
504Dic6—102no—
505Dic6—101no—
506Dic6—102no—
507Dic6—102no—
508C3×C8—102no—
509C3⋊C8—22no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—42no—
513C22×C5—124no—
514C22×C5—122no—
515C22×C5—242no—
516C22×C5—242no—
517C22×C5#88211yescharacteristic
518C22×C5#88211yescharacteristic
519C22×C5C2×D3×D411yescharacteristic
520C2×D5—62no—
521C2×D5—122no—
522C4×C5—22no—
523C4×C5#88211yescharacteristic
524C4×C5#88211yescharacteristic
525C4×C5C22×D1211yescharacteristic
526C4×C5C2×D3×D411yescharacteristic
527Dic5—42no—
528Dic5—62no—
529Dic5—64no—
530C24—61no—
531#41—21no—
532#41—21no—
533#41—152no—
534#41—152no—
535#41—304no—
536#41—304no—
537#41—308no—
538#41—308no—
539#41—304no—
540#41—304no—
541#41—301no—
542#41—301no—
543#41#120312yes—
544#41C2×D3×D512yes—
545C2×Q8—152no—
546C2×Q8—152no—
547C2×Q8—151no—
548C2×Q8—304no—
549C2×Q8—302no—
550C2×Q8—304no—
551C2×Q8—304no—
552C2×Q8—304no—
553C2×Q8—301no—
554C2×Q8—301no—
555C2×Q8—301no—
556C2×Q8—301no—
557C2×Q8#120311yescharacteristic
558C2×D4—21no—
559C2×D4—32no—
560C2×D4—61no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4—61no—
564C2×D4—61no—
565C2×D4—151no—
566C2×D4—302no—
567C2×D4—301no—
568C2×D4#120311yescharacteristic
569C22×C4—21no—
570C22×C4—101no—
571C22×C4—152no—
572C22×C4—302no—
573C22×C4—302no—
574C22×C4—301no—
575C22×C4C2×D3×D511yescharacteristic
576SD16—64no—
577SD16—304no—
578D8—64no—
579D8—304no—
580M16—32no—
581M16—52no—
582M16—61no—
583M16—101no—
584C2×C8—61no—
585C2×C8—101no—
586C22⋊C4—308no—
587C42—52no—
588C42—101no—
589C3×C5C2×#45411yescharacteristic, complemented, Hall
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—42no—
593C22×C3#408311yescharacteristic
594C22×C3#408311yescharacteristic
595C22×C3C2×D4×D511yescharacteristic
596C2×D3—44no—
597C2×D3—42no—
598C2×D3—82no—
599C2×D3—82no—
600C2×D3—102no—
601C2×D3—202no—
602C3×C4—22no—
603C3×C4—202no—
604C3×C4#408311yescharacteristic
605C3×C4#408311yescharacteristic
606C3×C4C2×D4×D511yescharacteristic
607C3×C4C22×C22⋊D511yescharacteristic
608Dic3—102no—
609Dic3—104no—
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—42no—
613C2×C5—242no—
614C2×C5#482712yescomplemented
615C2×C5C2×#88211yescharacteristic
616D5—122no—
617C23—21no—
618C23—62no—
619C23—124no—
620C23—121no—
621C23—121no—
622C23—301no—
623C23#679011yescharacteristic
624Q8—21no—
625Q8—152no—
626Q8—308no—
627Q8—302no—
628Q8—302no—
629Q8—302no—
630Q8—302no—
631Q8—301no—
632Q8C2×#120312yes—
633D4—22no—
634D4—22no—
635D4—21no—
636D4—62no—
637D4—62no—
638D4—121no—
639D4—121no—
640D4—152no—
641D4—308no—
642D4—302no—
643D4—302no—
644D4—301no—
645D4C2×#120312yes—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—102no—
650C2×C4—154no—
651C2×C4—202no—
652C2×C4—308no—
653C2×C4—308no—
654C2×C4—302no—
655C2×C4—302no—
656C2×C4—301no—
657C2×C4—302no—
658C2×C4—302no—
659C2×C4C2×#120311yescharacteristic
660C2×C4C2×#120311yescharacteristic
661C2×C4#679011yescharacteristic
662C2×C4#679011yescharacteristic
663C2×C4#679011yescharacteristic
664C2×C4C22×D3×D511yescharacteristic
665C8—62no—
666C8—102no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—42no—
670C2×C3#6549012yescomplemented
671C2×C3C2×#408311yescharacteristic
672D3—82no—
673D3—202no—
674C5C2×#482711yescharacteristic, complemented, Sylow
675C22—22no—
676C22—22no—
677C22—42no—
678C22—124no—
679C22—122no—
680C22—242no—
681C22—242no—
682C22—302no—
683C22—602no—
684C22#9157311yescharacteristic
685C22#9157311yescharacteristic
686C22C2×#679011yescharacteristic
687C4—22no—
688C4—202no—
689C4—304no—
690C4—302no—
691C4#9157311yescharacteristic
692C4#9157311yescharacteristic
693C4C22×#120311yescharacteristic
694C4C2×#679011yescharacteristic
695C3C2×#6549011yescharacteristic, complemented, Sylow
696C2—21no—
697C2—21no—
698C2—42no—
699C2—242no—
700C2—602no—
701C2#1174946112yesdirect product factor
702C2C2×#9157311yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#120
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#454
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#92101C2semidirect
2. C2×C5×#949C2semidirect
3. C2×#91373C2semidirect
4. C2×#91304C2semidirect
5. C2×C3×#3969C2semidirect
6. #11749461C2direct (N × H)
7. C2×#90981C2semidirect
8. C2×#90963C2semidirect
14. #92101C22semidirect
24. C5×#949C22semidirect
32. #91373C22semidirect
35. #91304C22semidirect
37. C3×#3969C22semidirect
38. #90981C22semidirect
39. #90963C22semidirect
45. C2×#3969D3semidirect
109. C2×#949D5semidirect
143. #3969C2×D3semidirect
213. #949C2×D5semidirect
456. C2×C3×C5#454semidirect
589. C3×C5C2×#454semidirect
614. C2×C5#4827semidirect
670. C2×C3#65490semidirect
674. C5C2×#4827semidirect
695. C3C2×#65490semidirect
701. C2#11749461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921012
C2×C5×#9492
C2×#913732
C2×#913042
C2×C3×#39692
#117494612
C2×#909812
C2×#909632
C2×#654903
C2×#48275