Finite Group Databasebeta

← #29667640

Subgroups — #29667640

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457145C211yesmaximal, characteristic
2#21457037C211yesmaximal, characteristic, complemented
3#21456942C211yesmaximal, characteristic, complemented
4#21445359C211yesmaximal, characteristic, complemented
5#21445352C211yesmaximal, characteristic, complemented
6#21445347C211yesmaximal, characteristic, complemented
7#21445342C211yesmaximal, characteristic, complemented
8#21445235C211yesmaximal, characteristic, complemented
9#21445228C211yesmaximal, characteristic, complemented
10#21445223C211yesmaximal, characteristic, complemented
11#21445218C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444512C211yesmaximal, characteristic, complemented
14C2×#16839510C211yesmaximal, characteristic, complemented
15C61×#2994C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840172—21no—
19#16840167C2211yescharacteristic
20#16840167C2211yescharacteristic
21#16840121—21no—
22#16840109C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840090—21no—
25#16840076—21no—
26#16840076—21no—
27#16840073—21no—
28#16840059—21no—
29#16840057C2211yescharacteristic
30#16840057C2211yescharacteristic
31#16840057C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840052C2211yescharacteristic
34#16840052C2211yescharacteristic
35#16840043—21no—
36#16840043—21no—
37#16839996—21no—
38#16839993—21no—
39#16839974—21no—
40#16839962C2211yescharacteristic
41#16839957C2211yescharacteristic
42#16839819C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839510C2211yescharacteristic
51#16839510C2211yescharacteristic
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436C2211yescharacteristic
60C61×#435—21no—
61C8×D4×C61—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#424—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×#11758222—21no—
68C22×Dic122—21no—
69C2×#11758201—21no—
70C2×#11758199—21no—
71C22×#92418—21no—
72#14519777—21no—
73#14519777—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519765—21no—
80#14519751—21no—
81#14519751—21no—
82C4×D244—21no—
83C4×D244—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86#14519711—21no—
87#14519711—21no—
88#14519711—21no—
89#14519711—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519699—21no—
105#14519699—21no—
106#14519699—21no—
107#14519699—21no—
108#14519698—21no—
109#14519698—21no—
110#14519698—21no—
111#14519697—21no—
112#14519697—21no—
113C22⋊#92418—21no—
114#14519688—21no—
115C2×M16×C61—21no—
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118#126×C61—21no—
119#125×C61D411yescharacteristic
120#124×C61D411yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61D411yescharacteristic
123#121×C61D411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61C2311yescharacteristic
127#117×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C2×D411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—41no—
152C22×Dic61—41no—
153#11758222—82no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×C4×D61—41no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—41no—
162C2×Dic122—82no—
163M16×C61—81no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—81no—
167C2×C8×C61—81no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61—21no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61#4111yescharacteristic
187C42×C61C2411yescharacteristic
188#11758201—81no—
189#11758199—81no—
190#11758198—41no—
191#11758198—41no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—41no—
199C4⋊Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—81no—
205C23×C61—21no—
206C23×C61#12111yescharacteristic
207C22×D61—41no—
208Q8×C61—21no—
209Q8×C61—21no—
210D4×C61—21no—
211D4×C61—21no—
212D4×C61—42no—
213C2×C4×C61—22no—
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—41no—
222C2×C4×C61—41no—
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C22⋊D61—82no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—82no—
234D244—41no—
235D244—41no—
236D244—41no—
237D244—41no—
238D244—81no—
239C4×D61—82no—
240Dic122—82no—
241Dic122—81no—
242Dic122—81no—
243Dic122—81no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#19591—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61#47212yes—
261C22×C61C2×#12111yescharacteristic
262C2×D61—81no—
263C2×D61—81no—
264C2×D61—81no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61#57711yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57811yescharacteristic
275C4×C61#57811yescharacteristic
276Dic61—81no—
277Dic61—81no—
278Dic61—81no—
279#3247—611no—
280#3238—611no—
281#3226—611no—
282#2994D6111yescharacteristic, complemented
283#1698—611no—
284#1697—611no—
285#1696—611no—
286#1695—611no—
287#1678—611no—
288#1677—611no—
289#1676—611no—
290#1675—611no—
291#1573—611no—
292#1551—611no—
293C2×#333—611no—
294C2×C61—22no—
295C2×C61—81no—
296C2×C61#304611yescharacteristic
297C2×C61#306311yescharacteristic
298C2×C61C2×#47211yescharacteristic
299D61—161no—
300#532—611no—
301C2×C4⋊Q8—611no—
302#529C2×D6111yescharacteristic
303#501—1221no—
304#500—611no—
305#500—611no—
306#489—1221no—
307#486—611no—
308#486—611no—
309#483—1221no—
310#480—1221no—
311#480—1221no—
312#480—1221no—
313#478—1221no—
314#477—611no—
315#477—611no—
316#477—611no—
317#476—611no—
318#476—611no—
319#476—611no—
320#474—1221no—
321#474—1221no—
322#466—1221no—
323#465—1221no—
324#463—1221no—
325#460—611no—
326#459—611no—
327#446C2×D6111yescharacteristic
328C8×Q8C2×D6111yescharacteristic
329#436C2×D6111yescharacteristic
330#435—21no—
331C8×D4—21no—
332C8×D4C2×D6111yescharacteristic
333#433—21no—
334#432—611no—
335#431C2×D6111yescharacteristic
336#424—21no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8C2×D6111yescharacteristic
339#335—611no—
340#335—611no—
341#334—611no—
342#334—611no—
343#333—611no—
344#333—611no—
345#333—611no—
346#333—611no—
347#333—611no—
348#333—611no—
349#331—611no—
350#331—611no—
351C61#1959111yescharacteristic, complemented, Sylow
352C2×#41—1221no—
353C22×Q8—1221no—
354C2×SD16—1221no—
355C2×D8—1221no—
356C2×M16—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—1221no—
360C4⋊Q8—611no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8—1221no—
364C4⋊Q8—1221no—
365C4⋊Q8—1221no—
366#127—611no—
367#126—21no—
368#125D24411yescharacteristic
369#124—1221no—
370#124D24411yescharacteristic
371#123—21no—
372C22⋊Q8D24411yescharacteristic
373#121—1221no—
374#121—1221no—
375#121D24411yescharacteristic
376C4×Q8C22×D6111yescharacteristic
377C4×D4—21no—
378C4×D4—1221no—
379C4×D4—1221no—
380C4×D4C22×D6111yescharacteristic
381#117—21no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C42C22×D6111yescharacteristic
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—1221no—
403C4⋊C8C22⋊D6111yescharacteristic
404C4⋊C8C22⋊D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406C4⋊C8C22×D6111yescharacteristic
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#102—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—1221no—
422C22⋊C8C22⋊D6111yescharacteristic
423C22⋊C8C22⋊D6111yescharacteristic
424#97—21no—
425#97—1221no—
426C4×C8—21no—
427C4×C8C22×D6111yescharacteristic
428C4×C8C22×D6111yescharacteristic
429#41—4882no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8—4882no—
434C2×Q8—2441no—
435C2×Q8C2×D24411yescharacteristic
436C2×D4—21no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—2441no—
441C2×D4C2×D24411yescharacteristic
442C22×C4—21no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4C2×D24411yescharacteristic
446C22×C4#1175822211yescharacteristic
447C22×C4C2×C22⋊D6111yescharacteristic
448SD16—4881no—
449D8—4881no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—81no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—4881no—
460C2×C8C2×C22⋊D6111yescharacteristic
461C2×C8C2×C22⋊D6111yescharacteristic
462C2×C8C2×C22⋊D6111yescharacteristic
463C2×C8C2×C22⋊D6111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—2441no—
475C4⋊C4—2441no—
476C4⋊C4C2×D24411yescharacteristic
477C4⋊C4C2×D24411yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—2441no—
484C22⋊C4—2441no—
485C42—21no—
486C42C2×D24411yescharacteristic
487C42#1175822211yescharacteristic
488C42C2×C22⋊D6111yescharacteristic
489C42C23×D6111yescharacteristic
490C23—21no—
491C23—2441no—
492C23#1451975111yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—4881no—
496Q8—4881no—
497Q8—4881no—
498Q8—4882no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—4881no—
503D4—4882no—
504D4—2441no—
505D4—2441no—
506D4—2441no—
507D4—2441no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—4882no—
519C2×C4—4882no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4#1451975111yescharacteristic
524C2×C4#1451975111yescharacteristic
525C2×C4#1451975111yescharacteristic
526C2×C4C22×C22⋊D6111yescharacteristic
527C2×C4C22×D24411yescharacteristic
528C2×C4C2×#1175822211yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—4881no—
545C22—4881no—
546C22—4881no—
547C22#1684003212yes—
548C22C2×#1451975111yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—4881no—
557C4—4881no—
558C4—4881no—
559C4#1684057311yescharacteristic
560C4#1684057411yescharacteristic
561C4#1684057711yescharacteristic
562C4#1684057911yescharacteristic
563C2—22no—
564C2—81no—
565C2—9761no—
566C2#2145536911yescharacteristic
567C2#2145551011yescharacteristic
568C2C2×#1684003211yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2994C2
socleC22×C61C2×#121
prime radical#21457145C2
hypercenter#2994D61
hypocenterC61#19591
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #21457037C2semidirect
3. #21456942C2semidirect
4. #21445359C2semidirect
5. #21445352C2semidirect
6. #21445347C2semidirect
7. #21445342C2semidirect
8. #21445235C2semidirect
9. #21445228C2semidirect
10. #21445223C2semidirect
11. #21445218C2semidirect
12. #21444604C2semidirect
13. #21444512C2semidirect
14. C2×#16839510C2semidirect
15. C61×#2994C2semidirect
282. #2994D61semidirect
351. C61#19591semidirect

Maximal subgroups

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

subgroupindex
#214571452
#214570372
#214569422
#214453592
#214453522
#214453472
#214453422
#214452352
#214452282
#214452232
#214452182
#214446042
#214445122
C2×#168395102
C61×#29942
#1959161