Finite Group Databasebeta

← #29779444

Subgroups — #29779444

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450427C211yesmaximal, characteristic, complemented
2#21447320C211yesmaximal, characteristic, complemented
3#21447232C211yesmaximal, characteristic
4#21447136C211yesmaximal, characteristic
5#21446967C211yesmaximal, characteristic, complemented
6#21446785C211yesmaximal, characteristic, complemented
7#21446672C211yesmaximal, characteristic
8#21446519C211yesmaximal, characteristic
9#21446508C211yesmaximal, characteristic, complemented
10#21446508C211yesmaximal, characteristic, complemented
11#21446394C211yesmaximal, characteristic, complemented
12#21446153C211yesmaximal, characteristic
13#21445694C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic
15C61×#2454C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×#14519708C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519700C2211yescharacteristic
20C2×#14519700C2211yescharacteristic
21C2×#14519700C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519688C2211yescharacteristic
26C2×#14519688C2211yescharacteristic
27C2×C4×#92418C2211yescharacteristic
28C61⋊#401—21no—
29#16839700—21no—
30#16839668C2211yescharacteristic
31#16839668C2211yescharacteristic
32#16839668C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839643—21no—
35#16839629—21no—
36#16839628C2211yescharacteristic
37C4×C4⋊Dic61C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#125×C61C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C61×#399—21no—
51C61×#396—21no—
52C61×#390C2211yescharacteristic
53C61×#390C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#389C2211yescharacteristic
56C61×#385—21no—
57C61×#380—21no—
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C2×#11758200—22no—
61C2×#11758200—22no—
62C2×#11758200—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×#11758196—21no—
71C2×C4×Dic61—21no—
72#14519708—22no—
73C4⋊#92418—22no—
74#14519700—22no—
75#14519700—22no—
76#14519700—41no—
77#14519698—22no—
78#14519698—22no—
79#14519698—22no—
80#14519688—22no—
81#14519688—41no—
82C4×#92418—41no—
83#14519684—21no—
84#14519684—21no—
85#14519684—21no—
86#14519684—21no—
87#14519684—21no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93C22×D4×C61C2311yescharacteristic
94C23×C4×C61—21no—
95#125×C61—22no—
96#125×C61—41no—
97C4×D4×C61—22no—
98C4×D4×C61—41no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61D411yescharacteristic
104C2×C4⋊C4×C61D411yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116#95×C61—21no—
117#95×C61—21no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C24×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61#4112yes—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61—81no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61—41no—
157C4⋊C4×C61—42no—
158C4⋊C4×C61—42no—
159C4⋊C4×C61—81no—
160C4⋊C4×C61—81no—
161C4⋊C4×C61#4112yes—
162C22⋊C4×C61—42no—
163C22⋊C4×C61—42no—
164C22⋊C4×C61—81no—
165C22⋊C4×C61—81no—
166C22⋊C4×C61—81no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173#11758200—44no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180#11758196—42no—
181C4×Dic61—42no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418#4112yes—
193C2×#92418#4112yes—
194C23×C61—22no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61C22×D411yescharacteristic
202D4×C61—22no—
203D4×C61—22no—
204D4×C61—41no—
205D4×C61—41no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—22no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—84no—
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×C4×C612−1+411yescharacteristic
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252Dic122—41no—
253Dic122—41no—
254Dic122—41no—
255Dic122—41no—
256#92418—22no—
257#92418—22no—
258#92418—41no—
259#92418—41no—
260#29100—611nomaximal, Sylow
261C22×C61—42no—
262C22×C61—42no—
263C22×C61—42no—
264C22×C61—81no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61#53211yescharacteristic
269C22×C61#54611yescharacteristic
270C22×C61#54811yescharacteristic
271C22×C61#57511yescharacteristic
272C22×C61#57511yescharacteristic
273C22×C61#57711yescharacteristic
274C22×C61#57711yescharacteristic
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—42no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61#52911yescharacteristic
285C4×C61#53911yescharacteristic
286C4×C61#55111yescharacteristic
287C4×C61#55611yescharacteristic
288Dic61—81no—
289Dic61—81no—
290Dic61—81no—
291Dic61—81no—
292#2514—611no—
293#2454D6111yescharacteristic
294#2088—611no—
295#2073—611no—
296#2055—611no—
297#2026—611no—
298#1991—611no—
299#1968—611no—
300#1936—611no—
301#1935—611no—
302#1935—611no—
303#1919—611no—
304#1877—611no—
305#1771—611no—
306#1762—611no—
307C2×C61—82no—
308C2×C61#256011yescharacteristic
309C2×C61#317411yescharacteristic
310C2×C61#318311yescharacteristic
311C2×C61#331111yescharacteristic
312C2×C61#331711yescharacteristic
313C2×C61#337611yescharacteristic
314C2×C61#337611yescharacteristic
315C22×SD16—611no—
316C2×#125C2×D6111yescharacteristic
317C2×C4×D4C2×D6111yescharacteristic
318C2×#106—611no—
319C2×C4⋊C8—611no—
320C2×#103—611no—
321C2×#103—611no—
322C2×#103—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×#102—611no—
326C2×#97—611no—
327C2×#97—611no—
328C2×C4×C8—611no—
329#401—1221no—
330#400—1221no—
331#399—21no—
332#396—21no—
333#391—611no—
334#391—611no—
335#391—611no—
336#390C2×D6111yescharacteristic
337#390C2×D6111yescharacteristic
338#389—611no—
339#389C2×D6111yescharacteristic
340#389C2×D6111yescharacteristic
341#387—1221no—
342#385—21no—
343#383—1221no—
344#382—611no—
345#380—21no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4C2×D6111yescharacteristic
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#336—611no—
357#336—611no—
358C61#2910011yescharacteristic, complemented, Sylow
359C22×Q8—611no—
360C22×D4C22×D6111yescharacteristic
361C23×C4—21no—
362C2×SD16—1222no—
363C2×SD16—1222no—
364C2×SD16—2441no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369#125—22no—
370#125—41no—
371C4×D4—22no—
372C4×D4—41no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4C22⋊D6111yescharacteristic
382C2×C4⋊C4C22⋊D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—1221no—
392C2×C42C22×D6111yescharacteristic
393C2×C42C22×D6111yescharacteristic
394C2×C42C22×D6111yescharacteristic
395#106—1222no—
396C4⋊C8—1222no—
397#103—1222no—
398#103—1222no—
399#103—2441no—
400#102—1222no—
401#102—1222no—
402#102—1222no—
403#97—1222no—
404#97—2441no—
405C4×C8—2441no—
406#95—21no—
407#95—21no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95C22⋊D6111yescharacteristic
419#95C22⋊D6111yescharacteristic
420C24—21no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4#1175822612yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—81no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4C2×C22⋊D6111yescharacteristic
444C22×C4C2×C22⋊D6111yescharacteristic
445C22×C4C2×C22⋊D6111yescharacteristic
446C22×C4C2×C22⋊D6111yescharacteristic
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C23×D6111yescharacteristic
450SD16—2444no—
451C2×C8—612no—
452C2×C8—612no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—2442no—
481C4⋊C4#1175822412yes—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—2442no—
494C23—22no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23C22×C22⋊D6111yescharacteristic
502Q8—2441no—
503Q8—2441no—
504Q8—2441no—
505Q8—2441no—
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4#41×D6111yescharacteristic
551C2×C4#41×D6111yescharacteristic
552C2×C4C2×#1175822411yescharacteristic
553C2×C4C2×#1175822611yescharacteristic
554C2×C4#1451982211yescharacteristic
555C2×C4#1451982511yescharacteristic
556C8—1222no—
557C8—1222no—
558C8—2441no—
559C8—2441no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#1684030811yescharacteristic
568C22#1684040611yescharacteristic
569C22#1684042311yescharacteristic
570C22#1684056011yescharacteristic
571C22#1684056011yescharacteristic
572C22#1684057311yescharacteristic
573C22#1684057311yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—4881no—
584C4—4881no—
585C4—4881no—
586C4—4881no—
587C4#1684029811yescharacteristic
588C4#1684035811yescharacteristic
589C4#1684043911yescharacteristic
590C4#1684048311yescharacteristic
591C2—82no—
592C2#2145095911yescharacteristic
593C2#2145644111yescharacteristic
594C2#2145654211yescharacteristic
595C2#2145785511yescharacteristic
596C2#2145794511yescharacteristic
597C2#2145864611yescharacteristic
598C2#2145864611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2454C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2454D61
hypocenterC61#29100
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. #21450427C2semidirect
2. #21447320C2semidirect
5. #21446967C2semidirect
6. #21446785C2semidirect
9. #21446508C2semidirect
10. #21446508C2semidirect
11. #21446394C2semidirect
13. #21445694C2semidirect
358. C61#29100semidirect

Maximal subgroups

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

subgroupindex
#214504272
#214473202
#214472322
#214471362
#214469672
#214467852
#214466722
#214465192
#214465082
#214463942
#214461532
#214456942
#214456442
C61×#24542
#2910061