Finite Group Databasebeta

← C2×#11747484 #14423284

Subgroups — C2×#11747484 #14423284

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6777C211yesmaximal, characteristic
2C2×#91786C211yesmaximal, characteristic, complemented
3C22×#6659C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C2×C5×#809C211yesmaximal, characteristic, complemented
6C2×C3×#3941C211yesmaximal, characteristic, complemented
7C2×#90957C211yesmaximal, characteristic, complemented
8#11747484C218yesmaximal, direct product factor
9C2×#65065—31nomaximal, Hall
10C23×D3×D5—21no—
11C22×C4×D15C2211yescharacteristic
12C22×Dic30C2211yescharacteristic, complemented
13C22×C5×D12C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×#1201—21no—
16C2×#6777—22no—
17C2×#6777—24no—
18C2×#6777—24no—
19C2×#6777C2214yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
21C2×#6714—21no—
22C2×C4⋊Dic15—21no—
23#91786—22no—
24#91786C2214yescomplemented
25C22×C5×C3⋊C8C2211yescharacteristic, complemented
26C22×C3×#168C2211yescharacteristic, complemented
27C2×#6659—24no—
28C2×#6659C2214yescomplemented
29C2×#6657—24no—
30C2×#6657C2214yescomplemented
31C5×#809C2214yescomplemented
32C3×#3941C2214yescomplemented
33#90957C2214yescomplemented
34C2×#4776—51nomaximal, Hall
35C22×D4×D5—31no—
36C22×#687—31no—
37C22×#677—31no—
38C2×#4043—31no—
39C2×C5×#102—31no—
40C2×#3952—31no—
41C2×#3941D311yescharacteristic, complemented
42#65065—38no—
43C23×D15D411yescharacteristic
44C23×C5×D3—21no—
45C23×C3×D5—21no—
46C22×D3×D5—28no—
47C22×D3×D5—24no—
48C22×D3×D5—44no—
49C22×D3×D5—44no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15—21no—
53C22×Dic15D411yescharacteristic
54C2×C4×D15—22no—
55C2×C4×D15—22no—
56C2×C4×D15D412yes—
57C2×C4×D15C2312yes—
58C2×Dic30—22no—
59C2×Dic30—22no—
60C2×Dic30—21no—
61C2×Dic30C2312yescomplemented
62C2×C5×D12—21no—
63C2×C5×D12—22no—
64C2×C5×D12D414yes—
65C2×C5×D12C2312yes—
66C2×C3×D20—21no—
67C2×C3×D20—22no—
68C2×C3×D20D414yes—
69C2×C3×D20C2312yes—
70C2×#1201—28no—
71C2×#1201—24no—
72#6777—216no—
73#6777—28no—
74#6777—28no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2312yescomplemented
77#6714—24no—
78C4⋊Dic15—24no—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2312yescomplemented
81C2×C3×#168—22no—
82C2×C3×#168C2312yescomplemented
83#6659—28no—
84#6657—28no—
85C22×D3×D4—51no—
86C22×#214—51no—
87C22×#204—51no—
88C2×#897—51no—
89C2×C3×#102—51no—
90C2×(C2×D3)⋊C8—51no—
91C2×#809D511yescharacteristic, complemented
92#4776—58no—
93C24×D5—61no—
94C22×C5×D4—31no—
95C22×C22⋊D5—61no—
96C2×D4×D5—34no—
97C2×D4×D5—62no—
98C2×D4×D5—64no—
99C2×D4×D5—64no—
100C22×D20C2×D311yescharacteristic
101C22×C4×D5—31no—
102C22×Dic10—31no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
105C2×#687—34no—
106C2×#687—64no—
107C2×#685—61no—
108C2×C4⋊Dic5—61no—
109C22×#168C2×D311yescharacteristic, complemented
110C2×#677—34no—
111C2×#677—64no—
112#4043—34no—
113#4043—62no—
114C5×#102—34no—
115#3952—34no—
116#3941C2×D314yescomplemented
117C2×#450—151noSylow
118C23×C3×C5C2×D411yescharacteristic
119C22×D15—22no—
120C22×D15—22no—
121C22×D15SD1614yescomplemented
122C22×D15C2×D412yes—
123C22×C5×D3—24no—
124C22×C5×D3—22no—
125C22×C5×D3—42no—
126C22×C5×D3—42no—
127C22×C3×D5—24no—
128C22×C3×D5—22no—
129C22×C3×D5—42no—
130C22×C3×D5—42no—
131C2×D3×D5—216no—
132C2×D3×D5—48no—
133C2×D3×D5—432no—
134C2×D3×D5—48no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—42no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—42no—
144C2×Dic15C2×D412yes—
145C4×D15—24no—
146C4×D15—22no—
147C4×D15—22no—
148Dic30—22no—
149Dic30—22no—
150Dic30—42no—
151C5×D12—24no—
152C5×D12—22no—
153C5×D12C2×D414yes—
154C3×D20—24no—
155C3×D20—22no—
156C3×D20C2×D414yes—
157#1201—216no—
158C3×#168—22no—
159C5×C3⋊C8—22no—
160C24×D3—101no—
161C22×C3×D4—51no—
162C22×#67—101no—
163C2×D3×D4—54no—
164C2×D3×D4—102no—
165C2×D3×D4—104no—
166C2×D3×D4—104no—
167C22×D12C2×D511yescharacteristic
168C22×C4×D3—51no—
169C22×Dic6—51no—
170C22×C3×C8—51no—
171C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
172C2×#214—54no—
173C2×#214—104no—
174C2×(C2×D3)⋊C4—101no—
175C2×C4⋊Dic3—101no—
176C22×C3⋊C8C2×D511yescharacteristic, complemented
177C2×#204—54no—
178C2×#204—104no—
179#897—54no—
180#897—102no—
181C3×#102—54no—
182(C2×D3)⋊C8—54no—
183#809C2×D514yescomplemented
184C24×C5—61no—
185C23×D5—21no—
186C23×D5—31no—
187C23×D5—64no—
188C23×D5—68no—
189C23×D5—124no—
190C23×D5—124no—
191C2×C5×D4—34no—
192C2×C5×D4—32no—
193C2×C5×D4—62no—
194C2×C5×D4—61no—
195C22×C4×C5—21no—
196C22×C4×C5C22×D311yescharacteristic
197C2×C22⋊D5—64no—
198C2×C22⋊D5—68no—
199C22×Dic5—31no—
200C22×Dic5—61no—
201D4×D5—68no—
202D4×D5—616no—
203D4×D5—68no—
204C2×D20—22no—
205C2×D20—21no—
206C2×D20D1214yes—
207C2×D20C22×D312yes—
208C2×C4×D5—32no—
209C2×C4×D5—32no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10—32no—
213C2×Dic10—62no—
214C2×Dic10—62no—
215C2×Dic10—61no—
216C2×C5×C8—32no—
217C2×C5×C8—62no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4C22×D312yescomplemented
220#687—68no—
221#685—64no—
222C4⋊Dic5—64no—
223C2×#168—22no—
224C2×#168C22×D312yescomplemented
225#677—68no—
226C23×D4—151no—
227C22×SD16—151no—
228C22×SD16—151no—
229C2×C22⋊Q8—151no—
230#450—158no—
231C2×#102—31no—
232C2×#102—51no—
233C2×C22⋊C8—151no—
234C22×C3×C5#12012yes—
235C22×C3×C5C2×SD1612yes—
236C22×C3×C5AGL(1,ℤ/8)12yes—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—22no—
240C2×D15—28no—
241C2×D15C2×SD1614yescomplemented
242C2×C5×D3—24no—
243C2×C5×D3—42no—
244C2×C5×D3—42no—
245C2×C5×D3—48no—
246C2×C3×D5—24no—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—48no—
250D3×D5—432no—
251C3×C4×C5—42no—
252C3×C4×C5#12012yes—
253C3×C4×C5C22×D411yescharacteristic
254C3×C4×C5C22×D411yescharacteristic
255Dic15—22no—
256Dic15—42no—
257C24×C3—101no—
258C23×D3—21no—
259C23×D3—51no—
260C23×D3—104no—
261C23×D3—108no—
262C23×D3—204no—
263C23×D3—204no—
264C2×C3×D4—54no—
265C2×C3×D4—52no—
266C2×C3×D4—102no—
267C2×C3×D4—101no—
268C22×C3×C4—21no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—104no—
271C2×#67—108no—
272C22×Dic3—51no—
273C22×Dic3—101no—
274D3×D4—108no—
275D3×D4—1016no—
276D3×D4—108no—
277C2×D12—22no—
278C2×D12—21no—
279C2×D12D2014yes—
280C2×D12C22×D512yes—
281C2×C4×D3—52no—
282C2×C4×D3—52no—
283C2×C4×D3—102no—
284C2×C4×D3—102no—
285C2×Dic6—52no—
286C2×Dic6—102no—
287C2×Dic6—102no—
288C2×Dic6—101no—
289C2×C3×C8—52no—
290C2×C3×C8—102no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4C22×D512yescomplemented
293#214—108no—
294(C2×D3)⋊C4—104no—
295C4⋊Dic3—104no—
296C2×C3⋊C8—22no—
297C2×C3⋊C8C22×D512yescomplemented
298#204—108no—
299C23×C5—64no—
300C23×C5—62no—
301C23×C5—122no—
302C23×C5—122no—
303C23×C5D3×D411yescharacteristic
304C22×D5—24no—
305C22×D5—22no—
306C22×D5—34no—
307C22×D5—32no—
308C22×D5—42no—
309C22×D5—42no—
310C22×D5—616no—
311C22×D5—62no—
312C22×D5—62no—
313C22×D5—128no—
314C22×D5—128no—
315C22×D5—1232no—
316C5×D4—34no—
317C5×D4—64no—
318C5×D4—62no—
319C2×C4×C5—22no—
320C2×C4×C5—42no—
321C2×C4×C5C2×D1212yes—
322C2×C4×C5D3×D412yes—
323C2×C4×C5D3×D411yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—616no—
326C2×Dic5—32no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—122no—
330D20—24no—
331D20—22no—
332D20C2×D1214yes—
333C4×D5—64no—
334C4×D5—62no—
335C4×D5—62no—
336Dic10—62no—
337Dic10—62no—
338Dic10—122no—
339C5×C8—62no—
340#168—22no—
341C25—301no—
342C22×Q8—151no—
343C22×D4—31no—
344C22×D4—51no—
345C22×D4—154no—
346C22×D4—302no—
347C22×D4—301no—
348C22×D4—304no—
349C22×D4—304no—
350C23×C4—151no—
351C2×SD16—154no—
352C2×SD16—154no—
353C2×SD16—304no—
354C2×SD16—304no—
355C22×C8—31no—
356C22×C8—51no—
357C22⋊Q8—154no—
358C22⋊Q8—302no—
359C2×C4⋊C4—301no—
360C2×C4⋊C4D3×D511yescharacteristic, complemented
361C2×C22⋊C4—301no—
362#102—34no—
363#102—54no—
364C22⋊C8—154no—
365C2×C3×C5#45014yescomplemented
366C2×C3×C5C2×#12011yescharacteristic
367C2×C3×C5C22×SD1611yescharacteristic
368C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
369D15—24no—
370C3×D5—44no—
371C5×D3—44no—
372C23×C3—102no—
373C23×C3—104no—
374C23×C3—202no—
375C23×C3—202no—
376C23×C3D4×D511yescharacteristic
377C22×D3—22no—
378C22×D3—24no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—52no—
382C22×D3—54no—
383C22×D3—1016no—
384C22×D3—102no—
385C22×D3—102no—
386C22×D3—208no—
387C22×D3—208no—
388C22×D3—2032no—
389C3×D4—54no—
390C3×D4—102no—
391C3×D4—104no—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4C2×D2012yes—
395C2×C3×C4D4×D512yes—
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398#67—1016no—
399C2×Dic3—52no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—202no—
403D12—22no—
404D12—24no—
405D12C2×D2014yes—
406C4×D3—102no—
407C4×D3—102no—
408C4×D3—104no—
409Dic6—102no—
410Dic6—102no—
411Dic6—202no—
412C3×C8—102no—
413C3⋊C8—22no—
414C22×C5—64no—
415C22×C5—122no—
416C22×C5—122no—
417C22×C5—128no—
418C22×C5#88212yes—
419C22×C5#91112yes—
420C22×C5D3×SD1612yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—24no—
423C2×D5—34no—
424C2×D5—42no—
425C2×D5—42no—
426C2×D5—48no—
427C2×D5—62no—
428C2×D5—62no—
429C2×D5—68no—
430C2×D5—1232no—
431C4×C5—42no—
432C4×C5#88212yes—
433C4×C5C22×D1211yescharacteristic
434C4×C5C2×D3×D411yescharacteristic
435Dic5—62no—
436Dic5—122no—
437C24—61no—
438C24—101no—
439C24—151no—
440C24—304no—
441C24—308no—
442C24—604no—
443C24—604no—
444C2×Q8—152no—
445C2×Q8—301no—
446C2×Q8—302no—
447C2×Q8—302no—
448C2×D4—34no—
449C2×D4—32no—
450C2×D4—54no—
451C2×D4—52no—
452C2×D4—62no—
453C2×D4—61no—
454C2×D4—102no—
455C2×D4—101no—
456C2×D4—304no—
457C2×D4—308no—
458C2×D4—308no—
459C2×D4—3016no—
460C2×D4—308no—
461C22×C4—21no—
462C22×C4—151no—
463C22×C4—152no—
464C22×C4—152no—
465C22×C4—302no—
466C22×C4—302no—
467C22×C4—301no—
468C22×C4C2×D3×D511yescharacteristic
469SD16—308no—
470SD16—308no—
471C2×C8—32no—
472C2×C8—52no—
473C2×C8—62no—
474C2×C8—102no—
475C4⋊C4—21no—
476C4⋊C4—304no—
477C4⋊C4C2×D3×D512yescomplemented
478C22⋊C4—304no—
479C3×C5C2×#45011yescharacteristic, complemented, Hall
480C22×C3—104no—
481C22×C3—202no—
482C22×C3—208no—
483C22×C3—202no—
484C22×C3#402812yes—
485C22×C3#405712yes—
486C22×C3D5×SD1612yes—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—24no—
489C2×D3—42no—
490C2×D3—48no—
491C2×D3—42no—
492C2×D3—54no—
493C2×D3—102no—
494C2×D3—102no—
495C2×D3—108no—
496C2×D3—2032no—
497C3×C4—42no—
498C3×C4#402812yes—
499C3×C4C22×D2011yescharacteristic
500C3×C4C2×D4×D511yescharacteristic
501Dic3—102no—
502Dic3—202no—
503C2×C5—124no—
504C2×C5#477614yescomplemented
505C2×C5C2×#88211yescharacteristic
506C2×C5C2×#91111yescharacteristic
507C2×C5C2×D3×SD1611yescharacteristic
508D5—44no—
509D5—64no—
510C23—64no—
511C23—62no—
512C23—104no—
513C23—102no—
514C23—122no—
515C23—122no—
516C23—154no—
517C23—152no—
518C23—202no—
519C23—202no—
520C23—3016no—
521C23—302no—
522C23—302no—
523C23—608no—
524C23—6032no—
525C23—608no—
526C23#679011yescharacteristic
527Q8—302no—
528Q8—302no—
529Q8—602no—
530D4—34no—
531D4—54no—
532D4—64no—
533D4—62no—
534D4—104no—
535D4—102no—
536D4—3016no—
537C2×C4—22no—
538C2×C4—42no—
539C2×C4—152no—
540C2×C4—302no—
541C2×C4—304no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—602no—
546C2×C4D5×D1212yes—
547C2×C4D3×D2012yes—
548C2×C4#679011yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—102no—
552C2×C3—204no—
553C2×C3#6506514yescomplemented
554C2×C3C2×#402811yescharacteristic
555C2×C3C2×#405711yescharacteristic
556C2×C3C2×D5×SD1611yescharacteristic
557D3—44no—
558D3—104no—
559C5C2×#477611yescharacteristic, complemented, Sylow
560C22—64no—
561C22—104no—
562C22—122no—
563C22—128no—
564C22—122no—
565C22—154no—
566C22—202no—
567C22—208no—
568C22—202no—
569C22—302no—
570C22—308no—
571C22—302no—
572C22—6032no—
573C22#9147612yes—
574C22#9148212yes—
575C22#9150512yes—
576C22C2×#679011yescharacteristic
577C4—42no—
578C4—302no—
579C4—602no—
580C4#9147612yes—
581C4C2×D5×D1211yescharacteristic
582C4C2×D3×D2011yescharacteristic
583C3C2×#6506511yescharacteristic, complemented, Sylow
584C2—124no—
585C2—204no—
586C2—304no—
587C2#1174748414yesdirect product factor
588C2C2×#9147611yescharacteristic
589C2C2×#9148211yescharacteristic
590C2C2×#9150511yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6777C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#450
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91786C2semidirect
3. C22×#6659C2semidirect
4. C22×#6657C2semidirect
5. C2×C5×#809C2semidirect
6. C2×C3×#3941C2semidirect
7. C2×#90957C2semidirect
8. #11747484C2direct (N × H)
12. C22×Dic30C22semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
24. #91786C22semidirect
25. C22×C5×C3⋊C8C22semidirect
26. C22×C3×#168C22semidirect
28. C2×#6659C22semidirect
30. C2×#6657C22semidirect
31. C5×#809C22semidirect
32. C3×#3941C22semidirect
33. #90957C22semidirect
41. C2×#3941D3semidirect
61. C2×Dic30C23semidirect
76. C3×C5×C4⋊C4C23semidirect
80. C2×C5×C3⋊C8C23semidirect
82. C2×C3×#168C23semidirect
91. C2×#809D5semidirect
104. C2×C5×C4⋊C4C2×D3semidirect
109. C22×#168C2×D3semidirect
116. #3941C2×D3semidirect
121. C22×D15SD16semidirect
171. C2×C3×C4⋊C4C2×D5semidirect
176. C22×C3⋊C8C2×D5semidirect
183. #809C2×D5semidirect
219. C5×C4⋊C4C22×D3semidirect
224. C2×#168C22×D3semidirect
241. C2×D15C2×SD16semidirect
292. C3×C4⋊C4C22×D5semidirect
297. C2×C3⋊C8C22×D5semidirect
360. C2×C4⋊C4D3×D5semidirect
365. C2×C3×C5#450semidirect
477. C4⋊C4C2×D3×D5semidirect
479. C3×C5C2×#450semidirect
504. C2×C5#4776semidirect
553. C2×C3#65065semidirect
559. C5C2×#4776semidirect
583. C3C2×#65065semidirect
587. C2#11747484direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67772
C2×#917862
C22×#66592
C22×#66572
C2×C5×#8092
C2×C3×#39412
C2×#909572
#117474842
C2×#650653
C2×#47765