Finite Group Databasebeta

← #29837059

Subgroups — #29837059

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458250C211yesmaximal, characteristic, complemented
2#21448055C211yesmaximal, characteristic, complemented
3#21448024C211yesmaximal, characteristic, complemented
4#21448007C211yesmaximal, characteristic, complemented
5#21447966C211yesmaximal, characteristic, complemented
6#21447925C211yesmaximal, characteristic, complemented
7#21447913C211yesmaximal, characteristic, complemented
8#21447878C211yesmaximal, characteristic, complemented
9#21447759C211yesmaximal, characteristic, complemented
10#21447748C211yesmaximal, characteristic, complemented
11#21447683C211yesmaximal, characteristic, complemented
12#21447645C211yesmaximal, characteristic, complemented
13#21447535C211yesmaximal, characteristic, complemented
14#21447526C211yesmaximal, characteristic, complemented
15C61×#3280C211yesmaximal, characteristic
16#16840482—21no—
17C2×#14519723C2211yescharacteristic, complemented
18C2×#14519721C2211yescharacteristic
19C2×#14519721C2211yescharacteristic
20C2×#14519717C2211yescharacteristic
21C22×#11758185C2211yescharacteristic, complemented
22#16840167C2211yescharacteristic, complemented
23#16840104—21no—
24#16840104—21no—
25#16840048—21no—
26#16840003C2211yescharacteristic
27#16840003C2211yescharacteristic, complemented
28C4×Dic244C2211yescharacteristic, complemented
29#16839800C2211yescharacteristic
30#16839800C2211yescharacteristic, complemented
31#16839589C2211yescharacteristic, complemented
32#16839589C2211yescharacteristic, complemented
33#16839587C2211yescharacteristic, complemented
34C4⋊#11758185C2211yescharacteristic, complemented
35#16839566C2211yescharacteristic, complemented
36#16839566C2211yescharacteristic, complemented
37#16839566C2211yescharacteristic, complemented
38#16839565C2211yescharacteristic, complemented
39#16839563C2211yescharacteristic
40#16839563C2211yescharacteristic
41#16839563C2211yescharacteristic
42#16839563C2211yescharacteristic
43#16839563C2211yescharacteristic
44#16839563C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic, complemented
47#16839538C2211yescharacteristic, complemented
48C2×#135×C61C2211yescharacteristic
49C22×D8×C61C2211yescharacteristic
50C61×#546—21no—
51C61×#495C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C61×#466C2211yescharacteristic
54C61×#463—21no—
55C61×#450—21no—
56C61×#449—21no—
57C4×D8×C61C2211yescharacteristic
58C8×D4×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60#14519777—21no—
61#14519770—41no—
62#14519770—41no—
63#14519764—41no—
64#14519756—21no—
65#14519756—21no—
66C4×Dic122—21no—
67#14519742—41no—
68#14519736—21no—
69#14519736—21no—
70#14519723—41no—
71#14519721—22no—
72#14519721—41no—
73#14519717—41no—
74C2×#11758185—41no—
75C2×#11758185C2311yescharacteristic
76C2×#11758185C2311yescharacteristic
77C2×#11758185C2311yescharacteristic
78C2×#11758185C2311yescharacteristic
79#14519711—21no—
80#14519711C2311yescharacteristic
81#14519711C2311yescharacteristic
82#14519711C2311yescharacteristic
83#14519709—21no—
84#14519709—21no—
85#14519702—21no—
86#14519702—21no—
87#14519702—21no—
88C2×#41×C61—21no—
89C22×D4×C61—21no—
90#135×C61—22no—
91#135×C61—41no—
92C2×Q16×C61C2311yescharacteristic
93C2×SD16×C61—21no—
94C2×SD16×C61—21no—
95C2×D8×C61—22no—
96C2×D8×C61—21no—
97C2×D8×C61—41no—
98C2×D8×C61C2311yescharacteristic
99C2×D8×C61C2311yescharacteristic
100C22×C8×C61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102#124×C61—21no—
103#123×C61—41no—
104C22⋊Q8×C61—21no—
105#121×C61—21no—
106#121×C61—41no—
107#120×C61—41no—
108C4×D4×C61—21no—
109C4×D4×C61D411yescharacteristic
110C2×C22⋊C4×C61—41no—
111#107×C61C2311yescharacteristic
112C4⋊C8×C61D411yescharacteristic
113#103×C61—21no—
114#102×C61—21no—
115#102×C61—21no—
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C24×C61—41no—
120#41×C61—42no—
121#41×C61—81no—
122C2×Q8×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—42no—
126C2×D4×C61—41no—
127C2×D4×C61—41no—
128C2×D4×C61—41no—
129C2×D4×C61—81no—
130C2×D4×C61D811yescharacteristic
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C2×Dic122—21no—
136C2×Dic122—41no—
137Q16×C61—21no—
138Q16×C61—21no—
139SD16×C61—42no—
140SD16×C61—81no—
141D8×C61—21no—
142D8×C61—21no—
143D8×C61—21no—
144D8×C61—42no—
145D8×C61#4112yes—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61C2×D411yescharacteristic
151C2×C8×C61C2×D411yescharacteristic
152C2×C8×C61C2×D411yescharacteristic
153C2×C8×C61C2411yescharacteristic
154C4⋊C4×C61—21no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61D811yescharacteristic
157C22⋊C4×C61—41no—
158C22⋊C4×C61—41no—
159C22⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61D811yescharacteristic
163C22⋊C4×C61D811yescharacteristic
164C42×C61C2×D411yescharacteristic
165C22⋊Dic61—41no—
166C22⋊Dic61—41no—
167C22⋊Dic61—41no—
168C22⋊Dic61—41no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—41no—
173#11758196—41no—
174#11758196—41no—
175#11758196—41no—
176C4×Dic61—41no—
177C4×Dic61—41no—
178C4×Dic61—41no—
179Dic244—21no—
180Dic244—21no—
181#11758185—21no—
182#11758185—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61—82no—
188C23×C61—82no—
189C23×C61—161no—
190C23×C61C2×D811yescharacteristic
191C23×C61C2×D811yescharacteristic
192Q8×C61—41no—
193Q8×C61—41no—
194D4×C61—22no—
195D4×C61—41no—
196D4×C61—41no—
197D4×C61—41no—
198D4×C61—41no—
199D4×C61—82no—
200D4×C61—82no—
201D4×C61—161no—
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—82no—
209C2×C4×C61—161no—
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C2×D811yescharacteristic
212C2×C4×C61C2×D811yescharacteristic
213C2×C4×C61C2×D811yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219Dic122—41no—
220Dic122—41no—
221Dic122—82no—
222C8×C61—21no—
223C8×C61—21no—
224C8×C61—21no—
225C8×C61C2×#4111yescharacteristic
226C8×C61H(5,𝔽2)11yescharacteristic
227#33878—611nomaximal, Sylow
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—42no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—164no—
241C22×C61C22×D811yescharacteristic
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61#54611yescharacteristic
249C4×C61#57711yescharacteristic
250Dic61—81no—
251Dic61—81no—
252Dic61—81no—
253Dic61—81no—
254#3342—611no—
255#3280D6111yescharacteristic
256#2243—611no—
257#2237—611no—
258#2234—611no—
259#2226—611no—
260#2219—611no—
261#2217—611no—
262#2211—611no—
263#2189—611no—
264#2187—611no—
265#2175—611no—
266#2168—611no—
267#2140—611no—
268#2138—611no—
269C2×C61—41no—
270C2×C61—41no—
271C2×C61—82no—
272C2×C61—161no—
273C2×C61#329411yescharacteristic
274C2×C61#341411yescharacteristic
275C2×C61#341611yescharacteristic
276C2×#135C2×D6111yescharacteristic
277C22×D8C2×D6111yescharacteristic
278#556—1221no—
279#546—21no—
280C2×Q32—611no—
281C2×SD32—611no—
282C2×SD32—611no—
283C2×M32—611no—
284C22×C16—611no—
285#500—611no—
286#495C2×D6111yescharacteristic
287#485—1221no—
288#485—1221no—
289#475—1221no—
290#467—611no—
291#467—611no—
292#467C2×D6111yescharacteristic
293#466C2×D6111yescharacteristic
294#463—21no—
295#450—21no—
296#449—21no—
297C4×Q16—611no—
298C4×D8C2×D6111yescharacteristic
299C8×D4C2×D6111yescharacteristic
300#427—611no—
301#427—611no—
302#367—611no—
303#367—611no—
304#366—611no—
305C4⋊C16—611no—
306#358—611no—
307#358—611no—
308#358—611no—
309#358—611no—
310#357—611no—
311#357—611no—
312#357—611no—
313#357—611no—
314#357—611no—
315#357—611no—
316C22⋊C16—611no—
317C22⋊C16—611no—
318#346—611no—
319C61#3387811yescharacteristic, complemented, Sylow
320C2×#41—21no—
321C22×D4—21no—
322#135—22no—
323#135—41no—
324C2×Q16—611no—
325C2×Q16C22×D6111yescharacteristic
326C2×SD16—21no—
327C2×SD16—21no—
328C2×D8—22no—
329C2×D8—21no—
330C2×D8—41no—
331C2×D8C22×D6111yescharacteristic
332C2×D8C22×D6111yescharacteristic
333C22×C8C22×D6111yescharacteristic
334C22×C8C22×D6111yescharacteristic
335C4⋊Q8—1221no—
336#126—2441no—
337#126—2441no—
338#124—21no—
339#124—2441no—
340#123—41no—
341C22⋊Q8—21no—
342C22⋊Q8—1221no—
343C22⋊Q8—1221no—
344#121—21no—
345#121—41no—
346#120—41no—
347C4×Q8—1221no—
348C4×Q8—2441no—
349C4×D4—21no—
350C4×D4C22⋊D6111yescharacteristic
351#117—1221no—
352#117—1221no—
353C2×C22⋊C4—41no—
354Q32—2441no—
355SD32—1222no—
356SD32—2441no—
357M32—2441no—
358C2×C16—611no—
359C2×C16—611no—
360C2×C16—611no—
361C2×C16—611no—
362C2×C16—2441no—
363#107—611no—
364#107—611no—
365#107—611no—
366#107—1221no—
367#107C22×D6111yescharacteristic
368#106—1221no—
369#106—1221no—
370C4⋊C8C22⋊D6111yescharacteristic
371#103—21no—
372#103—1221no—
373#103—1221no—
374#103—1221no—
375#102—21no—
376#102—21no—
377C22⋊C8C22⋊D6111yescharacteristic
378C22⋊C8C22⋊D6111yescharacteristic
379C4×C8C22×D6111yescharacteristic
380C24—41no—
381#41—42no—
382#41—81no—
383C2×Q8—21no—
384C2×Q8—1221no—
385C2×Q8—2441no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—42no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—81no—
393C2×D4#1175819911yescharacteristic
394C22×C4—41no—
395C22×C4—41no—
396C22×C4C2×C22⋊D6111yescharacteristic
397C22×C4C2×C22⋊D6111yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—1221no—
401Q16—1221no—
402SD16—42no—
403SD16—81no—
404D8—21no—
405D8—21no—
406D8—21no—
407D8—42no—
408D8#1175822412yes—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×C22⋊D6111yescharacteristic
414C2×C8C2×C22⋊D6111yescharacteristic
415C2×C8C2×C22⋊D6111yescharacteristic
416C2×C8C23×D6111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—41no—
419C4⋊C4—1221no—
420C4⋊C4—1221no—
421C4⋊C4—1221no—
422C4⋊C4—2441no—
423C4⋊C4—2441no—
424C4⋊C4—2441no—
425C4⋊C4—2441no—
426C4⋊C4#1175819911yescharacteristic
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4#1175819911yescharacteristic
437C22⋊C4#1175819911yescharacteristic
438C42—2441no—
439C42—2441no—
440C42—2441no—
441C42C2×C22⋊D6111yescharacteristic
442C16—1221no—
443C16—1221no—
444C16—1221no—
445C16—1221no—
446C23—41no—
447C23—41no—
448C23—82no—
449C23—82no—
450C23—161no—
451C23C2×#1175819911yescharacteristic
452C23C2×#1175819911yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—4882no—
456Q8—2441no—
457Q8—2441no—
458D4—22no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—82no—
464D4—82no—
465D4—161no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—82no—
473C2×C4—161no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4C2×#1175819911yescharacteristic
479C2×C4C2×#1175819911yescharacteristic
480C2×C4C2×#1175819911yescharacteristic
481C2×C4C2×#1175819911yescharacteristic
482C2×C4C22×C22⋊D6111yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8C2×#1175822411yescharacteristic
487C8#1451982211yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—164no—
501C22C22×#1175819911yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—4881no—
509C4—4881no—
510C4—4881no—
511C4—4881no—
512C4#1684040611yescharacteristic
513C4#1684057311yescharacteristic
514C2—41no—
515C2—41no—
516C2—82no—
517C2—161no—
518C2#2145763211yescharacteristic
519C2#2145895311yescharacteristic
520C2#2145896611yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
Fitting, prime radicalC61×#3280C2
socleC22×C61C22×D8
hypercenter#3280D61
hypocenterC61#33878
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #21458250C2semidirect
2. #21448055C2semidirect
3. #21448024C2semidirect
4. #21448007C2semidirect
5. #21447966C2semidirect
6. #21447925C2semidirect
7. #21447913C2semidirect
8. #21447878C2semidirect
9. #21447759C2semidirect
10. #21447748C2semidirect
11. #21447683C2semidirect
12. #21447645C2semidirect
13. #21447535C2semidirect
14. #21447526C2semidirect
17. C2×#14519723C22semidirect
21. C22×#11758185C22semidirect
22. #16840167C22semidirect
27. #16840003C22semidirect
28. C4×Dic244C22semidirect
30. #16839800C22semidirect
31. #16839589C22semidirect
32. #16839589C22semidirect
33. #16839587C22semidirect
34. C4⋊#11758185C22semidirect
35. #16839566C22semidirect
36. #16839566C22semidirect
37. #16839566C22semidirect
38. #16839565C22semidirect
46. C22⋊#11758185C22semidirect
47. #16839538C22semidirect
319. C61#33878semidirect

Maximal subgroups

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

subgroupindex
#214582502
#214480552
#214480242
#214480072
#214479662
#214479252
#214479132
#214478782
#214477592
#214477482
#214476832
#214476452
#214475352
#214475262
C61×#32802
#3387861