Finite Group Databasebeta

← #29695422

Subgroups — #29695422

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×#16840397C211yesmaximal, characteristic
2C2×#16839827C211yesmaximal, characteristic, complemented
3C2×#102×D61C212yesmaximal, complemented
4C4⋊C4×D244C211yesmaximal, characteristic, complemented
5#21446626C211yesmaximal, characteristic, complemented
6#21446244C212yesmaximal, complemented
7#21446133C212yesmaximal, complemented
8#21445820C211yesmaximal, characteristic, complemented
9#21445748C212yesmaximal, complemented
10C4×#14519697C211yesmaximal, characteristic, complemented
11C61×#1982C211yesmaximal, characteristic, complemented
12C22×D4×D61—21no—
13C22×D4×D61C2212yes—
14C22×C8×D61C2212yescomplemented
15#16840397—24no—
16#16840397C418yescomplemented
17C2×#14519748—21no—
18C2×#14519748C2212yes—
19C2×#14519745—22no—
20C2×C4×D244—21no—
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C4⋊C4×D61C2212yescomplemented
24#16839827—24no—
25C2×#14519699C2212yes—
26C2×#14519698C2212yescomplemented
27C2×#14519698C2212yescomplemented
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30#102×D61—28no—
31C2×#14519689C2212yescomplemented
32C2×C4×#92418C2211yescharacteristic, complemented
33#16839660—21no—
34#16839636—22no—
35#16839632C2211yescharacteristic, complemented
36#16839619C2212yescomplemented
37#16839525C2212yescomplemented
38#16839524C2211yescharacteristic, complemented
39#16839524C2211yescharacteristic, complemented
40C2×#127×C61C2211yescharacteristic
41C2×C4⋊C8×C61C2211yescharacteristic, complemented
42C2×#102×C61C2212yescomplemented
43C2×#102×C61C2212yescomplemented
44C4×C4⋊C4×C61C2211yescharacteristic, complemented
45C24×D61—22no—
46C22×D244D411yescharacteristic
47C22×D244C2311yescharacteristic
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C2×D4×D61—28no—
51C2×D4×D61—24no—
52C2×D4×D61—24no—
53C2×D4×D61—24no—
54C2×D4×D61—42no—
55C2×D4×D61—42no—
56C2×D4×D61—44no—
57C2×D4×D61—44no—
58C2×D4×D61C2×C418yescomplemented
59C22×C4×D61—21no—
60C22×C4×D61—22no—
61C22×C4×D61C2312yes—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C2×C8×D61—24no—
65C2×C8×D61—24no—
66C2×C8×D61—42no—
67#14519748—24no—
68#14519748—28no—
69#14519748C2×C418yescomplemented
70#14519745—216no—
71C4×D244—22no—
72C4×D244—44no—
73C4×D244C2×C414yes—
74C4×D244C2×C414yescomplemented
75C4×D244D414yes—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61D411yescharacteristic
79C2×C4⋊Dic61C2312yes—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—22no—
82C4⋊C4×D61—24no—
83C4⋊C4×D61—42no—
84C2×C22⋊Dic61—22no—
85C2×#11758198—21no—
86C2×#11758198—22no—
87C2×#11758198D412yes—
88#14519699—24no—
89#14519698—24no—
90#14519698—42no—
91#14519697—22no—
92#14519697D414yescomplemented
93#14519689—24no—
94C4×#92418—22no—
95#14519684—22no—
96C22×D4×C61—21no—
97C22×D4×C61—21no—
98C22×D4×C61C2312yes—
99C22×C8×C61C2312yes—
100#127×C61—22no—
101#127×C61C2×C414yescomplemented
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C42×C61—21no—
105C2×C42×C61C2311yescharacteristic
106C4⋊C8×C61—22no—
107#102×C61—24no—
108#102×C61—42no—
109#95×C61—21no—
110C24×C61—22no—
111C23×D61—21no—
112C23×D61—28no—
113C23×D61—44no—
114C23×D61—44no—
115C23×D61—44no—
116C23×D61—44no—
117C23×D61—82no—
118C23×D61—82no—
119C23×D61C2×D412yes—
120C2×D4×C61—24no—
121C2×D4×C61—24no—
122C2×D4×C61—22no—
123C2×D4×C61—22no—
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C2×D4×C61—22no—
127C2×D4×C61—42no—
128C2×D4×C61—42no—
129C2×D4×C61—81no—
130C2×D4×C61—81no—
131C2×D4×C61C22×C414yes—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C2×C22⋊D61—28no—
138C2×C22⋊D61—28no—
139C2×C22⋊D61—44no—
140C2×C22⋊D61—44no—
141C2×C22⋊D61—44no—
142C2×C22⋊D61—44no—
143C22×Dic61—21no—
144C22×Dic61—22no—
145C22×Dic61C2×D412yes—
146D4×D61—216no—
147D4×D61—48no—
148D4×D61—48no—
149D4×D61—48no—
150D4×D61—432no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244C22⋊C414yes—
155C2×D244D814yes—
156C2×D244SD1614yes—
157C2×D244C22×C412yes—
158C2×D244C2×D412yes—
159C2×D244#4112yes—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—24no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61—44no—
168C2×C4×D61—44no—
169C2×C4×D61—82no—
170C2×C4×D61C22×C414yes—
171C2×C4×D61C2×D414yes—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61C2×D412yescomplemented
179C42×C61—42no—
180C42×C61C22×C412yes—
181C42×C61C2×D412yes—
182C22⋊Dic61—28no—
183#11758198—24no—
184#11758198—44no—
185#11758198C22⋊C418yes—
186C4⋊Dic61—21no—
187C4⋊Dic61—22no—
188C4⋊Dic61—22no—
189C4⋊Dic61—42no—
190C4⋊Dic61—81no—
191C4⋊Dic61C22⋊C414yes—
192C4⋊Dic61C22×C412yes—
193#11758196—44no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C2×D412yescomplemented
200C8×D61—48no—
201C23×C61—24no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61C22×D411yescharacteristic
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—416no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—416no—
222C22×D61—88no—
223C22×D61—88no—
224C22×D61—88no—
225C22×D61—88no—
226C22×D61—88no—
227C22×D61C2×C22⋊C414yes—
228C22×D61C2×D814yes—
229C22×D61C2×SD1614yes—
230D4×C61—24no—
231D4×C61—24no—
232D4×C61—42no—
233D4×C61—42no—
234D4×C61—48no—
235D4×C61—84no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—22no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61C2×C22⋊C412yes—
245C2×C4×C61C2×C22⋊C412yes—
246C2×C4×C61C2×D812yes—
247C2×C4×C61C2×SD1612yes—
248C2×C4×C61C23×C411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C2×C4×C61H(5,𝔽2)11yescharacteristic
254C22⋊D61—416no—
255C22⋊D61—416no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61C2×C22⋊C414yes—
265D244—22no—
266D244—22no—
267D244—22no—
268D244#102116yescomplemented
269D244C4×D414yescomplemented
270C4×D61—24no—
271C4×D61—24no—
272C4×D61—24no—
273C4×D61—24no—
274C4×D61—48no—
275C4×D61—88no—
276C8×C61—42no—
277#92418—22no—
278#92418—41no—
279D4×#102—611nomaximal, Sylow
280C22×C61—44no—
281C22×C61—44no—
282C22×C61—44no—
283C22×C61—82no—
284C22×C61—82no—
285C22×C61—82no—
286C22×C61—82no—
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—24no—
296C2×D61—24no—
297C2×D61—24no—
298C2×D61—24no—
299C2×D61—24no—
300C2×D61—24no—
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—42no—
307C2×D61—832no—
308C2×D61C2×#10218yescomplemented
309C4×C61—22no—
310C4×C61—42no—
311C4×C61—81no—
312C4×C61C2×#10214yescomplemented
313C4×C61C2×C4×D411yescharacteristic
314C4×C61#51811yescharacteristic
315C4×C61D4211yescharacteristic
316C4×C61#54611yescharacteristic
317Dic61—24no—
318Dic61—42no—
319Dic61—82no—
320C2×D42—611no—
321C2×C8×D4—611no—
322C22×#102—612no—
323D4×C4⋊C4—611no—
324#1982D6111yescharacteristic, complemented
325#1957—611no—
326#1893—612no—
327#1874—612no—
328#1802—611no—
329#1786—612no—
330C4×#102—611no—
331C2×C61—84no—
332C2×C61D4×C22⋊C411yescharacteristic
333C2×C61C22×#10211yescharacteristic
334C2×C61#289711yescharacteristic
335C2×C61D4×D811yescharacteristic
336C2×C61D4×SD1611yescharacteristic
337C2×C61#329411yescharacteristic
338C2×C61#329511yescharacteristic
339D61—28no—
340D61—44no—
341C23×D4—612no—
342C23×D4—1221no—
343C23×C8—612no—
344D42—618no—
345D42—1224no—
346C2×#127C2×D6111yescharacteristic
347C2×#121—612no—
348C2×#121—1221no—
349C2×#120—1222no—
350C2×C4×D4—611no—
351C2×C4×D4—611no—
352C2×C4×D4—1221no—
353C22×C4⋊C4—612no—
354C8×D4—1224no—
355C2×C4⋊C8C2×D6111yescharacteristic, complemented
356C2×#102—611no—
357C2×#102—612no—
358C2×#102—612no—
359C2×#102—611no—
360C2×#102—612no—
361C2×#102—1228no—
362C2×#102C2×D6112yescomplemented
363C2×#102C2×D6112yescomplemented
364C2×C22⋊C8—612no—
365C2×C4×C8—611no—
366#389—1221no—
367#385—1222no—
368#384—611no—
369#380—612no—
370C4×C4⋊C4C2×D6111yescharacteristic, complemented
371#340—612no—
372#340—611no—
373#340—611no—
374C61D4×#10211yescharacteristic, complemented, Sylow
375C25—1222no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—618no—
379C22×D4—611no—
380C22×D4—611no—
381C22×D4—1224no—
382C22×D4—1222no—
383C22×D4—1224no—
384C22×D4—1224no—
385C22×D4—1228no—
386C22×D4—1222no—
387C22×D4—2442no—
388C22×D4—2442no—
389C22×D4—2444no—
390C22×D4—2444no—
391C22×D4C22×D6112yes—
392C23×C4—612no—
393C23×C4—1222no—
394C23×C4—1221no—
395C22×C8—611no—
396C22×C8—611no—
397C22×C8—1224no—
398C22×C8—1224no—
399C22×C8—2442no—
400C22×C8C22×D6112yes—
401#127—22no—
402#127C4×D6114yescomplemented
403#121—618no—
404#121—1228no—
405#121—1224no—
406#120—12216no—
407C4×D4—614no—
408C4×D4—614no—
409C4×D4—614no—
410C4×D4—1222no—
411C4×D4—2444no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—612no—
415C2×C4⋊C4—1224no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1222no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—2442no—
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C4⋊C4C22×D6111yescharacteristic
422C2×C22⋊C4—612no—
423C2×C22⋊C4—1222no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1222no—
426C2×C42—21no—
427C2×C42C22×D6111yescharacteristic
428C4⋊C8—22no—
429#102—24no—
430#102—42no—
431#102—614no—
432#102—1222no—
433#102—1224no—
434#102—1224no—
435#102—2442no—
436C22⋊C8—1224no—
437C4×C8—1222no—
438#95—21no—
439#95—1222no—
440C24—22no—
441C24—612no—
442C24—1228no—
443C24—1221no—
444C24—4882no—
445C24—4882no—
446C24—2444no—
447C24—2444no—
448C24—2444no—
449C24—2444no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4—612no—
462C2×D4—612no—
463C2×D4—612no—
464C2×D4—614no—
465C2×D4—614no—
466C2×D4—614no—
467C2×D4—1228no—
468C2×D4—12216no—
469C2×D4—1228no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—1221no—
473C2×D4—2448no—
474C2×D4—2448no—
475C2×D4—2448no—
476C2×D4—2444no—
477C2×D4—2444no—
478C2×D4—24432no—
479C2×D4—2444no—
480C2×D4—2444no—
481C2×D4C2×C4×D6114yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—612no—
485C22×C4—614no—
486C22×C4—614no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1221no—
492C22×C4—1224no—
493C22×C4—1222no—
494C22×C4—4882no—
495C22×C4—2444no—
496C22×C4—2444no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4D4×D6111yescharacteristic
500C22×C4D4×D6111yescharacteristic
501C22×C4C23×D6111yescharacteristic
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—612no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—2448no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—614no—
516C4⋊C4—612no—
517C4⋊C4—1221no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—4881no—
521C4⋊C4—2444no—
522C4⋊C4—2442no—
523C4⋊C4D4×D6112yescomplemented
524C22⋊C4—618no—
525C22⋊C4—1228no—
526C22⋊C4—1224no—
527C22⋊C4—2444no—
528C42—42no—
529C42C2×C4×D6112yes—
530C42D4×D6112yes—
531C23—24no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—614no—
539C23—614no—
540C23—614no—
541C23—1222no—
542C23—1222no—
543C23—1222no—
544C23—1222no—
545C23—1222no—
546C23—1222no—
547C23—1222no—
548C23—4888no—
549C23—4888no—
550C23—4888no—
551C23—4888no—
552C23—4888no—
553C23—24416no—
554C23—24416no—
555C23—2441no—
556C23—2441no—
557C23—2441no—
558C23—2441no—
559C23C2×D4×D6111yescharacteristic
560D4—24no—
561D4—24no—
562D4—48no—
563D4—42no—
564D4—42no—
565D4—84no—
566D4—614no—
567D4—6116no—
568D4—1222no—
569D4—1222no—
570D4—1222no—
571D4—24416no—
572D4—24416no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—614no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1224no—
587C2×C4—1224no—
588C2×C4—1222no—
589C2×C4—4888no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2448no—
596C2×C4C22⋊C4×D6112yes—
597C2×C4C22⋊C4×D6112yes—
598C2×C4D8×D6112yes—
599C2×C4SD16×D6112yes—
600C2×C4C22×C4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C2×D4×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4#1451982211yescharacteristic
605C2×C4#1451982311yescharacteristic
606C8—42no—
607C8—1222no—
608C8—2441no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—618no—
617C22—1224no—
618C22—1224no—
619C22—1224no—
620C22—1224no—
621C22—1224no—
622C22—1224no—
623C22—1224no—
624C22—48832no—
625C22—2442no—
626C22—2442no—
627C22—2442no—
628C22—2442no—
629C22—2442no—
630C22—2442no—
631C22C2×C22⋊C4×D6111yescharacteristic
632C22#1684039611yescharacteristic
633C22#1684040911yescharacteristic
634C22C2×D8×D6111yescharacteristic
635C22C2×SD16×D6111yescharacteristic
636C22#1684056611yescharacteristic
637C22#1684057211yescharacteristic
638C4—22no—
639C4—42no—
640C4—81no—
641C4—1224no—
642C4—4882no—
643C4—2442no—
644C4#102×D6114yescomplemented
645C4C4×D4×D6111yescharacteristic
646C4#1684023411yescharacteristic
647C4#1684039711yescharacteristic
648C4#1684040511yescharacteristic
649C2—84no—
650C2—1228no—
651C2—2444no—
652C2#2144864011yescharacteristic
653C2C2×#102×D6111yescharacteristic
654C2#2145434411yescharacteristic
655C2#2145749111yescharacteristic
656C2#2145751011yescharacteristic
657C2#2145763511yescharacteristic
658C2#2145764611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1982C2
socleC23×C61C22×D4
prime radicalC2×#16840397C2
cosocleC22×C4×C61C24
hypercenter#1982D61
hypocenterC61D4×#102
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#16839827C2semidirect
3. C2×#102×D61C2semidirect
4. C4⋊C4×D244C2semidirect
5. #21446626C2semidirect
6. #21446244C2semidirect
7. #21446133C2semidirect
8. #21445820C2semidirect
9. #21445748C2semidirect
10. C4×#14519697C2semidirect
11. C61×#1982C2semidirect
14. C22×C8×D61C22semidirect
16. #16840397C4semidirect
23. C2×C4⋊C4×D61C22semidirect
26. C2×#14519698C22semidirect
27. C2×#14519698C22semidirect
31. C2×#14519689C22semidirect
32. C2×C4×#92418C22semidirect
35. #16839632C22semidirect
36. #16839619C22semidirect
37. #16839525C22semidirect
38. #16839524C22semidirect
39. #16839524C22semidirect
41. C2×C4⋊C8×C61C22semidirect
42. C2×#102×C61C22semidirect
43. C2×#102×C61C22semidirect
44. C4×C4⋊C4×C61C22semidirect
58. C2×D4×D61C2×C4semidirect
69. #14519748C2×C4semidirect
74. C4×D244C2×C4semidirect
92. #14519697D4semidirect
101. #127×C61C2×C4semidirect
178. C4⋊C4×C61C2×D4semidirect
199. C2×#92418C2×D4semidirect
268. D244#102semidirect
269. D244C4×D4semidirect
308. C2×D61C2×#102semidirect
312. C4×C61C2×#102semidirect
324. #1982D61semidirect
355. C2×C4⋊C8C2×D61semidirect
362. C2×#102C2×D61semidirect
363. C2×#102C2×D61semidirect
370. C4×C4⋊C4C2×D61semidirect
374. C61D4×#102semidirect
402. #127C4×D61semidirect
523. C4⋊C4D4×D61semidirect
644. C4#102×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403972
C2×#168398272
C2×#102×D612
C4⋊C4×D2442
#214466262
#214462442
#214461332
#214458202
#214457482
C4×#145196972
C61×#19822
D4×#10261