Subgroups — #35292115

Order 21248.

170 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24909247	C₂	1	2	yes	maximal
2	C₂×M₆₄×C₈₃	C₂	1	1	yes	maximal, characteristic
3	#19127739	—	2	2	no	—
4	#19127529	C₄	1	4	yes	complemented
5	#19127527	—	2	2	no	—
6	C₂²×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
7	M₆₄×C₈₃	—	2	2	no	—
8	C₂×C₃₂×C₈₃	C₄	1	2	yes	complemented
9	#14581751	—	4	2	no	—
10	#14581726	—	2	4	no	—
11	#14581724	—	4	2	no	—
12	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₈₃	C₂×C₄	1	2	yes	—
14	C₂×C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
16	C₂×C₁₆×C₈₃	Q₈	1	1	yes	characteristic
17	C₃₂×C₈₃	—	2	2	no	—
18	C₄⋊Dic₈₃	—	4	4	no	—
19	C₂²⋊Dic₈₃	—	8	2	no	—
20	C₄×Dic₈₃	—	8	2	no	—
21	C₂²×C₄×C₈₃	D₈	1	1	yes	characteristic
22	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
23	C₂×C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₈₃	SD₁₆	1	2	yes	—
25	C₂×C₈×C₈₃	Q₁₆	1	1	yes	characteristic
26	C₁₆×C₈₃	C₄²	1	1	yes	characteristic
27	C₁₆×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₁₆×C₈₃	C₄⋊C₄	1	2	yes	—
29	C₂³×C₈₃	D₁₆	1	1	yes	characteristic
30	C₂×C₄×C₈₃	#102	1	2	yes	—
31	C₂×C₄×C₈₃	#107	1	1	yes	characteristic
32	C₂×C₄×C₈₃	SD₃₂	1	2	yes	—
33	C₂×C₄×C₈₃	Q₃₂	1	1	yes	characteristic
34	C₂×Dic₈₃	—	8	4	no	—
35	C₈×C₈₃	#95	1	1	yes	characteristic
36	C₈×C₈₃	#103	1	2	yes	—
37	C₈×C₈₃	#106	1	1	yes	characteristic
38	C₂²×C₈₃	—	4	1	no	—
39	C₂²×C₈₃	#357	1	2	yes	—
40	C₂²×C₈₃	#366	1	1	yes	characteristic
41	C₄×C₈₃	#340	1	1	yes	characteristic
42	C₄×C₈₃	#358	1	2	yes	—
43	C₄×C₈₃	#367	1	1	yes	characteristic
44	Dic₈₃	—	16	4	no	—
45	#7475	—	83	1	no	maximal, Sylow
46	C₂×C₈₃	—	2	2	no	—
47	C₂×C₈₃	—	2	1	no	—
48	C₂×C₈₃	#1380	1	1	yes	characteristic
49	C₂×M₆₄	D₈₃	1	1	yes	characteristic
50	#2158	—	83	2	no	—
51	C₈₃	#7475	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₁₆	C₂×D₈₃	1	1	yes	characteristic
53	#427	—	166	2	no	—
54	M₆₄	—	2	2	no	—
55	C₂×C₃₂	Dic₈₃	1	2	yes	complemented
56	#367	—	83	4	no	—
57	#366	—	166	2	no	—
58	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
59	#117	—	332	2	no	—
60	C₂×C₁₆	Dic₁₆₆	1	1	yes	characteristic
61	C₂×C₁₆	C₄×D₈₃	1	2	yes	—
62	C₂×C₁₆	C₂×Dic₈₃	1	1	yes	characteristic
63	C₂×C₁₆	C₂²⋊D₈₃	1	2	yes	—
64	#107	—	166	4	no	—
65	#106	—	332	2	no	—
66	C₃₂	—	2	2	no	—
67	C₂²×C₄	D₆₆₄	1	1	yes	characteristic
68	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
69	C₂×C₈	C₄⋊Dic₈₃	1	1	yes	characteristic
70	C₂×C₈	#13050579	1	2	yes	—
71	C₂×C₈	Dic₃₃₂	1	1	yes	characteristic
72	C₄⋊C₄	—	332	4	no	—
73	C₂²⋊C₄	—	664	2	no	—
74	C₄²	—	664	2	no	—
75	C₁₆	C₄×Dic₈₃	1	1	yes	characteristic
76	C₁₆	C₂²⋊Dic₈₃	1	1	yes	characteristic
77	C₁₆	Dic₈₃⋊C₄	1	2	yes	—
78	C₂³	D₁₃₂₈	1	1	yes	characteristic
79	C₂×C₄	—	664	4	no	—
80	C₂×C₄	#14581714	1	2	yes	—
81	C₂×C₄	#14581726	1	1	yes	characteristic
82	C₂×C₄	#14581737	1	2	yes	—
83	C₂×C₄	Dic₆₆₄	1	1	yes	characteristic
84	C₈	C₈₃⋊#95	1	1	yes	characteristic
85	C₈	#14581717	1	2	yes	—
86	C₈	#14581724	1	1	yes	characteristic
87	C₂²	—	4	1	no	—
88	C₂²	#19127503	1	2	yes	—
89	C₂²	#19127527	1	1	yes	characteristic
90	C₄	—	1328	4	no	—
91	C₄	#19127464	1	1	yes	characteristic
92	C₄	#19127506	1	2	yes	—
93	C₄	#19127529	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	—	2	1	no	—
96	C₂	#24905555	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19127529
commutator	C₁₆×C₈₃	C₄²
Frattini	C₂²×C₁₆	C₂×D₈₃
Fitting	C₂×M₆₄×C₈₃	C₂
socle	C₂×C₈₃	#1380
prime radical	C₂³×C₈₃	D₁₆
cosocle	C₂²×C₁₆×C₈₃	C₂²
hypercenter	C₂×M₆₄	D₈₃
hypocenter	C₈₃	#7475
LCS	G ▷ C₁₆×C₈₃ ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
4. #19127529	C₄	semidirect
8. C₂×C₃₂×C₈₃	C₄	semidirect
51. C₈₃	#7475	semidirect
55. C₂×C₃₂	Dic₈₃	semidirect

Maximal subgroups

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

subgroup	index
#24909247	2
C₂×M₆₄×C₈₃	2
#7475	83