Finite Group Databasebeta

← C2×#21461839 #30615702

Subgroups — C2×#21461839 #30615702

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C22×#14519841C212yesmaximal, complemented
3C2×#16840733C211yesmaximal, characteristic, complemented
4#21461839C218yesmaximal, direct product factor
5C2×#16840632C212yesmaximal, complemented
6C2×#16840272C211yesmaximal, characteristic
7C22×#11758213C2212yes—
8C2×#14519856—28no—
9C2×#14519856—22no—
10C2×#14519856C2214yescomplemented
11C22×C4⋊#6923—21no—
12C22×C22⋊#6923—21no—
13C22×C4×#6923C2212yes—
14C2×#14519841—28no—
15C2×#14519841C2218yescomplemented
16#16840733—22no—
17#16840733C2214yescomplemented
18C2×#14519834—21no—
19C2×C22⋊#92420—21no—
20#16840632C2218yescomplemented
21C22×#11758224C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23#16840272—22no—
24#16840272—22no—
25#16840272C414yescomplemented
26#16840272C2214yes—
27C2×#14519759—21no—
28C2×#14519757C411yescharacteristic, complemented
29C2×#14519756C411yescharacteristic, complemented
30C2×#14519748C411yescharacteristic, complemented
31C2×#14519745—21no—
32C2×D4×Dic61—21no—
33C2×#14519737—21no—
34C2×#14519735C2211yescharacteristic
35C2×#121×C61C411yescharacteristic, complemented
36C23×#6923—22no—
37C2×#11758213—24no—
38C2×#11758213—24no—
39C2×#11758213—22no—
40C2×#11758213C2314yes—
41C22×#92420—22no—
42#14519856—216no—
43#14519856—216no—
44C2×C4⋊#6923—28no—
45C2×C4⋊#6923—24no—
46C2×C22⋊#6923—28no—
47C2×C22⋊#6923—24no—
48C2×C4×#6923—22no—
49C2×C4×#6923—24no—
50C2×C4×#6923D418yescomplemented
51C2×C4×#6923C2314yes—
52#14519841—216no—
53#14519834—24no—
54C22⋊#92420—24no—
55C24×D61D411yescharacteristic
56C2×#11758224—24no—
57C2×#11758224—21no—
58C2×#11758224—21no—
59C2×#11758224—24no—
60C2×#11758224C2×C412yes—
61C2×#11758224C2312yes—
62C22×Dic122C2×C411yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C23×Dic61D411yescharacteristic
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C412yes—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D412yes—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D412yes—
75C22×C4×D61C2312yes—
76C22×C4×D61C2311yescharacteristic
77#14519759—24no—
78#14519759—24no—
79#14519757—22no—
80#14519757C2×C414yescomplemented
81#14519756—22no—
82#14519756C2×C414yescomplemented
83#14519748—22no—
84#14519748C2×C414yescomplemented
85#14519745—24no—
86#14519745—24no—
87D4×Dic61—24no—
88D4×Dic61—24no—
89#14519737—24no—
90#14519737—24no—
91#14519735—21no—
92#14519735—21no—
93#14519735C2×C412yes—
94#14519735C2312yes—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C22×D4×C61—21no—
104C22×D4×C61C2×C411yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106#121×C61—22no—
107#121×C61C2×C414yescomplemented
108C2×C4⋊C4×C61C2×C411yescharacteristic
109C2×C22⋊C4×C61—21no—
110C24×C61—21no—
111C24×C61C22⋊C411yescharacteristic
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—42no—
115C23×D61—42no—
116C23×D61C22⋊C411yescharacteristic
117C23×D61C22⋊C412yes—
118C23×D61C2×D411yescharacteristic
119C23×D61C2×D412yes—
120C22×#6923—28no—
121C22×#6923—24no—
122C22×#6923—44no—
123C22×#6923—44no—
124C2×D4×C61—24no—
125C2×D4×C61—21no—
126C2×D4×C61—24no—
127C2×D4×C61—44no—
128C2×D4×C61C22×C412yes—
129C22×C4×C61—24no—
130C22×C4×C61—21no—
131C22×C4×C61C22⋊C411yescharacteristic
132C22×C4×C61C22⋊C412yes—
133C22×C4×C61C22×C412yes—
134C22×C4×C61C22×C411yescharacteristic
135C2×C22⋊D61—22no—
136C2×C22⋊D61—24no—
137C2×C22⋊D61—22no—
138C2×C22⋊D61—44no—
139C2×C22⋊D61—42no—
140C2×C22⋊D61—42no—
141C22×Dic61—24no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—44no—
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C412yes—
149C22×Dic61C2×D412yes—
150C22×Dic61C2×D411yescharacteristic
151#11758224—28no—
152#11758224—24no—
153#11758224—24no—
154#11758224—42no—
155#11758224—44no—
156#11758224—42no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—24no—
160C2×C4×D61—24no—
161C2×C4×D61—28no—
162C2×C4×D61—24no—
163C2×C4×D61—28no—
164C2×C4×D61—24no—
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61C22⋊C412yes—
168C2×C4×D61C22⋊C412yes—
169C2×C4×D61C22⋊C412yes—
170C2×C4×D61C22×C412yes—
171C2×C4×D61C22×C411yescharacteristic
172C2×C4×D61C2×D412yes—
173C2×C4×D61C2×D412yes—
174C2×C4×D61C2×D414yes—
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61#4114yes—
178C2×C4×D61C2411yescharacteristic
179C2×Dic122—24no—
180C2×Dic122—21no—
181C2×Dic122C22×C412yes—
182C22⋊#6923—216no—
183C2×#92420—24no—
184C2×#92420—44no—
185C4⋊#6923—216no—
186C4×#6923—28no—
187C4×#6923—24no—
188C4×#6923C2×D418yescomplemented
189#11758213—24no—
190#11758213—24no—
191#11758213—44no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61C22×C412yes—
194C22⋊C4×C61—24no—
195C22⋊Dic61—24no—
196C22⋊Dic61—24no—
197#11758198—22no—
198#11758198—24no—
199#11758198—22no—
200C4⋊Dic61—21no—
201C4⋊Dic61—24no—
202C4⋊Dic61C22×C412yes—
203#11758196—24no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61—42no—
213C23×C61C2×C22⋊C412yes—
214C23×C61C2×C22⋊C411yescharacteristic
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—24no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61—48no—
228C22×D61—48no—
229C22×D61C2×C22⋊C412yes—
230C22×D61C2×C22⋊C411yescharacteristic
231C22×D61#12012yes—
232C22×D61#12312yes—
233C22×D61C22×D411yescharacteristic
234C2×#6923—28no—
235C2×#6923—44no—
236C2×#6923—44no—
237C2×#6923—416no—
238D4×C61—24no—
239D4×C61—48no—
240D4×C61—42no—
241C2×C4×C61—22no—
242C2×C4×C61—24no—
243C2×C4×C61—24no—
244C2×C4×C61—22no—
245C2×C4×C61—42no—
246C2×C4×C61C2×C22⋊C412yes—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C4×D414yes—
249C2×C4×C61C23×C411yescharacteristic
250C22⋊D61—48no—
251C22⋊D61—42no—
252C22⋊D61—42no—
253C22⋊D61—44no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—44no—
262C2×Dic61—44no—
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61#12114yes—
266C2×Dic61C22×D411yescharacteristic
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—24no—
270C4×D61—24no—
271C4×D61—24no—
272C4×D61—24no—
273C4×D61—24no—
274C4×D61C4×D414yes—
275C4×D61#12012yes—
276C4×D61#12114yes—
277C4×D61#12312yes—
278C4×D61C22×D412yes—
279C4×D61C2×#4112yes—
280Dic122—24no—
281Dic122—42no—
282#92420—44no—
283C2×#1897—611nomaximal, Sylow
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—44no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—84no—
292C22×C61#38612yes—
293C22×C61#42112yes—
294C22×C61#42112yes—
295C22×C61C22×C22⋊C411yescharacteristic
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—24no—
301C2×D61—24no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—44no—
306C2×D61—44no—
307C2×D61—48no—
308C2×D61—44no—
309C2×D61#38612yes—
310C2×D61C2×#12011yescharacteristic
311C2×D61C2×#12311yescharacteristic
312#6923—48no—
313C4×C61—22no—
314C4×C61—42no—
315C4×C61#38612yes—
316C4×C61C2×C4×D412yes—
317Dic61—22no—
318Dic61—42no—
319Dic61—42no—
320Dic61#38612yes—
321Dic61C2×#12112yes—
322C2×#525—611no—
323C22×#117—611no—
324C22×#104—612no—
325C2×#407—611no—
326#1897—618no—
327C2×#339—612no—
328C2×C61—42no—
329C2×C61—82no—
330C2×C61#189714yescomplemented
331C2×C61C2×#38611yescharacteristic
332C2×C61C2×#42111yescharacteristic
333C2×C61C2×#42111yescharacteristic
334D61—21no—
335D61—21no—
336D61—22no—
337D61—42no—
338C22×#41—611no—
339C24×C4—611no—
340C22×M16—612no—
341#525—614no—
342#525—614no—
343#525—1222no—
344#525—1222no—
345C2×#123—1221no—
346C2×C22⋊Q8—611no—
347C2×C22⋊Q8—611no—
348C2×#121—611no—
349C2×#121#692311yescharacteristic, complemented
350C2×#120—1221no—
351C2×C4×D4—1221no—
352C2×C4×D4—1221no—
353C2×#117—614no—
354C2×#117—611no—
355C2×#117—1228no—
356C2×#117—1222no—
357C22×C4⋊C4—1221no—
358C22×C22⋊C4—1221no—
359C22×C42—612no—
360C2×#104—618no—
361C2×#104—1228no—
362#407—614no—
363#407—1222no—
364C2×C22⋊C8—1221no—
365C2×C22⋊C8—1221no—
366#339—618no—
367C61C2×#189711yescharacteristic, complemented, Sylow
368C25—611no—
369C2×#41—612no—
370C2×#41—612no—
371C2×#41—1221no—
372C2×#41—1221no—
373C2×#41—1224no—
374C2×#41—1224no—
375C22×Q8—611no—
376C22×D4—21no—
377C22×D4—1221no—
378C22×D4—1221no—
379C22×D4C2×#692311yescharacteristic
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—612no—
384C23×C4—611no—
385C23×C4—612no—
386C23×C4—612no—
387C23×C4—611no—
388C23×C4—612no—
389C23×C4—1224no—
390C23×C4—1224no—
391C23×C4—1221no—
392C23×C4—1222no—
393C23×C4C2×#692311yescharacteristic
394C2×M16—614no—
395C2×M16—1222no—
396C2×M16—1224no—
397C2×M16—1224no—
398C22×C8—1222no—
399#123—1224no—
400#123—1224no—
401C22⋊Q8—614no—
402C22⋊Q8—614no—
403C22⋊Q8—1222no—
404C22⋊Q8—1222no—
405#121—22no—
406#121—614no—
407#121—1222no—
408#121C2×#692314yescomplemented
409#120—1224no—
410#120—1224no—
411C4×D4—1224no—
412C4×D4—1224no—
413C4×D4—1224no—
414C4×D4—1224no—
415#117—612no—
416#117—612no—
417#117—12216no—
418#117—1221no—
419#117—1221no—
420#117—12216no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1224no—
424C2×C4⋊C4—1228no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4C2×#692311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1224no—
432C2×C22⋊C4—1228no—
433C2×C22⋊C4—1221no—
434C2×C42—614no—
435C2×C42—618no—
436C2×C42—1221no—
437C2×C42—1222no—
438C2×C42—1224no—
439#104—12216no—
440C22⋊C8—1224no—
441C22⋊C8—1224no—
442C24—21no—
443C24—611no—
444C24—611no—
445C24—612no—
446C24—612no—
447C24—1222no—
448C24—1222no—
449C24—2442no—
450C24—2442no—
451C24C22⋊#692311yescharacteristic
452#41—1224no—
453#41—1228no—
454#41—1224no—
455#41—2442no—
456#41—2444no—
457#41—2442no—
458C2×Q8—612no—
459C2×Q8—1221no—
460C2×Q8—1224no—
461C2×D4—24no—
462C2×D4—21no—
463C2×D4—24no—
464C2×D4—44no—
465C2×D4—1224no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—2442no—
469C2×D4—2442no—
470C2×D4—2444no—
471C2×D4C22×#692312yes—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—614no—
478C22×C4—614no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—611no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—1224no—
491C22×C4—1224no—
492C22×C4—1224no—
493C22×C4—1228no—
494C22×C4—1224no—
495C22×C4—1228no—
496C22×C4—1224no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1224no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1224no—
503C22×C4—1228no—
504C22×C4—1224no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—2444no—
508C22×C4—2444no—
509C22×C4—2444no—
510C22×C4C22⋊#692312yes—
511C22×C4C22⋊#692311yescharacteristic
512C22×C4C22×#692312yes—
513C22×C4C22×#692311yescharacteristic
514M16—1224no—
515M16—1224no—
516M16—2444no—
517C2×C8—1224no—
518C2×C8—2444no—
519C4⋊C4—21no—
520C4⋊C4—612no—
521C4⋊C4—1224no—
522C4⋊C4—12216no—
523C4⋊C4—1221no—
524C4⋊C4—1224no—
525C4⋊C4C22×#692312yes—
526C22⋊C4—24no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1224no—
530C22⋊C4—1224no—
531C22⋊C4—12216no—
532C22⋊C4—1224no—
533C42—618no—
534C42—1222no—
535C42—1222no—
536C42—1228no—
537C42—1224no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—612no—
546C23—612no—
547C23—611no—
548C23—611no—
549C23—612no—
550C23—1222no—
551C23—1222no—
552C23—1224no—
553C23—1222no—
554C23—1222no—
555C23—1222no—
556C23—1222no—
557C23—1222no—
558C23—2442no—
559C23—2442no—
560C23—2442no—
561C23—2442no—
562C23—2448no—
563C23—2448no—
564C23C2×C22⋊#692312yes—
565C23C2×C22⋊#692311yescharacteristic
566Q8—1224no—
567Q8—2442no—
568D4—24no—
569D4—48no—
570D4—42no—
571D4—2442no—
572D4—2442no—
573D4—2444no—
574D4—2448no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—42no—
580C2×C4—614no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—612no—
584C2×C4—614no—
585C2×C4—612no—
586C2×C4—614no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—1224no—
591C2×C4—1224no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1222no—
598C2×C4—1224no—
599C2×C4—1224no—
600C2×C4—1228no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—2444no—
604C2×C4—2444no—
605C2×C4—24416no—
606C2×C4—2444no—
607C2×C4—2444no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4C2×C22⋊#692312yes—
611C2×C4C2×C22⋊#692311yescharacteristic
612C2×C4D4×#692314yes—
613C2×C4C23×#692311yescharacteristic
614C8—2444no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—44no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—84no—
623C22—611no—
624C22—611no—
625C22—612no—
626C22—1224no—
627C22—1224no—
628C22—1221no—
629C22—1221no—
630C22—1221no—
631C22—1221no—
632C22—1222no—
633C22—1222no—
634C22—1222no—
635C22—2444no—
636C22—2444no—
637C22—2448no—
638C22—2444no—
639C22#1684071012yes—
640C22#1684075912yes—
641C22#1684076012yes—
642C22C22×C22⋊#692311yescharacteristic
643C4—22no—
644C4—42no—
645C4—612no—
646C4—612no—
647C4—1222no—
648C4—2448no—
649C4—2442no—
650C4—2442no—
651C4#1684071012yes—
652C4C2×D4×#692312yes—
653C2—42no—
654C2—82no—
655C2—1221no—
656C2—1221no—
657C2—1222no—
658C2—2442no—
659C2#2146183914yesdirect product factor
660C2C2×#1684071011yescharacteristic
661C2C2×#1684076011yescharacteristic
662C2C2×#1684075911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#121×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840272C2
cosocleC2×C4×D61C24
hypercenterC2×#121#6923
hypocenterC61C2×#1897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
2. C22×#14519841C2semidirect
3. C2×#16840733C2semidirect
4. #21461839C2direct (N × H)
5. C2×#16840632C2semidirect
10. C2×#14519856C22semidirect
15. C2×#14519841C22semidirect
17. #16840733C22semidirect
20. #16840632C22semidirect
25. #16840272C4semidirect
28. C2×#14519757C4semidirect
29. C2×#14519756C4semidirect
30. C2×#14519748C4semidirect
35. C2×#121×C61C4semidirect
50. C2×C4×#6923D4semidirect
80. #14519757C2×C4semidirect
82. #14519756C2×C4semidirect
84. #14519748C2×C4semidirect
107. #121×C61C2×C4semidirect
188. C4×#6923C2×D4semidirect
330. C2×C61#1897semidirect
349. C2×#121#6923semidirect
367. C61C2×#1897semidirect
408. #121C2×#6923semidirect
659. C2#21461839direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198562
C22×#145198412
C2×#168407332
#214618392
C2×#168406322
C2×#168402722
C2×#189761