Subgroups — #49119449

Order 36224.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826897	C₂	1	1	yes	maximal, characteristic
2	#31826293	C₂	1	1	yes	maximal, characteristic, complemented
3	M₆₄×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#22583632	—	2	1	no	—
5	Dic₂₂₆₄	C₄	1	1	yes	characteristic, complemented
6	#22583555	—	2	1	no	—
7	D₄₅₂₈	C₄	1	1	yes	characteristic, complemented
8	#22583544	—	2	1	no	—
9	C₂×C₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₂₈₃	—	2	1	no	—
11	#17985392	—	4	1	no	—
12	Dic₁₁₃₂	—	2	1	no	—
13	#17985381	—	4	1	no	—
14	D₂₂₆₄	—	2	1	no	—
15	C₄⋊Dic₂₈₃	—	4	1	no	—
16	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
17	C₁₆×C₂₈₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₈₃	D₄	1	1	yes	characteristic
19	Dic₅₆₆	—	4	1	no	—
20	D₁₁₃₂	—	4	1	no	—
21	C₂²⋊D₂₈₃	—	8	1	no	—
22	C₂×Dic₂₈₃	—	8	1	no	—
23	C₄×D₂₈₃	—	8	1	no	—
24	C₂×C₄×C₂₈₃	D₈	1	1	yes	characteristic
25	C₈×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
27	C₂²×C₂₈₃	D₁₆	1	1	yes	characteristic
28	C₂×D₂₈₃	—	8	1	no	—
29	C₄×C₂₈₃	#102	1	1	yes	characteristic
30	C₄×C₂₈₃	SD₃₂	1	1	yes	characteristic
31	Dic₂₈₃	—	8	1	no	—
32	Dic₂₈₃	—	16	1	no	—
33	C₂×C₂₈₃	—	2	1	no	—
34	C₂×C₂₈₃	#357	1	1	yes	characteristic
35	D₂₈₃	—	16	1	no	—
36	C₂₈₃	#1418	1	1	yes	characteristic, complemented, Sylow
37	#1418	—	283	1	no	maximal, Sylow
38	#508	—	283	1	no	—
39	M₆₄	D₂₈₃	1	1	yes	characteristic, complemented
40	#367	—	283	1	no	—
41	#135	—	566	1	no	—
42	Q₃₂	—	283	1	no	—
43	SD₃₂	—	566	1	no	—
44	D₁₆	—	283	1	no	—
45	C₂×C₁₆	C₂×D₂₈₃	1	1	yes	characteristic
46	#107	—	566	1	no	—
47	C₃₂	—	2	1	no	—
48	#41	—	1132	1	no	—
49	Q₁₆	—	566	1	no	—
50	SD₁₆	—	1132	1	no	—
51	D₈	—	566	1	no	—
52	C₂×C₈	D₁₁₃₂	1	1	yes	characteristic
53	C₄⋊C₄	—	1132	1	no	—
54	C₁₆	C₄×D₂₈₃	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₂₈₃	1	1	yes	characteristic
56	Q₈	—	1132	1	no	—
57	D₄	—	1132	1	no	—
58	D₄	—	2264	1	no	—
59	C₂×C₄	—	2264	1	no	—
60	C₂×C₄	—	2264	1	no	—
61	C₂×C₄	D₂₂₆₄	1	1	yes	characteristic
62	C₈	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
63	C₈	#17985381	1	1	yes	characteristic
64	C₂²	—	2264	1	no	—
65	C₂²	D₄₅₂₈	1	1	yes	characteristic
66	C₄	—	4528	1	no	—
67	C₄	—	2264	1	no	—
68	C₄	#22583532	1	1	yes	characteristic
69	C₄	#22583555	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	4528	1	no	—
72	C₂	#31826267	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31826267
commutator	C₁₆×C₂₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₃
Fitting	M₆₄×C₂₈₃	C₂
socle	C₂×C₂₈₃	#357
prime radical	#31826897	C₂
cosocle	C₂×C₁₆×C₂₈₃	C₂²
hypercenter	M₆₄	D₂₈₃
hypocenter	C₂₈₃	#1418
LCS	G ▷ C₁₆×C₂₈₃ ▷ C₈×C₂₈₃ ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #31826293	C₂	semidirect
3. M₆₄×C₂₈₃	C₂	semidirect
5. Dic₂₂₆₄	C₄	semidirect
7. D₄₅₂₈	C₄	semidirect
36. C₂₈₃	#1418	semidirect
39. M₆₄	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#31826897	2
#31826293	2
M₆₄×C₂₈₃	2
#1418	283