Subgroups — #49119301

Order 36224.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826838	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×#17985381	—	2	1	no	—
5	C₂×#17985381	—	2	1	no	—
6	#22583610	C₄	1	1	yes	characteristic
7	#22583607	C₄	1	1	yes	characteristic
8	#22583550	—	2	1	no	—
9	M₃₂×C₂₈₃	—	2	1	no	—
10	C₄×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₆₆	—	2	1	no	—
12	C₂×D₁₁₃₂	—	2	1	no	—
13	C₂×D₁₁₃₂	—	4	1	no	—
14	#17985381	—	4	1	no	—
15	#17985381	—	4	1	no	—
16	#17985381	—	4	1	no	—
17	#17985381	—	4	1	no	—
18	C₄⋊Dic₂₈₃	—	4	1	no	—
19	C₂₈₃⋊C₁₆	—	4	1	no	—
20	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
22	C₄²×C₂₈₃	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₂₈₃	—	4	1	no	—
24	C₂²×D₂₈₃	—	4	1	no	—
25	Dic₅₆₆	—	4	1	no	—
26	Dic₅₆₆	—	4	1	no	—
27	D₁₁₃₂	—	4	1	no	—
28	D₁₁₃₂	—	4	1	no	—
29	D₁₁₃₂	—	8	2	no	—
30	C₂×Dic₂₈₃	—	4	1	no	—
31	C₂×C₄×C₂₈₃	—	2	1	no	—
32	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₂₈₃	D₈	1	1	yes	characteristic
34	C₈×C₂₈₃	D₈	1	1	yes	characteristic
35	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
36	C₈×C₂₈₃	SD₁₆	1	1	yes	characteristic
37	C₂²×C₂₈₃	#100	1	1	yes	characteristic
38	C₂×D₂₈₃	—	8	2	no	—
39	C₂×D₂₈₃	—	8	1	no	—
40	C₄×C₂₈₃	—	2	2	no	—
41	C₄×C₂₈₃	#102	1	1	yes	characteristic
42	C₄×C₂₈₃	#102	1	1	yes	characteristic
43	Dic₂₈₃	—	8	1	no	—
44	C₂×C₂₈₃	—	2	1	no	—
45	C₂×C₂₈₃	#331	1	1	yes	characteristic
46	D₂₈₃	—	16	1	no	—
47	C₂₈₃	#1359	1	1	yes	characteristic, complemented, Sylow
48	#1359	—	283	1	no	maximal, Sylow
49	#492	—	283	1	no	—
50	#364	—	283	1	no	—
51	#364	D₂₈₃	1	1	yes	characteristic, complemented
52	C₂×SD₁₆	—	566	1	no	—
53	C₂×SD₁₆	—	566	1	no	—
54	C₄⋊Q₈	—	283	1	no	—
55	#127	—	283	1	no	—
56	M₃₂	—	2	1	no	—
57	M₃₂	—	566	1	no	—
58	C₄×C₈	C₂×D₂₈₃	1	1	yes	characteristic
59	C₂×Q₈	—	566	1	no	—
60	C₂×D₄	—	566	1	no	—
61	C₂×D₄	—	1132	1	no	—
62	SD₁₆	—	1132	1	no	—
63	SD₁₆	—	1132	1	no	—
64	SD₁₆	—	1132	1	no	—
65	SD₁₆	—	1132	1	no	—
66	C₂×C₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
67	C₂×C₈	D₁₁₃₂	1	1	yes	characteristic
68	C₄⋊C₄	—	1132	1	no	—
69	C₄²	C₄×D₂₈₃	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	1132	1	no	—
72	C₂³	—	1132	1	no	—
73	Q₈	—	1132	1	no	—
74	Q₈	—	1132	1	no	—
75	D₄	—	1132	1	no	—
76	D₄	—	1132	1	no	—
77	D₄	—	2264	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	1132	1	no	—
80	C₂×C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
81	C₈	#17985377	1	1	yes	characteristic
82	C₈	D₂₂₆₄	1	1	yes	characteristic
83	C₈	#17985379	1	1	yes	characteristic
84	C₈	#17985381	1	1	yes	characteristic
85	C₂²	—	2264	2	no	—
86	C₂²	—	2264	1	no	—
87	C₂²	#22583526	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	2264	1	no	—
90	C₄	#22583530	1	1	yes	characteristic
91	C₄	#22583532	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4528	1	no	—
94	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	#22583607	C₄
cosocle	C₄×C₈×C₂₈₃	C₂²
hypercenter	#364	D₂₈₃
hypocenter	C₂₈₃	#1359
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
47. C₂₈₃	#1359	semidirect
51. #364	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#31826838	2
#31826286	2
#364×C₂₈₃	2
#1359	283