Subgroups — #24905637

Order 10624.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128055	C₂	1	1	yes	maximal, characteristic
2	#19127498	C₂	1	1	yes	maximal, characteristic
3	#354×C₈₃	C₂	1	1	yes	maximal, characteristic
4	#14581784	C₄	1	1	yes	characteristic, complemented
5	#14581716	—	2	1	no	—
6	#14581713	—	2	1	no	—
7	#14581711	—	2	1	no	—
8	C₄×C₈₃⋊C₈	C₄	1	1	yes	characteristic, complemented
9	#124×C₈₃	C₂²	1	1	yes	characteristic
10	#99×C₈₃	—	2	1	no	—
11	#13050574	—	4	1	no	—
12	C₂×C₈₃⋊C₈	—	2	1	no	—
13	C₄⋊Dic₈₃	—	2	1	no	—
14	Dic₈₃⋊C₄	—	4	1	no	—
15	C₂×Q₈×C₈₃	D₄	1	1	yes	characteristic
16	C₂×D₄×C₈₃	D₄	1	1	yes	characteristic
17	C₂²⋊C₄×C₈₃	—	4	1	no	—
18	C₂²⋊C₄×C₈₃	—	4	1	no	—
19	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₈₃	—	2	1	no	—
21	Q₈×C₈₃	—	4	1	no	—
22	D₄×C₈₃	—	4	1	no	—
23	C₂×C₄×C₈₃	—	2	1	no	—
24	C₂×C₄×C₈₃	—	2	1	no	—
25	C₂×C₄×C₈₃	—	8	1	no	—
26	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₈₃	—	4	1	no	—
28	C₈₃⋊C₈	—	4	1	no	—
29	C₈₃⋊C₈	—	8	1	no	—
30	C₂²×C₈₃	—	4	1	no	—
31	C₂²×C₈₃	—	8	1	no	—
32	C₂²×C₈₃	#99	1	1	yes	characteristic
33	C₄×C₈₃	—	2	1	no	—
34	C₄×C₈₃	—	4	1	no	—
35	C₄×C₈₃	—	4	1	no	—
36	C₄×C₈₃	—	16	1	no	—
37	Dic₈₃	—	8	1	no	—
38	C₂×C₈₃	—	2	1	no	—
39	C₂×C₈₃	—	8	1	no	—
40	C₂×C₈₃	#354	1	1	yes	characteristic
41	#1414	—	83	1	no	maximal, Sylow
42	C₈₃	#1414	1	1	yes	characteristic, complemented, Sylow
43	#488	—	83	1	no	—
44	#355	—	83	1	no	—
45	#354	D₈₃	1	1	yes	characteristic
46	#125	—	83	1	no	—
47	#124	C₂×D₈₃	1	1	yes	characteristic
48	#103	—	166	1	no	—
49	#102	—	166	1	no	—
50	#101	—	166	1	no	—
51	#99	—	2	1	no	—
52	C₄×C₈	—	83	1	no	—
53	C₂×Q₈	D₃₃₂	1	1	yes	characteristic
54	C₂×D₄	C₂²⋊D₈₃	1	1	yes	characteristic
55	M₁₆	—	332	1	no	—
56	C₂×C₈	—	166	1	no	—
57	C₄⋊C₄	—	332	1	no	—
58	C₄⋊C₄	—	166	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₂²⋊C₄	—	4	1	no	—
61	C₄²	C₄×D₈₃	1	1	yes	characteristic
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	8	1	no	—
68	C₂×C₄	—	332	1	no	—
69	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
70	C₈	—	332	1	no	—
71	C₈	—	664	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#14581706	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	16	1	no	—
79	C₄	—	664	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#19127495	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19127495
commutator	C₄²×C₈₃	C₂×C₄
Frattini	#124	C₂×D₈₃
Fitting	#354×C₈₃	C₂
socle	C₂×C₈₃	#354
prime radical	C₂×D₄×C₈₃	D₄
cosocle	#124×C₈₃	C₂²
hypercenter	#354	D₈₃
hypocenter	C₈₃	#1414
LCS	G ▷ C₄²×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
4. #14581784	C₄	semidirect
8. C₄×C₈₃⋊C₈	C₄	semidirect
42. C₈₃	#1414	semidirect