Subgroups — #35292266

Order 21248.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24905632	C₂	1	2	yes	maximal, complemented
2	C₈₃×#1709	C₂	1	1	yes	maximal, characteristic
3	#19127500	—	2	2	no	—
4	#494×C₈₃	C₂²	1	1	yes	characteristic
5	#493×C₈₃	C₄	1	1	yes	characteristic
6	#486×C₈₃	—	2	2	no	—
7	C₈²×C₈₃	C₄	1	1	yes	characteristic
8	#14581711	—	4	2	no	—
9	C₂×Q₁₆×C₈₃	—	4	1	no	—
10	C₂×D₈×C₈₃	—	4	1	no	—
11	C₄⋊Q₈×C₈₃	D₄	1	2	yes	—
12	#127×C₈₃	—	2	1	no	—
13	#102×C₈₃	—	4	4	no	—
14	C₄×C₈×C₈₃	—	2	1	no	—
15	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
16	#13050574	—	8	2	no	—
17	C₂×Q₈×C₈₃	—	2	2	no	—
18	C₂×D₄×C₈₃	—	4	2	no	—
19	C₂×D₄×C₈₃	—	4	1	no	—
20	Q₁₆×C₈₃	—	8	2	no	—
21	D₈×C₈₃	—	8	2	no	—
22	C₂×C₈×C₈₃	—	2	1	no	—
23	C₂×C₈×C₈₃	—	2	2	no	—
24	C₄⋊C₄×C₈₃	—	4	2	no	—
25	C₄²×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂³×C₈₃	—	8	1	no	—
27	Q₈×C₈₃	—	8	2	no	—
28	D₄×C₈₃	—	8	2	no	—
29	D₄×C₈₃	—	8	4	no	—
30	C₂×C₄×C₈₃	—	2	1	no	—
31	C₂×C₄×C₈₃	—	4	2	no	—
32	C₂×C₄×C₈₃	#99	1	1	yes	characteristic
33	C₈×C₈₃	—	2	2	no	—
34	C₈×C₈₃	—	4	2	no	—
35	C₈₃⋊C₈	—	16	2	no	—
36	C₂²×C₈₃	—	16	2	no	—
37	C₂²×C₈₃	—	16	1	no	—
38	C₂²×C₈₃	#353	1	1	yes	characteristic
39	C₄×C₈₃	—	2	2	no	—
40	C₄×C₈₃	—	2	1	no	—
41	C₄×C₈₃	—	8	2	no	—
42	#7531	—	83	1	no	maximal, Sylow
43	C₂×C₈₃	—	2	1	no	—
44	C₂×C₈₃	—	32	1	no	—
45	C₂×C₈₃	#1408	1	1	yes	characteristic
46	#1709	D₈₃	1	1	yes	characteristic
47	#1411	—	83	2	no	—
48	C₈₃	#7531	1	1	yes	characteristic, complemented, Sylow
49	#494	C₂×D₈₃	1	1	yes	characteristic
50	#493	Dic₈₃	1	1	yes	characteristic
51	#486	—	2	2	no	—
52	#356	—	166	2	no	—
53	C₈²	Dic₈₃	1	1	yes	characteristic
54	C₂×Q₁₆	—	4	1	no	—
55	C₂×D₈	—	4	1	no	—
56	C₄⋊Q₈	C₂²⋊D₈₃	1	2	yes	—
57	#127	—	2	1	no	—
58	#102	—	4	4	no	—
59	#101	—	332	2	no	—
60	C₄×C₈	—	2	1	no	—
61	C₄×C₈	C₂×Dic₈₃	1	1	yes	characteristic
62	C₂×Q₈	—	2	2	no	—
63	C₂×D₄	—	4	2	no	—
64	C₂×D₄	—	4	1	no	—
65	Q₁₆	—	8	2	no	—
66	D₈	—	8	2	no	—
67	M₁₆	—	664	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₄⋊C₄	—	4	2	no	—
71	C₄²	C₂²⋊Dic₈₃	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	8	2	no	—
74	D₄	—	8	2	no	—
75	D₄	—	8	4	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	2	no	—
78	C₂×C₄	#14581707	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	4	2	no	—
81	C₈	—	1328	2	no	—
82	C₂²	—	16	2	no	—
83	C₂²	—	16	1	no	—
84	C₂²	#19127494	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	2	1	no	—
87	C₄	—	8	2	no	—
88	C₂	—	2	1	no	—
89	C₂	—	32	1	no	—
90	C₂	#24905626	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#24905626
commutator	C₄×C₈×C₈₃	C₂×C₄
Frattini	#494	C₂×D₈₃
Fitting	C₈₃×#1709	C₂
socle	C₂×C₈₃	#1408
prime radical	#493×C₈₃	C₄
cosocle	#494×C₈₃	C₂²
hypercenter	#1709	D₈₃
hypocenter	C₈₃	#7531
LCS	G ▷ C₄×C₈×C₈₃ ▷ C₄²×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #494 ◁ #1709

Complements

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

N	H ≅ G/N	type
1. #24905632	C₂	semidirect
48. C₈₃	#7531	semidirect

Maximal subgroups

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

subgroup	index
#24905632	2
C₈₃×#1709	2
#7531	83