Subgroups — #49119422

Order 36224.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826860	C₂	1	1	yes	maximal, characteristic
2	#31826260	C₂	1	1	yes	maximal, characteristic
3	#355×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985382	—	2	1	no	—
5	C₂×#17985380	—	2	1	no	—
6	#22583610	C₄	1	1	yes	characteristic, complemented
7	#22583525	—	2	1	no	—
8	#22583521	C₄	1	1	yes	characteristic, complemented
9	#124×C₂₈₃	C₂²	1	1	yes	characteristic
10	#101×C₂₈₃	—	2	1	no	—
11	C₂×Dic₅₆₆	—	2	1	no	—
12	#17985382	—	4	2	no	—
13	#17985380	—	4	2	no	—
14	C₂×C₂₈₃⋊C₈	—	2	1	no	—
15	C₄⋊Dic₂₈₃	—	4	1	no	—
16	C₂²⋊Dic₂₈₃	—	4	1	no	—
17	C₂×Q₈×C₂₈₃	D₄	1	1	yes	characteristic
18	C₂×D₄×C₂₈₃	D₄	1	1	yes	characteristic
19	M₁₆×C₂₈₃	—	4	1	no	—
20	C₂²⋊C₄×C₂₈₃	—	4	1	no	—
21	C₄²×C₂₈₃	C₂×C₄	1	1	yes	characteristic
22	Dic₅₆₆	—	4	1	no	—
23	Dic₅₆₆	—	4	1	no	—
24	C₂×Dic₂₈₃	—	4	1	no	—
25	C₂×Dic₂₈₃	—	8	1	no	—
26	C₂₈₃⋊C₈	—	2	2	no	—
27	C₂³×C₂₈₃	—	2	1	no	—
28	Q₈×C₂₈₃	—	4	1	no	—
29	D₄×C₂₈₃	—	4	1	no	—
30	C₂×C₄×C₂₈₃	—	2	1	no	—
31	C₂×C₄×C₂₈₃	—	2	1	no	—
32	C₂×C₄×C₂₈₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₂₈₃	—	8	1	no	—
34	C₂²×C₂₈₃	—	4	1	no	—
35	C₂²×C₂₈₃	—	8	1	no	—
36	C₂²×C₂₈₃	#99	1	1	yes	characteristic
37	C₄×C₂₈₃	—	2	1	no	—
38	C₄×C₂₈₃	—	4	1	no	—
39	C₄×C₂₈₃	—	4	1	no	—
40	Dic₂₈₃	—	8	1	no	—
41	Dic₂₈₃	—	16	1	no	—
42	C₂×C₂₈₃	—	2	1	no	—
43	C₂×C₂₈₃	—	8	1	no	—
44	C₂×C₂₈₃	#353	1	1	yes	characteristic
45	C₂₈₃	#1407	1	1	yes	characteristic, complemented, Sylow
46	#1407	—	283	1	no	maximal, Sylow
47	#497	—	283	1	no	—
48	#355	D₂₈₃	1	1	yes	characteristic
49	#354	—	283	1	no	—
50	C₂×Q₁₆	—	566	1	no	—
51	C₂×SD₁₆	—	566	1	no	—
52	C₄⋊Q₈	—	283	1	no	—
53	#124	C₂×D₂₈₃	1	1	yes	characteristic
54	#101	—	2	1	no	—
55	#99	—	566	1	no	—
56	#97	—	283	1	no	—
57	C₂×Q₈	—	566	1	no	—
58	C₂×Q₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
59	C₂×D₄	D₁₁₃₂	1	1	yes	characteristic
60	Q₁₆	—	1132	2	no	—
61	SD₁₆	—	1132	2	no	—
62	M₁₆	—	4	1	no	—
63	C₂×C₈	—	566	1	no	—
64	C₄⋊C₄	—	1132	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	1132	1	no	—
67	C₄²	C₄×D₂₈₃	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	1132	1	no	—
71	Q₈	—	1132	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	1132	1	no	—
76	C₂×C₄	—	2264	1	no	—
77	C₂×C₄	(C₂×D₂₈₃)⋊C₄	1	1	yes	characteristic
78	C₈	—	8	1	no	—
79	C₈	—	566	2	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#22583524	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	4528	1	no	—
87	C₄	—	2264	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#31826257	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31826257
commutator	C₄²×C₂₈₃	C₂×C₄
Frattini	#124	C₂×D₂₈₃
Fitting	#355×C₂₈₃	C₂
socle	C₂×C₂₈₃	#353
prime radical	C₂×D₄×C₂₈₃	D₄
cosocle	#124×C₂₈₃	C₂²
hypercenter	#355	D₂₈₃
hypocenter	C₂₈₃	#1407
LCS	G ▷ C₄²×C₂₈₃ ▷ C₂×C₄×C₂₈₃ ▷ C₂²×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
6. #22583610	C₄	semidirect
8. #22583521	C₄	semidirect
45. C₂₈₃	#1407	semidirect

Maximal subgroups

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

subgroup	index
#31826860	2
#31826260	2
#355×C₂₈₃	2
#1407	283