Finite Group Databasebeta

← C2×#11749061 #14423533

Subgroups — C2×#11749061 #14423533

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×C5×#214C211yesmaximal, characteristic, complemented
3C2×#91383C211yesmaximal, characteristic, complemented
4C22×#6663C211yesmaximal, characteristic, complemented
5C2×C3×#3964C211yesmaximal, characteristic, complemented
6#11749061C218yesmaximal, direct product factor
7C2×#90974C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic, complemented
9C2×#65462—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×#1220—21no—
12C23×Dic15—21no—
13C2×#6819—24no—
14C2×#6819—22no—
15C2×#6819—24no—
16C2×#6819C2214yes—
17C22×C4×D15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C2×C5×#214—24no—
21C2×C5×#214C2214yescomplemented
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25C2×#6668—21no—
26C2×#6667—21no—
27#91383—22no—
28#91383C2214yescomplemented
29C2×#6663—24no—
30C2×#6663C2214yescomplemented
31C3×#3964C2214yescomplemented
32#90974C2214yescomplemented
33#90957C2214yescomplemented
34C2×#4783—51nomaximal, Hall
35C22×#711—31no—
36C22×C5×SD16—31no—
37C2×#4092—31no—
38C22×#689—31no—
39C2×#3964D311yescharacteristic, complemented
40#65462—38no—
41C2×#3952—31no—
42C2×#3948—31no—
43C24×C3×C5—21no—
44C23×D15D411yescharacteristic
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4—22no—
47C2×C3×C5×D4D414yes—
48C2×C3×C5×D4C2312yes—
49C22×C3×C4×C5C2311yescharacteristic
50C2×#1220—28no—
51C2×#1220—24no—
52C22×Dic15—28no—
53C22×Dic15—21no—
54C22×Dic15—24no—
55C22×Dic15D411yescharacteristic
56#6819—216no—
57#6819—28no—
58#6819—28no—
59C2×C4×D15—22no—
60C2×C4×D15—22no—
61C2×C4×D15D412yes—
62C2×C4×D15C2312yes—
63C2×Dic30—21no—
64C2×Dic30—22no—
65C2×Dic30D414yes—
66C2×Dic30C2312yes—
67C22×C5×Dic3—21no—
68C2×C5×Dic6—22no—
69C2×C5×Dic6—22no—
70C2×C5×Dic6—21no—
71C2×C5×Dic6C2312yes—
72C22×C3×Dic5—21no—
73C5×#214—28no—
74C2×C5×C3⋊C8—22no—
75C2×C5×C3⋊C8C2312yes—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5C2312yes—
78C2×C3×#168—22no—
79C2×C3×#168C2312yes—
80#6668—24no—
81#6667—24no—
82#6663—28no—
83C22×#237—51no—
84C22×#214D511yescharacteristic, complemented
85C22×Dic12—51no—
86C2×#897—51no—
87C2×C3×#102—51no—
88C2×(C2×D3)⋊C8—51no—
89C2×#810—51no—
90#4783—58no—
91C22×C5×Q8—31no—
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—34no—
102C2×C5×SD16—64no—
103C22×C5×C8—31no—
104#4092—34no—
105#4092—62no—
106C2×#689—34no—
107C2×#689—64no—
108C2×#685—61no—
109C2×C4⋊Dic5C2×D311yescharacteristic
110C2×#683—61no—
111C22×#168C2×D311yescharacteristic
112#3964C2×D314yescomplemented
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×D4—24no—
126C3×C5×D4—22no—
127C3×C5×D4C2×D414yes—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2×D412yes—
131C2×C3×C4×C5C2411yescharacteristic
132#1220—216no—
133C2×Dic15—216no—
134C2×Dic15—24no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15C2×D412yes—
138C4×D15—24no—
139C4×D15—22no—
140C4×D15—22no—
141Dic30—24no—
142Dic30—22no—
143Dic30C2×D414yes—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—42no—
146C5×Dic6—22no—
147C5×Dic6—22no—
148C5×Dic6—42no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—42no—
151C3×#168—22no—
152C5×C3⋊C8—22no—
153C22×C3×D4C2×D511yescharacteristic
154C22×#67—101no—
155C23×Dic3—101no—
156C2×#237—54no—
157C2×#237—104no—
158C2×#237—102no—
159C2×#237—104no—
160C22×C4×D3—51no—
161C22×Dic6—51no—
162C22×Dic6C2×D511yescharacteristic
163C22×C3×C8—51no—
164C2×C3×C4⋊C4—51no—
165C2×#214—24no—
166C2×#214C2×D514yescomplemented
167C2×(C2×D3)⋊C4—101no—
168C2×C4⋊Dic3—101no—
169C22×C3⋊C8C2×D511yescharacteristic
170C2×Dic12—54no—
171C2×Dic12—104no—
172#897—54no—
173#897—102no—
174C3×#102—54no—
175(C2×D3)⋊C8—54no—
176#810—54no—
177C24×C5—21no—
178C23×D5—31no—
179C2×C5×Q8—32no—
180C2×C5×Q8—61no—
181C2×C5×Q8—62no—
182C2×C5×Q8—62no—
183C2×C5×D4—21no—
184C2×C5×D4—22no—
185C2×C5×D4D1214yes—
186C2×C5×D4C22×D312yes—
187C22×C4×C5—61no—
188C22×C4×C5C22×D311yescharacteristic
189C2×C22⋊D5—64no—
190C2×C22⋊D5—68no—
191C22×Dic5—21no—
192C22×Dic5—31no—
193C22×Dic5—64no—
194C22×Dic5—68no—
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—62no—
206C2×Dic10—61no—
207C5×SD16—68no—
208C2×C5×C8—32no—
209C2×C5×C8—62no—
210#689—68no—
211#685—64no—
212C4⋊Dic5—21no—
213C4⋊Dic5C22×D312yes—
214#683—64no—
215C2×#168—22no—
216C2×#168C22×D312yes—
217C22×#41—151no—
218C22×Q16—151no—
219C22×SD16—31no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—151no—
223C2×#102—51no—
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#12012yes—
238C3×C4×C5C22×D411yescharacteristic
239C3×C4×C5C22×D411yescharacteristic
240Dic15—24no—
241Dic15—22no—
242C3×Dic5—42no—
243C5×Dic3—42no—
244C24×C3—21no—
245C23×D3—51no—
246C2×C3×D4—22no—
247C2×C3×D4—21no—
248C2×C3×D4C22⋊D514yes—
249C2×C3×D4C22×D512yes—
250C22×C3×C4—101no—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—104no—
253C2×#67—108no—
254C22×Dic3—21no—
255C22×Dic3—51no—
256C22×Dic3—104no—
257C22×Dic3—108no—
258C22×Dic3—101no—
259#237—108no—
260#237—1016no—
261#237—108no—
262C2×C4×D3—52no—
263C2×C4×D3—52no—
264C2×C4×D3—102no—
265C2×C4×D3—102no—
266C2×Dic6—22no—
267C2×Dic6—22no—
268C2×Dic6—21no—
269C2×Dic6—54no—
270C2×Dic6—52no—
271C2×Dic6—101no—
272C2×Dic6—102no—
273C2×Dic6C22×D512yes—
274C2×C3×C8—52no—
275C2×C3×C8—102no—
276C3×C4⋊C4—52no—
277C3×C4⋊C4—101no—
278#214—28no—
279(C2×D3)⋊C4—104no—
280C4⋊Dic3—104no—
281C2×C3⋊C8—22no—
282C2×C3⋊C8C22×D512yes—
283Dic12—108no—
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—62no—
294C5×Q8—62no—
295C5×Q8—122no—
296C5×D4—24no—
297C5×D4—22no—
298C5×D4C2×D1214yes—
299C2×C4×C5—62no—
300C2×C4×C5—122no—
301C2×C4×C5C2×D1212yes—
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5D3×D412yes—
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—616no—
306C2×Dic5—22no—
307C2×Dic5—32no—
308C2×Dic5—42no—
309C2×Dic5—616no—
310C2×Dic5—64no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C4×D5—64no—
314C4×D5—62no—
315C4×D5—62no—
316Dic10—34no—
317Dic10—64no—
318Dic10—62no—
319C5×C8—62no—
320#168—22no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8—31no—
326C22×Q8—151no—
327C22×D4—301no—
328C22×D4D3×D511yescharacteristic
329C23×C4—151no—
330C23×C4—301no—
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—34no—
334C2×SD16—64no—
335C22×C8—31no—
336C22×C8—51no—
337C22⋊Q8—154no—
338C22⋊Q8—302no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—301no—
341C2×C22⋊C4—301no—
342#103—154no—
343#102—54no—
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×D4—22no—
361C3×D4—24no—
362C3×D4C2×C22⋊D514yes—
363C2×C3×C4—102no—
364C2×C3×C4—202no—
365C2×C3×C4D4×D512yes—
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4C2×C22⋊D512yes—
368C2×C3×C4C23×D511yescharacteristic
369#67—1016no—
370C2×Dic3—22no—
371C2×Dic3—42no—
372C2×Dic3—52no—
373C2×Dic3—1016no—
374C2×Dic3—102no—
375C2×Dic3—104no—
376C2×Dic3—102no—
377C4×D3—102no—
378C4×D3—102no—
379C4×D3—104no—
380Dic6—22no—
381Dic6—22no—
382Dic6—42no—
383Dic6—54no—
384Dic6—102no—
385Dic6—104no—
386C3×C8—102no—
387C3⋊C8—22no—
388C22×C5—24no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—48no—
392C22×C5#88212yes—
393C22×C5#91212yes—
394C22×C5#91512yes—
395C22×C5C2×D3×D411yescharacteristic
396C2×D5—62no—
397C2×D5—62no—
398C2×D5—62no—
399C2×D5—124no—
400C4×C5—122no—
401C4×C5#88212yes—
402C4×C5C22×D1211yescharacteristic
403C4×C5C2×D3×D411yescharacteristic
404Dic5—42no—
405Dic5—64no—
406Dic5—62no—
407C24—21no—
408C24—151no—
409#41—308no—
410#41—3016no—
411#41—308no—
412C2×Q8—32no—
413C2×Q8—61no—
414C2×Q8—62no—
415C2×Q8—62no—
416C2×Q8—154no—
417C2×Q8—152no—
418C2×Q8—302no—
419C2×Q8—301no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—304no—
423C2×D4—308no—
424C2×D4#120314yes—
425C2×D4C2×D3×D512yes—
426C22×C4—61no—
427C22×C4—101no—
428C22×C4—151no—
429C22×C4—152no—
430C22×C4—152no—
431C22×C4—304no—
432C22×C4—308no—
433C22×C4—301no—
434C22×C4—302no—
435C22×C4—302no—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—68no—
439C2×C8—32no—
440C2×C8—52no—
441C2×C8—62no—
442C2×C8—102no—
443C4⋊C4—52no—
444C4⋊C4—101no—
445C4⋊C4—304no—
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—202no—
461C3×C4#408312yes—
462C3×C4C2×D4×D511yescharacteristic
463C3×C4C22×C22⋊D511yescharacteristic
464Dic3—42no—
465Dic3—104no—
466Dic3—102no—
467C2×C5—44no—
468C2×C5#478314yescomplemented
469C2×C5C2×#88211yescharacteristic
470C2×C5C2×#91211yescharacteristic
471C2×C5C2×#91511yescharacteristic
472D5—122no—
473C23—22no—
474C23—24no—
475C23—42no—
476C23—42no—
477C23—152no—
478C23—302no—
479C23—302no—
480C23—302no—
481C23#679011yescharacteristic
482Q8—62no—
483Q8—62no—
484Q8—122no—
485Q8—154no—
486Q8—302no—
487Q8—304no—
488D4—22no—
489D4—24no—
490D4—3016no—
491D4C2×#120314yes—
492C2×C4—62no—
493C2×C4—102no—
494C2×C4—122no—
495C2×C4—152no—
496C2×C4—202no—
497C2×C4—3016no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—304no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—304no—
504C2×C4C2×#120312yes—
505C2×C4#679012yes—
506C2×C4#679011yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—62no—
509C8—102no—
510C2×C3—44no—
511C2×C3#6546214yescomplemented
512C2×C3C2×#406111yescharacteristic
513C2×C3C2×#406211yescharacteristic
514C2×C3C2×#408311yescharacteristic
515D3—202no—
516C5C2×#478311yescharacteristic, complemented, Sylow
517C22—24no—
518C22—48no—
519C22—42no—
520C22—42no—
521C22—302no—
522C22—302no—
523C22—302no—
524C22—604no—
525C22#9148812yes—
526C22#9149712yes—
527C22#9157312yes—
528C22C2×#679011yescharacteristic
529C4—122no—
530C4—202no—
531C4—302no—
532C4—304no—
533C4#9157312yes—
534C4C22×#120311yescharacteristic
535C4C2×#679011yescharacteristic
536C3C2×#6546211yescharacteristic, complemented, Sylow
537C2—44no—
538C2—602no—
539C2#1174906114yesdirect product factor
540C2C2×#9148811yescharacteristic
541C2C2×#9149711yescharacteristic
542C2C2×#9157311yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6819C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C5×#214C2semidirect
3. C2×#91383C2semidirect
4. C22×#6663C2semidirect
5. C2×C3×#3964C2semidirect
6. #11749061C2direct (N × H)
7. C2×#90974C2semidirect
8. C2×#90957C2semidirect
21. C2×C5×#214C22semidirect
28. #91383C22semidirect
30. C2×#6663C22semidirect
31. C3×#3964C22semidirect
32. #90974C22semidirect
33. #90957C22semidirect
39. C2×#3964D3semidirect
84. C22×#214D5semidirect
112. #3964C2×D3semidirect
166. C2×#214C2×D5semidirect
346. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
468. C2×C5#4783semidirect
511. C2×C3#65462semidirect
516. C5C2×#4783semidirect
536. C3C2×#65462semidirect
539. C2#11749061direct (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×C5×#2142
C2×#913832
C22×#66632
C2×C3×#39642
#117490612
C2×#909742
C2×#909572
C2×#654623
C2×#47835