Finite Group Databasebeta

← #29783248

Subgroups — #29783248

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451780C211yesmaximal, characteristic
2#21448465C211yesmaximal, characteristic, complemented
3#21447322C211yesmaximal, characteristic, complemented
4#21447195C211yesmaximal, characteristic, complemented
5#21447191C211yesmaximal, characteristic
6#21447135C211yesmaximal, characteristic
7#21446674C211yesmaximal, characteristic
8#21446545C211yesmaximal, characteristic, complemented
9#21446513C211yesmaximal, characteristic
10#21446507C211yesmaximal, characteristic, complemented
11#21446404C211yesmaximal, characteristic, complemented
12#21446177C211yesmaximal, characteristic
13#21446090C211yesmaximal, characteristic, complemented
14#21445675C211yesmaximal, characteristic, complemented
15C61×#1926C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×#14519709C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519687C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839690—21no—
29#16839690—21no—
30#16839687—21no—
31#16839685—21no—
32#16839667C2211yescharacteristic
33#16839667C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839646—21no—
42#16839646—21no—
43#16839629—21no—
44#16839626—21no—
45#16839608C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#106×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C2×#11758200—22no—
61C2×#11758200—22no—
62C2×#11758200—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C4×Dic122—22no—
66C4×Dic122—22no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61C2311yescharacteristic
82C2×C4×Dic61C2311yescharacteristic
83#14519709—22no—
84#14519708—22no—
85#14519706—22no—
86#14519706—22no—
87#14519702—22no—
88#14519702—22no—
89#14519700—41no—
90#14519698—22no—
91#14519687—41no—
92C8×Dic61—41no—
93#14519684—21no—
94#14519684—21no—
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
104#14519684D411yescharacteristic
105#14519684D411yescharacteristic
106C22×D4×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116#106×C61—41no—
117#102×C61—22no—
118#102×C61—41no—
119#95×C61—21no—
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—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C2×Dic122—21no—
142C2×Dic122—21no—
143C2×Dic122—21no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122#4112yes—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61#4112yes—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C22⋊C4×C61—81no—
160C22⋊C4×C61—81no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—81no—
164C22⋊Dic61—81no—
165C22⋊Dic61—81no—
166C22⋊Dic61—81no—
167C22⋊Dic61—81no—
168#11758200—44no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—81no—
175C4⋊Dic61#4112yes—
176#11758196—24no—
177#11758196—81no—
178#11758196—81no—
179#11758196—81no—
180#11758196—81no—
181C4×Dic61—24no—
182C4×Dic61—21no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418#4112yes—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61C22×D411yescharacteristic
200D4×C61—41no—
201D4×C61—41no—
202D4×C61—41no—
203D4×C61—41no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
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×C61—41no—
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61H(5,𝔽2)11yescharacteristic
224C2×C4×C612−1+411yescharacteristic
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—41no—
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—
249Dic122—22no—
250Dic122—22no—
251Dic122—41no—
252Dic122—41no—
253C8×C61—22no—
254C8×C61—41no—
255#92418—22no—
256#92418—41no—
257#29442—611nomaximal, Sylow
258C22×C61—81no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61—81no—
265C22×C61#52511yescharacteristic
266C22×C61#53211yescharacteristic
267C22×C61#53711yescharacteristic
268C22×C61#57711yescharacteristic
269C22×C61#57711yescharacteristic
270C22×C61#57711yescharacteristic
271C22×C61#57711yescharacteristic
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61#55111yescharacteristic
278C4×C61#55211yescharacteristic
279C4×C61#55311yescharacteristic
280C4×C61#55611yescharacteristic
281Dic61—42no—
282Dic61—42no—
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61—81no—
288Dic61—81no—
289#2644—611no—
290#2320—611no—
291#2088—611no—
292#2066—611no—
293#2065—611no—
294#2055—611no—
295#1968—611no—
296#1941—611no—
297#1936—611no—
298#1935—611no—
299#1926D6111yescharacteristic
300#1920—611no—
301#1880—611no—
302#1865—611no—
303#1768—611no—
304C2×C61—161no—
305C2×C61#260111yescharacteristic
306C2×C61#312511yescharacteristic
307C2×C61#312611yescharacteristic
308C2×C61#317311yescharacteristic
309C2×C61#317411yescharacteristic
310C2×C61#326011yescharacteristic
311C2×C61#326311yescharacteristic
312C22×SD16—611no—
313C2×C4×Q8—611no—
314C2×#106—611no—
315C2×#106—611no—
316C2×#106C2×D6111yescharacteristic
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×#103—611no—
320C2×#103—611no—
321C2×#103—611no—
322C2×#102—611no—
323C2×#102C2×D6111yescharacteristic
324C2×#102C2×D6111yescharacteristic
325C2×#97—611no—
326C2×C4×C8—611no—
327#397—1221no—
328#397—1221no—
329#397—1221no—
330#396—1221no—
331#391—611no—
332#391—611no—
333#390—611no—
334#390—611no—
335#390C2×D6111yescharacteristic
336#389—611no—
337#389—611no—
338#389—611no—
339#389—611no—
340#389—611no—
341#387—1221no—
342#387—1221no—
343#383—1221no—
344#382—1221no—
345C4×C4⋊C4C2×D6111yescharacteristic
346#376—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340C2×D6111yescharacteristic
353#336—611no—
354#336C2×D6111yescharacteristic
355C61#2944211yescharacteristic, complemented, Sylow
356C22×Q8—611no—
357C22×D4C22×D6111yescharacteristic
358C2×SD16—1222no—
359C2×SD16—1222no—
360C2×SD16—2441no—
361C22×C8—611no—
362C22×C8—611no—
363C22×C8C22×D6111yescharacteristic
364C22×C8C22×D6111yescharacteristic
365C4×Q8—1222no—
366C4×Q8—1222no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1221no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4C22×D6111yescharacteristic
377C2×C4⋊C4C22×D6111yescharacteristic
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C42—21no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42—1221no—
389C2×C42C22×D6111yescharacteristic
390#106—41no—
391#106—1222no—
392#106—1222no—
393C4⋊C8—1222no—
394C4⋊C8—1222no—
395#103—1222no—
396#103—1222no—
397#103—2441no—
398#102—22no—
399#102—41no—
400#102—1222no—
401#97—2441no—
402C4×C8—2441no—
403#95—21no—
404#95—611no—
405#95—611no—
406#95—611no—
407#95—611no—
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—
417C24—21no—
418C2×Q8—612no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4D4×D6111yescharacteristic
442C22×C4D4×D6111yescharacteristic
443C22×C4C23×D6111yescharacteristic
444SD16—2444no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—612no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8#1175822212yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—612no—
464C4⋊C4—1224no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—4881no—
471C4⋊C4—4881no—
472C4⋊C4—4881no—
473C4⋊C4—4881no—
474C4⋊C4—4881no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—4881no—
478C22⋊C4—4881no—
479C22⋊C4—4881no—
480C22⋊C4—4881no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—1224no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C2×D4×D6111yescharacteristic
497Q8—1222no—
498Q8—1222no—
499Q8—2441no—
500Q8—2441no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4#41×D6111yescharacteristic
545C2×C4#41×D6111yescharacteristic
546C2×C4#41×D6111yescharacteristic
547C2×C4C2×#1175822211yescharacteristic
548C2×C4#1451982211yescharacteristic
549C2×C4#1451982411yescharacteristic
550C8—22no—
551C8—41no—
552C8—1222no—
553C8—2441no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22#1684027011yescharacteristic
562C22#1684030911yescharacteristic
563C22#1684034111yescharacteristic
564C22#1684056811yescharacteristic
565C22#1684056911yescharacteristic
566C22#1684057211yescharacteristic
567C22#1684057211yescharacteristic
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—4881no—
574C4—4881no—
575C4—2441no—
576C4—2441no—
577C4—2441no—
578C4—2441no—
579C4—2442no—
580C4—2442no—
581C4#1684044211yescharacteristic
582C4#1684045111yescharacteristic
583C4#1684046111yescharacteristic
584C4#1684047911yescharacteristic
585C2—161no—
586C2#2145142211yescharacteristic
587C2#2145609911yescharacteristic
588C2#2145610611yescharacteristic
589C2#2145643411yescharacteristic
590C2#2145644311yescharacteristic
591C2#2145726311yescharacteristic
592C2#2145728611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1926C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#1926D61
hypocenterC61#29442
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #21448465C2semidirect
3. #21447322C2semidirect
4. #21447195C2semidirect
8. #21446545C2semidirect
10. #21446507C2semidirect
11. #21446404C2semidirect
13. #21446090C2semidirect
14. #21445675C2semidirect
355. C61#29442semidirect

Maximal subgroups

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

subgroupindex
#214517802
#214484652
#214473222
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