Finite Group Databasebeta

← #29835271

Subgroups — #29835271

Order 15616.

524 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#21456433C211yesmaximal, characteristic, complemented
2#21454717C211yesmaximal, characteristic, complemented
3#21448037C211yesmaximal, characteristic, complemented
4#21448032C211yesmaximal, characteristic, complemented
5#21447991C211yesmaximal, characteristic, complemented
6#21447990C211yesmaximal, characteristic, complemented
7#21447885C211yesmaximal, characteristic, complemented
8#21447768C211yesmaximal, characteristic, complemented
9#21447763C211yesmaximal, characteristic
10#21447720C211yesmaximal, characteristic, complemented
11#21447718C211yesmaximal, characteristic, complemented
12#21447713C211yesmaximal, characteristic, complemented
13#21447711C211yesmaximal, characteristic, complemented
14#21447634C211yesmaximal, characteristic, complemented
15C61×#2212C211yesmaximal, characteristic, complemented
16#16840559C2211yescharacteristic
17#131×D61—21no—
18#16840381—21no—
19#16840203C2211yescharacteristic
20#16840198C2211yescharacteristic
21#16840160C2211yescharacteristic, complemented
22#16840121—21no—
23#16840017C2211yescharacteristic
24#16840012C2211yescharacteristic
25#16839988—21no—
26#16839884C2211yescharacteristic
27#16839883C2211yescharacteristic
28#16839881—21no—
29#16839880C2211yescharacteristic
30#16839877—21no—
31#16839874C2211yescharacteristic, complemented
32#16839869C2211yescharacteristic, complemented
33SD16×Dic61—21no—
34#16839809C2211yescharacteristic
35#16839777—21no—
36#16839716C2211yescharacteristic
37#16839586C2211yescharacteristic, complemented
38#16839586C2211yescharacteristic, complemented
39#16839585C2211yescharacteristic, complemented
40#16839585C2211yescharacteristic, complemented
41#16839583C2211yescharacteristic, complemented
42#16839578C2211yescharacteristic, complemented
43#16839575C2211yescharacteristic, complemented
44#16839573C2211yescharacteristic
45#16839573C2211yescharacteristic
46#16839572C2211yescharacteristic
47#16839572C2211yescharacteristic
48#16839543C2211yescharacteristic
49#16839543C2211yescharacteristic
50#16839539C2211yescharacteristic, complemented
51#16839539C2211yescharacteristic, complemented
52C61×#510C2211yescharacteristic
53C61×#509C2211yescharacteristic
54C61×#495C2211yescharacteristic, complemented
55C61×#443C2211yescharacteristic
56C61×#364C2211yescharacteristic, complemented
57C61×#362C2211yescharacteristic, complemented
58C61×#361C2211yescharacteristic, complemented
59#41×D61—21no—
60#14519809—21no—
61#14519806—21no—
62#14519804—21no—
63#14519801—21no—
64#14519799C2311yescharacteristic
65#14519797—21no—
66#14519785—21no—
67#14519785—41no—
68#14519784—21no—
69#14519783—21no—
70#14519783—41no—
71C2×#11758189C2311yescharacteristic
72M16×D61—21no—
73M16×D61—41no—
74C2×C8×D61—41no—
75C2×C8×D61D411yescharacteristic
76#14519777—21no—
77#14519770—41no—
78#14519763—41no—
79#14519761—41no—
80#14519754—41no—
81#14519753—21no—
82#14519748—21no—
83Q8×Dic61—21no—
84D4×Dic61—21no—
85#14519734D411yescharacteristic
86#14519723—21no—
87#14519721—21no—
88#14519720—21no—
89#14519718—21no—
90#14519717C2311yescharacteristic
91#14519717C2311yescharacteristic
92#14519713C2311yescharacteristic
93#14519712—21no—
94#14519709—21no—
95#14519709C2311yescharacteristic
96#14519709C2311yescharacteristic
97#14519705—21no—
98#14519704—21no—
99#14519703—21no—
100#14519701—21no—
101#14519701—21no—
102#14519698—21no—
103#14519698—21no—
104#14519688D411yescharacteristic
105#14519687C2311yescharacteristic
106C8×Dic61D411yescharacteristic
107#135×C61C2311yescharacteristic
108C2×Q16×C61C2311yescharacteristic
109C2×SD16×C61—21no—
110C2×D8×C61C2311yescharacteristic
111#131×C61—21no—
112#124×C61—21no—
113Q32×C61—21no—
114SD32×C61—21no—
115SD32×C61—21no—
116D16×C61—21no—
117M32×C61C2311yescharacteristic
118M32×C61C2311yescharacteristic
119#108×C61C2311yescharacteristic
120#104×C61—21no—
121C4×C8×C61C2311yescharacteristic
122#41×C61—21no—
123C2×Q8×C61—21no—
124C2×D4×C61—21no—
125C2×C22⋊D61—41no—
126C22×Dic61—41no—
127#11758226—21no—
128Q8×D61—21no—
129#11758224—21no—
130#11758224—41no—
131D4×D61—21no—
132D4×D61—41no—
133#11758222—21no—
134#11758222—41no—
135C2×C4×D61—41no—
136C2×C4×D61C2×D411yescharacteristic
137C2×Dic122—41no—
138Q16×C61—21no—
139Q16×C61—21no—
140Q16×C61#4111yescharacteristic
141SD16×C61—21no—
142SD16×C61—41no—
143SD16×C61—41no—
144D8×C61—21no—
145D8×C61—21no—
146D8×C61#4111yescharacteristic
147M16×C61—21no—
148M16×C61—41no—
149C2×C8×C61—41no—
150C2×C8×C61C2×D411yescharacteristic
151C2×C8×C61C2411yescharacteristic
152C22⋊C4×C61—41no—
153C22⋊C4×C61—41no—
154C42×C61C2×D411yescharacteristic
155C22⋊Dic61—41no—
156C22⋊Dic61—41no—
157#11758202—21no—
158#11758201—21no—
159#11758200—21no—
160#11758199—21no—
161#11758198—21no—
162#11758198—41no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166C4⋊Dic61—41no—
167#11758196—21no—
168#11758196—41no—
169C4×Dic61—41no—
170C4×Dic61C2×D411yescharacteristic
171#11758194—21no—
172#11758194—41no—
173C2×#92418—41no—
174C2×#92418C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176Dic244#4111yescharacteristic
177D488#4111yescharacteristic
178#11758190—21no—
179#11758189—21no—
180#11758189—21no—
181#11758189—41no—
182#11758189—41no—
183#11758189—41no—
184C8×D61—21no—
185C8×D61—21no—
186C8×D61—41no—
187C8×D61—41no—
188C8×D61—41no—
189C16×C61—21no—
190C16×C61—21no—
191#11758185—21no—
192#11758185—21no—
193C23×C61—41no—
194C22×D61—41no—
195C22×D61AGL(1,ℤ/8)11yescharacteristic
196Q8×C61—21no—
197Q8×C61—41no—
198Q8×C61—41no—
199D4×C61—21no—
200D4×C61—41no—
201D4×C61—41no—
202D4×C61—41no—
203C2×C4×C61—21no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61C22×D411yescharacteristic
207C22⋊D61—41no—
208C22⋊D61—41no—
209C22⋊D61—41no—
210C22⋊D61—161no—
211C2×Dic61—21no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—161no—
216C2×Dic61AGL(1,ℤ/8)11yescharacteristic
217D244—21no—
218D244—41no—
219C4×D61—21no—
220C4×D61—21no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224Dic122—21no—
225Dic122—41no—
226Dic122—161no—
227C8×C61—41no—
228C8×C61AGL(1,ℤ/8)11yescharacteristic
229C8×C61AGL(1,ℤ/8)11yescharacteristic
230C8×C61C2×#4111yescharacteristic
231C8×C61C2×#4111yescharacteristic
232#92418—21no—
233#92418—21no—
234#92418—41no—
235#33691—611nomaximal, Sylow
236C22×C61—41no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
241C2×D61—21no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—82no—
245C4×C61—41no—
246C4×C61—41no—
247C4×C61—81no—
248C4×C61#52511yescharacteristic
249C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
250Dic61—21no—
251Dic61—41no—
252Dic61—41no—
253Dic61—81no—
254Dic61—81no—
255#3173—611no—
256#2955—611no—
257#2239—611no—
258#2238—611no—
259#2230—611no—
260#2230—611no—
261#2212—611no—
262#2212D6111yescharacteristic, complemented
263#2191—611no—
264#2190—611no—
265AGL(1,ℤ/16)—611no—
266AGL(1,ℤ/16)—611no—
267#2180—611no—
268#2180—611no—
269#2166—611no—
270C2×C61—21no—
271C2×C61—81no—
272C2×C61—161no—
273C2×C61#310911yescharacteristic
274D61—41no—
275D61—81no—
276#575—611no—
277C2×#131—1221no—
278#542—1221no—
279#510—611no—
280#510C2×D6111yescharacteristic
281#509—611no—
282#509C2×D6111yescharacteristic
283#498—611no—
284#495C2×D6111yescharacteristic, complemented
285#489—1221no—
286#470—611no—
287#469—611no—
288#465—1221no—
289#444—611no—
290#444—611no—
291#444—1221no—
292#443—611no—
293#443—1221no—
294#443C2×D6111yescharacteristic
295#442—611no—
296#441—611no—
297C4×SD16—1221no—
298#430—611no—
299#421—1221no—
300#405—611no—
301#365—611no—
302#365—611no—
303#365—611no—
304#365—611no—
305#364—611no—
306#364C2×D6111yescharacteristic, complemented
307#362—611no—
308#362C2×D6111yescharacteristic, complemented
309#361—611no—
310#361C2×D6111yescharacteristic, complemented
311#360—611no—
312#360—611no—
313#360—611no—
314#360—611no—
315#349—611no—
316#349—611no—
317#347—611no—
318#347—611no—
319C61#3369111yescharacteristic, complemented, Sylow
320C2×#41—1221no—
321#137—1221no—
322#137—1221no—
323AGL(1,ℤ/8)—1221no—
324AGL(1,ℤ/8)—1221no—
325#135—611no—
326#135—1221no—
327#135C22×D6111yescharacteristic
328C2×Q16C22×D6111yescharacteristic
329C2×SD16—21no—
330C2×D8C22×D6111yescharacteristic
331#131—21no—
332#131—1221no—
333#131—1221no—
334#131—1221no—
335#131—2441no—
336#131—2441no—
337C2×M16—611no—
338C2×M16—1221no—
339C2×M16—2441no—
340C22×C8—611no—
341C22×C8—2441no—
342C4⋊Q8—1221no—
343#126—2441no—
344#124—21no—
345#124—2441no—
346#123—2441no—
347C22⋊Q8—1221no—
348C22⋊Q8—2441no—
349#121—1221no—
350C4×Q8—1221no—
351C4×D4—1221no—
352#117—611no—
353Q32—21no—
354Q32—1221no—
355SD32—21no—
356SD32—21no—
357SD32—1221no—
358SD32—1221no—
359D16—21no—
360D16—1221no—
361M32—611no—
362M32—611no—
363M32C22×D6111yescharacteristic
364M32C22×D6111yescharacteristic
365#108—611no—
366#108—1221no—
367#108C22×D6111yescharacteristic
368#106—611no—
369#106—611no—
370#106—1221no—
371#104—21no—
372#104—1221no—
373#104—1221no—
374#104—1221no—
375#103—1221no—
376#103—1221no—
377#102—1221no—
378#102—1221no—
379#97—611no—
380#97—611no—
381C4×C8—611no—
382C4×C8C22×D6111yescharacteristic
383#41—21no—
384#41—1221no—
385#41—1221no—
386#41—1221no—
387#41—2441no—
388#41—2441no—
389C2×Q8—21no—
390C2×Q8—1221no—
391C2×Q8—2441no—
392C2×D4—21no—
393C2×D4—1221no—
394C2×D4—2441no—
395C2×D4—2441no—
396C22×C4—611no—
397C22×C4—2441no—
398C22×C4—2441no—
399Q16—21no—
400Q16—21no—
401Q16—611no—
402Q16—1221no—
403Q16#1175822411yescharacteristic
404SD16—21no—
405SD16—41no—
406SD16—41no—
407SD16—1221no—
408SD16—1221no—
409SD16—1221no—
410D8—21no—
411D8—21no—
412D8—611no—
413D8—1221no—
414D8#1175822411yescharacteristic
415M16—21no—
416M16—41no—
417M16—1221no—
418M16—1221no—
419M16—1221no—
420M16—2441no—
421M16—2441no—
422M16—2441no—
423M16—2441no—
424C2×C8—41no—
425C2×C8—611no—
426C2×C8—611no—
427C2×C8—1221no—
428C2×C8—1221no—
429C2×C8—2441no—
430C2×C8—2441no—
431C2×C8—2441no—
432C2×C8—2441no—
433C2×C8D4×D6111yescharacteristic
434C2×C8C23×D6111yescharacteristic
435C4⋊C4—1221no—
436C4⋊C4—1221no—
437C4⋊C4—1221no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—1221no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C22⋊C4—2441no—
447C42—611no—
448C42—2441no—
449C42D4×D6111yescharacteristic
450C16—21no—
451C16—21no—
452C16—1221no—
453C16—1221no—
454C23—41no—
455C23—611no—
456C23—2441no—
457Q8—21no—
458Q8—41no—
459Q8—41no—
460Q8—1221no—
461Q8—9761no—
462Q8—2441no—
463D4—21no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—1221no—
468D4—9761no—
469D4—2441no—
470D4—2441no—
471D4—2441no—
472D4—2441no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—611no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—9761no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4C2×D4×D6111yescharacteristic
488C8—41no—
489C8—1221no—
490C8—1221no—
491C8—2441no—
492C8#1451980111yescharacteristic
493C8#1451980111yescharacteristic
494C8#41×D6111yescharacteristic
495C8C2×#1175822411yescharacteristic
496C22—41no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—1221no—
501C22—4882no—
502C22—2441no—
503C22—2441no—
504C22AGL(1,ℤ/8)×D6111yescharacteristic
505C4—41no—
506C4—41no—
507C4—81no—
508C4—1221no—
509C4—4881no—
510C4—4881no—
511C4—2441no—
512C4—2441no—
513C4#1684027211yescharacteristic
514C4C2×#1451980111yescharacteristic
515C2—21no—
516C2—81no—
517C2—161no—
518C2—4881no—
519C2—2441no—
520C2#2145590911yescharacteristic
subgroupG/H
centerC2#21455909
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2212C2
socleC2×C61#3109
prime radical#21447763C2
hypercenter#2212D61
hypocenterC61#33691
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2212

Complements

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

NH ≅ G/Ntype
1. #21456433C2semidirect
2. #21454717C2semidirect
3. #21448037C2semidirect
4. #21448032C2semidirect
5. #21447991C2semidirect
6. #21447990C2semidirect
7. #21447885C2semidirect
8. #21447768C2semidirect
10. #21447720C2semidirect
11. #21447718C2semidirect
12. #21447713C2semidirect
13. #21447711C2semidirect
14. #21447634C2semidirect
15. C61×#2212C2semidirect
21. #16840160C22semidirect
31. #16839874C22semidirect
32. #16839869C22semidirect
37. #16839586C22semidirect
38. #16839586C22semidirect
39. #16839585C22semidirect
40. #16839585C22semidirect
41. #16839583C22semidirect
42. #16839578C22semidirect
43. #16839575C22semidirect
50. #16839539C22semidirect
51. #16839539C22semidirect
54. C61×#495C22semidirect
56. C61×#364C22semidirect
57. C61×#362C22semidirect
58. C61×#361C22semidirect
262. #2212D61semidirect
284. #495C2×D61semidirect
306. #364C2×D61semidirect
308. #362C2×D61semidirect
310. #361C2×D61semidirect
319. C61#33691semidirect

Maximal subgroups

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

subgroupindex
#214564332
#214547172
#214480372
#214480322
#214479912
#214479902
#214478852
#214477682
#214477632
#214477202
#214477182
#214477132
#214477112
#214476342
C61×#22122
#3369161