Finite Group Databasebeta

← #29739022

Subgroups — #29739022

Order 15616.

714 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#21451059C211yesmaximal, characteristic, complemented
2#21448767C211yesmaximal, characteristic
3#21447342C211yesmaximal, characteristic
4#21447193C211yesmaximal, characteristic
5#21447189C211yesmaximal, characteristic
6#21446585C211yesmaximal, characteristic, complemented
7#21446584C211yesmaximal, characteristic, complemented
8#21446574C211yesmaximal, characteristic, complemented
9#21446536C211yesmaximal, characteristic, complemented
10#21446399C211yesmaximal, characteristic, complemented
11#21446398C211yesmaximal, characteristic, complemented
12#21445974C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, characteristic
14#102×Dic61C211yesmaximal, characteristic
15C61×#2092C211yesmaximal, characteristic
16C2×D4×Dic61C2211yescharacteristic
17C2×#14519733—21no—
18C2×#14519710C2211yescharacteristic
19C2×#14519709C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839703—21no—
29#16839702—21no—
30#16839665C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839659—21no—
34#16839656—21no—
35#16839650—21no—
36#16839631C2211yescharacteristic
37#16839631C2211yescharacteristic
38#16839627C2211yescharacteristic
39#16839626—21no—
40#16839620—21no—
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758196C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#107×C61C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#382C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C23×Dic61—21no—
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62D4×Dic61—22no—
63D4×Dic61Q814yes—
64#14519733—44no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196D411yescharacteristic
76C2×#11758196D411yescharacteristic
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61C2311yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85#14519710—41no—
86#14519709—22no—
87#14519708—41no—
88#14519708—41no—
89C4⋊#92418—22no—
90#14519706—22no—
91#14519706—22no—
92#14519698—22no—
93#14519698—41no—
94C8×Dic61—22no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684D411yescharacteristic
103#14519684D411yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C42×C61C2311yescharacteristic
113#107×C61—41no—
114#106×C61—22no—
115#102×C61—22no—
116#102×C61—41no—
117#95×C61—21no—
118#95×C61—21no—
119C24×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61C2×Q812yes—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132C22×Dic61—21no—
133C22×Dic61—24no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61#4112yes—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C22⋊C4×C61—42no—
156C22⋊C4×C61—81no—
157C42×C61—21no—
158C42×C61—21no—
159C22⋊Dic61—24no—
160C22⋊Dic61—42no—
161C22⋊Dic61—81no—
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—81no—
170C4⋊Dic61C2×Q812yes—
171#11758196—22no—
172#11758196—22no—
173#11758196—42no—
174#11758196—42no—
175#11758196—81no—
176#11758196—81no—
177#11758196—81no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—42no—
181C4×Dic61—42no—
182C4×Dic61—42no—
183C4×Dic61C2×Q812yes—
184C4×Dic61#4112yes—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418#4112yes—
191C23×C61—22no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61C22×D411yescharacteristic
199D4×C61—22no—
200D4×C61—22no—
201D4×C61—41no—
202D4×C61—41no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61C22×Q811yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61H(5,𝔽2)11yescharacteristic
223C2×C4×C612−1+411yescharacteristic
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—22no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—48no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61C22⋊Q812yes—
246C2×Dic61C22⋊Q812yes—
247C2×Dic61#13512yes—
248C2×Dic61AGL(1,ℤ/8)12yes—
249C8×C61—22no—
250C8×C61—41no—
251#92418—22no—
252#92418—41no—
253#26091—611nomaximal, Sylow
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61C2×C22⋊Q811yescharacteristic
262C22×C61#54711yescharacteristic
263C22×C61#55011yescharacteristic
264C22×C61C2×#13511yescharacteristic
265C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C61#57711yescharacteristic
267C22×C61#57711yescharacteristic
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61#53311yescharacteristic
274C4×C61#54411yescharacteristic
275C4×C61#55211yescharacteristic
276C4×C61#55311yescharacteristic
277Dic61—22no—
278Dic61—42no—
279Dic61—41no—
280Dic61—41no—
281Dic61—81no—
282Dic61—81no—
283Dic61—81no—
284Dic61#47814yes—
285#2571—611no—
286#2354—611no—
287#2092—611no—
288#2092D6111yescharacteristic
289#2065—611no—
290#2065—611no—
291#1949—611no—
292#1949—611no—
293#1947—611no—
294#1939—611no—
295#1919—611no—
296#1919—611no—
297#1844—611no—
298#1802—611no—
299C4×#102—611no—
300C2×C61—82no—
301C2×C61#244111yescharacteristic
302C2×C61C2×#47811yescharacteristic
303C2×C61#308411yescharacteristic
304C2×C61#334011yescharacteristic
305C2×C61#335411yescharacteristic
306C2×C61#339411yescharacteristic
307C2×C61#339711yescharacteristic
308C2×C4×D4—611no—
309C2×#117—1221no—
310C2×#107—611no—
311C2×#107C2×D6111yescharacteristic
312C2×#106—611no—
313C2×#106—611no—
314C2×#106—611no—
315C2×#106C2×D6111yescharacteristic
316C2×C4⋊C8—611no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×#102—611no—
320C2×#102—611no—
321C2×#102C2×D6111yescharacteristic
322C2×#102C2×D6111yescharacteristic
323C2×C4×C8—611no—
324#400—1221no—
325#400—1221no—
326#390—611no—
327#390C2×D6111yescharacteristic
328#389—611no—
329#389—611no—
330#389—1221no—
331#388—1221no—
332#388—1221no—
333#384—611no—
334#384—611no—
335#382—611no—
336#382—1221no—
337#382C2×D6111yescharacteristic
338#380—1221no—
339C4×C4⋊C4—611no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#336—611no—
350#336C2×D6111yescharacteristic
351C61#2609111yescharacteristic, complemented, Sylow
352C22×D4C22×D6111yescharacteristic
353C23×C4—1221no—
354C22×C8—611no—
355C22×C8—611no—
356C22×C8C22×D6111yescharacteristic
357C22×C8C22×D6111yescharacteristic
358C4×D4—614no—
359C4×D4—1222no—
360#117—2444no—
361C2×C4⋊C4—611no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4—1221no—
369C2×C4⋊C4—1221no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1221no—
373C2×C4⋊C4C22×D6111yescharacteristic
374C2×C4⋊C4C22×D6111yescharacteristic
375C2×C4⋊C4C22×D6111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—1221no—
384C2×C42—1221no—
385C2×C42—1221no—
386C2×C42C22×D6111yescharacteristic
387#107—41no—
388#107—2441no—
389#106—22no—
390#106—1222no—
391#106—2441no—
392#106—2441no—
393C4⋊C8—1222no—
394C4⋊C8—1222no—
395C4⋊C8—1222no—
396#102—22no—
397#102—41no—
398#102—1222no—
399#102—2441no—
400C4×C8—1222no—
401#95—21no—
402#95—21no—
403#95—611no—
404#95—611no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4Q8×D6112yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—1224no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4D4×D6111yescharacteristic
434C22×C4D4×D6111yescharacteristic
435C22×C4C23×D6111yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—612no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8#1175822412yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—612no—
455C4⋊C4—1222no—
456C4⋊C4—1222no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—4881no—
465C4⋊C4—4881no—
466C4⋊C4—4881no—
467C4⋊C4—4881no—
468C4⋊C4—2442no—
469C4⋊C4—2442no—
470C22⋊C4—42no—
471C22⋊C4—81no—
472C22⋊C4—1224no—
473C22⋊C4—4881no—
474C22⋊C4—2442no—
475C42—21no—
476C42—21no—
477C42—612no—
478C42—612no—
479C42—1221no—
480C42—1221no—
481C42—2442no—
482C42—2442no—
483C42—2442no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×D4×D6111yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—612no—
512C2×C4—612no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1222no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—2448no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4C2×Q8×D6111yescharacteristic
537C2×C4#41×D6111yescharacteristic
538C2×C4#41×D6111yescharacteristic
539C2×C4C2×#1175822411yescharacteristic
540C2×C4#1451982211yescharacteristic
541C2×C4#1451982411yescharacteristic
542C8—22no—
543C8—41no—
544C8—1222no—
545C8—2441no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C22⋊Q8×D6111yescharacteristic
554C22#1684041011yescharacteristic
555C22#1684043211yescharacteristic
556C22#135×D6111yescharacteristic
557C22AGL(1,ℤ/8)×D6111yescharacteristic
558C22#1684056911yescharacteristic
559C22#1684057211yescharacteristic
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—614no—
566C4—1222no—
567C4—4881no—
568C4—4881no—
569C4—4881no—
570C4—2441no—
571C4—2442no—
572C4—2441no—
573C4#1684031411yescharacteristic
574C4#1684039111yescharacteristic
575C4#1684044911yescharacteristic
576C4#1684045711yescharacteristic
577C2—82no—
578C2#2144952511yescharacteristic
579C2#478×D6111yescharacteristic
580C2#2145568211yescharacteristic
581C2#2145823011yescharacteristic
582C2#2145841211yescharacteristic
583C2#2145881211yescharacteristic
584C2#2145883611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2092C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2092D61
hypocenterC61#26091
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
1. #21451059C2semidirect
6. #21446585C2semidirect
7. #21446584C2semidirect
8. #21446574C2semidirect
9. #21446536C2semidirect
10. #21446399C2semidirect
11. #21446398C2semidirect
12. #21445974C2semidirect
351. C61#26091semidirect

Maximal subgroups

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

subgroupindex
#214510592
#214487672
#214473422
#214471932
#214471892
#214465852
#214465842
#214465742
#214465362
#214463992
#214463982
#214459742
#214458172
#102×Dic612
C61×#20922
#2609161