Finite Group Databasebeta

← #29570143

Subgroups — #29570143

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#407×D61C211yesmaximal, characteristic
2#21448200C211yesmaximal, characteristic
3C4×C22⋊C4×D61C211yesmaximal, characteristic
4#21443705C211yesmaximal, characteristic, complemented
5#21443705C211yesmaximal, characteristic, complemented
6#21443704C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×M16×D61C412yescomplemented
10C2×#14519734—21no—
11C2×C22⋊C4×D61—21no—
12C2×C42×D61—21no—
13#16839726C2211yescharacteristic
14#16839725C412yescomplemented
15#16839724—21no—
16#16839724—21no—
17C22⋊C8×D61—21no—
18C22⋊C8×D61—21no—
19#16839624C412yescomplemented
20#16839621C412yescomplemented
21#16839620—21no—
22#16839617—21no—
23C22⋊C4×Dic61—21no—
24C4×#11758198—21no—
25C4×#11758198—21no—
26C4×C22⋊Dic61C2211yescharacteristic
27C4×C22⋊Dic61C2211yescharacteristic
28#16839609C412yescomplemented
29#95×D61C412yescomplemented
30C61×#407C2211yescharacteristic
31C4×C22⋊C4×C61C2211yescharacteristic
32C4×C22⋊C4×C61C2211yescharacteristic
33C24×D61D411yescharacteristic
34C23×Dic61D411yescharacteristic
35C22×C4×D61—22no—
36C22×C4×D61—44no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61C2×C411yescharacteristic
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61C2×C411yescharacteristic
41C22×C4×D61C2×C411yescharacteristic
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×C4×D61D411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×C4×D61Q811yescharacteristic
48C22×C4×D61Q811yescharacteristic
49C2×#11758194C2×C412yescomplemented
50C2×#11758189—22no—
51M16×D61—44no—
52C2×C8×D61—22no—
53#14519734—44no—
54C2×#11758196—22no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×#11758198—22no—
58C2×#11758198—22no—
59C2×#11758198—22no—
60C22⋊C4×D61—28no—
61C2×C4×Dic61—21no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—22no—
64C42×D61—44no—
65C22⋊#92418—21no—
66C22⋊#92418—21no—
67#14519689—22no—
68#14519689—22no—
69#14519684—22no—
70#14519684—22no—
71#14519684C2×C412yes—
72#14519684C2×C412yescomplemented
73C23×C4×C61C2311yescharacteristic
74C2×M16×C61C2×C412yescomplemented
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C42×C61—21no—
78C2×C42×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81#95×C61C2×C412yes—
82#95×C61C2×C412yescomplemented
83C24×C61C2×D411yescharacteristic
84C23×D61—24no—
85C23×D61—42no—
86C23×D61—42no—
87C23×D61C22⋊C411yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C23×D61C22⋊C411yescharacteristic
90C23×D61C22⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C23×D61C4⋊C411yescharacteristic
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—42no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×Q811yescharacteristic
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61—42no—
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C4⋊C411yescharacteristic
110C22×Dic61C4⋊C411yescharacteristic
111C2×C4×D61—24no—
112C2×C4×D61—24no—
113C2×C4×D61—24no—
114C2×C4×D61—28no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61—44no—
125C2×C4×D61—44no—
126C2×C4×D61C4211yescharacteristic
127C2×C4×D61C4211yescharacteristic
128C2×C4×D61C4211yescharacteristic
129C2×C4×D61C4211yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C22⋊C411yescharacteristic
133C2×C4×D61C22⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138C2×C4×D61C4⋊C411yescharacteristic
139C2×C4×D61C4⋊C411yescharacteristic
140C2×C4×D61C4⋊C411yescharacteristic
141C2×C4×D61C4⋊C411yescharacteristic
142M16×C61—42no—
143C2×C8×C61—22no—
144C22⋊C4×C61—24no—
145C22⋊C4×C61—42no—
146C42×C61—42no—
147C42×C61—42no—
148C22⋊Dic61—24no—
149C22⋊Dic61—42no—
150#11758198—28no—
151#11758198—44no—
152#11758198—44no—
153#11758196—44no—
154C4×Dic61—44no—
155C4×Dic61—42no—
156C4×Dic61—42no—
157#11758194—42no—
158C2×#92418—22no—
159#11758189—44no—
160C8×D61—44no—
161C23×C61—22no—
162C23×C61—22no—
163C23×C61—41no—
164C23×C61C2×C22⋊C411yescharacteristic
165C23×C61C2×C22⋊C411yescharacteristic
166C23×C61C2×C4⋊C411yescharacteristic
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—416no—
185C22×D61#9511yescharacteristic
186C22×D61#9511yescharacteristic
187C22×D61#9511yescharacteristic
188C22×D61#9511yescharacteristic
189C22×D61#10414yes—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—24no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61C2×C4211yescharacteristic
203C2×C4×C61C2×C22⋊C411yescharacteristic
204C2×C4×C61C2×C4⋊C411yescharacteristic
205C2×C4×C61C2×C4⋊C411yescharacteristic
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—22no—
209C2×Dic61—24no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61#9511yescharacteristic
219C2×Dic61#9511yescharacteristic
220C2×Dic61#9511yescharacteristic
221C2×Dic61#9511yescharacteristic
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—22no—
225C4×D61—22no—
226C4×D61—22no—
227C4×D61—22no—
228C4×D61—22no—
229C4×D61—22no—
230C4×D61—22no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—41no—
234C4×D61—41no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—416no—
238C4×D61#9914yes—
239C8×C61—42no—
240#92418—42no—
241#8051—611nomaximal, Sylow
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—44no—
250C22×C61C2×#9511yescharacteristic
251C22×C61C2×#10412yes—
252C22×C61#42112yes—
253C2×D61—28no—
254C2×D61—21no—
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—44no—
264C2×D61—44no—
265C2×D61—44no—
266C2×D61—44no—
267C2×D61—44no—
268C2×D61#33912yes—
269C2×D61#33912yes—
270C2×D61#34212yes—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—44no—
275C4×C61—82no—
276C4×C61C2×#9912yes—
277Dic61—21no—
278Dic61—21no—
279Dic61—21no—
280Dic61—44no—
281Dic61—82no—
282Dic61#34212yes—
283C2×#407—611no—
284#2280—611no—
285C2×C4×C22⋊C4—611no—
286#1297—611no—
287#1297—611no—
288#1297—611no—
289#1297D6111yescharacteristic, complemented
290C2×C61—22no—
291C2×C61—22no—
292C2×C61—41no—
293C2×C61C2×#33911yescharacteristic
294C2×C61#173311yescharacteristic
295C2×C61C2×#34211yescharacteristic
296D61—22no—
297D61—22no—
298D61—22no—
299D61—41no—
300C24×C4—611no—
301C22×M16—612no—
302C2×#117—1221no—
303C22×C22⋊C4—1221no—
304C22×C42—1221no—
305#407—611no—
306#407—612no—
307#407—1221no—
308#407—1221no—
309#407C2×D6111yescharacteristic
310C2×C22⋊C8—1221no—
311C2×C22⋊C8—1221no—
312#381—612no—
313#380—612no—
314#380—1221no—
315#379—1221no—
316C4×C22⋊C4—611no—
317C4×C22⋊C4—611no—
318C4×C22⋊C4—612no—
319C4×C22⋊C4—1221no—
320C4×C22⋊C4—1221no—
321C4×C22⋊C4—1221no—
322C4×C22⋊C4C2×D6111yescharacteristic
323C4×C22⋊C4C2×D6111yescharacteristic
324C2×#95—612no—
325C61#805111yescharacteristic, complemented, Sylow
326C25—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—611no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—1222no—
341C23×C4—2444no—
342C23×C4C22×D6111yescharacteristic
343C2×M16—612no—
344C2×M16—1222no—
345C2×M16—2444no—
346C2×M16C4×D6112yescomplemented
347C22×C8—1222no—
348#117—2444no—
349C2×C4⋊C4—1222no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—1228no—
353C2×C22⋊C4—1222no—
354C2×C22⋊C4—1221no—
355C2×C22⋊C4—1222no—
356C2×C22⋊C4—1222no—
357C2×C22⋊C4—1221no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—1222no—
361C2×C42—1221no—
362C2×C42—1221no—
363C2×C42—2444no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—1222no—
367C22⋊C8—1222no—
368C22⋊C8—1221no—
369C22⋊C8—1221no—
370#95—612no—
371#95—612no—
372#95—1222no—
373#95—1222no—
374#95C4×D6112yes—
375#95C4×D6112yescomplemented
376C24—611no—
377C24—611no—
378C24—611no—
379C24—611no—
380C24—611no—
381C24—611no—
382C24—1224no—
383C24—2442no—
384C24—2442no—
385C24D4×D6111yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—42no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—1224no—
412C22×C4—1224no—
413C22×C4—1224no—
414C22×C4—1228no—
415C22×C4—1222no—
416C22×C4—1222no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4—2442no—
422C22×C4—2442no—
423C22×C4—2442no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4—2444no—
427C22×C4—2444no—
428C22×C4—2442no—
429C22×C4C2×C4×D6111yescharacteristic
430C22×C4C2×C4×D6111yescharacteristic
431C22×C4C2×C4×D6111yescharacteristic
432C22×C4D4×D6111yescharacteristic
433C22×C4D4×D6111yescharacteristic
434C22×C4Q8×D6111yescharacteristic
435M16—42no—
436M16—2444no—
437M16—2442no—
438C2×C8—22no—
439C2×C8—1222no—
440C2×C8—2444no—
441C4⋊C4—2444no—
442C22⋊C4—24no—
443C22⋊C4—42no—
444C22⋊C4—1228no—
445C22⋊C4—1224no—
446C22⋊C4—2444no—
447C22⋊C4—2444no—
448C22⋊C4—2442no—
449C42—42no—
450C42—42no—
451C42—2442no—
452C42—2442no—
453C42—2444no—
454C23—22no—
455C23—22no—
456C23—41no—
457C23—611no—
458C23—611no—
459C23—611no—
460C23—614no—
461C23—611no—
462C23—1222no—
463C23—1222no—
464C23—1222no—
465C23—1222no—
466C23—1222no—
467C23—1222no—
468C23—1222no—
469C23—1222no—
470C23—1222no—
471C23—1222no—
472C23—2441no—
473C23—2441no—
474C23—2441no—
475C23—2441no—
476C23—2441no—
477C23—2441no—
478C23—2441no—
479C23—24416no—
480C23C22⋊C4×D6111yescharacteristic
481C23C22⋊C4×D6111yescharacteristic
482C23C4⋊C4×D6111yescharacteristic
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—611no—
496C2×C4—614no—
497C2×C4—611no—
498C2×C4—611no—
499C2×C4—611no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1222no—
505C2×C4—1222no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—1224no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—24416no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2442no—
524C2×C4—2442no—
525C2×C4—2442no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4C42×D6111yescharacteristic
529C2×C4C22⋊C4×D6111yescharacteristic
530C2×C4C4⋊C4×D6111yescharacteristic
531C2×C4C4⋊C4×D6111yescharacteristic
532C8—42no—
533C8—2442no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—44no—
542C22—612no—
543C22—612no—
544C22—612no—
545C22—1228no—
546C22—1221no—
547C22—1221no—
548C22—1221no—
549C22—1221no—
550C22—1221no—
551C22—1221no—
552C22—1221no—
553C22—1221no—
554C22—1221no—
555C22—2444no—
556C22—2444no—
557C22—2444no—
558C22—2444no—
559C22—2444no—
560C22#95×D6111yescharacteristic
561C22#104×D6112yes—
562C22#1683977712yes—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—44no—
567C4—82no—
568C4—612no—
569C4—1221no—
570C4—1221no—
571C4—1221no—
572C4—4882no—
573C4—2444no—
574C4#99×D6112yes—
575C2—22no—
576C2—22no—
577C2—41no—
578C2—1222no—
579C2—1222no—
580C2—1222no—
581C2—2441no—
582C2#339×D6111yescharacteristic
583C2#2144552711yescharacteristic
584C2#342×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#8051
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
4. #21443705C2semidirect
5. #21443705C2semidirect
6. #21443704C2semidirect
7. C61×#1297C2semidirect
9. C2×M16×D61C4semidirect
14. #16839725C4semidirect
19. #16839624C4semidirect
20. #16839621C4semidirect
28. #16839609C4semidirect
29. #95×D61C4semidirect
49. C2×#11758194C2×C4semidirect
72. #14519684C2×C4semidirect
74. C2×M16×C61C2×C4semidirect
82. #95×C61C2×C4semidirect
289. #1297D61semidirect
325. C61#8051semidirect
346. C2×M16C4×D61semidirect
375. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
#407×D612
#214482002
C4×C22⋊C4×D612
#214437052
#214437042
C61×#12972
#805161