Finite Group Databasebeta

← #29679942

Subgroups — #29679942

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic61C211yesmaximal, characteristic
2#21448197C212yesmaximal, complemented
3#21445891C212yesmaximal, complemented
4#21445805C214yesmaximal, complemented
5#21445734C211yesmaximal, characteristic
6#99×Dic61C214yesmaximal, complemented
7C61×#1781C211yesmaximal, characteristic
8C24×Dic61C411yescharacteristic, complemented
9C24×Dic61C2211yescharacteristic
10C2×D4×Dic61—22no—
11C2×D4×Dic61—22no—
12C2×D4×Dic61—22no—
13C2×D4×Dic61—22no—
14C2×D4×Dic61C412yescomplemented
15C2×D4×Dic61C412yescomplemented
16C2×D4×Dic61C2212yes—
17C2×D4×Dic61C2212yes—
18C2×#14519733—22no—
19C22×C4⋊Dic61C411yescharacteristic, complemented
20C22×C22⋊Dic61C411yescharacteristic, complemented
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C4×Dic61C411yescharacteristic, complemented
23C2×#14519692C2214yes—
24#16839623—22no—
25#16839620—22no—
26#16839620C2214yescomplemented
27#16839618C2212yes—
28C22⋊C4×Dic61—22no—
29C22⋊C4×Dic61C2214yescomplemented
30#16839528C2218yescomplemented
31C23×D4×C61C2211yescharacteristic
32C2×#99×C61C2214yes—
33C61×#379C2212yes—
34C23×Dic61—21no—
35C23×Dic61—21no—
36C23×Dic61—21no—
37C23×Dic61—21no—
38C23×Dic61—44no—
39C23×Dic61—44no—
40C23×Dic61C2×C411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C412yes—
44C23×Dic61C2×C412yes—
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61D412yes—
49C23×Dic61D412yes—
50C23×Dic61D412yes—
51C23×Dic61D412yes—
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54D4×Dic61—24no—
55D4×Dic61—24no—
56D4×Dic61—24no—
57D4×Dic61—24no—
58D4×Dic61—24no—
59D4×Dic61—24no—
60D4×Dic61—24no—
61D4×Dic61—24no—
62#14519733—48no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61C2×C412yes—
66C2×C4⋊Dic61C2×C412yes—
67C2×#11758196—24no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—22no—
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61C2×C412yes—
75C2×C22⋊Dic61C2×C412yes—
76C2×C22⋊Dic61C2×C412yes—
77C2×C22⋊Dic61C2314yes—
78C2×C22⋊Dic61C2312yes—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—24no—
84C2×C4×Dic61C2×C412yes—
85C2×C4×Dic61C2×C412yes—
86#14519692—28no—
87#14519684—24no—
88#14519684—24no—
89C25×C61C2×C411yescharacteristic
90C25×C61C2311yescharacteristic
91C22×D4×C61—22no—
92C22×D4×C61—22no—
93C22×D4×C61—28no—
94C22×D4×C61C2×C412yes—
95C22×D4×C61C2312yes—
96C23×C4×C61C2×C411yescharacteristic
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61C2314yes—
100#99×C61—28no—
101C24×C61—21no—
102C24×C61—21no—
103C24×C61—24no—
104C24×C61—24no—
105C24×C61—42no—
106C24×C61—42no—
107C24×C61—42no—
108C24×C61—42no—
109C24×C61C22×C411yescharacteristic
110C24×C61C22×C411yescharacteristic
111C24×C61C22×C412yes—
112C24×C61C2×D412yes—
113C24×C61C2×D412yes—
114C24×C61C2411yescharacteristic
115C2×D4×C61—216no—
116C2×D4×C61—216no—
117C2×D4×C61—24no—
118C2×D4×C61—24no—
119C2×D4×C61—24no—
120C2×D4×C61—24no—
121C2×D4×C61—24no—
122C2×D4×C61#4118yes—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—24no—
126C22×C4×C61—24no—
127C22×C4×C61C22×C412yes—
128C22×Dic61—24no—
129C22×Dic61—28no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—24no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—44no—
142C22×Dic61—44no—
143C22×Dic61—42no—
144C22×Dic61—42no—
145C22×Dic61—42no—
146C22×Dic61—44no—
147C22×Dic61—44no—
148C22×Dic61—44no—
149C22×Dic61—44no—
150C22×Dic61—44no—
151C22×Dic61—44no—
152C22×Dic61—44no—
153C22×Dic61—42no—
154C22×Dic61—42no—
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C22⋊C411yescharacteristic
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C22⋊C412yes—
159C22×Dic61C22⋊C412yes—
160C22×Dic61C22⋊C412yes—
161C22×Dic61C22⋊C412yes—
162C22×Dic61C22⋊C412yes—
163C22×Dic61C22⋊C412yes—
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C412yes—
168C22×Dic61C22×C412yes—
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D412yes—
173C22×Dic61C2×D412yes—
174C22×Dic61C2×D412yes—
175C22⋊C4×C61—28no—
176C22⋊C4×C61—44no—
177C22⋊C4×C61—44no—
178C22⋊Dic61—24no—
179C22⋊Dic61—24no—
180C22⋊Dic61—24no—
181C22⋊Dic61—24no—
182C22⋊Dic61—28no—
183C22⋊Dic61—44no—
184C22⋊Dic61—44no—
185C4⋊Dic61—24no—
186C4⋊Dic61—24no—
187#11758196—48no—
188C4×Dic61—22no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192C4×Dic61—48no—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—24no—
197C23×C61—24no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—24no—
202C23×C61—24no—
203C23×C61—24no—
204C23×C61—24no—
205C23×C61—41no—
206C23×C61—42no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—42no—
210C23×C61—41no—
211C23×C61—42no—
212C23×C61—416no—
213C23×C61—416no—
214C23×C61—42no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61C2×C22⋊C412yes—
220C23×C61C2×C22⋊C411yescharacteristic
221C23×C61C2×C22⋊C411yescharacteristic
222C23×C61#11714yescomplemented
223C23×C61C23×C411yescharacteristic
224C23×C61C22×D412yes—
225C23×C61C2×#4114yes—
226D4×C61—216no—
227D4×C61—216no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—44no—
233C2×C4×C61—44no—
234C2×C4×C61—44no—
235C2×C4×C61#11714yescomplemented
236C2×Dic61—22no—
237C2×Dic61—24no—
238C2×Dic61—24no—
239C2×Dic61—24no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—44no—
256C2×Dic61—44no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—44no—
262C2×Dic61—44no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—44no—
266C2×Dic61—44no—
267C2×Dic61—44no—
268C2×Dic61#9914yescomplemented
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C412yes—
272C2×Dic61C2×C22⋊C412yes—
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275#20722—611nomaximal, Sylow
276C22×C61—28no—
277C22×C61—22no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—22no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—24no—
289C22×C61—44no—
290C22×C61—48no—
291C22×C61—48no—
292C22×C61—44no—
293C22×C61—44no—
294C22×C61—44no—
295C22×C61—48no—
296C22×C61—48no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61C2×#9912yes—
300C22×C61#41012yes—
301C22×C61C22×C22⋊C411yescharacteristic
302C22×C61C2×#11712yes—
303C22×C61#52514yes—
304C4×C61—24no—
305C4×C61—84no—
306Dic61—21no—
307Dic61—21no—
308Dic61—22no—
309Dic61—22no—
310Dic61—42no—
311Dic61—42no—
312Dic61—84no—
313Dic61C2×#9912yes—
314Dic61C2×#9912yes—
315C22×C4×D4—611no—
316#2280—612no—
317#1819—612no—
318#1799—614no—
319#1781—611no—
320#1781D6111yescharacteristic
321C4×#99—614no—
322C2×C61—24no—
323C2×C61—22no—
324C2×C61—22no—
325C2×C61—22no—
326C2×C61—42no—
327C2×C61—44no—
328C2×C61#228011yescharacteristic
329C2×C61C22×#9911yescharacteristic
330C2×C61C2×#41011yescharacteristic
331C23×D4C2×D6111yescharacteristic
332C24×C4—611no—
333C24×C4—611no—
334C2×C4×D4—612no—
335C2×C4×D4—612no—
336C2×C4×D4—612no—
337C2×C4×D4—612no—
338C2×C4×D4—1222no—
339C2×C4×D4—1222no—
340C2×C4×D4—1222no—
341C2×C4×D4—1222no—
342C2×#117—1222no—
343C22×C4⋊C4—611no—
344C22×C22⋊C4—611no—
345C22×C22⋊C4—611no—
346C22×C42—611no—
347C2×#99—614no—
348C2×#99C2×D6114yes—
349#381—1222no—
350#380—614no—
351#380—1222no—
352#379—612no—
353#379C2×D6112yes—
354C4×C22⋊C4—614no—
355C4×C22⋊C4—1222no—
356#342—618no—
357C61#2072211yescharacteristic, complemented, Sylow
358C25C4×D6111yescharacteristic
359C25C22×D6111yescharacteristic
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—28no—
363C22×D4C4×D6112yes—
364C22×D4C22×D6112yes—
365C23×C4—611no—
366C23×C4—612no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—612no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—612no—
378C23×C4—612no—
379C23×C4—1221no—
380C23×C4—1221no—
381C23×C4—1221no—
382C23×C4—1221no—
383C23×C4—2444no—
384C23×C4—2444no—
385C23×C4C4×D6111yescharacteristic
386C4×D4—1224no—
387C4×D4—1224no—
388C4×D4—1224no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1224no—
392C4×D4—1224no—
393C4×D4—1224no—
394#117—2448no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—1222no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1224no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—612no—
403C2×C22⋊C4—612no—
404C2×C22⋊C4—612no—
405C2×C22⋊C4—612no—
406C2×C22⋊C4—614no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1222no—
410C2×C22⋊C4—1222no—
411C2×C22⋊C4—1222no—
412C2×C22⋊C4—1222no—
413C2×C22⋊C4C22×D6114yes—
414C2×C42—612no—
415C2×C42—612no—
416C2×C42—1221no—
417C2×C42—1221no—
418C2×C42—1221no—
419C2×C42—1221no—
420C2×C42—1224no—
421#99—28no—
422#99—1228no—
423#95—1224no—
424#95—1224no—
425C24—24no—
426C24—21no—
427C24—21no—
428C24—24no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24C2×C4×D6111yescharacteristic
434C24C2×C4×D6111yescharacteristic
435C24C2×C4×D6112yes—
436C24D4×D6112yes—
437C24D4×D6112yes—
438C24C23×D6111yescharacteristic
439C2×D4—216no—
440C2×D4—216no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4#1175822418yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—612no—
460C22×C4—612no—
461C22×C4—612no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—612no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—1228no—
472C22×C4—1224no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1224no—
482C22×C4—2444no—
483C22×C4—2442no—
484C22×C4—2444no—
485C22×C4—2442no—
486C22×C4—2444no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4—2444no—
491C22×C4—2444no—
492C22×C4—2444no—
493C22×C4—2444no—
494C22×C4—2444no—
495C22×C4—2444no—
496C22×C4—2442no—
497C22×C4—2442no—
498C22×C4C2×C4×D6112yes—
499C4⋊C4—1224no—
500C4⋊C4—1224no—
501C4⋊C4—2448no—
502C22⋊C4—28no—
503C22⋊C4—44no—
504C22⋊C4—44no—
505C22⋊C4—1224no—
506C22⋊C4—1224no—
507C22⋊C4—1224no—
508C22⋊C4—1224no—
509C22⋊C4—1228no—
510C22⋊C4—2444no—
511C22⋊C4—2444no—
512C42—1222no—
513C42—1222no—
514C42—1222no—
515C42—1222no—
516C42—2448no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—24no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—416no—
539C23—416no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23C22⋊C4×D6112yes—
544C23C22⋊C4×D6111yescharacteristic
545C23C22⋊C4×D6111yescharacteristic
546C23#1451973314yescomplemented
547C23C22×C4×D6111yescharacteristic
548C23C2×D4×D6112yes—
549C23C2×#1175822414yes—
550D4—216no—
551D4—216no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—614no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—1224no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—1224no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1224no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—2444no—
579C2×C4—2444no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2444no—
588C2×C4—2444no—
589C2×C4—2444no—
590C2×C4—2444no—
591C2×C4—2444no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4#1451973314yescomplemented
599C22—28no—
600C22—21no—
601C22—21no—
602C22—22no—
603C22—21no—
604C22—21no—
605C22—22no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—24no—
610C22—22no—
611C22—22no—
612C22—44no—
613C22—48no—
614C22—48no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—48no—
619C22—48no—
620C22—42no—
621C22—42no—
622C22#99×D6112yes—
623C22#1683973412yes—
624C22C2×C22⋊C4×D6111yescharacteristic
625C22C2×#1451973312yes—
626C22#1684026814yes—
627C4—24no—
628C4—84no—
629C4—612no—
630C4—612no—
631C4—1222no—
632C4—1222no—
633C4—1221no—
634C4—1221no—
635C4—4884no—
636C4—2442no—
637C4—2442no—
638C2—24no—
639C2—22no—
640C2—22no—
641C2—22no—
642C2—42no—
643C2—44no—
644C2#2144819711yescharacteristic
645C2C2×#99×D6111yescharacteristic
646C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1781C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D4×C61C22
cosocleC24×C61C24
hypercenter#1781D61
hypocenterC61#20722
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
2. #21448197C2semidirect
3. #21445891C2semidirect
4. #21445805C2semidirect
6. #99×Dic61C2semidirect
8. C24×Dic61C4semidirect
14. C2×D4×Dic61C4semidirect
15. C2×D4×Dic61C4semidirect
19. C22×C4⋊Dic61C4semidirect
20. C22×C22⋊Dic61C4semidirect
22. C22×C4×Dic61C4semidirect
26. #16839620C22semidirect
29. C22⋊C4×Dic61C22semidirect
30. #16839528C22semidirect
222. C23×C61#117semidirect
235. C2×C4×C61#117semidirect
268. C2×Dic61#99semidirect
357. C61#20722semidirect
546. C23#14519733semidirect
598. C2×C4#14519733semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic612
#214481972
#214458912
#214458052
#214457342
#99×Dic612
C61×#17812
#2072261