Finite Group Databasebeta

← D4×#14519697 #29695413

Subgroups — D4×#14519697 #29695413

Order 15616.

2014 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D244C211yesmaximal, characteristic
2C2×D4×#92418C211yesmaximal, characteristic, complemented
3C22×#14519697C212yesmaximal, complemented
4#21446746C211yesmaximal, characteristic, complemented
5#21446624C211yesmaximal, characteristic, complemented
6#21446245C212yesmaximal, complemented
7#21446136C212yesmaximal, complemented
8#21445816C211yesmaximal, characteristic, complemented
9#21445749C212yesmaximal, complemented
10C4×#14519697C211yesmaximal, characteristic, complemented
11D4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×D244C2212yes—
13C22×D4×D61—21no—
14C23×#92418C2212yescomplemented
15D4×D244—24no—
16D4×D244C418yescomplemented
17C2×#14519774C2211yescharacteristic
18C2×#14519752—21no—
19C2×#14519751C2212yes—
20C2×#14519747—22no—
21C2×C4×D244C2211yescharacteristic
22D4×#92418—24no—
23C2×C4⋊#92418C2211yescharacteristic, complemented
24C2×#14519697—28no—
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2212yes—
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2212yescomplemented
29C2×#14519697C2212yescomplemented
30C2×#14519697C2212yescomplemented
31C2×#14519697C2212yescomplemented
32C2×C22⋊#92418C2212yescomplemented
33C2×C4×#92418C2211yescharacteristic, complemented
34#16839524C2211yescharacteristic, complemented
35#16839524C2211yescharacteristic, complemented
36#16839524C2212yescomplemented
37C2×C4×D4×C61—21no—
38C2×C4×D4×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2212yescomplemented
40C61×#389—21no—
41C61×#385—22no—
42C61×#384C2211yescharacteristic, complemented
43C61×#380C2212yescomplemented
44C4×C4⋊C4×C61C2211yescharacteristic, complemented
45C24×D61—22no—
46C22×D244—24no—
47C22×D244—24no—
48C22×D244—22no—
49C22×D244—21no—
50C22×D244—24no—
51C22×D244—21no—
52C22×D244—42no—
53C22×D244—42no—
54C22×D244C2×C418yescomplemented
55C22×D244C2312yes—
56C22×D244C2311yescharacteristic
57C22×C22⋊D61—22no—
58C2×D4×D61—28no—
59C2×D4×D61—44no—
60C2×D4×D61—44no—
61C22×C4×D61—21no—
62C22×#92418—24no—
63C22×#92418—24no—
64C22×#92418—42no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2312yes—
67C22×#92418C2311yescharacteristic
68#14519774—22no—
69#14519774C2×C414yescomplemented
70#14519752—28no—
71#14519751—24no—
72#14519751C2×C418yescomplemented
73#14519747—216no—
74C4×D244—22no—
75C4×D244C2×C414yescomplemented
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758198—21no—
78C2×#11758198—22no—
79C4⋊#92418—22no—
80#14519697—24no—
81#14519697—22no—
82#14519697—24no—
83#14519697—24no—
84#14519697—42no—
85#14519697—42no—
86#14519697D414yesdirect product factor
87C22⋊#92418—24no—
88C4×#92418—22no—
89C22×D4×C61D411yescharacteristic
90C23×C4×C61—22no—
91C23×C4×C61C2312yes—
92C4×D4×C61—44no—
93C4×D4×C61C2×C414yes—
94C4×D4×C61D414yes—
95C2×C4⋊C4×C61—24no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—42no—
100C2×C4⋊C4×C61D411yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2312yes—
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61D412yes—
106C2×C42×C61—21no—
107C2×C42×C61C2311yescharacteristic
108#95×C61—21no—
109#95×C61—22no—
110C24×C61C2×D412yes—
111C23×D61—21no—
112C23×D61—22no—
113C23×D61—28no—
114C23×D61—44no—
115C23×D61—44no—
116C23×D61—44no—
117C23×D61—44no—
118C23×D61—82no—
119C23×D61—82no—
120C2×D4×C61C22⋊C414yes—
121C2×D4×C61D814yes—
122C2×D4×C61SD1614yes—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—44no—
131C22×C4×C61—44no—
132C22×C4×C61—82no—
133C22×C4×C61C22×C414yes—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D414yes—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—28no—
140C2×C22⋊D61—44no—
141C2×C22⋊D61—44no—
142C22×Dic61—21no—
143D4×D61—432no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—216no—
152C2×D244—24no—
153C2×D244—28no—
154C2×D244—22no—
155C2×D244—24no—
156C2×D244—48no—
157C2×D244—48no—
158C2×D244—48no—
159C2×D244—44no—
160C2×D244—44no—
161C2×D244—42no—
162C2×D244—42no—
163C2×D244—81no—
164C2×D244—81no—
165C2×D244C22×C414yes—
166C2×D244C22×C412yes—
167C2×D244C2×D412yes—
168C2×D244#4112yes—
169C2×C4×D61—24no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—44no—
178C4⋊C4×C61—42no—
179C4⋊C4×C61—81no—
180C4⋊C4×C61C22⋊C414yes—
181C4⋊C4×C61C2×D412yescomplemented
182C22⋊C4×C61—44no—
183C22⋊C4×C61C22⋊C418yes—
184C42×C61—42no—
185C42×C61C22×C412yes—
186C42×C61C2×D412yes—
187#11758198—24no—
188#11758198—28no—
189C4⋊Dic61—21no—
190C4⋊Dic61C22×C412yes—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—22no—
199C2×#92418—48no—
200C2×#92418C2×D412yescomplemented
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61C2×C22⋊C414yes—
206C23×C61C2×D814yes—
207C23×C61C2×SD1614yes—
208C23×C61C22×D411yescharacteristic
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—24no—
213C22×D61—416no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61—416no—
225C22×D61—88no—
226C22×D61—88no—
227C22×D61—88no—
228C22×D61—88no—
229C22×D61—88no—
230D4×C61#102116yescomplemented
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—42no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—41no—
248C2×C4×C61—88no—
249C2×C4×C61C2×C22⋊C412yes—
250C2×C4×C61C2×C22⋊C414yes—
251C2×C4×C61C2×C22⋊C412yes—
252C2×C4×C61C2×D812yes—
253C2×C4×C61C2×SD1612yes—
254C2×C4×C61C23×C411yescharacteristic
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61H(5,𝔽2)11yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C22⋊D61—416no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264D244—24no—
265D244—22no—
266D244—24no—
267D244—22no—
268D244—22no—
269D244—416no—
270D244—42no—
271D244—42no—
272D244—48no—
273D244—84no—
274D244C4×D414yescomplemented
275C4×D61—48no—
276#92418—22no—
277#92418—42no—
278#92418—41no—
279D4×#102—611nomaximal, Sylow
280C22×C61—24no—
281C22×C61—24no—
282C22×C61—24no—
283C22×C61—24no—
284C22×C61—24no—
285C22×C61—24no—
286C22×C61C2×#10218yescomplemented
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61D4211yescharacteristic
289C22×C61#54611yescharacteristic
290C22×C61C22×D811yescharacteristic
291C22×C61C22×SD1611yescharacteristic
292C22×C61#57611yescharacteristic
293C22×C61#57711yescharacteristic
294C2×D61—24no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—44no—
302C2×D61—44no—
303C2×D61—44no—
304C2×D61—832no—
305C2×D61—82no—
306C2×D61—82no—
307C2×D61—82no—
308C2×D61—82no—
309C4×C61—24no—
310C4×C61—22no—
311C4×C61—42no—
312C4×C61—82no—
313C4×C61—81no—
314C4×C61C2×#10214yescomplemented
315C4×C61C2×C4×D411yescharacteristic
316C4×C61#51811yescharacteristic
317C4×C61D4211yescharacteristic
318C4×C61#54611yescharacteristic
319Dic61—42no—
320C2×D42—611no—
321C2×C8×D4—611no—
322C22×#102—612no—
323D4×C4⋊C4D6111yescharacteristic, complemented
324#1982—611no—
325#1957—611no—
326#1893—612no—
327#1874—612no—
328#1802—611no—
329#1786—612no—
330C4×#102—611no—
331C2×C61—28no—
332C2×C61D4×C22⋊C411yescharacteristic
333C2×C61C22×#10211yescharacteristic
334C2×C61#289711yescharacteristic
335C2×C61D4×D811yescharacteristic
336C2×C61D4×SD1611yescharacteristic
337C2×C61#329411yescharacteristic
338C2×C61#329511yescharacteristic
339D61—44no—
340D61—84no—
341C23×D4—612no—
342C23×D4—1221no—
343C23×C8—612no—
344D42—618no—
345D42—1224no—
346C2×#127—611no—
347C2×#121—612no—
348C2×#121—1221no—
349C2×#120—1222no—
350C2×C4×D4—21no—
351C2×C4×D4—611no—
352C2×C4×D4C2×D6111yescharacteristic
353C22×C4⋊C4C2×D6112yescomplemented
354C8×D4—1224no—
355C2×C4⋊C8—611no—
356C2×#102—611no—
357C2×#102—612no—
358C2×#102—611no—
359C2×#102—612no—
360C2×#102—612no—
361C2×#102—612no—
362C2×#102—612no—
363C2×#102—1228no—
364C2×C22⋊C8—612no—
365C2×C4×C8—611no—
366#389—21no—
367#385—22no—
368#384C2×D6111yescharacteristic, complemented
369#380C2×D6112yescomplemented
370C4×C4⋊C4C2×D6111yescharacteristic, complemented
371#340—612no—
372#340—611no—
373#340—611no—
374C61D4×#10211yescharacteristic, complemented, Sylow
375C25—1222no—
376C22×D4—618no—
377C22×D4—611no—
378C22×D4—612no—
379C22×D4—1224no—
380C22×D4—1224no—
381C22×D4—1222no—
382C22×D4—1228no—
383C22×D4—1224no—
384C22×D4—1221no—
385C22×D4—1222no—
386C22×D4—1221no—
387C22×D4—2442no—
388C22×D4—2442no—
389C22×D4—2444no—
390C22×D4—2444no—
391C22×D4C22⋊D6111yescharacteristic
392C23×C4—22no—
393C23×C4—1221no—
394C23×C4C22×D6112yes—
395C22×C8—611no—
396C22×C8—612no—
397C22×C8—611no—
398C22×C8—1224no—
399C22×C8—1224no—
400C22×C8—2442no—
401#127—614no—
402#127—1222no—
403#121—618no—
404#121—1224no—
405#121—1228no—
406#120—12216no—
407C4×D4—44no—
408C4×D4—614no—
409C4×D4—1222no—
410C4×D4C4×D6114yes—
411C4×D4D24414yes—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4C22⋊D6111yescharacteristic
419C2×C4⋊C4C22×D6112yes—
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C4⋊C4C22×D6111yescharacteristic
422C2×C22⋊C4—22no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1222no—
425C2×C22⋊C4C22⋊D6112yes—
426C2×C42—21no—
427C2×C42C22×D6111yescharacteristic
428C4⋊C8—1222no—
429#102—614no—
430#102—1224no—
431#102—1222no—
432#102—1224no—
433#102—1224no—
434#102—2442no—
435#102—2442no—
436C22⋊C8—1224no—
437C4×C8—1222no—
438#95—21no—
439#95—22no—
440C24—1221no—
441C24—1228no—
442C24—1222no—
443C24—4882no—
444C24—4882no—
445C24—2444no—
446C24—2444no—
447C24—2444no—
448C24—2444no—
449C24C2×C22⋊D6112yes—
450C2×D4—612no—
451C2×D4—614no—
452C2×D4—612no—
453C2×D4—612no—
454C2×D4—12216no—
455C2×D4—1228no—
456C2×D4—1222no—
457C2×D4—1221no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1221no—
461C2×D4—1222no—
462C2×D4—1221no—
463C2×D4—1222no—
464C2×D4—1224no—
465C2×D4—1228no—
466C2×D4—1224no—
467C2×D4—4881no—
468C2×D4—4881no—
469C2×D4—2448no—
470C2×D4—2448no—
471C2×D4—2448no—
472C2×D4—2444no—
473C2×D4—2444no—
474C2×D4—2444no—
475C2×D4—2444no—
476C2×D4—24432no—
477C2×D4—2442no—
478C2×D4—2442no—
479C2×D4#1175819814yes—
480C2×D4#1175819914yes—
481C2×D4#1175820114yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—82no—
492C22×C4—1221no—
493C22×C4—1224no—
494C22×C4—2442no—
495C22×C4—2442no—
496C22×C4C2×C4×D6114yes—
497C22×C4C2×D24414yes—
498C22×C4C2×C22⋊D6111yescharacteristic
499C22×C4C2×C22⋊D6112yes—
500C22×C4C2×C22⋊D6111yescharacteristic
501C22×C4C23×D6111yescharacteristic
502C2×C8—612no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1222no—
506C2×C8—1221no—
507C2×C8—1222no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1222no—
511C2×C8—2448no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—44no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4—612no—
521C4⋊C4—1221no—
522C4⋊C4#1175819814yes—
523C4⋊C4D4×D6112yescomplemented
524C22⋊C4—44no—
525C22⋊C4—1224no—
526C22⋊C4—1228no—
527C22⋊C4#1175819818yes—
528C42—42no—
529C42C2×C4×D6112yes—
530C42C2×D24412yes—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—1222no—
536C23—1222no—
537C23—1222no—
538C23—1224no—
539C23—4888no—
540C23—4888no—
541C23—4888no—
542C23—4888no—
543C23—4888no—
544C23—24416no—
545C23—24416no—
546C23—2442no—
547C23—2442no—
548C23—2442no—
549C23—2442no—
550C23—2442no—
551C23—2442no—
552C23—2441no—
553C23—2441no—
554C23—2441no—
555C23—2441no—
556C23C2×#1175819814yes—
557C23C2×#1175819914yes—
558C23C2×#1175820114yes—
559C23C22×C22⋊D6111yescharacteristic
560D4—614no—
561D4—1224no—
562D4—1222no—
563D4—1224no—
564D4—1222no—
565D4—1222no—
566D4—4884no—
567D4—24416no—
568D4—24416no—
569D4—2448no—
570D4—2442no—
571D4—2442no—
572D4#14519697116yesdirect product factor
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—88no—
591C2×C4—1222no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2448no—
595C2×C4C2×#1175819812yes—
596C2×C4C2×#1175819814yes—
597C2×C4C2×#1175819812yes—
598C2×C4C2×#1175819912yes—
599C2×C4C2×#1175820112yes—
600C2×C4C22×C4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C22×D24411yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4#1451982211yescharacteristic
605C2×C4#1451982311yescharacteristic
606C8—1222no—
607C8—2442no—
608C8—2441no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—1224no—
616C22—48832no—
617C22—4882no—
618C22—4882no—
619C22—4882no—
620C22—4882no—
621C22—2444no—
622C22—2444no—
623C22—2444no—
624C22—2442no—
625C22—2442no—
626C22—2442no—
627C22—2442no—
628C22—2442no—
629C22—2442no—
630C22C2×#1451969718yescomplemented
631C22C22×#1175819811yescharacteristic
632C22D4×C22⋊D6111yescharacteristic
633C22#1684040011yescharacteristic
634C22C22×#1175819911yescharacteristic
635C22C22×#1175820111yescharacteristic
636C22#1684056511yescharacteristic
637C22#1684057011yescharacteristic
638C4—22no—
639C4—24no—
640C4—42no—
641C4—82no—
642C4—81no—
643C4—2442no—
644C4C2×#1451969714yescomplemented
645C4C4×D4×D6111yescharacteristic
646C4#1684023411yescharacteristic
647C4D4×D24411yescharacteristic
648C4#1684040711yescharacteristic
649C2—28no—
650C2—4884no—
651C2—2444no—
652C2D4×#1175819811yescharacteristic
653C2C22×#1451969711yescharacteristic
654C2#2145434211yescharacteristic
655C2D4×#1175819911yescharacteristic
656C2D4×#1175820111yescharacteristic
657C2#2145762611yescharacteristic
658C2#2145763711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×C4⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×D4×D244C2
cosocleC22×C4×C61C24
hypercenterD4×C4⋊C4D61
hypocenterC61D4×#102
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D4×#92418C2semidirect
3. C22×#14519697C2semidirect
4. #21446746C2semidirect
5. #21446624C2semidirect
6. #21446245C2semidirect
7. #21446136C2semidirect
8. #21445816C2semidirect
9. #21445749C2semidirect
10. C4×#14519697C2semidirect
11. D4×C4⋊C4×C61C2semidirect
14. C23×#92418C22semidirect
16. D4×D244C4semidirect
23. C2×C4⋊#92418C22semidirect
28. C2×#14519697C22semidirect
29. C2×#14519697C22semidirect
30. C2×#14519697C22semidirect
31. C2×#14519697C22semidirect
32. C2×C22⋊#92418C22semidirect
33. C2×C4×#92418C22semidirect
34. #16839524C22semidirect
35. #16839524C22semidirect
36. #16839524C22semidirect
39. C22×C4⋊C4×C61C22semidirect
42. C61×#384C22semidirect
43. C61×#380C22semidirect
44. C4×C4⋊C4×C61C22semidirect
54. C22×D244C2×C4semidirect
69. #14519774C2×C4semidirect
72. #14519751C2×C4semidirect
75. C4×D244C2×C4semidirect
86. #14519697D4direct (N × H)
181. C4⋊C4×C61C2×D4semidirect
200. C2×#92418C2×D4semidirect
230. D4×C61#102semidirect
274. D244C4×D4semidirect
286. C22×C61C2×#102semidirect
314. C4×C61C2×#102semidirect
323. D4×C4⋊C4D61semidirect
353. C22×C4⋊C4C2×D61semidirect
368. #384C2×D61semidirect
369. #380C2×D61semidirect
370. C4×C4⋊C4C2×D61semidirect
374. C61D4×#102semidirect
523. C4⋊C4D4×D61semidirect
572. D4#14519697direct (N × H)
630. C22C2×#14519697semidirect
644. C4C2×#14519697semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D2442
C2×D4×#924182
C22×#145196972
#214467462
#214466242
#214462452
#214461362
#214458162
#214457492
C4×#145196972
D4×C4⋊C4×C612
D4×#10261