Finite Group Databasebeta

← C2×#11748757 #14331515

Subgroups — C2×#11748757 #14331515

Order 1920.

2072 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1204C211yesmaximal, characteristic, complemented
2C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic
4C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic
5C2×#91115C211yesmaximal, characteristic, complemented
6C2×C3×#3963C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748757C218yesmaximal, direct product factor
9C2×#65236—31nomaximal, Hall
10C24×C5×D3C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1204—24no—
18C22×#1204—24no—
19C22×#1204—24no—
20C22×#1204C2214yescomplemented
21C2×C5×(C2×D3)⋊C4—24no—
22C2×C5×(C2×D3)⋊C4C2214yes—
23C2×(C2×D3)⋊Dic5—24no—
24C2×(C2×D3)⋊Dic5—24no—
25C2×(C2×D3)⋊Dic5C2214yes—
26C2×(C2×D3)⋊Dic5C2214yes—
27#91115C2214yescomplemented
28C3×#3963C2214yescomplemented
29#90994C2214yescomplemented
30C2×#4673—51nomaximal, Hall
31C23×Dic10—31no—
32C22×C5×C22⋊C4—31no—
33C22×C22⋊Dic5—31no—
34C22×C22⋊Dic5—31no—
35C2×#3963—31no—
36C2×#3963—31no—
37C2×#3963D311yescharacteristic, complemented
38#65236—38no—
39C24×C3×C5C2311yescharacteristic
40C23×C5×D3—22no—
41C23×C5×D3—22no—
42C23×C5×D3—22no—
43C23×C5×D3—22no—
44C23×C5×D3—22no—
45C23×C5×D3—22no—
46C23×C5×D3Q814yescomplemented
47C23×C5×D3C2312yes—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5C2312yes—
52C22×Dic15—22no—
53C22×Dic15—22no—
54C22×Dic15—22no—
55C22×Dic15—22no—
56C22×Dic15—22no—
57C22×Dic15D414yes—
58C22×Dic15C2312yes—
59C22×Dic15C2312yes—
60C22×C5×Dic3—22no—
61C22×C5×Dic3—22no—
62C22×C5×Dic3D414yes—
63C22×C5×Dic3C2312yes—
64C22×C3×Dic5—22no—
65C22×C3×Dic5—22no—
66C22×C3×Dic5—22no—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5D414yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2312yes—
72C2×#1204—232no—
73C2×#1204—28no—
74C2×#1204—28no—
75C2×#1204—28no—
76C5×(C2×D3)⋊C4—28no—
77(C2×D3)⋊Dic5—28no—
78(C2×D3)⋊Dic5—28no—
79C23×Dic6—51no—
80C22×(C2×D3)⋊C4—51no—
81C22×(C2×D3)⋊C4—51no—
82C22×(C2×D3)⋊C4D511yescharacteristic
83C2×C3×#95—51no—
84C2×C3⋊#95—51no—
85C2×C3⋊#95—51no—
86#4673—58no—
87C25×C5—31no—
88C23×C4×C5—31no—
89C23×C4×C5C2×D311yescharacteristic
90C23×Dic5—31no—
91C23×Dic5—31no—
92C23×Dic5C2×D311yescharacteristic
93C23×Dic5C2×D311yescharacteristic
94C22×Dic10—34no—
95C22×Dic10—64no—
96C22×Dic10—64no—
97C22×Dic10—64no—
98C2×C5×C22⋊C4—34no—
99C2×C5×C22⋊C4—64no—
100C2×C22⋊Dic5—34no—
101C2×C22⋊Dic5—34no—
102C2×C22⋊Dic5—64no—
103C2×C22⋊Dic5—64no—
104#3963—34no—
105#3963—34no—
106#3963C2×D314yescomplemented
107C2×#393—151noSylow
108C23×C3×C5C2×D412yes—
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2×D412yes—
111C23×C3×C5C2×Q812yes—
112C23×C3×C5#4112yes—
113C23×C3×C5#4112yes—
114C23×C3×C5#4112yes—
115C23×C3×C5C2411yescharacteristic
116C22×C5×D3—28no—
117C22×C5×D3—28no—
118C22×C5×D3—28no—
119C22×C5×D3—22no—
120C22×C5×D3—22no—
121C22×C5×D3—22no—
122C22×C5×D3—22no—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3—44no—
126C22×C5×D3—44no—
127C22×C5×D3—44no—
128C22×C5×D3—44no—
129C22×C5×D3C2×Q814yescomplemented
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—44no—
134C2×Dic15—28no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—44no—
141C2×Dic15C2×D414yes—
142C2×C5×Dic3—28no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3C2×D414yes—
146C2×C3×Dic5—28no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—44no—
153C2×C3×Dic5C2×D414yes—
154#1204—232no—
155C24×D3C2×D511yescharacteristic
156C23×C3×C4—51no—
157C23×C3×C4—51no—
158C23×C3×C4C2×D511yescharacteristic
159C23×Dic3—51no—
160C23×Dic3—51no—
161C23×Dic3C2×D511yescharacteristic
162C22×Dic6—54no—
163C22×Dic6—104no—
164C22×Dic6—104no—
165C22×Dic6—104no—
166C2×(C2×D3)⋊C4—24no—
167C2×(C2×D3)⋊C4—54no—
168C2×(C2×D3)⋊C4—54no—
169C2×(C2×D3)⋊C4—104no—
170C2×(C2×D3)⋊C4—104no—
171C2×(C2×D3)⋊C4C2×D514yes—
172C3×#95—54no—
173C3⋊#95—54no—
174C3⋊#95—54no—
175C24×C5—34no—
176C24×C5—32no—
177C24×C5—62no—
178C24×C5—62no—
179C24×C5—62no—
180C24×C5—62no—
181C24×C5—62no—
182C24×C5—62no—
183C24×C5C22×D311yescharacteristic
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—34no—
188C22×C4×C5—32no—
189C22×C4×C5—62no—
190C22×C4×C5—62no—
191C22×C4×C5C22×D312yes—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—34no—
198C22×Dic5—32no—
199C22×Dic5—32no—
200C22×Dic5—62no—
201C22×Dic5—62no—
202C22×Dic5—62no—
203C22×Dic5—62no—
204C22×Dic5—62no—
205C22×Dic5D1214yes—
206C22×Dic5C22×D312yes—
207C22×Dic5C22×D312yes—
208C2×Dic10—68no—
209C2×Dic10—68no—
210C2×Dic10—632no—
211C2×Dic10—68no—
212C5×C22⋊C4—68no—
213C22⋊Dic5—68no—
214C22⋊Dic5—68no—
215C23×Q8—151no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—151no—
218C22×C22⋊C4—151no—
219#393—158no—
220C2×#95—51no—
221C2×#95—151no—
222C2×#95—151no—
223C22×C3×C5#12014yes—
224C22×C3×C5C22⋊Q814yes—
225C22×C3×C5C22⋊Q814yes—
226C22×C3×C5C22⋊Q814yes—
227C22×C3×C5#12414yes—
228C22×C3×C5#12414yes—
229C22×C3×C5#12414yes—
230C22×C3×C5C22×D411yescharacteristic
231C22×C3×C5C22×D411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5C22×Q811yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C2×C5×D3—24no—
238C2×C5×D3—24no—
239C2×C5×D3—24no—
240C2×C5×D3—42no—
241C2×C5×D3—42no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C2×C5×D3—416no—
245C3×C4×C5—42no—
246Dic15—24no—
247Dic15—42no—
248C3×Dic5—24no—
249C3×Dic5—42no—
250C5×Dic3—24no—
251C24×C3C22×D511yescharacteristic
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3Dic1014yescomplemented
259C23×D3C22×D512yes—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—54no—
264C22×C3×C4—52no—
265C22×C3×C4—52no—
266C22×C3×C4—102no—
267C22×C3×C4—102no—
268C22×C3×C4—102no—
269C22×C3×C4—102no—
270C22×C3×C4—102no—
271C22×C3×C4C22×D512yes—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—54no—
275C22×Dic3—52no—
276C22×Dic3—52no—
277C22×Dic3—102no—
278C22×Dic3—102no—
279C22×Dic3—102no—
280C22×Dic3—102no—
281C22×Dic3—102no—
282C22×Dic3C22⋊D514yes—
283C22×Dic3C22×D512yes—
284C2×Dic6—108no—
285C2×Dic6—108no—
286C2×Dic6—1032no—
287C2×Dic6—108no—
288(C2×D3)⋊C4—28no—
289(C2×D3)⋊C4—108no—
290(C2×D3)⋊C4—108no—
291C23×C5—34no—
292C23×C5—68no—
293C23×C5—68no—
294C23×C5—68no—
295C23×C5—62no—
296C23×C5—62no—
297C23×C5—62no—
298C23×C5—62no—
299C23×C5—62no—
300C23×C5—62no—
301C23×C5—124no—
302C23×C5—124no—
303C23×C5—124no—
304C23×C5—124no—
305C23×C5C2×D1212yes—
306C23×C5#23512yes—
307C23×C5#23512yes—
308C23×C5D3×D412yes—
309C23×C5D3×D412yes—
310C23×C5#23712yes—
311C23×C5D3×Q812yes—
312C23×C5C23×D311yescharacteristic
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—34no—
317C2×C4×C5—44no—
318C2×C4×C5—68no—
319C2×C4×C5—62no—
320C2×C4×C5—62no—
321C2×Dic5—28no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—34no—
328C2×Dic5—44no—
329C2×Dic5—68no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—124no—
336C2×Dic5C2×D1214yes—
337Dic10—632no—
338C25—31no—
339C22×Q8—154no—
340C22×Q8—304no—
341C22×Q8—304no—
342C22×Q8—304no—
343C23×C4—31no—
344C23×C4—51no—
345C23×C4—51no—
346C23×C4—151no—
347C23×C4—151no—
348C23×C4D3×D511yescharacteristic
349C2×C22⋊C4—34no—
350C2×C22⋊C4—64no—
351C2×C22⋊C4—154no—
352C2×C22⋊C4—154no—
353C2×C22⋊C4—304no—
354C2×C22⋊C4—304no—
355#95—54no—
356#95—154no—
357#95—154no—
358C2×C3×C5#39318yescomplemented
359C2×C3×C5C2×#12011yescharacteristic
360C2×C3×C5C2×C22⋊Q811yescharacteristic
361C2×C3×C5C2×C22⋊Q811yescharacteristic
362C2×C3×C5C2×C22⋊Q811yescharacteristic
363C2×C3×C5C2×#12411yescharacteristic
364C2×C3×C5C2×#12411yescharacteristic
365C2×C3×C5C2×#12411yescharacteristic
366C5×D3—44no—
367C23×C3C2×Dic1012yes—
368C23×C3#70912yes—
369C23×C3D4×D512yes—
370C23×C3D4×D512yes—
371C23×C3#71112yes—
372C23×C3#71112yes—
373C23×C3C2×C22⋊D512yes—
374C23×C3C23×D511yescharacteristic
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—28no—
382C22×D3—28no—
383C22×D3—28no—
384C22×D3—44no—
385C22×D3—44no—
386C22×D3—44no—
387C22×D3—44no—
388C22×D3C2×Dic1014yescomplemented
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—44no—
393C2×C3×C4—54no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4—108no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—204no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—28no—
404C2×Dic3—54no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—108no—
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3—102no—
411C2×Dic3—204no—
412C2×Dic3C2×C22⋊D514yes—
413Dic6—1032no—
414C22×C5—64no—
415C22×C5—64no—
416C22×C5—64no—
417C22×C5—1216no—
418C22×C5—122no—
419C22×C5—122no—
420C22×C5—122no—
421C22×C5—122no—
422C22×C5#87514yes—
423C22×C5#88214yes—
424C22×C5#88514yes—
425C22×C5#88514yes—
426C22×C5#89614yes—
427C22×C5#89614yes—
428C22×C5#89714yes—
429C22×C5C22×D1211yescharacteristic
430C22×C5C2×#23511yescharacteristic
431C22×C5C2×#23511yescharacteristic
432C22×C5C2×D3×D411yescharacteristic
433C22×C5C2×D3×D411yescharacteristic
434C22×C5C2×#23711yescharacteristic
435C22×C5C2×D3×Q811yescharacteristic
436C4×C5—42no—
437C4×C5—64no—
438Dic5—24no—
439Dic5—42no—
440Dic5—64no—
441Dic5—122no—
442C24—34no—
443C24—32no—
444C24—62no—
445C24—62no—
446C24—62no—
447C24—62no—
448C24—62no—
449C24—62no—
450C24C2×D3×D511yescharacteristic
451C2×Q8—308no—
452C2×Q8—308no—
453C2×Q8—308no—
454C2×Q8—3032no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—34no—
459C22×C4—32no—
460C22×C4—54no—
461C22×C4—52no—
462C22×C4—52no—
463C22×C4—62no—
464C22×C4—62no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—154no—
471C22×C4—152no—
472C22×C4—152no—
473C22×C4—302no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—302no—
477C22×C4—302no—
478C22×C4C2×D3×D512yes—
479C22⋊C4—68no—
480C22⋊C4—308no—
481C22⋊C4—308no—
482C3×C5C2×#39311yescharacteristic, complemented, Hall
483C22×C3#402414yes—
484C22×C3#402414yes—
485C22×C3#403114yes—
486C22×C3#403114yes—
487C22×C3#407014yes—
488C22×C3#408214yes—
489C22×C3#408314yes—
490C22×C3C22×Dic1011yescharacteristic
491C22×C3C2×#70911yescharacteristic
492C22×C3C2×D4×D511yescharacteristic
493C22×C3C2×D4×D511yescharacteristic
494C22×C3C2×#71111yescharacteristic
495C22×C3C2×#71111yescharacteristic
496C22×C3C22×C22⋊D511yescharacteristic
497C2×D3—24no—
498C2×D3—24no—
499C2×D3—24no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—42no—
503C2×D3—42no—
504C2×D3—416no—
505C3×C4—42no—
506C3×C4—104no—
507C3×C4—202no—
508Dic3—24no—
509Dic3—104no—
510Dic3—202no—
511C2×C5—124no—
512C2×C5#467318yescomplemented
513C2×C5C2×#87511yescharacteristic
514C2×C5C2×#88211yescharacteristic
515C2×C5C2×#88511yescharacteristic
516C2×C5C2×#88511yescharacteristic
517C2×C5C2×#89611yescharacteristic
518C2×C5C2×#89611yescharacteristic
519C2×C5C2×#89711yescharacteristic
520C23—34no—
521C23—68no—
522C23—68no—
523C23—62no—
524C23—62no—
525C23—62no—
526C23—62no—
527C23—62no—
528C23—62no—
529C23—68no—
530C23—124no—
531C23—124no—
532C23—124no—
533C23—124no—
534C23D3×Dic1012yes—
535C23#677112yes—
536C23D5×D1212yes—
537C23#677712yes—
538C23#678012yes—
539C23#678212yes—
540C23D3×C22⋊D512yes—
541C23C22×D3×D511yescharacteristic
542Q8—3032no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—34no—
547C2×C4—44no—
548C2×C4—54no—
549C2×C4—68no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—108no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—154no—
559C2×C4—204no—
560C2×C4—308no—
561C2×C4—302no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4—302no—
566C2×C4—604no—
567C2×C3#6523618yescomplemented
568C2×C3C2×#402411yescharacteristic
569C2×C3C2×#402411yescharacteristic
570C2×C3C2×#403111yescharacteristic
571C2×C3C2×#403111yescharacteristic
572C2×C3C2×#407011yescharacteristic
573C2×C3C2×#408211yescharacteristic
574C2×C3C2×#408311yescharacteristic
575D3—44no—
576C5C2×#467311yescharacteristic, complemented, Sylow
577C22—64no—
578C22—64no—
579C22—64no—
580C22—122no—
581C22—122no—
582C22—122no—
583C22—1216no—
584C22—122no—
585C22#9135014yes—
586C22#9135214yes—
587C22#9141714yes—
588C22#9143614yes—
589C22#9146414yes—
590C22#9147514yes—
591C22#9152514yes—
592C22C2×D3×Dic1011yescharacteristic
593C22C2×#677111yescharacteristic
594C22C2×D5×D1211yescharacteristic
595C22C2×#677711yescharacteristic
596C22C2×#678011yescharacteristic
597C22C2×#678211yescharacteristic
598C22C2×D3×C22⋊D511yescharacteristic
599C4—42no—
600C4—64no—
601C4—104no—
602C4—202no—
603C4—304no—
604C4—602no—
605C3C2×#6523611yescharacteristic, complemented, Sylow
606C2—124no—
607C2#1174875718yesdirect product factor
608C2C2×#9135011yescharacteristic
609C2C2×#9135211yescharacteristic
610C2C2×#9141711yescharacteristic
611C2C2×#9143611yescharacteristic
612C2C2×#9146411yescharacteristic
613C2C2×#9147511yescharacteristic
614C2C2×#9152511yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC24×C5×D3C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#393
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×#1204C2semidirect
5. C2×#91115C2semidirect
6. C2×C3×#3963C2semidirect
7. C2×#90994C2semidirect
8. #11748757C2direct (N × H)
20. C22×#1204C22semidirect
27. #91115C22semidirect
28. C3×#3963C22semidirect
29. #90994C22semidirect
37. C2×#3963D3semidirect
46. C23×C5×D3Q8semidirect
106. #3963C2×D3semidirect
129. C22×C5×D3C2×Q8semidirect
258. C23×D3Dic10semidirect
358. C2×C3×C5#393semidirect
388. C22×D3C2×Dic10semidirect
482. C3×C5C2×#393semidirect
512. C2×C5#4673semidirect
567. C2×C3#65236semidirect
576. C5C2×#4673semidirect
605. C3C2×#65236semidirect
607. C2#11748757direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12042
C22×C5×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic52
C2×#911152
C2×C3×#39632
C2×#909942
#117487572
C2×#652363
C2×#46735