Subgroups — #35320806

Order 21248.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24905541	C₂	1	6	yes	maximal
2	C₈₃×#1726	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈₃⋊C₁₆	C₂²	1	4	yes	—
4	C₂×#97×C₈₃	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₈₃	C₂²	1	3	yes	—
6	#376×C₈₃	C₄	1	1	yes	characteristic
7	C₂×C₈₃⋊C₁₆	—	2	12	no	—
8	C₂²×C₈×C₈₃	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
10	C₂×C₄²×C₈₃	C₂×C₄	1	3	yes	—
11	#97×C₈₃	—	2	6	no	—
12	C₄×C₈×C₈₃	—	2	6	no	—
13	#95×C₈₃	C₈	1	4	yes	—
14	C₈₃⋊C₁₆	—	4	4	no	—
15	C₂²×C₄×C₈₃	C₂×C₈	1	6	yes	—
16	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₈×C₈₃	—	2	3	no	—
18	C₂×C₈×C₈₃	—	2	3	no	—
19	C₂×C₈×C₈₃	M₁₆	1	6	yes	—
20	C₂×C₈×C₈₃	#41	1	6	yes	—
21	C₄²×C₈₃	—	2	3	no	—
22	C₄²×C₈₃	—	2	3	no	—
23	C₂³×C₈₃	C₂²×C₈	1	1	yes	characteristic
24	C₂×C₄×C₈₃	—	2	6	no	—
25	C₂×C₄×C₈₃	—	2	12	no	—
26	C₂×C₄×C₈₃	#117	1	3	yes	—
27	C₂×C₄×C₈₃	C₂×M₁₆	1	3	yes	—
28	C₈×C₈₃	—	2	6	no	—
29	C₈×C₈₃	#126	1	4	yes	—
30	C₂²×C₈₃	#431	1	3	yes	—
31	C₂²×C₈₃	#504	1	4	yes	—
32	C₄×C₈₃	—	4	6	no	—
33	C₄×C₈₃	#383	1	1	yes	characteristic
34	C₄×C₈₃	#432	1	3	yes	—
35	#12895	—	83	1	no	maximal, Sylow
36	C₂×C₈₃	#1839	1	1	yes	characteristic
37	C₂×C₈₃	#2164	1	6	yes	—
38	#1726	D₈₃	1	1	yes	characteristic
39	#1374	—	83	6	no	—
40	C₈₃	#12895	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₁₆	—	83	4	no	—
42	C₂×#97	Dic₈₃	1	3	yes	—
43	C₂×C₄×C₈	C₂×D₈₃	1	3	yes	—
44	#376	Dic₈₃	1	1	yes	characteristic
45	C₂²×C₈	C₂×Dic₈₃	1	3	yes	—
46	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
47	C₂×C₄²	C₂×Dic₈₃	1	3	yes	—
48	C₂×C₁₆	—	166	12	no	—
49	#97	—	2	6	no	—
50	C₄×C₈	—	2	6	no	—
51	#95	C₈₃⋊C₈	1	4	yes	—
52	C₂²×C₄	C₂×C₈₃⋊C₈	1	6	yes	—
53	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
54	C₂×C₈	—	2	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	#13050574	1	6	yes	—
57	C₂×C₈	#13050590	1	6	yes	—
58	C₄²	—	2	3	no	—
59	C₄²	—	2	3	no	—
60	C₁₆	—	332	4	no	—
61	C₂³	C₂²×C₈₃⋊C₈	1	1	yes	characteristic
62	C₂×C₄	—	2	12	no	—
63	C₂×C₄	—	2	6	no	—
64	C₂×C₄	#14581751	1	3	yes	—
65	C₂×C₄	C₂×#13050574	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	#14581786	1	4	yes	—
68	C₂²	#19127754	1	3	yes	—
69	C₂²	#19128118	1	4	yes	—
70	C₄	—	4	6	no	—
71	C₄	#19127569	1	1	yes	characteristic
72	C₄	#19127758	1	3	yes	—
73	C₂	#24907606	1	1	yes	characteristic
74	C₂	#24909270	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₈₃
commutator, socle, prime radical	C₂³×C₈₃	C₂²×C₈
Fitting	C₈₃×#1726	C₂
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	#1726	D₈₃
hypocenter	C₈₃	#12895
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
40. C₈₃	#12895	semidirect

Maximal subgroups

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

subgroup	index
#24905541	2
C₈₃×#1726	2
#12895	83