Finite Group Databasebeta

← C2×#11751274 #14423492

Subgroups — C2×#11751274 #14423492

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×#6819C211yesmaximal, characteristic
2C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
3C2×#91835C211yesmaximal, characteristic, complemented
4C22×#6718C211yesmaximal, characteristic, complemented
5C2×#91116C211yesmaximal, characteristic, complemented
6#11751274C218yesmaximal, direct product factor
7C2×#91104C211yesmaximal, characteristic, complemented
8C2×#91100C211yesmaximal, characteristic, complemented
9C2×#65462—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×#1220—21no—
13C23×Dic15—21no—
14C2×#6819—24no—
15C2×#6819—22no—
16C2×#6819—24no—
17C2×#6819C2214yes—
18C22×C4×D15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C2×C3×C5×SD16—24no—
21C2×C3×C5×SD16C2214yescomplemented
22C22×C3×C5×C8C2211yescharacteristic
23#91835—22no—
24#91835C2214yescomplemented
25C2×#6718—24no—
26C2×#6718C2214yescomplemented
27C2×#6714—21no—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712—21no—
30C22×C3⋊#168C2211yescharacteristic
31#91116C2214yescomplemented
32#91104C2214yescomplemented
33#91100C2214yescomplemented
34C2×#5173—51nomaximal, Hall
35C22×#711—31no—
36C22×C5×SD16D311yescharacteristic, complemented
37C2×#4092—31no—
38C22×#689—31no—
39C2×#3964—31no—
40#65462—38no—
41C2×#3952—31no—
42C2×#3948—31no—
43C24×C3×C5—21no—
44C23×D15D411yescharacteristic
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—22no—
47C2×C3×C5×Q8—22no—
48C2×C3×C5×Q8C2312yes—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4D414yes—
52C2×C3×C5×D4C2312yes—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—28no—
56C2×#1220—24no—
57C22×Dic15—28no—
58C22×Dic15—21no—
59C22×Dic15—24no—
60C22×Dic15—21no—
61C22×Dic15D411yescharacteristic
62#6819—216no—
63#6819—28no—
64#6819—28no—
65C2×C4×D15—22no—
66C2×C4×D15—22no—
67C2×C4×D15D412yes—
68C2×C4×D15C2312yes—
69C2×Dic30—21no—
70C2×Dic30—22no—
71C2×Dic30D414yes—
72C2×Dic30C2312yes—
73C3×C5×SD16—28no—
74C2×C3×C5×C8—22no—
75C2×C3×C5×C8C2312yes—
76#6718—28no—
77#6714—24no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80#6712—24no—
81C2×C3⋊#168—22no—
82C2×C3⋊#168C2312yes—
83C22×#237—51no—
84C22×C3×SD16D511yescharacteristic, complemented
85C2×#946—51no—
86C22×#216—51no—
87C2×#832—51no—
88#5173—58no—
89C2×(C2×D3)⋊C8—51no—
90C2×#816—51no—
91C22×C5×Q8C2×D311yescharacteristic
92C22×C5×D4C2×D311yescharacteristic
93C22×C22⋊D5—61no—
94C23×Dic5—61no—
95C2×#711—34no—
96C2×#711—64no—
97C2×#711—62no—
98C2×#711—64no—
99C22×C4×D5—31no—
100C22×Dic10—31no—
101C2×C5×SD16—24no—
102C2×C5×SD16C2×D314yescomplemented
103C22×C5×C8C2×D311yescharacteristic
104#4092—34no—
105#4092—62no—
106C2×#689—34no—
107C2×#689—64no—
108C2×#685—61no—
109C2×C4⋊Dic5—31no—
110C2×#683—61no—
111C22×#168—31no—
112#3964—34no—
113#3952—34no—
114#3948—34no—
115C2×#452—151noSylow
116C23×C3×C5—24no—
117C23×C3×C5—22no—
118C23×C3×C5—42no—
119C23×C3×C5—42no—
120C23×C3×C5C2×D411yescharacteristic
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—22no—
124C22×D15C2×D412yes—
125C3×C5×Q8—22no—
126C3×C5×Q8—22no—
127C3×C5×Q8—42no—
128C3×C5×D4—24no—
129C3×C5×D4—22no—
130C3×C5×D4C2×D414yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2411yescharacteristic
137#1220—216no—
138C2×Dic15—216no—
139C2×Dic15—24no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—42no—
144C2×Dic15C2×D412yes—
145C4×D15—24no—
146C4×D15—22no—
147C4×D15—22no—
148Dic30—24no—
149Dic30—22no—
150Dic30C2×D414yes—
151C3×C5×C8—22no—
152C3⋊#168—22no—
153C22×C3×Q8C2×D511yescharacteristic
154C22×C3×D4C2×D511yescharacteristic
155C22×#67—101no—
156C23×Dic3—101no—
157C2×#237—54no—
158C2×#237—104no—
159C2×#237—102no—
160C2×#237—104no—
161C22×C4×D3—51no—
162C22×Dic6—51no—
163C2×C3×SD16—24no—
164C2×C3×SD16C2×D514yescomplemented
165C22×C3×C8C2×D511yescharacteristic
166#946—54no—
167#946—102no—
168C2×#216—54no—
169C2×#216—104no—
170C2×(C2×D3)⋊C4—101no—
171C2×C4⋊Dic3—51no—
172C2×Dic3⋊C4—101no—
173C22×C3⋊C8—51no—
174#832—54no—
175(C2×D3)⋊C8—54no—
176#816—54no—
177C24×C5—21no—
178C23×D5—31no—
179C2×C5×Q8—21no—
180C2×C5×Q8—22no—
181C2×C5×Q8—22no—
182C2×C5×Q8C22×D312yes—
183C2×C5×D4—21no—
184C2×C5×D4—22no—
185C2×C5×D4#6714yes—
186C2×C5×D4C22×D312yes—
187C22×C4×C5—21no—
188C22×C4×C5C22×D311yescharacteristic
189C2×C22⋊D5—64no—
190C2×C22⋊D5—68no—
191C22×Dic5—31no—
192C22×Dic5—64no—
193C22×Dic5—68no—
194C22×Dic5—61no—
195C22×Dic5—61no—
196#711—68no—
197#711—616no—
198#711—68no—
199C2×C4×D5—32no—
200C2×C4×D5—32no—
201C2×C4×D5—62no—
202C2×C4×D5—62no—
203C2×Dic10—34no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—62no—
207C5×SD16—28no—
208C2×C5×C8—22no—
209C2×C5×C8C22×D312yes—
210#689—68no—
211#685—64no—
212C4⋊Dic5—32no—
213C4⋊Dic5—61no—
214#683—64no—
215C2×#168—32no—
216C2×#168—62no—
217C22×#41—151no—
218C22×Q16—151no—
219C22×SD16D1511yescharacteristic, complemented
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—151no—
223C2×#102—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5—24no—
226C22×C3×C5—42no—
227C22×C3×C5—42no—
228C22×C3×C5—48no—
229C22×C3×C5#12012yes—
230C22×C3×C5#13512yes—
231C22×C3×C5#13712yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—22no—
235C2×D15—22no—
236C2×D15—44no—
237C3×C4×C5—42no—
238C3×C4×C5#12012yes—
239C3×C4×C5C22×D411yescharacteristic
240C3×C4×C5C22×D411yescharacteristic
241Dic15—24no—
242Dic15—22no—
243Dic15—42no—
244C24×C3—21no—
245C23×D3—51no—
246C2×C3×Q8—21no—
247C2×C3×Q8—22no—
248C2×C3×Q8—22no—
249C2×C3×Q8C22×D512yes—
250C2×C3×D4—22no—
251C2×C3×D4—21no—
252C2×C3×D4C22⋊D514yes—
253C2×C3×D4C22×D512yes—
254C22×C3×C4—21no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—104no—
257C2×#67—108no—
258C22×Dic3—51no—
259C22×Dic3—104no—
260C22×Dic3—108no—
261C22×Dic3—101no—
262C22×Dic3—101no—
263#237—108no—
264#237—1016no—
265#237—108no—
266C2×C4×D3—52no—
267C2×C4×D3—52no—
268C2×C4×D3—102no—
269C2×C4×D3—102no—
270C2×Dic6—54no—
271C2×Dic6—52no—
272C2×Dic6—101no—
273C2×Dic6—102no—
274C3×SD16—28no—
275C2×C3×C8—22no—
276C2×C3×C8C22×D512yes—
277#216—108no—
278(C2×D3)⋊C4—104no—
279C4⋊Dic3—52no—
280C4⋊Dic3—101no—
281Dic3⋊C4—104no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—102no—
284C23×C5—24no—
285C23×C5—22no—
286C23×C5—42no—
287C23×C5—42no—
288C23×C5D3×D411yescharacteristic
289C22×D5—32no—
290C22×D5—62no—
291C22×D5—62no—
292C22×D5—62no—
293C5×Q8—22no—
294C5×Q8—22no—
295C5×Q8—42no—
296C5×D4—24no—
297C5×D4—22no—
298C5×D4C2×#6714yes—
299C2×C4×C5—22no—
300C2×C4×C5—42no—
301C2×C4×C5D3×D411yescharacteristic
302C2×C4×C5D3×D412yes—
303C2×C4×C5C2×#6712yes—
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—616no—
306C2×Dic5—32no—
307C2×Dic5—616no—
308C2×Dic5—64no—
309C2×Dic5—62no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5—122no—
313C4×D5—64no—
314C4×D5—62no—
315C4×D5—62no—
316Dic10—34no—
317Dic10—64no—
318Dic10—62no—
319C5×C8—22no—
320#168—62no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8—151no—
326C22×Q8C2×D1511yescharacteristic
327C22×D4—301no—
328C22×D4C2×D1511yescharacteristic
329C23×C4—151no—
330C23×C4—301no—
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—24no—
334C2×SD16C2×D1514yescomplemented
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—44no—
346C2×C3×C5#45214yescomplemented
347C2×C3×C5C2×#12011yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350D15—42no—
351C23×C3—22no—
352C23×C3—24no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3D4×D511yescharacteristic
356C22×D3—52no—
357C22×D3—102no—
358C22×D3—102no—
359C22×D3—102no—
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—42no—
363C3×D4—22no—
364C3×D4—24no—
365C3×D4C2×C22⋊D514yes—
366C2×C3×C4—22no—
367C2×C3×C4—42no—
368C2×C3×C4D4×D512yes—
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4C2×C22⋊D512yes—
371C2×C3×C4C23×D511yescharacteristic
372#67—1016no—
373C2×Dic3—52no—
374C2×Dic3—1016no—
375C2×Dic3—102no—
376C2×Dic3—104no—
377C2×Dic3—102no—
378C2×Dic3—102no—
379C2×Dic3—202no—
380C4×D3—102no—
381C4×D3—102no—
382C4×D3—104no—
383Dic6—54no—
384Dic6—102no—
385Dic6—104no—
386C3×C8—22no—
387C3⋊C8—102no—
388C22×C5—24no—
389C22×C5—48no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5#91512yes—
393C22×C5#91612yes—
394C22×C5#93712yes—
395C22×C5C2×D3×D411yescharacteristic
396C2×D5—62no—
397C2×D5—62no—
398C2×D5—62no—
399C2×D5—124no—
400C4×C5—42no—
401C4×C5#93712yes—
402C4×C5C2×D3×D411yescharacteristic
403C4×C5C22×#6711yescharacteristic
404Dic5—64no—
405Dic5—62no—
406Dic5—122no—
407C24—21no—
408C24—151no—
409#41—308no—
410#41—3016no—
411#41—308no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—154no—
416C2×Q8—152no—
417C2×Q8—301no—
418C2×Q8—302no—
419C2×Q8C22×D1512yes—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—304no—
423C2×D4—308no—
424C2×D4#122014yes—
425C2×D4C22×D1512yes—
426C22×C4—21no—
427C22×C4—151no—
428C22×C4—152no—
429C22×C4—152no—
430C22×C4—304no—
431C22×C4—308no—
432C22×C4—301no—
433C22×C4—302no—
434C22×C4—302no—
435C22×C4—301no—
436C22×C4C22×D1511yescharacteristic
437Q16—308no—
438SD16—28no—
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—24no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—48no—
452C22×C3#406112yes—
453C22×C3#406212yes—
454C22×C3#408312yes—
455C22×C3C2×D4×D511yescharacteristic
456C2×D3—102no—
457C2×D3—102no—
458C2×D3—102no—
459C2×D3—204no—
460C3×C4—42no—
461C3×C4#408312yes—
462C3×C4C2×D4×D511yescharacteristic
463C3×C4C22×C22⋊D511yescharacteristic
464Dic3—104no—
465Dic3—102no—
466Dic3—202no—
467C2×C5—44no—
468C2×C5#517314yescomplemented
469C2×C5C2×#91511yescharacteristic
470C2×C5C2×#91611yescharacteristic
471C2×C5C2×#93711yescharacteristic
472D5—122no—
473C23—24no—
474C23—22no—
475C23—42no—
476C23—42no—
477C23—152no—
478C23—302no—
479C23—302no—
480C23—302no—
481C23D4×D1511yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—42no—
485Q8—154no—
486Q8—304no—
487Q8—302no—
488D4—24no—
489D4—22no—
490D4—3016no—
491D4C2×#122014yes—
492C2×C4—22no—
493C2×C4—42no—
494C2×C4—152no—
495C2×C4—3016no—
496C2×C4—302no—
497C2×C4—304no—
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—44no—
511C2×C3#6546214yescomplemented
512C2×C3C2×#406111yescharacteristic
513C2×C3C2×#406211yescharacteristic
514C2×C3C2×#408311yescharacteristic
515D3—202no—
516C5C2×#517311yescharacteristic, complemented, Sylow
517C22—24no—
518C22—48no—
519C22—42no—
520C22—42no—
521C22—302no—
522C22—302no—
523C22—302no—
524C22—604no—
525C22#9180412yes—
526C22#9180512yes—
527C22#9182612yes—
528C22C2×D4×D1511yescharacteristic
529C4—42no—
530C4—302no—
531C4—304no—
532C4—602no—
533C4#9182612yes—
534C4C2×D4×D1511yescharacteristic
535C4C22×#122011yescharacteristic
536C3C2×#6546211yescharacteristic, complemented, Sylow
537C2—44no—
538C2—602no—
539C2#1175127414yesdirect product factor
540C2C2×#9180411yescharacteristic
541C2C2×#9180511yescharacteristic
542C2C2×#9182611yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×SD16C2
socleC23×C3×C5C2×D4
prime radicalC22×#6819C2
hypercenterC22×SD16D15
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×SD16C2semidirect
3. C2×#91835C2semidirect
4. C22×#6718C2semidirect
5. C2×#91116C2semidirect
6. #11751274C2direct (N × H)
7. C2×#91104C2semidirect
8. C2×#91100C2semidirect
21. C2×C3×C5×SD16C22semidirect
24. #91835C22semidirect
26. C2×#6718C22semidirect
31. #91116C22semidirect
32. #91104C22semidirect
33. #91100C22semidirect
36. C22×C5×SD16D3semidirect
84. C22×C3×SD16D5semidirect
102. C2×C5×SD16C2×D3semidirect
164. C2×C3×SD16C2×D5semidirect
219. C22×SD16D15semidirect
334. C2×SD16C2×D15semidirect
346. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
468. C2×C5#5173semidirect
511. C2×C3#65462semidirect
516. C5C2×#5173semidirect
536. C3C2×#65462semidirect
539. C2#11751274direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68192
C22×C3×C5×SD162
C2×#918352
C22×#67182
C2×#911162
#117512742
C2×#911042
C2×#911002
C2×#654623
C2×#51735