Finite Group Databasebeta

← #29606784

Subgroups — #29606784

Order 15616.

1830 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×C4×Dic122C211yesmaximal, characteristic, complemented
2C2×#16839675C211yesmaximal, characteristic
3C2×#16839654C212yesmaximal
4C2×#16839653C211yesmaximal, characteristic
5#21444089C211yesmaximal, characteristic, complemented
6#21444084C211yesmaximal, characteristic, complemented
7#21444083C212yesmaximal, complemented
8#21444065C211yesmaximal, characteristic
9#21444063C212yesmaximal
10#21444043C212yesmaximal, complemented
11C61×#1434C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C2×C4×Dic122—28no—
14C2×C4×Dic122—24no—
15C22×C4⋊Dic61C2211yescharacteristic
16C22×C4⋊Dic61C2212yes—
17C22×#11758196C2212yes—
18C22×#11758196C2211yescharacteristic
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×C4×Dic61C2212yes—
25#16839675C418yescomplemented
26#16839654—28no—
27#16839653—24no—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C42×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122—24no—
44C22×Dic122—24no—
45C22×Dic122C2×C414yes—
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2312yes—
50C23×Dic61C2312yes—
51C4×Dic122—232no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—24no—
54C2×C4⋊Dic61—24no—
55C2×C4⋊Dic61—42no—
56C2×C4⋊Dic61—42no—
57C2×#11758196—24no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758196—22no—
61C2×#11758196—42no—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×#11758198—24no—
65C2×#11758198—24no—
66C2×#11758198—22no—
67C2×#11758198—22no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—42no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198C2×C414yes—
74C2×#11758198C2×C418yes—
75C2×C4×Dic61—24no—
76C2×C4×Dic61—24no—
77C2×C4×Dic61D418yes—
78#14519684—22no—
79#14519684—22no—
80#14519684—24no—
81#14519684—24no—
82#14519684—42no—
83#14519684—42no—
84#14519684C2×C418yes—
85C23×C4×C61C2312yes—
86C23×C4×C61C2312yes—
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C2×C42×C61—24no—
91C2×C42×C61D414yes—
92#95×C61—24no—
93#95×C61—22no—
94#95×C61—42no—
95#95×C61C2×C414yes—
96C24×C61C2411yescharacteristic
97C23×D61—22no—
98C23×D61—21no—
99C23×D61—22no—
100C23×D61—21no—
101C23×D61—21no—
102C23×D61—22no—
103C23×D61—21no—
104C23×D61—21no—
105C23×D61—21no—
106C23×D61—22no—
107C23×D61C22×C412yes—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61C22×C414yes—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D414yes—
136C22×C4×C61#4112yes—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—21no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61C22×C412yes—
162C22×Dic61C22×C414yes—
163C22×Dic61C2×D414yes—
164C22×Dic61C2×D414yes—
165C22×Dic61#4114yes—
166C2×Dic122—216no—
167C2×Dic122—28no—
168C2×Dic122—28no—
169C2×Dic122—28no—
170C2×Dic122—216no—
171C42×C61—28no—
172#11758198—28no—
173#11758198—216no—
174#11758198—48no—
175#11758198—44no—
176#11758198—44no—
177C4⋊Dic61—28no—
178C4⋊Dic61—48no—
179#11758196—216no—
180#11758196—44no—
181C4×Dic61—216no—
182C23×C61C23×C411yescharacteristic
183C23×C61C22×D412yes—
184C23×C61C22×D411yescharacteristic
185C23×C61C2×#4112yes—
186C23×C61C2×#4111yescharacteristic
187C23×C61H(5,𝔽2)11yescharacteristic
188C23×C61H(5,𝔽2)12yes—
189C23×C612−1+411yescharacteristic
190C23×C612−1+411yescharacteristic
191C23×C612−1+411yescharacteristic
192C23×C612−1+412yes—
193C22×D61—24no—
194C22×D61—22no—
195C22×D61—22no—
196C22×D61—22no—
197C22×D61—24no—
198C22×D61—41no—
199C22×D61—42no—
200C22×D61—41no—
201C22×D61—42no—
202C22×D61—41no—
203C22×D61—42no—
204C22×D61—41no—
205C22×D61—42no—
206C22×D61—41no—
207C22×D61—42no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—42no—
211C22×D61—41no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—24no—
220C2×C4×C61—24no—
221C2×C4×C61—24no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—24no—
225C2×C4×C61—24no—
226C2×C4×C61—24no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61C4×D414yes—
244C2×C4×C61#12014yes—
245C2×Dic61—24no—
246C2×Dic61—24no—
247C2×Dic61—24no—
248C2×Dic61—24no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—41no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—41no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—42no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—42no—
270C2×Dic61—41no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61C4×D418yes—
274Dic122—232no—
275#14301—611nomaximal, Sylow
276C22×C61C2×C4×D412yes—
277C22×C61C2×C4×D411yescharacteristic
278C22×C61#51911yescharacteristic
279C22×C61#52011yescharacteristic
280C22×C61#52012yes—
281C22×C61C2×#12011yescharacteristic
282C22×C61#52512yes—
283C22×C61#52511yescharacteristic
284C22×C61#53512yes—
285C22×C61#53511yescharacteristic
286C22×C61#53612yes—
287C22×C61#53612yes—
288C22×C61#53611yescharacteristic
289C22×C61#53611yescharacteristic
290C22×C61#53712yes—
291C22×C61#53711yescharacteristic
292C22×C61#54111yescharacteristic
293C22×C61#54112yes—
294C22×C61#54212yes—
295C22×C61#54211yescharacteristic
296C22×C61#54212yes—
297C22×C61#54212yes—
298C22×C61#54212yes—
299C2×D61—44no—
300C2×D61—42no—
301C2×D61—44no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61—82no—
308C2×D61—81no—
309C2×D61—82no—
310C4×C61—24no—
311C4×C61—24no—
312C4×C61—44no—
313C4×C61—42no—
314C4×C61—82no—
315Dic61—28no—
316Dic61—42no—
317Dic61—44no—
318Dic61—81no—
319Dic61—81no—
320C22×C4×Q8—611no—
321C2×#393—611no—
322C2×#388—611no—
323C2×#388—612no—
324#1446—611no—
325#1444—612no—
326#1444—611no—
327#1439—612no—
328#1439—611no—
329#1434—612no—
330#1434D6111yescharacteristic, complemented
331C2×C61C4×#12011yescharacteristic
332C2×C61#232312yes—
333C2×C61#232311yescharacteristic
334C2×C61#232612yes—
335C2×C61#232611yescharacteristic
336C2×C61#261411yescharacteristic
337C2×C61#261511yescharacteristic
338C2×C61#263211yescharacteristic
339C2×C61#263212yes—
340C2×C61#263711yescharacteristic
341C2×C61#263712yes—
342D61—82no—
343C23×Q8—611no—
344C2×C4×Q8—1228no—
345C2×C4×Q8—1224no—
346C22×C4⋊C4—612no—
347C22×C4⋊C4—611no—
348C22×C4⋊C4—611no—
349C22×C4⋊C4—612no—
350C22×C22⋊C4—612no—
351C22×C22⋊C4—611no—
352C22×C22⋊C4—611no—
353C22×C22⋊C4—612no—
354C22×C22⋊C4—611no—
355C22×C42—612no—
356C22×C42C2×D6111yescharacteristic
357#393—618no—
358#388—1228no—
359#388—1224no—
360C2×#95—612no—
361C2×#95—611no—
362C2×#95—612no—
363C2×#95—612no—
364C2×#95—611no—
365C2×#95—612no—
366C2×#95—612no—
367C2×#95C2×D6112yes—
368C2×#95C2×D6111yescharacteristic
369C2×#95C2×D6112yes—
370C2×#95C2×D6111yescharacteristic
371C61#1430111yescharacteristic, complemented, Sylow
372C25—611no—
373C22×Q8—614no—
374C22×Q8—1224no—
375C22×Q8—1224no—
376C22×Q8—1222no—
377C22×Q8—1222no—
378C23×C4—612no—
379C23×C4—612no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4C22×D6112yes—
384C23×C4C22×D6112yes—
385C23×C4C22×D6111yescharacteristic
386C23×C4C22×D6111yescharacteristic
387C23×C4C22×D6111yescharacteristic
388C4×Q8—12232no—
389C2×C4⋊C4—1224no—
390C2×C4⋊C4—1224no—
391C2×C4⋊C4—1224no—
392C2×C4⋊C4—1224no—
393C2×C4⋊C4—1222no—
394C2×C4⋊C4—1224no—
395C2×C4⋊C4—1222no—
396C2×C4⋊C4—2442no—
397C2×C4⋊C4—2442no—
398C2×C4⋊C4—2442no—
399C2×C22⋊C4—618no—
400C2×C22⋊C4—614no—
401C2×C22⋊C4—1224no—
402C2×C22⋊C4—1224no—
403C2×C22⋊C4—1222no—
404C2×C22⋊C4—1222no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—1222no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1224no—
409C2×C22⋊C4—2442no—
410C2×C22⋊C4—2442no—
411C2×C22⋊C4—2442no—
412C2×C42—24no—
413C2×C42—618no—
414C2×C42—1224no—
415C2×C42—1224no—
416C2×C42D24414yes—
417#95—22no—
418#95—24no—
419#95—42no—
420#95—618no—
421#95—1224no—
422#95—1224no—
423#95—1222no—
424#95—1222no—
425#95—2442no—
426#95—2442no—
427#95C4×D6114yes—
428C24—612no—
429C24—1222no—
430C24—1221no—
431C24—1222no—
432C24—1221no—
433C24—1221no—
434C24—1222no—
435C24—1221no—
436C24—1221no—
437C24—1222no—
438C24—1221no—
439C24C23×D6111yescharacteristic
440C2×Q8—12216no—
441C2×Q8—1228no—
442C2×Q8—12216no—
443C2×Q8—1228no—
444C2×Q8—1228no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—614no—
468C22×C4—614no—
469C22×C4—614no—
470C22×C4—612no—
471C22×C4—614no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1221no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1222no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4C2×C4×D6114yes—
497C22×C4C2×C4×D6112yes—
498C22×C4C2×D24412yes—
499C22×C4C2×D24412yes—
500C22×C4C2×D24412yes—
501C22×C4#1175822212yes—
502C22×C4D4×D6114yes—
503C4⋊C4—12216no—
504C4⋊C4—1228no—
505C4⋊C4—2444no—
506C4⋊C4—2448no—
507C22⋊C4—12216no—
508C22⋊C4—1228no—
509C22⋊C4—2444no—
510C22⋊C4—2448no—
511C22⋊C4—2444no—
512C42—28no—
513C42—12216no—
514C23—1224no—
515C23—1222no—
516C23—1222no—
517C23—1222no—
518C23—1224no—
519C23—2441no—
520C23—2442no—
521C23—2441no—
522C23—2442no—
523C23—2441no—
524C23—2442no—
525C23—2442no—
526C23—2441no—
527C23—2441no—
528C23—2442no—
529C23—2441no—
530C23—2441no—
531C23—2442no—
532C23—2442no—
533C23—2441no—
534C23—2442no—
535C23—2442no—
536C23—2442no—
537C23C22×C4×D6111yescharacteristic
538C23C2×D4×D6112yes—
539C23C22×D24411yescharacteristic
540C23#41×D6112yes—
541C23C2×#1175822211yescharacteristic
542C23#1451982211yescharacteristic
543C23#1451982312yes—
544C23#1451982411yescharacteristic
545C23#1451982411yescharacteristic
546C23#1451982412yes—
547C23#1451982511yescharacteristic
548Q8—12232no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—618no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1224no—
580C2×C4—1224no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1222no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1224no—
587C2×C4—1224no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2442no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2442no—
595C2×C4—2441no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2441no—
600C2×C4—2442no—
601C2×C4—2441no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4C4×D24414yes—
606C2×C4#1451974714yes—
607C22—4881no—
608C22—4881no—
609C22—4881no—
610C22—4882no—
611C22—4881no—
612C22—4882no—
613C22—2444no—
614C22—2442no—
615C22—2444no—
616C22—2442no—
617C22—2442no—
618C22C4×D4×D6112yes—
619C22C2×C4×D24411yescharacteristic
620C22#1684023811yescharacteristic
621C22#1684024111yescharacteristic
622C22#1684024212yes—
623C22C2×#1451974711yescharacteristic
624C22#1684027112yes—
625C22#1684027411yescharacteristic
626C22#1684032812yes—
627C22#1684033111yescharacteristic
628C22#1684033412yes—
629C22#1684033412yes—
630C22#1684033811yescharacteristic
631C22#1684033811yescharacteristic
632C22#1684034212yes—
633C22#1684034311yescharacteristic
634C22#1684037011yescharacteristic
635C22#1684037112yes—
636C22#1684037612yes—
637C22#1684037711yescharacteristic
638C22#1684037812yes—
639C22#1684037812yes—
640C22#1684038312yes—
641C4—24no—
642C4—24no—
643C4—42no—
644C4—44no—
645C4—82no—
646C4—1228no—
647C4—4881no—
648C4—4881no—
649C4—2444no—
650C4—2442no—
651C2—4882no—
652C2C4×#1451974711yescharacteristic
653C2#2144850012yes—
654C2#2144850211yescharacteristic
655C2#2144852812yes—
656C2#2144853011yescharacteristic
657C2#2145154111yescharacteristic
658C2#2145154511yescharacteristic
659C2#2145168211yescharacteristic
660C2#2145168312yes—
661C2#2145172911yescharacteristic
662C2#2145173312yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1434D61
hypocenterC61#14301
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic122C2semidirect
5. #21444089C2semidirect
6. #21444084C2semidirect
7. #21444083C2semidirect
10. #21444043C2semidirect
11. C61×#1434C2semidirect
25. #16839675C4semidirect
330. #1434D61semidirect
371. C61#14301semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1222
C2×#168396752
C2×#168396542
C2×#168396532
#214440892
#214440842
#214440832
#214440652
#214440632
#214440432
C61×#14342
#1430161