Finite Group Databasebeta

← C2×#11749022 #14423213

Subgroups — C2×#11749022 #14423213

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic, complemented
2C22×#6715C211yesmaximal, characteristic, complemented
3C2×#91450C211yesmaximal, characteristic, complemented
4C22×#6653C211yesmaximal, characteristic, complemented
5C2×C5×#832C211yesmaximal, characteristic, complemented
6#11749022C218yesmaximal, direct product factor
7C2×#90964C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65062—31nomaximal, Hall
10C24×C3×D5—21no—
11C22×C3×C5×D4C2211yescharacteristic
12C22×D60C2211yescharacteristic, complemented
13C22×C3×C22⋊D5—21no—
14C2×C3×D4×D5—24no—
15C2×C3×D4×D5—24no—
16C2×C3×D4×D5—22no—
17C2×C3×D4×D5C2214yescomplemented
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×#1202—21no—
21C2×#6715—24no—
22C2×#6715C2214yescomplemented
23C22×C3⋊#168C2211yescharacteristic, complemented
24C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
25C22×C5×C3⋊C8C2211yescharacteristic, complemented
26C2×#6667—21no—
27#91450—22no—
28#91450C2214yescomplemented
29C2×#6653—24no—
30C2×#6653C2214yescomplemented
31C5×#832C2214yescomplemented
32#90964C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5217—51nomaximal, Hall
35C22×D4×D5D311yescharacteristic, complemented
36C22×#686—31no—
37C22×D40—31no—
38C2×#4041—31no—
39C2×C5×#102—31no—
40C2×#3952—31no—
41C2×#3941—31no—
42#65062—38no—
43C24×C3×C5—21no—
44C23×D15—21no—
45C23×C3×D5—28no—
46C23×C3×D5—21no—
47C23×C3×D5—24no—
48C23×C3×D5—44no—
49C23×C3×D5—44no—
50C23×C3×D5D411yescharacteristic
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4D414yescomplemented
54C2×C3×C5×D4C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C2×D60—22no—
57C2×D60—22no—
58C2×D60—21no—
59C2×D60C2312yescomplemented
60C22×C5×Dic3—21no—
61C2×C3×C22⋊D5—28no—
62C2×C3×C22⋊D5—24no—
63C22×C3×Dic5D411yescharacteristic
64C3×D4×D5—216no—
65C3×D4×D5—28no—
66C3×D4×D5—28no—
67C2×C3×D20—21no—
68C2×C3×D20—22no—
69C2×C3×D20D414yescomplemented
70C2×C3×D20C2312yes—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5D412yes—
74C2×C3×C4×D5C2312yes—
75C2×#1202—24no—
76C2×#1202—44no—
77#6715—28no—
78C2×C3⋊#168—22no—
79C2×C3⋊#168C2312yescomplemented
80C5×C4⋊Dic3—21no—
81C5×C4⋊Dic3C2312yescomplemented
82C2×C5×C3⋊C8—22no—
83C2×C5×C3⋊C8C2312yescomplemented
84#6667—24no—
85#6653—28no—
86C23×C3×D4—51no—
87C22×#213—51no—
88C22×#213—51no—
89C2×#930—51no—
90#5217—58no—
91C2×#832—51no—
92C2×#832D511yescharacteristic, complemented
93C2×#830—51no—
94C24×D5—21no—
95C22×C5×D4C2×D311yescharacteristic
96C22×C22⋊D5—21no—
97C2×D4×D5—24no—
98C2×D4×D5—24no—
99C2×D4×D5—22no—
100C2×D4×D5C2×D314yescomplemented
101C22×D20—31no—
102C22×D20—61no—
103C22×D20C2×D311yescharacteristic
104C22×C4×D5C2×D311yescharacteristic
105C22×C5×C8—31no—
106C2×C5×C4⋊C4—31no—
107C2×#686—34no—
108C2×#686—64no—
109C2×#685—61no—
110C22×#168—31no—
111C2×D40—34no—
112C2×D40—64no—
113#4041—34no—
114#4041—62no—
115C5×#102—34no—
116#3952—34no—
117#3941—34no—
118C2×#447—151noSylow
119C23×C3×C5—24no—
120C23×C3×C5—22no—
121C23×C3×C5—42no—
122C23×C3×C5—42no—
123C23×C3×C5C2×D411yescharacteristic
124C22×D15—22no—
125C22×D15—42no—
126C22×D15—42no—
127C22×D15—42no—
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5—216no—
131C22×C3×D5—24no—
132C22×C3×D5—22no—
133C22×C3×D5—48no—
134C22×C3×D5—432no—
135C22×C3×D5—42no—
136C22×C3×D5—42no—
137C22×C3×D5—48no—
138C22×C3×D5D814yescomplemented
139C22×C3×D5C2×D412yes—
140C3×C5×D4—24no—
141C3×C5×D4—22no—
142C3×C5×D4C2×D414yescomplemented
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2411yescharacteristic
147D60—22no—
148D60—22no—
149D60—42no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—42no—
152C3×C22⋊D5—216no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C2×D412yes—
155C3×D20—24no—
156C3×D20—22no—
157C3×D20C2×D414yescomplemented
158C3×C4×D5—24no—
159C3×C4×D5—22no—
160C3×C4×D5—22no—
161#1202—48no—
162C3⋊#168—22no—
163C5×C3⋊C8—22no—
164C25×C3—101no—
165C22×C3×D4—54no—
166C22×C3×D4—51no—
167C22×C3×D4—102no—
168C22×C3×D4—101no—
169C22×C3×D4—104no—
170C22×C3×D4—104no—
171C22×C3×D4C2×D511yescharacteristic
172C23×C3×C4—51no—
173C22×#67—101no—
174C22×D12—51no—
175C2×#213—54no—
176C2×#213—54no—
177C2×#213—104no—
178C2×#213—104no—
179#930—54no—
180#930—102no—
181C2×(C2×D3)⋊C4—101no—
182C2×C4⋊Dic3C2×D511yescharacteristic, complemented
183C22×C3⋊C8—51no—
184C22×C3⋊C8C2×D511yescharacteristic, complemented
185#832—54no—
186#832C2×D514yescomplemented
187#830—54no—
188C24×C5—21no—
189C23×D5—28no—
190C23×D5—21no—
191C23×D5—24no—
192C23×D5—44no—
193C23×D5—44no—
194C23×D5—61no—
195C23×D5#6711yescharacteristic
196C2×C5×D4—21no—
197C2×C5×D4—22no—
198C2×C5×D4#6714yescomplemented
199C2×C5×D4C22×D312yes—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—28no—
203C2×C22⋊D5—24no—
204C22×Dic5#6711yescharacteristic
205D4×D5—216no—
206D4×D5—28no—
207D4×D5—28no—
208C2×D20—22no—
209C2×D20—21no—
210C2×D20—32no—
211C2×D20—62no—
212C2×D20—62no—
213C2×D20—64no—
214C2×D20—61no—
215C2×D20—124no—
216C2×D20#6714yescomplemented
217C2×D20C22×D312yes—
218C2×C4×D5—22no—
219C2×C4×D5—22no—
220C2×C4×D5#6712yes—
221C2×C4×D5C22×D312yes—
222C2×C5×C8—32no—
223C2×C5×C8—62no—
224C5×C4⋊C4—32no—
225C5×C4⋊C4—61no—
226#686—68no—
227#685—64no—
228C2×#168—32no—
229C2×#168—62no—
230D40—68no—
231C23×D4—51no—
232C22×D8—151no—
233C22×D8—151no—
234C2×#121—151no—
235#447—158no—
236C2×#102—31no—
237C2×#102—151no—
238C2×C22⋊C8—151no—
239C22×C3×C5—24no—
240C22×C3×C5—42no—
241C22×C3×C5—42no—
242C22×C3×C5—48no—
243C22×C3×C5#12012yes—
244C22×C3×C5C2×D812yes—
245C22×C3×C5AGL(1,ℤ/8)12yes—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—42no—
248C2×D15—42no—
249C2×D15—42no—
250C2×D15—84no—
251C2×C3×D5—22no—
252C2×C3×D5—22no—
253C2×C3×D5—28no—
254C2×C3×D5—24no—
255C2×C3×D5—432no—
256C2×C3×D5—42no—
257C2×C3×D5—42no—
258C2×C3×D5—48no—
259C2×C3×D5C2×D814yescomplemented
260C3×C4×C5#12012yes—
261C3×C4×C5C22×D411yescharacteristic
262C3×C4×C5C22×D411yescharacteristic
263C3×Dic5—22no—
264C5×Dic3—42no—
265C24×C3—21no—
266C24×C3—51no—
267C24×C3—104no—
268C24×C3—108no—
269C24×C3—101no—
270C24×C3—204no—
271C24×C3—204no—
272C23×D3—101no—
273C2×C3×D4—22no—
274C2×C3×D4—21no—
275C2×C3×D4—54no—
276C2×C3×D4—52no—
277C2×C3×D4—104no—
278C2×C3×D4—108no—
279C2×C3×D4—1016no—
280C2×C3×D4—108no—
281C2×C3×D4—108no—
282C2×C3×D4—102no—
283C2×C3×D4—101no—
284C2×C3×D4D2014yescomplemented
285C2×C3×D4C22×D512yes—
286C22×C3×C4—51no—
287C22×C3×C4—52no—
288C22×C3×C4—52no—
289C22×C3×C4—102no—
290C22×C3×C4—102no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—104no—
293C2×#67—204no—
294C22×Dic3—21no—
295C2×D12—52no—
296C2×D12—102no—
297C2×D12—102no—
298C2×D12—101no—
299#213—108no—
300#213—108no—
301(C2×D3)⋊C4—104no—
302C4⋊Dic3—21no—
303C4⋊Dic3C22×D512yescomplemented
304C2×C3⋊C8—22no—
305C2×C3⋊C8—52no—
306C2×C3⋊C8—102no—
307C2×C3⋊C8C22×D512yescomplemented
308C23×C5—24no—
309C23×C5—22no—
310C23×C5—42no—
311C23×C5—42no—
312C23×C5C2×#6711yescharacteristic
313C22×D5—22no—
314C22×D5—22no—
315C22×D5—216no—
316C22×D5—24no—
317C22×D5—22no—
318C22×D5—432no—
319C22×D5—48no—
320C22×D5—42no—
321C22×D5—42no—
322C22×D5—48no—
323C22×D5—62no—
324C22×D5—122no—
325C22×D5—122no—
326C22×D5—122no—
327C22×D5#21314yescomplemented
328C22×D5C2×#6712yes—
329C5×D4—24no—
330C5×D4—22no—
331C5×D4C2×#6714yescomplemented
332C2×C4×C5—62no—
333C2×C4×C5—122no—
334C2×C4×C5C2×#6712yes—
335C2×C4×C5C2×#6711yescharacteristic
336C2×C4×C5C2×#6712yes—
337C2×C4×C5C23×D311yescharacteristic
338C22⋊D5—216no—
339C2×Dic5—22no—
340C2×Dic5C2×#6712yes—
341D20—24no—
342D20—22no—
343D20—62no—
344D20—62no—
345D20—128no—
346D20—122no—
347D20C2×#6714yescomplemented
348C4×D5—24no—
349C4×D5—22no—
350C4×D5—22no—
351C5×C8—62no—
352#168—62no—
353C25—101no—
354C22×D4—54no—
355C22×D4—51no—
356C22×D4—102no—
357C22×D4—101no—
358C22×D4—104no—
359C22×D4—104no—
360C22×D4—151no—
361C22×D4—301no—
362C22×D4D3×D511yescharacteristic
363C23×C4—51no—
364C2×D8—154no—
365C2×D8—154no—
366C2×D8—304no—
367C2×D8—304no—
368C22×C8—31no—
369C22×C8—151no—
370#121—154no—
371#121—302no—
372C2×C4⋊C4—31no—
373C2×C22⋊C4—301no—
374#102—34no—
375#102—154no—
376C22⋊C8—154no—
377C2×C3×C5—44no—
378C2×C3×C5#44714yescomplemented
379C2×C3×C5C2×#12011yescharacteristic
380C2×C3×C5C22×D811yescharacteristic
381C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
382D15—82no—
383C3×D5—24no—
384C3×D5—44no—
385C23×C3—22no—
386C23×C3—24no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—52no—
390C23×C3—54no—
391C23×C3—1016no—
392C23×C3—102no—
393C23×C3—102no—
394C23×C3—102no—
395C23×C3—104no—
396C23×C3—208no—
397C23×C3—2032no—
398C23×C3—208no—
399C23×C3—202no—
400C23×C3—202no—
401C23×C3D4×D511yescharacteristic
402C22×D3—102no—
403C22×D3—202no—
404C22×D3—202no—
405C22×D3—202no—
406C3×D4—22no—
407C3×D4—24no—
408C3×D4—54no—
409C3×D4—1016no—
410C3×D4—102no—
411C3×D4—104no—
412C3×D4C2×D2014yescomplemented
413C2×C3×C4—52no—
414C2×C3×C4—102no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4—104no—
418C2×C3×C4C2×D2012yes—
419C2×C3×C4D4×D512yes—
420C2×C3×C4D4×D511yescharacteristic
421C2×C3×C4C23×D511yescharacteristic
422#67—208no—
423C2×Dic3—22no—
424C2×Dic3—42no—
425D12—102no—
426D12—102no—
427D12—202no—
428C3⋊C8—22no—
429C3⋊C8—102no—
430C22×C5—24no—
431C22×C5—48no—
432C22×C5—42no—
433C22×C5—42no—
434C22×C5C2×#21312yes—
435C22×C5#93212yes—
436C22×C5#95312yes—
437C22×C5C22×#6711yescharacteristic
438C2×D5—28no—
439C2×D5—22no—
440C2×D5—22no—
441C2×D5—24no—
442C2×D5—432no—
443C2×D5—48no—
444C2×D5—42no—
445C2×D5—42no—
446C2×D5—122no—
447C2×D5—122no—
448C2×D5—122no—
449C2×D5—244no—
450C2×D5C2×#21314yescomplemented
451C4×C5—122no—
452C4×C5#95312yes—
453C4×C5C22×#6711yescharacteristic
454C4×C5C22×#6711yescharacteristic
455Dic5—22no—
456C24—21no—
457C24—51no—
458C24—104no—
459C24—108no—
460C24—101no—
461C24—204no—
462C24—204no—
463C24—301no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—54no—
467C2×D4—52no—
468C2×D4—104no—
469C2×D4—108no—
470C2×D4—1016no—
471C2×D4—108no—
472C2×D4—108no—
473C2×D4—102no—
474C2×D4—101no—
475C2×D4—152no—
476C2×D4—304no—
477C2×D4—302no—
478C2×D4—302no—
479C2×D4—301no—
480C2×D4—604no—
481C2×D4#120214yescomplemented
482C2×D4C2×D3×D512yes—
483C22×C4—51no—
484C22×C4—52no—
485C22×C4—52no—
486C22×C4—61no—
487C22×C4—102no—
488C22×C4—102no—
489C22×C4C2×D3×D511yescharacteristic
490D8—308no—
491D8—308no—
492C2×C8—32no—
493C2×C8—62no—
494C2×C8—152no—
495C2×C8—302no—
496C4⋊C4—32no—
497C4⋊C4—61no—
498C22⋊C4—304no—
499C3×C5C2×#44711yescharacteristic, complemented, Hall
500C22×C3—24no—
501C22×C3—48no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—54no—
505C22×C3—102no—
506C22×C3—108no—
507C22×C3—102no—
508C22×C3—104no—
509C22×C3—2032no—
510C22×C3—208no—
511C22×C3—202no—
512C22×C3—202no—
513C22×C3#402812yes—
514C22×C3D5×D812yes—
515C22×C3#406012yes—
516C22×C3C2×D4×D511yescharacteristic
517C2×D3—202no—
518C2×D3—202no—
519C2×D3—202no—
520C2×D3—404no—
521C3×C4—102no—
522C3×C4#402812yes—
523C3×C4C22×D2011yescharacteristic
524C3×C4C2×D4×D511yescharacteristic
525Dic3—42no—
526C2×C5—44no—
527C2×C5#521714yescomplemented
528C2×C5C22×#21311yescharacteristic
529C2×C5C2×#93211yescharacteristic
530C2×C5C2×#95311yescharacteristic
531D5—24no—
532D5—44no—
533D5—242no—
534C23—22no—
535C23—24no—
536C23—42no—
537C23—42no—
538C23—54no—
539C23—52no—
540C23—1016no—
541C23—102no—
542C23—102no—
543C23—102no—
544C23—104no—
545C23—208no—
546C23—2032no—
547C23—208no—
548C23—202no—
549C23—202no—
550C23—302no—
551C23—602no—
552C23—602no—
553C23—602no—
554C23D5×#6711yescharacteristic
555D4—22no—
556D4—24no—
557D4—54no—
558D4—1016no—
559D4—102no—
560D4—104no—
561D4—302no—
562D4—302no—
563D4—608no—
564D4—602no—
565D4C2×#120214yescomplemented
566C2×C4—52no—
567C2×C4—62no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—104no—
572C2×C4—122no—
573C2×C4C2×#120212yes—
574C2×C4D5×#6712yes—
575C2×C4D5×#6711yescharacteristic
576C2×C4C22×D3×D511yescharacteristic
577C8—62no—
578C8—302no—
579C2×C3—44no—
580C2×C3—104no—
581C2×C3—204no—
582C2×C3#6506214yescomplemented
583C2×C3C2×#402811yescharacteristic
584C2×C3C2×D5×D811yescharacteristic
585C2×C3C2×#406011yescharacteristic
586D3—402no—
587C5C2×#521711yescharacteristic, complemented, Sylow
588C22—24no—
589C22—48no—
590C22—42no—
591C22—42no—
592C22—54no—
593C22—102no—
594C22—108no—
595C22—102no—
596C22—104no—
597C22—2032no—
598C22—208no—
599C22—202no—
600C22—202no—
601C22—602no—
602C22—602no—
603C22—602no—
604C22—1204no—
605C22D5×#21312yes—
606C22#9149112yes—
607C22#9156412yes—
608C22C2×D5×#6711yescharacteristic
609C4—102no—
610C4—122no—
611C4#9156412yes—
612C4C22×#120211yescharacteristic
613C4C2×D5×#6711yescharacteristic
614C3C2×#6506211yescharacteristic, complemented, Sylow
615C2—44no—
616C2—104no—
617C2—204no—
618C2—1202no—
619C2#1174902214yesdirect product factor
620C2C2×D5×#21311yescharacteristic
621C2C2×#9149111yescharacteristic
622C2C2×#9156411yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#447
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
1. C22×C3×D4×D5C2semidirect
2. C22×#6715C2semidirect
3. C2×#91450C2semidirect
4. C22×#6653C2semidirect
5. C2×C5×#832C2semidirect
6. #11749022C2direct (N × H)
7. C2×#90964C2semidirect
8. C2×#90955C2semidirect
12. C22×D60C22semidirect
17. C2×C3×D4×D5C22semidirect
22. C2×#6715C22semidirect
23. C22×C3⋊#168C22semidirect
24. C2×C5×C4⋊Dic3C22semidirect
25. C22×C5×C3⋊C8C22semidirect
28. #91450C22semidirect
30. C2×#6653C22semidirect
31. C5×#832C22semidirect
32. #90964C22semidirect
33. #90955C22semidirect
35. C22×D4×D5D3semidirect
53. C2×C3×C5×D4D4semidirect
59. C2×D60C23semidirect
69. C2×C3×D20D4semidirect
79. C2×C3⋊#168C23semidirect
81. C5×C4⋊Dic3C23semidirect
83. C2×C5×C3⋊C8C23semidirect
92. C2×#832D5semidirect
100. C2×D4×D5C2×D3semidirect
138. C22×C3×D5D8semidirect
142. C3×C5×D4C2×D4semidirect
157. C3×D20C2×D4semidirect
182. C2×C4⋊Dic3C2×D5semidirect
184. C22×C3⋊C8C2×D5semidirect
186. #832C2×D5semidirect
198. C2×C5×D4#67semidirect
216. C2×D20#67semidirect
259. C2×C3×D5C2×D8semidirect
284. C2×C3×D4D20semidirect
303. C4⋊Dic3C22×D5semidirect
307. C2×C3⋊C8C22×D5semidirect
327. C22×D5#213semidirect
331. C5×D4C2×#67semidirect
347. D20C2×#67semidirect
378. C2×C3×C5#447semidirect
412. C3×D4C2×D20semidirect
450. C2×D5C2×#213semidirect
481. C2×D4#1202semidirect
499. C3×C5C2×#447semidirect
527. C2×C5#5217semidirect
565. D4C2×#1202semidirect
582. C2×C3#65062semidirect
587. C5C2×#5217semidirect
614. C3C2×#65062semidirect
619. C2#11749022direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C22×#67152
C2×#914502
C22×#66532
C2×C5×#8322
#117490222
C2×#909642
C2×#909552
C2×#650623
C2×#52175