Subgroups — #19128015

Order 5312.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14581766	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14581726	C₂	1	2	yes	maximal, complemented
4	#14581714	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₈₃	—	2	1	no	—
8	C₂²×Dic₈₃	—	2	1	no	—
9	C₄⋊Dic₈₃	—	2	1	no	—
10	C₄⋊Dic₈₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₈₃	C₂²	1	2	yes	—
12	(C₂×D₈₃)⋊C₄	—	2	1	no	—
13	C₂²×C₄×C₈₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₈₃	C₂²	1	2	yes	—
15	C₂³×C₈₃	D₄	1	1	yes	characteristic
16	C₂²×D₈₃	—	2	1	no	—
17	C₂×C₄×C₈₃	—	2	2	no	—
18	C₂×C₄×C₈₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₈₃	C₂³	1	1	yes	characteristic
20	C₂²⋊D₈₃	—	4	2	no	—
21	C₂×Dic₈₃	—	2	1	no	—
22	C₂×Dic₈₃	—	2	2	no	—
23	C₂×Dic₈₃	—	4	2	no	—
24	D₃₃₂	—	2	2	no	—
25	C₈×C₈₃	—	2	2	no	—
26	C₂²×C₈₃	—	2	1	no	—
27	C₂²×C₈₃	—	2	1	no	—
28	C₂²×C₈₃	D₈	1	2	yes	—
29	C₂²×C₈₃	C₂×D₄	1	1	yes	characteristic
30	C₂×D₈₃	—	4	1	no	—
31	C₂×D₈₃	—	4	1	no	—
32	C₂×D₈₃	—	4	1	no	—
33	C₄×C₈₃	—	2	1	no	—
34	C₄×C₈₃	#41	1	2	yes	—
35	Dic₈₃	—	4	2	no	—
36	Dic₈₃	—	4	1	no	—
37	C₂×C₈₃	—	2	2	no	—
38	C₂×C₈₃	#123	1	1	yes	characteristic
39	C₂×C₈₃	C₂×D₈	1	1	yes	characteristic
40	C₂×C₈₃	#137	1	1	yes	characteristic
41	D₈₃	—	8	1	no	—
42	C₈₃	#480	1	1	yes	characteristic, complemented, Sylow
43	#480	—	83	1	no	maximal, Sylow
44	#121	—	83	1	no	—
45	C₂×C₄⋊C₄	—	83	1	no	—
46	#107	—	83	2	no	—
47	#102	—	83	2	no	—
48	C₂²⋊C₈	D₈₃	1	1	yes	characteristic, complemented
49	C₂×D₄	—	83	1	no	—
50	C₂×D₄	—	166	1	no	—
51	C₂²×C₄	—	166	1	no	—
52	C₂²×C₄	C₂×D₈₃	1	1	yes	characteristic
53	C₂×C₈	C₂×D₈₃	1	2	yes	—
54	C₄⋊C₄	—	83	2	no	—
55	C₄⋊C₄	—	83	1	no	—
56	C₄⋊C₄	—	166	1	no	—
57	C₂²⋊C₄	—	166	1	no	—
58	C₂³	—	166	1	no	—
59	C₂³	D₃₃₂	1	1	yes	characteristic
60	D₄	—	332	2	no	—
61	D₄	—	166	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	332	2	no	—
64	C₂×C₄	—	166	1	no	—
65	C₂×C₄	—	166	2	no	—
66	C₂×C₄	D₃₃₂	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₈₃	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	332	1	no	—
72	C₂²	—	332	1	no	—
73	C₂²	—	332	1	no	—
74	C₂²	D₆₆₄	1	2	yes	—
75	C₂²	C₂×D₃₃₂	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	332	2	no	—
78	C₄	—	332	1	no	—
79	C₄	#13050589	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	664	1	no	—
82	C₂	#14581776	1	1	yes	characteristic
83	C₂	C₂×D₆₆₄	1	1	yes	characteristic
84	C₂	#14581825	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₃₂
commutator	C₂×C₄×C₈₃	C₂³
Frattini	C₂×C₄	C₂²×D₈₃
Fitting	C₂²⋊C₈×C₈₃	C₂
socle	C₂²×C₈₃	C₂×D₄
hypercenter	C₂²⋊C₈	D₈₃
hypocenter	C₈₃	#480
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊Dic₈₃	C₂	semidirect
3. #14581726	C₂	semidirect
4. #14581714	C₂	semidirect
5. C₂²⋊C₈×C₈₃	C₂	semidirect
42. C₈₃	#480	semidirect
48. C₂²⋊C₈	D₈₃	semidirect