Finite Group Databasebeta

← C2×#11748736 #14331513

Subgroups — C2×#11748736 #14331513

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×C3×#685C211yesmaximal, characteristic
3C22×#6665C211yesmaximal, characteristic
4C22×#6665C211yesmaximal, characteristic
5C2×#91115C211yesmaximal, characteristic, complemented
6C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748736C218yesmaximal, direct product factor
9C2×#64962—31nomaximal, Hall
10C24×C3×D5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1204—24no—
18C22×#1204—24no—
19C22×#1204—24no—
20C22×#1204C2214yescomplemented
21C2×C3×#685—24no—
22C2×C3×#685C2214yes—
23C2×#6665—24no—
24C2×#6665—24no—
25C2×#6665C2214yes—
26C2×#6665C2214yes—
27#91115C2214yescomplemented
28C5×C3⋊#95C2214yescomplemented
29#90994C2214yescomplemented
30C2×#4947—51nomaximal, Hall
31C23×Dic10—31no—
32C22×#685—31no—
33C22×#685—31no—
34C22×#685D311yescharacteristic
35C2×C5×#95—31no—
36C2×#3963—31no—
37C2×#3963—31no—
38#64962—38no—
39C24×C3×C5C2311yescharacteristic
40C23×C3×D5—22no—
41C23×C3×D5—22no—
42C23×C3×D5—22no—
43C23×C3×D5—22no—
44C23×C3×D5—22no—
45C23×C3×D5—22no—
46C23×C3×D5Q814yescomplemented
47C23×C3×D5C2312yes—
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×Dic3—22no—
63C22×C5×Dic3—22no—
64C22×C5×Dic3—22no—
65C22×C5×Dic3D414yes—
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2312yes—
68C22×C3×Dic5—22no—
69C22×C3×Dic5—22no—
70C22×C3×Dic5D414yes—
71C22×C3×Dic5C2312yes—
72C2×#1204—232no—
73C2×#1204—28no—
74C2×#1204—28no—
75C2×#1204—28no—
76C3×#685—28no—
77#6665—28no—
78#6665—28no—
79C23×Dic6—51no—
80C22×C3×C22⋊C4—51no—
81C22×#217—51no—
82C22×#217—51no—
83C2×C3⋊#95—51no—
84C2×C3⋊#95—51no—
85C2×C3⋊#95D511yescharacteristic, complemented
86#4947—58no—
87C24×D5C2×D311yescharacteristic
88C23×C4×C5—31no—
89C23×C4×C5—31no—
90C23×C4×C5C2×D311yescharacteristic
91C23×Dic5—31no—
92C23×Dic5—31no—
93C23×Dic5C2×D311yescharacteristic
94C22×Dic10—34no—
95C22×Dic10—64no—
96C22×Dic10—64no—
97C22×Dic10—64no—
98C2×#685—24no—
99C2×#685—34no—
100C2×#685—34no—
101C2×#685—64no—
102C2×#685—64no—
103C2×#685C2×D314yes—
104C5×#95—34no—
105#3963—34no—
106#3963—34no—
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×C3×D5—28no—
117C22×C3×D5—28no—
118C22×C3×D5—28no—
119C22×C3×D5—22no—
120C22×C3×D5—22no—
121C22×C3×D5—22no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—44no—
126C22×C3×D5—44no—
127C22×C3×D5—44no—
128C22×C3×D5—44no—
129C22×C3×D5C2×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×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—44no—
149C2×C5×Dic3C2×D414yes—
150C2×C3×Dic5—28no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C2×D414yes—
154#1204—232no—
155C25×C3—51no—
156C23×C3×C4—51no—
157C23×C3×C4C2×D511yescharacteristic
158C23×Dic3—51no—
159C23×Dic3—51no—
160C23×Dic3C2×D511yescharacteristic
161C23×Dic3C2×D511yescharacteristic
162C22×Dic6—54no—
163C22×Dic6—104no—
164C22×Dic6—104no—
165C22×Dic6—104no—
166C2×C3×C22⋊C4—54no—
167C2×C3×C22⋊C4—104no—
168C2×#217—54no—
169C2×#217—54no—
170C2×#217—104no—
171C2×#217—104no—
172C3⋊#95—54no—
173C3⋊#95—54no—
174C3⋊#95C2×D514yescomplemented
175C24×C5C22×D311yescharacteristic
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5Dic614yescomplemented
183C23×D5C22×D312yes—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—34no—
188C22×C4×C5—32no—
189C22×C4×C5—32no—
190C22×C4×C5—62no—
191C22×C4×C5—62no—
192C22×C4×C5—62no—
193C22×C4×C5—62no—
194C22×C4×C5—62no—
195C22×C4×C5C22×D312yes—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—34no—
199C22×Dic5—32no—
200C22×Dic5—32no—
201C22×Dic5—62no—
202C22×Dic5—62no—
203C22×Dic5—62no—
204C22×Dic5—62no—
205C22×Dic5—62no—
206C22×Dic5#6714yes—
207C22×Dic5C22×D312yes—
208C2×Dic10—68no—
209C2×Dic10—68no—
210C2×Dic10—632no—
211C2×Dic10—68no—
212#685—28no—
213#685—68no—
214#685—68no—
215C23×Q8—151no—
216C22×C22⋊C4—51no—
217C22×C22⋊C4—151no—
218C22×C22⋊C4—151no—
219#393—158no—
220C2×#95—31no—
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×C3×D5—24no—
238C2×C3×D5—24no—
239C2×C3×D5—24no—
240C2×C3×D5—42no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—416no—
245C3×C4×C5—42no—
246Dic15—24no—
247Dic15—42no—
248C3×Dic5—24no—
249C5×Dic3—24no—
250C5×Dic3—42no—
251C24×C3—54no—
252C24×C3—52no—
253C24×C3—102no—
254C24×C3—102no—
255C24×C3—102no—
256C24×C3—102no—
257C24×C3—102no—
258C24×C3—102no—
259C24×C3C22×D511yescharacteristic
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—54no—
264C22×C3×C4—52no—
265C22×C3×C4—102no—
266C22×C3×C4—102no—
267C22×C3×C4C22×D512yes—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—54no—
274C22×Dic3—52no—
275C22×Dic3—52no—
276C22×Dic3—102no—
277C22×Dic3—102no—
278C22×Dic3—102no—
279C22×Dic3—102no—
280C22×Dic3—102no—
281C22×Dic3D2014yes—
282C22×Dic3C22×D512yes—
283C22×Dic3C22×D512yes—
284C2×Dic6—108no—
285C2×Dic6—108no—
286C2×Dic6—1032no—
287C2×Dic6—108no—
288C3×C22⋊C4—108no—
289#217—108no—
290#217—108no—
291C23×C5C2×Dic612yes—
292C23×C5#23512yes—
293C23×C5D3×D412yes—
294C23×C5D3×D412yes—
295C23×C5#23712yes—
296C23×C5#23712yes—
297C23×C5C2×#6712yes—
298C23×C5C23×D311yescharacteristic
299C22×D5—28no—
300C22×D5—28no—
301C22×D5—28no—
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5—22no—
308C22×D5—44no—
309C22×D5—44no—
310C22×D5—44no—
311C22×D5—44no—
312C22×D5C2×Dic614yescomplemented
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×C4×C5—62no—
322C2×C4×C5—62no—
323C2×C4×C5—62no—
324C2×C4×C5—124no—
325C2×Dic5—28no—
326C2×Dic5—22no—
327C2×Dic5—22no—
328C2×Dic5—34no—
329C2×Dic5—68no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—124no—
336C2×Dic5C2×#6714yes—
337Dic10—632no—
338C25—51no—
339C22×Q8—154no—
340C22×Q8—304no—
341C22×Q8—304no—
342C22×Q8—304no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—51no—
346C23×C4—151no—
347C23×C4—151no—
348C23×C4D3×D511yescharacteristic
349C2×C22⋊C4—54no—
350C2×C22⋊C4—104no—
351C2×C22⋊C4—154no—
352C2×C22⋊C4—154no—
353C2×C22⋊C4—304no—
354C2×C22⋊C4—304no—
355#95—34no—
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
366C3×D5—44no—
367C23×C3—54no—
368C23×C3—102no—
369C23×C3—102no—
370C23×C3—102no—
371C23×C3—102no—
372C23×C3—102no—
373C23×C3—102no—
374C23×C3—108no—
375C23×C3—108no—
376C23×C3—108no—
377C23×C3—204no—
378C23×C3—204no—
379C23×C3—204no—
380C23×C3—204no—
381C23×C3C2×D2012yes—
382C23×C3#70912yes—
383C23×C3#70912yes—
384C23×C3D4×D512yes—
385C23×C3D4×D512yes—
386C23×C3#71112yes—
387C23×C3Q8×D512yes—
388C23×C3C23×D511yescharacteristic
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×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—28no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—44no—
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×D2014yes—
413Dic6—1032no—
414C22×C5#87814yes—
415C22×C5#87814yes—
416C22×C5#88514yes—
417C22×C5#88514yes—
418C22×C5#92414yes—
419C22×C5#93614yes—
420C22×C5#93714yes—
421C22×C5C22×Dic611yescharacteristic
422C22×C5C2×#23511yescharacteristic
423C22×C5C2×D3×D411yescharacteristic
424C22×C5C2×D3×D411yescharacteristic
425C22×C5C2×#23711yescharacteristic
426C22×C5C2×#23711yescharacteristic
427C22×C5C22×#6711yescharacteristic
428C2×D5—24no—
429C2×D5—24no—
430C2×D5—24no—
431C2×D5—416no—
432C2×D5—42no—
433C2×D5—42no—
434C2×D5—42no—
435C2×D5—42no—
436C4×C5—42no—
437C4×C5—64no—
438C4×C5—122no—
439Dic5—24no—
440Dic5—64no—
441Dic5—122no—
442C24—54no—
443C24—52no—
444C24—102no—
445C24—102no—
446C24—102no—
447C24—102no—
448C24—102no—
449C24—102no—
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—32no—
461C22×C4—54no—
462C22×C4—52no—
463C22×C4—62no—
464C22×C4—62no—
465C22×C4—62no—
466C22×C4—62no—
467C22×C4—62no—
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—108no—
480C22⋊C4—308no—
481C22⋊C4—308no—
482C3×C5C2×#39311yescharacteristic, complemented, Hall
483C22×C3—104no—
484C22×C3—104no—
485C22×C3—104no—
486C22×C3—202no—
487C22×C3—202no—
488C22×C3—202no—
489C22×C3—202no—
490C22×C3—2016no—
491C22×C3#402114yes—
492C22×C3#402814yes—
493C22×C3#403114yes—
494C22×C3#403114yes—
495C22×C3#404214yes—
496C22×C3#404214yes—
497C22×C3#404314yes—
498C22×C3C22×D2011yescharacteristic
499C22×C3C2×#70911yescharacteristic
500C22×C3C2×#70911yescharacteristic
501C22×C3C2×D4×D511yescharacteristic
502C22×C3C2×D4×D511yescharacteristic
503C22×C3C2×#71111yescharacteristic
504C22×C3C2×Q8×D511yescharacteristic
505C3×C4—42no—
506C3×C4—104no—
507Dic3—24no—
508Dic3—42no—
509Dic3—104no—
510Dic3—202no—
511C2×C5#494718yescomplemented
512C2×C5C2×#87811yescharacteristic
513C2×C5C2×#87811yescharacteristic
514C2×C5C2×#88511yescharacteristic
515C2×C5C2×#88511yescharacteristic
516C2×C5C2×#92411yescharacteristic
517C2×C5C2×#93611yescharacteristic
518C2×C5C2×#93711yescharacteristic
519D5—44no—
520C23—54no—
521C23—108no—
522C23—108no—
523C23—102no—
524C23—102no—
525C23—102no—
526C23—102no—
527C23—102no—
528C23—102no—
529C23—108no—
530C23—204no—
531C23—204no—
532C23—204no—
533C23—204no—
534C23D5×Dic612yes—
535C23#677112yes—
536C23D3×D2012yes—
537C23#677712yes—
538C23#677912yes—
539C23#678012yes—
540C23D5×#6712yes—
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—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—108no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—124no—
559C2×C4—154no—
560C2×C4—308no—
561C2×C4—302no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4—302no—
566C2×C4—604no—
567C2×C3—204no—
568C2×C3#6496218yescomplemented
569C2×C3C2×#402111yescharacteristic
570C2×C3C2×#402811yescharacteristic
571C2×C3C2×#403111yescharacteristic
572C2×C3C2×#403111yescharacteristic
573C2×C3C2×#404211yescharacteristic
574C2×C3C2×#404211yescharacteristic
575C2×C3C2×#404311yescharacteristic
576C5C2×#494711yescharacteristic, complemented, Sylow
577C22—104no—
578C22—104no—
579C22—104no—
580C22—202no—
581C22—202no—
582C22—2016no—
583C22—202no—
584C22—202no—
585C22#9134914yes—
586C22#9135314yes—
587C22#9142214yes—
588C22#9143014yes—
589C22#9146414yes—
590C22#9147414yes—
591C22#9153414yes—
592C22C2×D5×Dic611yescharacteristic
593C22C2×#677111yescharacteristic
594C22C2×D3×D2011yescharacteristic
595C22C2×#677711yescharacteristic
596C22C2×#677911yescharacteristic
597C22C2×#678011yescharacteristic
598C22C2×D5×#6711yescharacteristic
599C4—42no—
600C4—64no—
601C4—104no—
602C4—122no—
603C4—304no—
604C4—602no—
605C3C2×#6496211yescharacteristic, complemented, Sylow
606C2—204no—
607C2#1174873618yesdirect product factor
608C2C2×#9134911yescharacteristic
609C2C2×#9135311yescharacteristic
610C2C2×#9142211yescharacteristic
611C2C2×#9143011yescharacteristic
612C2C2×#9146411yescharacteristic
613C2C2×#9147411yescharacteristic
614C2C2×#9153411yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC24×C3×D5C22
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×C5×C3⋊#95C2semidirect
7. C2×#90994C2semidirect
8. #11748736C2direct (N × H)
20. C22×#1204C22semidirect
27. #91115C22semidirect
28. C5×C3⋊#95C22semidirect
29. #90994C22semidirect
46. C23×C3×D5Q8semidirect
85. C2×C3⋊#95D5semidirect
129. C22×C3×D5C2×Q8semidirect
174. C3⋊#95C2×D5semidirect
182. C23×D5Dic6semidirect
312. C22×D5C2×Dic6semidirect
358. C2×C3×C5#393semidirect
482. C3×C5C2×#393semidirect
511. C2×C5#4947semidirect
568. C2×C3#64962semidirect
576. C5C2×#4947semidirect
605. C3C2×#64962semidirect
607. C2#11748736direct (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×C3×#6852
C22×#66652
C2×#911152
C2×C5×C3⋊#952
C2×#909942
#117487362
C2×#649623
C2×#49475