Finite Group Databasebeta

← #29645898

Subgroups — #29645898

Order 15616.

1646 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2#21454447C212yesmaximal, complemented
3#21444158C214yesmaximal, complemented
4#21444144C214yesmaximal, complemented
5#21444140C211yesmaximal, characteristic, complemented
6#21444139C212yesmaximal, complemented
7C61×#1460C211yesmaximal, characteristic, complemented
8C22×D4×D61C411yescharacteristic
9C23×C4×D61C412yes—
10C2×C4×D244C2211yescharacteristic
11C2×D4×Dic61C411yescharacteristic
12C2×#14519739C411yescharacteristic
13C2×C4×C22⋊D61C412yes—
14C2×#14519737C2212yes—
15C4×D4×D61—22no—
16C4×D4×D61—22no—
17C4×D4×D61—22no—
18C4×D4×D61—22no—
19C2×C4⋊C4×D61C411yescharacteristic
20C2×C22⋊C4×D61C2212yes—
21C2×C42×D61C2211yescharacteristic
22#16839818—22no—
23#16839816C2214yescomplemented
24#16839815C2212yescomplemented
25#16839813—22no—
26#16839784—22no—
27#16839724C2214yes—
28C4×#11758189—22no—
29#16839486C2214yescomplemented
30#16839485C2218yescomplemented
31C2×C4×D4×C61C2211yescharacteristic
32C61×#431C2212yescomplemented
33C61×#323C2214yescomplemented
34C24×D61C2×C412yes—
35C22×D244C2×C411yescharacteristic
36C22×C22⋊D61C2×C412yes—
37C2×D4×D61—24no—
38C2×D4×D61—24no—
39C2×D4×D61—22no—
40C2×D4×D61—22no—
41C23×Dic61C2×C412yes—
42C22×C4×D61—22no—
43C22×C4×D61—22no—
44C22×C4×D61—22no—
45C22×C4×D61—22no—
46C22×C4×D61—48no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C412yes—
50C22×C4×D61C2×C412yes—
51C22×C4×D61C2×C412yes—
52C22×C4×D61C2311yescharacteristic
53C2×#11758189—24no—
54C4×D244—22no—
55C4×D244—22no—
56D4×Dic61—22no—
57D4×Dic61—22no—
58#14519739—22no—
59#14519739—22no—
60C4×C22⋊D61—24no—
61C4×C22⋊D61—24no—
62#14519737—24no—
63#14519737—24no—
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758196C2×C412yes—
66C4⋊C4×D61—22no—
67C4⋊C4×D61—22no—
68C2×C22⋊Dic61C2×C412yes—
69C2×#11758198C2×C412yes—
70C2×#11758198C2312yes—
71C22⋊C4×D61—24no—
72C22⋊C4×D61—24no—
73C2×C4×Dic61C2×C411yescharacteristic
74C2×C4×Dic61C2×C411yescharacteristic
75C2×C4×Dic61C2311yescharacteristic
76C42×D61D412yes—
77C42×D61D412yes—
78C42×D61D412yes—
79C42×D61D412yes—
80C4⋊#92418—22no—
81#14519706—24no—
82C22⋊#92418C2314yes—
83#14519689—24no—
84#14519687—24no—
85C4×#92418—22no—
86C22×D4×C61C2×C411yescharacteristic
87C23×C4×C61C2×C412yes—
88C4×D4×C61—22no—
89C4×D4×C61—22no—
90C2×C4⋊C4×C61C2×C411yescharacteristic
91C2×C22⋊C4×C61C2312yes—
92C2×C42×C61C2311yescharacteristic
93C4⋊C8×C61—22no—
94C22⋊C8×C61C2314yes—
95C4×C8×C61—22no—
96C24×C61C22×C412yes—
97C23×D61—24no—
98C23×D61—22no—
99C23×D61—22no—
100C23×D61—24no—
101C23×D61—44no—
102C23×D61—44no—
103C23×D61C22×C411yescharacteristic
104C23×D61C22×C412yes—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61M1614yescomplemented
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—44no—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C22×C412yes—
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C2411yescharacteristic
115C2×C22⋊D61—24no—
116C2×C22⋊D61—24no—
117C2×C22⋊D61—24no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—44no—
121C22×Dic61C22×C411yescharacteristic
122C22×Dic61C22×C411yescharacteristic
123C22×Dic61C22×C412yes—
124C22×Dic61C22×C411yescharacteristic
125D4×D61—216no—
126D4×D61—216no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244M1614yescomplemented
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—24no—
133C2×C4×D61—22no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—42no—
140C2×C4×D61—48no—
141C2×C4×D61—48no—
142C2×C4×D61—48no—
143C2×C4×D61—48no—
144C2×C4×D61—44no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C4×D61C22⋊C411yescharacteristic
148C2×C4×D61C22⋊C411yescharacteristic
149C2×C4×D61C22⋊C411yescharacteristic
150C2×C4×D61C22⋊C412yes—
151C2×C4×D61C22⋊C412yes—
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C2×D412yes—
154C2×C4×D61C2×D412yes—
155C2×C8×C61—24no—
156C4⋊C4×C61—22no—
157C22⋊C4×C61—24no—
158C42×C61C2×D412yes—
159C42×C61C2×D412yes—
160C22⋊Dic61—24no—
161#11758198—24no—
162#11758198—24no—
163C4⋊Dic61—22no—
164#11758196—24no—
165C4×Dic61C22⋊C412yes—
166C4×Dic61C22⋊C412yes—
167C4×Dic61C22⋊C412yes—
168C4×Dic61C22⋊C412yes—
169C4×Dic61C2×D412yes—
170C4×Dic61C2×D412yes—
171C2×#92418—24no—
172#11758189—48no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61C2×M1614yes—
178C23×C61C23×C411yescharacteristic
179C22×D61—21no—
180C22×D61—21no—
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—28no—
184C22×D61—28no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—44no—
188C22×D61—416no—
189C22×D61—416no—
190C22×D61—44no—
191C22×D61—44no—
192C22×D61—44no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61C2×C22⋊C411yescharacteristic
196C22×D61C2×C22⋊C411yescharacteristic
197C22×D61C2×M1614yes—
198D4×C61—28no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—41no—
202C2×C4×C61—44no—
203C2×C4×C61—44no—
204C2×C4×C61—42no—
205C2×C4×C61C2×C22⋊C411yescharacteristic
206C2×C4×C61C2×C22⋊C412yes—
207C2×C4×C61C2×C22⋊C411yescharacteristic
208C2×C4×C61C2×M1612yes—
209C2×C4×C61C2×M1612yes—
210C2×C4×C61C22×D412yes—
211C22⋊D61—216no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—41no—
217C2×Dic61—44no—
218C2×Dic61—44no—
219C2×Dic61—42no—
220C2×Dic61C2×C22⋊C412yes—
221C2×Dic61C2×C22⋊C412yes—
222C2×Dic61C2×C22⋊C411yescharacteristic
223C2×Dic61C2×C22⋊C411yescharacteristic
224D244—28no—
225C4×D61—24no—
226C4×D61—22no—
227C4×D61—24no—
228C4×D61—24no—
229C4×D61—22no—
230C4×D61—22no—
231C4×D61—42no—
232C4×D61—44no—
233C4×D61—44no—
234C4×D61—44no—
235C4×D61—44no—
236C4×D61—44no—
237C4×D61—44no—
238C4×D61#10014yes—
239C8×C61—44no—
240#92418—44no—
241#17364—611nomaximal, Sylow
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—24no—
245C22×C61—44no—
246C22×C61—44no—
247C22×C61—42no—
248C22×C61—42no—
249C22×C61C22×C22⋊C411yescharacteristic
250C22×C61C22×M1611yescharacteristic
251C22×C61C22×M1611yescharacteristic
252C2×D61—24no—
253C2×D61—24no—
254C2×D61—21no—
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—24no—
259C2×D61—416no—
260C2×D61—416no—
261C2×D61—44no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—44no—
265C2×D61#41012yes—
266C2×D61C2×#10012yes—
267C4×C61—22no—
268C4×C61—21no—
269C4×C61—42no—
270C4×C61#40714yes—
271C4×C61C2×#10012yes—
272Dic61—22no—
273Dic61—22no—
274Dic61—21no—
275Dic61—42no—
276Dic61C2×#10012yes—
277C22×C4×D4—611no—
278#2920—612no—
279#1466—614no—
280#1462—614no—
281#1460—612no—
282#1460—611no—
283#1460D6111yescharacteristic, complemented
284C2×C61—21no—
285C2×C61—21no—
286C2×C61—44no—
287C2×C61C2×#40711yescharacteristic
288C2×C61C2×#41011yescharacteristic
289C2×C61C22×#10011yescharacteristic
290D61—22no—
291D61—22no—
292D61—44no—
293C23×D4—611no—
294C24×C4—612no—
295C2×C4×D4—611no—
296C2×C4×D4—612no—
297C2×C4×D4—611no—
298C2×C4×D4—612no—
299C2×C4×D4—611no—
300C2×C4×D4—1222no—
301C2×C4×D4—1222no—
302C2×C4×D4—1222no—
303C2×C4×D4—1222no—
304C2×C4×D4C2×D6111yescharacteristic
305C22×C4⋊C4—611no—
306C22×C22⋊C4—612no—
307C22×C42—611no—
308#432—614no—
309#432—1222no—
310#431—612no—
311#431—1222no—
312#431C2×D6112yescomplemented
313#423—1222no—
314#407—614no—
315C4×M16—1222no—
316#323—614no—
317#323—618no—
318#323C2×D6114yescomplemented
319C61#1736411yescharacteristic, complemented, Sylow
320C25—612no—
321C22×D4—612no—
322C22×D4—611no—
323C22×D4—1222no—
324C22×D4—1222no—
325C22×D4—1224no—
326C22×D4—1224no—
327C22×D4C4×D6111yescharacteristic
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—612no—
332C23×C4—612no—
333C23×C4—612no—
334C23×C4—612no—
335C23×C4—1222no—
336C23×C4—1222no—
337C23×C4—1222no—
338C23×C4—1222no—
339C23×C4—2448no—
340C23×C4C4×D6112yes—
341C2×M16—1224no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—1224no—
345C4×D4—1224no—
346C4×D4—1222no—
347C4×D4—1222no—
348C4×D4—1224no—
349C4×D4—1224no—
350C4×D4—1222no—
351C4×D4—1222no—
352C4×D4—1222no—
353C4×D4—1222no—
354C2×C4⋊C4—612no—
355C2×C4⋊C4—611no—
356C2×C4⋊C4—1222no—
357C2×C4⋊C4—1222no—
358C2×C4⋊C4C4×D6111yescharacteristic
359C2×C22⋊C4—612no—
360C2×C22⋊C4—612no—
361C2×C22⋊C4—612no—
362C2×C22⋊C4—1224no—
363C2×C22⋊C4—1224no—
364C2×C22⋊C4C22×D6112yes—
365C2×C42—611no—
366C2×C42—611no—
367C2×C42—611no—
368C2×C42—612no—
369C2×C42—612no—
370C2×C42—612no—
371C2×C42—612no—
372C2×C42C22×D6111yescharacteristic
373C4⋊C8—22no—
374C4⋊C8—1224no—
375C4⋊C8—1222no—
376C22⋊C8—614no—
377C22⋊C8—1224no—
378C22⋊C8C22×D6114yes—
379#97—1224no—
380C4×C8—22no—
381C4×C8—1222no—
382C24—611no—
383C24—612no—
384C24—1222no—
385C24—1222no—
386C24—1224no—
387C24—1224no—
388C24—2444no—
389C24—2444no—
390C24C2×C4×D6112yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—614no—
394C2×D4—1224no—
395C2×D4—12216no—
396C2×D4—12216no—
397C2×D4—1224no—
398C2×D4—1224no—
399C2×D4—1222no—
400C2×D4—1222no—
401C2×D4#1175818914yescomplemented
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—44no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—612no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—612no—
416C22×C4—612no—
417C22×C4—1224no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—2444no—
429C22×C4—2448no—
430C22×C4—2442no—
431C22×C4—2448no—
432C22×C4—2448no—
433C22×C4—2448no—
434C22×C4—2444no—
435C22×C4—2444no—
436C22×C4—2444no—
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4C2×C4×D6112yes—
439C22×C4C2×C4×D6111yescharacteristic
440C22×C4C23×D6111yescharacteristic
441M16—2448no—
442C2×C8—24no—
443C2×C8—1224no—
444C4⋊C4—22no—
445C4⋊C4—1224no—
446C4⋊C4—1222no—
447C22⋊C4—24no—
448C22⋊C4—1224no—
449C22⋊C4—1224no—
450C22⋊C4—1224no—
451C42—612no—
452C42—612no—
453C42—612no—
454C42—612no—
455C42—612no—
456C42—612no—
457C42D4×D6112yes—
458C42D4×D6112yes—
459C23—22no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—611no—
464C23—611no—
465C23—614no—
466C23—1222no—
467C23—1222no—
468C23—1228no—
469C23—1228no—
470C23—1221no—
471C23—1221no—
472C23—1222no—
473C23—1222no—
474C23—2442no—
475C23—2442no—
476C23—2444no—
477C23—2444no—
478C23—2444no—
479C23—24416no—
480C23—24416no—
481C23—2444no—
482C23C2×#1175818914yes—
483C23C22×C4×D6111yescharacteristic
484D4—28no—
485D4—12216no—
486D4—1228no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—611no—
494C2×C4—614no—
495C2×C4—612no—
496C2×C4—612no—
497C2×C4—611no—
498C2×C4—1222no—
499C2×C4—1224no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—1224no—
505C2×C4—1224no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—2442no—
509C2×C4—2444no—
510C2×C4—2444no—
511C2×C4—2444no—
512C2×C4—2444no—
513C2×C4—2444no—
514C2×C4—2444no—
515C2×C4—2441no—
516C2×C4—2444no—
517C2×C4—2444no—
518C2×C4—2442no—
519C2×C4C22⋊C4×D6111yescharacteristic
520C2×C4C22⋊C4×D6112yes—
521C2×C4C22⋊C4×D6111yescharacteristic
522C2×C4M16×D6112yes—
523C2×C4C2×#1175818912yes—
524C2×C4C2×D4×D6112yes—
525C8—44no—
526C8—2444no—
527C22—21no—
528C22—21no—
529C22—24no—
530C22—44no—
531C22—44no—
532C22—42no—
533C22—42no—
534C22—612no—
535C22—612no—
536C22—1224no—
537C22—1224no—
538C22—1221no—
539C22—1221no—
540C22—1221no—
541C22—1221no—
542C22—1224no—
543C22—2444no—
544C22—2444no—
545C22—24416no—
546C22—24416no—
547C22—2442no—
548C22—2442no—
549C22C2×C22⋊C4×D6111yescharacteristic
550C22C2×M16×D6111yescharacteristic
551C22C22×#1175818911yescharacteristic
552C4—22no—
553C4—21no—
554C4—42no—
555C4—612no—
556C4—1222no—
557C4—1222no—
558C4—1221no—
559C4—2442no—
560C4#1683972414yes—
561C4#100×D6112yes—
562C2—21no—
563C2—21no—
564C2—44no—
565C2—1222no—
566C2—1222no—
567C2—2444no—
568C2C2×#1683972411yescharacteristic
569C2#410×D6111yescharacteristic
570C2C2×#100×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1460C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×C4×C61C24
hypercenter#1460D61
hypocenterC61#17364
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #21444158C2semidirect
4. #21444144C2semidirect
5. #21444140C2semidirect
6. #21444139C2semidirect
7. C61×#1460C2semidirect
23. #16839816C22semidirect
24. #16839815C22semidirect
29. #16839486C22semidirect
30. #16839485C22semidirect
32. C61×#431C22semidirect
33. C61×#323C22semidirect
107. C2×D4×C61M16semidirect
129. C2×D244M16semidirect
283. #1460D61semidirect
312. #431C2×D61semidirect
318. #323C2×D61semidirect
319. C61#17364semidirect
401. C2×D4#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
#214544472
#214441582
#214441442
#214441402
#214441392
C61×#14602
#1736461