Finite Group Databasebeta

← C2×#11749042 #14423449

Subgroups — C2×#11749042 #14423449

Order 1920.

1624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6819C211yesmaximal, characteristic, complemented
2C22×C3×#686C211yesmaximal, characteristic, complemented
3C2×#91465C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C2×C5×#832C211yesmaximal, characteristic, complemented
6#11749042C218yesmaximal, direct product factor
7C2×#90975C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic, complemented
9C2×#65070—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×#1220—21no—
12C23×Dic15—21no—
13C2×#6819—24no—
14C2×#6819—22no—
15C2×#6819—24no—
16C2×#6819C2214yescomplemented
17C22×C4×D15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×#1202—21no—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×#686—24no—
24C2×C3×#686C2214yescomplemented
25C22×C3×#168C2211yescharacteristic
26C2×#6665—21no—
27#91465—22no—
28#91465C2214yescomplemented
29C2×#6657—24no—
30C2×#6657C2214yescomplemented
31C5×#832C2214yescomplemented
32#90975C2214yescomplemented
33#90957C2214yescomplemented
34C2×#5158—51nomaximal, Hall
35C22×#711—31no—
36C22×#686D311yescharacteristic, complemented
37C22×#677—31no—
38C2×#4041—31no—
39C2×C5×#102—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65070—38no—
43C24×C3×C5—21no—
44C23×D15D411yescharacteristic
45C23×C3×D5—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4D414yescomplemented
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—28no—
52C2×#1220—24no—
53C22×Dic15—28no—
54C22×Dic15—21no—
55C22×Dic15—24no—
56C22×Dic15D411yescharacteristic
57#6819—216no—
58#6819—28no—
59#6819—28no—
60C2×C4×D15—22no—
61C2×C4×D15—22no—
62C2×C4×D15D412yes—
63C2×C4×D15C2312yes—
64C2×Dic30—21no—
65C2×Dic30—22no—
66C2×Dic30D414yescomplemented
67C2×Dic30C2312yes—
68C22×C5×Dic3—21no—
69C2×C3×D20—22no—
70C2×C3×D20—22no—
71C2×C3×D20—21no—
72C2×C3×D20C2312yes—
73C2×#1202—24no—
74C2×#1202—44no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yes—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2312yes—
79C3×#686—28no—
80C2×C3×#168—22no—
81C2×C3×#168C2312yes—
82#6665—24no—
83#6657—28no—
84C22×#237—51no—
85C22×C3×D8—51no—
86C2×#938—51no—
87C22×#214—51no—
88C2×#832D511yescharacteristic, complemented
89#5158—58no—
90C2×(C2×D3)⋊C8—51no—
91C2×#816—51no—
92C22×C5×D4C2×D311yescharacteristic
93C22×C22⋊D5—61no—
94C23×Dic5—61no—
95C2×#711—34no—
96C2×#711—64no—
97C2×#711—62no—
98C2×#711—64no—
99C22×D20—61no—
100C22×D20C2×D311yescharacteristic
101C22×C4×D5—31no—
102C22×Dic10—31no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4—31no—
105C2×#686—24no—
106C2×#686C2×D314yescomplemented
107C2×#685—61no—
108C22×#168C2×D311yescharacteristic
109C2×#677—34no—
110C2×#677—64no—
111#4041—34no—
112#4041—62no—
113C5×#102—34no—
114#3952—34no—
115#3942—34no—
116C2×#449—151noSylow
117C23×C3×C5—24no—
118C23×C3×C5—22no—
119C23×C3×C5—42no—
120C23×C3×C5—42no—
121C23×C3×C5C2×D411yescharacteristic
122C22×D15—22no—
123C22×D15—22no—
124C22×D15—22no—
125C22×D15C2×D412yes—
126C22×C3×D5—22no—
127C22×C3×D5—42no—
128C22×C3×D5—42no—
129C22×C3×D5—42no—
130C3×C5×D4—24no—
131C3×C5×D4—22no—
132C3×C5×D4C2×D414yescomplemented
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2411yescharacteristic
137#1220—216no—
138C2×Dic15—216no—
139C2×Dic15—24no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15C2×D412yes—
143C4×D15—24no—
144C4×D15—22no—
145C4×D15—22no—
146Dic30—24no—
147Dic30—22no—
148Dic30C2×D414yescomplemented
149C2×C5×Dic3—22no—
150C2×C5×Dic3—42no—
151C3×D20—22no—
152C3×D20—22no—
153C3×D20—42no—
154#1202—48no—
155C3×#168—22no—
156C5×C3⋊C8—22no—
157C22×C3×D4—51no—
158C22×C3×D4C2×D511yescharacteristic
159C22×#67—101no—
160C22×#67—101no—
161C23×Dic3—101no—
162C2×#237—54no—
163C2×#237—104no—
164C2×#237—102no—
165C2×#237—104no—
166C22×C4×D3—51no—
167C22×Dic6—51no—
168C2×C3×D8—54no—
169C2×C3×D8—104no—
170C22×C3×C8—51no—
171C2×#217—101no—
172#938—54no—
173#938—102no—
174C2×#214—54no—
175C2×#214—104no—
176C2×C4⋊Dic3C2×D511yescharacteristic
177C22×C3⋊C8C2×D511yescharacteristic
178#832C2×D514yescomplemented
179(C2×D3)⋊C8—54no—
180#816—54no—
181C24×C5—21no—
182C23×D5—21no—
183C23×D5—31no—
184C2×C5×D4—21no—
185C2×C5×D4—22no—
186C2×C5×D4#6714yescomplemented
187C2×C5×D4C22×D312yes—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—64no—
191C2×C22⋊D5—68no—
192C22×Dic5—31no—
193C22×Dic5—64no—
194C22×Dic5—68no—
195C22×Dic5—61no—
196#711—68no—
197#711—616no—
198#711—68no—
199C2×D20—22no—
200C2×D20—22no—
201C2×D20—21no—
202C2×D20—64no—
203C2×D20—124no—
204C2×D20C22×D312yes—
205C2×C4×D5—32no—
206C2×C4×D5—32no—
207C2×C4×D5—62no—
208C2×C4×D5—62no—
209C2×Dic10—34no—
210C2×Dic10—32no—
211C2×Dic10—61no—
212C2×Dic10—62no—
213C2×C5×C8—32no—
214C2×C5×C8—62no—
215C5×C4⋊C4—32no—
216C5×C4⋊C4—61no—
217#686—28no—
218#685—64no—
219C2×#168—22no—
220C2×#168C22×D312yes—
221#677—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—51no—
225C2×#121—151no—
226#449—158no—
227C2×#103—151no—
228C2×#102—31no—
229C2×C22⋊C8—151no—
230C22×C3×C5—24no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5—48no—
234C22×C3×C5#12012yes—
235C22×C3×C5#13512yes—
236C22×C3×C5AGL(1,ℤ/8)12yes—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—22no—
240C2×D15—22no—
241C2×D15—44no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—84no—
246C3×C4×C5#12012yes—
247C3×C4×C5C22×D411yescharacteristic
248C3×C4×C5C22×D411yescharacteristic
249Dic15—24no—
250Dic15—22no—
251C5×Dic3—42no—
252C24×C3—21no—
253C24×C3—101no—
254C23×D3—51no—
255C2×C3×D4—22no—
256C2×C3×D4—21no—
257C2×C3×D4—52no—
258C2×C3×D4—102no—
259C2×C3×D4—102no—
260C2×C3×D4—101no—
261C2×C3×D4D2014yescomplemented
262C2×C3×D4C22×D512yes—
263C22×C3×C4C22×D511yescharacteristic
264C2×#67—104no—
265C2×#67—104no—
266C2×#67—108no—
267C2×#67—204no—
268C22×Dic3—21no—
269C22×Dic3—51no—
270C22×Dic3—104no—
271C22×Dic3—108no—
272C22×Dic3—101no—
273#237—108no—
274#237—1016no—
275#237—108no—
276C2×C4×D3—52no—
277C2×C4×D3—52no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C2×Dic6—54no—
281C2×Dic6—52no—
282C2×Dic6—102no—
283C2×Dic6—101no—
284C3×D8—108no—
285C2×C3×C8—52no—
286C2×C3×C8—102no—
287#217—104no—
288#214—108no—
289C4⋊Dic3—21no—
290C4⋊Dic3C22×D512yes—
291C2×C3⋊C8—22no—
292C2×C3⋊C8C22×D512yes—
293C23×C5—24no—
294C23×C5—22no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5D3×D411yescharacteristic
298C22×D5—22no—
299C22×D5—32no—
300C22×D5—42no—
301C22×D5—42no—
302C22×D5—42no—
303C22×D5—62no—
304C22×D5—62no—
305C22×D5—62no—
306C5×D4—24no—
307C5×D4—22no—
308C5×D4C2×#6714yescomplemented
309C2×C4×C5—62no—
310C2×C4×C5—122no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D412yes—
313C2×C4×C5C2×#6712yes—
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—616no—
316C2×Dic5—32no—
317C2×Dic5—616no—
318C2×Dic5—64no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321D20—22no—
322D20—22no—
323D20—42no—
324D20—128no—
325C4×D5—64no—
326C4×D5—62no—
327C4×D5—62no—
328Dic10—34no—
329Dic10—64no—
330Dic10—62no—
331C5×C8—62no—
332#168—22no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8—151no—
338C22×D4—51no—
339C22×D4—301no—
340C22×D4—301no—
341C22×D4D3×D511yescharacteristic
342C23×C4—151no—
343C23×C4—301no—
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—54no—
347C2×D8—104no—
348C22×C8—31no—
349C22×C8—51no—
350#121—154no—
351#121—302no—
352C2×C4⋊C4—31no—
353C2×C22⋊C4—301no—
354#103—154no—
355#102—34no—
356C22⋊C8—154no—
357C2×C3×C5—44no—
358C2×C3×C5#44914yescomplemented
359C2×C3×C5C2×#12011yescharacteristic
360C2×C3×C5C2×#13511yescharacteristic
361C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
362D15—42no—
363C3×D5—82no—
364C23×C3—22no—
365C23×C3—24no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—102no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3—202no—
372C23×C3D4×D511yescharacteristic
373C22×D3—52no—
374C22×D3—102no—
375C22×D3—102no—
376C22×D3—102no—
377C3×D4—22no—
378C3×D4—24no—
379C3×D4—102no—
380C3×D4—102no—
381C3×D4—202no—
382C3×D4C2×D2014yescomplemented
383C2×C3×C4C2×D2012yes—
384C2×C3×C4D4×D512yes—
385C2×C3×C4D4×D511yescharacteristic
386C2×C3×C4C23×D511yescharacteristic
387#67—1016no—
388#67—208no—
389C2×Dic3—22no—
390C2×Dic3—42no—
391C2×Dic3—52no—
392C2×Dic3—1016no—
393C2×Dic3—102no—
394C2×Dic3—104no—
395C2×Dic3—102no—
396C4×D3—102no—
397C4×D3—102no—
398C4×D3—104no—
399Dic6—54no—
400Dic6—102no—
401Dic6—104no—
402C3×C8—102no—
403C3⋊C8—22no—
404C22×C5—24no—
405C22×C5—48no—
406C22×C5—42no—
407C22×C5—42no—
408C22×C5#91112yes—
409C22×C5#91212yes—
410C22×C5#93712yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—42no—
415C2×D5—62no—
416C2×D5—62no—
417C2×D5—62no—
418C2×D5—84no—
419C2×D5—124no—
420C4×C5—122no—
421C4×C5#93712yes—
422C4×C5C2×D3×D411yescharacteristic
423C4×C5C22×#6711yescharacteristic
424Dic5—64no—
425Dic5—62no—
426C24—21no—
427C24—101no—
428C24—151no—
429#41—308no—
430#41—3016no—
431#41—308no—
432C2×Q8—154no—
433C2×Q8—152no—
434C2×Q8—302no—
435C2×Q8—301no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—52no—
439C2×D4—102no—
440C2×D4—102no—
441C2×D4—101no—
442C2×D4—304no—
443C2×D4—304no—
444C2×D4—308no—
445C2×D4—604no—
446C2×D4#120214yescomplemented
447C2×D4C2×D3×D512yes—
448C22×C4—61no—
449C22×C4—151no—
450C22×C4—152no—
451C22×C4—152no—
452C22×C4—304no—
453C22×C4—308no—
454C22×C4—301no—
455C22×C4—302no—
456C22×C4—302no—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—108no—
460C2×C8—32no—
461C2×C8—52no—
462C2×C8—62no—
463C2×C8—102no—
464C4⋊C4—32no—
465C4⋊C4—61no—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—24no—
469C22×C3—42no—
470C22×C3—48no—
471C22×C3—42no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3—404no—
476C22×C3#402812yes—
477C22×C3#405712yes—
478C22×C3#406212yes—
479C22×C3C2×D4×D511yescharacteristic
480C2×D3—102no—
481C2×D3—102no—
482C2×D3—102no—
483C2×D3—204no—
484C3×C4#402812yes—
485C3×C4C22×D2011yescharacteristic
486C3×C4C2×D4×D511yescharacteristic
487Dic3—42no—
488Dic3—104no—
489Dic3—102no—
490C2×C5—44no—
491C2×C5#515814yescomplemented
492C2×C5C2×#91111yescharacteristic
493C2×C5C2×#91211yescharacteristic
494C2×C5C2×#93711yescharacteristic
495D5—82no—
496D5—122no—
497C23—22no—
498C23—24no—
499C23—42no—
500C23—42no—
501C23—102no—
502C23—152no—
503C23—202no—
504C23—202no—
505C23—202no—
506C23—302no—
507C23—302no—
508C23—302no—
509C23#679011yescharacteristic
510Q8—154no—
511Q8—302no—
512Q8—304no—
513D4—22no—
514D4—24no—
515D4—102no—
516D4—102no—
517D4—202no—
518D4—3016no—
519D4—608no—
520D4C2×#120214yescomplemented
521C2×C4—62no—
522C2×C4—122no—
523C2×C4—152no—
524C2×C4—3016no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—304no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4—304no—
531C2×C4C2×#120212yes—
532C2×C4#679012yes—
533C2×C4#679011yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—62no—
536C8—102no—
537C2×C3—44no—
538C2×C3—402no—
539C2×C3#6507014yescomplemented
540C2×C3C2×#402811yescharacteristic
541C2×C3C2×#405711yescharacteristic
542C2×C3C2×#406211yescharacteristic
543D3—202no—
544C5C2×#515811yescharacteristic, complemented, Sylow
545C22—24no—
546C22—48no—
547C22—42no—
548C22—42no—
549C22—202no—
550C22—202no—
551C22—202no—
552C22—302no—
553C22—302no—
554C22—302no—
555C22—404no—
556C22—604no—
557C22#9148212yes—
558C22#9149712yes—
559C22#9157212yes—
560C22C2×#679011yescharacteristic
561C4—122no—
562C4—302no—
563C4—304no—
564C4#9157212yes—
565C4C22×#120211yescharacteristic
566C4C2×#679011yescharacteristic
567C3C2×#6507011yescharacteristic, complemented, Sylow
568C2—44no—
569C2—402no—
570C2—602no—
571C2#1174904214yesdirect product factor
572C2C2×#9148211yescharacteristic
573C2C2×#9149711yescharacteristic
574C2C2×#9157211yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6819C2semidirect
2. C22×C3×#686C2semidirect
3. C2×#91465C2semidirect
4. C22×#6657C2semidirect
5. C2×C5×#832C2semidirect
6. #11749042C2direct (N × H)
7. C2×#90975C2semidirect
8. C2×#90957C2semidirect
16. C2×#6819C22semidirect
24. C2×C3×#686C22semidirect
28. #91465C22semidirect
30. C2×#6657C22semidirect
31. C5×#832C22semidirect
32. #90975C22semidirect
33. #90957C22semidirect
36. C22×#686D3semidirect
48. C2×C3×C5×D4D4semidirect
66. C2×Dic30D4semidirect
88. C2×#832D5semidirect
106. C2×#686C2×D3semidirect
132. C3×C5×D4C2×D4semidirect
148. Dic30C2×D4semidirect
178. #832C2×D5semidirect
186. C2×C5×D4#67semidirect
261. C2×C3×D4D20semidirect
308. C5×D4C2×#67semidirect
358. C2×C3×C5#449semidirect
382. C3×D4C2×D20semidirect
446. C2×D4#1202semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#5158semidirect
520. D4C2×#1202semidirect
539. C2×C3#65070semidirect
544. C5C2×#5158semidirect
567. C3C2×#65070semidirect
571. C2#11749042direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68192
C22×C3×#6862
C2×#914652
C22×#66572
C2×C5×#8322
#117490422
C2×#909752
C2×#909572
C2×#650703
C2×#51585