Finite Group Databasebeta

← C2×#11751288 #14423498

Subgroups — C2×#11751288 #14423498

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×#6821C211yesmaximal, characteristic
2C22×C3×C5×Q16C211yesmaximal, characteristic, complemented
3C2×#91835C211yesmaximal, characteristic, complemented
4C22×#6717C211yesmaximal, characteristic, complemented
5C2×#91119C211yesmaximal, characteristic, complemented
6#11751288C218yesmaximal, direct product factor
7C2×#91105C211yesmaximal, characteristic, complemented
8C2×#91104C211yesmaximal, characteristic, complemented
9C2×#65476—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×Q8C2211yescharacteristic
12C2×#6821—24no—
13C2×#6821—24no—
14C2×#6821—22no—
15C2×#6821C2214yes—
16C22×D60—21no—
17C22×D60C2211yescharacteristic
18C22×C4×D15—21no—
19C22×C4×D15C2211yescharacteristic
20C2×C3×C5×Q16—24no—
21C2×C3×C5×Q16C2214yescomplemented
22C22×C3×C5×C8C2211yescharacteristic
23#91835—22no—
24#91835C2214yescomplemented
25C2×#6717—24no—
26C2×#6717C2214yescomplemented
27C2×#6714—21no—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712—21no—
30C22×C3⋊#168C2211yescharacteristic
31#91119C2214yescomplemented
32#91105C2214yescomplemented
33#91104C2214yescomplemented
34C2×#5187—51nomaximal, Hall
35C22×#713—31no—
36C22×C5×Q16D311yescharacteristic, complemented
37C2×#4092—31no—
38C22×#688—31no—
39C2×#3967—31no—
40#65476—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C23×D15—21no—
44C23×D15D411yescharacteristic
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8—22no—
49C2×C3×C5×Q8—22no—
50C2×C3×C5×Q8D414yes—
51C2×C3×C5×Q8C2312yes—
52C2×C3×C5×Q8C2312yes—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C22×Dic15D411yescharacteristic
58#6821—216no—
59#6821—28no—
60#6821—28no—
61C2×D60—28no—
62C2×D60—24no—
63C2×D60—21no—
64C2×D60—22no—
65C2×D60D414yes—
66C2×D60C2312yes—
67C2×C4×D15—28no—
68C2×C4×D15—22no—
69C2×C4×D15—22no—
70C2×C4×D15—24no—
71C2×C4×D15D412yes—
72C2×C4×D15C2312yes—
73C3×C5×Q16—28no—
74C2×C3×C5×C8—22no—
75C2×C3×C5×C8C2312yes—
76#6717—28no—
77#6714—24no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80#6712—24no—
81C2×C3⋊#168—22no—
82C2×C3⋊#168C2312yes—
83C22×#239—51no—
84C22×C3×Q16D511yescharacteristic, complemented
85C2×#946—51no—
86C22×#215—51no—
87C2×#835—51no—
88#5187—58no—
89C2×#821—51no—
90C2×(C2×D3)⋊C8—51no—
91C22×C5×Q8C2×D311yescharacteristic
92C22×C5×Q8C2×D311yescharacteristic
93C2×#713—34no—
94C2×#713—62no—
95C2×#713—64no—
96C2×#713—64no—
97C22×D20—31no—
98C22×D20—61no—
99C22×C4×D5—31no—
100C22×C4×D5—61no—
101C2×C5×Q16—24no—
102C2×C5×Q16C2×D314yescomplemented
103C22×C5×C8C2×D311yescharacteristic
104#4092—34no—
105#4092—62no—
106C2×#688—34no—
107C2×#688—64no—
108C2×#685—61no—
109C2×C4⋊Dic5—31no—
110C2×#683—61no—
111C22×#168—31no—
112#3967—34no—
113#3953—34no—
114#3952—34no—
115C2×#452—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—22no—
118C22×D15—24no—
119C22×D15—22no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—42no—
123C22×D15—42no—
124C22×D15C2×D412yes—
125C3×C5×Q8—24no—
126C3×C5×Q8—22no—
127C3×C5×Q8—22no—
128C3×C5×Q8—22no—
129C3×C5×Q8—42no—
130C3×C5×Q8C2×D414yes—
131C2×C3×C4×C5—24no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—42no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—42no—
142C2×Dic15C2×D412yes—
143D60—216no—
144D60—24no—
145D60—22no—
146D60C2×D414yes—
147C4×D15—216no—
148C4×D15—24no—
149C4×D15—22no—
150C4×D15—22no—
151C3×C5×C8—22no—
152C3⋊#168—22no—
153C22×C3×Q8C2×D511yescharacteristic
154C22×C3×Q8C2×D511yescharacteristic
155C2×#239—54no—
156C2×#239—102no—
157C2×#239—104no—
158C2×#239—104no—
159C22×D12—51no—
160C22×D12—101no—
161C22×C4×D3—51no—
162C22×C4×D3—101no—
163C2×C3×Q16—24no—
164C2×C3×Q16C2×D514yescomplemented
165C22×C3×C8C2×D511yescharacteristic
166#946—54no—
167#946—102no—
168C2×#215—54no—
169C2×#215—104no—
170C2×(C2×D3)⋊C4—101no—
171C2×C4⋊Dic3—51no—
172C2×Dic3⋊C4—101no—
173C22×C3⋊C8—51no—
174#835—54no—
175#821—54no—
176(C2×D3)⋊C8—54no—
177C23×D5—31no—
178C23×D5—61no—
179C2×C5×Q8—22no—
180C2×C5×Q8—21no—
181C2×C5×Q8—21no—
182C2×C5×Q8—22no—
183C2×C5×Q8—22no—
184C2×C5×Q8#6714yes—
185C2×C5×Q8C22×D312yes—
186C2×C5×Q8C22×D312yes—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C22×Dic5—31no—
191C22×Dic5—61no—
192#713—68no—
193#713—616no—
194#713—68no—
195C2×D20—34no—
196C2×D20—32no—
197C2×D20—64no—
198C2×D20—68no—
199C2×D20—61no—
200C2×D20—62no—
201C2×C4×D5—32no—
202C2×C4×D5—32no—
203C2×C4×D5—64no—
204C2×C4×D5—68no—
205C2×C4×D5—62no—
206C2×C4×D5—62no—
207C5×Q16—28no—
208C2×C5×C8—22no—
209C2×C5×C8C22×D312yes—
210#688—68no—
211#685—64no—
212C4⋊Dic5—32no—
213C4⋊Dic5—61no—
214#683—64no—
215C2×#168—32no—
216C2×#168—62no—
217C22×#41—151no—
218C22×Q16D1511yescharacteristic, complemented
219C22×SD16—151no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—151no—
223C2×#102—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5#12012yes—
226C22×C3×C5#13512yes—
227C22×C3×C5#13712yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×D15—22no—
230C2×D15—24no—
231C2×D15—22no—
232C2×D15—22no—
233C2×D15—42no—
234C2×D15—42no—
235C2×D15—44no—
236C2×D15—48no—
237C3×C4×C5—24no—
238C3×C4×C5—42no—
239C3×C4×C5#12012yes—
240C3×C4×C5C22×D411yescharacteristic
241C3×C4×C5C22×D411yescharacteristic
242Dic15—22no—
243Dic15—42no—
244C23×D3—51no—
245C23×D3—101no—
246C2×C3×Q8—21no—
247C2×C3×Q8—22no—
248C2×C3×Q8—21no—
249C2×C3×Q8—22no—
250C2×C3×Q8—22no—
251C2×C3×Q8C22⋊D514yes—
252C2×C3×Q8C22×D512yes—
253C2×C3×Q8C22×D512yes—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4C22×D511yescharacteristic
257C22×Dic3—51no—
258C22×Dic3—101no—
259#239—108no—
260#239—1016no—
261#239—108no—
262C2×D12—54no—
263C2×D12—52no—
264C2×D12—104no—
265C2×D12—108no—
266C2×D12—101no—
267C2×D12—102no—
268C2×C4×D3—52no—
269C2×C4×D3—52no—
270C2×C4×D3—104no—
271C2×C4×D3—108no—
272C2×C4×D3—102no—
273C2×C4×D3—102no—
274C3×Q16—28no—
275C2×C3×C8—22no—
276C2×C3×C8C22×D512yes—
277#215—108no—
278(C2×D3)⋊C4—104no—
279C4⋊Dic3—52no—
280C4⋊Dic3—101no—
281Dic3⋊C4—104no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—102no—
284C23×C5D3×D411yescharacteristic
285C22×D5—32no—
286C22×D5—62no—
287C22×D5—62no—
288C22×D5—64no—
289C22×D5—62no—
290C22×D5—62no—
291C22×D5—122no—
292C22×D5—122no—
293C5×Q8—24no—
294C5×Q8—22no—
295C5×Q8—22no—
296C5×Q8—22no—
297C5×Q8—42no—
298C5×Q8C2×#6714yes—
299C2×C4×C5—24no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—42no—
303C2×C4×C5D3×D411yescharacteristic
304C2×C4×C5D3×D412yes—
305C2×C4×C5C2×#6712yes—
306C2×C4×C5C23×D311yescharacteristic
307C2×Dic5—32no—
308C2×Dic5—62no—
309C2×Dic5—62no—
310C2×Dic5—122no—
311D20—34no—
312D20—616no—
313D20—64no—
314D20—62no—
315C4×D5—616no—
316C4×D5—64no—
317C4×D5—62no—
318C4×D5—62no—
319C5×C8—22no—
320#168—62no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8C2×D1511yescharacteristic
326C22×Q8C2×D1511yescharacteristic
327C22×D4—151no—
328C22×D4—301no—
329C23×C4—151no—
330C23×C4—301no—
331C2×Q16—24no—
332C2×Q16C2×D1514yescomplemented
333C2×SD16—154no—
334C2×SD16—304no—
335C22×C8—151no—
336C22×C8C2×D1511yescharacteristic
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—154no—
345C2×C3×C5#45214yescomplemented
346C2×C3×C5C2×#12011yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5C2×#13711yescharacteristic
349D15—42no—
350D15—44no—
351C23×C3D4×D511yescharacteristic
352C22×D3—52no—
353C22×D3—102no—
354C22×D3—102no—
355C22×D3—102no—
356C22×D3—104no—
357C22×D3—102no—
358C22×D3—202no—
359C22×D3—202no—
360C3×Q8—22no—
361C3×Q8—24no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—42no—
365C3×Q8C2×C22⋊D514yes—
366C2×C3×C4—22no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—42no—
370C2×C3×C4D4×D512yes—
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4C2×C22⋊D512yes—
373C2×C3×C4C23×D511yescharacteristic
374C2×Dic3—52no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C2×Dic3—202no—
378D12—54no—
379D12—1016no—
380D12—102no—
381D12—104no—
382C4×D3—1016no—
383C4×D3—102no—
384C4×D3—102no—
385C4×D3—104no—
386C3×C8—22no—
387C3⋊C8—102no—
388C22×C5#91812yes—
389C22×C5#91912yes—
390C22×C5#93712yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—62no—
393C2×D5—62no—
394C2×D5—64no—
395C2×D5—62no—
396C2×D5—124no—
397C2×D5—128no—
398C2×D5—122no—
399C2×D5—122no—
400C4×C5—24no—
401C4×C5—42no—
402C4×C5#93712yes—
403C4×C5C2×D3×D411yescharacteristic
404C4×C5C22×#6711yescharacteristic
405Dic5—62no—
406Dic5—122no—
407C24—151no—
408C24—301no—
409#41—308no—
410#41—3016no—
411#41—308no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8#122014yes—
418C2×Q8C22×D1512yes—
419C2×Q8C22×D1512yes—
420C2×D4—154no—
421C2×D4—152no—
422C2×D4—304no—
423C2×D4—308no—
424C2×D4—301no—
425C2×D4—302no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—151no—
429C22×C4—152no—
430C22×C4—152no—
431C22×C4—304no—
432C22×C4—308no—
433C22×C4—302no—
434C22×C4—302no—
435C22×C4—301no—
436C22×C4C22×D1511yescharacteristic
437Q16—28no—
438SD16—308no—
439C2×C8—22no—
440C2×C8—152no—
441C2×C8—302no—
442C2×C8C22×D1512yes—
443C4⋊C4—152no—
444C4⋊C4—304no—
445C4⋊C4—301no—
446C22⋊C4—304no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3#406412yes—
449C22×C3#406512yes—
450C22×C3#408312yes—
451C22×C3C2×D4×D511yescharacteristic
452C2×D3—102no—
453C2×D3—102no—
454C2×D3—104no—
455C2×D3—102no—
456C2×D3—202no—
457C2×D3—202no—
458C2×D3—204no—
459C2×D3—208no—
460C3×C4—24no—
461C3×C4—42no—
462C3×C4#408312yes—
463C3×C4C2×D4×D511yescharacteristic
464C3×C4C22×C22⋊D511yescharacteristic
465Dic3—102no—
466Dic3—202no—
467C2×C5#518714yescomplemented
468C2×C5C2×#91811yescharacteristic
469C2×C5C2×#91911yescharacteristic
470C2×C5C2×#93711yescharacteristic
471D5—122no—
472D5—124no—
473C23—152no—
474C23—302no—
475C23—302no—
476C23—304no—
477C23—302no—
478C23—302no—
479C23—602no—
480C23—602no—
481C23D4×D1511yescharacteristic
482Q8—24no—
483Q8—22no—
484Q8—22no—
485Q8—22no—
486Q8—42no—
487Q8C2×#122014yes—
488D4—154no—
489D4—3016no—
490D4—304no—
491D4—302no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—42no—
496C2×C4—152no—
497C2×C4—3016no—
498C2×C4—302no—
499C2×C4—304no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—602no—
504C2×C4D4×D1511yescharacteristic
505C2×C4D4×D1512yes—
506C2×C4C2×#122012yes—
507C2×C4C23×D1511yescharacteristic
508C8—22no—
509C8—302no—
510C2×C3#6547614yescomplemented
511C2×C3C2×#406411yescharacteristic
512C2×C3C2×#406511yescharacteristic
513C2×C3C2×#408311yescharacteristic
514D3—202no—
515D3—204no—
516C5C2×#518711yescharacteristic, complemented, Sylow
517C22—304no—
518C22—302no—
519C22—302no—
520C22—302no—
521C22—604no—
522C22—608no—
523C22—602no—
524C22—602no—
525C22#9180712yes—
526C22#9180812yes—
527C22#9182612yes—
528C22C2×D4×D1511yescharacteristic
529C4—24no—
530C4—42no—
531C4—302no—
532C4—602no—
533C4#9182612yes—
534C4C2×D4×D1511yescharacteristic
535C4C22×#122011yescharacteristic
536C3C2×#6547611yescharacteristic, complemented, Sylow
537C2—602no—
538C2—604no—
539C2#1175128814yesdirect product factor
540C2C2×#9180711yescharacteristic
541C2C2×#9180811yescharacteristic
542C2C2×#9182611yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×Q16C2
socleC23×C3×C5C2×D4
prime radicalC22×#6821C2
hypercenterC22×Q16D15
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×Q16C2semidirect
3. C2×#91835C2semidirect
4. C22×#6717C2semidirect
5. C2×#91119C2semidirect
6. #11751288C2direct (N × H)
7. C2×#91105C2semidirect
8. C2×#91104C2semidirect
21. C2×C3×C5×Q16C22semidirect
24. #91835C22semidirect
26. C2×#6717C22semidirect
31. #91119C22semidirect
32. #91105C22semidirect
33. #91104C22semidirect
36. C22×C5×Q16D3semidirect
84. C22×C3×Q16D5semidirect
102. C2×C5×Q16C2×D3semidirect
164. C2×C3×Q16C2×D5semidirect
218. C22×Q16D15semidirect
332. C2×Q16C2×D15semidirect
345. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
467. C2×C5#5187semidirect
510. C2×C3#65476semidirect
516. C5C2×#5187semidirect
536. C3C2×#65476semidirect
539. C2#11751288direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68212
C22×C3×C5×Q162
C2×#918352
C22×#67172
C2×#911192
#117512882
C2×#911052
C2×#911042
C2×#654763
C2×#51875