Finite Group Databasebeta

← C2×#11756342 #14481195

Subgroups — C2×#11756342 #14481195

Order 1920.

2008 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
1C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
2C2×#91835C211yesmaximal, characteristic
3C2×#91833C211yesmaximal, characteristic, complemented
4#11756342C2116yesmaximal, direct product factor
5C2×#91787C212yesmaximal
6C2×#91786C211yesmaximal, characteristic
7C2×#91779C211yesmaximal, characteristic, complemented
8C2×#91778C212yesmaximal, complemented
9C2×#91765C212yesmaximal
10C2×#91761C211yesmaximal, characteristic
11C2×#91759C212yesmaximal, complemented
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#65917—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×Dic30C2211yescharacteristic
17C3×C4×C5×Q8C2218yescomplemented
18C2×C3×C5×C4⋊C4C2212yes—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C42×C5C2212yes—
22#91835C2218yes—
23#91833C2218yescomplemented
24C2×#6714C2212yes—
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2212yes—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2212yes—
30C2×C4⋊Dic15C2212yes—
31C2×#6712C2212yes—
32C2×#6712C2212yes—
33C2×#6712C2212yes—
34C2×#6712C2212yes—
35C2×#6712C2211yescharacteristic
36C2×#6712C2211yescharacteristic
37C2×#6712C2212yes—
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2212yes—
40#91787C22116yes—
41#91786C2218yes—
42#91779C2218yescomplemented
43#91778C22116yescomplemented
44#91765C22116yes—
45#91761C2218yes—
46#91759C22116yescomplemented
47C4×Dic30C2218yescomplemented
48C2×#5583—51nomaximal, Hall
49C2×C4×C5×Q8D311yescharacteristic, complemented
50C2×#4092—31no—
51C2×#4090—31no—
52#65917—316no—
53C2×#4044—32no—
54C2×#4043—31no—
55C2×#4036—31no—
56C2×#4035—32no—
57C2×#4022—32no—
58C2×#4018—31no—
59C2×#4016—32no—
60C2×C4×Dic10—31no—
61C23×D15C2311yescharacteristic
62C2×C3×C5×Q8—24no—
63C2×C3×C5×Q8C2314yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2312yes—
72C22×Dic15C2312yes—
73C22×Dic15C2311yescharacteristic
74C2×C4×D15—24no—
75C2×C4×D15C2314yes—
76C2×Dic30—24no—
77C2×Dic30C2314yes—
78C3×C5×C4⋊C4C2318yes—
79C3×C5×C4⋊C4C2314yes—
80C3×C42×C5C2314yes—
81C3×C42×C5C2318yes—
82#6714C2314yes—
83#6714C2314yes—
84#6714C2318yes—
85#6714C2318yes—
86C4⋊Dic15C2314yes—
87C4⋊Dic15C2318yes—
88C4⋊Dic15C2318yes—
89#6712C2318yes—
90#6712C2314yes—
91#6712C2318yes—
92#6712C2318yes—
93#6712C2314yes—
94#6712C2318yes—
95#6712C2318yes—
96C4×Dic15C2318yes—
97C4×Dic15C2314yes—
98C2×C3×C4×Q8D511yescharacteristic, complemented
99C2×#946—51no—
100C2×#944—51no—
101#5583—516no—
102C2×#898—52no—
103C2×#897—51no—
104C2×#890—51no—
105C2×#889—52no—
106C2×#876—52no—
107C2×#872—51no—
108C2×#870—52no—
109C2×C4×Dic6—51no—
110C22×C5×Q8C2×D311yescharacteristic
111C22×C4×D5—31no—
112C22×Dic10—31no—
113C4×C5×Q8C2×D318yescomplemented
114C2×C5×C4⋊C4C2×D312yes—
115C2×C5×C4⋊C4C2×D311yescharacteristic
116C2×C42×C5C2×D311yescharacteristic
117C2×C42×C5C2×D312yes—
118#4092—38no—
119#4090—38no—
120C2×#685—31no—
121C2×#685—31no—
122C2×#685—32no—
123C2×#685—32no—
124C2×C4⋊Dic5—31no—
125C2×C4⋊Dic5—32no—
126C2×C4⋊Dic5—32no—
127C2×#683—32no—
128C2×#683—31no—
129C2×#683—32no—
130C2×#683—32no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683—32no—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—31no—
136#4044—316no—
137#4043—38no—
138#4036—38no—
139#4035—316no—
140#4022—316no—
141#4018—38no—
142#4016—316no—
143C4×Dic10—38no—
144C2×#541—151noSylow
145C23×C3×C5C2411yescharacteristic
146C22×D15—22no—
147C22×D15—22no—
148C22×D15—22no—
149C22×D15C2412yes—
150C3×C5×Q8—28no—
151C2×C3×C4×C5—24no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—24no—
155C2×C3×C4×C5#4114yes—
156C2×C3×C4×C5C2412yes—
157C2×C3×C4×C5C2412yes—
158C2×C3×C4×C5C2414yes—
159C2×C3×C4×C5C2414yes—
160C2×C3×C4×C5C2412yes—
161C2×Dic15—24no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—24no—
165C2×Dic15—22no—
166C2×Dic15C2412yes—
167C2×Dic15C2414yes—
168C2×Dic15C2412yes—
169C2×Dic15C2414yes—
170C2×Dic15C2412yes—
171C4×D15—28no—
172Dic30—28no—
173C22×C3×Q8C2×D511yescharacteristic
174C22×C4×D3—51no—
175C22×Dic6—51no—
176C3×C4×Q8C2×D518yescomplemented
177C2×C3×C4⋊C4C2×D512yes—
178C2×C3×C4⋊C4C2×D511yescharacteristic
179C2×C3×C42C2×D511yescharacteristic
180C2×C3×C42C2×D512yes—
181#946—58no—
182#944—58no—
183C2×(C2×D3)⋊C4—51no—
184C2×(C2×D3)⋊C4—51no—
185C2×(C2×D3)⋊C4—52no—
186C2×(C2×D3)⋊C4—52no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—52no—
189C2×C4⋊Dic3—52no—
190C2×Dic3⋊C4—52no—
191C2×Dic3⋊C4—51no—
192C2×Dic3⋊C4—52no—
193C2×Dic3⋊C4—52no—
194C2×Dic3⋊C4—51no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197C2×C4×Dic3—52no—
198C2×C4×Dic3—51no—
199#898—516no—
200#897—58no—
201#890—58no—
202#889—516no—
203#876—516no—
204#872—58no—
205#870—516no—
206C4×Dic6—58no—
207C23×D5—31no—
208C2×C5×Q8—24no—
209C2×C5×Q8C22×D314yes—
210C22×C4×C5C22×D311yescharacteristic
211C22×C4×C5C22×D311yescharacteristic
212C22×C4×C5C22×D312yes—
213C22×C4×C5C22×D312yes—
214C22×C4×C5C22×D311yescharacteristic
215C22×Dic5—32no—
216C22×Dic5—31no—
217C22×Dic5—31no—
218C22×Dic5—32no—
219C22×Dic5—31no—
220C2×C4×D5—34no—
221C2×C4×D5—64no—
222C2×Dic10—34no—
223C2×Dic10—64no—
224C5×C4⋊C4C22×D318yes—
225C5×C4⋊C4C22×D314yes—
226C42×C5C22×D314yes—
227C42×C5C22×D318yes—
228#685—34no—
229#685—34no—
230#685—38no—
231#685—38no—
232C4⋊Dic5—34no—
233C4⋊Dic5—38no—
234C4⋊Dic5—38no—
235#683—38no—
236#683—34no—
237#683—38no—
238#683—38no—
239#683—34no—
240#683—38no—
241#683—38no—
242C4×Dic5—38no—
243C4×Dic5—34no—
244#541—1516no—
245C2×C4⋊Q8—151no—
246C2×#126—152no—
247C2×#126—152no—
248C2×#125—152no—
249C2×#125—151no—
250C2×#125—152no—
251C2×C22⋊Q8—151no—
252C2×C22⋊Q8—151no—
253C2×C4×Q8—151no—
254C2×C4×Q8D1511yescharacteristic, complemented
255C2×#117—151no—
256C22×C3×C5C2×#4112yes—
257C22×C3×C52−1+412yes—
258C22×C3×C52−1+412yes—
259C22×C3×C5C2511yescharacteristic
260C2×D15—22no—
261C2×D15—22no—
262C2×D15—22no—
263C2×D15—44no—
264C3×C4×C5—24no—
265C3×C4×C5—22no—
266C3×C4×C5—22no—
267C3×C4×C5—24no—
268C3×C4×C5C2×#4114yes—
269Dic15—24no—
270Dic15—22no—
271Dic15—24no—
272Dic15—22no—
273Dic15—22no—
274C23×D3—51no—
275C2×C3×Q8—24no—
276C2×C3×Q8C22×D514yes—
277C22×C3×C4C22×D511yescharacteristic
278C22×C3×C4C22×D511yescharacteristic
279C22×C3×C4C22×D512yes—
280C22×C3×C4C22×D512yes—
281C22×C3×C4C22×D511yescharacteristic
282C22×Dic3—51no—
283C22×Dic3—52no—
284C22×Dic3—51no—
285C22×Dic3—52no—
286C22×Dic3—51no—
287C2×C4×D3—54no—
288C2×C4×D3—104no—
289C2×Dic6—54no—
290C2×Dic6—104no—
291C3×C4⋊C4C22×D518yes—
292C3×C4⋊C4C22×D514yes—
293C3×C42C22×D514yes—
294C3×C42C22×D518yes—
295(C2×D3)⋊C4—54no—
296(C2×D3)⋊C4—54no—
297(C2×D3)⋊C4—58no—
298(C2×D3)⋊C4—58no—
299C4⋊Dic3—54no—
300C4⋊Dic3—58no—
301C4⋊Dic3—58no—
302Dic3⋊C4—58no—
303Dic3⋊C4—54no—
304Dic3⋊C4—58no—
305Dic3⋊C4—58no—
306Dic3⋊C4—54no—
307Dic3⋊C4—58no—
308Dic3⋊C4—58no—
309C4×Dic3—58no—
310C4×Dic3—54no—
311C23×C5C23×D311yescharacteristic
312C22×D5—32no—
313C22×D5—62no—
314C22×D5—62no—
315C22×D5—62no—
316C5×Q8—28no—
317C2×C4×C5—24no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—24no—
321C2×C4×C5#23514yes—
322C2×C4×C5C23×D312yes—
323C2×C4×C5C23×D312yes—
324C2×C4×C5C23×D314yes—
325C2×C4×C5C23×D314yes—
326C2×C4×C5C23×D312yes—
327C2×Dic5—32no—
328C2×Dic5—34no—
329C2×Dic5—32no—
330C2×Dic5—34no—
331C2×Dic5—32no—
332C2×Dic5—64no—
333C2×Dic5—62no—
334C2×Dic5—64no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C4×D5—68no—
338Dic10—68no—
339C22×Q8—151no—
340C22×Q8C2×D1511yescharacteristic
341C23×C4—151no—
342C4⋊Q8—158no—
343#126—1516no—
344#126—1516no—
345#125—1516no—
346#125—158no—
347#125—1516no—
348C22⋊Q8—158no—
349C22⋊Q8—158no—
350C4×Q8—158no—
351C4×Q8C2×D1518yescomplemented
352#117—158no—
353C2×C4⋊C4—151no—
354C2×C4⋊C4—151no—
355C2×C4⋊C4—151no—
356C2×C4⋊C4—152no—
357C2×C4⋊C4—152no—
358C2×C4⋊C4—152no—
359C2×C4⋊C4—152no—
360C2×C4⋊C4—152no—
361C2×C4⋊C4—152no—
362C2×C4⋊C4—152no—
363C2×C4⋊C4C2×D1511yescharacteristic
364C2×C4⋊C4C2×D1512yes—
365C2×C22⋊C4—151no—
366C2×C22⋊C4—151no—
367C2×C22⋊C4—152no—
368C2×C22⋊C4—152no—
369C2×C42—151no—
370C2×C42—152no—
371C2×C42C2×D1511yescharacteristic
372C2×C42C2×D1512yes—
373C2×C3×C5#54114yescomplemented
374C2×C3×C5C22×#4111yescharacteristic
375C2×C3×C5C2×2−1+411yescharacteristic
376C2×C3×C5C2×2−1+411yescharacteristic
377D15—42no—
378C23×C3C23×D511yescharacteristic
379C22×D3—52no—
380C22×D3—102no—
381C22×D3—102no—
382C22×D3—102no—
383C3×Q8—28no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4#70914yes—
389C2×C3×C4C23×D512yes—
390C2×C3×C4C23×D512yes—
391C2×C3×C4C23×D514yes—
392C2×C3×C4C23×D514yes—
393C2×C3×C4C23×D512yes—
394C2×Dic3—52no—
395C2×Dic3—54no—
396C2×Dic3—52no—
397C2×Dic3—54no—
398C2×Dic3—52no—
399C2×Dic3—104no—
400C2×Dic3—102no—
401C2×Dic3—104no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C4×D3—108no—
405Dic6—108no—
406C22×C5C2×#23512yes—
407C22×C5#100712yes—
408C22×C5#101012yes—
409C22×C5C24×D311yescharacteristic
410C2×D5—62no—
411C2×D5—62no—
412C2×D5—62no—
413C2×D5—124no—
414C4×C5—24no—
415C4×C5—22no—
416C4×C5—22no—
417C4×C5—24no—
418C4×C5C2×#23514yes—
419Dic5—64no—
420Dic5—62no—
421Dic5—64no—
422Dic5—62no—
423Dic5—62no—
424C24—151no—
425C2×Q8—24no—
426C2×Q8—154no—
427C2×Q8—304no—
428C2×Q8C22×D1514yes—
429C22×C4—151no—
430C22×C4—152no—
431C22×C4—151no—
432C22×C4—152no—
433C22×C4—151no—
434C22×C4—154no—
435C22×C4—304no—
436C22×C4C22×D1511yescharacteristic
437C22×C4C22×D1511yescharacteristic
438C22×C4C22×D1512yes—
439C22×C4C22×D1512yes—
440C22×C4C22×D1511yescharacteristic
441C4⋊C4—154no—
442C4⋊C4—154no—
443C4⋊C4—154no—
444C4⋊C4—158no—
445C4⋊C4—158no—
446C4⋊C4—158no—
447C4⋊C4—158no—
448C4⋊C4—158no—
449C4⋊C4—158no—
450C4⋊C4—158no—
451C4⋊C4C22×D1514yes—
452C4⋊C4C22×D1518yes—
453C22⋊C4—154no—
454C22⋊C4—154no—
455C22⋊C4—158no—
456C22⋊C4—158no—
457C42—154no—
458C42—158no—
459C42C22×D1514yes—
460C42C22×D1518yes—
461C3×C5C2×#54111yescharacteristic, complemented, Hall
462C22×C3C2×#70912yes—
463C22×C3#414712yes—
464C22×C3#415012yes—
465C22×C3C24×D511yescharacteristic
466C2×D3—102no—
467C2×D3—102no—
468C2×D3—102no—
469C2×D3—204no—
470C3×C4—24no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—24no—
474C3×C4C2×#70914yes—
475Dic3—104no—
476Dic3—102no—
477Dic3—104no—
478Dic3—102no—
479Dic3—102no—
480C2×C5#558314yescomplemented
481C2×C5C22×#23511yescharacteristic
482C2×C5C2×#100711yescharacteristic
483C2×C5C2×#101011yescharacteristic
484D5—122no—
485C23—152no—
486C23—302no—
487C23—302no—
488C23—302no—
489C23C23×D1511yescharacteristic
490Q8—28no—
491Q8—308no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—152no—
497C2×C4—154no—
498C2×C4—152no—
499C2×C4—154no—
500C2×C4—152no—
501C2×C4—302no—
502C2×C4—304no—
503C2×C4—302no—
504C2×C4—304no—
505C2×C4—302no—
506C2×C4—308no—
507C2×C4#681714yes—
508C2×C4C23×D1512yes—
509C2×C4C23×D1512yes—
510C2×C4C23×D1514yes—
511C2×C4C23×D1514yes—
512C2×C4C23×D1512yes—
513C2×C3#6591714yescomplemented
514C2×C3C22×#70911yescharacteristic
515C2×C3C2×#414711yescharacteristic
516C2×C3C2×#415011yescharacteristic
517D3—202no—
518C5C2×#558311yescharacteristic, complemented, Sylow
519C22—302no—
520C22—302no—
521C22—302no—
522C22—604no—
523C22C2×#681712yes—
524C22#9209812yes—
525C22#9210112yes—
526C22C24×D1511yescharacteristic
527C4—24no—
528C4—22no—
529C4—22no—
530C4—24no—
531C4—302no—
532C4—304no—
533C4—302no—
534C4—304no—
535C4—302no—
536C4C2×#681714yes—
537C3C2×#6591711yescharacteristic, complemented, Sylow
538C2—602no—
539C2#1175634214yesdirect product factor
540C2C22×#681711yescharacteristic
541C2C2×#9209811yescharacteristic
542C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×Q8C2
socleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4×Q8D15
hypocenterC3×C5C2×#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×Q8C2semidirect
3. C2×#91833C2semidirect
4. #11756342C2direct (N × H)
7. C2×#91779C2semidirect
8. C2×#91778C2semidirect
11. C2×#91759C2semidirect
12. C2×C4×Dic30C2semidirect
17. C3×C4×C5×Q8C22semidirect
23. #91833C22semidirect
42. #91779C22semidirect
43. #91778C22semidirect
46. #91759C22semidirect
47. C4×Dic30C22semidirect
49. C2×C4×C5×Q8D3semidirect
98. C2×C3×C4×Q8D5semidirect
113. C4×C5×Q8C2×D3semidirect
176. C3×C4×Q8C2×D5semidirect
254. C2×C4×Q8D15semidirect
351. C4×Q8C2×D15semidirect
373. C2×C3×C5#541semidirect
461. C3×C5C2×#541semidirect
480. C2×C5#5583semidirect
513. C2×C3#65917semidirect
518. C5C2×#5583semidirect
537. C3C2×#65917semidirect
539. C2#11756342direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×Q82
C2×#918352
C2×#918332
#117563422
C2×#917872
C2×#917862
C2×#917792
C2×#917782
C2×#917652
C2×#917612
C2×#917592
C2×C4×Dic302
C2×#659173
C2×#55835