Finite Group Databasebeta

← #29569751

Subgroups — #29569751

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#407×D61C211yesmaximal, characteristic
2#21448200C211yesmaximal, characteristic
3#21448199C211yesmaximal, characteristic
4#21443673C211yesmaximal, characteristic, complemented
5#21443672C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#1284C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×M16×D61—21no—
10C2×#14519734C412yescomplemented
11C2×#14519733—21no—
12#16839726C2211yescharacteristic
13#16839725—21no—
14#16839724—21no—
15#16839724C412yescomplemented
16C22⋊C8×D61—21no—
17C22⋊C8×D61C412yescomplemented
18#16839625C2211yescharacteristic
19#16839624—21no—
20#16839621—21no—
21#16839621—21no—
22#16839621C412yescomplemented
23#16839620—21no—
24#16839617—21no—
25#16839617—21no—
26C4×#11758198C412yescomplemented
27C4×C22⋊Dic61C2211yescharacteristic
28#16839609—21no—
29#16839609C412yescomplemented
30C61×#407C2211yescharacteristic
31C61×#381C2211yescharacteristic
32C4×C22⋊C4×C61C2211yescharacteristic
33C24×D61D411yescharacteristic
34C23×Dic61D411yescharacteristic
35C22×C4×D61—44no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61C2×C411yescharacteristic
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61C2×C411yescharacteristic
41C22×C4×D61C2×C411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×C4×D61D411yescharacteristic
46C22×C4×D61Q811yescharacteristic
47C22×C4×D61Q811yescharacteristic
48C2×#11758194—21no—
49C2×#11758189—22no—
50M16×D61—44no—
51C2×C8×D61—22no—
52#14519734—44no—
53#14519733—44no—
54C2×#11758196—22no—
55C2×#11758196—22no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×#11758198—22no—
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×#11758198—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61C2×C412yes—
64C22⋊#92418—21no—
65C22⋊#92418C2×C412yes—
66#14519689—22no—
67#14519689—22no—
68#14519684—21no—
69#14519684—21no—
70#14519684—22no—
71#14519684C2×C412yes—
72C23×C4×C61C2311yescharacteristic
73C2×M16×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C42×C61C2×C412yes—
77C22⋊C8×C61—21no—
78C22⋊C8×C61C2×C412yes—
79#95×C61—21no—
80#95×C61—21no—
81#95×C61C2×C412yes—
82C24×C61C2×D411yescharacteristic
83C23×D61—42no—
84C23×D61—42no—
85C23×D61—42no—
86C23×D61C22⋊C411yescharacteristic
87C23×D61C22⋊C411yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C23×D61C22⋊C411yescharacteristic
90C23×D61C4⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—42no—
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×Q811yescharacteristic
101C22×Dic61—24no—
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C4⋊C411yescharacteristic
109C22×Dic61C4⋊C411yescharacteristic
110C2×C4×D61—24no—
111C2×C4×D61—24no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
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×D61C4211yescharacteristic
123C2×C4×D61C4211yescharacteristic
124C2×C4×D61C4211yescharacteristic
125C2×C4×D61C4211yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C4⋊C411yescharacteristic
131C2×C4×D61C4⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138M16×C61—42no—
139C2×C8×C61—22no—
140C22⋊C4×C61—42no—
141C22⋊C4×C61—42no—
142C42×C61—42no—
143C22⋊Dic61—42no—
144C22⋊Dic61—42no—
145#11758198—44no—
146#11758198—44no—
147#11758198—44no—
148#11758198—44no—
149#11758196—44no—
150#11758196—44no—
151C4×Dic61—44no—
152C4×Dic61—42no—
153#11758194—42no—
154C2×#92418—22no—
155#11758189—44no—
156C8×D61—44no—
157C23×C61—22no—
158C23×C61—22no—
159C23×C61—41no—
160C23×C61C2×C22⋊C411yescharacteristic
161C23×C61C2×C22⋊C411yescharacteristic
162C23×C61C2×C4⋊C411yescharacteristic
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—416no—
182C22×D61#9511yescharacteristic
183C22×D61#9511yescharacteristic
184C22×D61#9511yescharacteristic
185C22×D61#9511yescharacteristic
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—42no—
197C2×C4×C61—42no—
198C2×C4×C61C2×C4211yescharacteristic
199C2×C4×C61C2×C22⋊C411yescharacteristic
200C2×C4×C61C2×C4⋊C411yescharacteristic
201C2×C4×C61C2×C4⋊C411yescharacteristic
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—22no—
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61#9511yescharacteristic
214C2×Dic61#9511yescharacteristic
215C2×Dic61#9511yescharacteristic
216C2×Dic61#9511yescharacteristic
217C2×Dic61#9914yes—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—22no—
225C4×D61—22no—
226C4×D61—41no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—41no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—41no—
234C8×C61—42no—
235#92418—42no—
236#7946—611nomaximal, Sylow
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—44no—
245C22×C61C2×#9511yescharacteristic
246C22×C61C2×#9912yes—
247C22×C61#42112yes—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—44no—
260C2×D61—44no—
261C2×D61—44no—
262C2×D61—44no—
263C2×D61—44no—
264C2×D61—44no—
265C2×D61H(3,ℤ/4)12yes—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—82no—
271C4×C61—82no—
272Dic61—21no—
273Dic61—21no—
274Dic61—82no—
275Dic61—82no—
276Dic61#34212yes—
277Dic61#34212yes—
278C2×#407—611no—
279#2280—611no—
280#2280—611no—
281#1284—611no—
282#1284—611no—
283#1284—611no—
284#1284D6111yescharacteristic, complemented
285C2×C61—22no—
286C2×C61—22no—
287C2×C61—41no—
288C2×C61C2×H(3,ℤ/4)11yescharacteristic
289C2×C61#173311yescharacteristic
290C2×C61C2×#34211yescharacteristic
291D61—22no—
292D61—41no—
293D61—41no—
294D61—41no—
295C24×C4—611no—
296C22×M16—1221no—
297C2×#117—612no—
298C2×#117—1221no—
299#407—611no—
300#407—612no—
301#407—1221no—
302#407—1221no—
303#407C2×D6111yescharacteristic
304C2×C22⋊C8—612no—
305C2×C22⋊C8—1221no—
306#381—611no—
307#381—1221no—
308#381C2×D6111yescharacteristic
309#380—612no—
310#380—1221no—
311#380—1221no—
312#380—1221no—
313#379—1221no—
314#379—1221no—
315C4×C22⋊C4—612no—
316C4×C22⋊C4—611no—
317C4×C22⋊C4—612no—
318C4×C22⋊C4—1221no—
319C4×C22⋊C4C2×D6111yescharacteristic
320C61#794611yescharacteristic, complemented, Sylow
321C25—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—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—2444no—
336C23×C4C22×D6111yescharacteristic
337C2×M16—21no—
338C2×M16—1222no—
339C2×M16—1221no—
340C2×M16—2444no—
341C22×C8—1222no—
342#117—2444no—
343#117—2444no—
344C2×C4⋊C4—1222no—
345C2×C4⋊C4—1222no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—1222no—
349C2×C22⋊C4—1222no—
350C2×C22⋊C4—1222no—
351C2×C22⋊C4—1222no—
352C2×C22⋊C4—1221no—
353C2×C22⋊C4—1221no—
354C2×C42—612no—
355C2×C42—1222no—
356C2×C42C4×D6112yes—
357C22⋊C8—21no—
358C22⋊C8—612no—
359C22⋊C8—1222no—
360C22⋊C8—1222no—
361C22⋊C8—1221no—
362C22⋊C8C4×D6112yes—
363#95—21no—
364#95—21no—
365#95—612no—
366#95—1222no—
367#95—1221no—
368#95—1221no—
369#95C4×D6112yes—
370C24—611no—
371C24—611no—
372C24—611no—
373C24—611no—
374C24—611no—
375C24—611no—
376C24—2442no—
377C24—2442no—
378C24—2442no—
379C24D4×D6111yescharacteristic
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—42no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
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—1224no—
406C22×C4—1224no—
407C22×C4—1224no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4C2×C4×D6111yescharacteristic
421C22×C4C2×C4×D6111yescharacteristic
422C22×C4C2×C4×D6111yescharacteristic
423C22×C4D4×D6111yescharacteristic
424C22×C4D4×D6111yescharacteristic
425C22×C4Q8×D6111yescharacteristic
426M16—42no—
427M16—2444no—
428M16—2442no—
429C2×C8—22no—
430C2×C8—1222no—
431C2×C8—2444no—
432C4⋊C4—2444no—
433C4⋊C4—2444no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—2444no—
437C22⋊C4—2444no—
438C22⋊C4—2444no—
439C22⋊C4—2444no—
440C22⋊C4—2442no—
441C22⋊C4—2442no—
442C42—42no—
443C42—2442no—
444C42—2444no—
445C23—22no—
446C23—22no—
447C23—41no—
448C23—611no—
449C23—611no—
450C23—611no—
451C23—611no—
452C23—1222no—
453C23—1222no—
454C23—1222no—
455C23—1222no—
456C23—1222no—
457C23—1222no—
458C23—1222no—
459C23—2441no—
460C23—2441no—
461C23—2441no—
462C23—2441no—
463C23—2441no—
464C23—2441no—
465C23—2441no—
466C23—2441no—
467C23—2441no—
468C23—2441no—
469C23—2441no—
470C23—24416no—
471C23C22⋊C4×D6111yescharacteristic
472C23C22⋊C4×D6111yescharacteristic
473C23C4⋊C4×D6111yescharacteristic
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—614no—
487C2×C4—611no—
488C2×C4—611no—
489C2×C4—611no—
490C2×C4—611no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—1222no—
494C2×C4—1222no—
495C2×C4—1222no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—1222no—
499C2×C4—1222no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2442no—
513C2×C4—2442no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4C42×D6111yescharacteristic
519C2×C4C22⋊C4×D6111yescharacteristic
520C2×C4C4⋊C4×D6111yescharacteristic
521C2×C4C4⋊C4×D6111yescharacteristic
522C8—42no—
523C8—2442no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—44no—
532C22—612no—
533C22—1221no—
534C22—1221no—
535C22—1221no—
536C22—1221no—
537C22—1221no—
538C22—1221no—
539C22—1221no—
540C22—1221no—
541C22—1221no—
542C22—1221no—
543C22—1221no—
544C22—2444no—
545C22—2444no—
546C22—2444no—
547C22—2444no—
548C22—2444no—
549C22—2444no—
550C22#95×D6111yescharacteristic
551C22#99×D6112yes—
552C22#1683977712yes—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—82no—
558C4—82no—
559C4—612no—
560C4—612no—
561C4—1221no—
562C4—1221no—
563C4—4882no—
564C4—4882no—
565C2—22no—
566C2—22no—
567C2—41no—
568C2—1222no—
569C2—2441no—
570C2—2441no—
571C2—2441no—
572C2H(3,ℤ/4)×D6111yescharacteristic
573C2#2144552711yescharacteristic
574C2#342×D6111yescharacteristic
subgroupG/H
centerC22#95×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1284C2
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1284D61
hypocenterC61#7946
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
4. #21443673C2semidirect
5. #21443672C2semidirect
6. #21443671C2semidirect
7. C61×#1284C2semidirect
10. C2×#14519734C4semidirect
15. #16839724C4semidirect
17. C22⋊C8×D61C4semidirect
22. #16839621C4semidirect
26. C4×#11758198C4semidirect
29. #16839609C4semidirect
284. #1284D61semidirect
320. C61#7946semidirect

Maximal subgroups

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

subgroupindex
#407×D612
#214482002
#214481992
#214436732
#214436722
#214436712
C61×#12842
#794661