Subgroups — #564×Dic₈₃ #35567126

Order 21248.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24910649	C₂	1	15	yes	maximal
2	#125×Dic₈₃	C₂	1	15	yes	maximal
3	C₂×#564×C₈₃	C₂	1	1	yes	maximal, characteristic
4	#19127600	C₂²	1	30	yes	—
5	#19127587	C₂²	1	60	yes	—
6	#19127567	C₂²	1	15	yes	—
7	C₄⋊C₄×Dic₈₃	C₂²	1	30	yes	—
8	C₄²×Dic₈₃	C₂²	1	5	yes	—
9	#564×C₈₃	C₄	1	16	yes	complemented
10	C₂×#125×C₈₃	C₂²	1	15	yes	—
11	C₂×C₄⋊Dic₈₃	C₂³	1	30	yes	—
12	C₂×C₄×Dic₈₃	C₂³	1	15	yes	—
13	C₂×C₄×Dic₈₃	C₂³	1	15	yes	—
14	C₈₃⋊#95	C₂³	1	60	yes	—
15	#125×C₈₃	C₂×C₄	1	120	yes	—
16	C₂×C₄⋊C₄×C₈₃	C₂³	1	30	yes	—
17	C₂×C₄²×C₈₃	C₂³	1	5	yes	—
18	C₂²×Dic₈₃	C₂⁴	1	15	yes	—
19	C₂²×Dic₈₃	C₂⁴	1	1	yes	characteristic
20	C₄⋊Dic₈₃	—	4	30	no	—
21	C₄×Dic₈₃	—	2	30	no	—
22	C₄×Dic₈₃	—	4	15	no	—
23	C₂²×C₄×C₈₃	C₂⁴	1	15	yes	—
24	C₄⋊C₄×C₈₃	C₂²×C₄	1	120	yes	—
25	C₄²×C₈₃	C₂²×C₄	1	20	yes	—
26	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
27	C₂×C₄×C₈₃	—	2	15	no	—
28	C₂×C₄×C₈₃	—	2	15	no	—
29	C₂×C₄×C₈₃	C₂³×C₄	1	30	yes	—
30	C₂×Dic₈₃	—	2	15	no	—
31	C₂×Dic₈₃	—	2	30	no	—
32	C₂×Dic₈₃	2₋¹⁺⁴	1	6	yes	—
33	C₂²×C₈₃	C₂⁴×C₄	1	1	yes	characteristic
34	C₂²×C₈₃	C₂×2₋¹⁺⁴	1	3	yes	—
35	C₂²×C₈₃	#585	1	3	yes	—
36	C₄×C₈₃	—	2	30	no	—
37	Dic₈₃	—	4	15	no	—
38	Dic₈₃	#564	1	4	yes	direct product factor
39	C₄×#564	—	83	1	no	maximal, Sylow
40	C₂×C₈₃	C₄×2₋¹⁺⁴	1	3	yes	—
41	C₂×C₈₃	C₂×#564	1	1	yes	characteristic
42	C₂×C₈₃	#3531	1	3	yes	—
43	C₂×#564	D₈₃	1	1	yes	characteristic
44	#2382	—	83	15	no	—
45	C₄×#125	—	83	15	no	—
46	C₈₃	C₄×#564	1	1	yes	characteristic, complemented, Sylow
47	#564	Dic₈₃	1	16	yes	direct product factor
48	C₂×#125	C₂×D₈₃	1	15	yes	—
49	#389	—	83	30	no	—
50	#387	—	83	60	no	—
51	#382	—	83	15	no	—
52	C₄×C₄⋊C₄	—	83	30	no	—
53	C₄³	—	83	5	no	—
54	#125	C₂×Dic₈₃	1	120	yes	—
55	C₂×C₄⋊C₄	—	83	30	no	—
56	C₂×C₄⋊C₄	C₂²×D₈₃	1	30	yes	—
57	C₂×C₄²	—	83	15	no	—
58	C₂×C₄²	—	83	15	no	—
59	C₂×C₄²	C₂²×D₈₃	1	5	yes	—
60	#95	—	83	60	no	—
61	C₂²×C₄	—	83	1	no	—
62	C₂²×C₄	—	83	15	no	—
63	C₂²×C₄	C₂³×D₈₃	1	15	yes	—
64	C₄⋊C₄	—	332	30	no	—
65	C₄⋊C₄	C₂²×Dic₈₃	1	120	yes	—
66	C₄²	—	332	15	no	—
67	C₄²	—	166	30	no	—
68	C₄²	C₂²×Dic₈₃	1	20	yes	—
69	C₂³	C₂⁴×D₈₃	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	83	6	no	—
73	C₂×C₄	—	166	15	no	—
74	C₂×C₄	—	166	30	no	—
75	C₂×C₄	C₂³×Dic₈₃	1	30	yes	—
76	C₂²	C₂⁴×Dic₈₃	1	1	yes	characteristic
77	C₂²	2₋¹⁺⁴×D₈₃	1	3	yes	—
78	C₂²	#19128538	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	332	15	no	—
81	C₄	—	83	4	no	—
82	C₂	2₋¹⁺⁴×Dic₈₃	1	3	yes	—
83	C₂	#564×D₈₃	1	1	yes	characteristic
84	C₂	#24921611	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₈₃
commutator	C₂²×C₈₃	C₂⁴×C₄
Fitting	C₂×#564×C₈₃	C₂
socle, prime radical, cosocle	C₂³×C₈₃	C₂⁵
hypercenter	C₂×#564	D₈₃
hypocenter	C₈₃	C₄×#564
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×#564

Complements

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

N	H ≅ G/N	type
9. #564×C₈₃	C₄	semidirect
38. Dic₈₃	#564	direct (N × H)
46. C₈₃	C₄×#564	semidirect
47. #564	Dic₈₃	direct (N × H)

Maximal subgroups

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

subgroup	index
#24910649	2
#125×Dic₈₃	2
C₂×#564×C₈₃	2
C₄×#564	83

Subgroups — #564×Dic83 #35567126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #564×Dic₈₃ #35567126