Finite Group Databasebeta

← #29739026

Subgroups — #29739026

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#21448764C211yesmaximal, characteristic
3#21447343C211yesmaximal, characteristic
4#21447337C211yesmaximal, characteristic
5#21447192C211yesmaximal, characteristic
6#21447188C211yesmaximal, characteristic
7#21446586C211yesmaximal, characteristic, complemented
8#21446574C211yesmaximal, characteristic, complemented
9#21446534C211yesmaximal, characteristic, complemented
10#21446400C211yesmaximal, characteristic, complemented
11#21446397C211yesmaximal, characteristic, complemented
12#21445974C211yesmaximal, characteristic, complemented
13#21445818C211yesmaximal, characteristic
14#21445633C211yesmaximal, characteristic
15C61×#1949C211yesmaximal, characteristic, complemented
16C2×#14519739C2211yescharacteristic
17C2×#14519734—21no—
18C2×#14519710C2211yescharacteristic
19C2×#14519709C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839703—21no—
30#16839702—21no—
31#16839664C2211yescharacteristic
32#16839663C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839659—21no—
36#16839653—21no—
37#16839651—21no—
38#16839631C2211yescharacteristic
39#16839631C2211yescharacteristic
40#16839627C2211yescharacteristic
41#16839626—21no—
42#16839621—21no—
43C4⋊C4×Dic61C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4×#11758196C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#107×C61C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C61×#382C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63#14519739—22no—
64#14519739Q814yes—
65#14519734—44no—
66C2×C4⋊Dic61—21no—
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×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61C2311yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86#14519710—41no—
87#14519709—41no—
88#14519708—22no—
89#14519708—22no—
90#14519706—22no—
91#14519706—22no—
92#14519699—22no—
93#14519699—41no—
94#14519697—22no—
95#14519697—41no—
96C8×Dic61—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684D411yescharacteristic
104#14519684D411yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113#107×C61—41no—
114#106×C61—41no—
115C4⋊C8×C61—22no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119C23×D61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2411yescharacteristic
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61C2×D411yescharacteristic
131C22×Dic61C2×D411yescharacteristic
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244C2×Q812yes—
140C2×C4×D61—24no—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
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—
155C4⋊C4×C61—21no—
156C4⋊C4×C61C2×Q812yes—
157C42×C61—21no—
158C42×C61—21no—
159C42×C61—42no—
160#11758198—24no—
161#11758198—42no—
162#11758198—42no—
163#11758198—81no—
164#11758198—81no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—81no—
172#11758196—22no—
173#11758196—22no—
174#11758196—42no—
175#11758196—42no—
176#11758196—81no—
177#11758196—81no—
178#11758196—81no—
179C4×Dic61—21no—
180C4×Dic61—21no—
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×C61C22×D411yescharacteristic
192C22×D61—22no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C2×C4×C61—22no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
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×C61C22×Q811yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61H(5,𝔽2)11yescharacteristic
222C2×C4×C612−1+411yescharacteristic
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61C22⋊Q812yes—
241C2×Dic61C22⋊Q812yes—
242C2×Dic61#13512yes—
243C2×Dic61AGL(1,ℤ/8)12yes—
244D244—22no—
245D244—22no—
246D244—41no—
247D244—41no—
248C4×D61—48no—
249C8×C61—22no—
250C8×C61—41no—
251#92418—22no—
252#92418—41no—
253#26091—611nomaximal, Sylow
254C22×C61C2×C22⋊Q811yescharacteristic
255C22×C61#54711yescharacteristic
256C22×C61#55011yescharacteristic
257C22×C61C2×#13511yescharacteristic
258C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C61#57711yescharacteristic
260C22×C61#57711yescharacteristic
261C2×D61—42no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—81no—
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C4×C61—42no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61#53311yescharacteristic
275C4×C61#54411yescharacteristic
276C4×C61#55211yescharacteristic
277C4×C61#55311yescharacteristic
278Dic61—22no—
279Dic61—41no—
280Dic61—41no—
281Dic61—81no—
282Dic61—81no—
283Dic61—81no—
284Dic61#47814yes—
285#2571—611no—
286#2354—611no—
287#2092—611no—
288#2092—611no—
289#2065—611no—
290#2065—611no—
291#1949—611no—
292#1949D6111yescharacteristic, complemented
293#1947—611no—
294#1939—611no—
295#1919—611no—
296#1919—611no—
297#1844—611no—
298#1802—611no—
299C4×#102—611no—
300C2×C61#244111yescharacteristic
301C2×C61C2×#47811yescharacteristic
302C2×C61#308411yescharacteristic
303C2×C61#334011yescharacteristic
304C2×C61#335411yescharacteristic
305C2×C61#339411yescharacteristic
306C2×C61#339711yescharacteristic
307D61—82no—
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⋊C8C2×D6111yescharacteristic
319C2×#102—611no—
320C2×#102—611no—
321C2×#102—611no—
322C2×#102—611no—
323C2×C4×C8—611no—
324#400—1221no—
325#400—1221no—
326#390—611no—
327#390—611no—
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⋊C4C2×D6111yescharacteristic
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340C2×D6111yescharacteristic
348#340C2×D6111yescharacteristic
349#336—611no—
350#336—611no—
351C61#2609111yescharacteristic, complemented, Sylow
352C22×D4—611no—
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—1221no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4—1221no—
369C2×C4⋊C4—1221no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4C22×D6111yescharacteristic
373C2×C4⋊C4C22×D6111yescharacteristic
374C2×C4⋊C4C22×D6111yescharacteristic
375C2×C4⋊C4C22×D6111yescharacteristic
376C2×C22⋊C4—1221no—
377C2×C22⋊C4—1221no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C42—21no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—1221no—
385C2×C42—1221no—
386C2×C42C22×D6111yescharacteristic
387#107—41no—
388#107—2441no—
389#106—41no—
390#106—1222no—
391#106—1222no—
392#106—2441no—
393C4⋊C8—22no—
394C4⋊C8—1222no—
395C4⋊C8—1222no—
396#102—1222no—
397#102—1222no—
398#102—2441no—
399#102—2441no—
400C4×C8—1222no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—611no—
405#95—611no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412C24—1221no—
413C2×D4—612no—
414C2×D4—1221no—
415C2×D4—1221no—
416C2×D4—1221no—
417C2×D4—1221no—
418C2×D4—1221no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—1224no—
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#1175822212yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
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—4881no—
464C4⋊C4—4881no—
465C4⋊C4—4881no—
466C4⋊C4—4881no—
467C4⋊C4—2442no—
468C4⋊C4—2442no—
469C4⋊C4Q8×D6112yes—
470C22⋊C4—1224no—
471C22⋊C4—4881no—
472C22⋊C4—4881no—
473C22⋊C4—2442no—
474C22⋊C4—2442no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—612no—
479C42—612no—
480C42—1221no—
481C42—1221no—
482C42—2442no—
483C42—2442no—
484C23—1222no—
485C23—2441no—
486C23—2441no—
487C23—2441no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23C2×D4×D6111yescharacteristic
492D4—1222no—
493D4—1222no—
494D4—2441no—
495D4—2441no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
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—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—2448no—
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×#1175822211yescharacteristic
540C2×C4#1451982211yescharacteristic
541C2×C4#1451982511yescharacteristic
542C8—22no—
543C8—41no—
544C8—1222no—
545C8—2441no—
546C22—4881no—
547C22—4881no—
548C22—4881no—
549C22—4881no—
550C22—2442no—
551C22—2442no—
552C22—2442no—
553C22C22⋊Q8×D6111yescharacteristic
554C22#1684041311yescharacteristic
555C22#1684043011yescharacteristic
556C22#135×D6111yescharacteristic
557C22AGL(1,ℤ/8)×D6111yescharacteristic
558C22#1684056911yescharacteristic
559C22#1684057111yescharacteristic
560C4—41no—
561C4—42no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—614no—
567C4—1222no—
568C4—4881no—
569C4—4881no—
570C4—4881no—
571C4—2441no—
572C4—2441no—
573C4#1684031611yescharacteristic
574C4#1684038911yescharacteristic
575C4#1684044411yescharacteristic
576C4#1684046111yescharacteristic
577C2—4882no—
578C2#2144952911yescharacteristic
579C2#478×D6111yescharacteristic
580C2#2145568411yescharacteristic
581C2#2145822811yescharacteristic
582C2#2145841011yescharacteristic
583C2#2145881011yescharacteristic
584C2#2145884211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1949C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1949D61
hypocenterC61#26091
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. #21451059C2semidirect
7. #21446586C2semidirect
8. #21446574C2semidirect
9. #21446534C2semidirect
10. #21446400C2semidirect
11. #21446397C2semidirect
12. #21445974C2semidirect
15. C61×#1949C2semidirect
292. #1949D61semidirect
351. C61#26091semidirect

Maximal subgroups

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

subgroupindex
#214510592
#214487642
#214473432
#214473372
#214471922
#214471882
#214465862
#214465742
#214465342
#214464002
#214463972
#214459742
#214458182
#214456332
C61×#19492
#2609161