Finite Group Databasebeta

← C2×#11748531 #14423543

Subgroups — C2×#11748531 #14423543

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C2×#91813C211yesmaximal, characteristic, complemented
3C22×#6662C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C2×C5×#830C211yesmaximal, characteristic, complemented
6#11748531C218yesmaximal, direct product factor
7C2×#90971C211yesmaximal, characteristic, complemented
8C2×#90965C211yesmaximal, characteristic, complemented
9C2×#65022—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C3×C22⋊D5—21no—
13C2×C3×#709—22no—
14C2×C3×#709—24no—
15C2×C3×#709—24no—
16C2×C3×#709C2214yes—
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5—21no—
19C22×C3×Dic10C2211yescharacteristic
20C2×#6719—21no—
21C2×C4⋊Dic15C2211yescharacteristic
22#91813—22no—
23#91813C2214yescomplemented
24C2×#6712—21no—
25C22×C5×C3⋊C8C2211yescharacteristic
26C22×C5×C3⋊C8C2211yescharacteristic
27C2×#6662—24no—
28C2×#6662C2214yescomplemented
29C2×#6657—24no—
30C2×#6657C2214yescomplemented
31C5×#830C2214yescomplemented
32#90971C2214yescomplemented
33#90965C2214yescomplemented
34C2×#5239—51nomaximal, Hall
35C22×#709D311yescharacteristic
36C2×#4070—31no—
37C22×Dic20—31no—
38C22×#677—31no—
39C2×C5×C22⋊C8—31no—
40C2×#3953—31no—
41C2×#3948—31no—
42#65022—38no—
43C24×C3×C5D411yescharacteristic
44C23×C3×D5—21no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×C4×C5D412yes—
49C22×C3×C4×C5C2312yes—
50C22×C3×C4×C5C2311yescharacteristic
51C22×Dic15—21no—
52C22×Dic15—21no—
53C2×Dic30—22no—
54C2×Dic30—22no—
55C2×Dic30—21no—
56C2×Dic30C2312yes—
57C2×C3×C22⋊D5—28no—
58C2×C3×C22⋊D5—24no—
59C22×C3×Dic5—21no—
60C3×#709—216no—
61C3×#709—28no—
62C3×#709—28no—
63C2×C3×D20—21no—
64C2×C3×D20—22no—
65C2×C3×D20D414yes—
66C2×C3×D20C2312yes—
67C2×C3×C4×D5—28no—
68C2×C3×C4×D5—24no—
69C2×C3×Dic10—21no—
70C2×C3×Dic10—22no—
71C2×C3×Dic10D414yes—
72C2×C3×Dic10C2312yes—
73#6719—24no—
74C4⋊Dic15—21no—
75C4⋊Dic15C2312yes—
76#6712—24no—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8—22no—
79C2×C5×C3⋊C8C2312yes—
80C2×C5×C3⋊C8C2312yes—
81#6662—28no—
82#6657—28no—
83C22×C3×#41—51no—
84C22×#216—51no—
85C22×#214—51no—
86C2×#924—51no—
87#5239—58no—
88C2×#835—51no—
89C2×#832—51no—
90C2×#830D511yescharacteristic, complemented
91C23×C4×C5C2×D311yescharacteristic
92C22×C22⋊D5—21no—
93C2×#709—22no—
94C2×#709—24no—
95C2×#709—24no—
96C2×#709C2×D314yes—
97C22×D20C2×D311yescharacteristic
98C22×C4×D5—21no—
99C22×Dic10—31no—
100C22×Dic10C2×D311yescharacteristic
101C22×C5×C8—31no—
102C22×C5×C8—31no—
103C2×C22⋊Dic5—61no—
104C2×C4⋊Dic5—31no—
105#4070—34no—
106#4070—62no—
107C2×#683—61no—
108C2×Dic20—34no—
109C2×Dic20—64no—
110C2×#677—34no—
111C2×#677—64no—
112C5×C22⋊C8—34no—
113#3953—34no—
114#3948—34no—
115C2×#452—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—22no—
118C23×C3×C5—22no—
119C23×C3×C5C2×D412yes—
120C23×C3×C5C2×D411yescharacteristic
121C22×C3×D5—24no—
122C22×C3×D5—22no—
123C22×C3×D5—42no—
124C22×C3×D5—42no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—24no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—42no—
137C2×Dic15—42no—
138Dic30—22no—
139Dic30—22no—
140Dic30—42no—
141C3×C22⋊D5—216no—
142C2×C3×Dic5—24no—
143C2×C3×Dic5—22no—
144C3×D20—24no—
145C3×D20—22no—
146C3×D20C2×D414yes—
147C3×C4×D5—216no—
148C3×Dic10—24no—
149C3×Dic10—22no—
150C3×Dic10C2×D414yes—
151C5×C3⋊C8—22no—
152C5×C3⋊C8—22no—
153C2×C3×#41—54no—
154C2×C3×#41—104no—
155C2×C3×#41—104no—
156C2×C3×#41—102no—
157C22×C3×Q8—51no—
158C22×C3×D4—51no—
159C22×C3×D4—101no—
160C23×C3×C4—101no—
161C23×C3×C4C2×D511yescharacteristic
162C22×Dic6—51no—
163C2×#217—101no—
164C2×#216—54no—
165C2×#216—104no—
166C2×#214—54no—
167C2×#214—104no—
168C2×C4⋊Dic3—51no—
169#924—54no—
170#924—102no—
171C2×Dic3⋊C4—101no—
172C22×C3⋊C8C2×D511yescharacteristic
173C22×C3⋊C8C2×D511yescharacteristic
174#835—54no—
175#832—54no—
176#830C2×D514yescomplemented
177C24×C5#6711yescharacteristic
178C23×D5—21no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5#6711yescharacteristic
182C22×C4×C5#6712yes—
183C22×C4×C5C22×D312yes—
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5—28no—
186C2×C22⋊D5—24no—
187C22×Dic5—21no—
188C22×Dic5—61no—
189C22×Dic5—61no—
190#709—216no—
191#709—28no—
192#709—28no—
193C2×D20—21no—
194C2×D20—22no—
195C2×D20#6714yes—
196C2×D20C22×D312yes—
197C2×C4×D5—28no—
198C2×C4×D5—24no—
199C2×Dic10—21no—
200C2×Dic10—22no—
201C2×Dic10—32no—
202C2×Dic10—62no—
203C2×Dic10—62no—
204C2×Dic10—61no—
205C2×Dic10#6714yes—
206C2×Dic10C22×D312yes—
207C2×C5×C8—32no—
208C2×C5×C8—32no—
209C2×C5×C8—62no—
210C2×C5×C8—62no—
211C22⋊Dic5—64no—
212C4⋊Dic5—32no—
213C4⋊Dic5—61no—
214#683—64no—
215Dic20—68no—
216#677—68no—
217C22×#41—51no—
218C22×Q16—151no—
219C22×SD16—151no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—151no—
223C2×#102—151no—
224C2×C22⋊C8—31no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5—44no—
229C22×C3×C5#12012yes—
230C22×C3×C5#13512yes—
231C22×C3×C5#13712yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C3×D5—24no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—48no—
237C3×C4×C5—22no—
238C3×C4×C5#12012yes—
239C3×C4×C5C22×D411yescharacteristic
240C3×C4×C5C22×D411yescharacteristic
241Dic15—42no—
242Dic15—42no—
243C3×Dic5—24no—
244C24×C3—101no—
245C24×C3D2011yescharacteristic
246C3×#41—108no—
247C3×#41—108no—
248C3×#41—1016no—
249C2×C3×Q8—54no—
250C2×C3×Q8—52no—
251C2×C3×Q8—101no—
252C2×C3×Q8—102no—
253C2×C3×D4—54no—
254C2×C3×D4—52no—
255C2×C3×D4—108no—
256C2×C3×D4—104no—
257C2×C3×D4—101no—
258C2×C3×D4—102no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—108no—
262C22×C3×C4—101no—
263C22×C3×C4—104no—
264C22×C3×C4D2011yescharacteristic
265C22×C3×C4D2012yes—
266C22×C3×C4C22×D512yes—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—101no—
269C22×Dic3—101no—
270C2×Dic6—52no—
271C2×Dic6—102no—
272C2×Dic6—102no—
273C2×Dic6—101no—
274#217—104no—
275#216—108no—
276#214—108no—
277C4⋊Dic3—52no—
278C4⋊Dic3—101no—
279Dic3⋊C4—104no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—22no—
282C2×C3⋊C8C22×D512yes—
283C2×C3⋊C8C22×D512yes—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5C2×#6712yes—
288C23×C5C2×#6711yescharacteristic
289C22×D5—24no—
290C22×D5—22no—
291C22×D5—42no—
292C22×D5—42no—
293C2×C4×C5—22no—
294C2×C4×C5—24no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5C2×#6712yes—
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C2×#6712yes—
300C2×C4×C5C2×#6712yes—
301C2×C4×C5C23×D311yescharacteristic
302C22⋊D5—216no—
303C2×Dic5—24no—
304C2×Dic5—22no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5—122no—
308C2×Dic5—122no—
309D20—24no—
310D20—22no—
311D20C2×#6714yes—
312C4×D5—216no—
313Dic10—24no—
314Dic10—22no—
315Dic10—62no—
316Dic10—62no—
317Dic10—122no—
318Dic10C2×#6714yes—
319C5×C8—62no—
320C5×C8—62no—
321C2×#41—54no—
322C2×#41—104no—
323C2×#41—104no—
324C2×#41—102no—
325C22×Q8—51no—
326C22×Q8—151no—
327C22×D4—51no—
328C22×D4—101no—
329C23×C4—101no—
330C23×C4D3×D511yescharacteristic
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—154no—
334C2×SD16—304no—
335C22×C8—31no—
336C22×C8—31no—
337C22⋊Q8—154no—
338C22⋊Q8—302no—
339C2×C4⋊C4—151no—
340C2×C4⋊C4—301no—
341C2×C22⋊C4—301no—
342#103—154no—
343#102—154no—
344C22⋊C8—34no—
345C2×C3×C5—42no—
346C2×C3×C5#45214yescomplemented
347C2×C3×C5C2×#12011yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350C3×D5—44no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—102no—
355C23×C3—104no—
356C23×C3—202no—
357C23×C3—202no—
358C23×C3C2×D2012yes—
359C23×C3C2×D2011yescharacteristic
360C3×Q8—54no—
361C3×Q8—102no—
362C3×Q8—104no—
363C3×D4—54no—
364C3×D4—1016no—
365C3×D4—102no—
366C3×D4—104no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—1016no—
372C2×C3×C4—102no—
373C2×C3×C4—104no—
374C2×C3×C4C2×D2012yes—
375C2×C3×C4C2×D2011yescharacteristic
376C2×C3×C4D4×D512yes—
377C2×C3×C4D4×D512yes—
378C2×C3×C4C23×D511yescharacteristic
379C2×Dic3—102no—
380C2×Dic3—102no—
381C2×Dic3—202no—
382C2×Dic3—202no—
383Dic6—102no—
384Dic6—102no—
385Dic6—202no—
386C3⋊C8—22no—
387C3⋊C8—22no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—22no—
391C22×C5—44no—
392C22×C5#95012yes—
393C22×C5#95112yes—
394C22×C5#95312yes—
395C22×C5C22×#6711yescharacteristic
396C2×D5—24no—
397C2×D5—48no—
398C2×D5—42no—
399C2×D5—42no—
400C4×C5—22no—
401C4×C5#95312yes—
402C4×C5C22×#6711yescharacteristic
403C4×C5C22×#6711yescharacteristic
404Dic5—24no—
405Dic5—122no—
406Dic5—122no—
407C24—101no—
408C24#120211yescharacteristic
409#41—108no—
410#41—108no—
411#41—1016no—
412C2×Q8—54no—
413C2×Q8—52no—
414C2×Q8—101no—
415C2×Q8—102no—
416C2×Q8—152no—
417C2×Q8—301no—
418C2×Q8—302no—
419C2×Q8—302no—
420C2×D4—54no—
421C2×D4—52no—
422C2×D4—108no—
423C2×D4—104no—
424C2×D4—101no—
425C2×D4—102no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—108no—
429C22×C4—101no—
430C22×C4—104no—
431C22×C4—301no—
432C22×C4—301no—
433C22×C4#120212yes—
434C22×C4#120211yescharacteristic
435C22×C4C2×D3×D512yes—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—308no—
439C2×C8—32no—
440C2×C8—32no—
441C2×C8—62no—
442C2×C8—62no—
443C4⋊C4—152no—
444C4⋊C4—301no—
445C4⋊C4—304no—
446C22⋊C4—304no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—44no—
452C22×C3—104no—
453C22×C3—202no—
454C22×C3—202no—
455C22×C3—208no—
456C22×C3#402812yes—
457C22×C3#405012yes—
458C22×C3#405512yes—
459C22×C3C22×D2011yescharacteristic
460C3×C4—22no—
461C3×C4—104no—
462C3×C4#402812yes—
463C3×C4C2×D4×D511yescharacteristic
464C3×C4C2×D4×D511yescharacteristic
465Dic3—202no—
466Dic3—202no—
467C2×C5—42no—
468C2×C5#523914yescomplemented
469C2×C5C2×#95011yescharacteristic
470C2×C5C2×#95111yescharacteristic
471C2×C5C2×#95311yescharacteristic
472D5—44no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—102no—
477C23—104no—
478C23—202no—
479C23—202no—
480C23C2×#120212yes—
481C23C2×#120211yescharacteristic
482Q8—54no—
483Q8—102no—
484Q8—104no—
485Q8—302no—
486Q8—302no—
487Q8—602no—
488D4—54no—
489D4—1016no—
490D4—102no—
491D4—104no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—1016no—
497C2×C4—102no—
498C2×C4—104no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—602no—
502C2×C4—602no—
503C2×C4C2×#120212yes—
504C2×C4C2×#120211yescharacteristic
505C2×C4D5×#6712yes—
506C2×C4D5×#6712yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—62no—
509C8—62no—
510C2×C3—42no—
511C2×C3—204no—
512C2×C3#6502214yescomplemented
513C2×C3C2×#402811yescharacteristic
514C2×C3C2×#405011yescharacteristic
515C2×C3C2×#405511yescharacteristic
516C5C2×#523911yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—22no—
520C22—44no—
521C22—104no—
522C22—202no—
523C22—202no—
524C22—208no—
525C22#9131112yes—
526C22#9131312yes—
527C22#9156412yes—
528C22C22×#120211yescharacteristic
529C4—22no—
530C4—104no—
531C4—602no—
532C4—602no—
533C4#9156412yes—
534C4C2×D5×#6711yescharacteristic
535C4C2×D5×#6711yescharacteristic
536C3C2×#6502211yescharacteristic, complemented, Sylow
537C2—42no—
538C2—204no—
539C2#1174853114yesdirect product factor
540C2C2×#9131111yescharacteristic
541C2C2×#9131311yescharacteristic
542C2C2×#9156411yescharacteristic
subgroupG/H
centerC23C2×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×#709C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91813C2semidirect
3. C22×#6662C2semidirect
4. C22×#6657C2semidirect
5. C2×C5×#830C2semidirect
6. #11748531C2direct (N × H)
7. C2×#90971C2semidirect
8. C2×#90965C2semidirect
23. #91813C22semidirect
28. C2×#6662C22semidirect
30. C2×#6657C22semidirect
31. C5×#830C22semidirect
32. #90971C22semidirect
33. #90965C22semidirect
90. C2×#830D5semidirect
176. #830C2×D5semidirect
346. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
468. C2×C5#5239semidirect
512. C2×C3#65022semidirect
516. C5C2×#5239semidirect
536. C3C2×#65022semidirect
539. C2#11748531direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×#918132
C22×#66622
C22×#66572
C2×C5×#8302
#117485312
C2×#909712
C2×#909652
C2×#650223
C2×#52395