Finite Group Databasebeta

← #29611237

Subgroups — #29611237

Order 15616.

2430 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic61C211yesmaximal, characteristic
2C2×#16839647C212yesmaximal, complemented
3C2×#16839637C211yesmaximal, characteristic
4C2×#16839635C211yesmaximal, characteristic
5#21444054C212yesmaximal, complemented
6#21444053C212yesmaximal, complemented
7#21444043C212yesmaximal, complemented
8#21444041C211yesmaximal, characteristic
9#21444041C211yesmaximal, characteristic
10#21444041C211yesmaximal, characteristic
11C61×C22⋊#95C211yesmaximal, characteristic
12C24×Dic61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2212yes—
15C22×#11758196C2211yescharacteristic
16C22×#11758196C2211yescharacteristic
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C4×Dic61—28no—
20C22×C4×Dic61—24no—
21C22×C4×Dic61C2212yes—
22C22×C4×Dic61C2212yes—
23#16839647—28no—
24#16839637C418yescomplemented
25#16839635—24no—
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C24×C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C23×Dic61—22no—
41C23×Dic61—22no—
42C23×Dic61—22no—
43C23×Dic61—22no—
44C23×Dic61—24no—
45C23×Dic61—24no—
46C23×Dic61—24no—
47C23×Dic61—24no—
48C23×Dic61C2×C414yes—
49C23×Dic61Q814yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2312yes—
55C23×Dic61C2312yes—
56C2×C4⋊Dic61—24no—
57C2×C4⋊Dic61—24no—
58C2×C4⋊Dic61C2×C418yescomplemented
59C2×#11758196—22no—
60C2×#11758196—22no—
61C2×#11758196—24no—
62C2×#11758196—24no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—22no—
66C2×C22⋊Dic61—22no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61C2×C414yes—
69C2×C4×Dic61—232no—
70C2×C4×Dic61—24no—
71C2×C4×Dic61—24no—
72C2×C4×Dic61—24no—
73C2×C4×Dic61—24no—
74C2×C4×Dic61—24no—
75C2×C4×Dic61D418yes—
76#14519684—22no—
77#14519684—22no—
78#14519684—24no—
79#14519684—24no—
80#14519684—24no—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684C2×C418yescomplemented
85C25×C61C2311yescharacteristic
86C23×C4×C61—22no—
87C23×C4×C61—22no—
88C23×C4×C61—24no—
89C23×C4×C61—24no—
90C23×C4×C61D414yes—
91C23×C4×C61C2312yes—
92C23×C4×C61C2312yes—
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C2×C22⋊C4×C61—22no—
96C2×C22⋊C4×C61—22no—
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61C2×C414yes—
101#95×C61—24no—
102#95×C61—24no—
103C24×C61—22no—
104C24×C61—22no—
105C24×C61—22no—
106C24×C61—22no—
107C24×C61C22×C412yes—
108C24×C61C2×D412yes—
109C24×C61C2×Q812yes—
110C24×C61#4112yes—
111C24×C61#4112yes—
112C24×C61#4112yes—
113C24×C61#4112yes—
114C24×C61C2411yescharacteristic
115C22×C4×C61—216no—
116C22×C4×C61—216no—
117C22×C4×C61—28no—
118C22×C4×C61—22no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—28no—
125C22×C4×C61—28no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61C22×C414yes—
140C22×C4×C61C2×D412yes—
141C22×C4×C61C2×D414yes—
142C22×C4×C61C2×D412yes—
143C22×C4×C61#4114yes—
144C22×Dic61—216no—
145C22×Dic61—216no—
146C22×Dic61—28no—
147C22×Dic61—28no—
148C22×Dic61—28no—
149C22×Dic61—28no—
150C22×Dic61—28no—
151C22×Dic61—28no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—216no—
161C22×Dic61—216no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—21no—
171C22×Dic61—22no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61C22×C412yes—
181C22×Dic61C22×C412yes—
182C22×Dic61C22×C414yes—
183C22×Dic61C2×D414yes—
184C22×Dic61C2×D414yes—
185C22×Dic61C2×Q814yes—
186C22×Dic61#4114yes—
187C22×Dic61#4114yes—
188C22⋊C4×C61—28no—
189C22⋊C4×C61—44no—
190C22⋊Dic61—28no—
191C22⋊Dic61—44no—
192C4⋊Dic61—216no—
193#11758196—44no—
194#11758196—44no—
195C4×Dic61—216no—
196C4×Dic61—216no—
197C23×C61—24no—
198C23×C61—24no—
199C23×C61—22no—
200C23×C61—24no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—22no—
204C23×C61—24no—
205C23×C61—24no—
206C23×C61—24no—
207C23×C61—24no—
208C23×C61—24no—
209C23×C61—24no—
210C23×C61—24no—
211C23×C61—24no—
212C23×C61—24no—
213C23×C61#11714yes—
214C23×C61C4×D414yes—
215C23×C61C4×Q814yes—
216C23×C61C22⋊Q814yes—
217C23×C61#12314yes—
218C23×C61#12514yes—
219C23×C61#12614yes—
220C23×C61C23×C411yescharacteristic
221C23×C61C22×D411yescharacteristic
222C23×C61C22×D412yes—
223C23×C61C22×Q811yescharacteristic
224C23×C61C2×#4111yescharacteristic
225C23×C61C2×#4111yescharacteristic
226C23×C61C2×#4111yescharacteristic
227C23×C61C2×#4112yes—
228C23×C61C2×#4111yescharacteristic
229C23×C61C2×#4112yes—
230C23×C61C2×#4112yes—
231C2×C4×C61—232no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—24no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61#12014yes—
255C2×C4×C61#12314yes—
256C2×Dic61—232no—
257C2×Dic61—232no—
258C2×Dic61—24no—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—24no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—24no—
270C2×Dic61—24no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—24no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—42no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61C4×D418yes—
291C2×Dic61C22⋊Q818yes—
292#14695—611nomaximal, Sylow
293C22×C61—24no—
294C22×C61—24no—
295C22×C61—28no—
296C22×C61—28no—
297C22×C61—24no—
298C22×C61—24no—
299C22×C61—28no—
300C22×C61—24no—
301C22×C61—24no—
302C22×C61—28no—
303C22×C61#38718yescomplemented
304C22×C61C2×#11711yescharacteristic
305C22×C61C2×C4×D412yes—
306C22×C61C2×C4×D411yescharacteristic
307C22×C61C2×C4×Q811yescharacteristic
308C22×C61C4×#4112yes—
309C22×C61C2×#12011yescharacteristic
310C22×C61C2×C22⋊Q812yes—
311C22×C61C2×C22⋊Q811yescharacteristic
312C22×C61C2×#12311yescharacteristic
313C22×C61C2×#12311yescharacteristic
314C22×C61#52512yes—
315C22×C61#52512yes—
316C22×C61#52512yes—
317C22×C61#52512yes—
318C22×C61#52511yescharacteristic
319C22×C61#52511yescharacteristic
320C22×C61C2×#12511yescharacteristic
321C22×C61C2×#12611yescharacteristic
322C22×C61#52912yes—
323C22×C61#52912yes—
324C22×C61#52912yes—
325C22×C61#52912yes—
326C22×C61#53312yes—
327C4×C61—24no—
328C4×C61—24no—
329C4×C61—44no—
330C4×C61—82no—
331Dic61—28no—
332Dic61—28no—
333Dic61—42no—
334Dic61—42no—
335Dic61—81no—
336Dic61—81no—
337C23×C42—611no—
338C2×#387—612no—
339C2×#385—611no—
340C2×#385—611no—
341#1436—612no—
342#1436—612no—
343#1434—612no—
344C22⋊#95—611no—
345C22⋊#95—611no—
346C22⋊#95—611no—
347C22⋊#95D6111yescharacteristic
348C2×C61—28no—
349C2×C61C2×#38711yescharacteristic
350C2×C61#229012yes—
351C2×C61C4×#12011yescharacteristic
352C2×C61C4×#12311yescharacteristic
353C2×C61C4×C22⋊Q812yes—
354C2×C61#284811yescharacteristic
355C2×C61#284911yescharacteristic
356C2×C61#285112yes—
357C2×C61#285212yes—
358C2×C61#285311yescharacteristic
359C2×C61#285511yescharacteristic
360C24×C4—611no—
361C24×C4—611no—
362C24×C4C2×D6111yescharacteristic
363C22×C4⋊C4—612no—
364C22×C4⋊C4—611no—
365C22×C4⋊C4—611no—
366C22×C22⋊C4—611no—
367C22×C22⋊C4—611no—
368C22×C22⋊C4C2×D6111yescharacteristic
369C22×C22⋊C4C2×D6111yescharacteristic
370C22×C42—612no—
371C22×C42—612no—
372C22×C42—1228no—
373C22×C42—1224no—
374#387—1228no—
375#385—618no—
376#385—1224no—
377C2×#95—612no—
378C2×#95—612no—
379C2×#95—612no—
380C2×#95—612no—
381C2×#95—612no—
382C2×#95—612no—
383C2×#95—612no—
384C2×#95—611no—
385C2×#95—611no—
386C2×#95C2×D6112yes—
387C2×#95C2×D6112yes—
388C61#1469511yescharacteristic, complemented, Sylow
389C25C22×D6111yescharacteristic
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—612no—
395C23×C4—612no—
396C23×C4—614no—
397C23×C4—614no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—611no—
401C23×C4—611no—
402C23×C4—1224no—
403C23×C4—1224no—
404C23×C4—1224no—
405C23×C4—1224no—
406C23×C4—1222no—
407C23×C4—1222no—
408C23×C4—1222no—
409C23×C4—1222no—
410C23×C4D24414yes—
411C23×C4C22×D6112yes—
412C23×C4C22×D6112yes—
413C23×C4C22×D6111yescharacteristic
414C23×C4C22×D6111yescharacteristic
415C2×C4⋊C4—618no—
416C2×C4⋊C4—1224no—
417C2×C4⋊C4—1224no—
418C2×C4⋊C4—1222no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4—1224no—
421C2×C4⋊C4—1224no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—614no—
428C2×C22⋊C4—1222no—
429C2×C22⋊C4—1222no—
430C2×C22⋊C4—1222no—
431C2×C22⋊C4—1222no—
432C2×C22⋊C4—1222no—
433C2×C22⋊C4C4×D6114yes—
434C2×C42—618no—
435C2×C42—1224no—
436C2×C42—1224no—
437C2×C42—12232no—
438C2×C42—1224no—
439C2×C42—1224no—
440C2×C42—1224no—
441#95—24no—
442#95—24no—
443#95—618no—
444#95—1224no—
445#95—1224no—
446#95—1224no—
447#95—1224no—
448#95—1224no—
449#95—1224no—
450#95—1222no—
451#95—1222no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24C2×C4×D6112yes—
457C24C2×D24412yes—
458C24#1175822212yes—
459C24#1175822412yes—
460C24#1175822412yes—
461C24#1175822412yes—
462C24Q8×D6112yes—
463C24C23×D6111yescharacteristic
464C22×C4—216no—
465C22×C4—216no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—614no—
489C22×C4—614no—
490C22×C4—614no—
491C22×C4—614no—
492C22×C4—614no—
493C22×C4—614no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—12216no—
497C22×C4—12216no—
498C22×C4—1228no—
499C22×C4—1228no—
500C22×C4—12216no—
501C22×C4—12216no—
502C22×C4—1228no—
503C22×C4—1228no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1222no—
512C22×C4—1228no—
513C22×C4—1228no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1222no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1222no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1222no—
526C22×C4—1222no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1222no—
532C22×C4C2×C4×D6114yes—
533C22×C4C2×D24412yes—
534C22×C4C2×D24412yes—
535C22×C4D4×D6114yes—
536C22×C4#1175822414yes—
537C4⋊C4—12216no—
538C4⋊C4—2444no—
539C4⋊C4—2444no—
540C22⋊C4—28no—
541C22⋊C4—44no—
542C22⋊C4—1228no—
543C22⋊C4—2444no—
544C42—12216no—
545C42—12216no—
546C23—24no—
547C23—24no—
548C23—22no—
549C23—24no—
550C23—22no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—22no—
556C23—22no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23#1451973314yes—
563C23C4×D24414yes—
564C23#1451974214yes—
565C23#1451975714yes—
566C23#1451976114yes—
567C23#1451976714yes—
568C23#1451977014yes—
569C23C22×C4×D6111yescharacteristic
570C23C2×D4×D6112yes—
571C23C22×D24411yescharacteristic
572C23C2×Q8×D6111yescharacteristic
573C23#41×D6112yes—
574C23#41×D6112yes—
575C23C2×#1175822411yescharacteristic
576C23C2×#1175822411yescharacteristic
577C23C2×#1175822411yescharacteristic
578C23C2×#1175822412yes—
579C23C2×#1175822211yescharacteristic
580C2×C4—232no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—618no—
604C2×C4—618no—
605C2×C4—12232no—
606C2×C4—12232no—
607C2×C4—1224no—
608C2×C4—1224no—
609C2×C4—1224no—
610C2×C4—1224no—
611C2×C4—1224no—
612C2×C4—1224no—
613C2×C4—1224no—
614C2×C4—1224no—
615C2×C4—1224no—
616C2×C4—1224no—
617C2×C4—1224no—
618C2×C4—1224no—
619C2×C4—1224no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1224no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2442no—
628C2×C4—2442no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2442no—
632C2×C4—2442no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2442no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2442no—
639C2×C4#1451974714yes—
640C2×C4#1451976114yes—
641C22—24no—
642C22—24no—
643C22—28no—
644C22—28no—
645C22—24no—
646C22—28no—
647C22—24no—
648C22—24no—
649C22—24no—
650C22—28no—
651C22#1683964718yescomplemented
652C22C2×#1451973311yescharacteristic
653C22C4×D4×D6112yes—
654C22C2×C4×D24411yescharacteristic
655C22C2×#1451974211yescharacteristic
656C22C4×#1175822412yes—
657C22C2×#1451974711yescharacteristic
658C22C22⋊Q8×D6112yes—
659C22C2×#1451975711yescharacteristic
660C22C2×#1451976111yescharacteristic
661C22C2×#1451976111yescharacteristic
662C22#1684026812yes—
663C22#1684026812yes—
664C22#1684027112yes—
665C22#1684027212yes—
666C22#1684027411yescharacteristic
667C22#1684027411yescharacteristic
668C22C2×#1451976711yescharacteristic
669C22C2×#1451977011yescharacteristic
670C22#1684028912yes—
671C22#1684028912yes—
672C22#1684029212yes—
673C22#1684029312yes—
674C22#1684031412yes—
675C4—24no—
676C4—24no—
677C4—44no—
678C4—82no—
679C4—1228no—
680C4—1228no—
681C4—4881no—
682C4—4881no—
683C4—2442no—
684C4—2442no—
685C2—28no—
686C2C2×#1683964711yescharacteristic
687C2#2144825912yes—
688C2C4×#1451974711yescharacteristic
689C2C4×#1451976111yescharacteristic
690C2#2144835112yes—
691C2#2145410711yescharacteristic
692C2#2145411311yescharacteristic
693C2#2145412512yes—
694C2#2145413212yes—
695C2#2145414211yescharacteristic
696C2#2145415911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC22⋊#95D61
hypocenterC61#14695
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16839647C2semidirect
5. #21444054C2semidirect
6. #21444053C2semidirect
7. #21444043C2semidirect
24. #16839637C4semidirect
58. C2×C4⋊Dic61C2×C4semidirect
84. #14519684C2×C4semidirect
303. C22×C61#387semidirect
388. C61#14695semidirect
651. C22#16839647semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic612
C2×#168396472
C2×#168396372
C2×#168396352
#214440542
#214440532
#214440432
#214440412
C61×C22⋊#952
#1469561