Finite Group Databasebeta

← C2×#11756384 #14481201

Subgroups — C2×#11756384 #14481201

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×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×#91833C211yesmaximal, characteristic, complemented
4C2×#91815C211yesmaximal, characteristic
5C2×#91813C211yesmaximal, characteristic
6#11756384C2116yesmaximal, direct product factor
7C2×#91779C211yesmaximal, characteristic, complemented
8C2×#91779C212yesmaximal, complemented
9C2×#91778C212yesmaximal, complemented
10C2×#91776C211yesmaximal, characteristic, complemented
11C2×#91768C212yesmaximal
12C2×#91768C212yesmaximal
13C2×#65959—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×Dic30C2211yescharacteristic
17C3×C5×C22⋊Q8C2218yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2212yes—
20C2×C3×C5×C22⋊C4C2212yes—
21C2×#6719C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6719C2212yes—
24Q8×Dic15C2218yescomplemented
25#91833C2218yescomplemented
26#91815C2218yes—
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2212yes—
30C2×C4⋊Dic15C2211yescharacteristic
31C2×C4⋊Dic15C2212yes—
32#91813C2218yes—
33C2×#6712C2212yes—
34C2×#6712C2212yes—
35C2×#6712C2212yes—
36C2×#6712C2212yes—
37C2×#6712C2212yes—
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2211yescharacteristic
40C2×C4×Dic15C2212yes—
41C2×C4×Dic15C2212yes—
42#91779C22116yescomplemented
43#91779C2218yescomplemented
44#91778C22116yescomplemented
45#91776C2218yescomplemented
46#91768C22116yes—
47#91768C22116yes—
48C2×#5625—51nomaximal, Hall
49C2×C5×C22⋊Q8D311yescharacteristic
50C2×Q8×Dic5—31no—
51C2×#4090—31no—
52C2×#4072—31no—
53C2×#4070—31no—
54#65959—316no—
55C2×#4036—31no—
56C2×#4036—32no—
57C2×#4035—32no—
58C2×#4033—31no—
59C2×#4025—32no—
60C2×#4025—32no—
61C24×C3×C5C2311yescharacteristic
62C2×C3×C5×Q8—24no—
63C2×C3×C5×Q8C2314yes—
64C22×C3×C4×C5—24no—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2314yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2312yes—
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2312yes—
76C2×Dic30—24no—
77C2×Dic30C2314yes—
78C3×C5×C4⋊C4C2314yes—
79C3×C5×C4⋊C4C2318yes—
80C3×C5×C22⋊C4C2318yes—
81#6719C2318yes—
82#6719C2314yes—
83#6719C2314yes—
84C4⋊Dic15C2318yes—
85C4⋊Dic15C2318yes—
86C4⋊Dic15C2314yes—
87C4⋊Dic15C2314yes—
88C4⋊Dic15C2314yes—
89#6712C2318yes—
90#6712C2318yes—
91#6712C2318yes—
92#6712C2318yes—
93#6712C2318yes—
94C4×Dic15C2318yes—
95C4×Dic15C2318yes—
96C4×Dic15C2314yes—
97C4×Dic15C2314yes—
98C2×C3×C22⋊Q8D511yescharacteristic
99C2×Q8×Dic3—51no—
100C2×#944—51no—
101C2×#926—51no—
102C2×#924—51no—
103#5625—516no—
104C2×#890—52no—
105C2×#890—51no—
106C2×#889—52no—
107C2×#887—51no—
108C2×#879—52no—
109C2×#879—52no—
110C22×C5×Q8C2×D311yescharacteristic
111C23×C4×C5C2×D311yescharacteristic
112C22×Dic10—31no—
113C5×C22⋊Q8C2×D318yes—
114C2×C5×C4⋊C4C2×D311yescharacteristic
115C2×C5×C4⋊C4C2×D312yes—
116C2×C5×C22⋊C4C2×D312yes—
117C2×C22⋊Dic5—32no—
118C2×C22⋊Dic5—31no—
119C2×C22⋊Dic5—31no—
120Q8×Dic5—38no—
121#4090—38no—
122#4072—38no—
123C2×C4⋊Dic5—32no—
124C2×C4⋊Dic5—32no—
125C2×C4⋊Dic5—31no—
126C2×C4⋊Dic5—31no—
127C2×C4⋊Dic5—31no—
128#4070—38no—
129C2×#683—32no—
130C2×#683—32no—
131C2×#683—32no—
132C2×#683—32no—
133C2×#683—32no—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—32no—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—31no—
138#4036—316no—
139#4036—38no—
140#4035—316no—
141#4033—38no—
142#4025—316no—
143#4025—316no—
144C2×#541—151noSylow
145C23×C3×C5—22no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5C2412yes—
149C23×C3×C5C2411yescharacteristic
150C3×C5×Q8—28no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—24no—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5—28no—
155C2×C3×C4×C5#4114yes—
156C2×C3×C4×C5C2414yes—
157C2×C3×C4×C5C2414yes—
158C2×C3×C4×C5C2412yes—
159C2×C3×C4×C5C2412yes—
160C2×Dic15—24no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—24no—
164C2×Dic15—22no—
165C2×Dic15—22no—
166C2×Dic15C2412yes—
167C2×Dic15C2412yes—
168C2×Dic15C2412yes—
169C2×Dic15C2414yes—
170C2×Dic15C2414yes—
171C2×Dic15C2412yes—
172Dic30—28no—
173C22×C3×Q8C2×D511yescharacteristic
174C23×C3×C4C2×D511yescharacteristic
175C22×Dic6—51no—
176C3×C22⋊Q8C2×D518yes—
177C2×C3×C4⋊C4C2×D511yescharacteristic
178C2×C3×C4⋊C4C2×D512yes—
179C2×C3×C22⋊C4C2×D512yes—
180C2×#217—52no—
181C2×#217—51no—
182C2×#217—51no—
183Q8×Dic3—58no—
184#944—58no—
185#926—58no—
186C2×C4⋊Dic3—52no—
187C2×C4⋊Dic3—52no—
188C2×C4⋊Dic3—51no—
189C2×C4⋊Dic3—51no—
190C2×C4⋊Dic3—51no—
191#924—58no—
192C2×Dic3⋊C4—52no—
193C2×Dic3⋊C4—52no—
194C2×Dic3⋊C4—52no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197C2×C4×Dic3—52no—
198C2×C4×Dic3—52no—
199C2×C4×Dic3—51no—
200C2×C4×Dic3—51no—
201#890—516no—
202#890—58no—
203#889—516no—
204#887—58no—
205#879—516no—
206#879—516no—
207C24×C5C22×D311yescharacteristic
208C2×C5×Q8—24no—
209C2×C5×Q8C22×D314yes—
210C22×C4×C5—24no—
211C22×C4×C5C22×D312yes—
212C22×C4×C5C22×D312yes—
213C22×C4×C5C22×D311yescharacteristic
214C22×C4×C5C22×D314yes—
215C22×C4×C5C22×D311yescharacteristic
216C22×Dic5—32no—
217C22×Dic5—31no—
218C22×Dic5—31no—
219C22×Dic5—31no—
220C22×Dic5—32no—
221C22×Dic5—31no—
222C2×Dic10—34no—
223C2×Dic10—64no—
224C5×C4⋊C4C22×D314yes—
225C5×C4⋊C4C22×D318yes—
226C5×C22⋊C4C22×D318yes—
227C22⋊Dic5—38no—
228C22⋊Dic5—34no—
229C22⋊Dic5—34no—
230C4⋊Dic5—38no—
231C4⋊Dic5—38no—
232C4⋊Dic5—34no—
233C4⋊Dic5—34no—
234C4⋊Dic5—34no—
235#683—38no—
236#683—38no—
237#683—38no—
238#683—38no—
239#683—38no—
240C4×Dic5—38no—
241C4×Dic5—38no—
242C4×Dic5—34no—
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⋊Q8D1511yescharacteristic
253C2×C4×Q8—151no—
254C2×C4×Q8—151no—
255C2×#117—151no—
256C22×C3×C5—22no—
257C22×C3×C5—22no—
258C22×C3×C5—22no—
259C22×C3×C5—44no—
260C22×C3×C5C2×#4112yes—
261C22×C3×C52−1+412yes—
262C22×C3×C52−1+412yes—
263C22×C3×C5C2511yescharacteristic
264C3×C4×C5—22no—
265C3×C4×C5—24no—
266C3×C4×C5—24no—
267C3×C4×C5C2×#4114yes—
268Dic15—24no—
269Dic15—22no—
270Dic15—24no—
271Dic15—22no—
272Dic15—22no—
273Dic15—22no—
274C24×C3C22×D511yescharacteristic
275C2×C3×Q8—24no—
276C2×C3×Q8C22×D514yes—
277C22×C3×C4—24no—
278C22×C3×C4C22×D512yes—
279C22×C3×C4C22×D512yes—
280C22×C3×C4C22×D511yescharacteristic
281C22×C3×C4C22×D514yes—
282C22×C3×C4C22×D511yescharacteristic
283C22×Dic3—51no—
284C22×Dic3—51no—
285C22×Dic3—51no—
286C22×Dic3—52no—
287C22×Dic3—52no—
288C22×Dic3—51no—
289C2×Dic6—54no—
290C2×Dic6—104no—
291C3×C4⋊C4C22×D514yes—
292C3×C4⋊C4C22×D518yes—
293C3×C22⋊C4C22×D518yes—
294#217—58no—
295#217—54no—
296#217—54no—
297C4⋊Dic3—58no—
298C4⋊Dic3—58no—
299C4⋊Dic3—54no—
300C4⋊Dic3—54no—
301C4⋊Dic3—54no—
302Dic3⋊C4—58no—
303Dic3⋊C4—58no—
304Dic3⋊C4—58no—
305Dic3⋊C4—58no—
306Dic3⋊C4—58no—
307C4×Dic3—58no—
308C4×Dic3—58no—
309C4×Dic3—54no—
310C4×Dic3—54no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5C23×D312yes—
315C23×C5C23×D311yescharacteristic
316C5×Q8—28no—
317C2×C4×C5—22no—
318C2×C4×C5—24no—
319C2×C4×C5—24no—
320C2×C4×C5—28no—
321C2×C4×C5#23714yes—
322C2×C4×C5C23×D314yes—
323C2×C4×C5C23×D314yes—
324C2×C4×C5C23×D312yes—
325C2×C4×C5C23×D312yes—
326C2×Dic5—32no—
327C2×Dic5—32no—
328C2×Dic5—32no—
329C2×Dic5—34no—
330C2×Dic5—34no—
331C2×Dic5—32no—
332C2×Dic5—64no—
333C2×Dic5—62no—
334C2×Dic5—64no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—62no—
338Dic10—68no—
339C22×Q8—151no—
340C22×Q8C2×D1511yescharacteristic
341C23×C4C2×D1511yescharacteristic
342C4⋊Q8—158no—
343#126—1516no—
344#126—1516no—
345#125—1516no—
346#125—158no—
347#125—1516no—
348C22⋊Q8—158no—
349C22⋊Q8C2×D1518yes—
350C4×Q8—158no—
351C4×Q8—158no—
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⋊C4C2×D1512yes—
369C2×C42—151no—
370C2×C42—151no—
371C2×C42—152no—
372C2×C42—152no—
373C2×C3×C5—42no—
374C2×C3×C5#54114yescomplemented
375C2×C3×C5C22×#4111yescharacteristic
376C2×C3×C5C2×2−1+411yescharacteristic
377C2×C3×C5C2×2−1+411yescharacteristic
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3C23×D512yes—
382C23×C3C23×D511yescharacteristic
383C3×Q8—28no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—28no—
388C2×C3×C4#71114yes—
389C2×C3×C4C23×D514yes—
390C2×C3×C4C23×D514yes—
391C2×C3×C4C23×D512yes—
392C2×C3×C4C23×D512yes—
393C2×Dic3—52no—
394C2×Dic3—52no—
395C2×Dic3—52no—
396C2×Dic3—54no—
397C2×Dic3—54no—
398C2×Dic3—52no—
399C2×Dic3—104no—
400C2×Dic3—102no—
401C2×Dic3—104no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405Dic6—108no—
406C22×C5—22no—
407C22×C5—22no—
408C22×C5—22no—
409C22×C5—44no—
410C22×C5C2×#23712yes—
411C22×C5#100712yes—
412C22×C5#101012yes—
413C22×C5C24×D311yescharacteristic
414C4×C5—22no—
415C4×C5—24no—
416C4×C5—24no—
417C4×C5C2×#23714yes—
418Dic5—64no—
419Dic5—62no—
420Dic5—64no—
421Dic5—62no—
422Dic5—62no—
423Dic5—62no—
424C24C22×D1511yescharacteristic
425C2×Q8—24no—
426C2×Q8—154no—
427C2×Q8—304no—
428C2×Q8C22×D1514yes—
429C22×C4—24no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—152no—
434C22×C4—151no—
435C22×C4—152no—
436C22×C4C22×D1514yes—
437C22×C4C22×D1512yes—
438C22×C4C22×D1512yes—
439C22×C4C22×D1511yescharacteristic
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⋊C4C22×D1518yes—
457C42—154no—
458C42—154no—
459C42—158no—
460C42—158no—
461C3×C5C2×#54111yescharacteristic, complemented, Hall
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—44no—
466C22×C3C2×#71112yes—
467C22×C3#414712yes—
468C22×C3#415012yes—
469C22×C3C24×D511yescharacteristic
470C3×C4—22no—
471C3×C4—24no—
472C3×C4—24no—
473C3×C4C2×#71114yes—
474Dic3—104no—
475Dic3—102no—
476Dic3—104no—
477Dic3—102no—
478Dic3—102no—
479Dic3—102no—
480C2×C5—42no—
481C2×C5#562514yescomplemented
482C2×C5C22×#23711yescharacteristic
483C2×C5C2×#100711yescharacteristic
484C2×C5C2×#101011yescharacteristic
485C23—22no—
486C23—22no—
487C23—22no—
488C23C23×D1512yes—
489C23C23×D1511yescharacteristic
490Q8—28no—
491Q8—308no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—28no—
496C2×C4—152no—
497C2×C4—152no—
498C2×C4—152no—
499C2×C4—154no—
500C2×C4—152no—
501C2×C4—154no—
502C2×C4—304no—
503C2×C4—302no—
504C2×C4—302no—
505C2×C4—304no—
506C2×C4—302no—
507C2×C4—302no—
508C2×C4#681914yes—
509C2×C4C23×D1514yes—
510C2×C4C23×D1514yes—
511C2×C4C23×D1512yes—
512C2×C4C23×D1512yes—
513C2×C3—42no—
514C2×C3#6595914yescomplemented
515C2×C3C22×#71111yescharacteristic
516C2×C3C2×#414711yescharacteristic
517C2×C3C2×#415011yescharacteristic
518C5C2×#562511yescharacteristic, complemented, Sylow
519C22—22no—
520C22—22no—
521C22—22no—
522C22—44no—
523C22C2×#681912yes—
524C22#9209812yes—
525C22#9210112yes—
526C22C24×D1511yescharacteristic
527C4—22no—
528C4—24no—
529C4—24no—
530C4—304no—
531C4—302no—
532C4—302no—
533C4—304no—
534C4—302no—
535C4—302no—
536C4C2×#681914yes—
537C3C2×#6595911yescharacteristic, complemented, Sylow
538C2—42no—
539C2#1175638414yesdirect product factor
540C2C22×#681911yescharacteristic
541C2C2×#9209811yescharacteristic
542C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊Q8D15
hypocenterC3×C5C2×#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
3. C2×#91833C2semidirect
6. #11756384C2direct (N × H)
7. C2×#91779C2semidirect
8. C2×#91779C2semidirect
9. C2×#91778C2semidirect
10. C2×#91776C2semidirect
24. Q8×Dic15C22semidirect
25. #91833C22semidirect
42. #91779C22semidirect
43. #91779C22semidirect
44. #91778C22semidirect
45. #91776C22semidirect
374. C2×C3×C5#541semidirect
461. C3×C5C2×#541semidirect
481. C2×C5#5625semidirect
514. C2×C3#65959semidirect
518. C5C2×#5625semidirect
537. C3C2×#65959semidirect
539. C2#11756384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊Q82
C2×Q8×Dic152
C2×#918332
C2×#918152
C2×#918132
#117563842
C2×#917792
C2×#917782
C2×#917762
C2×#917682
C2×#659593
C2×#56255