Subgroups — #49119297

Order 36224.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826842	C₂	1	1	yes	maximal, characteristic
2	#31826286	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₂₆₄	—	2	1	no	—
5	C₂×D₂₂₆₄	—	2	1	no	—
6	#22583607	C₄	1	2	yes	—
7	#22583550	—	2	1	no	—
8	M₃₂×C₂₈₃	—	2	1	no	—
9	C₄×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
10	C₂×D₁₁₃₂	—	2	2	no	—
11	C₂×D₁₁₃₂	—	4	2	no	—
12	D₂₂₆₄	—	4	1	no	—
13	D₂₂₆₄	—	4	1	no	—
14	D₂₂₆₄	—	4	1	no	—
15	D₂₂₆₄	—	4	1	no	—
16	C₂₈₃⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
19	C₄²×C₂₈₃	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₂₈₃	—	4	1	no	—
21	C₂²×D₂₈₃	—	4	2	no	—
22	D₁₁₃₂	—	4	2	no	—
23	D₁₁₃₂	—	4	2	no	—
24	D₁₁₃₂	—	8	4	no	—
25	C₂×C₄×C₂₈₃	—	2	1	no	—
26	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₂₈₃	D₈	1	1	yes	characteristic
28	C₈×C₂₈₃	D₈	1	1	yes	characteristic
29	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
31	C₂²×C₂₈₃	#100	1	1	yes	characteristic
32	C₂×D₂₈₃	—	8	4	no	—
33	C₂×D₂₈₃	—	8	2	no	—
34	C₄×C₂₈₃	—	2	2	no	—
35	C₄×C₂₈₃	#102	1	1	yes	characteristic
36	C₄×C₂₈₃	#102	1	1	yes	characteristic
37	C₂×C₂₈₃	—	2	1	no	—
38	C₂×C₂₈₃	#331	1	1	yes	characteristic
39	D₂₈₃	—	16	2	no	—
40	C₂₈₃	#1357	1	1	yes	characteristic, complemented, Sylow
41	#1357	—	283	1	no	maximal, Sylow
42	#493	—	283	1	no	—
43	#364	—	283	1	no	—
44	#364	D₂₈₃	1	1	yes	characteristic, complemented
45	C₂×D₈	—	566	1	no	—
46	C₂×D₈	—	566	1	no	—
47	#127	—	283	2	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	566	1	no	—
50	C₄×C₈	C₂×D₂₈₃	1	1	yes	characteristic
51	C₂×D₄	—	566	2	no	—
52	C₂×D₄	—	1132	2	no	—
53	D₈	—	1132	1	no	—
54	D₈	—	1132	1	no	—
55	D₈	—	1132	1	no	—
56	D₈	—	1132	1	no	—
57	C₂×C₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
58	C₂×C₈	D₁₁₃₂	1	1	yes	characteristic
59	C₄²	C₄×D₂₈₃	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	1132	1	no	—
62	C₂³	—	1132	2	no	—
63	D₄	—	1132	2	no	—
64	D₄	—	1132	2	no	—
65	D₄	—	2264	4	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
68	C₈	#17985377	1	1	yes	characteristic
69	C₈	D₂₂₆₄	1	1	yes	characteristic
70	C₈	#17985379	1	1	yes	characteristic
71	C₈	#17985381	1	1	yes	characteristic
72	C₂²	—	2264	4	no	—
73	C₂²	—	2264	2	no	—
74	C₂²	#22583526	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#22583530	1	1	yes	characteristic
77	C₄	#22583532	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	4528	2	no	—
80	C₂	#31826208	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31826208
commutator	C₄²×C₂₈₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₈₃
Fitting	#364×C₂₈₃	C₂
socle	C₂×C₂₈₃	#331
prime radical	#31826842	C₂
cosocle	C₄×C₈×C₂₈₃	C₂²
hypercenter	#364	D₂₈₃
hypocenter	C₂₈₃	#1357
LCS	G ▷ C₄²×C₂₈₃ ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #31826286	C₂	semidirect
3. #364×C₂₈₃	C₂	semidirect
40. C₂₈₃	#1357	semidirect
44. #364	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#31826842	2
#31826286	2
#364×C₂₈₃	2
#1357	283